Jack got 76% of the questions correct on his math test.What is 76% written as a fraction in simplest form?

Answer:

Step-by-step explanation:

Hello, please consider the following.

The "vertex form" is as below.

[tex]y=a(x-h)^2+k\\\\\text{Where (h, k) is the vertex of the parabola.}\\[/tex]

Let's do it!

[tex]f(x)=\dfrac{1}{2}x^2+3x-2\\\\f(x)=\dfrac{1}{2}\left(x^2+3*2*x\right) -2\\\\f(x)=\dfrac{1}{2}\left( (x+3)^2-3^2\right)-2\\\\f(x)=\dfrac{1}{2}(x+3)^2-\dfrac{9}{2}-\dfrac{4}{2}\\\\f(x)=\dfrac{1}{2}(x+3)^2-\dfrac{9+4}{2}\\\\\large \boxed{\sf \bf \ \ f(x)=\dfrac{1}{2}(x+3)^2-\dfrac{13}{2} \ \ }[/tex]

Thank you.

We have:

h - height

b = 2h - base

A = 36 - area

so:

[tex]A=\frac{1}{2}\cdot b\cdot h\\\\A=\frac{1}{2}\cdot 2\cdot h \cdot h\\\\A=h^2\\\\36=h^2\quad|\sqrt{(\dots)}\\\\\boxed{h=6}[/tex]

Answer:

The answer is

Step-by-step explanation:

To find the slope passing through two points we use the formula

Where

m is the slope

( x1 , y1) and ( x2 , y2) are the points

From the question the points are

(-8,-3) and (2, 3)

So the slope is

Hope this helps you

2^1 would be the answer.

2^2 x 2^3 is 32

2^4 is 16

32/16 is 2

2^1 is 2 so the answer is 2^1

Answer:

2¹

Step-by-step explanation:

When multiplying exponents of the same base, you can simply add the exponents together so 2² * 2³ = 2⁽²⁺³⁾ = 2⁵. When dividing exponents of the same base, you can simply subtract the exponents so 2⁵ / 2⁴ = 2⁽⁵⁻⁴⁾ = 2¹.

Answer:

-1

Step-by-step explanation:

3/2 * (-22/33)

Simplify by dividing the second fraction by 11

3/2 * (-2/3)

Rewriting

3/3 * (-2/2)

-1/1

Answer:

-1

Step-by-step explanation:

(a/b)(c/d) = (a*c)(

(3/2)(-22/33)

(3*-22)/(2*33) = -66/66 = -1

Answer:

Option a. Y=3x

Step-by-step explanation:

Let us use cross multiplication method.

Let the cost of 1 magazine be x.

No. of copies                               Cost

1)50                                                $150

2)1                                                      x

50x=150 x 1               equation(1)

x=150/50

x=$3

Now see equation (1),

150=50x

150=50 x 3

Here let us represent the cost as y and no. of copies as x.

Y=3x

Therefore, a. Y=3x is the right answer.

Thank you!

Answer:  Yes. The sales tax is 5% which equals $4.20 for $84

Step-by-step explanation:

[tex]\dfrac{0.60}{12}=0.05\qquad \rightarrow 5\%\\\\\\\dfrac{1.20}{24}=0.05\qquad \rightarrow 5\%\\\\\\\dfrac{1.80}{36}=0.05\qquad \rightarrow 5\%\\\\\\\dfrac{2.40}{48}=0.05\qquad \rightarrow 5\%[/tex]

The sales tax rate is proportional for the values in the table.

$84 x 0.05 = $4.20

The sales tax on a purchase of $84 is $4.20

2601|3

867|3

289|17

17|17

1

[tex]\sqrt{2601}=\sqrt{3^2\cdot17^2}=3\cdot17=51[/tex]

Answer: Brian invested $16000 in Fund B .

Step-by-step explanation:

Let x be the amount Brian invested in Fund B.

Given, The $8000 that he invested in Fund A returned a 4% profit. The amount that he invested in Fund B returned a 1% profit.

i.e. profit on Fund A = 4% of 8000 = 0.04 ×8000 = $320

Profit on Fund B = 1% of x = 0.01x

Together they earn 1% profit, i.e. Combined profit = 2% of (8000+x)

= 0.02(8000+x)

As per question,

Combined profit=Profit on Fund A+Profit on Fund B

[tex]\Rightarrow\ 0.02(8000+x) =320+0.01x\\\\\Rightarrow\ 0.02(8000) +0.02x=320+0.01x\\\\\Rightarrow\ 160+0.02x=320+0.01x\\\\\Rightarrow\ 0.02x-0.01x=320-160\\\\\Rightarrow\ 0.01x=160\\\\\Rightarrow\ x=\dfrac{160}{0.01}\\\\\Rightarrow\ x=16000[/tex]

Hence, Brian invested $16000 in Fund B .

Answer:

WY= 25

XY= 23

VZ=36

so,

WY/XY = YZ/VZ

25/23 = YZ/25 (then do cross multiply)

25×25 = 23 × YZ

625= 23 × YZ

625/23= YZ

27,17= YZ

#i'm indonesian

#hope it helps.

Answer:

[tex]\huge \boxed{13.04}[/tex]

Step-by-step explanation:

The triangles are congruent, we can use ratios to solve.

WY/XY = (WY+YZ)/VZ

Let the length of YZ be x.

25/23 = (25+x)/35

Cross multiply.

23(25+x) = 25 × 35

575 + 23x = 875

Subtract 575 from both sides.

575 + 23x - 575 = 875 - 575

23x = 300

Divide both sides by 23.

(23x)/23 = 300/23

x = 13.0434782609...

Answer:

about 72 dollars

Step-by-step explanation

"about" tells us to round our numbers. Therefore, 7.8 becomes 8. As each pound is $8.99, we multiply the two and get 71.92, which is "about" 72.

Answer:

$72

Step-by-step explanation:

To find the cost, multiply the price per pound by the number of pounds.

8.99(7.8)

= 70.12

This is closest to $72

Answer:

The answer is below

Step-by-step explanation:

The points of the triangle are  (- 5, 1), (2, 1), (2, - 1). The distance between two points is given by:

[tex]Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

The horizontal leg is formed by points with the same y axis. Therefore the points that make up the horizontal leg is (- 5, 1), (2, 1). The Distance of the horizontal leg is:

[tex]Horizontal\ leg=\sqrt{(2-(-5))^2+(1-1)^2}=\sqrt{7^2+0}=7\ units[/tex]

The vertical leg is formed by points with the same x axis. Therefore the points that make up the vertical leg is (2 1), (2, 1-). The Distance of the vertical leg is:

[tex]Vertical\ leg=\sqrt{(2-2)^2+(-1-1)^2}=\sqrt{0+(-2)^2}=2\ units[/tex]

The hypotenuse is gotten using Pythagorean theorem. It is gotten by:

Hypotenuse² = (Horizontal leg)² + (Vertical leg)²

Hypotenuse² = 7² + 2²

Hypotenuse² = 49 + 4 = 53

Hypotenuse = √53

Hypotenuse = 7.28 unit

Answer:

The answer are 7, 2 and 53

Step-by-step explanation:

Answer:

24 square units

Step-by-step explanation:

Use the formula for area of a parallelogram to solve.  The base is 6 units, and the height is 4 units.

A = bh

A = (6)(4)

A = 24 square units

The area of the parallelogram is 24 square units.

Answer:

4:7

Step-by-step explanation:

4 grape candies : 7 total candies (grape + cherry)

Answer:

It is simply 4:3

Answer:

[tex]\boxed{0.15}[/tex]

Step-by-step explanation:

Part 1: Solve for the total amount of marbles

To solve for the probability of certain events, a population is needed to derive this information from. In order to find this population, add up the amounts of each marble.

8 + 14 + 12 = 34 marbles

Part 2: Determine the probabilities

Now, given the amounts of marbles, simply multiply the ratios of blue marbles to total marbles and the ratio of clear marbles to total marbles to get the combined probability.

[tex]\frac{12}{34}*\frac{14}{33} = \frac{28}{187} \approxeq 0.1497 \approxeq 0.15 * 100 = 15[/tex]

The probability of these events occurring simultaneously is 15%.

Answer:

[tex]\huge\boxed{A)\ 7.618\times10^{-6}}[/tex]

Step-by-step explanation:

The scientific notation:

[tex]a\cdot10^n[/tex]

where

[tex]1\leq a<10;\ n\in\mathbb{Z}[/tex]

We have

[tex]761.8\times10^{-8}[/tex]

We need to move the decimal point two places to the left.

[tex]\underbrace{(7.618\times10^2)}_{=761.8}\times10^{-8}=7.618\times(10^2\times10^{-8})[/tex]

use

[tex]a^n\cdot a^m=a^{n+m}[/tex]

[tex]=7.618\times10^{2+(-8)}=7.618\times10^{-6}[/tex]

Answer:

a

Step-by-step explanation:

Answer:

239 ft².

Step-by-step explanation:

Let P represent the price for tiling.

Let S represent the size of the room.

From the question,

Price (P) varies directly as the size (S) i.e

P & S

P = KS

Where K is the constant of proportionality.

Next, we shall determine the value of K as follow

Price (P) = $ 4224

Size (S) = 264 ft²

Constant of proportionality (K) =?

P = KS

4224 = K × 264

Divide both side by 264

K = 4224/264

K = 16

Finally, we shall determine the size of the kitchen that will cost $ 3824 for tiling.

This is illustrated below:

Price (P) = $ 3824

Constant of proportionality (K) = 16

Size (S) =?

P = KS

3824 = 16 × S

Divide both side by 16

S = 3824/16

S = 239 ft²

Therefore, the size of the kitchen is 239 ft².

Answer:

It is a unit of radius that is radius of 1. Thus, the distant to the middle to any edge is always 1.

Step-by-step explanation:

flipped : [tex]-x^2[/tex]

moving down: [tex] -x^2+4[/tex]

shifting left [tex] -(x+1)^2+4[/tex]

expanding it: [tex] -x^2-2x+3[/tex]

Answer:

1. f(x)=x^2

f(x)=-x^2

2. f(x)=-x^2-4

3. f(x)=-(x+1)^2-4

Answer:

4a

Step-by-step explanation:

4a

the top and right are a-b, but you have to add the b’s back in, so really all sides are a

a+a+a+a=4a

Answer: 4a

Step-by-step explanation: perimeter is the length of all sides added together. Every length is given combine like variables and you will get 4a+2b-2b. 2b-2b is 0 which leaves you with 4a

Answer:

The point (-2, 4) is not a solution of the linear equation, 5·y =  3·x + 18

Please find attached the required graph of the linear equation 5·y =  3·x + 18 written in the form y = 3/5·x + 18/5

Step-by-step explanation:

The given equation is 5·y = 3·x + 18, from which we have;

y = 3/5·x + 18/5

To draw the graph, we generate for vales of y corresponding to values of x as follows;

x,      y

-6,    0

-5,    0.6

-4,    1.2

-3,    1.8

-2,    2.4

-1,      3

0,      3.6

1,       4.2

2,      4.8

3,      5.4

4,       6

5,       6.6

6,       7.2

7,        7.8

8,        8.4

9,        9

10,      9.6

11,       10.2

12,      10.8

13,      11.4

14,       12

15,      12.6

16,      13.2

Therefore, when y = 0, x = -6, when x = 0, y = 3.6, when x = -2, y = 2.4, when y = 4, x = -2, x = 6

Therefore, the point (-2, 4) is not a solution of the linear equation, 5·y =  3·x + 18

Answer:

0

Step-by-step explanation:

Notice that the last factor is null (9×0)

So the result will be null since any number that is multiplied by 0 equals 0.

[tex]\dfrac{x}{6}-7=-4\\\dfrac{x}{6}=3\\x=18[/tex]

Answer:

x = 18

Step-by-step explanation:

x/6 - 7 = -4

Add 7 to each side

x/6 - 7+7 = -4+7

x/6 = 3

Multiply each side by 6

x/6 *6 = 3*6

x = 18

Answer:

24 and 36

Step-by-step explanation:

2x + 3x = 60

5x = 60

x = 12

Dawn has 2(12) = 24

Jackson has 3(12) = 36

Step-by-step explanation:

To find the number of baseball cards each person received we must first find the total parts

That's

2 + 3 = 5

For Dawn

Dawn's part is 2

We have

2/5 × 60

For Jackson

Jackson's part is 3

That's

3/5 × 60

Hope this helps you

Answer:

∠ O = 61°, ∠ N = 119°

Step-by-step explanation:

In a parallelogram

Consecutive angles are supplementary

Opposite angles are congruent, thus

x + 2x - 3 = 180

3x - 3 = 180 ( add 3 to both sides )

3x = 183 ( divide both sides by 3 )

x = 61°

Thus

∠ O = ∠ M = x = 61°

∠ N = ∠ P = 2x - 3 = 2(61) - 3 = 122 - 3 = 119°

Answer:

Step-by-step explanation:

Let S be the sample space, n(S) = 60

a) Let A be the event that the selected athlete uses

s less than a minute, n(A) = 59

The probability that a randomly selected athlete uses less a minute,  P(A) = n(A)/n(S) = 59/60 = 0.9833

b) 1 - 0.9833 = 0.0167

c)  1 - 1 = 0

Answer:

1. GH

2. a

Step-by-step explanation:

Perpendicular: When 2 lines meet at 90 degrees

1. It is line segment GH because AB and GH meet at a 90 degree angle (since there is a box at angle GHF indicating that it is 90 degrees)

2. It has to be a units because it is a rectangle where the top and bottom are congruent and the sides are too

This is a rectangle since AB and CD are parallel and GH can be a transversal line, according to same side interior angles theorem EGH is a also 90 degrees. That means FEG is 90 degrees too because then the quadrilateral will add up to 360 degrees

Answer:

A = 62.35 cm²

Step-by-step explanation:

Use the area formula A = [tex]\frac{\sqrt{3}a^2}{4}[/tex], where a is the side length.

Plug in the values:

A = [tex]\frac{\sqrt{3}(12^2)}{4}[/tex]

A = [tex]\frac{\sqrt{3}(144)}{4}[/tex]

A = 62.35 cm²

Answer:

The lower quartile is 23.4

Step-by-step explanation:

The given data are;

47.2, 33.8, 43, 62, 5.8, 9, 61.4, 30.8, 68.2, 51.6, 13.2, 17.4, 64.2, 50.6, 29.4, 40.4

Rearranging the data, we have;

5.8, 9, 13.2, 17.4, 29.4, 30.8, 33.8, 40.4, 43, 47.2, 50.6, 51.6, 61.4, 62, 64.2, 68.2

The lower quartile, Q₁, is the (n + 1)/4 th term which is (16 +1)/4 = 4.25th term

However since we have an even set of numbers, we place a separator at the middle and we look for the median of the left half as follows

5.8, 9, 13.2, 17.4, 29.4, 30.8, 33.8, 40.4║ 43, 47.2, 50.6, 51.6, 61.4, 62, 64.2, 68.2

We have two numbers (17.4 + 29.4) at the median of the left set of numbers, we find the average of the two numbers to get the lower quartile

The lower quartile is therefore = (17.4 + 29.4)/2 = 23.4.