The product of two numbers is 32. The first number, x, is one-half of the second number, y. Which system of equations can be used to find the two numbers? A system of equations. x y equals 32. x equals StartFraction one-half EndFraction y. A system of equations. x y equals 32. x equals y minus StartFraction one-half EndFraction. A system of equations. x plus y equals 32. x equals y minus StartFraction one-half EndFraction. A system of equations. x plus y equals 32. x equals StartFraction one-half EndFraction y.

Answer: C) 17

Step-by-step explanation:

Let x be the number of large boxes

As per given,

Number of small boxes= 3 × (number of large boxes)

i.e. Number of small boxes= 3x

Allie is transporting boxes of two sizes: 12 cubic feet and 5 cubic feet.

Total volume = 12  (number of large boxes) + 5(Number of small boxes)

= 12 x+ 5 (3x)

= 12x+15x

= 27x

A moving van’s cargo area has a maximum volume of 480 cubic feet.

[tex]\Rightarrow\ 27x \leq480[/tex]

Divide both sides by 27 , we get

[tex]x\leq17.78[/tex]

i.e. maximum value x can take = 17

So, the maximum number of larger boxes that she can fit in the van = 17.

Hence, the correct option is C) 17 .

Answer:

2850

Step-by-step explanation:

We know that only 19% of people prefer the sedans, so we have to find 19% of 15,000. Set up a proportion: [tex]\frac{19}{100}=\frac{x}{15000}[/tex], cross multiply and get 2850.

Answer:

2850 sedans per month

Step-by-step explanation:

19 % want sedans

They expect to sell 15000 cars

Take the number of cars and multiply by the percent sedans

19% * 15000

Change to decimal form

.19*15000

2850

Answer:

5

Step-by-step explanation:

Due to the direction the line is facing it can be concluded that its slope is positive.

You need two definite points on the line to find the slope.

(x¹,y¹) ( x²,y²)

Points (5,20) (0, -5)

Slope = (y² - y¹) ÷ (x² - x¹)

= (-5 - 20) ÷ (0 -5)

= (-25) ÷ (-5)

= 5

Have a great day!

Answer:

5

Step-by-step explanation:

Since y equals 200 + 10x and y also equals 5x, then

200 + 10x = 50x

Subtract 10x from both sides.

200 = 40x

Divide both sides by 40.

5 = x

Answer: He must sell 5 sculptures.

Answer:

NL=10.82

Step-by-step explanation:

Start by finding the area of the triangle.  We do this by using c as the base.

1/2bh=1/2(12)(25)=150

Now that we know the area is 150, we turn the triangle so b is the base and use the formula again.  This time we’re looking for the height, which is NL.

1/2bh=

1/2(27.73)h=150

13.865h=150

h=10.8186

Rounded to the nearest hundredth, it’s NL=10.82

Answer:

  [tex]\textbf{A. }F(x)=\dfrac{1}{(x-3)^2}[/tex]

Step-by-step explanation:

The parent function 1/x² is shifted 3 units to the right. That means x has been replaced by x-3:

  F(x) = 1/(x -3)²

Replace f(x) with 0 and solve for x. We do this because the x intercepts always occur when y = 0. Keep in mind that y = f(x).

f(x)=x^3-9x^2+20x

0=x^3-9x^2+20x

x^3-9x^2+20x = 0

x(x^2-9x+20) = 0 .... factor out GCF x

x(x-5)(x-4) = 0 ... factor the stuff inside

x = 0 or x-5 = 0 or x-4 = 0 ... zero product property

x = 0 or x = 5 or x = 4

Answer:

<B = 32°

c = 9.43

Step-by-step explanation:

To find the measure of <B, add up the measures of the two angles that you know and subtract from 180°.

58° + 90° = 148°

180° - 148° = 32°

The measure of <B is 32°.

To find the length of side c, use the Pythagorean Theorem.

a² + b² = c²

5² + 8² = c²

25 + 64 = c²

89 = c²

c = √89

c = 9.433981132 ⇒ 9.43 (rounded to two decimal places)

The length of side c = 9.43.

Hope that helps.

hey mate, here is ur answer in the attachment!

Answer:

5/6π.

Step-by-step explanation:

The following data were obtained from the question:

Radius (r) = 12 cm

Area (A) = 60π cm²

Centre angle in radian (∅) =...?

Since we are to look for the centre angle in radian, the area of the sector will be given by:

A = ½r²∅

Inputting the values of the area, A and radius, r, the centre angle, ∅ can be obtained as follow:

A = ½r²∅

60π = ½ × 12² × ∅

60π = ½ × 144 × ∅

60π = 72 × ∅

Divide both side by 72

∅ = 60π/72

∅ = 5/6π

Therefore, the centre angle measured in radian is 5/6π.

Answer:

A = 9x² + 48x + 65

Step-by-step explanation:

Area of a Square Formula: A = lw

Since a square's length is equal to its width, we simply plug it into the formula:

A = (3x + 8)(3x + 8)

Then we simply use FOIL to expand the distribution)

First - 3x(3x) = 9x²

Outside - 8(3x) = 24x

Inside - 8(3x) = 24x

Last - 8(8) = 64

Lastly, we combine like terms

9x² + 24x + 24x + 64

9x² + 48x + 64

Answer:

False

Step-by-step explanation:

Given

A = [tex]\frac{1}{2}[/tex] bh ( multiply both sides by 2 to clear the fraction )

2A = bh ( divide both sides by b )

[tex]\frac{2A}{b}[/tex] = h

by bargaining with the owner, vying for discounts or insisting on multiple products for a complimentary value deal

Answer:  1) c    2) a     3) d

Step-by-step explanation:

[tex]\cos \theta = \dfrac{adjacent}{hypotenuse}\quad \\\\\\\cos 42.1=\dfrac{4.7}{x}\\\\\\x=\dfrac{4.7}{\cos 42.1}\\\\\\\large\boxed{x=6.33}\\[/tex]

******************************************************************************************

Reference angle is the angle measurement from the x-axis.  There is no such thing as a negative reference angle.

-183°  is 3° from the x-axis so the reference angle is  [tex]\large\boxed{3^o}[/tex]

*******************************************************************************************

Coterminal means the same angle location after one or more rotations either clockwise or counter-clockwise.

To find these angles, add or subtract 360° from the given angle to find one rotation, add or subtract 2(360°) from the given angle to find two rotations, etc.

To find ALL of the coterminals, add or subtract 360° as many times as the number of rotations.  Rotations can only be integers. In other words, you can only have ± 1, 2, 3, ... rotations. You cannot have a fraction of a rotation.

Given: 203°

Coterminal angles: 203° ± k360°, k ∈ I

Answer:

The largest integer that belongs to the interval (-∞, 31] is 31

Step-by-step explanation:

The given interval is (-∞, 31], from which the round bracket indicates that the number next to the bracket is not included in the inequality while the square [] (closed) bracket indicates that the number next to the bracket is included in the inequality

Therefore, 31 is inclusive in the inequality while -∞ is excluded.

The find the largest integer that belongs to the interval (-∞, 31] the numbers are arranged on the number line as follows

The numbers presented in number line form -∞, .....-1, 0, 1, 2,..., 31

Giving 31 as the largest integer in the inequality

Answer:

2 - bedroom apartment = 4

3 - bedroom apartment = 2

Step-by-step explanation:

Given the following :

2 - bedroom apartment = $700 / month

3 - bedroom apartment = $900 / month

Last month:

Number of vacant apartment = 6

Amount of Lost rent = $4600

Let a = 2 - bedroom apartment and b = 3 - bedroom apartment

Vacant apartment :

a + b = 6 - - - (1)

Lost rent :

700a + 900b = 4600 - - - (2)

From (1),, a = 6 - b

Substitute a = 6 - b into (2)

700(6 - b) + 900b = 4600

4200 - 700b + 900b = 4600

4200 + 200b = 4600

200b = 4600 - 4200

200b = 400

b = 400/200

b = 2

From (1) ;

a + b = 6

a + 2 = 6

a = 6 - 2

a = 4

a = 2 - bedroom apartment = 4

b = 3 - bedroom apartment = 2

Answer:

a. 12 / 50 = 0.24 or 24%; b. 21 / 50 = 0.42 or 42%

Step-by-step explanation:

1. to find the estimated probability that it will take at least 5 patients to find who it isn't effective on, count the outcomes of EEEE. this means that it was effective on 4 patients, therefore requiring a 5th patient to find the noneffective person.

a. 12 / 50 = 0.24 or 24%

2. to find the estimated probability that it will be effective on exactly 3/4, look for boxes with 3 E's and 1 N (in any order)

b. 21 / 50 = 0.42 or 42%

hope this helps :)

Answer:

Triangle klm

Step-by-step explanation:

edg 2020

Answer:

Step-by-step explanation:

Because of the Isosceles Triangle Theorem, both the base angles of that triangle measure a. We also know that a + b = 180 because of the definition of supplementary angles. So we have 2 equations from that info. First is the fact that

a + 7x = 180 and the second is

2x + a + a = 180 because of the Triangle Angle-Sum Theorem. If the left side of the first equation = 180 and the left side of the second equation also = 180, then by the transitive property of equality,

a + 7x = 2x + a + a and

a + 7x = 2x + 2a and

5x = a. Now that we know that a = 5x, we go back to our triangle and fill in 5x as a:

5x + 5x + 2x = 180 (the Triangle Angle-sum Theorem again) and

12x = 180 so

x = 15. If x = 15, then

a = 5(15) = 75,

b = 7(15) = 105, and

c = 2(15) = 30

Answer:

340 liters

Step-by-step explanation:

357/1.05=340

Here is your answer!!!

Cube root of 10648 is 22.

Answer:

22

Step-by-step explanation:

[tex]\sqrt[3]{10648}[/tex] factors into [tex]\sqrt[3]{22^{3} }[/tex]

You then apply the radical rule: [tex]\sqrt[n]{a^{n} }[/tex]=a

In in this case a = 22

Answer:

3. 8.60 units

Step-by-step explanation:

Distance from point M(-2, 4) to point N(5, -1) can be calculated using the distance formula, [tex]d = \sqrt{(x_{2} - x_1)^2 + (y_2 - y_1)^2}[/tex]

M(-2, 4) => (x1, y1)

N(5, -1) => (x2, y2)

Plug in the values into the formula

[tex] d = \sqrt{(5 - (-2))^2 + (-1 - 4)^2} [/tex]

[tex] d = \sqrt{(7)^2 + (-5)^2} [/tex]

[tex] d = \sqrt{49 + 25} [/tex]

[tex] d = \sqrt{74} [/tex]

[tex] d = 8.60 units [/tex]

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

It is half of equilateral triangle where 2√3 is its hight so:

[tex]2\sqrt3=\frac{k\sqrt3}2\\\\4\sqrt3=k\sqrt3\\\\k=4[/tex]

Answer:

1.67years

Step-by-step explanation:

in one it increases by 1.1% of 7.1 billion

=7.81 million

dat is it increases 7.7181 billion in 1 year

it reaches 12 billion in x years

therefore x years = 12 billion/ 7.7181 billion

= 1.67 years

don't forget to tag me as brainliest answer

Answer:

Step-by-step explanation: wjbsgstexrczlkcidgxtftwdcwdkfmw,d,f

Answer:

sqrt(6)

Step-by-step explanation:

In a 45-45-90 right triangle, the ratio of the lengths of the sides is

1 : 1 : sqrt(2)

u = sqrt(3) * sqrt(2) = sqrt(6)

Answer:

√6 meters

Step-by-step explanation: In a 45° right triangle, the two sides of the 90° angle are equal. a^2+b^2=c^2

2(√3)^2 = 6

√c^2 = √6.

Answer:

Step-by-step explanation:

Given the expression 1/6.43 +2/3.56 +1/8.51, If 'a' is a number, the reciprocal of such number is 1/a. According to the question, the reciprocal of 6.43, 3.56 and 8.51 are  1/6.43 and 1/3.56 and 1/8.51 respectively.

1/6.43 = 0.1555

2/3.56 = 2 * 1/3.56

= 2 * 0.2809

= 0.5618

1/8.51 = 0.1175

Taking the sum of the reciprocals;

1/6.43 +2/3.56 +1/8.51 = 0.1555 + 0.5618 + 0.1175

1/6.43 +2/3.56 +1/8.51 = 0.8348

Hence, the sum of 1/6.43, 2/3.56 and 1/8.51 is 0.8348

Answer:

p < 2

Step-by-step explanation:

9p + 23 < 41

p < 2

Answer:

p < 2

Step-by-step explanation:

9p + 23 < 41

9p < 18

p < 2

Answer:

3 cups

Step-by-step explanation:

We can use a proportion to find how many cups of chocolate chips she needs for 30 servings. Assuming c = cups of chocolate chips and b = batches

[tex]\frac{c}{b}[/tex]

[tex]\frac{1}{10} = \frac{c}{30}[/tex]

We can now multiply the diagonal values that don't include the missing variable (30 and 1) and then divide it by the value that is diagonal to the variable (10)

[tex]30 \cdot 1 = 30\\30 \div 10 = 3[/tex]

Therefore, she needs 3 cups of chocolate chips to make 30 servings.

Answer:

3 cups

Step-by-step explanation:

We can use ratios to solve

1 cup               x cups

---------------- = ----------------

10 servings     30 servings

Using cross products

1*30 = 10x

Divide by 10

30/10 = x

3 =x

3 cups

Answer:

A 99% confidence level is saying that you are 99% positive that you null hypothesis will not be rejected. The critical value that comes with the confidence level is the Z-score. The Z-score can usually be found using the Z-score table found online. The Z-score for 99% confidence is 2.575. If they give you the Z-score and tell you to find it on a right tail graph you subtract the given z-score from alpha which is .5 and find what you got on the z-score table.

Ex: Given Z-score- 0.0079

.0079 - .5(alpha)=  0.4921.

The closest area to 0.4921 is 0.4922 at z = 2.42.

Hope this helps