Find the length of the missing side of the triangle below.
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The change in the number of gallons of water in the tank after 7 days is 35 gallons.

The water tank leaks 5 gallons of water each day. To find the change in the number of gallons of water in the tank after 7 days, we multiply the amount leaked per day (5 gallons) by the number of days (7). The expression for the change in gallons can be written as:

Change in gallons = amount leaked per day × number of days

Change in gallons = 5 × 7

Change in gallons = 35 gallons

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Final answer:

The integer representing the change in the number of gallons of water in the tank after 7 days is -35, as the tank loses 5 gallons per day.

Explanation:

If a water tank leaks 5 gallons of water each day, the total amount of water it would lose in seven days is calculated by multiplying the daily water loss by the number of days. The calculation steps are:

Determine the daily water leakage: 5 gallons per day.

Multiply the daily leakage by the number of days: 5 gallons/day × 7 days.

Calculate the total leakage over seven days: 35 gallons.

As water is being lost from the tank, the change in the number of gallons in the tank after 7 days would be represented by a negative integer, since it is a decrease in the volume of water. Therefore, the integer representing the change in the water level is -35.

Answer:

see explanation

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (1, 2) and (x₂, y₂ ) = (6, 5)

m = [tex]\frac{5-2}{6-1}[/tex] = [tex]\frac{3}{5}[/tex], thus

y = [tex]\frac{3}{5}[/tex] x + c ← is the partial equation of the line

To find c substitute either of the 2 points into the partial equation

Using (1, 2), then

2 = [tex]\frac{3}{5}[/tex] + c ⇒ c = 2 - [tex]\frac{3}{5}[/tex] = [tex]\frac{7}{5}[/tex]

y = [tex]\frac{3}{5}[/tex] x + [tex]\frac{7}{5}[/tex] ← in slope- intercept form

Answer:

Step-by-step explanation:

right angle: an angle of 90°

vertical angles: each of the pairs of opposite angles made by two intersecting lines.

complementary angles: either of two angles whose sum is 90°.

Answer:

(2, 3)

Step-by-step explanation:

[tex] -2(2) + 6(3) = 14 \\ \\ -4 + 18 = 14 \\ \\ \\ 6(2) - 3(3) = 3 \\ \\ 12 - 9 = 3[/tex]

I am joyous to assist you anytime.

Answer:

No.

Step-by-step explanation:

35(4) = 140

34(5) = 170

140 does not equal 170, therefore it is NOT TRUE

Answer: 20 meters.

Step-by-step explanation:

The formula for calculate the area of a square is:

[tex]A=s^2[/tex]

Where "s" is the side length of the square:

The formula for calculate the area of a rectangle is:

[tex]A=lw[/tex]

Where "l" is the lenght and "w" is the width.

Based on the information provided, you know the sum of the areas of the square land and the adjacent land is 600 m². This is:

[tex]A_1+A_2=600\\\\s^2+lw=600[/tex]

Knowing that the width of the adjacent land is 10 meters:

[tex]s^2+10l=600[/tex]

Since  the lenght of the adjacent land and the side lenght of his actual land are equal:

[tex]l=s[/tex]

You can substitute this into [tex]s^2+10l=600[/tex]:

[tex]s^2+10s=600\\\\s^2+10s-600=0[/tex]

Applying the Quadratic formula, you get:

[tex]s=\frac{-b\±\sqrt{b^2-4ac} }{2a}\\\\s=\frac{-10\±\sqrt{(10)^2-4(1)(-600)} }{2(1)}\\\\s_1=20\\\\s_2=-30[/tex]

Since the side lenght cannot be negative, you can determine that this is:

[tex]s=20\ m[/tex]

Answer:

She should buy a total of 25, so one more can

Answer:

276,108>x>271,680

Answer: -5!

Step-by-step explanation:

Imagine a number line with negatives on the left and positives on the right. The bigger the number is, the more to the right it would be on a number line.

-5 is more to the left than -4. Hope this helps!

Answer:

120cm^3

Step-by-step explanation:

4*5*6=120

Answer:

Step-by-step explanation:

[tex]3(x+2)=4(x+1)\qquad\text{use the distributive property:}\ a(b+c)=ab+ac\\\\(3)(x)+(3)(2)=(4)(x)+(4)(1)\\\\3x+6=4x+4\qquad\text{subtract 6 from both sides}\\\\3x+6-6=4x+4-6\\\\3x=4x-2\qquad\text{subtract}\ 4x\ \text{from both sides}\\\\3x-4x=4x-4x-2\\\\-x=-2\qquad\text{change the signs}\\\\x=2[/tex]

Answer:

x=2

Step-by-step explanation:

Answer:

E:75

Step-by-step explanation:

[tex]\sqrt{21^{2} +72^{2}}[/tex]

Answer : The length of BC in the right triangle is, 75

Step-by-step explanation :

Using Pythagoras theorem in ΔBAC :

[tex](Hypotenuse)^2=(Perpendicular)^2+(Base)^2[/tex]

[tex](BC)^2=(AB)^2+(AC)^2[/tex]

Given:

Side AB = 21

Side AC = 72

Now put all the values in the above expression, we get the value of side BC.

[tex](BC)^2=(21)^2+(72)^2[/tex]

[tex]BC=\sqrt{(21)^2+(72)^2}[/tex]

[tex]BC=\sqrt{441+5184}[/tex]

[tex]BC=\sqrt{5625}[/tex]

[tex]BC=75[/tex]

Therefore, the length of BC in the right triangle is, 75

Answer:

I believe the answer is 5!

Step-by-step explanation:

Answer:

The amount invested at 4% was $600

The amount invested at 7.5%  was $3,600

Step-by-step explanation:

Let

x ----> the amount invested at 4%

$4,200-x -----> amount invested at 7.5%

we know that

The total interest earned is equal to the interest earned by the amount invested at 4% plus the interest earned by the amount invested at 7.5%

Remember that

[tex]4\%=4/100=0.04[/tex]

[tex]7.5\%=7.5/100=0.075[/tex]

[tex]7\%=7/100=0.07[/tex]

so

The linear equation that represent this situation is

[tex]0.04x+0.075(4,200-x)=0.07(4,200)[/tex]

Solve for x

[tex]0.04x+315-0.075x=294[/tex]

[tex]0.075x-0.04x=315-294[/tex]

[tex]0.035x=21[/tex]

[tex]x=\$600[/tex]

[tex]\$4,200-x=\$3,600[/tex]

therefore

The amount invested at 4% was $600

The amount invested at 7.5%  was $3,600

Final answer:

Morgan invested $600 in the account with 4% interest and $3,600 in the account with 7.5% interest by setting up a system of equations and solving for both variables.

Explanation:

Calculating Investment Distribution

To find out how much money Morgan put in each account, we need to set up a system of equations. Let's designate x as the amount put into the account with 4% interest, and y as the amount put into the account with 7.5% interest. We know the total investment is $4,200, so our first equation is x + y = 4200.

Morgan earned 7% interest on the total investment. The interest from each account can be represented as 0.04x for the 4% account and 0.075y for the 7.5% account. The total interest earned is 7% of $4,200, which is $294. This gives us the second equation: 0.04x + 0.075y = 294.

To solve the system, we can use the substitution or elimination method. If we solve the first equation for y, we get y = 4200 - x. Substitute this into the second equation to get: 0.04x + 0.075(4200 - x) = 294. Now solve for x:

So Morgan invested $600 in the 4% account. Now we can find y:

Therefore, Morgan invested $3,600 in the 7.5% account.

Answer:

30 units

Step-by-step explanation:

If point G is on line segment FH, then point G lies between points F and H.

Segment Addition Postulate states that given 2 points F and H, a third point G lies on the line segment FH if and only if the distances between the points satisfy the equation FG + GH = FH.

By segment addition postulate,

[tex]FG+GH=FH[/tex]

Given

FH = 4x,

GH = x,

FG = 2x + 10,

then

[tex]4x=x+2x+10\\ \\4x=3x+10\\ \\4x-3x=10\\ \\x=10\\ \\FG=2x+10=2\cdot 10+10=30\ units[/tex]

Answer:

FG=11

Step-by-step explanation:

Answer:

Hos son is alive for 525600 mins

Step-by-step explanation:

365 x 24 hrs=8760 hrs

8760 hrs x 60 min= 525600 mins

Multiplication is the process of multiplying. The number of minutes for which Martin's son is live is 525,600 minutes.

Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. For example, 3 × 4 means 3 is added to itself 4 times, and vice versa for the other number.

Given that Martin recently celebrated his son's birthday of when he turned 1 years old. Therefore, the number of minutes for which Martin's son is live is,

Number of minutes

= Number of days in a year × Number of hours in a day × Number of minutes in an hour

= 365 days × 24 hours × 60 minutes

= 525,600 minutes

Hence, the number of minutes for which Martin's son is live is 525,600 minutes.

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Answer:   [tex]\bold{\dfrac{1}{70}}[/tex]

Step-by-step explanation:

PEMDAS states to do parentheses first, then multiplication and division, and lastly subtract.

[tex]\bigg(3\dfrac{1}{3}-1\dfrac{5}{6}\bigg)\div2\dfrac{1}{7}-1\dfrac{1}{3}\cdot2.4\\\\\\\text{Step 1: Subtract}\ 3\dfrac{1}{3}\ and\ 1\dfrac{5}{6}\quad \longrightarrow \quad \dfrac{10}{3}\bigg(\dfrac{2}{2}\bigg)-\dfrac{11}{6}\quad =\dfrac{9}{6}\quad =\dfrac{3}{2}\\\\\implies \quad \dfrac{3}{2}\div2\dfrac{1}{7}-1\dfrac{1}{3}\cdot2.4[/tex]

[tex]\text{Step 2: multiply}\ \dfrac{3}{2}\ and\ 2\dfrac{1}{7}\quad \longrightarrow \quad \dfrac{3}{2}\times \dfrac{15}{7}\quad =\dfrac{45}{14}\\\\\implies \dfrac{45}{14}-1\dfrac{1}{3}\cdot 2.4\\\\\\\\\text{Step 3: multiply}\ 1\dfrac{1}{3}\ and\ 2.4\quad \longrightarrow \quad \dfrac{4}{3}\times 2\dfrac{4}{10}\quad =\dfrac{4}{3}\times \dfrac{12}{5}\quad =\dfrac{16}{5}\\\\\implies \dfrac{45}{14}-\dfrac{16}{5}[/tex]

[tex]\text{Step 4: subtract}\ \dfrac{45}{14}\ and\ \dfrac{16}{5}\quad \longrightarrow \quad \dfrac{45}{14}\bigg(\dfrac{5}{5}\bigg)-\dfrac{16}{5}\bigg(\dfrac{14}{14}\bigg)\quad =\dfrac{1}{70}\\\\\implies \large\boxed{\dfrac{1}{70}}[/tex]

Hey!

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

PEMDAS stands for the steps in solving an equation.

P - Parenthesis

E - Exponent's

M - Multiply

D - Divide

A - Addition

S - Subtract

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

Expression:

= 6 × 5 + 3 × 8

Multiply first since its the first step in this equation:

= (6 × 5) + (3 × 8)

Simplify:

= 30 + 24

Answer:

= 54

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

Hope This Helped! Good Luck!

*Further simplification is in bold*

Answer:

54

Step-by-step explanation:

1- 6x5+3×8= Work out the division and multiplication at each side from left to right. First do the times always. so for example 2×2=4; so 6×5= 30 and 3x8= 24

2- 30+ 24= Work out the sum. Then do the sum for example 3+2=6. So in this case 30+24; you can do as 30+20=50+4= 54

3- 30+24= 54

Feel free to ask more questions.

Jon makes $15 per hour and works 20 hours per week, giving him weekly earnings of $300. Over a year (52 weeks), this totals to $15,600.

The question is asking about how much Jon will earn in a year. We know that Jon makes $15 per hour and works 20 hours per week. To find out his weekly earnings, we multiply his hourly rate by the number of hours he works per week: $15 * 20 = $300.

There are generally 52 weeks in a year. So, to calculate Jon's annual earnings, we can multiply his weekly earnings by 52: $300 * 52 = $15,600.

So, Jon will earn $15,600 in a year if he continues to work at this same rate.

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Answer: Angle Q= 123

Step-by-step explanation:

4x+1+9x-3=180

X=14

9(14)-3=123

The measurement of angle Q is 123 degrees if angle P and angle Q are supplementary angles.

When two lines or rays converge at the same point, the measurement between them is called a "Angle."

It is given that:

Angle P and angle Q are supplementary angles. if angle P measures 4x + 1 and angle Q measures 9x -3,

As we know the sum of the supplementary angles is up to 180 degrees

Angle P + Angle Q = 180

4x + 1 + 9x  - 3 = 180

13x - 2 = 180

13x = 180 + 2

13x = 182

x = 182/13

x = 14

The measurement of the angle Q = 9x - 3

The measurement of the angle Q = 9(14) - 3

The measurement of the angle Q = 126 - 3

The measurement of the angle Q = 123 degrees

Thus, the measurement of angle Q is 123 degrees if the angle P and angle Q are supplementary angles.

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Answer:

Each pound costs $1.76. Hope this helps :)

Answer:

An improper fraction

Step-by-step explanation:

15/10 is 1 and 1/2, but it's a bigger number over a smaller number.

Answer:

Rational Number.

Step-by-step explanation:

It is a rational number because it is written as a/b where a and b are integers.

This one can simplify to 3/2.

Answer:

The answer is C

Step-by-step explanation:

To find the mean absolute deviation of the number of goals scored by the hockey team, subtract the mean from each value in the data set, find the absolute value of each difference, and then find the mean of the absolute differences. For the given data set, the mean absolute deviation is 1.44.

The mean absolute deviation of a data set is a measure of how spread out the data is. To find the mean absolute deviation of the number of goals scored by the hockey team, you need to follow these steps:

For the given data set (2, 4,0,3, 4, 1, 3, 1, 1, and 5), the mean is (2 + 4 + 0 + 3 + 4 + 1 + 3 + 1 + 1 + 5) ÷ 10 = 2.4. The absolute differences from the mean are 0.4, 1.6, 2.4, 0.4, 1.4, 1.4, 1.4, 1.4, 1.6, and 2.6. The mean of the absolute differences is (0.4 + 1.6 + 2.4 + 0.4 + 1.4 + 1.4 + 1.4 + 1.4 + 1.6 + 2.6) ÷ 10 = 1.44.

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To find the mean absolute deviation of the number of goals scored by the hockey team, calculate the mean of the data set and find the absolute deviation of each data point. Then, calculate the sum of the absolute deviations and divide by the total number of data points.

To find the mean absolute deviation of the number of goals scored, we need to follow these steps:

By following these steps, you can calculate the mean absolute deviation of the number of goals scored by the hockey team.

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Answer:

Step-by-step explanation:

Supplementary angles add up to 180 °.

x + z = 180° → x = 180° - z

180° - 42.1° = 137.9°

Answer:

The delivery person can bring up max 16 boxes at one time.

Step-by-step explanation:

The elevator can only hold max 850 lbs, and the delivery man weighs 180 lbs.

850-180=670

That means the delivery man can have up to 670 lbs of boxes on the elevator.

670/40=16.75

Which means that the delivery man can hold up to 16 boxes max at one time.

With the delivery person's weight and the maximum capacity of the elevator considered, the maximum number of 40 lb boxes of books the delivery person can bring up at once is 16.

This question is about problem-solving and arithmetics. In this context, the maximum weight the elevator can carry is 850 lb. The delivery person's weight of 180 lb must be included in this maximum. To figure out how many boxes of books at 40 lb each the delivery person can carry, one would have to subtract the delivery person's weight from the total maximum weight and then divide this total by the weight of each box.

By doing the subtraction, 850 lb (maximum capacity) - 180 lb (weight of delivery person) = 670 lb. This is the total weight of boxes that can be carried. Then, divide this remaining weight by the weight of each box: 670 lb / 40 lb = 16.75 boxes. Since one cannot have 0.75 of a box, the maximum number of boxes that can be carried at one time is 16.

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Answer:

41.6 days.

Step-by-step explanation:

1000 divided by 24 is 41.6 repeating

Answer: square root is a number that can be multiplied by itself to get that number in that radical aka checked half box.

Step-by-step explanation: square root of 18 is

Approx: ~4.2

Since that approx multiplied by itself is 19. Search up place values. Numbers after the decimals start from, tenths place, hundredths, thousands place and so on. This one asked for the tenths place. 0.2 the 2 is in the tenths place

Answer:

x = 2 ± [tex]\sqrt{13}[/tex]

Step-by-step explanation:

To find the zeros let y = 0, that is

x² - 4x - 9 = 0 ( add 9 to both sides )

x² - 4x = 9

To complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(- 2) x + 4 = 9 + 4

(x - 2)² = 13 ← take the square root of both sides

x - 2 = ± [tex]\sqrt{13}[/tex] ← add 2 to both sides

x = 2 ± [tex]\sqrt{13}[/tex]