One possible length of the third side of the given triangle is 15
Determining a possible length of a side of a triangleFrom the question, we are to determine a possible length of the third side of the triangle
From one of the properties of a triangle, we know that
The sum of any two sides of a triangle is greater than the third side and the positive difference of any two sides of a triangle is lesser than the third side.
Thus,
8 + 17 is greater than the third side
25 is greater than the third side
and
17 - 8 is lesser than the third side
9 is lesser than the third side
If the third side of the triangle is x,
Then,
9 < x < 25
Hence, a possible value of x is 15
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The maximum area istype your answer...ft in length by type your answer...ft in width
The measurements are
1. 4unit by 4 unit
2. 6 unit by 2 unit
3. 5 units by 3 units
4. 1 units by 7 units
To arrange the area from the largest to the smallest we have to compute the area of the measurements.
[tex]\begin{gathered} \text{area = lw} \\ \text{area}=\text{ 4}\times4=16units^2 \\ \text{area}=\text{ 6}\times2=12units^2 \\ \text{area}=\text{ 5}\times3=15units^2 \\ \text{area}=\text{ 1}\times7=7units^2 \end{gathered}[/tex]The arrangement from highest to smallest is represented as follows
4units by 4 units
5 units by 3 units
6 units by 2 units
1 unit by 7 units
-3x^4+27x^2+1200=0Find all the zeros of the equation y problem is the calculation after the info in the picture
Transform the variable x² into u
[tex]-3x^4+27x^2+1200=0\Longrightarrow-3u^2+27u+1200=0[/tex]Use the quadratic formula to solve for solutions in u, with a = -3, b = 27, c = 1200.
[tex]\begin{gathered} u=\frac{ -b \pm\sqrt{b^2 - 4ac}}{ 2a } \\ u=\frac{ -27 \pm\sqrt{27^2 - 4(-3)(1200)}}{ 2(-3) } \\ u=\frac{-27\pm\sqrt[]{729-(-14400)}}{-6} \\ u=\frac{ -27 \pm\sqrt{15129}}{ -6 } \\ u=\frac{ -27 \pm123\, }{ -6 } \\ \\ u_1=\frac{-27+123}{-6}=\frac{96}{-6}=-16 \\ u_2=\frac{-27-123}{-6}=\frac{-150}{-6}=25 \\ \\ \text{Which means that if we factor} \\ -3u^2+27u+1200=0 \\ \text{Then it is} \\ (u+16)(u-25)=0 \end{gathered}[/tex]Revert u back into x²
[tex]\begin{gathered} (u+16)(u-25)=0\Longrightarrow(x^2+16)(x^2-25)=0 \\ \\ \text{Recall the special factor} \\ (a^2-b^2)=(a+b)(a-b)\text{ and apply it to }(x^2-25) \\ \\ (x^2+16)(x^2-25)=0 \\ (x^2+16)(x+5)(x-5)=0 \end{gathered}[/tex]Equate to zero all the factors, and solve for x
[tex]\begin{gathered} x^2+16=0 \\ x^2=-16 \\ \sqrt[]{x^2}=-16 \\ x_1=\pm\sqrt[]{-16} \\ \\ x+5=0 \\ x_2=-5 \\ \\ x-5=0 \\ x_3=5 \end{gathered}[/tex]The real zeroes to the given equation is x = -5, and x = 5.
Nazir was given 5over7 of the fruit basket what fraction of the fruit basket was left over?
The fraction of the fruit basket is 2/7.
What is fraction?
Fraction represent the parts of a whole or collection of objects. A fraction has two parts. The number on the top of the line is called the numerator. It tells how many equal parts of the whole or collection are taken. The number below the line is called the denominator.
Total fraction = 1 or can be written as 7/7
Nazir given 5/7 of the fruit basket
1-5/7 = 7-5/7
= 2/7
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Use the appropriate form of the percentage formula.What percent of 14.4 is 11.7? Round to the nearest hundredth of a percent.
Hello there. To solve this question, we'll have to compare the values with two fractions:
To see how much of 14.4 is 11.7, in percentage, we start by considering 14.4 represents 100%, or 100, since we want to find the answer in percent as well.
Then we make:
[tex]\frac{11.7}{x}=\frac{14.4}{100}[/tex]Cross multiply the numbers:
[tex]11.7\cdot100=14.4\cdot x[/tex]Divide both sides of the equation by a factor 14.4
[tex]x=\frac{11.7\cdot100}{14.4}[/tex]Using a calculator, we get that x is equal to:
[tex]81.25[/tex]Therefore, 11.7 is 81.25% of 14.4!
solve for x: 2/3x-1=5
The given equation is
[tex]\frac{2}{3}x-1=5[/tex]First, we have to sum 1 on each side
[tex]\begin{gathered} \frac{2}{3}x-1+1=5+1 \\ \frac{2}{3}x=6 \end{gathered}[/tex]Now, we multiply the equation by 3/2
[tex]\begin{gathered} \frac{2}{3}x\cdot\frac{3}{2}=6\cdot\frac{3}{2} \\ x=\frac{18}{2} \\ x=9 \end{gathered}[/tex]Therefore, the solution is 9.witch of these ordered pairs is a solution to the inequality y - 2x < 3y - 2x < -3 (2,4)(-2,3)(3,4)(1,-1)
Explanation:
y - 2x < 3
To determine if the ordered [pair is a solution, we would insert the values into the inequality to confirm if the statement will be true.
a) (2,4) = (x, y)
4 - 2(2) < 3
4 - 4 <3
0 < 3
This is false
b) (-2, 3) = (x, y)
3 - 2(-2) < 3
3 + 4 <3
7 < 3
This is false
c) (3, 4) = (x, y)
4 - 2(3) < 3
4 - 6 < 3
-2 < 3
This is true
d) (1, -1) = (x, y)
-1 -2(1) < 3
-1 - 2 < 3
-3 < 3
Identify the domain of the function shown in the graph.
A. X≥ 0
B. x < 0
C. 0
-8-84-2
D. x is all numbers.
10-
8
8.
4+
2+
y
-2-
4.
-8-
-10+
2
4 6 8 10 12
Answer:
A. [tex] x \geq 0[/tex]
Step-by-step explanation:
The domain of a function is the set of [tex]x[/tex]-values.
b=3 y-intercept br Find the slope and y-intercept of the line represented by each table. 3. 0 3 6 9 0 2 х 12 10 19 28 2 37 у у A 4 6 8 x 3 4 5 slope m = slope m= y-intercept br y-intercept
The slope can be obtained using the formula
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]and the y intercept is the value of y when x is equal to zero.
3. We can choose the points (3,10) and (6,19), then
[tex]m=\frac{19-10}{6-3}=\frac{9}{3}=3[/tex]From this, we can use the slope-point form of the line equation to obtain the y intercept
[tex]\begin{gathered} y-10=3(x-3) \\ y=3x-9+10 \\ y=3x+1 \end{gathered}[/tex]Then,
slope =3, y-intercept=1.
4. We choose the points (2,2), (4,3)
[tex]m=\frac{3-2}{4-2}=\frac{1}{2}[/tex][tex]\begin{gathered} y-2=\frac{1}{2}(x-2) \\ y=\frac{1}{2}x-1+2 \\ y=\frac{1}{2}x+1 \end{gathered}[/tex]Then,
slope = 1/2, y-intercept =1
distribute and simply (x- 2)2+9
Weare asked to used distributive property and reduce the expression:
(x - 2 ) 2 + 9
so we apply distributive property to eliminate the parenthesis, multiplying the factor of "2" by "x" and by "-2":
2 x - 4 + 9
now combine like terms:
2 x + 5
If the question involved instead the following expression:
(x - 2)^2 + 9 (where the "2" was in fact a power affecting the binomial (x-2), then
true or false?17. The focci of an ellipse are located at 1/3 the length of the major axis from both sides of the center.
To solve this problem and find if the statement is true, we can start by remembering the general equation for an ellipse:
[tex]\frac{x^2}{a^2}+\frac{y^2}{b^2}=1[/tex]where a and b are the major axis and the minor axis for the ellipse, as shown in the following diagram:
The foci of an ellipse, are the focal points of the ellipse, for reference, we show them in the diagram:
The foci can be found using the following equation:
[tex]f=\sqrt[]{a^2-b^2}[/tex]To prove if the foci f is really 1/3 of the length of the major axis (in this case the major axis is a) we can give random values to a and b.
Values for a and b:
a=6
b=4
If the foci of the ellipse were located at 1/3 of the length of the major axis, we should find that the foci "f" is 1/3 of 6, thus, we should find that f=2, let's see if that is true by substituting a and b into the formula for f:
[tex]f=\sqrt[]{a^2-b^2}[/tex][tex]f=\sqrt[]{6^2-4^2^{}}[/tex][tex]\begin{gathered} f=\sqrt[]{36-16} \\ f=\sqrt[]{20} \end{gathered}[/tex]solving the square root we find the value of f:
[tex]f=4.47[/tex]Instead of 2 (which would have been 1/3 of the major axis), we find that f is 4.47, thus the statement "The foci of an ellipse are located at 1/3 the length of the major axis from both sides of the center." Is NOT TRUE.
Answer: False
A.) State the random Variable: select from one of the following - X= the number of heads observed - X=tossing a coin - X= number of coins tossed - X= the number of heads observed when you flip a coin three times - X= the probability that you observe heads B.) construct a probability distribution table for the number of heads obtained over three tosses. Enter the X values from smallest to largest C.) determine the shape of the probability distribution of x - left skewed -symmetric -right skewed - uniform D.) find the MEAN number of heads for this distribution E.) find the standard deviation for the number of heads for this distribution F.) find the probability of obtaining two or less heads over three tosses of a coin
SOLUTION:
Step 1:
In this question, we are given the following:
Step 2:
A.) State the random variable:
X= the number of heads observed when you flip a coin three times
Step 3:
B.) construct a probability distribution table for the number of heads obtained over three tosses. Enter the X values from smallest to largest:
X P(X)
0 1/8
1 3/8
2 3/8
3 1/8
Step 4:
C.) Determine the shape of the probability distribution of x
- symmetric
Step 5:
D.) find the MEAN number of heads for this distribution
[tex]\begin{gathered} Mean\text{= ( 0 X }\frac{1}{8})\text{ + ( 1 x }\frac{3}{8})\text{ + ( 2 x }\frac{3}{8})\text{ + (3 x }\frac{1}{8}) \\ \text{Mean = 0+ }\frac{3}{8}+\frac{6}{8}+\frac{3}{8} \\ \text{Mean = }\frac{12}{8} \\ \text{Mean = 1. 5} \end{gathered}[/tex]Step 6:
E.) find the standard deviation for the number of heads for this distribution:
[tex]S\tan dard\text{ Deviation = }\sqrt[]{(x\text{ -}\mu)^2\text{ P ( X = x )}}[/tex][tex]\begin{gathered} \sin ce\text{ }\mu\text{ = 1. 5, then we have that:} \\ \sqrt[]{\lbrack(0-1.5)^2X\text{ }\frac{1}{8}\rbrack+\lbrack(1\text{ - }1.5)^2\text{X }\frac{3}{8}\rbrack+\lbrack(2-1.5)^2}X\frac{3}{8}\rbrack+\lbrack(3-1.5)^2\text{ X }\frac{1}{8} \end{gathered}[/tex][tex]\begin{gathered} \sqrt[]{(2.\text{ 25 X }\frac{1}{8})\text{ + ( 0.25 X }\frac{3}{8})\text{ + ( 0. 25 X }\frac{3}{8})\text{ + (2.25 X }\frac{1}{8})} \\ =\text{ }\sqrt[]{0.28125+\text{ 0.09375 + 0.09375 + 0.28125}} \\ =\sqrt[]{0.75} \\ =0.866\text{ ( 3 decimal places)} \end{gathered}[/tex]
Step 7:
F.) find the probability of obtaining two or less heads over three tosses of a coin
[tex]P\text{ ( obtaining two or less heads) = }\frac{3}{8}+\text{ }\frac{3}{8}+\frac{1}{8}\text{ = }\frac{7}{8}[/tex]A lock on a fence door has a 3 digit combination. Each digit can be any number between 1 – 8. The combinations 123, 456, and 789 are invalid. How many combinations are possible?
There are a total of 8 possible numbers for each digit and there are 3 digits for the password. Since the problem didn't state that the numbers can't be repeated, then we can apply the following formula:
[tex]C_{n,m}\text{ = }\frac{n!}{m!(n\text{ - m)!}}[/tex]Where "n" is the range of possibilities for each number and "m" is the number of digits we want to arrange them. So applying the data from the problem gives us:
[tex]undefined[/tex]What is the domain
of the function?
The domain of the function is found as [-7, 6].
What is termed as the domain?A function is an mathematical object that accepts input, appears to apply a rule to it, and returns the result. A function can be thought of as a machine that requires in a number, performs some operation(s), and then outputs the result. The domain of a function is the collection of all its inputs. Its codomain is the set of possible outputs. The range refers to the outputs which are actually used.For the given question,
The graph of the function is given.
By the definition of the domain, the maximum and minimum values of the graph on x axis are 6 and -7 respectively.
Thus, the domain of the function is found as [-7, 6].
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Find the direction angle of the vector u = -3i+8j. That is, find the angle between 0 and 360° that u makes with the positive x-axis (measured counterclockwise)Do not round any intermediate computations, and round your answer to the nearest whole number.
we have the vector
u=-3i+8j
see the attached figure, to better understand the problem
we have that
tan(x)=8/3
x=tan^-1(8/3)
x=69.44 degrees
Find out the angle theta
theta=180-x
theta=180-69.44
theta=111 degreesWrite down all the numbers that are between 30 and 60 and have a difference of 4 between their digits.
Answer:
The whole numbers that are between 30 and 60 and have a difference of 4 are 31, 35, 39, 43, 47, 51, 55 and 59
Step-by-step explanation:
Hope this helps!!!
What is the range of the function f(x)=√x-8 + 6?Of(x) ≥-8O f(x) ≥-6Of(x) ≥ 6O f(x) ≥ 8
Hello!
We have the function below:
[tex]f(x)=\sqrt{x-8}+6[/tex]Let's analyze the graph of it:
Note that for the domain, it starts when x = 8.
For the range, it starts when y = 6.
So, the range of this function is:
[tex]\begin{gathered} [6,+\infty) \\ \text{ or} \\ \boxed{f(x)\geqslant6} \end{gathered}[/tex]Third alternative.
3. Lake City Jr. High Students:*** 12 out of every 18 ride a bus to school*** 9 out of every 15 live in Lake City*** 160 ride a bus to schoolHow many of the Jr. High students do not live in Lake City?
Let
x ----> total number of students Lake City Jr. High Students
we have that
12 out of every 18 rides a bus to school
160 ride a bus to school
Applying proportion
18/12=x/160
solve for x
x=(18/12)*160
x=240 total students
so
9 out of every 15 live in Lake City
that means
6 out of every 15 does not live in Lake City
Applying proportion
y -----> students that not live in Lake City
6/15=y/240
solve for y
y=(6/15)*240
y=96
therefore
96 students do not live in Lake CityPlease help find the x
Value of x is 28.
Define parallelogram.A parallelogram is a geometric object with sides that are parallel to one another in two dimensions. It is a form of polygon with four sides (sometimes known as a quadrilateral) in which each parallel pair of sides have the same length. A parallelogram has adjacent angles that add up to 180 degrees. A unique variety of quadrilateral called a parallelogram has both pairs of its opposite sides parallel and equal. First, it is important to understand that a parallelogram's inner angles add up to 360 degrees (sum of internal angles = 180(n-2) where n is the number of sides in the image).
Given Data
89°, (5x -8)° , (3x+4)° , 51°
As we know, the sum of angles of parallelogram is 360°.
So,
89 + 5x-8 +3x + 4 + 51 = 360
5x + 3x = 360 - 136
8x = 224
x = 28
Value of x is 28.
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Kyra multiplied 0.27 by a power of ten and got 2.7. What power of ten did she multiply by? Responses
The power of ten that she multiplied by is 1.
What is an exponent?The exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number. For example, in 6⁴ , 4 is the exponent and 6⁴ is called 6 raise to the power of 4.
Since Kyra multiplied 0.27 by a power of ten and got 2.7. This will be illustrated as:
= 0.27 × 10¹
= 2.7
Therefore, the power is 1.
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Given the equation 2(n + 7) - 5 = 29. What two steps are needed to simplify the left side of the equals? Choose the two that apply. *Add 5 to both sidesDistribute the 2Divide both sides by 2Combine like termsSubtract 7 from both sides
In order to simplify the left side of the equation, the first two steps are:
1) Distribute the 2:
[tex]\begin{gathered} 2\mleft(n+7\mright)-5=29 \\ 2n+14-5=29 \end{gathered}[/tex]2) Combine like terms:
[tex]\begin{gathered} 2n+14-5=29 \\ 2n+9=29 \end{gathered}[/tex]So the correct options are Distribute the 2 and Combine like terms.
It is an equation containg atleast one fraction whose numerator and deniminator are polynomials.A.rational functionB.rational equationC.ratuonal inequalityD.irrational equation
In a equation, if we have polynomials in the numerator and denominator, this equation is considered a rational equation, similar to the case where fractions are considered rational numbers.
So the correct option is B.
A farmer is building a fence to enclose a rectangular area against an existing wall, shown in the figure below.
Fenced in Region
Three of the sides will require fencing and the fourth wall already exists.
If the farmer has 184 feet of fencing, what is the largest area the farmer can enclose?
Find the greatest common factor of the following monomials2b^4 32b^6 22b^5
The answer is
[tex]2b^4[/tex]First let's see the divider of the coeficient:
2 is a prime
32 = 2^5 = 2*2*2*2*2
22 = 11*2
The GCD of all is 2
Now, we have b to the 4, 5 and 6. We can write it:
[tex]\begin{gathered} b^6=b^4\cdot b^2 \\ b^5=b^4\cdot b \end{gathered}[/tex]Now we have all to get the answer:
[tex]\begin{gathered} 32b^6=2^4b^2\cdot(2b^4) \\ 22b^5=11b\cdot(2b^4) \end{gathered}[/tex]And the remaining is 2b^4. As you can see, all the monomyals can be divided by 2b^4 and that's the greatest common factor
the volume of the prism below is 264 in3. what is the height of the prism
The volume of any prism = base area x height
Given Volume = 264 in^3
The prism is triangular based
Therefore, its base area = 1/2 x base x height
The base of the triangle= 8in
Height of the triangle = 6in
[tex]\begin{gathered} \text{ Base area = }\frac{1}{2}\text{ x 8 x 6} \\ \text{Base area= 24in}^2 \end{gathered}[/tex][tex]\begin{gathered} \text{ Recall, Volume = Base area x height} \\ H\text{eight = }\frac{\text{Volume}}{\text{Base area}} \\ \text{ Height=}\frac{264in^3}{24in^2} \\ \\ \text{Height}=11\text{ in} \end{gathered}[/tex]The height of the prism is 11 in.
Question: solve ABC below using either the law of sines or law of cosines. Round to the nearest tenth.
SOLUTION:
First we calculate for a with cosines rule
[tex]\begin{gathered} a^2=b^2+c^2-2bcCosA \\ b=\text{ 29yd, c= 23yd, A= 99}\degree \\ a^2=(29)^2+(23)^2-2(29)(23)Cos(99) \\ a^2=841^{}+529^{}-1334\times(-0.1564) \\ a^2=841^{}+529^{}-1334\times(-0.1564) \\ a^2=841^{}+529^{}+208.68 \\ a^2=1578.686 \\ a=\text{ }\sqrt[]{1578.686} \\ a=\text{ 39.73} \end{gathered}[/tex]Then we calculate angle B with sine rule
[tex]\begin{gathered} \frac{a}{\sin A}=\text{ }\frac{b}{\sin B} \\ A=\text{ 99}\degree,\text{ a= 39.73 yd, b= 29 yd} \\ \frac{39.73}{\sin 99}=\text{ }\frac{29}{\sin B} \\ \text{Cross multiplying} \\ \sin \text{ B= }\frac{29\sin 99}{39.73} \\ \sin \text{ B= }\frac{29\times0.987}{39.73} \\ \sin \text{ B= 0.720} \\ B=\text{ }\sin ^{-1}(0.720) \\ B=\text{ 46.05}\degree \end{gathered}[/tex]Then we find the last angle C
[tex]\begin{gathered} A\text{ + B + C= 180}\degree \\ 99\text{ + 46.05}\degree\text{ + C= 180}\degree \\ C=\text{ 180}\degree-\text{ 99}\degree-\text{ 46.05}\degree \\ C=\text{ 34.95}\degree \end{gathered}[/tex]Final answers:
Side
a= 39.7 yd (nearest tenth)
Angles
B= 46.1 degrees (nearest tenth)
C= 35.0 degrees (nearest tenth)
The Demand equation for an item currently being marketed is given by D(q) = -0.15 q2 + 56,
where D(g) is in $ that can be charged per unit, and q is in thousands of units that can be sold at
that price. (For example, q=20 means 20,000 units can be sold.) 15,000 units are to be sold, at
what price should each be set? (Be careful with units when you do your calculations!)
The appropriate price = $
- 4 is price should each be set in price demand equation.
What is the price demand equation?
The formula P(x) = -ax + b is frequently used to express price-demand (p). But occasionally you have to construct P(x) using pricing data. • The point slope equation shown below can be used to compute P(x): 200 units are sold at a price of $14.
D(q) = -0.15 q² + 56
to find the price , when 20,000 units are to be sold , replace q = 20 in D(q)
D(20) = - 0.15 × (20)² + 56
= - 0.15 × 400 + 56
= - 60 + 56
= - 4
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Find the side length of the square given the area
The area of square is given 72 sq.ft.
ExplanationTo determine the side of square.
Use the formula for area of square.
[tex]A=side^2[/tex]Substitute the values.
[tex]\begin{gathered} 72=side^2 \\ side=\sqrt{72} \\ side=\sqrt{2\times2\times2\times3\times3} \\ side=6\sqrt{2} \end{gathered}[/tex]AnswerHence the side length of square is
[tex]6\sqrt{2}ft[/tex]Please help me on my assignment The select is options x and y
SOLUTION
The domain of f is all the x-values, of the points on the graph, while the range is the corresponding y-values.
The domain of this function is all real numbers, hence the domain f is the interval
[tex](-\infty,\infty)[/tex]The range of f is from negative infinity to 7. Hence the range of f is interval
[tex](-\infty,7\rbrack[/tex]so I have couple question I need help on I could send an image of the work I need help on
Explanation:
1) (-3.4)^0
Note: anything raised to the power of zero is 1
Hence, (-3.4)^0 = 1
3)
Find (if possible) conditions on a and b such that the following system has no solution, onesolution and infinitely many solutions.2 – 2y = 1ac + by = 5.
We are given the following system of equations
[tex]\begin{gathered} x-2y=1 \\ ax+by=5 \end{gathered}[/tex]Let us find the conditions on a and b such that the following system has no solution, one
solution and infinitely many solutions.
No solution:
A system of equations has no solution when the two equations are parallel.
Recall that two parallel equations have equal slopes.
If the value of a = 1 and the value of b = -2 then the two equations will be parallel and hence they will have no solution.
[tex]\begin{gathered} x-2y=1 \\ x-2y=5 \end{gathered}[/tex]The graph of the above system of equations is shown below
