Question 7 Mai and Tyler are selling items to earn money for their elementary school. The school earns w dollars for every wreath sold and p dollars for every potted plant sold. Mai sells 14 wreaths and 3 potted plants and the school earns $70.50. Tyler sells 10 wreaths and 7 potted plants and the school earns $62.50. This situation is represented by this system of equations: { 14 w + 3 p = 70 . 50 10 w + 7 p = 62 . 50 Which statements are true in explaining why it makes sense that the solution of this system is also a solution to 4 w + ( − 4 p ) = 8 . 00 ? Select all that apply. (Lesson 2-15) Multiple select question. A) Because 10 w + 7 p is equal to 62.50, subtracting 10 w + 7 p from the left side of 14 w + 3 p = 70 . 50 and subtracting 62.50 from its right side keep the two sides equal. B) The equation 4 w + ( − 4 p ) = 8 . 00 is the result of adding the two equations in the system and then dividing the result by 6. C) The equation 4 w + ( − 4 p ) = 8 . 00 is the result of subtracting the second equation in the system from the first equation. D) The equation 4 w + ( − 4 p ) = 8 . 00 represents the difference between Mai's sales and Tyler's sales, or the result of subtracting Tyler's sales from Mai's. E) The left side of the equation 4 w + ( − 4 p ) = 8 . 00 shows the difference in terms of the items sold. The right side shows the difference in dollars. The cost per wreath, w, and the cost per potted plant, p, haven't changed.

Answer:

Complementary angles have a sum of 90°.

(x²-16x)+(3x) = 90

x² -13x - 90 = 0

(x-18)(x+5) = 0

x - 18 = 0 or x + 5 = 0

x = 18 or x = -5 (reject)

Substitute x into the angles.

18²-16(18) = 36

Smaller angle = 36°

3(18) = 54

Larger angle = 54°

Answer:

y=2x+11

Step-by-step explanation:

Firslty, we need to find the function, whcih we can do by substituting one into the other:

Now, for the domain we have more complicated approach.

We first have to find the domain for both f(x) and g(x).

The domain of f(x) is all real number, because it is a quadratic polynomial.

The domain of g(x) is all the real numbers except the x values that makes the square root interior negative, so all real numbers so that:

Now, the domain of the composite function f(g(x)) is the set of all the values of x in the domain of g(x) such that the corresponding g(x) is in the domain of f(x).

Since the domain of f(x) is all real numbers and g(x) is a real number function, all the values of g(x) will be in the domain of f(x), so we just need to check the values of x that are in the domain of g(x).

The domain of g(x), as we saw, is:

And any value of x will give a g(x) that will be in the domain of f(x) so, the domain of f(g(x)) is:

So, the correct alternative is:

Evaluating Algebraic Expressions

We are given the expression:

-6b + 2a

And it's required to find the value of the expression for a=-6.9 and b=1.9

Substituting the values:

-6(-1.9) + 2(-6.9)

= 11.4 - 13.8

Operating:

=-2.4

The value is -2.4

Answer:

the slope is 0 and  the equation is y = -2

Step-by-step explanation:

out of 500 people 200 like baseball and 120 people like to play game baseball/softball

suppose 48 out of every 120 people like baseball/softball.

of the people who like baseball/softball, 3 out of 5 play the game.

if you ask 500 people,

how many would you expect play baseball/softball

it means 40% like baseball and 60% like to play game

if there are 500 people

then 500 *(40/100)=200

thus 200 people like baseball

and 200*(60/100)=120

Hence 120 people to play game

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Answer:24

Step-by-step explanation:4+2=6,6+3=9,9+4=13,13+5=18,18+6=24

Answer:

24

Step-by-step explanation:

because in first piggy bank has 4 coins and second has 6 . difference=6-4=2

second has 6 coins and third has 9 . difference= 9 - 6 = 3 third has 9 coins and fourth has 13 . difference=13-9=4

fourth has 13 and fifth has 18 coins difference is 18 -13 =5

then,sixth has 24 because all have 2 3 4 5 difference then six has 6

The point slope form for the line with slope 1/2 and passing through the point ​(-3​,-8​) is y + 8  = m(x + 3)

A linear equation can be represented in point slope form as follows:

y - y₁ = m(x - x₁)

where

Therefore, the point slope form is represented as follows;

m = 1 / 2

It passes through the points ​(-3​,-8​).

Hence,

y + 8  = m(x + 3)

Therefore, the point slope form of the line is y + 8  = m(x + 3)

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Using the average sales per restaurant, the sales manager should report the Lemon-roasted chicken sandwiches as recording better sales performance than the Barbecued chicken sandwiches.

The averages represent the total sales generated at the lemon-roasted and barbecued restaurants, respectively, divided by the number in each group.

The average is the same as the mean of a data set.  It is computed by the mathematical operations of addition and division.

                                                        Lemon-roasted   Barbecued

The number of restaurants                        3                      5

Total sales during the testing period  6,000             7,200

Average sales per restaurant              2,000              1,440

Based on the average sales, the sales manager should report that the lemon-roasted chicken sandwiches are outperforming the barbecued restaurants.

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Answer:it’s (-1,8)

Step-by-step explanation:

Answer: Greater

Step-by-step explanation:

Answer:

179 is greater than 31

Answer:

30√2 cm

Step-by-step explanation:

Maximum length of the rod = Length of the diagonal of the cuboid

Length of diagonal of cuboid = [tex]\sqrt{l^2+w^2 + h^}[/tex]

where l = length, w =width and h = height

For this particular cuboid,

Diagonal length = [tex]\sqrt{30^2+24^2 + 18^2}[/tex]

[tex]\sqrt{800 + 576 + 324} \\\\\\= \sqrt{1500}\\\\= 30\sqrt{2} \text{ cm}[/tex]

Answer:

35

Step-by-step explanation:

90-55= 35 degress

Answer:

AB = 32

Step-by-step explanation:

Since line l bisects AB at point M, we have AM = MB.

[tex]4x = 5x - 4[/tex]

[tex]4x + 4 = 5x[/tex]

[tex]x = 4[/tex]

AM = 4(4) = 16, MB = 5(4) - 4 = 16.

So AB = AM + MB = 16 + 16 = 32.

Answer: 2 3/7

Step-by-step explanation:

Answer:numbers that are equal to 4/8 would be 2/4 and 1/2 and are you multiplying up?

Step-by-step explanation:

The number of Quarter coins that she has is 8 and the number of Dimes is 16.

It is given in the question that the woman has twice as many Dimes as the quarters in her purse.

We know that the value of Dimes is 0.10$ and the value of Quarters is

0.25 $

Let the number of Quarter coins is y and the number of Dimes coin be u.

According to the question above,

u = 2y  equation (i)

The total value z = 0.25y + 0.10u

Putting here the value of u from equation (i) we have,

z = 0.25y + 0.10(2y)

⇒ z = 0.25y + 0.20y

⇒ z = 0.45y equation (ii)

Now it has been mentioned that if the Dimes were Quarters and the Quarters were the Dimes, she would have $ 1.20 greater than she has now.

So we have,

z + 1.2 = 0.25u + 0.10y

Putting the value of u from above eqation (i),

z + 1.2 = 0.25(2y) + 0.10y

⇒ z + 1.2 = 0.50y + 0.10 y

⇒ z + 1.2 = 0.60y

Putting the value of z from equation (ii)

⇒ 0.45y + 1.2 = 0.60y

⇒ 0.45y - 0.60y = - 1.2

⇒ -0.15y = - 1.2

⇒ y = [tex]\frac{-1.2}{-0.15}[/tex]

⇒ y = 8

Therefore u = 2y

⇒ u = 2 x 8 = 16

Hence the number of Quarter coins is 8 and the number of Dimes is 16

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16 dimes, 8 quarters

I checked RSM it's correct

Probability that 5 of 6 stolen cars will be recovered with insurance records a car with a certain protection system will be recovered 91% of the time is equal to P(x=5)=0.3369 (approximately).

As given,

Insurance protection system recovered of a car=91%

p=0.91

q=1-p

 =1-0.91

 =0.09

n=6

x=5

Using Binomial theorem ,probability of 5 of 6 stolen cars will be recovered is:

ⁿCₓ(p)ˣ(q)ⁿ⁻ˣ

=⁶C₅(0.91)⁵(0.09)⁶⁻⁵

=[6!/(6-5)!5!] × (0.91)⁵× (0.09)

=6×(0.91)⁵×0.09

=0.3369

Therefore, probability that 5 of 6 stolen cars will be recovered with insurance records a car with a certain protection system will be recovered 91% of the time is equal to P(x=5)=0.3369 (approximately).

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Answer:

18 and 51

Step-by-step explanation:

the sum of the two other angles would be 69 degrees because there has to be 180 degrees in a triangle

given that we can create the equation 6x + 17x = 69 and solve for x

x = 3

so now we can plug in each part of that equation and find out the two angles

Answer:

11

Step-by-step explanation:

[tex]3^{2}[/tex] + 2

9 + 2

11

A. -234

B. -62

C. [tex]-72+151=79[/tex]

D. [tex]612+144=756[/tex]

least common mutiple of...

6 and 8: 24

8 and 12: 24

12 and 9: 36

6 and 9: 18

Answer:

see explanation

Step-by-step explanation:

given that V is directly proportional to h³ , then the equation relating them is

V = kh³ ← k is the constant of proportion

to find k use the condition V = 48 when h = 4 , then

48 = k × 4³ = 64k ( divide both sides by 64 )

[tex]\frac{48}{64}[/tex] = k , then k = 0.75

V = 0.75h³ ← equation of proportion

1

when h = 3 , then

V = 0.75 × 3³ = 0.75 × 27 = 20.25 cm³

2

when h = 6 , then

V = 0.75 × 6³ = 0.75 × 216 = 162 cm³

then

162 ÷ 20.25 = 8

the volume will be 8 times bigger

Answer:

[tex]\sqrt{5}[/tex]

Step-by-step explanation:

to simplify use the rule of radicals

[tex]\frac{\sqrt{x} }{\sqrt{y} }[/tex] ⇔ [tex]\sqrt{\frac{x}{y} }[/tex] , then

[tex]\frac{\sqrt{15} }{\sqrt{3} }[/tex] = [tex]\sqrt{\frac{15}{3} }[/tex] = [tex]\sqrt{5}[/tex]

The midpoint of the line segment given is (1, 4.5)

In geometry, the midpoint is the middle point of a line segment. It is equidistant from both endpoints, and it is the centroid both of the segment and of the endpoints. It bisects the segment equally into two halves.

The formula of midpoint of a line is given as

[tex]M_x_y = \frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}[/tex]

Substituting the given values;

[tex]M_x_y = \frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\\M_x_y = \frac{-2+4}{2}, \frac{7+2}{2} \\M_x_y = 1, \frac{9}{2} \\M_x_y = 1, 4.5[/tex]

The midpoint of the line AB is equal to (1, 4.5)

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The calculated answer after simplification in which Ryan has number of baseball cards is: 357 cards

How to simplify statement problems?

In mathematics, the statement based problems can be solved by forming the equations. And later, simplify those equation by equating to each other. This method is very common for the complicated problems to make the calculation easy.

According to the question, Ryan collected 2650 cards. In which, he has more baseball cards compared to football cards.

Now, let us assume, baseball cards be 'B'; football cards be 'F' and hockey cards be 'H'.

As per the question, the formed equation from the statement for the simplification is:

B + F + H = 2650

3B = F and H + 150 = F

Substituting above values in the formed equation to get the simplify answer,

B + 3B + 3B - 150 = 2650 ⇒ 7B = 2500 ⇒ B = 357

Now, the value of football cards is: F = 3(357) = 1071

And, the value of hockey cards is: H = 1071 - 150 = 921

Hence, after simplification Ryan has number of baseball cards is: 357 cards

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Answer:

  AB, DC, ED, GA

Step-by-step explanation:

You want to identify the segments that are skew to edge FH of cuboid ABCDEFGH.

Two lines are skew when no plane exists that can contain them both. That is, skew lines are not parallel and do not intersect.

Cuboid ABCDEFGH has 12 edges. Of those, 3 are parallel to FH, and 4 intersect FH. The remaining edges are skew to FH:

  AB, DC, ED, GA . . . . . segments skew to FH

Answer:

he has 556 pages in his book

Answer:

Slope:

JK = (1/3)

LK = (-2)

ML = (2/5)

MJ = (-3/2)

Quadrilateral JKLM is not a parallelogram because the slopes don't match.

Step-by-step explanation:

Slope = m

JK = (-4, 1), (2, 3)

       (x₁, y₁)  (x₂, y₂)

        y₂ - y₁         3 - 1               2            2           1

m = ------------ = ------------- = ---------- = --------- = -------

        x₂ - x₁         2 - (-4)         2 + 4         6           3

----------------------------------------------------------------------------------------------------------

LK = (5, -3), (2, 3)

       (x₁, y₁)  (x₂, y₂)

        y₂ - y₁         3 - (-3)        3 + 3          6

m = ------------ = ------------- = ---------- = --------- = -2

        x₂ - x₁         2 - 5              -3           -3

----------------------------------------------------------------------------------------------------------

ML = (0, -5), (5, -3)

       (x₁, y₁)  (x₂, y₂)

        y₂ - y₁        -3 - (-5)      -3 + 5         2

m = ------------ = ------------- = ---------- = ---------

        x₂ - x₁         5 - 0              5            5

----------------------------------------------------------------------------------------------------------

MJ = (0, -5), (-4, 1)

       (x₁, y₁)  (x₂, y₂)

        y₂ - y₁        1 - (-5)         1 + 5          6          -3

m = ------------ = ------------- = ---------- = --------- = -------

        x₂ - x₁         -4 - 0            -4            -4          2

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I hope this helps!