Answers
Here are the completed tables:
Coffee (ounces) 4 8 12 16
Cream (ounces) 3/8 3/32 1 1/8 1 1/2
Yards 4 8.7 13.6 25
Seconds 6.4 10 15.6 40
What are the missing values?Ratio is a concept that is used in mathematics to compare two or more numbers together. It shows the relationship between two or more numbers. Increase in the value of numbers that ratios to each other increase at a proportional rate.
The first step is to determine the amount of cream that is needed for 1 coffee = 3/8 ÷ 4
= 3/8 x 1/4 = 3/32
Amount of cream needed for 8 coffees = 3/32 x 8 = 3/4
Amount of cream needed for 16 coffees = 3/32 x 16 = 1 1/2
Now determine how much coffee is needed for 1 ounces of cream
4 ÷ 3/8
= 4 x 8/3 = 10 2/3
Amount of coffee needed for 1 1/8 ounces of cream = 10 2/3 x 1 1/8
32 / 3 x 9/8 = 12
Determine how many seconds is in 1 yard : 6.4 / 4 = 1.6
Seconds in 25 yards = 1.6 x 25 = 40
Determine how many yard is in 1 second : 4 / 4.6
Yards in 10 seconds = 4/4.6 x 10 = 8.7
Yards in 15.6 seconds = 4 / 4.6 x 15.6 = 13.6
To learn more about ratios, please check: https://brainly.com/question/9194979
#SPJ1
Related Questions
Which equation has the solution x = 5?
2x 8 = -2
52 – 7 = 12
-
7x - 4 = 101
9x - 2 = 47
Answers
Answer:
I think your missing some signs
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)
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
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
The telephone cable in the illustration currently runs from A to B to C to D.How much cable ( in yards) is required to run from A to D directly? yd
Answers
Given
[tex]\begin{gathered} A\text{ to B =106 yd} \\ B\text{ to C= 72yd} \\ C\text{ to D=48 yd} \end{gathered}[/tex]Solution
[tex]\begin{gathered} P\text{ to D = 106+48} \\ P\text{ to D =154} \end{gathered}[/tex]So to find A to D directly, We use pythagoras
[tex]\begin{gathered} AD^2=154^2+72^2 \\ AD^2=23716+5184 \\ AD^2=28900 \\ Take\text{ the square root of both sides} \\ AD=\sqrt[]{28900} \\ AD\text{ =170 } \end{gathered}[/tex]The final answer
170 yd is required to run from A to D directly
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
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]What is the solution to -3/7m<21?
m < 49
m > 49
m > -49
m < -49
Answers
Answer:
[tex]m>-49[/tex]
Step-by-step explanation:
[tex]m>21(-7/3)=-49[/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]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
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.
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]
Understanding of Multiplying by a Fraction Name: Draw a number line model to represent each multiplication problem. Then solve the problem.2/3×1/2=how do you do this
Answers
We have following:
1.
[tex]\frac{2}{3}\cdot\frac{1}{2}=\frac{2\cdot1}{3\cdot2}=\frac{2}{6}=\frac{1}{3}[/tex]2.
[tex]\frac{5}{6}\cdot\frac{3}{4}=\frac{5\cdot3}{6\cdot4}=\frac{15}{24}=\frac{5}{8}[/tex]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
To learn more about probability, visit :
https://brainly.com/question/11234923
#SPJ9
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.
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)
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
which of the following is equivalent to the fractions below after rationalizing the denominator and simplifying? 12/√2
Answers
SOLUTION
[tex]\frac{12}{\sqrt{2}}[/tex][tex]\frac{12}{\sqrt{2}}=\frac{12}{\sqrt{2}}\times\frac{\sqrt{2}}{\sqrt{2}}=\frac{12\sqrt{2}}{\sqrt{2}\times\sqrt{2}}[/tex][tex]\frac{12\sqrt{2}}{2}=6\sqrt{2}[/tex]Final answer:
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
Jaime want so make a square patio in his yard. He has enough concrete to pave an area of 193 square feet. If A represents the area of the patio, and s represents the side length of the patio, use the formula s=√A to find the length of each side of his patio. Round your answer to the nearest tenth of a foot.
Answers
Jaime wants to make a square patio in his yard.
Now, a square has all four sides equal.
We need to use the next equation given:
[tex]s=\sqrt{A}[/tex]Where s represents the side length and A represens the area of his patio.
Replace using A=193 ft², therefore:
[tex]\begin{gathered} s=\sqrt{193ft^2} \\ s=13.9ft \end{gathered}[/tex]Hence, the length of each side of his patio is 13.9 ft ( the value is rounded to the nearest tenth)
Urgent!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!A bicycle company produces y blcycles at a cost represented by the polynomial y ^ 2 + 10y + 400, 000 . The revenue for y represented by 3y^ 2 +10y+700. Find a polynomial that represents their profit. If the company only has enough materials to make 400 bicycles , should it make the bicycles ?
Answers
In order to calculate the profit, let's subtract the revenue and the cost:
[tex]\begin{gathered} \text{profit}=\text{revenue-cost} \\ \text{profit}=3y^2+10y+700-(y^2+10y+400000) \\ \text{profit}=2y^2-399300 \end{gathered}[/tex]Now, for 400 bicycles, let's calculate the profit:
[tex]\begin{gathered} \text{profit}=2\cdot400^2-399300 \\ \text{profit}=320000-399300 \\ \text{profit}=-79300 \end{gathered}[/tex]Since the profit is negative, the company should not make the bicycles.
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.
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.
Learn more about the arithmetic operation here:
brainly.com/question/20595275
#SPJ1
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
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.
what is 10-6+8/2x3 please help
Answers
Answer:
16
Step-by-step explanation:
10-6+ 8/2 *3
8/2=4
10-6+4*3
4*3=12
10-6+12
10-6= 4
4+12=16
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
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
For the equation, 2x+y=6, complete the following ordered pairs: (0,_), (_,0), (_,-6)
Answers
Answers in bold
(0, 6)
(3, 0)
(6, -6)
==============================================
Explanation:
The first point given is (0, _) where we don't know what goes in the blank just yet. Let's call this unknown y. The point is (0, y)
Plug in x = 0 to solve for y.
2x+y = 6
2*0+y = 6
0+y = 6
y = 6
Therefore, the point is (0,6) which is the y intercept. This is where the graph crosses the y axis.
------------------------
Next we move onto (_,0)
Plug in y = 0 to find x
2x+y = 6
2x+0 = 6
2x = 6
x = 6/2
x = 3
The point (_, 0) updates to (3,0) which is the x intercept. This is where the graph crosses the x axis.
------------------------
Lastly, we'll use y = -6 to find x.
2x+y = 6
2x-6 = 6
2x = 6+6
2x = 12
x = 12/2
x = 6
We go from (_, -6) to (6, -6)
------------------------
We can use a graphing tool like Desmos to visually confirm the answers. See below.
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.
