width = x
length = 2x+8
area = l x w
x(2x+8)=120
2x^2+8x−120=0
x^2+4−60=0
(x+10)(x−6)=0
x=−10 and x=6
width has to be a positive number
Width = 6
inches.
the base is 12 the height is 17. and the apothem is 10 inches they are all inches. Triangular pyramid volume
Grandpa schmidt is 75 years old. this is 9 years less than seven times the age of junior schmidt. how old is junior
Tammy takes a job after school to earn money to buy a violin. she knows that the more hours she works, the more money she will make.
a. the number of hours tammy works is a function of the amount of money she makes.
b. the amount of money tammy makes is a function of the number of hours she works.
c. tammy's job is a function of her interest in music.
Which graph represents the solution set of the system of inequalities?
{3y≥x−9
3x+y>−3
the solid line passes through (0,-3) and (0,9)
dotted line passes through (0,-3) and (0,-1)
see attached sketch
Answer:
The image shows the solution for the given inequalities.
Step-by-step explanation:
We are given the following information in the question:
[tex]3y \geq x-9\\3x+y>-3[/tex]
We have to plot the solution for the given inequality.
The image attached shows the solution to the given inequalities.
The red shaded portion is the solution to the first inequality and the blue shaded region is the solution for the second inequality.
The common shaded portion is the solution common to both the inequalities.
The dotted blue line is not a part of the solution for both the inequality.
A cyclist rides his bike at a rate of
11
feet per second. What is this rate in miles per hour? How many miles will the cyclist travel in
3
hours? In your computations, use the fact that
1
mile is equal to
5280
feet. Do not round your answers.
The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds. the probability of a player weighing less than 250 pounds is closest to:
Using the normal distribution, it is found that there is a 0.9772 = 97.72% probability of a player weighing less than 250 pounds.
Normal Probability DistributionIn a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.In this problem:
The mean is of [tex]\mu = 200[/tex].The standard deviation is of [tex]\sigma = 25[/tex].The probability of a player weighing less than 250 pounds is the p-value of Z when X = 250, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{250 - 200}{25}[/tex]
[tex]Z = 2[/tex]
[tex]Z = 2[/tex] has a p-value of 0.9772.
0.9772 = 97.72% probability of a player weighing less than 250 pounds.
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Please Help! Will give BRAINLIEST! I don't know how to do this.
Determine the x- and y-intercepts of the graph of y=−1/3x+3 .
Then plot the intercepts to graph the equation.
Answer:
you would graph (0,3) and (9,0)
Step-by-step explanation:
Consider the provided equation.
The x intercepts are the points where y value is zero. Similarly the y intercepts are the points where x values is zero.
In order to find the x intercept substitute y = 0 in the provided equation.
0=-1/3x + 3
-3=-1/3(x)
-9=-x
9=x
Thus, the x intercept is (9,0)
In order to find the y intercept substitute x = 0 in the provided equation.
y=-1/3(0) + 3
y=3
Thus, the y intercept is (0,3)
Now use the x and y intercepts to draw the graph of the equation.
The required graph is shown in figure 1.
Therefore, the x- and y- intercepts is (9,0) and (0,3)
Solve 3c − 5f = 55 for f. Show your work.
[tex]\(f = \frac{3c - 55}{5}\)[/tex] is the solution for the given expression.
To solve the equation 3c - 5f = 55 for f, you need to isolate the variable f by performing a series of mathematical operations. Let's go step by step:
Start with the equation:
3c - 5f = 55
Add 5f to both sides to move the term involving f to one side of the equation:
3c = 5f + 55
Subtract 55 from both sides to isolate the term with f:
3c - 55 = 5f
Now, divide both sides by 5 to solve for f:
(3c - 55) / 5 = f
f = (3c - 55) / 5
So, [tex]\(f = \frac{3c - 55}{5}\)[/tex] is the solution for (f).
Which regular polygon can be used to form a tessellation?
octagon
decagon
triangle
nonagon
The regular polygon that could be used for tessellation is:
Triangle.
Step-by-step explanation:Tessellation is a geometry that is formed by a repeating pattern of same shape without any gaps.
We can use only three regular polygon for the formation of Tessellation:
1) Equilateral Triangle
2) Square
3) Regular Hexagon.
Hence, from the given option the regular polygon that can be used to form a tessellation is:
Triangle.
find gh if g(5,-1) and h(1,-3). write your answer in simplest radical form.
Please help with 3 questions thank you.
1. an angle congruent to a given angle
2. x = 68, y = 75
3. corresponding angles
The sum of two consecutive odd integers is 24. find the integers. which equation can be used to find the first integer n
Suppose you have 52 feet of fencing to enclose a rectangular dog pen. The function A = 26x = x2 where x = width, gives you the area of the dog pen in square feet. what width gives you the maximum area? what is the maximum area? round to the nearest tenth if necessary.
maximum area is a square
the side of the square would be 52/4 = 13 feet
area = 13*13 = 169 square feet
Answer:
Width = 13 ft
Maximum Area = 169 ft²
Step-by-step explanation:
Given: A rectangular dog pen whose fencing is 52 feet.
Let length be y and width be x
Fencing = 2(l+b)
52 = 2 (x+y)
x + y = 26
y = 26 - x
Area of rectangular pen = Length x width
= y . x
[tex]A=x(26-x)[/tex]
[tex]A=26x-x^2[/tex]
It is parabolic equation. Maximum/Minimum at vertex.
[tex]x=-\dfrac{b}{2a}[/tex]
where, a=-1, b=26
[tex]x=\dfrac{26}{2}=13[/tex]
Now we put x=13 into A
[tex]A=13(26-13)[/tex]
[tex]A=169[/tex]
Hence, The width is 13 feet and Maximum area is 169 ft²
A spinner has 4 equally-sized sections, labeled A, B, C, and D. It is spun and a fair coin is tossed. What is the denominator of the simplified fraction representing the probability of spinning “C” and flipping “heads”? P(spinning C and flipping heads) =
Answer:
1/8
Step-by-step explanation:
Calculate population variance from population standard deviation
What is the justification for each step in the solution of the equation 3(2x + 7) - 4 = 53 - 3x?
Step 1: 3(2x + 7) - 4 = 53 - 3x
Step 2: 6x + 21 - 4 = 53 - 3x
Step 3: 6x + 17 = 53 - 3x
Step 4: 9x + 17 = 53
Step 5: 9x = 36
Step 6: x = 4
Final answer:
The equation 3(2x + 7) - 4 = 53 - 3x is solved through algebraic processes: distributing, combining like terms, transposing terms, isolating the variable, and dividing to solve for x, resulting in the solution x=4.
Explanation:
The justification for each step in solving the equation 3(2x + 7) - 4 = 53 - 3x involves algebraic manipulation:
Distribute the 3 into the parenthesis: 3(2x) + 3(7) - 4 = 53 - 3x becomes 6x + 21 - 4 = 53 - 3x.Combine like terms on the left side: 6x + 17 = 53 - 3x.Add 3x to both sides to get all x terms on one side: 9x + 17 = 53.Subtract 17 from both sides to isolate the term with x: 9x = 36.Divide both sides by 9 to solve for x: x = 4.Each step is justified by the rules of algebra which allow us to simplify and rearrange equations to isolate the variable. The final step gives us the solution x = 4.
if (2x-3) and (x+5) are multiplied to form the trinomial ax^2 +bx+c, what is the value of b
After using the trinomial The required value of b is 7.
What is a trinomial?
An algebraic expression with three terms is called a trinomial. One or more terms in an algebraic expression each have variables and constants. These expressions use separators like +, -,, and that are symbols or operations. This algebraic expression encompasses polynomials, monomials, binomials, and trinomials. An algebraic expression that is created by squaring a binomial expression is known as a perfect square trinomial. It takes the shape of ax2 + bx + c. Real numbers a, b, and c are present here, and a 0. Take the binomial (x + 2), for instance, and multiply it by (x + 2). The outcome is equal to x2 + 4x + 4.
Given, [tex](2x-3)[/tex] and [tex](x+5)[/tex] are multiplied [tex]= (2x-3)(x+5)[/tex]
[tex]= 2x(x+5) -3(x+5)[/tex]
[tex]= 2x^{2} +10x -3x-15\\= 2x^{2} +7x-15[/tex]
Now, comparing the calculated expression [tex]2x^{2} +7x-15[/tex] with the given equation [tex]ax^{2} +bx+c[/tex] , then we get, [tex]b=7[/tex]
Therefore, the required value [tex]b[/tex] is 7.
To learn more about trinomials
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You review a lease for a new apartment. The lease requires you pay the first month's rent, last month's rent and a security deposit of one month's rent, at the time of signing. The monthly rent is $500. How much will you need at the time of signing?
If the hypotenuse is 41 inches and one of the legs is 40 inches, what is the lengh of the other eleg in inches
What is gk can someone solve for gk
Answer:
7
Step-by-step explanation:
12 on the bottom right is 1 up the 11 on the bottom left, so 7 must be the right answer.
how do you do number 10?
Please i really need help on this one please!!!! :( I need an answer ASAP
Multiply r^2 + 7r + 10 / 3 by 3r - 30 / r^2 - 5r - 50
A. r + 2
B. 7r^2 - 20r - 300 / -5r - 5
C. (r + 5)( r + 2) / (r + 10)
D. 3r + 6 / 2
By factoring and simplifying the given polynomials, we found that the expressions simplify to r + 2. Therefore, the correct answer is option A. This process involves cancelling out common factors from the numerator and the denominator.
Polynomial Multiplication and Simplification
To solve the problem, we need to multiply the given rational expressions and simplify the result. The expressions are:
(r^2 + 7r + 10) / 3 and (3r - 30) / (r^2 - 5r - 50)
First, let's factor the polynomials where possible:
Factor the numerator of the first expression:[tex]r^2 + 7r + 10 = (r + 2)(r + 5)[/tex]Factor the denominator of the second expression: [tex]r^2 - 5r - 50 = (r - 10)(r + 5)[/tex]Now, the problem can be written as:
([tex](r + 2)(r + 5) / 3 ) * ( 3(r - 10) / (r - 10)(r + 5) )[/tex]
Next, we simplify by canceling out the common factors:
[tex]=( (r + 2)(r + 5) / 3 ) * ( 3(r - 10) / (r - 10)(r + 5) )[/tex]
The (r + 5) terms and the (r - 10) terms can be canceled:
[tex]= (r + 2) / 1[/tex]
So, the simplified answer is r + 2,
The correct option is A. r+2
How many solutions are ther to this equation.
can somebody help me with these please ☺
I can't figure this out I need helppp!!!!
cosx - 4 = sinx -4
(0,2pi)
Find solutions
The rule (x, y)→(x+2, y−4) represents a translation 2 units ______
left
right
up
down
and 4 units _______
left
right
up
down
The rule (x, y)→(x+2, y−4) represents a translation of 2 units right and 4 units down.
What is geometric transformation?It is defined as the change in coordinates and the shape of the geometrical body. It is also referred to as a two-dimensional transformation. In the geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.
It is given that:
The rule (x, y)→(x+2, y−4)
As we know, when we go right side of the x-axis we add to the x-coordinate, and when we go left side of the x-axis we subtract to the x-coordinate.
The rule (x, y)→(x+2, y−4) represents a translation of 2 units right.
When we go upside of the y-axis we add to the y-coordinate, and when we go down the side of the y-axis we subtract to the y-coordinate.
The rule (x, y)→(x+2, y−4) represents a translation 4 units down.
Thus, the rule (x, y)→(x+2, y−4) represents a translation of 2 units right and 4 units down.
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A probability distribution for all possible values of a sample statistic is known as a _____.
Answer:
Sampling Distribution
Step-by-step explanation:
A sample is a portion of the population chosen randomly or with certain techniques.
A statistic is a property of sample that describes the sample
Sampling distribution of statistic is a collection of all possible values of statistics for samples taken from the population. To be more precise it is probability distribution of all the outcomes of statistics of samples from the population.
Sample distribution of mean:
It can be defined as the probability distribution of all the feasible or possible means of samples of same size size taken from the population.
How do I use the graph of the function to find the domain and range of f.
Which statement best describes how to determine whether f(x)=9-4x^2 is an odd function