Answer:
45
Step-by-step explanation:
12/15=4/5
4/5=36/x
cross product
5*36=4*x
180=4x
x=180/4
x=45
If you place a 89-foot ladder against the top of a 80-foot building, how many feet will
the bottom of the ladder be from the bottom of the building?
Answer:
[tex]\large \boxed{\text{39 ft}}[/tex]
Step-by-step explanation:
Let x be the distance from the foot of the ladder to the base of the building.
We have a right triangle, so we can use Pythagoras' Theorem.
[tex]\begin{array}{rcl}80^{2} + x^{2}& = & 89^{2} \\6400+ x^{2} & = & 7921\\x^{2} & = & 1521\\x & = & \sqrt{1521}\\& = &\mathbf{39}\\\end{array}\\\text{The foot of the ladder will be $\large \boxed{\textbf{39 ft}}$ from the base of the building,}[/tex]
Write the polynomial function, in standard form, that has zeros -2, 5, and 0.
Answer:
f(x) = x³ - 3x² - 10x
Step-by-step explanation:
Given that the zeros are x = - 2, x = 5 and x = 0 then the factors are
(x + 2), (x - 5) and (x - 0) = x
The polynomial is the product of it's factors, thus
f(x) = x(x + 2)(x - 5) ← expand factors using FOIL
= x(x² - 3x - 10) ← distribute parenthesis by x
= x³ - 3x² - 10x
Can someone plz help me with this problem?
Answer:
option (2)
Step-by-step explanation:
Given the area (A) of a circle is
A = πr² ← r is the radius ( divide both sides by π )
[tex]\frac{A}{\pi }[/tex] = r² ( take the square root of both sides )
[tex]\sqrt{\frac{A}{\pi } }[/tex] = r → option (2)
Find the x and y intercepts of -2x - 4y = -12
Answer: x-intercept(6,0) & y-intercept(0,3)
Step-by-step explanation: To find the x-intercept, subsitutue zero in for y and solve for x, and vice versa to solve for y.
----------------------
Now you know the answer as well as the formula. Hope this helps, have a BLESSED AND WONDERFUL DAY!
- Cutiepatutie ☺❀❤
Hugo took these steps to solve the system of equations.
2 x minus 3 y = negative 11. 3 x + 2 y = negative 5.
Step 1 4 x minus 6 y = negative 11. 9 x + 6 y = negative 15.
Step 2 13 x = negative 26
Step 3 x = negative 2
Step 4 3 (negative 2) + 2 y = negative 5. Negative 6 + 2 y = negative 5. 2 y = 1. y = one-half.
Step 5 The solution is (Negative 2, one-half).
Is Hugo’s solution to the system of equations correct? Explain why or why not.
Yes, Hugo’s solution is correct.
No, Hugo should have gotten positive 2 in step three.
No, Hugo forgot to multiply both sides of the first equation in step one.
No, Hugo should have subtracted the equations instead of adding them in step 2.
Answer:
C
Step-by-step explanation:
Answer: C ) No, Hugo forgot to multiply both sides of the first equation in step one.
Step-by-step explanation:
GIVING BRAINLIEST NEED HELP PLZ!!!!
Simplify ( x - 2) - (6 x - 9)
Answer:
Subtracting polynomials is simply subtracting the like terms
(x-2)-(6x-9)
First you want to subtract your x from 6x
x-6x= -5x
Than you would subtract -2 and -9
-2- -9=7
-2+9=7
Your final answer would be
-5x+7
Hope this helps ;)
Step-by-step explanation:
The main road in Belleville is 7 3/10 Miles long so far 2 3/4 miles have been repaved. How many miles have not been repaved
Answer:
4 11/20
Step-by-step explanation:
The length of road unpaved is 7 3/10 less 2 3/4 miles The LCD of the fractions is 20 (both 10 and 4 divide evenly into 20).
Thus, the problem becomes 7 6/20 - 2 15/20.
We have to borrow 1 from that 7 because 15/20 is larger than 6/20. This results in
6 26/20 - 2 15/20, or
4 11/20
The total length of the main road in Belleville is [tex]7^{(3/10)}[/tex] miles. So far, [tex]2^{3/4}[/tex] miles have been repaved, leaving [tex]7^{(3/10)}[/tex] - [tex]2^{3/4}[/tex] miles that have not been repaved.
1. The total length of the main road is given as [tex]7^{(3/10)}[/tex] miles. In mathematical notation, [tex]7^{(3/10)}[/tex] represents the cube root of 7, which is then raised to the power of 3. So, the total length of the road is the cube root of 7, and then that result is cubed.
2. The length of the repaved portion is given as [tex]2^{3/4}[/tex] miles. In mathematical notation, [tex]2^{3/4}[/tex] represents the fourth root of 2, which is then raised to the power of 3. So, the repaved length is the fourth root of 2, and then that result is cubed.
3. To find the remaining length that has not been repaved, we simply subtract the repaved length from the total length:
Remaining length = [tex]7^{(3/10)}[/tex] - [tex]2^{3/4}[/tex]
Calculating the values, the total length is approximately 2.262 miles (rounded to three decimal places) and the repaved length is approximately 1.682 miles (rounded to three decimal places). Now, subtracting the repaved length from the total length, we get approximately 0.580 miles (rounded to three decimal places) as the length that has not been repaved.
Therefore, the remaining length that has not been repaved is approximately 0.580 miles (rounded to three decimal places).
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Factor and solve the equation x^3-x^2-30x=0
Answer:
Step-by-step explanation:
Miguel and Molly are cyclists. The graph shows the distance Miguel biked one day. Molly biked at a rate of 0.15 mile per minute. Which statement about their speed is true? Why
Answer:
Miguel traveled 0.2 mile per minute.
Step-by-step explanation:
3÷15=0.2
Speed can be interpreted from a graph's slope in a distance versus time plot. Comparing this to Molly's speed of 0.15 mile per minute, we could establish who is faster or slower. However, without the actual graph of Miguel's bicycling, we can't make a specific comparison.
Explanation:This question relates to graph interpretation and the concept of speed. Here, we're trying to compare the cycling speed of Miguel and Molly. Molly's speed is given as 0.15 mile per minute. Without the graph available, we cannot definitively compare their speeds. But let's briefly explain what we'd look for.
If we had Miguel's graph, we'd specifically examine the slope of the graph. In a distance vs. time plot, speed is represented by the slope of the graph. Therefore, if the slope of Miguel's graph indicated a value higher than 0.15 mile per minute (steep slope), Miguel was going faster. Conversely, if it showed a lesser value (gentle slope), Miguel was going slower.
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Am not good makeing word problems can you help me make one here we go 2/3 x 3 =c now help me make a word problem
Answer:
Emily decides marbles the ratio of marbles is 2 to 3 she adds 3 times more to that.
Step-by-step explanation:
Answer:
Step-by-step explanation:
I have 2/3 of milk and I need 6/3 so my neighbor gave me 3
help please 10 points !!images below
Answer for Question 1 is option 2
Answer for Question 2 is option 3
Answer for Question 3 is option 3
Step-by-step explanation:
For question 1 by plotting the two points we get the coordinates as (-2, 3) and (2, 1) where the x values are -2, 2 and the y values are 3, 1 respectively. By substituting values of x in the formula given we get that equation 2 satisfies the values of y as in the graph.
For question 2 the plotted line is split into two parts where one half is for values of x <2 and the other half is for values of x>2. By finding out the coordinates we get them as (2,-2), (1,-2.5) and (0,-3) for x<2 and by substituting the values of x in the formula we get option 3 as our answer.
For question 3 we need to find the value of y when x=3 and the first condition is only for values greater than 3 so we take the second condition and substitute the value of x=3 and we get the value of y as 5 so the answer is option 3
Teo earns 47.25$ in 7 h of work at Beck’s Burgers. How much will he earn in 12 hours?
Answer:
He will earn $81 in 12 hours.
Step-by-step explanation:
Given:
Teo earns 47.25$ in 7 hours of work at Beck’s Burgers.
Now, to find the money he will earn in 12 hours.
As, given Teo earns 47.25$ in 7 hours of work.
So, to get the money he will earn in 12 hours we solve by using unitary method:
If Teo earns in 7 hours $47.25.
Then, in 1 hour he earns = [tex]\frac{47.25}{7}[/tex]
Thus, in 12 hours he will earn = [tex]\frac{47.25}{7} \times 12[/tex]
= [tex]6.75\times 12[/tex]
= [tex]\$81.[/tex]
Therefore, he will earn $81 in 12 hours.
To determine the best fit undergraduate program, a high school senior researches the majors offered at the universities he is considering for admissions. The internet search reports that Arizona State University lists nine of their most popular majors and the percent of student population enrolled in the programs.
_______________________________________________
Popular Majors Percent of Student Body
Biology 8%
Business Marketing 20%
Communications/Journalism 6%
Education 5%
Engineering 7%
Interdisciplinary Studies 6%
Psychology 6%
Social Sciences 10%
Visual and Performing Arts 8%
----------------------------------------------------------
The university’s enrollment is expected to reach at least 20,000 students for the fall semester.
The minimum number of students who are expected to be working towards a Social Sciences degree is
The university requires that any student who is studying Visual and Performing Arts or Communications/Journalism must perform in one of the student productions before graduation. At least 20,000 students will be performing in the university’s student productions before graduation.
In the fall semester, % of the student population will be enrolled in a degree program not listed as one of the university’s most popular.
The most popular degree offered at Arizona State University is
For the fall semester, the university should expect that students will enroll in one of the two most popular
At least 2,000 students are expected to pursue a Social Sciences degree at Arizona State University. The most popular degree is Business Marketing, and about 6,000 students are estimated to enroll in the top two most popular programs (Business Marketing and Social Sciences) in the fall semester.
Explanation:Based on the information provided about
Arizona State University's
most popular majors and their respective percentages, you can determine the minimum number of students expected to be working towards a Social Sciences degree. The
Social Sciences
program makes up 10% of the student body. Therefore, if the enrollment is expected to reach at least 20,000 students, you can expect that at least 2,000 students (10% of 20,000) will be working towards a
Social Sciences
degree. As for the most popular degree, Business Marketing is listed as comprising 20% of the student body, making it the most popular degree. The two most popular programs, Business Marketing and Social Sciences, make up 30% of the student body. So the university might expect that at least 6,000 students (30% of 20,000) will enroll in one of the two most popular programs in the fall semester.
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The graphs of f(x) and g(x) are shown below.
On a coordinate plane, a straight line with a positive slope represents f (x) = x minus 3. The line goes through (0, negative 3) and (3, 0). On a coordinate plane, a straight line with a negative slope represents g (x) = negative 0.5 x. The line goes through (negative 4, 2), (0, 0), and (4, negative 2)
For what interval is the value of (f – g)(x) negative?
(negative infinity, negative 1)
(negative infinity, 2)
(0, 3)
(2, infinity)
Answer:
(negative infinity, 2)
Step-by-step explanation:
The two functions are given by f(x) = x - 3 and g(x) = - 0.5x
So, (f - g)(x) = x - 3 - ( - 0.5x) = 1.5x - 3
Then, for (f - g)(x) to be negative (1.5x - 3) < 0
⇒ 1.5x < 3
⇒ x < 2
Therefore, the interval will be (negative infinity, 2) for which the function (f - g)(x) will be negative. (Answer)
Answer:
negative infinity 2
Step-by-step explanation:
just did the test
how do i find the mid point in A(-3,13) B(15,7) and C(-3,11)
Answer:
Midpoint of AB=(6,10) ,Midpoint of BC=(6,9) and Midpoint of CA=(-3,12)
Step-by-step explanation:
Given that the points are A(-3,13), B(15,7) and C(-3,11)
To find the mid points :
To find midpoint of AB
Let [tex](x_1,y_1) and (x_2,y_2)[/tex] be the points A(-3,13),B(15,7) respectively
Midpoint of AB[tex]=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]
[tex]=(\frac{-3+15}{2},\frac{13+7}{2})[/tex]
[tex]=(\frac{12}{2},\frac{20}{2})[/tex]
[tex]=(6,10)[/tex]
Midpoint of AB=(6,10)
To find midpoint of BC
Let [tex](x_1,y_1) and (x_2,y_2)[/tex] be the points B(15,7),C(-3,11) respectively
Midpoint of BC[tex]=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]
[tex]=(\frac{15-3}{2},\frac{7+11}{2})[/tex]
[tex]=(\frac{12}{2},\frac{18}{2})[/tex]
[tex]=(6,9)[/tex]
Midpoint of BC=(6,9)
To find midpoint of CA
Let [tex](x_1,y_1) and (x_2,y_2)[/tex] be the points C(-3,11),A(-3,13),respectively
Midpoint of CA[tex]=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]
[tex]=(\frac{-3-3}{2},\frac{11+13}{2})[/tex]
[tex]=(\frac{-6}{2},\frac{24}{2})[/tex]
[tex]=(-3,12)[/tex]
Midpoint of CA=(-3,12)
Therefore Midpoint of AB=(6,10) ,Midpoint of BC=(6,9) and Midpoint of CA=(-3,12)
On a boat, a cabin's window is in the shape of an isosceles trapezoid, as shown below. What is the area of the window?
ANSWER: 182 inches
STEP-BY-STEP EXPLANATION:
Since, it is an isosceles trapezoid, then area of an isosceles triangle is given by: [tex]\frac{1 (a+b)}{2}[/tex] × h
where a and b are the two parallel sides of the triangle and h is the height of an isosceles triangle.
Now, a= 12 inches and b= 2+2+12=16 inches and h=13 inches.
[tex]\frac{1 (12+16)}{2}[/tex] × 13 = 182 inches
x² - 6x – 40=0
Complete the square
Answer:
Step-by-step explanation:
x^2 - 6x - 40 = 0.....get the -40 to the other side
x^2 - 6x = 40....now take half of ur x term (6)....so its 3...then square it (3^2 = 9)...now add 9 to both sides
x^2 - 6x + 9 = 40 + 9
(x - 3)(x - 3) = 49
(x - 3)^2 = 49...take sqrt of both sides, eliminating the ^2
x - 3 = sqrt 49
x = 3 (+ - ) 7
x = 3 + 7 = 10 or x = 3 - 7 = -4
so x = 10 or x = -4
what is the solution to this system of equations?
5x-3y=10
3x+3y=3
Answer:
y = 5/2 , x= 7/2
Step-by-step explanation:
5x - 3y = 10…....(1)
3x + 3y = 3......(2)
solving by elimination, we subtract equation (2) from equation (1)
so, 2x = 7
dividing both sides by 2
x= 7/2
substitute x=7/2 for the value of y in equation (1)
5(7/2) - 3y = 10
multiply both sides by 2
35 - 6y = 20
rearranging
-6y = -15
dividing both sides by -6
y = 5/2
What is the algebraic equation for this math trick
Pick a number
Add 2
Multiply by 3
Subtract 3
Divide by 3
Subtract the original number
Answer:
it will always be 1
Step-by-step explanation:
lets make an equation
pick a number : x
add 2 : x+2
multiply by 3 : (x+2)*3
subtract 3 : (x+2)*3-3
divide by 3 : ((x+2)*3-3)/3
if you simplify, you will get 1
step by step simplification
(x+2)*3 = 3x+6
3x+6-3=3x+3
(3x+3)/3 = x+1
x+1-x=1
Final answer:
The algebraic equation for the given math trick is: (((((x + 2) * 3) - 3) / 3) - x).
Explanation:
To represent the math trick you described algebraically, we can use the variable x to represent the initial number you pick. Following the steps you provided, the algebraic equation would be: ((((x + 2) * 3) - 3) / 3) - x. Let's break down each step:
Start with the initial number x.Add 2: x + 2.Multiply by 3: (x + 2) * 3.Subtract 3: ((x + 2) * 3) - 3.Divide by 3: (((x + 2) * 3) - 3) / 3.Subtract the original number x: ((((x + 2) * 3) - 3) / 3) - x.What is the complete factorization of 12x2 + 36x + 27?
A.
(x+3)(12x+ 9)
B. 3(2x + 3)2
C. 6(x + 2)2
D.
(6x + 3)(2x + 9)
Need help please
Answer:
B) 3(2x+3)^2
Step-by-step explanation:
12x^2+36x+27
factor out the 3 first,
3(4x^2+12x+9)
factor out the trinomial 4x^2+12x+9,
3(2x+3)(2x+3)
3(2x+3)^2
Answer:
B. 3(2x + 3)2
Step-by-step explanation:
whats the square root of 49
Answer:
The square root of 49 is 7. 7*7=49
Hope this helps,
:)
There are 1,198 souvenir paperweights that need to be packed in boxes. Each box will hold 12 paperweights. How many boxes will be needed?
Answer:
100 boxes
Step-by-step explanation:
Divide 1,198 with 12 because if there are 1,198 paperweights and each box holds 12 then how many boxes can hold these paperweights. Answer us 100 boxes
The number of hours in d days and 6 hours how to write in algebraic expression
In a day, there are 24 hours. Then the number of hours in d days and 6 hours is 24d + 6.
What is Algebra?Algebra is the study of mathematical symbols and the rule involves manipulating these mathematical symbols.
The number of hours in d days and 6 hours. Then the algebraic expression will be
We know that in a day, there are 24 hours.
Let the number of the days be d. Then the algebraic expression will be
→ 24 d + 6
Then the number of hours in d days and 6 hours is 24d + 6.
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A fruit company delivers its fruit in two types of boxes: large and small. A delivery of 4 large boxes and 8 small boxes has a total weight of 197 kilograms. A delivery of 2 large boxes and 3 small boxes has a total weight of 83 kilograms. How much does each type of box weigh?
A large box of fruit weighs 18.25 kilograms and a small box weighs 15.5 kilograms.
Step-by-step explanation:
Let,
Weight of large box = x
Weight of small box = y
According to given statement;
4x+8y=197 Eqn 1
2x+3y=83 Eqn 2
Multiplying Eqn 2 by 2
[tex]2(2x+3y=83)\\4x+6y=166\ \ \ Eqn\ 3[/tex]
Subtracting Eqn 3 from Eqn 1
[tex](4x+8y)-(4x+6y)=197-166\\4x+8y-4x-6y=31\\2y=31[/tex]
Dividing both sides by 2
[tex]\frac{2y}{2}=\frac{31}{2}\\y=15.5[/tex]
Putting y=15.5 in Eqn 2
[tex]2x+3(15.5)=83\\2x+46.5=83 \\2x=83-46.5\\2x=36.5[/tex]
Dividing both sides by 2
[tex]\frac{2x}{2}=\frac{36.5}{2}\\x=18.25[/tex]
A large box of fruit weighs 18.25 kilograms and a small box weighs 15.5 kilograms.
Keywords: linear equation, elimination method
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If f(x) = 5x + 4, which of the following is the inverse of f(x)
Answer:
f^-1 (x)=1/5x-4/5
Step-by-step explanation:
y=5x+4
x=5y+4
5y=x-4
y=1/5x-4/5
Answer:
I WOULD SAY THAT THE ANSWER IS C
Step-by-step explanation:
I GOT IT FROM A
P
E
X
Select all true statements.
Answer:
A) Sin A + Sin B = 1.2 Sin C
D) Sin C = 2.5 Sin A = 1.25 Sin B
E) Sin A + Sin C = 1.75 B
Step-by-step explanation:
Here, in the given triangle ABC
Base AC = 16 units, AB = 2 units, and BC = 8 units
Now, by Trigonometric Functions:
[tex]\frac{Sin A}{8} = \frac{Sin B}{16} =\frac{Sin C}{20}[/tex]
Comparing first two terms, we get:
[tex]\frac{Sin A}{8} = \frac{Sin B}{16} \\\implies 2Sin A = Sin B[/tex] ........... (1)
Also,
[tex]\frac{Sin B}{16} = \frac{Sin C}{20} \\\implies Sin C = 1.25 Sin B[/tex] ....... (2)
Comparing first and last terms, we get:
[tex]\frac{Sin C}{20} = \frac{Sin A}{8} \\\implies SinC = 2.5 Sin A[/tex] .......... (D)
Also, Sin A = 0.5 Sin B
So, the given statement Sin A = 2 Sin B is FALSE
⇒ 2.5 Sin A = 1.25 Sin B .......... (D)
Also, Sin B = 2 Sin A
⇒ Sin A + Sin B = Sin A + 2 Sin A = 3 Sin A
Also, Sin A = 0.4 Sin C
⇒3 Sin A = 3 x (0.4) Sin C = 1.2 Sin C ..
⇒Sin A + Sin B = 1.2 Sin C ........ (A)
B) Sin A - Sin B = 0.4 Sin C - 2 Sin A = 0.4 Sin C - 2 (0.4 Sin C)
= 0.4 Sin C - 0.8 Sin C = -0.4 Sin C
⇒Sin A - Sin B = -0.4 Sin C ........ (B)
So, the given statement is FALSE
E) Sin A + Sin C = 0.5 Sin B + 1.25 B = 1.75 B
⇒ Sin A + Sin C = 1.75 B ....(E)
Divide the following polynomials, then place the answer in the proper location on the grid. Use synthetic division. Write the answer in descending powers of x.
(3x2 + 7x - 18) (x - 3)
The answer for the given polynomial by synthetic division is 3x+16+(30/(x-3)).
Step-by-step explanation:
The given polynomial is (3x^2 +7x -18) divided by (x - 3)
Take (x-3)=0, then x=3
3 | 3 7 -18
9 48
3 16 30
step 1: write the coefficients of x^2, x and constant in first row. The divisor 3 is written separately on outside.
step 2: Write down the coefficient of x^2= 3 in the answer row as it is without any change.
step 3: Multiply each number in the answer row with the divisor and fill the answers in the second row.
step 4: The final step is to add the first row and second row. After addition, the answers are written in answer row and the last number in the answer row is the Remainder.
step 5: The remainder is written by dividing it with the divisor (x-3). The answer in the descending powers of x is 3x + 16 + (30/(x-3)).
The result of the division (3x^2 + 7x - 18) by (x - 3) using synthetic division is obtained as (3x + 16 + 30/(x - 3)).
Explanation:To perform the synthetic division, the divisor (x - 3) is represented by its root '3'. Write down the coefficients from the dividend polynomial (3, 7, -18) at the top of your division setup. Write '3' to the left, leave some space, and then write down '3', '7', -18.
Then, perform the synthetic division: step one, bring the first coefficient (3) straight down. Step two, multiply this number by the root of the divisor (3), which is also 3. Write this product (9) underneath the next coefficient (7). Add these two numbers (7 + 9) to get 16. Write this number under the line. Now, repeat the previous step by multiplying 16 by the root, 3, to get 48. Write this under -18, add to get 30.
The quotient of the division is the polynomials received from the synthetic division which is 3x + 16 with a remainder of 30. So, the result of division (3x^2 + 7x - 18) by (x - 3) is (3x + 16 + 30/(x - 3)).
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-f(x) = 2x + 6 Find f(-4)
What is the value of the expression when y = 2?
3(y + 2)
Answer:
12
Step-by-step explanation:
3[y+2]
2+2= 4
3 multiplied by 4 is 12
Answer: 12
Step-by-step explanation: Since y = +2, we simply plug a +2 in for y in the expression. So we have 3(2 + 2).
Following your order of operations, you should simplify what's inside the parentheses first so 2 + 2 simplifies to 4.
Bring down your 3 and you have 3(4) which equals 12.
Solve v^2-7v-33=0 by factoring