Find the length of RS.

Answer: -3

Step-by-step explanation:

Answer:

-3

Step-by-step explanation:

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.

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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: 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:

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:

the answer is 16mph

Step-by-step explanation:

Answer:

16 miles per hour

Step-by-step explanation:

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 Option is A, slope is -1/3

Step-by-step explanation:

Answer:

17 feet

Step-by-step explanation:

c=the length of the ramp  

a=8 ft

b=15 ft

Pythagorean Theorem

c²=a²+b²

c²=8²+15²

c²=64+225

c²=289

c=√289

c=17 ft

The length of the ramp of the triangular path is AC = 17 feet

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

The area of the triangle = ( 1/2 ) x Length x Base

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

if a² + b² = c² , it is a right triangle

if a² + b² < c² , it is an obtuse triangle

if a² + b² > c² , it is an acute triangle

Given data ,

Let the triangle be represented as ΔABC

Now , the base of the ramp is BC = 15 feet

The height of the ramp is AB = 8 feet

So , length of the ramp Ryan needs to build is AC is

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

AC = √ ( AB )² + ( BC )²

AC = √ ( 8 )² + ( 15 )²

AC = √ ( 64 + 225 )

AC = √289

AC = 17 feet

Therefore , the value of AC is 17 feet

Hence , the length of the ramp is 17 feet

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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:

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:

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:

V = 282.10 cm³

Step-by-step explanation:

[tex]V= \pi r^2\frac{h}{3}[/tex]                   Use this equation to find the volume of the cone

[tex]V=3.14(3.5)^{2} \frac{22}{3}[/tex]            Simplify the (3.5)²

V = 3.14(12.25)(22/3)    Multiply

V = 282.10 cm³

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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

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: 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:

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

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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:

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:

-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:

400

Step-by-step explanation:

Given:

Number of mocha cupcakes in a day = 340

Total number of cupcakes sold that day = [tex]85\%[/tex]

To find:

Total number of cupcakes sold by the bakery

Solution:

Let x denotes total number of cupcakes sold by the bakery.

According to question,

[tex]\frac{85}{100}x=340\\x=\frac{340}{85}\times 100=400[/tex]

So,

Total number of cupcakes sold by the bakery = 400

Answer:

P(t) = 27000 * (8/9)^(t/4)

Step-by-step explanation:

The population of penguins in Antarctica decays by 8/9 every 4 months, starting from an initial count of 27,000. The function for the penguin population P(t) after t months is P(t) = 27,000 × (8/9)^(t/4).

Talulah, an ecologist, has observed that the population of penguins in Antarctica decays by a factor of 8/9 every 4 months. To model this decay, we can use an exponential decay function. Given that the initial population (P0) is 27,000 penguins, the function P(t) that models the population at time t (in months) since the beginning of Talulah's study is:

P(t) = P0 × (decay factor)(t/rate period)

Where P0 is the initial population, the decay factor is 8/9, and the rate period is 4 months. Plugging in these values gives us:

P(t) = 27,000 × (8/9)(t/4)

This function allows researchers to predict the penguin population at any given time t months after Talulah's initial observation.

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Answer:

68.48 pounds

Step-by-step explanation:

€91.30  to pounds

€91.30  * (3 pounds/ 4€) = 68.475 pounds  about  68.48 pounds

Answer: Mike's arm span is 7.165 cm longer than the George's one.

Step-by-step explanation:

We have that the association between height and arm span is modeled by the equation

y = 4.5 + 0.977*x

where y is height and x is arm span.

Mike is 172 cm tall, so his arm span is:

172cm = 4.5 + 0.977*x

x = (172 - 4.5)/0.977 = 171.443 cm

and George is 165 cm tall, so his arm span is:

x = (165 - 4.5)/0.977 = 164.278 cm

Then the difference between their arm span is:

171.443cm - 164.278cm = 7.165 cm

So Mike's arm span is 7.165 cm longer than the George's one.

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:

0.0195?

Step-by-step explanation:

Answer:

21 : 24

Step-by-step explanation:

Sum the parts of the ratio, 7 + 8 = 15 parts

divide 45 by 15 to find one part of the ratio

45 ÷ 15 = 3 ← value of 1 part of ratio, thus

7 parts = 7 × 3 = 21

8 parts = 8 × 3 = 24

45 divided in the ratio 7 : 8 is 21 : 24