Exercise 19

Find the values of x and y. Then find the measures of the interior angles of the polygon.

Answer:

Step-by-step explanation:

hello : y= 4x² + 5x + 2

the x-intercepts  when y=0  means : 4x² + 5x + 2=0

a=4   b= 5   c=2

∆ = b²- 4ac     ∆ = (5)²- 4(4)(2) =25-32 = -7

∆ < 0 no reals solutions no  x-intercepts  

Answer:

c

Step-by-step explanation:

The focus of the parabola is (–8,–51∕2), directrix is y = –61∕2 option (C) is correct.

It is defined as the graph of a quadratic function that has something bowl-shaped.

(x - h)² = 4a(y - k)

(h, k) is the vertex of the parabola:

a = √[(c-h)² + (d-k²]

(c, d) is the focus of the parabola:

We have an equation for the parabola:

The parabolic equation also in the form of quadratic equation.

Any equation of the form [tex]\rm ax^2+bx+c=0[/tex]  where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.

y = (-1∕2)(x – 8)² – 6

The vertex of the parabola is (h, k)

h = 8, k = -6

The focus of the parabola:

(c, d)

c = -6

d = -6 - 1/2 = -13/2 = -6 1/2

Directrix of the parabola:

y = -6 - (-1/2)

y = -6 + 1/2

y = -11/2 = -5 1/2

Thus, the focus of the parabola is (–8,–51∕2), directrix is y = –61∕2 option (C) is correct.

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Answer:

12x+14

Step-by-step explanation:

5x+5(2x+2)+7

5x+7x+7+7

12x+7+7

12x+14

Answer:

The probability to the nearest thousandth is 0.386

Step-by-step explanation:

Firstly, we will need to know the number of girls and the total number of students in the class.

We have the ratio as 3:5 for boys and girls with the number of boys being 18

What we have is thus;

3:5 = 18:g

3/5 = 18/g

3g = 90

g = 90/3

g = 30 girls

Thus, we have 18 boys and 30 girls with a total of 48 students.

The probability that the teacher selects a girl to write the question on the board is 30/48 = 5/8

Now, we intend selecting another girl to answer the question. This is like a probability without replacement. So this means that the number of girls we have now is 29 and the number of students we are selecting from is 47 students

Thus, the probability of selecting a girl to answer the question becomes 29/47

The joint probability is thus; 29/47 * 5/8 = 145/376 = 0.3856

To the nearest thousandth, we have 0.386

Answer:

u = 11

Step-by-step explanation:

6(u+5)=96

Divide both sides by 6

u+5=16

Subtract 5 from both sides

u=11

The variable, u, is equivalent to 11

Answer:

u=11

Step-by-step explanation:

If you multiply  the parentheses by the outside number (6) it will bring you

6u+30=96 then take away 30 from each side to get

6u=66 last step is to divide by six

u=11

Answer:

14.1 cm

Step-by-step explanation:

first find the base diagonal :

base di = Square root (8^2 + 6^2) = 10cm

so,

diagonal = Square root (10^2 + 10^2) = 14.1 cm (ANS)

Answer:

r = 12 inches

Step-by-step explanation:

In this question, we are asked to calculate the length of the radius of the circle.

This is accessible from using the length of an arc.

Mathematically, the length of an arc can be calculated using the formula;

Theta/360 * 2 * pi * r

Where Theta is the angle subtended at the center and r is the radius of he circle.

According to the question, Theta is 3pi/4 radians or let’s just say 0.75pi . This to degrees will be 135 degrees ( pi = 180 degrees)

Thus we have;

9 pi = 135/360 * 2 * pi * r

divide through by pi

9 = 270r/360

360 * 9 = 270r

r = (360 * 9)/270

r = 12 inches

Answer:

b

Step-by-step explanation:

Answer:

Step-by-step explanation:

hello : here is an solution

Answer:

160 days

Step-by-step explanation:

If it takes 8 days with 10 women to make 3 tree houses, then the rate of woman per tree house is 3/80. Multiplying this by 6 and dividing by 36, you get a rate of 1/160 or 160 days. Hope this helps!

Answer:

[tex] \hat y = 8.5*2 -5 = 12[/tex]

And the residual is defined as:

[tex] e_ i = y_i -\hat y_i [/tex]

And replacing we got:

[tex] e_i = 20-12 = 8[/tex]

Step-by-step explanation:

For this case we know that the amount of money 'y' made at a laundromat after 'x' months can be represented by the linear function:

[tex] y = 8.50 x -5[/tex]

And fter two months we know that the laundromat made 20 dollars. And if we use the linear function we got:

[tex] \hat y = 8.5*2 -5 = 12[/tex]

And the residual is defined as:

[tex] e_ i = y_i -\hat y_i [/tex]

And replacing we got:

[tex] e_i = 20-12 = 8[/tex]

Answer:

Step 2

Step-by-step explanation:

Michelle's step in trying to solve the equation is given below:

[tex]\begin{aligned} t-\dfrac35&=\dfrac45\\\\ t-\dfrac35+\dfrac35&=\dfrac45+\dfrac35&\green{\text{Step } 1}\\\\ t&=1&\blue{\text{Step } 2} \end{aligned}[/tex]

Michelle made a mistake in Step 2.

The right hand side of Step 1:  [tex]\dfrac45+\dfrac35\neq 1[/tex]

Rather, the correct sum is:

[tex]\dfrac45+\dfrac35=\dfrac75\\\\=1\dfrac25[/tex]

Answer:

Its 1/5

Step-by-step explanation:

Khan

Answer:

Length = 55 ft

Step-by-step explanation:

Given:

Area of rectangular floor= 605ft²

Length= x

Width= 1/5x

Formula for area of rectangular floor= Length × width

Put the given into the formula.

605 ft² = x × 1/5x

605 ft² = x²/5

multiplying both sides by 5

605 ft² × 5 = x²/5 × 5

x² = 605 ft² × 5

= 3025 ft²

x= √3025 ft²

x= 55 ft

Put x into the unknown above.

Length= x

Width= 1/5x

Length = 55 ft

Width= (1/5)×55 = 11 ft

Answer:

38°

Step-by-step explanation:

All triangles have a sum of 180°

180 - (119 + 23) = missing angle

180 - (142) = missing angle

38 = missing angle

So, the missing angle has a measurement of 38°

Answer:

D

Step-by-step explanation:

[tex]2x^2+2x+12=3x^2-x+2\\2x+12=x^2-x+2\\x^2-3x-10=0\\(x-5)(x+2)=0\\x=5, -2[/tex]

The correct answer is choice D. Hope this helps!

Answer:

{-5, 2}

Step-by-step explanation:

  [tex]2x^{2} + 2x + 12 = 3x^{2} -x + 2[/tex]    move everything to the right side

[tex]-2x^{2} -2x-12=-2x^{2} -2x-12[/tex]  add line 1 and 2 to get the below equation

                      [tex]0 = x^{2} -3x -10[/tex]   find multiples of -10 that add to give you -3

                                                    to get -10 we have to have (+)(-)

                                                           {-5, 2}

Answer

6

we keep subtracting by 6

12-6 = 6

A = 6

Answer:

(x-3)^2 = 4

Step-by-step explanation:

2 (x-3)^2 + 6 = 14

Subtract 6 from each side

2 (x-3)^2  = 8

Divide each side by 2

2/2 (x-3)^2 + 6 = 8/2

(x-3)^2 = 4

Answer:

Just divide

1944/216=9

9 feet deep

Hope this helps

Step-by-step explanation:

Answer:

The distance where the keys would drop from the base is 3.5m

Step-by-step explanation:

Height of the tower = 50m

Angle it makes to the ground = 86°

To solve this question, you have to understand that the tower isn't vertically upright and the height of the tower is different from the distance from the top of the tower to the ground.

The tower makes an angle 86° to the ground and that makes it not vertically straight because a vertically straight building is at 90° to the ground.

See attached document for better illustration.

The distance from where the keys drop to the base of the tower can be calculated using SOHCAHTOA

We have to use cosθ = adjacent / hypothenus

θ = 86°

Adjacent = ? = x

Hypothenus = 50m

Cos θ = x / hyp

Cos 86 = x / 50

X = 50 × cos 86

X = 50 × 0.06976

X = 3.488 = 3.5m

The distance where the keys would drop from the base of the tower is approximately 3.5m

Answer:

Step-by-step explanation:

This question can be translated to:

"The manager of the drinking water service in my town creates a water tank in the highlands so that the water can reach the entire town. The cube-shaped shelter is 8 meters long. If the shelter is full, how many liters of water can it contain?"

As you can observe, the volumetric form is a cube with 8 meters long each edge.

We know the volume of a cube is defined as

[tex]V=l^{3}[/tex]

Where [tex]l=8 \ m[/tex], replacing this value, we have

[tex]V=(8 \ m)^{3} \\V=512 \ m^{3}[/tex]

Therefore, the shelter can contain 512 cubic meters of water.

Answer:

FALSE

Step-by-step explanation:

The length of the base edge of a triangular pyramid may vary.

The height is not always twice the length of the base edge for any triangular pyramid, the dimensions are not fixed for any shape and can vary from one design to another.

more so, i may require a particular size or dimension of triangular based pyramid for my application that may not suit your application.

Answer:

For the watermelon at Harmless to cost the same as any watermelon at Biggy, the watermelon needs to be 21 pounds.

You should buy your watermelon at Harmless.

Step-by-step explanation:

1. So in order to figure out the number of pounds, you need to divide 3.99 by 0.19 which should give u 21 pounds.

2. So in order to figure out where u should buy the watermelon from, u have to do 18 pounds times $0.19 which should give u $3.42 at Harmless while at Biggy it would cost $3.99

Answer:

surface area of the rectangular shaped cereal box = 384  ft²

Step-by-step explanation:

The cereal box is a rectangular prism . The rectangular prism has a length of 9 inches, height of 12 inches and width of 4 inches . The surface area can be computed below .

Surface area of the prism is the sum of the area of all the faces. Therefore,

surface area = 2wl + 2lh + 2hw

where

l = length

w = width

h = height

surface area = 2wl + 2lh + 2hw

l = 9 inches

w = 4  inches

h = 12 inches

surface area = 2(4 × 9) + 2(9 × 12) + 2(12 × 4)

surface area = 2(36) + 2(108) + 2(48)

surface area = 72 + 216  + 96

surface area of the rectangular shaped cereal box = 384  ft²

Answer:

The cereal box is a rectangular prism . The rectangular prism has a length of 9 inches, height of 12 inches and width of 4 inches . The surface area can be computed below .

Surface area of the prism is the sum of the area of all the faces. Therefore,

surface area = 2wl + 2lh + 2hw

where

l = length

w = width

h = height

surface area = 2wl + 2lh + 2hw

l = 9 inches

w = 4  inches

h = 12 inches

surface area = 2(4 × 9) + 2(9 × 12) + 2(12 × 4)

surface area = 2(36) + 2(108) + 2(48)

surface area = 72 + 216  + 96

surface area of the rectangular shaped cereal box = 384  ft

Step-by-step explanation:

Answer:

The statement "500 divided by 50 is 10" is a true statement

Step-by-step explanation:

In mathematics, we have a term that we refer to as Place Value.

Place Value in mathematics can be defined as the value that a digit has based on its position or place in a number.

Examples of place value is:

Thousands represented by Th

Hundreds represented by H

Tens represented by T

Units represented by U

In the above question,

500 ÷ 50 gives us 10.

This is true because, 500 as a number, the Digit 5 has a place value of hundreds

50 as a number , the digit 5 has a place values of Tens.

10 as a number, the digit 1 has a place value of Tens.

In mathematics, the multiplication of 2 numbers in a place value of Tens always gives us a place value of hundreds.

For example, 10 × 50 = 500

Likewise, when we divide, a number with a place value of hundreds by a number with a place value of tens, we have a number with a place value of tens.

For example: 500 ÷ 50 = 10.

Therefore, the statement "500 divided by 50 is 10" is a true statement

Answer:

Step-by-step explanation:

Total gallons of punch mixture =  gallons of pineapple juice + orange juice + gallons of apple juice + gallons of Ginger ale

Given gallons of pineapple juice = 3/4 gallons

Orange juice = 1 1/2 gallons

Gallons of apple juice = 7/8

Total gallons of punch = 4 gallons

On substituting into the formula above:

4 = [tex]\frac{3}{4} +\frac{3}{2}+\frac{7}{8}+Gallons\ of\ ginger\ ale[/tex]

[tex]4=\frac{6+12+7}{8} + Gallons\ of\ ginger\ ale[/tex]]

gallons of ginger ale = [tex]4-\frac{25}{8}[/tex]

gallons ginger ale = [tex]\frac{7}{8}[/tex]

She needs 7/8 gallons of Ginger ale to make the total of 4 gallons of punch

Answer:

Emma would need 7/8 gallons of Ginger Ale to make the total of 4 gallons of punch.

Step-by-step explanation:

In the question, Emma used different quantities of juice to make a punch. To find the remainder, needed to make 4 gallons, we sum up the given quantities, and subtract it from the expected amount.

The summation of the given quantities of juice is as follows;

3/4 + 1 1/2 +7/8 = 25/8

We no subtract the quantity we already have from the expected amount, which is 4 gallons, thus;

4 - 25/8 = 7/8 gallons of Ginger Ale.

To confirm the answer, we sum up all the given quantities. Therefore;

3/4 + 1 1/2 + 7/8 + 7/8 = 4 gallons of punch.

Answer:

Arithmetic

Step-by-step explanation:

Since each number is 12 larger than the last, this is an arithmetic sequence. A geometric sequence is one in which each next number in the sequence is the previous one multiplied by a certain set coefficient, while in an arithmetic sequence it's a certain number added. Hope this helps!

Answer:

It is arithmetic because to get from one term to the next, you add 12, and in an arithmetic sequence, you add/subtract a common difference to get from one term to the next. Hope this helps!

Answer:

Brainliest please

The  Volume is 125 times bigger.

Step-by-step explanation:

V = [tex]\frac{4}{3}*\pi *r^{3}\\[/tex] is the normal formula.

If you multiply the radius by 5 the it changes to

V = [tex]\frac{4}{3}*\pi *(5r)^{3}[/tex]

And when you simplify you get

V = [tex]\frac{4}{3} * \pi * 125r^3[/tex]

And the only difference between the inital equation and this one is *125 and so the volume is 125 bigger if the radius is multiplied by 5.

Answer: C) About 30

Step-by-step explanation: 285/9= 31.6666666667 which rounded to the nearest ten is equal to 30

There should be about 30 decorations on each shelf.

The opposite of multiplication is division. Assuming that 3 gatherings of 4 make 12 in augmentation, 12 isolated into 3 equivalent gatherings give 4 in each gathering in division.

The primary objective of partitioning is to perceive the number of equivalent gatherings that are shaped or the number of are in each gathering while sharing decently.

Given  total lawn decorations = 285

and to arrange in 9 shelves

each shelves will have

285/9 = 31.6667

the nearest ten is 30.

Hence each shelf  have about 30 decorations.

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Answer:

A

Step-by-step explanation:

-8*2+6≤2(-3*2+1)

= -10≤-10

Answer:

2 and 1

Step-by-step explanation:

[tex]y = {x}^{2} + 3x - 7 \: will \: have \: two \: points \: of \: \\intersection \\ \\ y - x = 9 \: will \: have \:only \: one\: point \: of \:\\ intersection[/tex]

Answer:

a.20

Step-by-step explanation:

20 is standing out from the rest of the numbers