Two sides of a triangle measure 15 inches and 18 inches, respectively. which of these is not a possible length for the third side of the triangle?
a.4 inches
b.18 inches
c.24 inches
d.36 inches

It would take the newer pump 4.5 hours to drain the pool working alone.

Given that,

It takes an older pump twice as long to drain a certain pool as it does a newer pump.

Let us assume that,

The time it takes for the newer pump to drain the pool alone is x hours.

Hence, According to the information given, the older pump takes twice as long, so it would take 2x hour to drain the pool alone.

Now, When both pumps work together, their combined rate of draining the pool is additive.

Therefore, the equation is,

[tex]\dfrac{1}{x} + \dfrac{1}{2x} = \dfrac{1}{3}[/tex]

Simplify the equation for x,

[tex]\dfrac{(2 + 1)}{2x} = \dfrac{1}{3}[/tex]

[tex]\dfrac{(3)}{2x} = \dfrac{1}{3}[/tex]

Cross multiplication,

[tex]3 \times 3 = 2x[/tex]

[tex]2x = 9[/tex]

Dividing both sides by 2:

[tex]x = 4.5[/tex]

Therefore, it would take the newer pump 4.5 hours to drain the pool working alone.

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The amount of oil, in ounces, in the fuel mix can be found using a proportion with the given ratio and the amount of gasoline.

To find the number of ounces of oil, we need to use the given ratio and the amount of gasoline. The ratio of oil to gasoline is 5:18, meaning that for every 5 ounces of oil, there are 18 gallons of gasoline. Since we know that there are 36 gallons of gasoline, we can set up a proportion to find the number of ounces of oil:

5 ounces / 18 gallons = x ounces / 36 gallons

Cross multiplying, we get:

18x = 5 * 36

Simplifying further:

18x = 180

Dividing both sides by 18, we get:

x = 10 ounces

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a =16 is the solution of the given equation.

To solve the equation 6 = a/4 + 2, we'll perform two steps to isolate the variable 'a'.

Step 1: Subtract 2 from both sides of the equation:

6 - 2 = a/4 + 2 - 2

4 = a/4

Step 2: Multiply both sides of the equation by 4 to get rid of the fraction:

4 * 4 = (a/4) * 4

16 = a

Therefore, the solution to the equation is a = 16.

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Answer:

A. 55 dimes and 165 quarters

Step-by-step explanation:

Given,

The number of pennies in the Jar = 220,

∵ There are 3 quarters for every 4 pennies,

i.e. 4 pennies = 3 quarters,

⇒ 1 penny = [tex]\frac{3}{4}[/tex] quarter

⇒ 220 pennies = [tex]220\times \frac{3}{4}[/tex]

[tex]=\frac{660}{4}[/tex]

= 165 quarter.

Therefore, there are 165 quarters.

Now, there is 1 dime for every 3 quarters,

i.e.  3 quarters = 1 dime

⇒ 1 quarter = [tex]\frac{1}{3}[/tex] dime,

⇒ 165 quarters = [tex]\frac{165}{3}[/tex] = 55 dimes.

Therefore, there are 55 dimes.

Option 'A' is correct.

It is found that there are 43,800 minutes in a month.

Multiplication is the mathematical operation that is used to determine the product of two or more numbers. If an event can occur in m different ways and a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.

We knowt that there are 365 days per year, 24 hours per day, 12 months per year, and 60 minutes per hour.

1 day = 24 hour

1 hour = 60 minutes.

1 minutes = 60 seconds

Therefore, 24 hours = 24 x 60 = 1440 minutes

There are 1440 minutes in one day.

Then 30 days = 30 x 1440 = 43,800

Hence, It is found that there are 43,800 minutes in a month.

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Answer:

option 3 aka c

Step-by-step explanation:

Answer: 1. A) 3x−4y=10

2. [tex]y=-\frac{x}{4}+3[/tex]

3. In the attachment.

Explanation:

1. Given equation=[tex]y=\frac{3}{4}x-\frac{5}{2}[/tex]

To reduce it into standard form , multiply both sides by 4,we get

[tex]4y=4(\frac{3}{4}x-\frac{5}{2})\\\Rightarrow4y=3x-10......[distributive\ property]\\\Rightarrow3x-4y=10[/tex] which is option A.

2. Given linear equation : x+4y=12

The standard slope intercept form is given by y=mx+c where m is the slope and c is the constant.

To reduce given linear equation subtract x from both sides, we get

4y=12-x

Divide 4 on both sides.

[tex]\Rightarrow\ y=\frac{12-x}{4}=3-\frac{x}{4}\\\Rightarrow\ y=-\frac{x}{4}+3[/tex] is the slope-intercept form of the linear equation x + 4y = 12.

3. To graph equation [tex]y=\frac{1}{2}x[/tex] on the coordinate plane.

We need to find points to plot the line

Put x=0,we get y=0

Put x=2,we get y=1

Thus we have points (0,0) and (2,1) to plot the line on the graph.

Answer: 1. A) 3x−4y=10

Step-by-step explanation:

Answer:

the answer would be B. N=4

Answer:

Step-by-step explanation:

y=−7x+3x intercept when y = 0so-7x + 3 = 0-7x = -3   x = 3/7y intercept when x = 0 so y = 3

answer

x intercept (3/7 , 0)y intercept (0, 3)

perimeter = 2l +2w

length = 22

perimeter = 60

 60 = 2(22) +2w

60 = 44 +2w

 subtract 44 from both sides

16 = 2w

w = 16/2

w = 8

 width is 8 inches

Final answer:

The expected number of heads and tails when tossing a coin 10 times is 5 each.

Explanation:

If you toss a coin ten times:

Expected number of heads: 5

Expected number of tails: 5

This is because for each toss, the probability of getting a head is 0.5 (50%) and the same for a tail. Over multiple tosses, the outcomes tend to approach these expected values.

the value of (t) that satisfies the equation is approximately (37.6992).

Let's solve the equation [tex]\(-\frac{t}{4} = -3\pi\) for \(t\).[/tex]

Step 1: Multiply both sides by \(-4\) to isolate \(t\).

[tex]\[-\frac{t}{4} \times (-4) = -3\pi \times (-4)\][/tex]

This simplifies to:

[tex]\[ t = 12\pi \][/tex]

Step 2: Substitute the value of \(\pi\) to get the final answer.

[tex]\[ t = 12 \times 3.14159 \][/tex]

[tex]\[ t = 37.6992 \][/tex]

Therefore, the value of ( t ) is approximately ( 37.6992 ).

To solve the equation [tex]\(-\frac{t}{4} = -3\pi\) for \(t\)[/tex] , we first want to isolate (t) on one side of the equation. To do this, we can multiply both sides of the equation by (-4). This cancels out the fraction and leaves us with (t) on the left side:

[tex]\[-\frac{t}{4} \times (-4) = -3\pi \times (-4) \\t = 12\pi\][/tex]

Now, to get the numerical value of \(t\), we substitute the value of \(\pi\), which is approximately \(3.14159\), into the equation:

[tex]\[ t = 12 \times 3.14159 \][/tex]

[tex]\[ t \approx 37.6992 \][/tex]

Therefore, the value of (t) that satisfies the equation is approximately (37.6992).

complete question

−t/4=−3π

What is the answer to T

Answer:

The correct answer is f(-2)= -2

Step-by-step explanation:

Answer: The cost of 1 lemon is $1.2 and the cost of 1 lime is $0.4.

Step-by-step explanation:

Let x be the cost of 1 lemon and y be the cost of 1 lime.

Then for Ray, the equation representing total price will be :-

[tex]5x+3y=7.20[/tex]................................(1)

For Lia, the equation representing total price will be :-

[tex]4x+6y=7.20[/tex]..................................(2)

Dividing 2 on the both sides of equation (2), we get

[tex]2x+3y=3.60[/tex]...............................(3)

Subtracting (3) from (1), we get

[tex]3x=3.6\\\\\Rightarrow x=1.2[/tex]

Substitute value of x in (3), we get

[tex]2(1.2)+3y=3.6\\\\\Rightarrow2.4+3y=3.6\\\\\Rightarrow3y=1.2\\\\\Rightarrow y=0.4[/tex]

Thus, the cost of 1 lemon is $1.2 and the cost of 1 lime is $0.4.

Hi there! :)

Step-by-step explanation:

[tex]SLOPE=\frac{Y_2-Y_1}{X_2-X_1}=\frac{RISE}{RUN}[/tex]

[tex]\frac{1-7}{4-8}=\frac{-6}{-4}=\frac{-6/2}{-4/2}=\frac{-3}{-2}=\frac{3}{2}[/tex]

Slope is 3/2.

Final answer is 3/2.

Hope this helps!

Thanks!

Have a nice day! :)

:D

Answer:

S''(-3/2, 9/2)

Step-by-step explanation:

In a dilation, the coordinates of every ordered pair in the pre-image are multiplied by the scale factor to create the ordered pairs of the image.

The first dilation has a scale factor of 1/2.  This maps:

R(-6, 10)→R'(-6/2, 10/2) = R'(-3, 5)

S(-2, 6)→S'(-2/2, 6/2) = S'(-1, 3)

T(-10, 0)→T'(-10/2, 0/2) = T'(-5, 0)

The second dilation has a scale factor of 3/2:

R'(-3, 5)→R''(-9/2, 15/2)

S'(-1, 3)→S''(-3/2, 9/2)

T'(-5, 0)→T''(-15/2, 0)

This makes S'' have coordinates (-3/2, 9/2).

Answer: a :)

Step-by-step explanation:

The area of the rectangle is 80 square cm.

To find the area of a rectangle, we need to know the length and width. Let's denote the width of the rectangle as 'w'. As given, the length of the rectangle is 2 cm longer than its width, so the length can be represented as 'w + 2'.

The perimeter of a rectangle is the sum of all four sides. In this case, it is given as 36 cm. Using the formula for the perimeter of a rectangle, we can set up the equation:

2(w + w + 2) = 36

Simplifying the equation:

4w + 4 = 36

4w = 32

w = 8

Substituting the value of 'w' back into the expression for length:

Length = 8 + 2 = 10

The area of a rectangle is given by the formula: area = length × width. So, the area of this rectangle is:

Area = 10 × 8 = 80 square cm

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