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Answer: The length of the base of the triangle is 16 inches.

Step-by-step explanation:

Hi, to answer this question we have to apply the next formula

Area of a triangle (A) = base x height x 1/2

Replacing with the values given:

42 = b (5 1/4) 1/2

Solving for b (lenght of the base)

42 / (5 1/4) 1/2 = b

16 in = b

The length of the base of the triangle is 16 inches.

Feel free to ask for more if needed or if you did not understand something.

Final answer:

The length of the base of the triangle is 16 inches, calculated by using the area formula for a triangle and the given height.

Explanation:

To find the length of the base of the triangle, we use the formula for the area of a triangle, A = (b * h) / 2, where A is the area, b is the base, and h is the height. We know the area (A) is 42 square inches and the height (h) is 5 1/4 inches. Plugging these values into the formula gives us:

42 = (b*5.25) / 2

Multiplying both sides by 2 to isolate the term with b gives us:

84 = b* 5.25

Dividing both sides by 5.25 yields:

b = 84 / 5.25

Calculating this division, we get the length of the base (b):

b = 16 inches

The volume of water in the tank, with a length of 4 feet, width of 1.5 feet, and filled to within 4 inches of the top, is approximately 42.667 cubic feet.

To find the volume of water in the tank, we need to calculate the volume of the portion of the tank that is filled with water.

1. First, let's convert all the measurements to the same unit. Since the height of the tank is given in feet and the width is given in inches, let's convert the width to feet.

Given:

- Length = 4 feet

- Width = 18 inches

- Height = 3 feet

- Water level = 4 inches from the top

Converting width to feet:

1 foot = 12 inches

So, 18 inches = 18/12 = 1.5 feet

Now, we have:

- Length = 4 feet

- Width = 1.5 feet

- Height = 3 feet

- Water level = 4 inches from the top

2. Calculate the height of the water in the tank:

Total height of the tank = Height of tank - Distance from the top to the water level

Total height = 3 feet - 4 inches

Total height = 3 feet - (4/12) feet

Total height = 3 feet - 0.3333 feet

Total height = 2.6667 feet

3. Calculate the volume of water using the formula for the volume of a rectangular prism:

Volume = Length × Width × Height

Volume = 4 feet × 1.5 feet × 2.6667 feet

Volume ≈ 16 feet³ × 2.6667

Volume ≈ 42.667 feet³

So, the volume of water in the tank is approximately 42.667 cubic feet.

Answer:

23 units²

Step-by-step explanation:

height = 2

length = 4

width = 2.5

Formula = 2(wl + lh + hw) ⇒ 2 [(2.5 × 4) + (4 × 2) + (2 ×2.5)] = 23 units²

Hope this helps.

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Answer:

Step-by-step explanation:

Given

slope(m) = - 4

Points ( x1 , y1) = ( - 1 , 6)

Now

The equation of a line is given by

y - y1 = m( x - x1)

y - 6 = - 4 ( x + 1)

y - 6 = -4x - 4

4x + y - 6 + 4 = 0

4x + y - 2 = 0

Hope it helps:)

The equation of the line with a slope of -4 and passing through the point (-1, 6) is y = -4x + 2.

Given that the slope (m) is -4 and the point it passes through is (-1, 6), we can substitute these values into the point-slope form:

y - 6 = -4(x - (-1))

y - 6 = -4(x + 1)

Now, we can distribute the -4 to the terms inside the parentheses:

y - 6 = -4x - 4

Next, we can move the -6 to the other side of the equation by adding 6 to both sides:

y = -4x - 4 + 6

y = -4x + 2

Therefore, the equation of the line is y = -4x + 2.

Learn more about the lines here:

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Answer:

13 miles

Step-by-step explanation:

This problem can be represented as a right angle triangle (shown in the diagram).

The distance of the boat from the dock is the hypotenuse of the triangle, hence, we need to find the hypotenuse of the triangle. To do this, we apply Pythagoras theorem:

[tex]hyp^2 = opp^2 + adj^2[/tex]

where opp = side opposite angle of consideration = 12 miles

adj = side adjacent angle of consideration = 5 miles

Hence:

[tex]hyp^2 = 12^2 + 5^2\\\\\\hyp^2 = 144 + 25 = 169\\\\\\hyp = \sqrt{169}\\ \\\\hyp = 13 miles[/tex]

The boat is therefore, 13 miles from the dock.

Final answer:

To find the distance of the boat from the dock after traveling due south and then due west, apply the Pythagorean theorem to calculate the hypotenuse of a right-angled triangle, resulting in 13 miles.

Explanation:

The question involves finding the distance of the boat from the dock after it has traveled in a two-segment path: 5 miles due south and 12 miles due west. This problem can be solved by using the Pythagorean theorem, which is applied in the context of a right-angled triangle formed by the southward and westward paths of the boat as its legs.

Steps to Calculate Distance:

Represent the boat's journey as a right-angled triangle with the southward and westward paths forming the two legs.

Calculate the hypotenuse of the triangle, which represents the straight-line distance between the boat and the dock.

Use the Pythagorean theorem (a² + b² = c²) to find the distance.

For the distances given (5 miles and 12 miles), the calculation would be [tex]\sqrt{5² + 12²}[/tex]= [tex]\sqrt{169}[/tex] = 13  

Therefore, the boat is 13 miles away from the dock after traveling 5 miles due south and 12 miles due west.

Answer:

The population is decaying at a rate of 11% per minute.

Step-by-step explanation:

We have that € is the inicial sample of algae cells, and f(t) shows the sample after t minutes.

As € is multiplied by a number between 0 and 1, that means the sample will decrease it's size as the time passes.

The inicial sample is €, and after 1 minute the sample will be 0.89€, that is, it will decrease by 0.11€ or 11% of the previous sample.

So the correct option is:

The population is decaying at a rate of 11% per minute.

Answer:

The correct answer is b) The population is decaying at a rate of 11% per minute.

Step-by-step explanation:

Given the function

f(t) = 0.89€

We can see that every time the variable v grows 1, the population grows only 0.89.  So the population is decreasing. And the percentage of decreasing we get it by discounting 1 -0.89= 11%

Answer:

      1.reflection

     2. translation

     3. rotation

     4. rotation

      5. reflection

Step-by-step explanation:

Answer:

  yes

Step-by-step explanation:

The numbers satisfy the Pythagorean theorem:

  53^2 = 28^2 +45^2

  2809 = 784 +2025

(28, 45, 53) is a Pythagorean triple. These lengths will make a right triangle.

Answer:

16 adults

Step-by-step explanation:

There were 3 times more children than adults at the park.

That means that dividing the number of children by 3 would give us the number of adults.

48 / 3 = 16

Answer:

16:48 Therefore, 16 adults

Step-by-step explanation:

Answer:210

Step-by-step explanation:

After comparing the height of each person, we can confidently say that Krista is the tallest from all the given individuals.

Krista is taller than Jan. Jan is shorter than Len, but taller than Mick. Len is shorter than Krist. The question provides information that allows us to compare the height of each individual. Based on given information we were provided, Krista is taller than Jan, Len is shorter than Krista but taller than Mick, and Jan is shorter than Len but taller than Mick. This means that Krista is taller than Len, Jan, and Mick, making Krista the tallest.

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Answer:

He will spend 42 dollars

Step-by-step explanation:

7 times $6

= $42

(If that's what you're asking)

Answer:

7 × $ 6 = $42 so it all equals to 42 dollars

Answer:

the answer is 16mph

Step-by-step explanation:

Answer:

16 miles per hour

Step-by-step explanation:

Answer: 39 pounds of type A coffee were used.

Step-by-step explanation:

Let x represent the number of pounds of type A coffee that were used in the blend.

Let y represent the number of pounds of type B coffee that were used in the blend.

Type A coffee costs Lena $5.70 per pound, and type B coffee costs $4.25 per pound. The total cost of the mixture is $885.30. It means that

5.7x + 4.25y = 885.3- - - - - - - - - -1

This month's blend used four times as many pounds of type B coffee as type A. It means that

y = 4x

Substituting y = 4x into equation 1, it becomes

5.7x + 4.25 × 4x = 885.3

5.7x + 17x = 885.3

22.7x = 885.3

x = 885.3/22.7

x = 39

y = 4x = 4 × 39

y = 156

The weight of Type A coffee used was approximately 39 pounds. This is determined by setting up and solving an equation based on the provided costs per pound of the coffees and the total cost.

In this problem, we need to solve for the amount of Type A coffee. Let's represent the weight of Type A coffee as x and the weight of Type B coffee as 4x, as it's mentioned the weight of Type B is four times Type A. We know that the combination of Type A and B coffee costs $885.30, so we can set up the equation using the costs per pound for each type: (5.70*x) + (4.25*4x) = 885.30.

Solving this equation, we have 5.70x + 17x = 885.30, or 22.7x = 885.3. Dividing both sides by 22.7, we get x = 38.97 pounds. So, approximately 39 pounds of Type A coffee were used.

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Answer:

-3

Step-by-step explanation:

The equation is written in slope intercept form

y = mx+b  where m is the slope and b is the y intercept

y = 4x-3

4 is the slope and -3 is the y intercept

Answer:

Step-by-step explanation:

If the scale factor of the larger prims to the smaller prism is 3, that means each side is triple.

We know the a triangular prims has a volume defined by

[tex]V_{small} =\frac{b \times h_{1} }{2} \times h_{2}[/tex]

If we take that formula as the smaller prism, then the larer prism has a volum of

[tex]V_{large} =\frac{2b \times 2h_{1} }{2} \times 2h_{2}=8(\frac{b \times h_{1} \times h_{2} }{2} )[/tex]

If we compare, we can deduct that

[tex]V_{large}=8V_{small}[/tex]

In words, the volume of the larger prims is eight times greater than the smaller prism.

Answer:

Answer Choice 3

Step-by-step explanation:

on edge 2020

Answer:

1. 4

2.  6.4

3. 10.0828313253

Explanation:

2.

15/12=1.25

8/1.25=6.4

3. ill write explanation for 3 later im  occupied those are the correct answers

problably they want you to round to nearest tenth

Answer:

None are correct

Step-by-step explanation:

Because triangle ABC is the original as it says in the problem"Triangle ABC TO Triangle DEF" which means the answer should be Triangle DEF is 6 times larger than triangle ABC.

Answer:

peanuts are more expensive by $1.00.

Step-by-step explanation:

∵ The cost of eight pounds of peanuts = $24.00

∴ The cost of one pound of peanuts = [tex]\frac{24}{8}[/tex]

                                                           = $3.00 per pound

∵ The cost of six pounds of walnuts half as much = [tex]\frac{1}{2} \times 24[/tex]

                                                                               = $12.00

∴ the cost of one pound of walnuts = [tex]\frac{12}{6}[/tex]

                                                           = $2.00 per pound

Difference in the cost per pound = $3.00 - $2.00 = $1.00

Therefore, peanuts are more expensive by $1.00.

Answer:

net

Step-by-step explanation:

A two-dimensional shape has only two measurements and a three-dimensional shape has three measurements.

For example square, the triangle are two-dimensional shapes and cube, prism are three-dimensional shapes.

A 2 D image of a 3 D figure is most commonly know as a net.

A net is a two-dimensional pattern that can be folded to form the three-dimensional figure.

When you cut out the "net", fold it and stick it together you get a three-dimensional shape.

Answer:

Area of the floor is 234 feet²

Step-by-step explanation:

To find the area of the floor of a rectangular storage room that is 2,106 cubic feet and has a height of 9 feet , we will follow the steps below;

First, write down the formula for calculating its volume

volume = l×b×h

but area=l×b

volume = area × h

From the question given volume =  2106 cubic feet

height h = 9 feet

volume = area × h

2106 = area ×  9

Divide both-side of the equation by 9

2106/9 = area ×  9/9

234 = area

area = 234 feet²

Area of the floor is 234 feet²

Answer:

Read 12 pages every night in a chapter book with 144 pages.

Thus the first option is the best because you will use fewer number of days to complete the reading.

Step-by-step explanation:

For the first option;

Read 12 pages every night in a chapter book with 144 pages, the number of days taken to complete the book will be;

144/12= 12 days

For the second option

50 pages = 3 times

132 pages = ? ------perform cross product

(132*3)/ 50 =7.92 ≈ 8 times

3 times = 1 week

8 times = ?

(8*1)/3 = 2.64 weeks

1 week =7 days

2.64 weeks=?

2.64*7 = 18.5 days

Thus the first option is the best because you will use fewer number of days to complete the reading.

Answer:

48π ≈ 150.72

Step-by-step explanation:

The volume formula is V = 1/3Bh

The base area formula would be πr²

Since 8 is the diameter, 4 would be the radius

Now plug that in, π (4²) = 16π

Now multiply that by the height, 9, and get 144π

Multiply again by 1/3 and you'll get 48π

Answer:

150.72 ft^3

Step-by-step explanation:

The volume of a cone is

V = 1/3 pi r^2 h

We need to get the radius

r = d/2 = 8/2 =4

V = 1/3 (3.14) (4)^2 *9

V = 1/3 (3.14) 16 *9

V =150.72

Rounding to the nearest hundredth

V = 150.72

Answer: C(x) = 40X + 1900

Step-by-step explanation: given from the question,

daily fixed costs = $1900 and

daily variable costs = $40

the linear cost function C(x)=mx+b, where the y-intercept b represents the fixed cost of operating a business and the slope m represents the variable costs

The cost of manufacturing x bicycle per day will be

C(x) = 40X + 1900

Answer:

4x² - 9y²

General Formulas and Concepts:

Pre-Algebra

Algebra I

Step-by-step explanation:

Step 1: Define

Set up expression

12x² + 3xy - 5y² - (8x² + 3xy + 4y²)

Step 2: Simplify

Answer:

volume of tank = 2000 cm³

Step-by-step explanation:

given data

tank long = 25 cm

tank wide = 10 cm

tank deep = 8 cm

to find out

how many liters of water

solution

we get here volume of this tank that is express as

volume of tank = tank long × wide × deep    .......................1

put here value and we will get

volume of tank = 25 × 10 × 8

volume of tank = 2000 cm³

Answer:

We choose C

Step-by-step explanation:

the coordinates at 135° are at  ([tex]\frac{-\sqrt{2} }{2}[/tex], [tex]\frac{\sqrt{2} }{2}[/tex] )

As we can see, the x coordinate of the point is negative and the y coordinate of it is positive.

So this point is located at the quadrant ii

From  135 ° to 315°, it is rotated 180°

=> Each coordinate (x,y) is changed to (-x,-y)

= ([tex]\frac{\sqrt{2} }{2}[/tex], [tex]-\frac{\sqrt{2} }{2}[/tex] )  the new coordinate is located in quadrant iii

We choose C

Answer:

B. 1

Step-by-step explanation:

3x-1=2

3x=3

x=1