Factor the expression completely 18^2-32

Answer:

106°

Step-by-step explanation:

Given that the points B, C and D are colinear, it means that

2x + 40 = 5x + 10

collecting like terms

40 - 10 = 5x - 2x

3x = 30

x = 10

Hence the angle ∠E

= 5(10) + 10

= 60°

∠BCE = X + 4

= 10 + 4

= 14°

Given that the sum of angles in a triangle is 180°

∠D + 14 + 60 = 180

∠D = 180 - 74

= 106°

Hey there! I'm happy to help!

To find the volume of a rectangular prism, you simply multiply each of the three different sides!

18×9×17=2754

Therefore, the volume of this rectangular prism is c. 2754 units cubed.

Now you can find the volume of a rectangular prism! Have a wonderful day!

Answer:

See the answer below.

Step-by-step explanation:

We know that:  [tex]d=S\times t[/tex]

So, using the given data, we can write an equation for the total distance travelled as:

[tex]3\times S+4\times (S+10)=335\\\\\Rightarrow S\approx 42.1\:Km/h[/tex]

Best Regards!

Answer:

La cantidad de cartón necesaria para hacer el sólido es de 165 m² de cartón.

Step-by-step explanation:

La figura en la pregunta consta de tres formas

1) Una pirámide cuadrada

Altura inclinada = 5 m

Longitud lateral base = 3 m

2) un cubo

Longitud lateral, s = 3 m

3) Un prisma rectangular

Longitud = 6 m

Altura = 3 m

Ancho = 3 m

El área de superficie de la pirámide cuadrada, [tex]S_P[/tex] = 2 × Altura inclinada × Longitud del lado base

[tex]S_P[/tex] = 2 × 5 × 3 = 30 m²

El área de superficie del cubo, [tex]S_C[/tex] = 6 ×(Longitud lateral, s)²

[tex]S_c[/tex] = 6 × 3² = 54 m²

El área de superficie del prisma rectangular, [tex]S_R[/tex] = 4 × largo × alto + ancho × alto

[tex]S_R[/tex] = 4 × 6 × 3 +  3 × 3 = 81 m²

La cantidad de cartón necesaria para hacer el sólido, [tex]S_S[/tex] = [tex]S_P[/tex] +  [tex]S_C[/tex] +  [tex]S_R[/tex]

[tex]S_S[/tex] = 30 + 54 + 81 = 165 m².

La superficie del cartón necesaria para construir el sólido es de 165 m².

Answer:

Combining statement 1 and statement 2 is sufficient

Step-by-step explanation:

There are 3 items purchased

Most expensive item=20% discount

The other two items=10% discount each

Statement 1: The average (arithmetic mean) of the regular prices of the 3 items was $30.

Assume:

The 3 items cost: $40, $30 and $20 respectively,

Total discount =20% of $40 + 10% of $30 + 10% of $20

=$8 + $3 + $2

= $13

Assume

The 3 items cost: $50, $30 and $10 respectively,

Total discount = 20% of $50 +10% of $30 + 10% of $10

=$10 + $3 + $1

= $14

Therefore, statement 1 is INSUFFICIENT

Statement 2: The most expensive item was $50

The discount for the most expensive item at $50 = 20% of $50

= 0.2*$50

=$10

But we don't know the price of the other 2 items, so we can't determine the discounts.

Therefore, Statement 2 is also INSUFFICIENT

Combining statement 1 and 2

1) The average (arithmetic mean) of the regular prices of the 3 items was $30.

So, the SUM of the 3 items = $90

2) The most expensive item is $50

So the OTHER 2 items sum up to $40

$50 item gets 20% discount and the other two items ($40) each get 10% discount

The discount = 20% of $50 + 10% of $40

=0.20*50 + 0.1*40

=$10 + $4

=$14

Combining the two statements is sufficient

Answer:

Step-by-step explanation:

The area of a parallelogram is equal to the product of the length of its side and the height of the parallelogram perpendicular to that side.

H = 9 cm

S = 21 cm

A = S•H = 21 cm • 9 cm = 189 cm²

Answer:

yes it is a function

Step-by-step explanation:

Mathematics

In mathematics, a function is a binary relation over two sets that associates to every element of the first set exactly one element of the second set. Typical examples are functions from integers to integers or from the real numbers to real numbers.

Answer:

False

Step-by-step explanation:

A function has only 1 y value for any given x value.

You can use the "vertical line test" to check if a graph is of a function.  Move a vertical line (you can use the edge of a ruler) from left to right across the graph.  If at any point the line intersects the curve in two or more places, the curve is not a function.

A system of inequalities can be solved graphically.

See attachment for the required graph

The inequalities are given as:

[tex]\mathbf{x +3y > 6}[/tex]

[tex]\mathbf{y \ge 2x + 4}[/tex]

The options are not given.

So, I have attached the graph that illustrates the solution to the system of inequalities

From the graph, we have the solutions as:

Read more about graphs of inequalities at:

https://brainly.com/question/15748955

Answer:

  a) 18.6%

  b) 598,230

Step-by-step explanation:

a) In the first part of the question, you are given two population values and asked to find the percentage difference between them. A formula you can use for that is ...

  percentage difference = (difference)/(original value) × 100%

The difference of interest is the difference between the 2011 population and the 2001 population

  difference = 510,000 -430,000 = 80,000

The original value is the 2001 population, so the percentage difference is ...

  percentage difference = 80,000/430,000 × 100% = 0.1860 × 100% = 18.6%

This is a positive value, so represents an increase.

The percentage increase in population from 2001 to 2011 was 18.6%.

__

b) In the second part, you are given the percentage difference and asked to find the new value. We can rearrange the above formula to find the difference:

  difference = (percentage difference)/100% × original value

Then the difference between the 2021 population and the 2011 population will be ...

  difference = (17.3%)/100% × 510,000 = 0.173 × 510,000 = 88,230

So, the population in 2021 is expected to be 88,230 more than in 2011:

  2021 population = 520,000 +88,230 = 598,230

The predicted population in 2021 is 592,230.

Answer:

To create the sketch of a polynomial function there are key features are necessary and these are the vertex, axis of symetry, x and y intercepts

Step-by-step explanation:

To create the sketch of a polynomial function there are key features are necessary and these are the vertex, axis of symetry, x and y intercepts

One of the key features arte the vertex and this shows where it changes concativity.

While the x and y intercepts give you a couple of points of reference.

Also, the axis of symetry is only applicable to even degree polynomials

Answer:

its 55

Step-by-step explanation:

45-100=55( trust me its right.)

Answer:

9/21

Step-by-step explanation:

total there are 105 candies, 60+45

45 are red so 45/105

simplified 9/21

Answer:

0.987

Step-by-step explanation:

use stat on calculator

Answer:

193.33333 pounds

Step-by-step explanation:

Divide 87kg by 0.45

So, it's 87 ÷ 0.45 = 193.3333333

Answer: 190

Step-by-step explanation:

Step-by-step explanation:

hope it will help you..........

Answer:

Step-by-step explanation:

A radius to the tangent point always forms a right angle with the tangent.

m∠MNP = 90° so we can use Pythagorean theorem:

[tex]MN^2+NP^2=MP^2\\\\MN^2+48^2=50^2\\\\MN^2+2304=2500\\\\MN^2=196\\\\MN=\sqrt{196}\\\\MN=14\,ft[/tex]

Answer:

Step-by-step explanation:

9x + 8 = 7.5x + 17

1.5x = 9

x = 6 hours

Answer:

Step-by-step explanation:

Hello,

the line passes through (-8,11) means than y = 11 for x  = -8

I believe that you wanted to write the first one as below

[tex]y=-\dfrac{5}{8}x+6[/tex]

in that case for x = -8

y = - 5 * - 1 + 6 = 5 + 6 = 11

hope this helps

The solution is, : y = -5/8x +6, the equation represents the line that passes through (-8,11) and (4,7/2).

A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined both sides of a point and has no curve.

here, we have,

First we need to find the slope

m = (y2-y1)/ (x2-x1)

   = (7/2 -11)/(4--8)

   = (7/2 - 22/2)/(4+8)

   = (-15/2)/(12)

  = -15/24

Divide top and bottom by 3

  -5/8

Then we can use point slope form to write the equation

y-y1 = m (x-x1)

y- 11 =-5/8(x--8)

y- 11 =-5/8(x+8)

Distribute

y-11 =-5/8 x -5

Add 11 to each side

y-11 = -5/8x -5+11

y = -5/8x +6

Hence, The solution is, : y = -5/8x +6, the equation represents the line that passes through (-8,11) and (4,7/2).

To learn more on Equation 0f Straight-Line click:

brainly.com/question/11116168

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Answer:

Step-by-step explanation:

Given question is incomplete; here is the complete question.

∆ PQR shown in the figure below is transformed into ∆ STU by a dilation with center (0, 0) and a scale factor of 3.

Complete the following tasks,

- Draw ΔSTU on the same set of axes.

- Fill in the coordinates of the vertices of ΔSTU.

- Complete the statement that compares the two triangles.

When ΔPQR is transformed into ΔSTU by a dilation with center (0, 0) and a scale factor of 3,

Rule to followed to get the vertices of ΔSTU,

(x, y) → (3x, 3y)

P(1, 1) → S(3, 3)

Q(3, 2) → T(9, 6)

R(3, 1) → U(9, 3)

Length of QR = 2 - 1 = 1 unit

Length of PQ = [tex]\sqrt{(3-1)^2+(2-1)^2}=\sqrt{5}[/tex] units

Length of PR = 3 - 1 = 2 units

Length of ST = [tex]\sqrt{(9-3)^2+(6-3)^2}=3\sqrt{5}[/tex] units

Length of TU = 6 - 3 = 3 units

Length of SU = 9 - 3 = 6 units

Therefore, ratio of the corresponding sides of ΔPQR and ΔSTU,

[tex]\frac{\text{PQ}}{\text{ST}}=\frac{\text{QR}}{\text{TU}}=\frac{\text{PR}}{\text{SU}}[/tex]

[tex]\frac{\sqrt{5}}{3\sqrt{5}}=\frac{1}{3}=\frac{2}{6}[/tex]

[tex]\frac{1}{3}=\frac{1}{3}=\frac{1}{3}[/tex]

Since ratio of the corresponding sides are same,

Therefore, ΔPQR and ΔSTU are similar.

Answer:

Correct (1,9), (2,14)

Incorrect (1,8),(2,13)

Step-by-step explanation:

It is simple.

To find the correct values plug a x value.

For Example;

X=1

y=5(1)+4

y=5+4

y=9

so your X value is 1 and your Y value is 9

To solve for the incorrect values

Find the correct values and subtract 1 form the Y value.

Answer:

No, it doesn't make sense because the output is not feasible.

Step-by-step explanation:

We are told that the function g(x) represents the number of items collected.

Now, we are also told that x is the number of people who donated.

Now, if we want to consider a possible solution of (60, 10) .

It means, we now have; g(60) = 10

This means that 60 people donated and 10 items were collected.

It doesn't make sense that 60 people donated items and only 10 items were available to be collected.

Thus, we can say that ;

No, it doesn't make sense because the output is not feasible.

Answer:

(f ∘ g)(x) = 0.9x - 100

Step-by-step explanation:

Here in this question, we are interested in calculating (f ∘ g)(x)

From the question, we are given;

f(x) = x -100

g(x) = 0.9x

So (f ∘ g)(x) simply means we shall be representing the x in f(x) with the totality of the value of g(x)

Mathematically, what we are saying is that;

Find (f ∘ g)(x) = 0.9x - 100

Answer:

exact form: n=378/13

decimal form: n=29.0769....

mixed number form: n=[tex]29\frac{1}{13}[/tex]

Step-by-step explanation:

Answer:

n = 21

Step-by-step explanation:

[tex]\frac{n}{2}-\frac{3n}{9}+\frac{5n}{9}=21\\\\\frac{9n}{18}-\frac{6n}{18}+\frac{10n}{18}=21\\\\\frac{3n}{18}+\frac{10n}{18}=21\\\\\frac{13n}{18}=21\\\\13n=273\\\\n=21[/tex]

Steps:

1. Write as fractions

2. Make the fractions have the same denominator

3. Collect like terms

4. Collect like terms

5. Multiply both sides by 18

6. Divide both sides by 13.

Answer:

16

Step-by-step explanation:

perimeter of B = 21

divide by 3 to get each side: 21/3 = 7 = Y

perimeter of hexagon is 50. subtract 2Y: 50 - 14 = 36

divide 36 by 4 to find X = 9

add X + Y

Answer:

See below.

Step-by-step explanation:

[tex](6a+3b)(a-b)\\[/tex]

Distribute:

[tex]=(6a+3b)(a)-(6a+3b)(b)\\=6a^2+3ab-(6ab+3b^2)\\=6a^2+3ab-6ab-3b^2\\=6a^2-3b^2-3ab[/tex]

Answer:

6a^2-3b^2-6ba+3ba

Step-by-step explanation:

(6a+3b)(a+b)....expand the term

6axa - 6axb + 3bxa - 3b×b ....simplify

6a^2 - 6ba + 3ba - 3b^2, then reorder so highest order terms come first

6a^2 - 3b^2 - 6ba + 3ba

Answer:

9

Step-by-step explanation:

The diagram showing the three pieces of paper of three digit in which two of the letters were covered can be seen below.

From the diagram; we have;

243 , 1_7 , _26

Assuming the covered digits are _

The sum is 826.

i.e

243 + 1_7 + _26 = 826

The objective is to determine the sum of the two unknown digits

So; we need to think about what number can we add put in 1_7 to determine the covered digit in  _26

From ; 1_7 , we have the choice to pick from 0 - 9

Assuming the covered digit is 0; let's check if we are right

So; 243 + 107  +  _26 = 826

350 +   _26 = 826

_26 = 826 - 350

_26 = 476

So; the covered digit is in the position of 4 , but it doesn't tally together

i.e 426 is not the same as 476, which makes our assumption to be wrong.

Let consider the covered digit to be 5 for example.

So; 243 + 157  +  _26 = 826

400 +   _26 = 826

_26 = 826 - 400

_26 =  426

The covered digit is in the position of 4

SO;

426 = 426

Here , our assumption is right.

As such , the covered digits are 5 and 4

The sum of the two  covered digits are = 5 + 4 = 9

Answer: He can buy 5 loaves of bread.

After buying 5 loaves 15 p will be left.

Step-by-step explanation:

Given, In the supermarket a loaf of bread costs 37p .

To find: How many loaves can David buy with a [tex]\pounds 2[/tex] coin?

Since [tex]\pounds 1=100\text{ pence}[/tex]

Then, [tex]\pounds 2=200\text{ pence}[/tex]

Number of loaves he can buy = (Amount he has) ÷ (Cost of a loaf of bread)

= 200 p ÷ 37 p

[tex]=5\dfrac{15}{37}[/tex]

i.e. he can buy 5 loaves of bread and 15 p will be left.

Hence, He can buy 5 loaves of bread.

After buying 5 loaves 15 p will be left.

Answer:

Nathan weighs 12 more pounds than Marty.

Step-by-step explanation:

If Marty weighs 64 pounds and Nathan weighs 76 pounds, we can subtract the weight of Marty from Nathan to get our answer.

[tex]76-64=12[/tex]

In case Nathan was actually 476 pounds, the answer would be 412.

Answer:

1) A rectangular shape

2) Point  (30, 50)

3) (x - 30)² + (y - 50)² = 10²

4) Yes, the swimming pool will touch the flower beds

5) Point (45, 25)

Step-by-step explanation:

1) Given the number of shapes that are rectangles (4) and the number of circular shapes (1) to conserve more space Kylee should drw the swimming pool with a rectangular shape

2)  So as to avoid touching the flowerbeds which are 20 feet apart, the center of the swimming pool will be moved slightly up to (30, 50)

3) The equation that will draw the swimming pool is the equation of a circle, given as follows

(x - h)² + (y - k)² = r²

Where (h, k) is the coordinate of the center of the circle, and r is the radius of the circle,

Given that the diameter, D, of the circle = 20 feet, the radius, r = D/2 = 20/2 = 10 feet

The equation of the circle is therefore;

(x - 30)² + (y - 50)² = 10²

4) The coordinates of the center of the flower bed is (30, 45) which gives

(x - 30)² + (y - 45)² = 10²

Where the coordinates of the side of the flower pot is (20, 45), we have;

(20 - 30)² + (45 - 45)² = 10²

(-10)² = 10² = r²

Hence, point (20, 45) is on the circle

The other flower bed side has coordinates (40, 45) which gives

(40 - 30)² + (45 - 45)² = 10²

10² = r² = 10²

Point (40, 45) is also on the circle

Therefore, the swimming pool will touch the flower beds

5) At point (45, 25), we have;

(x - 45)² + (y - 25)² = 10²

The closest point is the patio with coordinates (40, 15) which gives;

(40 - 45)² + (15 - 25)² = 10² = 100

(-5)² + (-10)² = 125 > 100

Therefore, point (40, 15), is not on the circle.

Answer: I just did it and the answer is 0.43

Step-by-step explanation:

Using it's concept, it is found that the probability that the person is from Texas given that the person prefers Brand b is given by:

A. 0.43.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem, 105 people prefer brand B, and of those, 45 are from Texas, hence:

p = 45/105 = 0.43.

Which means that option A is correct.

More can be learned about probabilities at https://brainly.com/question/14398287

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Answer:

C

Step-by-step explanation:

The slope formula is y^2 - y^1 over x^2 - x^1    

hope this helps!

also the answer is just the inverse of that answer

Answer: 10x454x0.55=2,497 grams of fruit