Answer:
C.
Step-by-step explanation:
2 times 2 times 2 times 5 = 40
The prime factorization of 40 is 2 times 2 times 2 times 5, which can be written as 2^3 * 5. So, option C, "2 times 2 times 2 times 5," is the correct prime factorization of 40.
The prime factorization of the number 40 is 2^3 * 5. To arrive at this factorization, we break down 40 into its prime factors. We start by dividing 40 by the smallest prime number, 2. Since 40 is even, it can be divided by 2 evenly, resulting in 20. We continue this process until we can no longer divide by 2, which leaves us with 20. Now, we try to divide 20 by the next smallest prime, which is also 2. This division gives us 10. Once again, we divide by 2, and we are left with 5. Since 5 is a prime number, we cannot further divide it. Therefore, we have prime factorized 40 as 2 * 2 * 2 * 5, which can be expressed as 2^3 * 5, where the exponent 3 indicates that we have three 2s multiplied together, and the 5 is the prime factor on its own.
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Instructions:
Three of Carlos and Clarita's friends are purchasing school supplies at the bookstore. Stan buys a notebook, three packages of pencils, and two markers for $7.50. Jan buys two notebooks, six packages of pencils, and five markers for $15.50. Fran buys a notebook, two packages of pencils, and two markers for $6.25.
Question 1
Based on the information in the instructions, write a system of equations to model the situation. Let n represent the price of a notebook, p represent the price of a package of pencils, and m represent the price of a marker.
Question 2 How much does an individual notebook cost? Question 3 How much does a package of pencils cost? Question 4 How much does an individual marker cost?
Answer:
Notebook = $2.75
Pencil = $1.25
Markers = $ 0.50
Step-by-step explanation:
Stan:
n + 3p + 2m = 7.5
Jan:
2n + 6p + 5m = 15.50
Fran:
n + 2p + 2m = 6.25
Stan - Fran:
p = 1.25
Lets replace p with 1.25
n + 3(1.25) + 2m = 7.5
2n + 6(1.25) + 5m = 15.50
n + 2(1.25) + 2m = 6.25
Simplify
n + 3.75 + 2m = 7.5
2n + 7.5 + 5m = 15.50
n + 2.50 + 2m = 6.25
n + 2m = 3.75 stan
2n + 5m = 8 jan
n + 2m = 3.75 fran
stan = fran
jan - 2(stan)
m = 0.5
n = 2.75
What is the missing denominator in
the expression below?
Answer:
The denominator should be 3. Hope this helps.
If f ( x ) is a linear function, f ( − 2 ) = 0 , and f ( 4 ) = − 5 , find an equation for f ( x ) . f (x)=
Answer:
f(x).f(x) [tex]=\frac{25}{36} x^2 +\frac{25}{9}x+\frac{25}{9}[/tex]
Step-by-step explanation:
Given f(x) is a linear function.
Let f(x)= ax+c
given,f(-2)=0
∴a(-2)+c=0
⇔-2a +c=0
⇔c=2a ..........(1)
Again f(4) = -5
∴a.4+c=-5
⇔4a+c=5
⇔4a +2a=5 [∵ c= 2a]
⇔6a=5
⇔[tex]a=\frac{5}{6}[/tex]
Putting the value of a in equation (1)
[tex]c=2 \times \frac{5}{6}[/tex]
[tex]\Leftrightarrow c= \frac{5}{3}[/tex]
Therefore f(x) [tex]=\frac{5}{6} x+\frac{5}{3}[/tex]
f(x).f(x)
[tex]=(\frac{5}{6} x+\frac{5}{3})(\frac{5}{6} x+\frac{5}{3})[/tex]
[tex]=(\frac{5}{6} x+\frac{5}{3})^2[/tex]
[tex]=\frac{25}{36} x^2 +\frac{25}{9}x+\frac{25}{9}[/tex]
Can someone help me with the question in the image below
Answer:
x=8
Step-by-step explanation:
we know that
The diagonals of a parallelogram bisect each other. That means, each diagonal cuts the other into two equal parts.
so
[tex]5x=6x-8[/tex]
Solve for x
[tex]6x-5x=8\\x=8[/tex]
Determine whether the statement is true of false and support your reasoning: Mr. Flores has 100 pictures in a photo album. Of these pictures, 20 show his friends, 50 show his family, and 30 show his pet dachshund, Frou-Frou. Based on this information, the probability of Mr. Flores randomly selecting a picture of Frou-Frou is greater than the probability of randomly selecting a picture of his family
So, the given statement is false.
Step-by-step explanation:
Given , Mr. Flores has 100 pictures in a photo album. Of these picture , 20 show his friends , 50 show his family and 30 show his pet dachshund.
Probability formula:
[tex]P(A)=\frac{\textrm{Number of favorable outcomes to A}}{\textrm {Total number of out comes}}[/tex]
Total number of out come = 100
Number of photo of his family = 50
Therefore the probability of Mr. Flores selecting a picture of his family is
[tex]=\frac{50}{100}[/tex] [tex]=\frac{1}{2}[/tex] [tex]= \frac{5}{10}[/tex]
The probability of Mr. Flores selecting a picture of his friend is [tex]=\frac{20}{100}[/tex] [tex]=\frac{1}{5} = \frac{2}{10}[/tex]
The probability of Mr. Flores selecting a picture of his pet dachshund [tex]=\frac{30}{100}[/tex] [tex]=\frac{3}{10}[/tex]
Since [tex]\frac{5}{10}>\frac{3}{10}>\frac{2}{10}[/tex]
Therefore the probability of Mr. Flores randomly selecting a picture of his family is greater than the probability of randomly selecting a picture Frou -Frou.
So, the given statement is false.
There is 200 tickets if 18 where purchased in advanced what percentage where purchased in advanced
Answer: 9%
Step-by-step explanation:
You can just divide 200 in half which gives you 100. And divide 18 in half which gives you 9. 9/100, and since 100 is the percent’s denominator (if percent were viewed in fraction), it would be 9.
If 10% of 60 is 6, what is 5% of 60?
Explain how you found your answer
Answer:
3
Step-by-step explanation:
If we already know that 10% of 60 is 6 and that 5% is one half of 10%, we can just divide the 10% value by two to find the 5% of 60.
PLEASE HELP TRYING TO MAKE HONOR ROLL
The sum of two numbers is 36. Their difference is 14. What are the two numbers?
A. -14 and 50
B. -11 and 47
C. 11 and 25
D. 14 and 22
Answer:
it is B. -11 and 47
Step-by-step explanation:
you have to take away 47 and 11 and it equals 36.
1.125 divided by (3/4) (3/4) +6(14/3)
What If? If Taryn and Alastair want to earn an additional $735 ear
additional hours will each spend mowing lawns? Assume each
sat the rate shown in the table and charges by the hour. Explain
many additional hours wil
mows a
Jarun
and
13. Multistep Tomas makes balloon sculptures at a circus. In 180 minutes.
he uses 252 balloons to make 36 identical balloon sculptures.
a. How many minutes does it take to make one balloon
sculpture? How many balloons are used in one sculpture?
minutes
Solve the equation 11x + 7 = 73?
Answer:
6
Step-by-step explanation:
11x + 7 = 73
- 7 - 7
11x = 66
divide 66 by 11 and you get 6
Answer:
x = 6
Step-by-step explanation:
Step 1: Subtract 7 from both sides
11x + 7 - 7 = 73 - 7
11x = 66
Step 2: Divide both sides by 11
11x = 66
11x / 11 = 66 / 11
x = 6
Answer: x = 6
-37=x-9.9 , what’s the value of x ?
Answer:
x= 3.73737373737......
Step-by-step explanation:
To find x, divide -9.9 to both sides.
-37 = x-9.9
-9.9 -9.9
3.73737373737...= x
This is a repeating decimal.
A price decreased from 60$ to 45$ find the percent of decrease
would be a 25% decrease or .25
5. How can you use the Distributive Property to
factor the expression 6x + 15?
Answer:
Divide it all by 3, then put it outside the parentheses.
3(2x+5)
Step-by-step explanation:
The requried factors of the given expression are given as 3[x + 5].
What are the factors?A number or algebraic expression that evenly divides another number or expression—i.e., leaves no remainder—is referred to as a factor.
here,
The distributive property is given as,
a[b + c] = ab + bc
Now,
the given expression performing the distributive property in a way given as,
ab + bc = a[b + c]
Given expression,
= 6x + 15
= 3 × 2x + 3 × 5
= 3 [2x + 5]
Thus, the requried factors of the given expression are given as 3[x + 5].
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(PLEASE HELP THIS IS DUE IS 20 MINUTES, THERES ALSO TWO QUESTIONS)
1.) Micah has a garden. He constructs a scale model of the garden using the scale 1 inch: 2 feet. The garden has a length of 6 feet. What is the length of the garden in Micah’s model? (1 point show your work, 1 point correct answer)
2.)The figure on the left represents a scale drawing of the figure on the right. What is the scale? (2 pts. 1pt show work, 1 pt correct answer)
THE PICTURE IS FOR THE SECOND QUESTION
Answer:1. 3 inches
Step-by-step explanation:1 inch =2ft 2x3=6
To find the length of the garden in Micah's model, we need to set up a proportion using the given scale. The scale for the figure on the left to the figure on the right can be determined by comparing corresponding lengths.
Explanation:1.) To find the length of the garden in Micah's model, we need to use the scale 1 inch: 2 feet. Since the garden has a length of 6 feet, we can set up a proportion:
1 inch / 2 feet = x inches / 6 feet
Cross-multiplying, we get 2 feet * x inches = 1 inch * 6 feet
Simplifying, we have 2x inches = 6 inches, so x = 3 inches.
Therefore, the length of the garden in Micah's model is 3 inches.
2.) The scale of the figure on the left to the figure on the right can be determined by comparing the corresponding lengths. If we measure the lengths of a certain side of the left figure and the right figure, we can find the scale. For example, if the length of a side of the left figure is 2 cm, and the corresponding side on the right figure is 4 cm, the scale is 1 cm: 2 cm.
Therefore, the scale is 1 cm: 2 cm.
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Which system of equations has no solutions...please help quick
For a system to have no solutions the lines must be parallel (they cannot intersect).
So the answer is the graph on the top right.
Answer: top right and bottom right
Step-by-step explanation:
For there to be a solution the lines have to cross at one time so when they are not touching there is no solution
evaluate 15/k when k=3 ?
15/k
15/3
5
Hope this helps! ;)
Answer:
5
Step-by-step explanation:
Since k=3 you would put 3 under 15. Now the equation would look like this: 15/3 instead of 15/k. Then you would divide 15 by 3 which is 5.
a parking lot has total of 60 cars and trucks. the ratio of cars to trucks is 7:3 how many cars are in the parking lot. How many trucks are in the parking lot justify your anwsers
Mitchel owns a livestock trailer that can hold a maximum of 5,000 pounds. The average weight of each goat is 90 pounds, and the average weight of each calf is 360 pounds. Mitchel would like to know how many goats and calves he can transport in a single trip.
Mitchel can transport a 1:1 ratio of goats to calves in his livestock trailer, equating to 11 goats and 11 calves per trip, given their respective average weights of 90 and 360 pounds and the trailer's weight limit of 5000 pounds.
Explanation:Mitchel has a livestock trailer with a weight limit of 5,000 pounds. Given that each goat weights about 90 pounds and each calf about 360 pounds, we need to calculate how many of each animal the trailer can accommodate within its weight limit, while taking into account their average weights.
Let's look at one possible solution, using goats and calves in a 1:1 ratio. This would be 90 + 360 = 450 pounds per set of goat and calf. To fit within the trailer's weight limit, we then divide the total weight capacity by the weight of one set of animals: 5,000 / 450 = 11.11, which we round down to 11. This tells us that Mitchel can transport 11 goats and 11 calves in his trailer for each trip.
It's important to mention that this distribution can be adjusted according to need, as long as the total weight of the animals is kept below the trailer's weight limit.
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What is an equation of the line that passes through the point (3,6) and is parallel to the line 2x+3y=21
Answer: y= -2/3+8
Step-by-step explanation:
Solve n÷6>2. Graph the solution. The solution is?
please help!
Answer:
n>12
Step-by-step explanation:
n/6>2
n>2*6
n>12
The Graph of the inequality is shown below.
What is Inequality?Mathematical expressions with inequalities are those in which the two sides are not equal. Unlike to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.
We have the inequality,
n÷6>2
Multiply both side by 6 we get
(n ÷ 6 ) 6 > 2 x 6
n > 12.
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The graph shows the solution for which inequalities
Answer:
Option 3
Step-by-step explanation:
y is less than the y values on the red line and greater than the y values on the blue line.
Equation of the red line:
y-intercept is clearly 3
using (0,3) & (-2,2)
Slope = (y2-y1)/(x2-x1)
= (3-2)/(0-(-2)) = 1/2
y = (1/2)x + 3
Equation of the blue line:
y-intercept is clearly -2
Using (0,-2) & (1,1)
Slope = (1-(-2))/(1-0) = 3/1 = 3
y = 3x - 2
y < (1/2)x + 3 & y > 3x - 2
The graph shows the solution for the following inequalities; C. y ≥ 3x - 2 and y ≤ -1/2(x) + 3.
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):
[tex]y - y_1 = m(x - x_1)[/tex]
Where:
x and y represent the data points.m represent the slope.First of all, we would determine the slope for the red line by using these points (2, 4) and (0, 3);
[tex]Slope(m)=\frac{y_2-y_1}{x_2-x_1}[/tex]
Slope (m) = (3 - 4)/(0 - 2)
Slope (m) = 1/2
At point (0, 3) and a slope of 1/2, an inequality for this line can be calculated by using the point-slope form as follows:
y - 3= 1/2(x - 0)
y = 1/2(x) + 3
y ≤ 1/2(x) + 3 (since the solid line is shaded below).
At point (0, -2) and a slope of 3, an inequality for this line can be calculated by using the point-slope form as follows:
y + 2= 1/2(x - 0)
y = 3(x) - 2
y ≥ 3x - 2 (since the solid line is shaded below).
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Steve had s songs on his music player.
He bought n new songs. What is the
dependent variable? Explain.
Answer: n since that number depends on s, the songs he already had.
Final answer:
The dependent variable in Steve's music player scenario is the total number of songs after buying new songs, represented by T = s + n. As the number of new songs purchased (n) changes, the total (T) changes, demonstrating a linear relationship between n and T.
Explanation:
In the scenario where Steve had s songs on his music player and he bought n new songs, the dependent variable is the total number of songs Steve has after the purchase. To define this in terms of a mathematical relationship, we can express the total number of songs (T) as an equation:
T = s + n
Here, s is the original number of songs, and n is the number of new songs purchased. The dependent variable is T (the total number of songs), which depends on the value of n (the number of songs bought). If we change the independent variable n, the total number of songs T will also change.
To illustrate this with a dataset, suppose Steve originally had 5 songs (s = 5). If he buys:
1 new song (n = 1), then T = 5 + 1 = 6 songs in total.3 new songs (n = 3), then T = 5 + 3 = 8 songs in total.5 new songs (n = 5), then T = 5 + 5 = 10 songs in total.The relationship between the number of new songs purchased (n) and the total number of songs (T) is linear, as T increases by the same amount that n does.
A square wall has a surface area of 121ft? What is the length of the wall?
Ans 11ft
Step-by-step explanation:
Sq Area= length * length
Length=√area=√121=11
When rounded to the nearest thousand,
the number of pieces of trash collected
by the Beach Clean Up Crew was 8,000.
What numbers below could be the actual
number of pieces of trash collected?
A. 8,283
B. 8,507
C. 8,835
D. 7,582
E. 7,689
Please help me I have a fever and my brain isn't working.. If u do, I will give it as a brilliant answer.. Plus 20 points..
Which expression can be used to approximate the expression below, for all positive numbers a, b, and x, where a. 1 and b.
1?
log,
logo
logna
logna
logo
log,
log,b
logo
logo
Save and
Next
Submit
Step-by-step explanation:
We have,
[tex]\log _{a}x[/tex]
To find, the value of [tex]\log _{a}x[/tex] = ?
∴ [tex]\log _{a}x[/tex] , where a, b and x are positive
a ≠ 1 and b ≠ 1
We know that,
The logarithm identity,
[tex]\log_{p}m=\dfrac{\log_{y}m}{\log_{y}p}[/tex]
∴ [tex]\log _{a}x[/tex] = [tex]\dfrac{\log_{b}x}{\log_{b}a}[/tex]
Where, b is the common base of logarithm
∴ The value of [tex]\log _{a}x[/tex] = [tex]\dfrac{\log_{b}x}{\log_{b}a}[/tex]
Thus, the required option A) [tex]\dfrac{\log_{b}x}{\log_{b}a}[/tex] is correct.
Use row operations to solve the system
x + y – z = -2
4x – y + z = 7
X – 3y + 2z =-5
Answer:
(x, y, z) = (1, 12, 15)
Step-by-step explanation:
As with any set of linear equations, there are many possible routes to a solution. We might simplify the notation a bit by writing the coefficients in an augmented matrix. The columns, left to right, represent the coefficients of x, y, and z, in order, and the constant term.
The row operations we'll use are multiplying a row by a value and adding that result to another row, replacing the other row by the sum.
We can make things a little simpler by writing the second equation first. Then the augmented matrix we're starting with is ...
[tex]\left[\begin{array}{ccc|c}4&-1&1&7\\1&1&-1&-2\\1&-3&2&-5\end{array}\right][/tex]
Adding the second row to the first, we get ...
[tex]\left[\begin{array}{ccc|c}5&0&0&5\\1&1&-1&-2\\1&-3&2&-5\end{array}\right][/tex]
Dividing the first row by 5 gives ...
[tex]\left[\begin{array}{ccc|c}1&0&0&1\\1&1&-1&-2\\1&-3&2&-5\end{array}\right][/tex]
Subtracting this from the second row, and again from the third row, we are left with ...
[tex]\left[\begin{array}{ccc|c}1&0&0&1\\0&1&-1&-3\\0&-3&2&-6\end{array}\right][/tex]
Multiplying the second row by 3 and adding that to the third row, we get ...
[tex]\left[\begin{array}{ccc|c}1&0&0&1\\0&1&-1&-3\\0&0&-1&-15\end{array}\right][/tex]
Subtracting the third row from the second gives ...
[tex]\left[\begin{array}{ccc|c}1&0&0&1\\0&1&0&12\\0&0&-1&-15\end{array}\right][/tex]
Finally, multiplying the last row by -1, we have the solution:
[tex]\left[\begin{array}{ccc|c}1&0&0&1\\0&1&0&12\\0&0&1&15\end{array}\right][/tex]
This matrix corresponds to the equations ...
x = 1y = 12z = 15_____
The purpose of our choice of row operations is to make the diagonal elements 1 and the off-diagonal elements 0. That is how we end up with the final equations shown.
As we said, there are many ways to go about this. In general, one can ...
if necessary, swap rows until the diagonal term of interest is non-zero. If you are doing this using a computer program, generally you want the diagonal term to have the coefficient with the largest magnitude. When doing this by hand, you may want to arrange the rows to avoid fractions when you do the normalizing.divide the row by the coefficient of the diagonal element to "normalize" the diagonal element to a value of 1zero the other elements in that column by multiplying the row just normalized by the element in another row, then subtracting the product. (The 4th matrix shown above shows this for the first column.)proceed to the next diagonal element and repeat the process until all diagonal elements are 1. If you cannot make all diagonal elements 1, then the system of equations does not have a unique solution. If any row becomes all zeros, the system is "dependent" and has infinite solutions. If a row is zeros except for the rightmost column, the system is "inconsistent" and has no solutions.0 = 4x2+12x+9
Simplify the expression to solve the equation. x =
Answer:
-1.5
Step-by-step explanation:
The value of x is -3/2 or -1.5.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
4x²+12x+9 =0
Now, the solution for the expression is
4x²+12x+9 =0
4x²+6x+ 6x +9 =0
2x( 2x + 3)+ 3 (2x+ 3)= 0
(2x+ 3) (2x+ 3) = 0
x= -3/2, x= -3/2
Hence, the value of x is -3/2 or -1.5.
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Based on the given triangle, the cosine of the 30 degree angle is:
P.S.
It is not 1/3 (third option)
Answer:
[tex]\frac{\sqrt{3} }{2}[/tex]
Step-by-step explanation:
Remember SOHCAHTOA
The cosine of an angle in a right triangle is the adjacent sides length divided by the hypotenuses length
In this case, for the angle 30 degrees, the adjacent length is [tex]\sqrt{3}[/tex] and the hypotenuse's length is 2
So, the cosine of the 30 degree angle is the first option:
[tex]\frac{\sqrt{3} }{2}[/tex]
A circle has a diameter of 7.6 feet. Which measurement is closest to the circumference of the circle in feet?
The circumference of the circle is 23.89 ft
The circumference of a circle is the distance around it and it can be calculated by the formula:
Circumference = π x diameter
The circumference is therefore:
= 22/7 x 7.6
= 167.2 / 7
= 23.89 feet
The option given that is closest to 23.89 ft is the right answer.
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