Jose bought 3 pens and 6 pencils for $6.60. Amy bought 5 pens and 8 pencils for $10.00. How much does one pencil cost?
Appreciate it :)

Answer:

y= -1/3x-4

y=2x+2

Step-by-step explanation:

the slope is rise over run

Answer: b. Every 18 minutes, 28 more pizzas were set out on the buffet.

Step-by-step explanation:

The equation is in the form: y = mx + c

m is the gradient which represents the rate of change per a given value of x.

x here is every 9 minutes after 11:00. Every 18 minutes therefore will give x a value of 2 because 18/9 = 2.

The rate of change every 18 minutes is therefore;

= 14 * 2

= 28 pizzas

Answer:

Step-by-step explanation:

the 1st one is 1735

The 2nd one is 1573

Answer:

8 hours

Step-by-step explanation:

In the problem, it gives you the formula: d=rt, and in the rest of the problem it gives you the distance and the rate, so all you have to do is plug the numbers in and solve.

360m = 45mph(t)

Isolate the variable by dividing 360 by 45

360/45 = t

8 = t

This means that it will take 8 hours to travel 360 miles at a rate of 45 miles per hour.

Hope this helps :)

Final Answer: [tex]x = \frac{5y}{3}[/tex], [tex]y = 15[/tex]

Steps/Reasons/Explanation:

Question: [tex]\frac{x}{5} = \frac{y}{3}[/tex] and [tex]\frac{12}{y} = \frac{4}{5}[/tex]. What does [tex]x[/tex] equal and what does [tex]y[/tex] equal and how?

Solving for [tex]x[/tex] in the equation [tex]\frac{x}{5} = \frac{y}{3}[/tex].

Step 1: Multiply both sides by [tex]5[/tex].

[tex]x = \frac{y}{3} * 5[/tex]

Step 2: Simplify [tex]\frac{y}{3} * 5[/tex] to [tex]\frac{y * 5}{3}[/tex].

[tex]x = \frac{y * 5}{3}[/tex]

Step 3: Regroup terms.

[tex]x = \frac{5y}{3}[/tex]

Solving for [tex]y[/tex] in the equation [tex]\frac{12}{y} = \frac{4}{5}[/tex].

Step 1: Multiply both sides by [tex]y[/tex].

[tex]12 = \frac{4}{5}y[/tex]

Step 2: Simplify [tex]\frac{4}{5}y[/tex] to [tex]\frac{4y}{5}[/tex].

[tex]12 = \frac{4y}{5}[/tex]

Step 3: Multiply both sides by [tex]5[/tex].

[tex]12 * 5 = 4y[/tex]

Step 4: Simplify [tex]12 * 5[/tex] to [tex]60[/tex].

[tex]60 = 4y[/tex]

Step 5: Divide both sides by [tex]4[/tex].

[tex]\frac{60}{4} = y[/tex]

Step 6: Simplify [tex]\frac{60}{4}[/tex] to [tex]15[/tex].

[tex]15 = y[/tex]

Step 7: Switch sides.

[tex]y = 15[/tex]

~I hope I helped you :)~

Answer:

The girl was 144cm tall

Step-by-step explanation:

Total height of the three boys=3×156=468

Total height of the four children=4×153=612

Height of the girl=612-468=144cm

The average height of 3 boys was 156cm. Therefore, The girl was 144cm tall.

Let the thing that is changing be y and the thing with which the rate is being compared is x, then we have the average rate of change of y as x changes as:

[tex]\text{Average rate} = \dfrac{y_2 - y_1}{x_2 - x_1}[/tex]

The average height of 3 boys was 156cm.

When a girl joined them, the average height of the 4 children was 153cm.

Total height of the three boys = 3 × 156 = 468

Total height of the four children = 4 × 153 = 612

Height of the girl  = 612 - 468 = 144cm

Hence, the girl was 144cm tall.

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Answer:

2/5

Step-by-step explanation:

2/10+2/10=4/10

4/10 divided by 2/2= 2/5

Hope this helps!

Answer;

2/10 + 2/10 is 4/10 and then simplified it would be 2/5 because 2 goes into both 4 and 10.

2/10 + 2/10 = 4/10

4/10 = 2/5

Hope this Helps!

I believe it would be 60, 60 is the only multiple for 6.

Answer:

16. [tex]x = 80^\circ[/tex]

17. [tex]x = 55, y =70, z = 55[/tex]

18. [tex]x =8, y =3[/tex]

19. [tex]r = 66^\circ[/tex], [tex]t = 73^\circ[/tex]

20. [tex]y = 70^\circ, x = 55^\circ[/tex]

21. [tex]x =56^\circ, y = 62^\circ[/tex]

Step-by-step explanation:

16. Side [tex]AB = AC[/tex]

So, the opposite angles of the triangle will also be equal.

[tex]\angle B =\angle C = 50^\circ[/tex]

Using triangle sum property, angle of all the internal angles of a triangle is equal to [tex]180^\circ[/tex].

[tex]50+50+x = 180\\\Rightarrow x = \bold{80^\circ}[/tex]

17. Two sides are given as equal, [tex]x = z[/tex]

Angles on a straight line are always equal to [tex]180^\circ[/tex].

So,

[tex]x + 125 = 180\\\Rightarrow x = 55[/tex]

[tex]z = 55[/tex]

Using triangle sum property, angle of all the internal angles of a triangle is equal to [tex]180^\circ[/tex].

[tex]55+55+y = 180\\\Rightarrow y = \bold{70^\circ}[/tex]

18. All the angles are given equal to each other, therefore all the sides of the triangle will also be equal to each other.

[tex]4x+7 = 13y =39[/tex]

[tex]13y = 39\\\Rightarrow y = 3[/tex]

[tex]4x +7 = 39\\\Rightarrow 4x = 32\\\Rightarrow x = 8[/tex]

19. Two sides are given equal to each other, therefore angles opposite to them will be equal.

Using the triangle sum property in the left triangle:

[tex]r + 57 + 57 = 180\\\Rightarrow r = 66^\circ[/tex]

Using the property that vertically opposite angles are equal and the triangle sum property in the right triangle.

[tex]t+50+57 = 180 \\\Rightarrow t = 73^\circ[/tex]

20. All the sides are given equal to each other.

So, all the angles will be equal to [tex]60^\circ[/tex].

[tex]y - 10 = 60\\\Rightarrow y = 70^\circ[/tex]

[tex]x+5=60\\\Rightarrow x = 55^\circ[/tex]

21. Angles on a straight line are always equal to [tex]180^\circ[/tex].

Angles opposite to equal sides in a triangle are also equal.

[tex]118 + y = 180\\\Rightarrow y = 62^\circ[/tex]

Using triangle sum property:

[tex]x+2y = 180\\\Rightarrow x = 180 - 124 = \bold{56^\circ}[/tex]

Answer:  They spent $100 on ice cream.

Step-by-step explanation:

Given : Total friends  = 5

They bought each $24 worth of toppings.

Total price of toppings = (Total friends ) x (Worth of each topping)

= 5 x ($24)

= $ 120

Total expense = $220

Money amount on ice cream = (Total expense) - (Total price of toppings)

= $220 - $120

= $100

Hence, they spent $100 on ice cream.

Answer:

6.26666666667, your welcome :)

Answer:

x = -4,  y = 3/2

Step-by-step explanation:

simplify the 1st equation by dividing each term by 4 to get:

x + 2y = -1

-5x + 2y = 23

Subtract to get: 6x = -24

x = -4

find 'y':    2y - 5(-4) = 23

               2y + 20 = 23

               2y = 3

                y = 3/2

Answer:

y is equal to 1.5, and x is equal to -4

Step-by-step explanation:

given:

[tex]4x + 8y = -4[/tex]

[tex]2y - 5x = 23[/tex]

We can start by factoring 4 out of the first equation:

[tex]x + 2y = -1[/tex]

Now let's multiply it by -5:

[tex]-5x - 10y = 5[/tex]

We'll rearrange the other equation to match that (just for clarity):

[tex]-5x + 2y = 23[/tex]

Now let's subtract the modified equation from that:

[tex]\begin{array}{c}-5x + 2y = 23\\-5x - 10y = 5\\ \ \ \ \ \ \ \ \ \ \ 12y = 18\end{array}[/tex]

So y is equal to 18/12, or 1.5

Let's plug that into one of the first equations and see what we get:

[tex]2y - 5x = 23\\2(1.5) - 5x = 23\\3 - 5x = 23\\-5x = 20\\x = -4[/tex]

Giving us an x value of negative four.  Let's plug that into the other equation to confirm:

[tex]4x + 8y = -4\\4(-4) + 8y = -4\\-16 + 8y = -4\\-4 + 2y = -1\\2y = 3\\y = 1.5[/tex]

That matches up, so our answer is correct.

Answer:

C. [tex]\sqrt{18}[/tex]

Step-by-step explanation:

[tex]\frac{4\pi }{\pi }[/tex] = 4(whole number)

[tex]\sqrt{ 6^{2}}[/tex] = 6(whole number)

[tex]\sqrt{18}[/tex] = 4.2426406871192851464050661726291(goes on and on)

21.989(terminating number)

Irrational numbers are un-whole numbers that do not terminate and cannot be turned into a fraction.

The irrational number number in the options is C. √18.

Rational numbers are numbers which can be written in the form of a/b, b ≠ 0, and a and b are integers.

Irrational numbers cannot be written in this form.

Given options are 4π/π, √(6²), √18 and 21.989.

4π/π can be written as 4, which is a whole number and thus a rational number.

So, 4π/π is a rational number.

√(6²) = 6, which is also a rational number since it is a whole number.

√18 does not have a decimal which is ending.

So it is an irrational number.

21.989 has only 3 decimal places and can be written as 21989/1000 and is thus a rational number.

Hence the correct option is C.

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total number of marbles= 5+2+3+5 = 15 marbles

probability of a red marble - 2/15

probability of yellow marble - 5/15 = 1/3

Answer:

i) 2/15 ii) 1/3

Step-by-step explanation:

the number of marbles all together is 15

2 out of the 15 are red, so 2/15

5 out of 15 are yellow,so 5/15, simplified to 1/3

Answer:

32 words per minute

Answer:

89.5

Step-by-step explanation:

59.5

30.0

89.5

Answer:

34 is the asnwer congruent thats why.

Step-by-step explanation:

Answer:

B cuz both can be divided by 7

Answer: A

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

Hope it can help you.........

Answer:

Thus, the value of x = -36 when y = 15

Step-by-step explanation:

We know that if y varies directly with x, we can express the relationship such as

y ∝ x

y = kx

k = y/x

where 'k' is called constant of variation.

Given

y = -5

x = 12

Using the equation

k = y/x = -5/12

Thus, the value of k = -5/12

Finding x when y = 15

y = 15

k = -5/12

substituting y = 15 and k = -5/12 in the equation

y = kx

15 = -5/12 (x)

15×12 = -5x

180 = -5x

divding both sides by -5

-5x/-5 = 180/-5

x = -36

Thus, the value of x = -36 when y = 15

Given:

[tex]0.5(4x-8)+11=0.25(12x+20)-5[/tex]

To find:

The value of x.

Solution:

We have,

[tex]0.5(4x-8)+11=0.25(12x+20)-5[/tex]

Using distributive property, we get

[tex]0.5(4x)+0.5(-8)+11=0.25(12x)+0.25(20)-5[/tex]

[tex]2x-4+11=3x+5-5[/tex]

[tex]2x+7=3x[/tex]

Subtract 2x from both sides.

[tex]7=3x-2x[/tex]

[tex]7=x[/tex]

Therefore, the value of x is 7.

Answer:

Trey lives 384 feet.

Step-by-step explanation:

Let the average rate be represented by s, and the distance by d.

speed = [tex]\frac{distance}{time}[/tex]

⇒ distance = speed x time

i.e d = s x t

On his first trip,

d = s x 8

d = 8s ............ 1

on his trip home, the average rate was 16 miles per hour faster, so that;

d = (s + 16) x 6

d = 6s + 96 ............ 2

Equation 1 and 2, we have;

8s = 6s + 96

8s - 6s = 96

2s = 96

s = 48

The average rate is 48 miles per hour.

Thus from equation 1 (also equation 2 can be used),

d = 48 x 8

  = 384

Therefore, Trey lives 384 feet from the mountains.

Answer:

44

Step-by-step explanation:

Given that:

Fiona, Peter and Angad share some sweets in the ratio 5:4:3. Fiona gets 22 more

sweets than Angad. How many sweets does Peter get?

5 : 4 : 3

Total ratio = (5 + 4 + 3) = 12

Let total number of sweets = x

For Fiona :

(5 / 12) * x = 5x / 12

Peter :

(4 / 12) * x = 4x / 12

Angad:

(3 / 12) * x = 3x / 12

Sunce, Fiona gets 22 more Than Angad ;

Then;

5x / 12 = 22 + 3x /12

5x/12 = 22 + 3x/12

5x/12 - 3x/12 = 22

(5x - 3x) / 12 = 22

2x / 12 = 22

2x = 22 * 12

2x = 264

x = 132

Hence, total number of sweets = 132

Peter's share = (4x / 12) = (4 * 132) / 12 = 528/12 = 44

Peter got 44 sweets

Answer:

10 cups is 2.5 quarts

Answer:

2 1/2.

Step-by-step explanation:

Four quarts in a gallon, four cups in a quart, 16 oz in a cup, 8 oz in half a cup.

       Brainliest?

Answer:

the interest =20.74

whereas the total sum=8850(the sum is the nearest cent)

Answer:

The answer is C

Step-by-step explanation:

This is right because that's what I did

From the options given, the angles that form a linear pair are: c. m∠MRN and m∠NRO

The 3 lines are shown in the image attached below.

In the diagram, there are two linear pairs that are formed, they are:

Therefore, from the options given, the angles that form a linear pair are: c. m∠MRN and m∠NRO

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Answer:

Slope is -2/5 and y-intercept is -1/3

Step-by-step explanation:

To get the slope, we pick any two points and apply the slope formula

The slope formula is;

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

To get the slope, we select any two points

That will be;

(-3/4, -1/30) and (1/4,-13/30)

Substituting these in the slope formula, we have:

m = (-13/30 + 1/30)/(1/4 + 3/4)

m = 12/30 = -2/5

Generally, the equation of a straight line is;

y = mx + b

m is slope and b is the y-intercept

We already have the slope, to get the y-intercept, we select any of the points

-3/5 = -2/5(2/3) + b

= -3/5 + 4/15 = b

b = (-9 + 4)/15 = -5/15 = -1/3

Slope is -2/5 and y-intercept is -1/3

Answer:

A

Step-by-step explanation:

The slope is -2/5, and the y-intercept is -1/3.