If triangles MNP is an equilateral triangle, find x and the measure of each side.

Answer:

10.50p+15≤65

p≤ 100/21

Step-by-step explanation:

Let p represent pounds of Pumpkin Spice coffee.

We have been given that Lydia is at a coffee shop and knows she can spend no more than $65 before tax. She sees this price list in the coffee shop.

Item Price per pound

Dark Roast Coffee

$7.50

Pumpkin Spice Coffee

$10.50

Breakfast Tea

$23.50

Lydia wants to buy 2 pounds of Dark Roast coffee, so the cost of 2 pounds of Dark Roast coffee would be $7.50×2=$15 .

We are told that cost of each pound of Pumpkin Spice coffee is 10.50,socostof′ p'

pounds of Pumpkin Spice coffee would be 10.50

Since Lydia can spend no more than $65 before tax, so the cost of 2 pounds of Dark Roast coffee and 'p' pounds of Pumpkin Spice coffee must be less than or equal to 65.

We can represent this information in an inequality as:

10.50p+15≤65

Therefore, our required inequality would be 10.50p+15≤65

10.50+15-15≤65-75

10.50≤50

Divide both sides by 10.50:

10.50p/10.50 ≤ 50/10.50

P ≤ 50*2/10.50*2

P ≤ 100/21

P ≤ 4.76190

Therefore, Lydia can buy less than or equal to 100/21 pounds of Pumpkin Spice coffee.

An equation showing how many of each nut this nut bread contains is Y = 2p + 4w + 2t.

An equation is a mathematical expression of equality between two variables or expressions.

Equations are shown using the equation mark, symbol, or sign (=).

The number of walnuts in the nut bread = 1/2

The number of pecan nuts = 2

The number of walnuts which is double of pecan nuts = 4 (2 x 2)

The number of other nuts = 2 since walnuts equal 1/2 of the nuts

The total number of nuts = 8 (2 pecan, 4 walnuts, and 2 others)

Let the number of nuts in the bread = Y

Let the number of walnuts, w = 4

Let the number of pecan nuts, p = 2

Let the number of other nuts, t = 2 (8 - 4 - 2)

Thus, the equation of each nut contained in the nut bread is Y = 2p + 4w + 2t.

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According to the given number line A is on -7, X is on -2 and E is on 8.

As you can observe in the image below, X is 5 units away from A. At the same time, X is 10 units away from E.

The ratio of this relation would be 2:1 from E to A.

Kelly will take 5.64 minutes more to wash the car as compared to Kelly and Libby when they are working together

Time taken by Kelly to wash the car = 13 minutes

Time taken by Libby to wash the car = 17 minutes

Time taken by Kelly and Libby to wash the car together:

LCM of 13 and 17 is 221. So, the total work required to be done is 221 units

Hence, Kelly does 17 units of work each minute and Libby does 13 units of work each minute

If both work together, they will finish the work in = Total work required to be done/ Work done in a minute by Kelly + Work done in a minute by Libby

= 221/(17+13)

= 221/30 = 7.36 minutes

The extra time taken by Kelly working alone = 13-7.36  = 5.64 minutes

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To calculate the volume of a cylinder you have to multiply the area of the circle by the height of the cylinder.

We know that the radius of the circle is r=4 and the height of the cylinder is h=7, replace both values on the formula to determine the volume:

The volume of the cylinder is approximately 351.86 cubic units.

The circumference of a circle is given by the formula:

The diameter of the circle, d = 18cm

Radius = diameter / 2

r = d/2

r = 18/2

r = 9 cm

Answer: The new ratio of blue to yellow dye in its simplest form is 8/5.

Step-by-step explanation:

Blue and yellow dyes are mixed in an 8: 3 ratio to make 44 liters of a green-colored dye. A further 8 liters of yellow dye are added to the mixture. What is the new ratio of blue to yellow dye in its simplest form?

What is the Ratio?

The ratio can be defined as the comparison of the fraction of one quantity towards others. e.g.- water in milk.

Calculating the fraction of blue and yellow in the green dye,

Blue dye = 8/(3+8) * 44

Blue dye = 8/11 * 44

Blue dye = 32 liters

Similarly,

yellow dye = 3/11*44

yellow dye = 12

Now

Blue dye + yellow dye = 32+12 = 44

Now yellow dye is increased by 8 liters

the new volume fraction of yellow dye = 12+8

= 20

a fraction of blue dye remains the same,

the ratio of blue dye to new yellow dye in teal color.

= 32/20

=8/5

Thus, the new ratio of blue to yellow dye in its simplest form is 8/5.

Answer:

8/5

Step-by-step explanation:

Answer: (3x + 4)^2

Step-by-step explanation:

I think of a number => x

Multiply it by 3 => 3x

Add 4 => 3x + 4

Square the result => (3x + 4)^2

Given: Several students use stopwatches to measure how quickly a sensitive plant reacts to stimuli. They record the times in milliseconds.

Required: To determine which kind of data the students are recording.

Explanation: The given kinds of data can be summarized as follows-

→Qualitative data determines the quality of a single data. Example: The colour of cars in a parking lot.

→Audio data have the data in the form of audio. Example: The sound of different dogs barking.

→Quantitative data represents the quantity of some data. Example: Recording the number of the height of students in a class.

→Categorical Data represents the data of various categories. Example- Recording some person's age, sex, hair colour, etc.

Hence, measuring how quickly a sensitive plant reacts to stimuli is an example of Qualitative Data.

Final Answer: Option A (Qualitative Data) is correct.

Given the points: (1, 9) and (4, 3)

To find the slope:

m = -2

The average rate of change of f(x) on the interval [4, 8] is 21.

For a function f(x), the rate of change on an interval [a, b] is given by:

R = ( f(b) - f(a))/(b - a)

In this case the function is:

f(x) = x² + 9x

And the interval is [4, 8]

Then the rate of change is

R = ( f(8) - f(4))/(8 - 4)

we will get:

f(8) = 8² + 9*8 = 136

f(4) = 4² + 9*4 + 16 + 36 = 52

Replacing that we get:

R = (136 - 52)/4 = 21

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In order to add those fractions, we need to write them using a commom denominator. We can do so by finding a common multiple for the original denominators:

6, 4 and 3

Since 12 is a multiple of those three numbers, we can use 12 as a new denominator for each of the fractions:

5/6 = (5 * 2)/(6 * 2) = 10/12

3/4 = (3 * 3)/(4 * 3) = 9/12

2/3 = (2 * 4)/(3 * 4) = 8/12

Notice that 10/12 is equivalent to the the original fraction 5/6, because we obtained 10/12 by multiplying both the numerator and the denominator by the same factor. The same applies to the other pairs of fractions.

Now, we can add:

5/6 + 3/4 + 2/3 = 10/12 + 9/12 + 8/12

= (10 + 9 + 8)/12

= 27/12

Now, we can simplify the result by dividing both the numerator and the denominator by the same factor. Since both 27 and 12 are multiples of 3, we can write:

27/12 = (27 : 3)/(12 : 3)

= 9/4

Now, since 9 is greater than 4, we can write the fraction 9/4 as a mixed number:

9 = 8 + 1

= 2*4 + 1

9/4 = (2*4 + 1)/4

= 2*4/4 + 1/4

= 2 + 1/4

= 2 1/4 (using the notation of mixed number)

SOLUTION

Equation of a parabola is given by the equation

Where (h, h) are the coordinates of the vertex.

From the question given, the vertex is (2, 0)

So, h = 2, k = 0.

The y-intercept is given as (0, 12).

So, this means that x = 0 and y = 12

Substituting the values for h, k, x and y into the equation we have

Now, let's substitute the value of a into the equation to get equation for the parabola.

This becomes

We are to solve the equations

The equation can be rewritten as

Using substitution method

From equation 1

Substitute 1 - 2x for y into equation 2

This gives

Therefore, x = 2

Substitute 2 for x into equation 3

This gives

Therefore the solution to the equations is

x = 2, y = -3

504 bandages if it is each bandage is 3 cents.

Given,

Mr. Kermshner has 168 bandages march through June.

To find the how much is it if each bandage is 3 cents ?

Now, According to the question,

Based on the given conditions,

Formulate:

Total bandage is 168

and, each bandage is 3 cents

= 168 x 3

= 504

Alternative form = 5.04 x 10^2

Hence, 504 bandages if it is each bandage is 3 cents.

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Given:

There are given two equations:

Explanation:

To find the value by using the elimination method, we need to multiply by 4 into the equation (1) and 1 into the multiply by (2):

Then,

From the equation (1):

And,

From the equation (2):

Now,

From the equation (3) and equation (4):

Then,

Now,

Put the value of y into the equation (3):

Final answer:

Hence, the value of x and y is shown below:

Answer:

1. f(4) = 4

2. g(2) = -4

3. f(-5) = -14

4. g(-3) = 21

5. f(0) = -4

6. g(0) = 0
7. f(3) - 1 = 1

8. f(1/4) = -3.5 or -7/2

9. g(1/4) = -0.9375 or -15/16

10. f(a^2) = 2a^2 - 4

11. f(k+1) = 2k - 2

12. g(2n) = 2n^2 - 8n

13. f(3x) = 6x - 4

14. f(2) + 3 = 3

15. g(-4) = 32

Step-by-step explanation:

here’s a pic of my work:

Answer:

Yes

Step-by-step explanation:

The number of height is also the number of wegt

Answer: A = 7x

Step-by-step explanation:

Area = Length x  Width

A = L * W

L = 5x + 1        W = x

Plug the length and width into the equation for area.

A = (5x + 1) * x

A = 6x + x

A = 7x

Answer:

Easy;

Substitute m (miles) for 45.

250+6(45)

(6 dollars per mile, times 45 miles, plus the 250 flat rate)

250+270

520

So you would be charged 520 dollars total at the end of the evening.

Hope this helped!

Given that the radius of a circle is;

Recall that the area of a circle can be calculated using the formula;

substituting the value of r;

Therefore

number of banjos that have 5 or 6 strings: 4 + 8 + 8 + 3 = 23

total number of banjos: 6 + 4 + 4 + 8 + 8 + 3

The equation for H, in terns of t, representing the height , in inches, of the plant tt months after Lucy bought the plant is :

H=12+2t

Given, A plant that Lucy had purchased was placed in a pot next to a window in her home. The plant initially stood 12 inches tall and grew at a rate of 2 inches per month.

from the given information, the equation can be framed as:

H = 12 +2t

where the initial height of the plant is increased at a rate of two inches every month.

from the table substitute the value of months in t, to find the height of the plant in that particular month.

t = 0

H=12+2(0)

H=12

hence when t=0 then H=12

t=1

H=12+2(1)

H=12+2

H=14

after a month the height of the plant changes to 14 inches.

t=2

H=12+2(2)

H=12+4

H=16

after two months the height changes to 16 inches.

t=3

H=12+2(3)

H=12+6

H=18

after three months the height changes to 18 months.

t=4

H=12+2(4)

H=12+8

H=20

finally after four months the height of the plant changes to 20 months.

hence we get the required equation as H=12+2t

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The velocity of a body as a function of time is given as Vt=5e-2t+4 where t is in seconds, and V is in ms acceleration at t = 0.6s is -10x 0.30119m/[tex]s^{2}[/tex].

The velocity of a body  is given by

Vt=5e-2t+4

acceleration a(t)= [tex]v'(t)[/tex]

                           =   d/dt  [tex]v'(t)[/tex]

                          =  d/dt  5e-2t+4

                         = -10[tex]e^{-2t}[/tex]

put t = 0.6

acceleration at t= 0.6= a(0.6)

                            = [tex]-10e^{-2\times0.6}[/tex]

                            = -10x [tex]e^{-12}[/tex]

                            = -10x 0.30119m/[tex]s^{2}[/tex]

acceleration is the rate of change of the speed of an object with respect to time. Accelerations are vector quantities. The direction of the target's acceleration is obtained from the direction of the net force  on the target.

Three types of accelerated motion

The term uniform acceleration refers to  motion in which an object moves in a straight line with increasing speed at equal intervals of time.

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Probability = required outcome /all possible outcome

You have 5 cards on the deck. The exercise has reposition, i.e. you put the card back into the deck before picking the next one, so the total number of cards is always 5.

all possible outcome = 5

Divisor of 6 = 3, 6

Probability of picking a divisor of 6 = 2/5

Number less than 5 are : 3 and 4 = 2/5

The intersection between both events is equal to the product of both probabilities since the events are independent.

The probability of picking a divisor of 6 and then picking a number less than 5 is:

P(divisor of 6) and P(no.less than 5) = 2/5 * 2/5 = 4/25

The solution of the inequality −2p + 4.5 < −2.9 is number line with open circle plotted at 3.7 and arrow pointing right, the graph of the inequality  has been plotted.

The inequality is −2p + 4.5 < −2.9

Subtract 4.5 from both side

-2p + 4.5 - 4.5 <-2.9 - 4.5

-2p < -7.4

Divide both sides by -2

-2p/-2 < -7.4/-2

p > 3.7

Draw the graph using the result of the inequality

Hence, the solution of the inequality −2p + 4.5 < −2.9 is number line with open circle plotted at 3.7 and arrow pointing right, the graph of the inequality  graph has been plotted.

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Answer:

number line with open circle plotted at 3.7 and arrow pointing right

Step-by-step explanation:

hope this helps :)

The circumference, C, of a circle is computed as follows:

where D is the diameter of the circle. Substituting with D = 14 ft, we get:

The circumference of the trampoline is approximately 44 feet