A circle with radius x is shown below. The diagram is not drawn to scale.

Step-by-step explanation:

[tex]area = \frac{1}{2} (x + 3)(x + 5) = 24 \\ [/tex]

then

[tex](x + 3)(x + 5) = 48[/tex]

[tex] {x}^{2} + 8x + 15 = 48 [/tex]

[tex] {x}^{2} + 8x + 15 - 48 = 0 \\ {x}^{2} + 8x - 33 = 0[/tex]

[tex] {x}^{2} - 3x + 11x - 33 = 0 \\ x(x - 3) + 11(x - 3) = 0 \\ (x - 3)(x + 11) = 0[/tex]

so

[tex]x = 3 \: or \: x = - 11(reject \: because \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: x > 0)[/tex]

hence,

[tex]x = 3[/tex]

Thus, one leg is 8 and other leg is 6.

Since it is a right triangle then we have

[tex]hypotenuse = \sqrt{ {8}^{2} + {6}^{2} } = \sqrt{100} = 10[/tex]

Finally,

[tex]perimeter = 8 + 6 + 10 = 24(ft)[/tex]

Answer:

1.

Experimental : [tex]\frac{14}{25}[/tex] or 56%

Theoretical : [tex]\frac{1}{2}[/tex] or 50%

2.

22 customers

Step-by-step explanation:

Theoretical is how many times you'd expect it to land. So for coin flipping it would be either heads or tails. The probability it would land on heads would be 50% because it's either one or the other.

Experimental is how many times you actually landed it. You flipped a coin and it landed on heads 28 times, so you can put that over 50.

Since [tex]\frac{28}{50}[/tex] can be simplified to [tex]\frac{14}{25}[/tex] or 56%, that is the experimental probability.

For the second variation, we can assume that it is direct variation.

[tex]y=kx[/tex]

When [tex]y[/tex] increases, [tex]x[/tex] increases.

Let's solve for [tex]k[/tex].

[tex]11=50k \\ \\ k=\frac{11}{50}[/tex]

We can plug that in to the second equation since we already know how many customers there will be.

[tex]y=0.22k \\ \\ y=0.22(100) \\ \\ y=22[/tex]

It’s the second answer and the last answer :)

Answer:

The 5 is in the hundreds place.

480,516 is equivalent to 400,000 + 80,000 + 500 + 10 + 6

Step-by-step explanation:

Answer:

[tex]\frac{6\left(x+4\right)\left(x+3\right)}{24\left(x-3\right)\left(x+4\right)}=\frac{x+3}{4\left(x-3\right)}[/tex]

[tex]\mathrm{Cancel\:the\:common\:factor:}\:6\\=\frac{\left(x+4\right)\left(x+3\right)}{4\left(x-3\right)\left(x+4\right)}\\\mathrm{Cancel\:the\:common\:factor:}\:x+4[/tex]

Hope this helps!!!

[tex]Sofia[/tex]

The surface area of the triangular prism is 1950 square inches, computed by summing the areas of its constituent triangles and rectangles.

Surface area refers to the measure of the total area that the surface of an object occupies. It is a crucial geometric concept that varies for different shapes and dimensions in geometry, encompassing diverse forms like spheres, cubes, cuboids, cones, and cylinders. Each geometric shape possesses unique formulas for calculating its surface area.

Considering the provided net for a triangular prism with side lengths a, b, and c, and altitude d, the surface area is computed by summing the areas of its constituent shapes – two triangles and three rectangles. The formula for the total surface area is given as:

Total Surface Area = Surface Area of Triangle + Surface Area of Rectangle

Detailed calculations involve substituting the given values for side lengths and altitude into the formulas for the surface area of a triangle and a rectangle. For the triangular prism described, the total surface area is determined as:

Total Surface Area = d * a + b * a + 2 * c * b

Substituting the given values (d = 20, a = 44, b = 14, and c = 30), the calculation yields:

Total Surface Area = (22 * 45) + (12 * 45) + 2 * (30 * 14) = 1950

Therefore, the surface area of the given figure is 1950 square inches.

Final answer:

The surface area of the triangular prism is calculated by adding the areas of the two triangular faces and three rectangular faces. Upon calculation, the areas of two triangles are 600 square inches, and the rectangles are 900 and 280 square inches for sides a and b, respectively. However, none of the provided answer choices match the calculated surface area of 1780 square inches.

Explanation:

To find the surface area of a triangular prism, we need to find the area of all its faces. We have two triangular faces and three rectangular faces. The area of each triangular face is calculated using the formula A = bh/2, where b is the base and h is the height. Since side c is 30 inches and the altitude d is 20 inches, the area of one triangular face is:

A triangle = (c x d) / 2

= (30 inches x 20 inches) / 2

= 600 / 2

= 300 square inches

Since there are two triangular faces, we double this to get 600 square inches for both.

The rectangular faces consist of the sides a, b, and c. Their areas are a x d, b x d and c x d, respectively. So we calculate:

Side a: 45 inches x 20 inches = 900 square inches

Side b: 14 inches x 20 inches = 280 square inches

Side c (already computed as part of triangular faces)

Sum the areas of all these faces to get the total surface area:

Total surface area = (Area of triangles) + (Area of rectangles)

= 600 square inches (triangles) + 900 square inches (side a) + 280 square inches (side b)

= 1780 square inches

The correct answer must include the area of both triangular faces and all three rectangular faces. Since none of the given options match the computed total surface area, it's possible there may have been an error in the provided options or in the dimensions given for the prism.

Answer:

I'm pretty sure its a Trapezoid but don't quote me

Step-by-step explanation:

I don't really know

The shape of the cross section of the figure that is perpendicular to the rectangular base but does not pass through the top vertex is a rectangle.

A rectangle is a quadrilateral (having four sides and four angles) in which opposite sides are equal and parallel. The diagonals bisect each other, and each angle measures 90 degrees.

The shape of the cross section of the figure that is perpendicular to the rectangular base but does not pass through the top vertex is a rectangle.

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Answer:

the answer is c not sure if right

Answer:  [tex]\bold{d)\quad y = 3 cos (\dfrac{4}{3}x-2\pi) + 2}[/tex]

Step-by-step explanation:

[tex]\text{Period = }\dfrac{2\pi}{B}\\\\\\\dfrac{1}{2}\text{Period = }\dfrac{1}{2}\cdot \dfrac{2\pi}{B}\quad =\dfrac{2\pi}{2B}\\\\\\\text{In the given equation, B = }\dfrac{2}{3}\implies 2B=\dfrac{2\cdot 2}{3}\quad =\dfrac{4}{3}\\[/tex]

The only option that has B = 4/3 is the last one.

Answer:

First one.

Step-by-step explanation:

The domain of the function in the correct set notation is {x|x∈R x≠-3}.

The domain of a function is the set of all possible inputs that the function can have.

The function is given to be f(x)=1 /(2x+6).

Here, we can see that the function would become not be defined if the denominator becomes zero.

Therefore, the domain should not contain the values which make it not defined.

The value of x for which it becomes zero can be determined below:

2x+6=0

2x=-6

x=-3

Therefore, the domain must contain all values of real numbers except -3.

The domain of the function is found. The domain of the function is the set of all real numbers except -3. It can be written as {x|x∈R x≠-3}.

Therefore, we have found the domain of the function in the correct set notation is {x|x∈R x≠-3}.

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Answer:

6.44

Step-by-step explanation:

A=1/  4 divided by﹣a4+2(ab)2+2(ac)2﹣b4+2(bc)2﹣c4 =1/  4· divided by﹣24+2·(2·7)2+2·(2·8)2﹣74+2·(7·8)2﹣84    ≈6.4372

Sorry if it's a little complicated but that's how I learned it

Answer:

c.

6.4 units

Step-by-step explanation:

hmmm was going to do a quick mockup, but it might be too wide, so let's nevermind that piece.

so let's see, the center of this ellipse is at (3,1), and a focus point is at (8,1), notice, the y-coordinate is the same, meaning the distance between those two points is "c", which is 5, so c = 5.

We also know that the directrix is x = 36.8, well, that's a vertical line, if the line is vertical, that means the ellipse is running perpendicular to that, namely it has a major axis over the x-axis, so is horizontal.

[tex]\bf \textit{ellipse, horizontal major axis} \\\\ \cfrac{(x- h)^2}{ a^2}+\cfrac{(y- k)^2}{ b^2}=1 \qquad \begin{cases} center\ ( h, k)\\ vertices\ ( h\pm a, k)\\ c=\textit{distance from}\\ \qquad \textit{center to foci}\\ \qquad \sqrt{ a ^2- b ^2}\\ eccentricity\quad e=\cfrac{c}{a}\\\\ directrix=h\pm \cfrac{a^2}{c} \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]

[tex]\bf \stackrel{\textit{its directrix}}{x=h\pm\cfrac{a^2}{c}}\implies \stackrel{\textit{using one directrix}}{36.8=h+\cfrac{a^2}{c}}\qquad \begin{cases} h=3\\ k=1\\ c=5 \end{cases}\implies 36.8=3+\cfrac{a^2}{5} \\\\\\ 33.8=\cfrac{a^2}{5}\implies \boxed{169=a^2}\implies 13=a \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf \stackrel{\textit{recall that }}{c=\sqrt{a^2-b^2}}\implies 5=\sqrt{169-b^2}\implies 5^2=169-b^2\implies 5^2+b^2=169 \\\\\\ b^2=169-5^2\implies \boxed{b^2=144}\implies b=12 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \cfrac{(x-3)^2}{169}+\cfrac{(y-1)^2}{144}=1~\hfill[/tex]

Answer:

a  on edgn btw

Step-by-step explanation:

Answer:

Third option

m = 2.25

Step-by-step explanation:

The slope of the function is equal to its rate of change between two points.

For example, for a couple of points [tex](x_1, y_1),\ (x_2, y_2)[/tex]

The slope is:

[tex]m =\frac{y_2-y_1}{x_2-x_1}[/tex]

In this problem we have the following points

1.(2, 8.50) , 2. (5, 15.25), 3. (8, 22.00) , 4. (12, 31.00)

We calculate the slope between the first two points

[tex]m =\frac{15.25-8.50}{5-2}=2.25[/tex]

We calculate the slope between the points 3 and 4

[tex]m =\frac{31-22}{8-4}=2.25[/tex]

We calculate the slope between the points 2 and 3

[tex]m =\frac{22-15.25}{8-5}=2.25[/tex]

The slope is always the same. Therefore m is constant and the fution is a line of slope m = 2.25

Answer:it’s C 2.25

Step-by-step explanation:

Answer:

684

Step-by-step explanation:

A=a+b

2h=26+46

2·19=684

Answer:

684 m²

Step-by-step explanation:

The area (A) of a trapezoid is calculated using the formula

A = [tex]\frac{1}{2}[/tex] h (a + b)

where h is the perpendicular height and a, b the parallel bases

here h = 19, a = 46 and b = 26

A = [tex]\frac{1}{2}[/tex] × 19 × (46 + 26)

   = 9.5 × 72 = 684 m²

Answer:

2, 3, and 4

Step-by-step explanation:

The answer is:

The third option:

2.7 times as much.

To calculate how many more juice will the new can hold, we need to calculate the old can volume to the new can volume.

So, calculating we have:

Old can:

Since the cans have a right cylinder shape, we can calculate their volume using the following formula:

[tex]Volume_{RightCylinder}=Volume_{Can}=\pi r^{2} h[/tex]

Where,

[tex]r=radius=\frac{diameter}{2}\\h=height[/tex]

We are given the old can dimensions:

[tex]radius=\frac{5.2cm}{2}=2.6cm\\\\height=9.4cm[/tex]

So, calculating the volume, we have:

[tex]Volume_{Can}=\pi *2.6cm^{2} *9.4cm=199.7cm^{3}[/tex]

We have that the volume of the old can is:

[tex]Volume_{Can}=199.7cm^{2}[/tex]

New can:

We are given the new can dimensions, the diameter is increased but the height is the same, so:

[tex]radius=\frac{8.5cm}{2}=4.25cm\\\\height=9.4cm[/tex]

Calculating we have:

[tex]Volume_{Can}=\pi *4.25cm^{2} *9.4cm=533.40cm^{3}[/tex]

Now, dividing the volume of the new can by the old can volume to know how many times more juice will the new can hold, we have:

[tex]\frac{533.4cm^{3} }{199.7cm^{3}}=2.67=2.7[/tex]

Hence, we have that the new can hold 2.7 more juice than the old can, so, the answer is the third option:

2.7 times as much.

Have a nice day!

Answer: 125 squared ft

Area of the big rectangle ⬜️, 15ft x 10ft = 150 square ft

Area of the small square(which is spaced), 5ft x 5ft = 25 squared ft

Area of the give figure, 150squared ft- 25squared ft = 125 squared ft

Answer:

The answer is 125ft

The diameter is 8.5 feet

The Y is 100

Answer:

8

Step-by-step explanation:

To obtain the second term substitute n = 2 into the recursive rule, that is

f(2) = f(2 - 1) + 5 = f(1) + 5 = 3 + 5 = 8

Answer= .2 probability

Explanation: Since there is a total of 10 marbles, and 2 are red, you would divide the red marbles (2) out of the total marbles (10) which would get u .2. Since it’s asking for probability, we would keep .2 a decimal.

The probability of randomly picking a red marble from the bag is 2 out of 10, or 0.2 when expressed as a decimal, which equates to a 20% chance.

The subject of the question you asked is mathematics, specifically probability. In order to calculate the probability of an event happening, you divide the number of successful outcomes by the total number of outcomes. In this case, the successful outcome would be picking a red marble.

The total number of marbles in the bag is 5 (green) + 3 (blue) + 2 (red) = 10. The successful outcomes are 2 (the red marbles). Therefore, the probability of picking a red marble is 2/10 or 0.2.

To put this as a percentage, you multiply by 100, so the probability is 20%. This means that if you pick a marble out at random, there is a 20% chance that it will be red. This is assuming that after each pick, you put the marble back in the bag, also known as picking 'with replacement'.

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Answer:

Yes, I just checked it. All of it is right!

Step-by-step explanation:

Good Job!!

Answer:

a = 30

b = 40

C

Step-by-step explanation:

This requires that you use a proportion.

a / (a + 15) = 40 / 60

The small triangle's sides are in proportion to the large triangles sides.

Reduce the right. Divide top and bottom by 20

a/(a + 15) = 40/20 // 60/20

a/(a + 15) = 2/3                    

Cross multiply

3a = 2(a + 15)            Remove the brackets on the right.

3a = 2a + 30

Subtract 2a from both sides

3a-2a = 30

a = 30

Find B

b is done exactly the same way.

b/(b+20) = 2/3

3b = 2b + 40

3b - 2b = 40

b = 40

Answer: 3, 21, 9, 15, ... any thing you can divide three with

Step-by-step explanation:

Step-by-step explanation:

The odd number whose a factor is the number 3 is  a positive odd multiple of 3:

3, 9, 15, 21, 27, 33, 39, 45, 51, 57, ...

Answer:

The father did more.

13/28 needs to be mowed which is 0.4643 of the lawn needs to be mowed.

Step-by-step explanation:

The best way to compare the two is to change them to decimals. That will at least answer who mowed the most.

Father: 2/7 = 0.2857

Son: 1/4 = 0.25

Since the father mowed 2/7 of the lawn, he mowed the most.

You can use the decimals to get the second part.

Together they did 0.25 + 0.2857 = 0.5357

The amount of the lawn left is 1 - 0.5357 = 0.4643

================

If you must have this in fractions then

1/4 + 2/7 = 7/28 + 2*4/28 = 7/28 + 8/28 = 15/28

15/28 = 0.5357 which is just what we got above.

Amount left to do = 1- 15/28 = 13/28

13/28 = 0.4643 which is what we got about.

Answer:

F=10

Step-by-step explanation:

Answer:

700,000

Step-by-step explanation:

2 = million

7 = hundred thousands

4 = ten thousands

1 = thousands

2 = hundreds

0 = tens

3 = ones

I hope I helped!

Let me know if you need anything else!

~ Zoe

If 1 newton pushes it 0.3 meters, it would take 1.5 / 0.3 newtons, or 5 newtons to push it 1.5 meters

Answer: 5 Newton

Step-by-step explanation:

We know that the Hooke's law states that the force 'F' needed to stretch or compress a spring by some distance 'a' is proportional to that distance .

[tex]F=\dfrac{a}{c}[/tex], where c is the spring constant.

Given: A spring has spring constant 0.3 m/newton.

The  force is necessary to stretch the spring by 1.5 meters is given by :-

[tex]\Rightarrow\ F=\dfrac{1.5}{0.3}\\\\\Rightarrow\ F=5[/tex]

Hence, the  force is necessary to stretch the spring by 1.5 meters = 5 Newton .

Answer:

7/8ths of a pizza.

Step-by-step explanation:

3/8 + 1/2

Find the LCD and then combine.

7/8 in exact form, and 0.875 as a decimal.

Of the boys surveyed, more prefer cats. Of the girls survey, more prefer dogs. The does appear to be an association between gender and animal preference.

In this problem, we have that boys and girls have different preferences regarding animals, that is, from the table:

Hence there does appear to be an association between gender and animal preference.

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Answer:

1. 21

2. -4

3. 20

4. 1

5. 4

6. -6

Step-by-step explanation: