What is the closed linear form of the sequence 5, 7.5, 10, 12.5, 15,...

A) an = 5 + 2.5n

B) an = 5 - 2.5n

C) an = 2.5 + 2.5n

D) an = 2.5 - 2.5n

Answer:

There are 18 dimes and 12 quarters

Step-by-step explanation:

Remember that

1 Dime =$0.10

1  Quarter=$0.25

Let

x-----> the number of dimes

y-----> the number of quarters

we know that

x+y=30

x=30-y ------> equation A

0.10x+0.25y=4.80

Multiply by 100 both sides

10x+25y=480 ------> equation B

Substitute equation A in equation B and solve for y

10(30-y)+25y=480

300-10y+25y=480

15y=180

y=12 quarters

Find the value of x

x=30-y=30-12=18 dimes

therefore

There are 18 dimes and 12 quarters

Final answer:

To solve this problem, set up a system of equations and solve them simultaneously.

Explanation:

Let's solve this problem using a system of equations.

Let's assume that the number of quarters is 'x' and the number of dimes is 'y'.

We can set up two equations based on the given information:

Solving these equations simultaneously, we can find the values of 'x' and 'y', which represent the number of quarters and dimes respectively.

By substituting the value of x from Equation 1 into Equation 2, we get:

0.25(30 - y) + 0.10y = 4.80

7.50 - 0.25y + 0.10y = 4.80

-0.15y = -2.70

y = 18

Substituting the value of y into Equation 1, we get:

x + 18 = 30

x = 12

Therefore, there are 12 quarters and 18 dimes.

Answer:

since it double the value multiply by 2

Step-by-step explanation:

Answer:

14 inches

Step-by-step explanation:

i got it right

I believe the answer would be 659 feet. Take 42x3= 126 then 126x5 . I get 630 but that’s the closest I got ‍♀️

The total distance traveled by the Ferris wheel is D = 1,978 feet

A circle is a closed figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle

The circumference of circle = 2πr

The area of the circle = πr²

where r is the radius of the circle

The standard form of a circle is

( x - h )² + ( y - k )² = r²,

where r is the radius of the circle and (h,k) is the center of the circle.

The equation of circle is ( x - h )² + ( y - k )² = r²

For a unit circle , the radius r = 1

x² + y² = r² be equation (1)

Now , for a unit circle , the terminal side of angle θ is ( cos θ , sin θ )

Given data ,

The circumference of the Ferris wheel can be calculated using the formula:

C = πd

where d is the diameter of the wheel

C = π x 42 feet

C ≈ 131.88 feet

This means that for each rotation of the Ferris wheel, a passenger will travel approximately 131.88 feet

Since the Ferris wheel rotates 3 times per minute, the distance traveled by a passenger in one minute is

131.88 feet/rotation x 3 rotations/minute = 395.64 feet/minute

Therefore, during a 5-minute ride, a passenger will travel approximately

395.64 feet/minute x 5 minutes = 1,978.2 feet

Hence , the total distance is 1,978 feet

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Answer:

[tex]\large\boxed{B.\ a=8,\ b=4\sqrt5}[/tex]

Step-by-step explanation:

We have three similar triangles:

[tex]\triangle ABC\sim\triangle DBA\sim\triangle DAC[/tex]

therefore the sides are in proportion:

[tex]\dfrac{AD}{CD}=\dfrac{BD}{AD}[/tex]

We have AD = a, CD = 16 and BD = 4. Substitute:

[tex]\dfrac{a}{16}=\dfrac{4}{a}[/tex]              cross multiply

[tex](a)(a)=(16)(4)\\\\a^2=64\to a=\sqrt{64}\\\\a=8[/tex]

and other proportion:

[tex]\dfrac{AB}{BC}=\dfrac{BD}{AB}[/tex]

We have AB = b, BC = 16 + 4 = 20 and BD = 4. Substitute:

[tex]\dfrac{b}{20}=\dfrac{4}{b}[/tex]             cross multiply

[tex](b)(b)=(20)(4)\\\\b^2=80\to b=\sqrt{80}\\\\b=\sqrt{16\cdot5}\\\\b=\sqrt{16}\cdot\sqrt{5}\\\\b=4\sqrt{5}[/tex]

Option B is the correct option.

Condition for the similarity of two triangles,

"If two triangles are similar, corresponding sides of these triangles will be proportional"

From the picture attached,

ΔADC and ΔBDA are similar,

By the condition of the similarity, corresponding sides will be proportional.

[tex]\frac{DA}{BD}= \frac{DC}{DA}= \frac{AC}{BA}[/tex]

Substitute the measures given in the picture,

[tex]\frac{a}{4}= \frac{16}{a}= \frac{AC}{b}[/tex]

[tex]\frac{a}{4}=\frac{16}{a}[/tex]

[tex]a^2=64[/tex]

[tex]a=8[/tex]

Now apply Pythagoras theorem in ΔADB,

AB² = AD² + DB²

b² = a² + 4²

b² = 8² + 4² [Since, a = 8]

b = √80

b = 4√5

    Therefore, Option B will be the correct option.

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Answer:

From the measure the picture provides us, we can conclude that the prism is a cube, which also tells us that all 6 sides of this prism have equal surface area, so we only need to calculate one of them and multiply the result by 6:

The surface area of one side of the cube should be: 2/3 . 2/3 = 4/9 (ft²)

The surface area of the prism should be: 4/9 . 6 = 24/9 = 8/3 (ft²)

A prism is a polyhedron composed of an n-sided polygon basis. The surface area of the prism is 8/3 ft².

A prism is a polyhedron composed of an n-sided polygon basis, a second base that is a translated duplicate of the first, and n additional faces, all of which must be parallelograms, connecting the two bases. All parallel cross-sections to the bases are translations of the bases.

Given the length of the side is 2/3 ft. Therefore, the surface area of the given prism can be written as,

The surface area of the prism = 6s² = 6(2/3)² ft² = 8/3 ft²

Hence, the surface area of the prism is 8/3 ft².

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Answer:

The total volume of juice in a six-pack is [tex]254.3\ in^{2}[/tex]

Step-by-step explanation:

step 1

Find the volume of one can

The volume of the cylinder (can of juice) is

[tex]V=\pi r^{2} h[/tex]

we have

[tex]r=3/2=1.5\ in[/tex] ----> the radius is half the diameter

[tex]h=6\ in[/tex]

assume

[tex]\pi =3.14[/tex]

substitute

[tex]V=(3.14)(1.5)^{2} (6)[/tex]

[tex]V=42.39\ in^{2}[/tex]

step 2

Find the total volume of juice in a six-pack

Multiply the volume of one can by 6

[tex]42.39*(6)=254.3\ in^{2}[/tex]

The total volume of juice in a six-pack where each can is 6 inches tall and has a diameter of 3 inches is calculated using the volume of a cylinder formula. The total volume is 254.34 in³. This is achieved by calculating the volume of one can and multiplying by six.

To calculate the total volume of juice in a six-pack where each can is 6 inches tall and has a diameter of 3 inches, we first need to find the volume of one can using the formula for the volume of a cylinder, which is V = πr²h. Since the diameter is 3 inches, the radius (r) is half of that, which is 1.5 inches. Plugging the values into the formula, we get:

Therefore, the correct answer is 254.34 in³, which represents the total volume for a six-pack of juice cans.

Answer:

Step-by-step explanation:

The formula of an area of a circle:

[tex]A=\pi r^2[/tex]

r - radius

The formula of a circumference of a circle:

[tex]C=2\pi r[/tex]

We have:

[tex]C=3\pi[/tex]

Substitute:

[tex]2\pi r=3\pi[/tex]            divide both sides by 2π

[tex]r=1.5[/tex]

Substitute:

[tex]A=\pi(1.5)^2=2.25\pi[/tex]

This answer is correct, I double checked it and got it right on the assignment in OW. :)

Answer:

[tex\large\boxed{\log2-\log4=\log\frac{1}{2}}[/tex]

Step-by-step explanation:

[tex]\text{Use}\ \log_ab-\log_ac=\log_a\dfrac{b}{c}\\\\==========================\\\\\log2-\log4=\log\dfrac{2}{4}=\log\dfrac{1}{2}[/tex]

Answer:

The medicine treats swelling

Step-by-step explanation:

"The control group does not receive any medication; the treatment group receives the medication. The patients in the treatment group show reduced signs of swelling. What can Andria conclude from this experiment?"

If she does not give placebo, which she should, then we can only conclude that the medication might be effective. Might, because the thought of the medicine fixing swelling might actually be what helps them.

This takes us to the next topic- placebo experiments.

Most good experiments, to elaborate, are "double blind," one group receives a placebo, and another the medication, and neither know which.

In this case, assuming that the placebo was ineffective, we can conclude that the medicine is effective in treating swelling.

Answer:

45 cubic inches

I hope this helped you : )

Step-by-step explanation:

To find the volume you must use the formula ( Volume = Length x Width x Height)

So, ( 5 x 3 x 3 = 45)

45 cubic inches, it’s just l*w*h

For this case we have a function of the form[tex]y = f (x)[/tex]

Where:

[tex]f (x) = - 4x + 3[/tex]

We must find the value of the function when the variable x is -5.

Then, substituting, [tex]x = -5[/tex]

[tex]f (-5) = - 4 (-5) +3[/tex]

We have that by sign law[tex]- * - = +[/tex]

[tex]f (-5) = 20 + 3\\f (-5) = 23[/tex]

Answer:

[tex]f (-5) = 23[/tex]

ANSWER

[tex]f( - 5)=23[/tex]

EXPLANATION

The given function is

[tex]f(x)=-4x+3[/tex]

To find f(-5), we substitute x=-5 to obtain;

[tex]f( - 5)=-4( - 5)+3[/tex]

We multiply out to obtain:

[tex]f( - 5)=20+3[/tex]

We simplify to get,

[tex]f( - 5)=23[/tex]

Answer:

(-3,-4)

Look at attached pictures for work and the text below for the explanation of the work. The brown numbers represent the step number it is.

Step-by-step explanation:

Start by getting either the x or y values in both equations the same number but opposite sign. Ex 16 and -16. I did x. Then add the equations eliminating one variable, in mine it was x, and the solve for the other variable, in mine it was y. Then plug that variable back into one of the two original equations and solve for the other variable, in mine I solved for x.

Answer:

The answer is B

Step-by-step explanation:

Answer:

option B. square root of 3

Step-by-step explanation:

In the figure attached the length of one side of the cube is 1 cm.

In the triangle ABC, Side AB = 1 cm

Since side BC is the diagonal of 1 base of the given cube.

Therefore, mBC = [tex]\sqrt{1+1}=\sqrt{2}[/tex] cm

Now we have to calculate the length of diagonal AC.

AC = [tex]\sqrt{AB^{2}+BC^{2}}[/tex]

AC = [tex]\sqrt{1+2}=\sqrt{3}[/tex]

Therefore, option B. square root of 3 will the length of diagonal of the cube.

im not sure of this but I think u have to subtract 37 from 12 and that is 25

I don't know e thats any helpful

Answer:

0.125 m

Step-by-step explanation:

Answer:

0.125 meters

Step-by-step explanation:

There are 100 cm in a meter. 12.5/100= 0.125

Multiply the area of the base by the height

Answer:

C) multiply the area of the base by the height

Step-by-step explanation:

Prism is a three dimensional figures.

The volume of a prism calculated by multiplying the area of the base and  the height.

Volume of a prism = Base area * height.

For example:

Volume of a rectangular prism = base area * height = (lw)*h = lwh cubic units

Volume of a cube = Base area * height = (a*a)*a = a^2*a = a^3 cubic units

Volume of a cylinder = Base area * height = (πr^2)*h = πr^2 h

The answer is C) multiply the area of the base by the height

According to google your answer is c

Answer:

1/6

Step-by-step explanation:

Candy = 5/6

5 people = 5/6

1 person

= 5/6 ÷ 5

= 5/6 x 1/5

= 1/6

Answer:

1/6

Step-by-step explanation:

Answer:

2/9

Step-by-step explanation:

If you meant you want to find U,

1) Divide both side by 2. -> U = 4/9 divided by 2

2) You get U = 4/18, which you can further simplify by dividing 2 on top and bottom to get 2/9

____________________________________________________

Answer:

The center would be (-8,12).

____________________________________________________

Step-by-step explanation:

First,we're going to have to simplify the equation. Here is the work below:

[tex]x^2+y^2+16x-24y+159=0\\\\(x+8)^2-64+y^2-24y+159=0\\\\(x+8)^2+y^2-24y=-159+64\\\\(x+8)^2+(y-12)^2-144=-159+64\\\\(x+8)^2+(y-12)^2=144-159+64\\\\(x+8)^2+(y-12)^2=49\\\\[/tex]

Now, you must use the "form of a circle" equation in order to find out the center and radius of a circle.

The equation is:

[tex](x-h)^2+(y-k)^2=r^2\\\\r=7\\h=-8\\k=12[/tex]

Since we got the answer of:

[tex](x+8)^2+(y-12)^2=49[/tex]

It matches with our equation of [tex](x-h)^2+(y-k)^2=r^2[/tex]

Our "h" represents the x axis on the graph, our "k" represents our y axis on a graph.

Therefore our x value would be -8 and our y value would be 12.

Your FINAL answer should be (-8,12)

____________________________________________________

[tex] {x}^{2} + {y}^{2} + 16x - 24y + 159 = 0 \\ \\ 1. \: x = \frac{ - 16 + 2i \sqrt{(y - 19)(y - 5)} }{2} \: \frac{ - 16 - 2i \sqrt{(y - 19)(y - 5)} }{2} \\ \\ 2. \: x = - 8 + i \sqrt{(y - 19)(y - 5)} \: \: - 8 - i \sqrt{(y - 19)(y - 5)} [/tex]

Make sure you put a comma between them

Answer:

3.2 is the corrext amswr

Step-by-step explanation:

The answer is 3.2 because you only round up if it’s .5 or higher and round down if it’s .4 or lower

Answer:

it is the 2nd graph

Step-by-step explanation:

The graph of the linear equation is a right-angle triangle whose height is 2000 units and base is 200 units.

It is a system of an equation in which the highest power of the variable is always 1. A one-dimension figure that has no width. It is a combination of infinite points side by side.

A farmer can spend no more than $4,000 on fertilizer and seeds. The fertilizer costs $2 per pound and seeds cost $20 per pound.

To summarize the situation, the farmer writes the inequality

[tex]\rm 2 y + 20 x \leq 4,000\\\\y \leq 2000 - 10x[/tex]

where y be the number of pounds of fertilizer and x be the number of pounds of seeds.

Then the graph is shown below.

More about the linear system link is given below.

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Answer:

1. B

2. B

Step-by-step explanation:

** Attached picture of the situation

The bird caught the fish at point A, flew until B (which is 100 yds away, dropped the fish at C (which is horizontally 50 yards from A).

1.

We want the angle that the bird creates with the water (horizontal). It is angle BAC. With respect to the right triangle, we can say that we know "hypotenuse" and "adjacent" side to angle BAC. cosine relates hypotenuse and adjacent, thus we can write:

[tex]Cos(BAC)=\frac{50}{100}\\Cos(BAC)=\frac{1}{2}\\BAC=Cos^{-1}(\frac{1}{2})\\BAC=60[/tex]

correct answer is B

2.

Here, we want to find the distance (length) of segment BC. With respect to the angle BAC (we found to be 60), we can say BC is "opposite". We know hypotenuse to be 100. So let's use sine, since sine is ratio of opposite to hypotenuse. Thus, we can write:

[tex]Sin(BAC)=\frac{BC}{100}\\Sin(60)=\frac{BC}{100}\\BC=Sin(60)*100\\BC=86.6[/tex]

correct answer is B

The answers should be B)60 and B) 86.6

ANSWER

The height is 30 feet

EXPLANATION

The volume of a cylinder is calculated using the formula;

[tex]V = \pi {r}^{2} h[/tex]

The diameter is 24 ft. This implies that the radius of the cylinder is 12ft.

We substitute known values to get:

[tex]4320\pi= \pi{(12)}^{2} h[/tex]

[tex]4320\pi=144 \pi h[/tex]

Divide both sides by 144π

[tex]h = 30ft[/tex]

She rode 1,836 miles in total.

Answer:

median:36.5

mean:37

Step-by-step explanation:

to find medain put all of the numbers in order. then find the center number

for the mean add all of the numbers together ad divide it by the amount of data points there are

Answer:

median:                                  36.5

mean:                                       37

Step-by-step explanation:

Answer:

V = 256 mm3

Hope this helps you out!

Answer:

D,256

Step-by-step explanation:

Use multiplication to do 8*10*3.2 you get 256

Answer:

Parallelogram

Step-by-step explanation:

graphing them makes two sets of parallel lines

kx² + 8x + 8 = 0

We want this to have just one solution, we know this equation:

x = (-b ± √Δ)/2a

So if Δ = 0 we have just one solution.

Δ = b² - 4.a.c

0 = 8² - 4.k.8

0 = 64 - 32k

32k = 64

k = 2

2x² + 8x + 8 = 0

x² + 4x + 4 = 0

(x + 2)² = 0

x + 2 = 0

x = -2

The solution is -2.

The non-zero value of k for which the quadratic equation kx²+8x+8=0 has only one solution is '1'. This is arrived at by setting the discriminant of the quadratic equation (b² - 4ac) to zero and solving for 'k.'

The subject of this question is a mathematical concept known as a discriminant in a quadratic equation. A quadratic equation is generally in the form of ax²+bx+c = 0. The discriminant of the quadratic equation kx²+8x+8=0 is given by the formula b²-4ac, where 'a is the coefficient of x² (which is 'k' in this case), 'b' is the coefficient of x, and 'c' is the constant term. The discriminant must equal zero for the quadratic equation to have only one solution. Therefore, we have 8² - 4*k*8 = 0. Solving this equation gives k = 1, which is a non-zero value.

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Answer:

A

Step-by-step explanation:

The arc length is calculated as

arc = circumference × fraction of circle

     = 2π × 6 × [tex]\frac{135}{360}[/tex]

     = 12π × [tex]\frac{3}{8}[/tex]

     = [tex]\frac{36\pi }{8}[/tex] ≈ 14.1 in

Answer

14.1 in

Step-by-step explanation:

Length of the arc formula = circumference of the circle * central angle / 360

circumference of the circle formula = [tex]2\pi r[/tex]

where r is the radius of the circle

Radius = 6 in

central angle = 135 degrees

Length of the arc = [tex]2 \pi * radius* \frac{angle}{360}[/tex]

=[tex]2\pi*6* \frac{135}{360}[/tex]

= 14.137= 14.1 in