Complete the square.
3x^2-12x=96

Answer:

135 units²

Step-by-step explanation:

The area (A) of a parallelogram is calculated as

A = bh ( b is the base and h the perpendicular height )

To calculate h use Pythagoras' identity on the right triangle on the left

h² + 8² = 17²

h² + 64 = 289 ( subtract 64 from both sides )

h² = 225 ( take the square root of both sides )

h = [tex]\sqrt{225}[/tex] = 15 , thus

A = 9 × 15 = 135 units²

Answer:

E. -2, 4

Step-by-step explanation:

If the zeroes of a function are given as [tex]\alpha, \beta[/tex], then the function can be written as:

[tex](x-\alpha)(x-\beta) = 0[/tex]

Here, we are given that zeros of [tex]f(x)[/tex] are x=-1 and x=2.

As per above, we can write the function [tex]f(x)[/tex] as:

[tex](x- (-1))(x-2) = 0\\\Rightarrow (x+1)(x-2)=0[/tex]

So, [tex]f(x) =(x+1) (x-2)[/tex]

To find:

Zeroes of [tex]f(\frac{x}2)[/tex].

Solution:

We have found that [tex]f(x) =(x+1) (x-2)[/tex]

Replacing [tex]x[/tex] with [tex]\frac{x}2[/tex]:

[tex]f(\frac{x}2) =(\frac{x}2+1) (\frac{x}2-2)[/tex]

Now, Let us put it equal to 0 to find the zeroes.

[tex]f(\frac{x}2) =(\frac{x}2+1) (\frac{x}2-2) = 0\\\Rightarrow (\frac{x}2+1) = 0 \ OR\ (\frac{x}2-2) =0\\\Rightarrow \frac{x}{2} = -1\ OR\ \frac{x}{2}=2\\\Rightarrow \bold{x =-2, 4}[/tex]

So, the zeroes are -2, 4.

Answer:

She spend[tex]\frac{7}{24}[/tex] more on erasers than rulers.

Step-by-step explanation:

We are given that Isabelle bought some stationery.

Fraction of pencil = [tex]\frac{1}{3}[/tex]

Remaining stationary =[tex]1-\frac{1}{3}=\frac{2}{3}[/tex]

5/8 of the remainder were erasers

So, part of eraser in stationary=[tex]\frac{5}{8} \times \frac{2}{3}=\frac{5}{12}[/tex]

Remaining stationary(rulers)=[tex]\frac{2}{3}-\frac{5}{12}=\frac{1}{4}[/tex]

Cost of ruler = $0.50

Cost of [tex]\frac{1}{4}[/tex]rulers =[tex]0.50 \times \frac{1}{4}=\frac{1}{8}[/tex]

Cost of eraser=$1

Cost of [tex]\frac{5}{12}[/tex] eraser=[tex]\frac{5}{12}[/tex]

Difference in cost of eraser and rulers =[tex]\frac{5}{12}-\frac{1}{8}=\frac{7}{24}[/tex]

Hence She spend[tex]\frac{7}{24}[/tex] more on erasers than rulers.

Answer:

Step-by-step explanation:

y = -2x - 5

perp. slope: 1/2

y + 2 = 1/2(x + 1)

y + 4/2 = 1/2x + 1/2

y = 1/2x - 3/2

Answer:

70

Step-by-step explanation:

to solve : start wit the inside brackets first

10 [25-{8-6 (16-13)}÷5​   start 16-3

10[25-{8-6(3)}÷5           then multiply 6 and 3

10[25-{8-18}]÷5              then subtract 8-18

10[25-(-10)]÷5                

10[25+10)÷5                  add numbers inside brackets

10×35÷5=70                 multiply and divide

Answer:

3 / 19

Step-by-step explanation:

Given the following :

ratio of college graduates with a graduate degree to non-college graduates = 1:8

ratio of college graduates without a graduate degree to non-college graduates is 2:3

If college graduate with a degree = A

College graduate without a degree = B

Non-college graduate = C

College graduate to non college graduate = A:C

College graduate without degree to non college graduate = B:C

A:C = 1:8 - - - (1) ; B:C = 2:3 - - - (2)

Combining the two ratios :

To do so : the proportion of non college graduate should be the same in both ratios

To do this, multiply (1) by 3 and (2) by 8

A:C = 3 : 24

B:C = 16 : 24

combining both, we have :

A:B:C = 3:16:24

If one random college graduate is picked, what is the probability that they hold a graduate degree?

Total proportion of college graduate : (college graduates with degree + college graduates without degree)

A + B = (3 + 16) = 19

Proportion who hold a graduate degree = A = 3

Probability = require outcome / Total possible outcomes

Thus :

P = A / (A +B)

= 3/19

Answer:

Hey There. ☆~<___`£《》£`____>~☆ The correct answer is: 33% okay if you don't understand this. Just tell me Okay. k=11 And, let me know if you don't understand how I got this. So, I'm gonna write it out

U V total

S 26 42 68

T 21 k 32

Total 47 53 100

So, you want to look at the column and row labeled total, this is the key. for the row total, it sums up everything in the column above it. so for the u column, the total value is 47 while the two values above it are 26 and 21. These two values sum to 47. This is the same for all other columns, and you can use the same reasoning with the total column as well summing rows.

This gives you two ways to solve for k. either 21 + k = 32 or 42 + k = 53. Either way gets you the answer k = 11

Hope It Helps!~ ♡

ItsNobody~

Answer:

The answer is B

Step-by-step explanation:

Answer:

9.6km

Step-by-step explanation:

Do 6x1.6 ÷1= 9.6km

Answer:9.6km

Step-by-step explanation: Recall BSM(big-small-multiply),so

1.6km×6

Answer:

Each shade has a 22.5 degree angle from the middle

Each unshaded has a 67.5 degree angle from the middle.

Step-by-step explanation:

You can solve this by making each unshaded part equal to x and each shaded part equal 1/3x it is a circle so it has to equal 360 so you end up with:

x + 1/3x + x + 1/3x + x + 1/3x + x + 1/3x = 360

Combine Like terms:

16/3x = 360

Multiply both sides by the opposite:

(3/16) (16/3x) = (360) (3/16)

x=135/2 or x=67.5

Then you can plug 67.5 in for x:

1/3x ---> 1/3(67.5) = 22.5

Answer:

An= A1 * r^n-1

A5= 3 * r^5-1

48= 3*r^4

48÷3=r^4

16=r^4

r=

[tex] \sqrt[4]{16} [/tex]

r=2

The answer is D. 2

Espero que te sirva

hsじぇいrんふぉそ具jんじょおlっっっkjか、

Answer:

p=(-0.0125n) + 42.5

Step-by-step explanation:

Let p= price

n = number of shirts

m = slope of the line (note, the more shirts, the lower the price, so we know it's going to be negative)

b = y intercept

There are two points which are (1000, $30) and (3000, $5)

Our slope m = (p1-p2)/(n1-n2)

Filling in from our points m = (30-5)/(1000-3000)

m = 25/-2000

m = -0.0125

Since we have determined our slope, we can now find our equation

p-p1=m(n-n1)

p-30=(-0.0125)(n-1000)

p-30= (-0.0125n) + 12.5

p=(-0.0125n) + 42.5

Then, we can double check with the other point there:

p=(-0.0125n) + 42.5

5? (-0.0125x 3000) + 42.5

5= 5

Therefore,linear equation in the form p(n) is

p=(-0.0125n) + 42.5

Answer:

Formula for an opened end of a cylinder =

[tex]\pi r^2 +2\pi rh\\[/tex]

Closed at both end =

[tex]2\pi r^2 +2\pi r h[/tex]

Opened at both end =

[tex]2\pi rh[/tex]

Step-by-step explanation:

Answer:

Alice will have to pay $13.33

Ben will have to pay $23.33

Kelvin will have to pay $43.33

Step-by-step explanation:

Given that

Alice destination is 20 miles away

Ben destination is 30 miles away

Calvin destination is 40 miles away.

For a mile, taxi costs 2 dollars.

To find:

How much each person has to pay if they share the same taxi to their respective destinations?

Solution:

For the first 20 miles, the taxi will be shared by all 3 of them.

Charges for 20 miles = 20 [tex]\times[/tex] 2 = $40

This $40 will be shared among all 3.

Each will pay = [tex]\frac{40}{3} = \$13.33[/tex]

Charges for Alice = $13.33

Charges for Ben = $13.33

Charges for Calvin = $13.33

For the next 10 miles, the taxi will be shared by Ben and Calvin.

Charges for 10 miles = 10 [tex]\times[/tex] 2 = $20

This $20 will be shared between Ben and Calvin.

Each will pay = [tex]\frac{20}{2} = \$10[/tex]

Charges for Alice = $13.33

Charges for Ben = $13.33 + 10 = $23.33

Charges for Calvin = $13.33 + 10 = $23.33

For the next 10 miles, Calvin travels alone.

Charges for 10 miles = 10 [tex]\times[/tex] 2 = $20

This $20 will be paid by Calvin alone.

Charges for Alice = $13.33

Charges for Ben = $23.33

Charges for Calvin = $23.33 + 20 = $43.33

Greetings from Brasil...

2X/(X + 2) = 6/(X + 4)

2X(X + 4) = 6(X + 2)

2X² + 2X - 12 = 0     ÷2

2X²/2 + 2X/2 - 12/2 = 0/2

Δ = 25

S = {-3, 2}

By using factorization,  [tex]\frac{2x}{x+2} =\frac{6}{x+4}[/tex] , values of x are -2, 3.

Factorization can be defined as the process of breaking down a number into smaller numbers which when multiplied together arrive at the original number. These numbers are broken down into factors or divisors.

Given

[tex]\frac{2x}{x+2} =\frac{6}{x+4}[/tex]

⇒ 2x(x + 4) = 6(x + 2)

⇒ [tex]2x^{2} +8x = 6x + 12[/tex]

⇒ [tex]2x^{2} +8x-6x-12=0[/tex]

⇒ [tex]2x^{2} +2x -12=0[/tex]

Divide above equation by 2, we get

⇒ [tex]x^{2} +x -6=0[/tex]

⇒ [tex]x^{2} +2x-3x-6=0[/tex]

⇒ [tex]x(x+2)-3(x+2)=0[/tex]

⇒ [tex](x+2)(x-3)=0[/tex]

⇒ x = -2, 3

By using factorization,  [tex]\frac{2x}{x+2} =\frac{6}{x+4}[/tex] , values of x are -2, 3.

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Answer:

A. Sine A = 4/5

B. Cos A = 3/5

C. Tan A = 4/3

D. Tan B = 3/4

Step-by-step explanation:

We'll begin by calculating the value of b in the attached photo.

This can be obtained as follow:

Cos B = 4/5

Cos B = Adjacent /Hypothenus

Adjacent = 4

Hypothenus = 5

Using pythagoras theory, the value of b can be obtained as follow:

b² = 5² – 4²

b² = 25 – 16

b² = 9

Take the square root of both side.

b = √9

b = 3

A. Determination of Sine A

Sine A =?

Opposite = 4

Hypothenus = 5

Sine A = Opposite /Hypothenus

Sine A = 4/5

B. Determination of Cos A

Cos A =?

Adjacent = 3

Hypothenus = 5

Cos A = Adjacent /Hypothenus

Cos A = 3/5

C. Determination of Tan A.

Tan A =?

Opposite = 4

Adjacent = 3

Tan A = Opposite /Adjacent

Tan A = 4/3

D. Determination of Tan B

Tan B =?

Opposite = 3

Adjacent = 4

Tan B = Opposite /Adjacent

Tan B = 3/4

Answer:

D

Step-by-step explanation:

Just did it

A function assigns the values. The equation that represents the function shown on the graph is y=4x.

A function assigns the value of each element of one set to the other specific element of another set.

Given that the graph represents revenue in dollars as a function of greeting cards sold. Therefore, we can write the function as,

Revenue ∝ Number of cards sold

Since the Number of Cards Sold on the x-axis and Revenue in dollars on the y-axis. Therefore, we can write,

y ∝ x

Removing the proportionality, we will get,

y = k x

Now, substitute any point through which the graph of the function passes to get the value of k,

20 = k × 5

20/5 = k

k = 4

Thus, the function can be represented as,

y = kx

y = 4x

Hence, the equation that represents the function shown on the graph is y=4x.

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Answer:

+-(1,2,4,5,10,20)

Step-by-step explanation:

well if this is factors of -20 (bc 75-95=-20)

then it will be +-(1,2,4,5,10,20)

Answer:

(-9,2)

Step-by-step explanation:

The rule for reflecting over the x axis is

(x,y)→(x,−y)

(-9, -2) becomes ( -9, - -2) = (-9,2)

Answer:

(-9,2)

Step-by-step explanation:

It will be -9,2 because when you reflect across x axis you change the y axis not the x axis because if you imagine it it works like that

Answer:

78

Step-by-step explanation:

A 45-45-90 triangle has sides like..

So the height of the parallelogram is 6.5

6.5 x 12 = 78

Answer:

78 in^2

Step-by-step explanation:

The area of a parallelogram is

A = bh

A = ( 12) * h

We can find the height  from using trig functions

tan 45 = h /6.5

6.5 tan 45 = h

A = ( 12) * 6.5 tan 45

   =12 ( 6.5) * 1

   =78

Answer:

x=-1

Step-by-step explanation:

0.5 ( 5 - 7x ) = 8 - ( 4x + 6 )

- Distribute 0.5 by 5 and -7x

2.5 - 3.5x = 8 - ( 4x + 6 )

Second- Distribute the invisible one into 4x and 6

2.5 - 3.5x = 8 - 4x - 6

- Combine like terms: Subtract 6 from 8

2.5-3.5x= - 4x + 2

-Add 4x from both sides of the equation

2.5 + 0.5x = 2

-Subtract 2.5 from both sides of the equation

0.5x = 2- 2.5

0.5x = -0.5

-Then divide each side by 0.5x

0.5x  = -0.5

0.5      0.5

-Cancel the common factor of 0.5

x = - 0.5

      0.5

-Divide -0.5 by 0.5

X = -1

Answer:

Hill 1: F(x)  = -(x + 4)(x + 3)(x + 1)(x - 1)(x - 3)(x - 4)

Hill 2: F(x)  = -(x + 4)(x + 3)(x + 1)(x - 1)(x - 3)(x - 4)

Hill 3: F(x) = 4(x - 2)(x + 5)

Step-by-step explanation:

Hill 1

You must go up and down to make a peak, so your function must cross the x-axis six times. You need six zeros.

Also, the end behaviour must have F(x) ⟶ -∞ as x ⟶ -∞ and F(x) ⟶ -∞ as x⟶ ∞. You need a negative sign in front of the binomials.

One possibility is

F(x)  = -(x + 4)(x + 3)(x + 1)(x - 1)(x - 3)(x - 4)

Hill 2

Multiplying the polynomial by -½ makes the slopes shallower. You must multiply by -2 to make them steeper. Of course, flipping the hills converts them into valleys.

Adding 3 to a function shifts it up three units. To shift it three units to the right, you must subtract 3 from each value of x.

The transformed function should be

F(x)  = -2(x +1)(x)(x -2)(x -3)(x - 6)(x - 7)

Hill 3

To make a shallow parabola, you must divide it by a number. The factor should be ¼, not 4.

The zeroes of your picture run from -4 to +7.

One of the zeros of your parabola is +5 (2 less than 7).

Rather than put the other zero at ½, I would put it at (2 more than -4) to make the parabola cover the picture more evenly.

The function could be

F(x) = ¼(x - 2)(x + 5).

In the image below, Hill 1 is red, Hill 2 is blue, and Hill 3 is the shallow black parabola.

Answer:

Step-by-step explanation:

(a - b)² = a² - 2ab + b²

a = 0.1x

b = 0.2y

(0.1x - 0.2y)²= (0.1x)² - 2*0.1x*0.2y + (0.2y)²

                   = (0.1)²x² - 0.04xy + (0.2)²y²

                   = 0.01x² - 0.04xy + 0.04y²

Answer:

3(-8 + 1) = 3(-8) + 3(1)

Step-by-step explanation:

The distributive property is quite literally when you distribute numbers. This is the only instance of that happening here

The first two are the communitive property of addition, and the last one is the communitive property of multiplication.

Cheers.

Answer:

c

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

3x - 5 = 13

3x = 18 (Add 5 to both sides; 13 + 5 = 18)

x = 6 (Divide both sides by 3; 18 / 3 = 6)

Answer:

Step-by-step explanation:

√48 = √(3*16) = 4√3

                  √1                                      

√(1/49) = ------- = 1/7

                √49

                       √4

√(4/100) = --------------- = ±2/10 =                                                                                                                                                                                                                                                                                                                                                                              

                     √100

Answer:

Step-by-step explanation:

[tex]6\sqrt{x-2}+4<28\\6\sqrt{x-2}<28-4\\\sqrt{x-2}<\frac{24}{6}\\\sqrt{x-2}<4\\\\x-2 <16\\x<16-2\\x<14x-2 \geq 0\\x\geq 2\\so~2 \leq x < 14[/tex]

Answer:

Hey there!

1 gallon=400 square feet

2 3/8 gallon= 400 (2 3/8) square feet

2 3/8 gallon= 950 square feet.

Let me know if this helps :)

Answer:

31/16

or

1 15/16

Step-by-step explanation:

1/8 = 2/16

1/4 = 4/16

1/2 = 8/16

1 = 16/16

then:

1 + 1/2 + 1/4 + 1/8 + 1/16

= 16/16 + 8/16 + 4/16 + 2/16 + 1/16

=(16+8+4+2+1)/16

= 31/16

31/16 = 16/16 + 15/16 = 1 + 15/16 = 1 15/16

Answer:

The mother (Rhoda) is 46 years old.

The daughter (Tenica) is 18 years old

Step-by-step explanation:

Let the age of the mother (Rhoda) be m

Let the age of the daughter (Tenica) be d.

The sum of Rhonda and her daughter Tenica’s age is 64. This can be written as:

m + d = 64 ... (1)

The difference in their ages is 28. This can be written as:

m – d = 28 ... (2)

From the above illustrations, the equation obtained are:

m + d = 64 ... (1)

m – d = 28 ... (2)

Solving by elimination method:

Add equation 1 and 2 together

. m + d = 64

+ m – d = 28

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

2m = 92

Divide both side by 2

m = 92/2

m = 46

Substitute the value of m into any of the equation to obtain the value of d. Here, we shall use equation 1

m + d = 64

m = 46

46 + d = 64

Collect like terms

d = 64 – 46

d = 18

Therefore, the mother (Rhoda) is 46 years old and the daughter (Tenica) is 18 years old.

Estimate:

2.3 rounds down to 2

So after multiplying by 2, the area is estimated to be 4 cm squared.

Actual Area:

2.3 x 2 = 4.6

The actual area of the shape is 4.6 cm squared.

Hope this helped!

Answer:

4.6

Step-by-step explanation: