Answer:
y = 44
Step-by-step explanation:
Given
f(x) = [tex]\frac{(4x-4)(x-12)}{x-12}[/tex] ← cancel the factor (x - 12)
= 4x-4
Removing this factor creates a hole at
x - 12 = 0 ⇒ x = 12
Substitute x = 12 into the simplified f(x)
y = 4(12) - 4 = 48 - 4 = 44
That is hole at (12, 44 )
What quantity should be added to both sides of this equation to
complete the square?
x2 - 8x = 5
Answer:
o, we should add 16 on both sides in order to make it a complete square
Step-by-step explanation:
For making a perfect square we will add 16 on both sides of the given equation.
What is quadratic equation?The polynomial having a degree of two or the maximum power of the variable in a polynomial will be 2 is defined as the quadratic equation and it will cut two intercepts on the graph at the x-axis.
Given equation is:-
x² - 8x = 5
x² - 8x + 16 = 5 + 16
x² - 4x -4x + 16 = 5 + 16
x ( x - 4 ) -4 (x - 4 ) = 21
( x - 4 )² = 21
Therefore to make a perfect square we will add 16 on both sides of the given equation.
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Find the coefficient of the $x^2$ term in the expansion of the product$$(2x^2 3x 4)(5x^2 6x 7).$$
The coefficient of [tex]x^{2}[/tex] in [tex](2x^{2}-3x-4)-(5x^{2}+6x-7)[/tex] is -3.
A coefficient is a multiplicative factor in a polynomial, series, or expression in mathematics. It is typically a number, although it can also be any expression (including variables such as a, b and c). They may also be referred to as parameters if the coefficients are variables in and of themselves. The coefficient in an expression that is not related to any variables is called the constant coefficient (also known as constant term or free coefficient).
Given equation,
[tex](2x^{2}-3x-4)-(5x^{2}+6x-7)[/tex]
= [tex]2x^{2}-3x-4-5x^{2}-6x+7[/tex]
= [tex]-3x^{2}-9x+3[/tex]
Hence, coefficient of [tex]x^{2}[/tex] is -3.
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What is the surface area of the pyramid?
Answer:
166 square units
Step-by-step explanation:
Let’s find the area of the shapes that in the net.
First, we can see two of the triangles have a base of 2 and a height of 13. The formula for surface area of a triangle is bh÷2. (13x2)÷2=13. Since there are two triangles, we multiply 13 by 2 and get 26.
Second, we can see two of the triangles have a base of 10 and a height of 12. (10x12)÷2=60. Since there are two triangles, we multiply 60 by 2 and get 120.
Third, we can see a rectangle has a base of 10 and a height of 2. The formula for surface area of a rectangle is bh. 10x2=20.
Last, we add up all the areas:
20+120+26=166.
how would multiply polynomials if it was very difficult?
Step-by-step explanation:
The way that you would multiply polynomials is pretty easy. Say we had a binomial and a trinomial and we wanted to multiply them. As an example, we will use (2x + 4) (x^2 + x + 4).
You have to multiply each number with each other number. For example, we would multiply 2x by x^2, 2x by x, and 2x by 4 to get the first part of the bigger equation. These come out to being 2x^3 + 2x^2 + 8x when multiplied and added.
Then, you have to do the same thing for the 4 in the binomial. Multiply 4 by x^2, 4 by x, and 4 by 4 to get the second part of the bigger equation. These come out as 4x^2 + 4x + 16 when added and multiplied.
After both of those are done, simply add the two parts together and simplify.
2x^3 + 2x^2 + 8x + 4x^2 + 4x + 16
2x^3 + 6x^2 + 12x + 16
That is your example answer, and that is how you multiply polynomials.
Susan has a rectangle and a right triangle.
• The length of the rectangle is 4 more than its width, w.
.
• The length of the shorter leg of the triangle is equal to the rectangle's
width.
• The length of the longer leg of the triangle is twice the length of the
rectangle.
Answer:
A. 2w² + 8w
Step-by-step explanation:
rectangle: A = w(w+4) = w² + 4w
triangle: A = 1/2(2(w+4)(w)) = 1/2(2w+8)(w) = 1/2(2w²+8w) = w² + 4w
Total Area = w² + 4w + w² + 4w = 2w² + 8w
What is the area of the shaded region?
6 mm
21 mm2
24 mm
42 mm
48 mm2
4 mm
3 mm
2 mm
5 mm
Answer:
The area of the shaded region is, [tex]24mm^{2}[/tex]
Step-by-step explanation:
First we have to calculate the area of ΔABC and ΔXYZ.
Area of ΔABC = [tex]\frac{1}2}[/tex]×[tex]Base[/tex]×[tex]Height[/tex]
Area of ΔABC = [tex]\frac{1}{2}[/tex]×[tex]5mm[/tex]×[tex]12mm[/tex]
Area of ΔABC =[tex]30mm^{2}[/tex]
and,
Area of ΔXYZ = [tex]\frac{1}{2}[/tex]×[tex]Base[/tex]×[tex]Height[/tex]
Area of ΔXYZ = [tex]\frac{1}{2} X3mmX4mm[/tex]
Area of ΔXYZ = [tex]6mm^{2}[/tex]
Now we have to calculate the area of the shaded region.
Area of the shaded region = Area of ΔABC - Area of ΔXYZ
Area of the shaded region = [tex]30mm^{2} - 6mm^{2}[/tex]
Area of the shaded region = [tex]24mm^{2}[/tex]
Therefore, the area of the shaded region is, [tex]24mm^{2}[/tex]
-50 POINTS- (Curtisqn don’t even try you’re slow.)
SSS
SAS
ASA
SAA
HL
Matthew invested $5,800 in an account paying an interest rate of 4.9% compounded continuously. Assuming no deposits or withdrawals are made, how much money, to the nearest cent , would be in the account after 7 years?
Answer:
$8173
Step-by-step explanation:
For this problem you will use the formula P(t)=Pe^r(t). P=5800 r=4.9%=0.049
t=7 years. With using this formula you should get your answer. I hope this helps!
Question 22 This question has two parts. First, answer Part A. Then, answer Part B. Part A STATE YOUR ASSUMPTION Liling is making a quilt. She starts with two small squares of material and cuts them along the diagonal. Then she arranges the four resulting triangles to make a large square quilt block. She wants the large quilt block to have an area of 36 square inches. A. What side lengths should Liling use for the two small squares of material? Explain. Round to the nearest tenth, if necessary. In. ; For the block to have an area of 36 square inches, each side must be V2 in. Or about inches. By the inches. This means the hypotenuse of each small right triangle is V2 inches 45°-45°-90° Triangle Theorem, the sides of these triangles measure Part B Do b. Explain any assumption that you make to answer part a. Next Question Check Answer Privacy and Cookies | Terms of Use | Minimum Requirements Platform Status 2021 McGraw-Hill Education. All Rights Reserved.
Blank space 1: 3
Blank space 2: 4.242
Blank space 3: 6
Blank space 4: 6
Blank space 5: 3
This can be solved using triangle theorem.
What is triangle theorem?The first theorem, a triangle's three inner angles can be added up to 180 degrees. According to this theorem, if ABC is a triangle, then ∠A + ∠B + ∠C = 180°.The second theorem states that an isosceles triangle's base angles are congruent or that its opposing sides' angles are also equal in size.The third theorem states that the total of the equivalent internal angles is equal to the size of the exterior angle of a triangle.Given that,
Liling is making a quilt. She starts with two small squares of material and cuts them along the diagonal.
The bigger square = 36 sq. in.
Then the side of the bigger square = √36 inch = 6 inch
Next, The side of the bigger square = Diagonal of the smaller square
Let the side of the smaller square = a (let)
Diagonal (smaller square): a√2 = 6 inch
so, a = 3√2 inch
Thus, a = 3 x 1.414 = 4.242
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The complete question is as follows:
You just bought a new tablet computer for $500, including tax. There are no required payments for six months, but the company does charge 30% annual interest, compounded monthly, on any unpaid balance.
what is the effective annual rate of interest if you do not make any payments for a year?
The effective annual rate of interest if you do not make any payments for a year is 35%.
What is compound interest?Compound interest is the addition of interest to the principal sum of a loan or deposit. Mathematically -
[tex]$A = P(1 + \frac{r}{n})^{nt}[/tex]
where -
[A] = final amount
[P] = initial principal balance
[r] = interest rate
[n] = number of times interest applied per time period
[t] = number of time periods elapse
Given is that You just bought a new tablet computer for $500, including tax. There are no required payments for six months, but the company does charge 30% annual interest, compounded monthly, on any unpaid balance.
We can write -
A = 500(1 + 0.3/12)¹²⁽¹⁾
A = 500(1 + 0.025)¹²
A = 500 x (1.025)¹²
A = 675
Effective annual interest rate for a year is as follows -
A = 500(1 + r/1)⁽¹⁾⁽¹⁾
675 = 500(1 + r)
1 + r = 675/500
1 + r = 1.35
r = 0.35
r = 35%
Therefore, the effective annual rate of interest if you do not make any payments for a year is 35%.
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How do you find the third side of an isosceles triangle when given the angle?
The third side of the isosceles triangle is equal to the square root of 2 multiplied by the hypotenuse, multiplied by the sine of the opposite angle.
Given an isosceles triangle with an angle and two equal sides, we can use the Pythagorean Theorem to calculate the missing side.
The Pythagorean Theorem states that the sum of the squares of the two sides of a right triangle is equal to the square of the hypotenuse. Therefore, we can use this formula to calculate the missing side of the triangle.
First, let's call the two equal sides of the triangle 'a', and the angle opposite to them 'A'.
We can then use the Pythagorean Theorem to calculate the missing side, 'c', which is the third side of the triangle.
[tex]c^2 = a^2 + a^2\\c^2 = 2a^2\\c = sqrt(2a^2)[/tex]
To calculate 'c', we can first calculate 'a' by using the formula:
a = c * sin(A)
Then we plug 'a' into the equation for 'c':
c = sqrt(2*(c * sin(A))^2)
c = sqrt(2)*c*sin(A)
Therefore, the third side of the isosceles triangle is equal to the square root of 2 multiplied by the hypotenuse, multiplied by the sine of the opposite angle.
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Please help, it's much appreciated! <3333 It's midterms studying. 20 points!
A manufacturer makes trusses, or triangular supports, for the roofs of houses. Each truss is the shape of an isosceles triangle in which the sides are congruent. The length of the base is 4/3 the length of the congruent sides.
The perimeter of each truss is 60ft. Find each side length
Answer: The length of each side of the triangle is;
Equal sides, x = 21.02 = PQ = PR
QR = 28.03
Step-by-step explanation: The trusses made by the manufacturer have the shape of an isoscellestriangle and as such two congruent sides PQ ≅ PR) are equal and QR is the third side whose length is 4/3 of the congruent sides.
The perimeter of each truss is 70ft.
Let the length of each congruent side be x ft.
Therefore,
Perimeter = x + x + (4/3)x
Perimeter, p = 70 = 3.33x
x = 70/3.33
x = 21.02
Therefore, Length of QR is; QR = (4/3) x
QR = (4/3) × 21.02
QR = 28.03
An office manager is planning to set up three computer workstations and a file cabinet in a space that is 27 feet wide. The file cabinet takes up 3 feet. What is the width of the space available for each computer station?
Answer:
The width of the space available for each computer station is 8 feet-------------------------------
The width of the space for computer stations is:
27 - 3 = 24 feetEach computer station has a space of:
24/3 = 8 feetH)
find the exact value of sec 7pi / 4
Answer: sqrt(2)
Step-by-step explanation:
Remember that sec x = 1/cos x.
That means that sec 7pi/4 = 1/cos(7pi/4)
cos(7pi/4) = -cos(7pi/4 - pi)
= -cos(3pi/4)
cos(3pi/4) is a special angle which evaluates to -sqrt(2)/2.
Hence, -cos(3pi/4) evaluates to simply sqrt(2)/2
Since cos(7pi/4) is equal to -cos(3pi/4),
cos(7pi/4) is equal to sqrt(2)/2.
Lastly, sec 7pi/4 = 1/cos(7pi/4) , which is the reciprocal of sqrt(2)/2, that is 2/sqrt(2).
Rationalizing the answer 2/sqrt(2) gives sqrt(2)
Express the area of the entire rectangle.
Your answer should be a polynomial in standard form.
x+7 x+5
Given:
Consider the sides of the rectangle are (x+7) and (x+5) units.
To find:
The area of the entire rectangle in standard form.
Solution:
The area of the rectangle is:
[tex]A=l\times w[/tex]
Where, l is length and w is width of the rectangle.
So, the area of the given rectangle is:
[tex]A=(x+7)\times (x+5)[/tex]
[tex]A=(x)(x)+(x)(5)+(7)(x)+(7)(5)[/tex]
[tex]A=x^2+5x+7x+35[/tex]
[tex]A=x^2+12x+35[/tex]
Therefore, the area of the rectangle is [tex]A=x^2+12x+35[/tex].
Which represents the solution set of 5(x+5) <85?
Ox< 12
O x> 12
O x < 18
O x> 18
Answer: O x<12
Step-by-step explanation:
Step 1: Simplify both sides of the inequality.
5x+25<85
Step 2: Subtract 25 from both sides.
5x+25−25<85−25
5x<60
Step 3: Divide both sides by 5.
5x/5 < 60/5
x<12
Which of the following is an equivalent ratio for the 15/24?
5/4
30/40
5/8
Answer:
5/8
Step-by-step explanation:
15/3=5 and 24/3=8
Answer:
5/8
Step-by-step explanation:
divide both by 3
ou have $54.75. You earn additional money by mowing lawns. Then you purchase a new pair of shoes for $79.99 and have $34.76 left. How much money do you earn mowing lawns
Answer: 60
Step-by-step explanation:
If you subtract how much money you already had(54.75) from what you spent(79.99) you get 25.24. You then add 25.24 to the koney you had left(34.76) to get you answer of 60
Four thousand two hundred carnations were reserved for use on thge float. If this was 7/10 of the flowers needed, how many glowers would be on the float
The flowers on the float would be 6.000 flowers. The result is obtained by using fraction multiplication.
How to count a set of objects using fractions?Fraction represents the part of a set of objects. It has two parts separated by a dividing line, namely numerator at the top and denominator at the bottom.
For example:
1/4 (one-fourth)2/5 (two-fifth)It means one of four parts and two of five parts.
We have four thousand two hundred carnations on the float. It was 7/10 of flowers needed. Find the whole flowers on the float!
The carnations of a set of flowers is 7/10. It is 4200 carnations.
The carnations part is 7 and the whole part of flowers is 10.
Using fraction, the whole flowers would be
= 10/7 × 4200
= 6.000 flowers
Hence, the number of flowers needed to be on the float is 6.000 flowers.
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Easy points +Brainly (Pythagorean) Include "step by step explination" for brainly
Answer:
85 units²
Step-by-step explanation:
Add up your given areas to find the missing area using the Pythagorean Theorem:
a²+b²=c²
35+50=c²
85=c²
Therefore, the area of the blue square is 85 units²
Answer:
85 units²
Step-by-step explanation:
/_A and /_B are vertical angles. If m /_A = (5x + 2)° and m /_ B = (6x - 12)°, then find the value of x.
Answer:
x = 14
Step-by-step explanation:
Vertical angles are congruent ( equal to each other )
If ∠A and ∠B are vertical angles
Then 5x + 2 = 6x - 12
^ ( Note that we just created an equation that we can use to solve for x )
The rest comes down to basic algebra
5x + 2 = 6x - 12
step 1 subtract 5x from each side
5x - 5x cancels out
6x - 5x = x
we now have 2 = x - 12
step 2 add 12 to each side
- 12 + 12 cancels out
2 + 12 = 14
we're left with x = 14
find the area of the figure below. use 3.14 for pie
PLEASE HELP ME PLEASE
Which of the following will form the composite function G(Ax)) shown
below?
(Ax)) = 3(x + 1)
O A. Ax) = 5x + 1 and G(x) = 3x
O B. Ax) = 3x and g(x) = + 1
O c. Ax) = x+1 and g(x) = 3x
O D. Ax) = x3x and G(x) = 1
Answer:
A
Step-by-step explanation:
check the above attachment to verify the answer.
Given the figure below, find BD.
А
B
8
6
X + 3
2x
D
-2/3 + y = -2 1/6
....................
Answer:
y = -3/2 or -1.5
Step-by-step explanation:
-2/3 + y = -2 1/6
-2 1/6 = -13/6
So, our equation is
-2/3 + y = -13/6
Add 2/3 to both sides
y = -3/2
So, the answer is
y = -3/2 or -1.5
Answer:
Y= -3/2
in decimal form it is -1.5
in mixed number form it is -1 1/2
Step-by-step explanation:
Please help I really need it now!!!
Answer:
d. alternate interior angles are congruent
Yvonne had a rope that measured 2/5 long. She
needed smaller ropes that measured 3/5 ft for a
project in her science class. How many smaller
ropes can she make from the larger rope?
Answer:
Number of smaller ropes she can make from the larger rope = 2/3
Step-by-step explanation:
Total length of rope = 2/5 ft
Length of smaller rope = 3/5 ft
How many smaller ropes can she make from the larger rope?
Number of smaller ropes she can make from the larger rope = Total length of rope / Length of smaller rope
= 2/5 ÷ 3/5
= 2/5 × 5/3
= (2*5)/(5*3)
= 10/15
= 2/3
Number of smaller ropes she can make from the larger rope = 2/3
33
Problem 2
m, p, and z represent the lengths of the three sides of this right triangle.
m
i
Z
Р
Select all the equations that represent the relationship between m, p, and z.
Therefore , the solution of the given problem of equation comes out to bem² + p² =z².
Equation: What is it?The Latin word equ has the meaning of equivalent. Many of the English language's changeable terms, including adequate, temperate, and equality, contain Latin roots in their base words. The Latin root word equ enters our lexicon rather easily because both sides of an equation are, by essence, "equal" to one another.
Here,
Given : a triangle of m,p,z of length of right triangle :
By using Pythagoras theorem :
The relationship comes out to be :
=> m² + p² =z²
Thus , relationship between m , p and z is m² + p² =z² as per Pythagoras theorem.
Therefore , the solution of the given problem of equation comes out to be m² + p² =z².
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Khalil buy 8 pound of apple for $12. 0. He want to know and ue the unit rate of cot per pound True or Fale: Uing the unit rate of the cot per pound, do 5 pound of apple cot $7. 50?
False. Using the unit rate of cost per pound, 5 pounds of apples cost $6.00.
Cost per pound = $12.00 / 8 pounds = $1.50
5 pounds of apples cost = 5 pounds x $1.50 = $7.50
The unit rate of cost per pound can be calculated by dividing the total cost of 8 pounds of apples by the total number of pounds. In this case, the unit rate of cost per pound is $1.50. This means that for every pound of apples, the cost is $1.50. To calculate the cost of 5 pounds of apples, we need to multiply the unit rate of cost per pound by the number of pounds. In this case, 5 pounds of apples cost $7.50, which is calculated by multiplying $1.50 by 5. Therefore, the statement that using the unit rate of cost per pound, 5 pounds of apples cost $7.50 is false.
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Tina bought 20 apples and bananas for her class. Apples cost $1.50 each. Bananas cost $1.25 each. Tina spent $28 in all. How many apples (a) and how many bananas (b) did she buy?
Answer:
She bought 10 apples and 10 bananas
Step-by-step explanation:
10 apples - $1.50 each x 10 apples = $15.00
10 bananas - $1.25 each x 10 bananas = $12.50
15.00+12.50=$27.50
x+y=28.00
1.50x+1.25y=28