Answers
The value of a is 5, b is 4, c is 0, d is 3, e is 6 and R is 6 after following the long division method.
According to the question,
We have to divide 430 by 8 by following the long division method.
Note that when we follow long division method then the number by which we are dividing (divisor) is to be multiplied in such a way that the result remains less than the number in the dividend.
Now, we will solve it step by step.
In dividing 43 by 8, we have to multiply 8 by 5. Then, we get 40.
So, we have a = 5, b = 4 and c = 0.
Now, after this we have 30 and the number that we get after multiplication is 24. So, 3 has to be multiplied in 8 to get 24.
So, we have d = 3.
Now, when we will subtract 24 from 30, we will get 6.
So, we have e = 6.
And e is also the remainder, R. So, we have R = 6.
Hence, the values of a, b, c, d, e, and R are 5, 4, 0, 3, 6, and 6 respectively.
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Related Questions
Wendy plotted points J and K on a coordinate plane, as shown
Answers
c(2,4)
ExplanationA right triangle is a type of triangle that has one of its angles equal to 90 degrees.
due to the line Jk is vertical , the line KL or JL must be horizontal to make a 90° angle
Step 1
so, the point we are looking for must have lie on the y-coordinate
[tex]\begin{gathered} y-component=-3 \\ y-component=4 \end{gathered}[/tex]therefore, the only possible option with y-coordinate equals 4 is
[tex](2,4)[/tex]therefore, the answer is
c(2,4)
I hope this helps you
Instructions: For the following quadratic functions, write the function in factored form and then find the -intercepts, axis of symmetry, vertex, and domain and range.
Answers
Given the function:
[tex]y=x²-2x-8[/tex]we have that the factored form is:
[tex]y=(x-4)(x+2)[/tex]with this representation, we can see that the x-intercepts are:
[tex]\begin{gathered} x=4 \\ x=-2 \end{gathered}[/tex]Next, the axis of symmetry can be found with the following expression:
[tex]x=-\frac{b}{2a}[/tex]in this case, a = 1 and b = -2 (since a and b are the main coefficients on the equation), then, the axis of symmetry is:
[tex]x=-\frac{-(2)}{2(1)}=1\Rightarrow x=1[/tex]The vertex can be found by evaluating the axis of symmetry on the equation. then, if we make x = 1, we get:
[tex]y=(1)²-2(1)-8=1-2-8=-9[/tex]therefore, the vertex is the point (1,-9).
Finally, the domain of the function is the set of all real numbers (-inf,inf), since it is a polynomial function. The range is [-9,inf), since the vertex is located at the point (1,-9)
Solve the problems. A regular pentagon and an equilateral triangle have the same perimeter. The perimeter of the pentagon is 5 (3x + 2) inches. The perimeter of the triangle is 4 (x - 2) inches. What is the perimeter of each figure? A 12 inches B 20 inches C 36 inches D 40 inches
Answers
Start by finding the value of x by making both expressions equal
[tex]5\cdot(\frac{1}{2}x+2)=4(x-2)[/tex]distribut 5 and 4 on their corresponding sides
[tex]\begin{gathered} \frac{5}{2}x+10=4x-8 \\ \end{gathered}[/tex]let all xs' to one side and all constants to the other
[tex]\begin{gathered} \frac{5}{2}x-4x=-8-10 \\ \frac{-3}{2}x=-18 \end{gathered}[/tex]solve x by dividing by -3 and multiplying by 2
[tex]\begin{gathered} x=-18\cdot(\frac{2}{-3}) \\ x=12 \end{gathered}[/tex]after finding the value of x into either one of the equations
[tex]4(x-2)[/tex][tex]\begin{gathered} 4\cdot(12-2) \\ 4\cdot10 \\ 40 \end{gathered}[/tex]the perimeter of each figure is 40 inches.
As of 01 January 2017, Delta mainline aircraft fly to 233 destinations; when combined with its Delta Connection regional affiliates, Delta-flagged aircraft fly to a total of 320 destinations serving 57 countries across all six inhabited continents. Delta operates a fleet of 764 aircraft within 4,804 flights per day. Round the number of aircraft to the nearest hundred
Answers
When we are rounding a number to the nearest hundred we need to check the tens. If the tens algarism is greater or equal to 5, then we round up and if it is lower than that we round down.
Delta operates a fleet of 764 aircrafts. The tens on this number is the algarism "6", therefore we should round up. Delta operates approximately 800 aircrafts.
There is a field trip to the zoo. tickets are $7 each adult, children tickets are $5 each. The total amount collected was $566. How many tickets were sold per adults and how many were sold per child
Answers
Answer:48 adult tickets, 46 child tickets
Step-by-step explanation: 7+5=12 12*47=564 566-564=2
Ok, so now we have to back up a little and do 12*46=552 566-552=14
14/7=2 Sooooooooooooooo. ((7+5)*46)+(7+7)=566
There are 2 sets of balls numbered 1 through 19 placed in a bowl. If 2 balls are randomly chosen without replacement, find the probability that the balls have the samenumber. Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
Answers
The probability that the two chosen balls from each set have the same number is 0.027027.
We assume that both sets of balls are mixed together to make a single set. The two balls are drawn at random from the bowl since order is unimportant, and they are picked without replacement. We use the entire number of balls in the bowl to determine the total number of combinations made by randomly selecting two balls. The value of n is 2*19 = 38, along with the number of balls being chosen, r = 2.
N = 38C2 = 703
Divide the total number of outcomes where the two randomly picked balls have the same number by the total number of ways to choose two balls from the bowl to obtain the probability that the two randomly chosen balls have the same number.
P = 19/703 = 1/37 = 0.027027
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What is the solution set for -4 x - 10 ≤ 2?
Answers
Adding 10 to both sides.
[tex]\begin{gathered} -4x-10+10\le2+10 \\ -4x\le12 \\ \text{ Dividing both sides by -4, we have} \\ \frac{-4x}{-4}\ge\frac{12}{-4} \\ x\ge-3 \end{gathered}[/tex]So the solution set is the set
[tex]\mleft\lbrace x\in\mathfrak{\Re }\colon x\ge-3\mright\rbrace[/tex]Rational Functions 16m^2———-24m^7(Simplify)
Answers
The given rational function is
[tex]\frac{16m^2}{24m^7}[/tex]To simplify it we will divide 16 and 24 by their greatest common factor and subtract the powers of m
[tex]16\rightarrow1\times16,2\times8,4\times4[/tex]Then the factors of 16 are 1, 2, 4, 8, 16
[tex]24\rightarrow1\times24,2\times12,3\times8,4\times6[/tex]The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24
The common factors of 16 and 24 are 1, 2, 4, 8
The greatest one is 8
Then we will divide 16 and 24 by 8 to simplify the fraction
[tex]\begin{gathered} \frac{16m^2}{24m^7}= \\ \\ \frac{\frac{16}{8}m^2}{\frac{24}{8}m^7}= \\ \\ \frac{2m^2}{3m^7} \end{gathered}[/tex]Now, we will subtract the powers of m
[tex]\frac{2m^2}{3m^7}=\frac{2}{3}m^{2-7}=\frac{2}{3}m^{-5}[/tex]To put the fraction in the simplest form we will write m^-5 by a positive power by changing its place from up to downing
[tex]\frac{2}{3}m^{-5}=\frac{2}{3m^5}[/tex]The answer is
[tex]\frac{16m^2}{24m^7}=\frac{2}{3m^5}[/tex]Solve the inequality. Write the solution set in interval notation.9−xx+11≥0Select one:a. [-11, 9)b. (-∞, -11] U [9, ∞)c. (-∞, -11) U (9, ∞)d. (-11, 9]
Answers
We need to solve the following inequality:
[tex]\frac{9-x}{x+11}\ge0[/tex]Then we have that for the inequality would be complied we have two implicit conditions:
[tex]9-x\text{ }\ge\text{ 0}[/tex]And at the same time:
[tex]x+11>0[/tex]You have to be careful because we already know that the denominator of a fraction can not be zero, it's, for this reason, the second inequality.
But, in a second case, we can also have both numerator and denominator as negative numbers, it also gives us a number bigger or equal to zero.
So we have the inequalities:
[tex]9-x\leq0[/tex]And:
[tex]x+11<0[/tex]Firstly we can focus on the first case if we solve for x:
[tex]9-x\ge0[/tex][tex]x\leq9[/tex]And the denominator inequality of this case:
[tex]x+11>0[/tex][tex]x>-11[/tex]And how we must have the agreed interval between the conditions, we have that the first result for this case is the interval:
(-11,9], or in a equivalent form: -11
From the second case, when both numerator and denominator we have:
[tex]9-x\leq0[/tex][tex]x\ge9[/tex]And from the denominator inequality:
[tex]x+11<0[/tex][tex]x<-11[/tex]So a second result is an interval that doesn't exist because a number biggest of 9 and smallest than -11 doesn't exist in the real number.
Then we obtain the final result, and the correct answer is:
(-11,9], or in a equivalent form: -11
D.
Complete the following statement.
The area under the curve associated with a z score of 3 is ____.
1: 0.4897
2: 0.4987
3: 0.6782
4: 0.5467
Answers
Answer:
the answer is 2
Step-by-step explanation:
check and see
y=x^2+10x+8A.) Identify the coefficients (a, b, and c) B.) Tell whether the graph opens up or opens down C.) Find the vertex. Write as a coordinate. D.) Find the axis of symmetry. Write as an equation. E.) Find the y-intercept Write as a coordinate.
Answers
Answer:
Explanation:
A.
The standard form of a quadratic equation is given as;
[tex]y=ax^2+bx+c[/tex]Given the below quadratic equation;
[tex]x^2+10x+8[/tex]If we compare the given quadratic equation with the standard form of a quadratic equation, we can see that;
[tex]a=1,b=10,and\text{ c = }8[/tex]B.
We can tell if the graph of the given equation will open up or down by considering the coefficients of x^2.
If the coefficient of x^2 is greater than zero, then the parabola will open upwards but if the coefficient of x^2 is less than zero, then the parabola will open downwards.
Since the coefficient of x^2 in the given equation is greater than zero, then the parabola will open upwards.
C.
To find t
Your study partner says that the product of
-12m-3m is -15m. What mistake did your study partner make?
Answers
The product of -12m and -3m is -36 m² after applying the arithmetic operation.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that is +, -, ×, and ÷.
It is given that:
Your study partner says that the product of -12m . -3m is -15m
As we know, the arithmetic operation is the operation in which we do the addition of numbers, subtraction, multiplication, and division.
Applying the arithmetic operation:
= (-12)(-3)
= -36 m²
Or
= -(12+12+12)(-1)
= -(36)(-1)
= +36
Thus, the product of -12m and -3m is -36 m² after applying the arithmetic operation.
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super easy one to one function!!! 50 POINTS HELP!!
Answers
The correct value of the given function is (E) g⁻¹(-3) = 3.
What are functions?A mathematical expression, rule, or law establishes the relationship between an independent variable and a dependent variable (the dependent variable). A function is a type of rule that produces one output for a single input. Source of the image: Alex Federspiel. This is illustrated by the equation y=x2. Any input for x results in a single output for y. Considering that x is the input value, we would say that y is a function of x. Four broad categories can be used to classify different types of functions. dependent upon element Function is a one-to-one relationship, a many-to-one relationship, onto function, one-to-one and into function.
So, g⁻¹(-3):
x = -1g(x) = -3Then, g(x)·x = (-1)(-3) = 3
Then, g⁻¹(-3) = 3.Therefore, the correct value of the given function is (E) g⁻¹(-3) = 3.
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1) What is the slope of the line containing the
points (3,4) and (-6, 10)?
Answers
Answer:
[tex]m=-\frac{2}{3}[/tex]
Step-by-step explanation:
The slope, [tex]m[/tex], between two points, [tex](x_1, y_1), (x_2,y_2)[/tex], is given by the formula
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex], therefore, [tex]m[/tex], between [tex](3,4), (-6,10)[/tex] is [tex]m=\frac{10-4}{-6-3}=-\frac{6}{9}=-\frac{2}{3}[/tex]
estimate the answer by rounding each number to the nearest 10172+36.2+766.1+17.6
Answers
Given the expression :
[tex]172+36.2+766.1+17.6[/tex]We will estimate the answer by rounding each number to the nearest 10
Look at the digit in the units place if 5 or greater add to the digit at the tens place
So,
[tex]\begin{gathered} 172\approx170 \\ 36.2\approx40 \\ 766.1\approx770 \\ 17.6\approx20 \end{gathered}[/tex]so, the answer will be :
[tex]170+40+770+20=1000[/tex]So, the answer is : 1,000
Find the area between the graph of ….and the r-axis on the interval [9, 16]. Write the exact answer. Do not round.
Answers
The area under a curve between two points can be found by doing a definite integral between the two points.
To find the area between the curve y = f(x) between x = a and x = b, integrate y = f(x) between the limits of a and b.
Given the function;
[tex]f(x)=7\sqrt[]{x}[/tex]and the x-interval is;
[tex]\lbrack9,16\rbrack[/tex]Thus, the area A between the graph and the x-interval is;
[tex]A=\int ^{16}_97\sqrt[]{x}dx[/tex]Next, we evaluate the integral, we have;
[tex]\begin{gathered} \int 7\sqrt[]{x}dx=\int 7x^{\frac{1}{2}}dx \\ \int 7\sqrt[]{x}dx=\frac{7x^{\frac{1}{2}+1}}{\frac{1}{2}+1} \\ \int 7\sqrt[]{x}dx=\frac{7x^{\frac{3}{2}}}{\frac{3}{2}} \\ \int 7\sqrt[]{x}dx=\frac{14x^{\frac{3}{2}}}{3}+c \\ \text{Where c is the integral constant} \end{gathered}[/tex]Then, we should apply the integral limits, we have;
[tex]\begin{gathered} \int ^{16}_97\sqrt[]{x}dx=\lbrack\frac{14x^{\frac{3}{2}}}{3}\rbrack^{16}_9 \\ \int ^{16}_97\sqrt[]{x}dx=(\frac{14}{3}(16)^{\frac{3}{2}})-(\frac{14}{3}(9)^{\frac{3}{2}}) \\ \int ^{16}_97\sqrt[]{x}dx=\frac{14}{3}(64-27) \\ \int ^{16}_97\sqrt[]{x}dx=\frac{14}{3}(37) \\ \int ^{16}_97\sqrt[]{x}dx=\frac{518}{3} \end{gathered}[/tex]Thus, the area A between the graph and the x-interval is;
[tex]A=\frac{518}{3}\text{square units}[/tex]Help me math can you help me set 2Directions: Find the slope between each pair of points Show all work on a separate sheet ofpaper. After completing each set, find matching answers. One will have a letter and the other anumber. Write the letter in the matching numbered box at the bottom of the page.
Answers
(T) Given: pair of points (7,5) and (10,9)
To find: The Slope?
Explanation:
We can find the slope by using the formula
[tex]Slope=\frac{y_2-y_1}{x_2-x_1}[/tex]We have given the points
(7,5) and (10,9)
Hence,
[tex]\begin{gathered} x_1=7 \\ y_1=5 \\ x_2=10 \\ y_2=9 \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} Slope=\frac{9-5}{10-7} \\ \\ Slope=\frac{4}{3} \end{gathered}[/tex]Thus, slope = 4/3.
(B) Given: pair of points (-8,2) and (-5,-4)
To find: The Slope?
Explanation:
We can find the slope by using the formula
[tex]Slope=\frac{y_2-y_1}{x_2-x_1}[/tex]We have given the points
(-8,2) and (-5,-4)
Hence,
[tex]\begin{gathered} x_1=-8 \\ y_1=2 \\ x_2=-5 \\ y_2=-4 \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} Slope=\frac{-4-2}{-5-(-8_)} \\ \\ Slope=\frac{-6}{3} \\ \\ Slope=-2 \end{gathered}[/tex]Thus, slope =-2.
(H) Given: pair of points (2,-2) and (-4,-1)
To find: The Slope?
Explanation:
We can find the slope by using the formula
[tex]Slope=\frac{y_2-y_1}{x_2-x_1}[/tex]We have given the points
(2,-2) and (-4,-1)
Hence,
[tex]\begin{gathered} x_1=2 \\ y_1=-2 \\ x_2=-4 \\ y_2=-1 \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} Slope=\frac{-1-(-2)}{-4-2} \\ \\ Slope=\frac{1}{-6} \\ \\ Slope=-\frac{1}{6} \end{gathered}[/tex]Thus, slope =-1/6.
(S) Given: pair of points (-4,9) and (-11,7)
To find: The Slope?
Explanation:
We can find the slope by using the formula
[tex]Slope=\frac{y_2-y_1}{x_2-x_1}[/tex]We have given the points
(-4,9) and (-11,7)
Hence,
[tex]\begin{gathered} x_1=-4 \\ y_1=9 \\ x_2=-11 \\ y_2=7 \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} Slope=\frac{7-9}{-11-(-4)} \\ \\ Slope=\frac{-2}{-11+4}=\frac{-2}{-7} \\ \\ Slope=\frac{2}{7} \end{gathered}[/tex]Thus, slope = 2/7.
(O) Given: pair of points (5,-1) and (4,-6)
To find: The Slope?
Explanation:
We can find the slope by using the formula
[tex]Slope=\frac{y_2-y_1}{x_2-x_1}[/tex]We have given the points
(5,-1) and (4,-6)
Hence,
[tex]\begin{gathered} x_1=5 \\ y_1=-1 \\ x_2=4 \\ y_2=-6 \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} Slope=\frac{-6-(-1)}{4-5} \\ \\ Slope=\frac{-6+1}{-1}=\frac{-5}{-1} \\ \\ Slope=5 \end{gathered}[/tex]Thus, slope = 5.
(16) Given: pair of points (-5,-2) and (9,2)
To find: The Slope?
Explanation:
We can find the slope by using the formula
[tex]Slope=\frac{y_2-y_1}{x_2-x_1}[/tex]We have given the points
(-5,-2) and (9,2)
Hence,
[tex]\begin{gathered} x_1=-5 \\ y_1=-2 \\ x_2=9 \\ y_2=2 \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} Slope=\frac{2-(-2)}{9-(-5)} \\ \\ Slope=\frac{2+2}{9+5}=\frac{4}{14} \\ \\ Slope=\frac{2}{7} \end{gathered}[/tex]Thus, slope =2/7.
(8) Given: pair of points (-10,-6) and (2,-8)
To find: The Slope?
Explanation:
We can find the slope by using the formula
[tex]Slope=\frac{y_2-y_1}{x_2-x_1}[/tex]We have given the points
(-10,-6) and (2,-8)
Hence,
[tex]\begin{gathered} x_1=-10 \\ y_1=-6 \\ x_2=2 \\ y_2=-8 \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} Slope=\frac{-8-(-6)}{2-(-10)} \\ \\ Slope=\frac{-8+6}{2+10}=\frac{-2}{12} \\ \\ Slope=-\frac{1}{6} \end{gathered}[/tex]Thus, slope = -1/6.
(3) Given: pair of points (-2,1) and (-8,-7)
To find: The Slope?
Explanation:
We can find the slope by using the formula
[tex]Slope=\frac{y_2-y_1}{x_2-x_1}[/tex]We have given the points
(-2,1) and (-8,-7)
Hence,
[tex]\begin{gathered} x_1=-2 \\ y_1=1 \\ x_2=-8 \\ y_2=-7 \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} Slope=\frac{-7-1}{-8-(-2)} \\ \\ Slope=\frac{-8}{-8+2}=\frac{-8}{-6} \\ \\ Slope=\frac{4}{3} \end{gathered}[/tex]Thus, slope = 4/3.
(5) Given: pair of points (-4,-2) and (-3,3)
To find: The Slope?
Explanation:
We can find the slope by using the formula
[tex]Slope=\frac{y_2-y_1}{x_2-x_1}[/tex]We have given the points
(-4,-2) and (-3,3)
Hence,
[tex]\begin{gathered} x_1=-4 \\ y_1=-2 \\ x_2=-3 \\ y_2=3 \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} Slope=\frac{3-(-2)}{-3-(-4)} \\ \\ Slope=\frac{3+2}{-3+4}=\frac{5}{1} \\ \\ Slope=5 \end{gathered}[/tex]Thus, slope = 5.
(14) Given: pair of points (-2,-4) and (-7,6)
To find: The Slope?
Explanation:
We can find the slope by using the formula
[tex]Slope=\frac{y_2-y_1}{x_2-x_1}[/tex]We have given the points
(-2,-4) and (-7,6)
Hence,
[tex]\begin{gathered} x_1=-2 \\ y_1=-4 \\ x_2=-7 \\ y_2=6 \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} Slope=\frac{6-(-4)}{-7-(-2)} \\ \\ Slope=\frac{6+4}{-7+2}=\frac{10}{-5} \\ \\ Slope=-2 \end{gathered}[/tex]Thus, slope = -2.
Answer:
(T ) = (3)
(B) = (14)
(H) = (8)
(S) = (16)
(O) = (5)
How can I find x using the sine rule?
Answers
===================================================
Explanation:
Refer to the diagram below.
I've added point labels A,B,C,D to the existing drawing you provided. I also added the label "y" to represent the unknown length AC.
Triangle DAC is isosceles with DC = AC as the two congruent sides. This is shown by the tickmarks.
One useful property of isosceles triangles is that they have congruent base angles. The base angles are opposite the congruent sides.
Since angle ADC = 40, this makes angle DAC = 40 as well.
-----------------------------------------
We'll use this fact to find angle CAB
angle DAB = (angle DAC) + (angle CAB)
80 = (40) + (angle CAB)
angle CAB = 80-40
angle CAB = 40
-----------------------------------------
Move your focus to triangle CAB.
We found or know this already about the triangle
angle C = 30 (given)angle A = 40 (just computed earlier)Let's find angle B
C+A+B = 180
30+40+B = 180
70+B = 180
B = 180-70
B = 110
Use the law of sines (aka sine rule) to find the value of y, which is side AC.
So,
sin(B)/b = sin(C)/c
sin(B)/y = sin(C)/3
sin(110)/y = sin(30)/3
3*sin(110) = ysin(30)
y = 3*sin(110)/sin(30)
y = 5.638156
which is approximate.
-----------------------------------------
The previous section was all about finding the length of AC. That's approximately 5.638156 units.
We'll move our attention back to triangle DAC.
We know this about the angles
angle D = 40angle A = 40angle C = 180-A-D = 180-40-40 = 100and we determined that side d = 5.638156 which is the length of AC mentioned earlier.
Apply another round of law of sines
sin(D)/d = sin(C)/c
sin(40)/5.638156 = sin(100)/x
xsin(40) = 5.638156*sin(100)
x = 5.638156*sin(100)/sin(40)
x = 8.638156
This value is approximate as well.
Round the values however your teacher instructs.
I used GeoGebra to confirm the x value is correct.
Write an algebraic expression for the word phrase.
10 times the product of g and h
010(g + h)
010(g-h)
010 (g+h)
O10gh
Answers
Answer:
10gh (Last Choice)
Step-by-step explanation:
A 5000-seat theater has tickets for sale at $28 and $40. How many tickets should be sold at each price for a sellout performance to generate a total revenue of $155,600?CARDThe number of tickets for sale at $28 should be
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
total seats = 5000
total revenue = $155600
Step 02:
system of equations:
x = # of $28 tickets
y = # of $40 tickets
equation 1:
x + y = 5000
equation 2:
28x + 40y = 155600
x + y = 5000 * (-28)
28x + 40y = 155600
-28x - 28y = - 140000
28x + 40y = 155600
-----------------------------------
12y = 15600
y = 15600 / 12
y = 1300
y in eq. 1:
x + y = 5000
x + 1300 = 5000
x = 5000 - 13000
x = 3700
The answer is:
x = 3700 of $28 tickets
y = 1300 of $40 tickets
Please answer all parts of the questions and show all work. Be sure to show all steps.
Answers
Answer:
• (a)See graph below
,• (b)The rock will be 258 feet high at t=2.39 seconds and at t=3.61 seconds.
Explanation:
Given the equation modeling the height, h(t) of the rock after t seconds:
[tex]h(t)=-16t^2+96t+120[/tex]Part A
To sketch the graph, we use the intercepts and the vertex.
When t=0:
[tex]\begin{gathered} h(0)=-16(0)^2+96(0)+120 \\ h(0)=120\text{ feet} \\ \implies(0,120) \end{gathered}[/tex]The y-intercept is (0,120)
When h(t)=0:
[tex]\begin{gathered} h(t)=-16t^2+96t+120=0 \\ \text{ We solve for t using the quadratic formula} \\ t=\dfrac{-b\pm\sqrt{b^2-4ac} }{2a} \\ t=\dfrac{-96\pm\sqrt{96^2-4(-16)(120)}}{2(-16)}=\dfrac{-96\pm\sqrt{16896}}{-32} \\ t=\dfrac{-96+\sqrt{16896}}{-32}\text{ or }t=\dfrac{-96-\sqrt{16896}}{-32} \\ t=-1.06\text{ or }t=7.06 \end{gathered}[/tex]The only possible x-intercept is (7.06, 0).
To find the vertex, we use the vertex formula below:
[tex]\begin{gathered} (h,k)=\left(-\frac{b}{2a},\frac{4ac-b^2}{4a}\right) \\ =\left(-\frac{96}{2(-16)},\frac{4(-16)(120)-96^2}{4(-16)}\right) \\ =(3,264) \end{gathered}[/tex]Use these points to sketch the graph as shown below:
Part B
When the rock is 258 feet high: h(t)=258
[tex]\begin{gathered} -16t^2+96t+120=258 \\ -16t^2+96t+120-258=0 \\ \implies-16t^2+96t-138=0 \end{gathered}[/tex]We solve the equation for t:
[tex]\begin{gathered} \text{ We solve for t using the quadratic formula} \\ t=\dfrac{-b\pm\sqrt{b^2-4ac} }{2a} \\ a=-16,b=96,c=-138 \\ t=\dfrac{-96\pm\sqrt{96^2-4(-16)(-138)}}{2(-16)}=\dfrac{-96\pm\sqrt{384}}{-32} \\ t=\dfrac{-96+\sqrt{384}}{-32}\text{ or }t=\dfrac{-96-\sqrt{384}}{-32} \\ t=2.39\text{ or }t=3.61 \end{gathered}[/tex]The rock will be 258 feet high at t=2.39 seconds and at t=3.61 seconds.
Evaluate each expression by replaceing n with 1, 2, 3, 4
Answers
We are asked to evaluate each of the expressions for n = 1, 2, 3, 4
We simply need to substitute the value of n into the expression and simplify the expression.
Expression 1:
[tex]\begin{gathered} for\; n=1\colon\; \; 4n-1=4(1)-1=4-1=3 \\ for\; n=2\colon\; \; 4n-1=4(2)-1=8-1=7 \\ for\; n=3\colon\; \; 4n-1=4(3)-1=12-1=11 \\ for\; n=4\colon\; \; 4n-1=4(3)-1=16-1=15 \end{gathered}[/tex]Expression 2:
[tex]\begin{gathered} for\; n=1\colon\; \; 3-n^2=3-(1)^2=3-1=2 \\ for\; n=2\colon\; \; 3-n^2=3-(2)^2=3-4=-1 \\ for\; n=3\colon\; \; 3-n^2=3-(3)^2=3-9=-6 \\ for\; n=4\colon\; \; 3-n^2=3-(4)^2=3-16=-13 \end{gathered}[/tex]Expression 3:
[tex]\begin{gathered} for\; n=1\colon\; \; \frac{1}{n-2}=\frac{1}{1-2}=\frac{1}{-1}=-1 \\ for\; n=2\colon\; \; \frac{1}{n-2}=\frac{1}{2-2}=\frac{1}{0}=\text{undefined} \\ for\; n=3\colon\; \; \frac{1}{n-2}=\frac{1}{3-2}=\frac{1}{1}=1 \\ for\; n=4\colon\; \; \frac{1}{n-2}=\frac{1}{4-2}=\frac{1}{2}=0.5 \end{gathered}[/tex]Expression 4:
[tex]\begin{gathered} for\; n=1\colon\; \; \frac{n^2}{n-1}=\frac{(1)^2}{1-1}=\frac{1}{0}=\text{undefined} \\ for\; n=2\colon\; \; \frac{n^2}{n-1}=\frac{(2)^2}{2-1}=\frac{4}{1}=4 \\ for\; n=3\colon\; \; \frac{n^2}{n-1}=\frac{(3)^2}{3-1}=\frac{9}{2}=4.5 \\ for\; n=4\colon\; \; \frac{n^2}{n-1}=\frac{(4)^2}{4-1}=\frac{16}{3}=5.3 \end{gathered}[/tex]Expression 5:
[tex]\begin{gathered} for\; n=1\colon\; \; 2n+4=2(1)+4=2+4=6 \\ for\; n=2\colon\; \; 2n+4=2(2)+4=4+4=8 \\ for\; n=3\colon\; \; 2n+4=2(3)+4=6+4=10 \\ for\; n=4\colon\; \; 2n+4=2(4)+4=8+4=12 \end{gathered}[/tex]4. Solve the system of equations (show ALL work!). What is the value of y?– 5x + 3y =- 334x + 3y =- 6A. 39B. 13C. 3D. -6
Answers
Step 1. The system of equations we have is:
[tex]\begin{gathered} -5x+3y=-33 \\ 4x+3y=-6 \end{gathered}[/tex]And we are required to find the value of y.
Step 2. To solve this system of equations, we will use the equal values method. This method consists in finding two equal expressions and equaling them into one equation.
For this, we solve for 3y in the two given equations:
[tex]\begin{gathered} 3y=-33+5x \\ 3y=-6-4x \end{gathered}[/tex]Step 3. Now we make the two expressions for 3y equal to each other:
[tex]-33+5x=-6-4x[/tex]Step 4. Solve for x.
To solve for x, move all of the terms that contain x to one side of the equation, and all of the numbers to the opposite side:
[tex]5x+4x=-6+33[/tex]Combine the like terms:
[tex]9x=27[/tex]Divide both sides by 9:
[tex]\begin{gathered} x=\frac{27}{9} \\ \downarrow\downarrow \\ x=3 \end{gathered}[/tex]Step 5. Now that we know the value of x is x=3, we substitute this value into the first equation:
[tex]\begin{gathered} -5x+3y=-33 \\ -5(3)+3y=-33 \end{gathered}[/tex]And solve for y:
[tex]\begin{gathered} -15+3y=-33 \\ 3y=-33+15 \\ 3y=-18 \\ y=-\frac{18}{3} \\ \boxed{y=-6} \end{gathered}[/tex]Answer:
D. -6
Identify the initial value, the growth or decay factor, and the growth or decay rate of the exponential function below. f(x) = 2(94)* 13. Growth or decay 14. Initial value 15. Growth or decay factor 16. Growth or decay rate
Answers
the general expression of the growth function is :
[tex]\begin{gathered} y=b(a)^x\text{ where b is the intial value, a is the growth rate} \\ \text{ and if x = +ve then the function is of growth} \\ \text{and if -ve then the fucntion is decaying} \end{gathered}[/tex]The given expression :
[tex]f(x)=2(0.94)^x[/tex]On comparing with the general equation :
b = 2
a = 0.94
Intial value = 2
As the variable x is positive so the functioni is Growth function
Growth factor is the factor by which a quantity multiplies itself over time.
So, here growth factor = 0.94 0r 94%
Growth rate is the addend by which a quantity increases (or decreases) over time.
so,
[tex]\begin{gathered} f(x)=2(0.95)^x \\ f(x)\text{ for one year x = 1} \\ f(x)=2(0.95)^1 \\ f(x)=1.88 \\ \text{Growth rate= 1.88 + 2} \\ \text{Growth rate = 3.88} \end{gathered}[/tex]Answer :
13 ) Growth
14) 2
15) 0.94
16) 3.88
Solve 10^×=3I see that the answer is 0.477 but i would like to know step by step on how they got the answer. i dont understand how the term "take the log of both sides"
Answers
Answer:
x=0.4771
Explanation:
Given the equation:
[tex]10^x=3[/tex]Whenever the unknown is in the exponent, it is best to take the logarithm of both sides of the equation.
[tex]\log10^x=\log3[/tex]Next, apply the power law of logarithms to the left-hand side of the equation above:
[tex]\begin{gathered} \log a^n=n\log a \\ \implies\log10^x=x\log10 \end{gathered}[/tex]Thus, the last result can be written in the form below:
[tex]\begin{gathered} x\log10=\log3 \\ \text{ The log of 10 is 1} \\ x\times1=\log3 \\ x=0.4771 \end{gathered}[/tex]The value of x is approximately 0.4771.
Find the domain of the graphed function.55-5O A. x2-4O B. x is all real numbers.O C. -45x54D. -4$X2
Answers
SOLUTION
The domian of the lies on the value of x,
Looking at the graph, we can see that it covers the value of x from -4 to 2
since the graph is end region of the curve is shaded, then the endpoint is inclusive
Hence the domain of the graph is
[tex]-4\leq x\leq2[/tex]Therefore the right option is D
If m angle JMK =67, find the m angle JKM
Answers
SOLUTION:
Step 1:
In this question, we are given the following:
If m angle JMK =67, find the m angle JKM
Step 2:
From step 1, we can see that:
[tex]\begin{gathered} \angle JMK=67^0 \\ \text{and } \\ \angle MJK=90^0 \\ \text{Then , we have that:} \end{gathered}[/tex][tex]\angle JKM=90^0-67^{0\text{ }}=23^0[/tex]CONCLUSION:
From the above solution, we can see clearly that the final answer is:
[tex]\angle JKM=23^0[/tex]
A therapist wants to study the effects of yoga and meditation on stress relief. She has 60 volunteers who experience varying levels of stress. She believes that the volunteers’ professions could have an effect on the results. A preliminary survey reveals that 22 of the volunteers are in high-stress professions. The therapist randomly assigns 11 of these subjects to practice yoga and the remaining 11 to practice meditation. Nineteen of the other 38 volunteers are randomly assigned to practice yoga and the remaining 19 to practice meditation. Before the experiment begins, all the participants will be asked to rate their stress levels on a scale of 0 to 10, with 0 representing "no stress” and 10 representing "highest level of stress.” At the end of one month, the subjects will be asked to rate their stress levels again. The differences in stress levels will be compared for the different stress-relieving activities within the two types of professions.
Which of the following is the best description of the experimental design?
a. observational study
b. matched pairs design
c. randomized block design
d. completely randomized design
Answers
Answer:
observational study...
Step-by-step explanation:
The best description of the experimental design is matched pairs design.
What is the "Matched pair design" technique?Prior to being divided into groups, individuals are paired up based on common traits in an experimental design known as a matched-pairs design. One person from the pair is then randomly allocated to the treatment group, while the other is assigned to the control group.
An experiment in which a condition thought to be a likely source of the effect is compared to the same circumstance by the scientist without including or employing the suspected condition is known as a control experiment. Because they are not subjected to the variables and the neutral treatment, the control group often ensures the success of an experiment. An experimental group, on the other hand, is a group of individuals who are exposed to the independent variable.
In a matched pairs design, individuals are paired up according to a variable, and one person from each pair is then randomly assigned to each group. In order to pair each member of an experimental group with a member of the control group, this technique is commonly used.
A matched pair design is typically employed when there is a limited number of participants available for an experimental study or research project.
Therefore, The matched pairs design is the best way to describe the experimental layout.
Learn more about Matched pair design technique here:
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Write as a single exponent 7 5 ∙7 8 (7 3) 2
Answers
The equivalent expression of (7)⁵ x (7)⁸ x (7³)² is (7)¹⁹
How to rewrite the expression?The expression is given as
(7)⁵ x (7)⁸ x (7³)²
The base of the above expression are the same
i.e. Base = 7
This means that we can apply the law of indices
When the law of indices is applied, we have the following equation:
(7)⁵ x (7)⁸ x (7³)² = (7)⁵⁺⁸⁺³ˣ²
Evaluate the product in the equation
(7)⁵ x (7)⁸ x (7³)² = (7)⁵⁺⁸⁺⁶
Evaluate the sum in the above equation
So, we have
(7)⁵ x (7)⁸ x (7³)² = (7)¹⁹
Hence, the simplified expression of the expression given as (7)⁵ x (7)⁸ x (7³)² is (7)¹⁹
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At batting practice Alexis hit 8 balls out of 15 into the outfield. Which equation below can be used to determine the percentage of balls it into the outfield?A. 15/8 = x/100B. 15/100 = x/8C. 8x = (100)(15)D. 15/8 = 100/x
Answers
EXPLANATION
Since Alexis hit, the appropriate relationship should consider a division between the number of balls Alexis hit and the total.
Dividing them gives the following expression:
[tex]\frac{8}{15}[/tex]Now, in order to represent as a percentage, we must multiply this fraction by 100:
[tex]\frac{8}{15}*100[/tex]Equaling the fraction to x, assuming that x represents the computed percentage:
[tex]\frac{8}{15}*100=x[/tex]Dividing both sides by 100:
[tex]\frac{8}{15}=\frac{x}{100}[/tex]Reversing the fractions:
[tex]\frac{15}{8}=\frac{100}{x}[/tex]In conclusion, the equation that gives the appropriate relationship is OPTION D
