I wills send you a picture

Answers

Answer 1

Draw the tank

we can use the formula of the volume of a cylinder

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

we can repalce the value of the volume (320pi) and the height

[tex]\begin{gathered} 320\pi=\pi\times r^2\times20 \\ 320\pi=20r^2\pi \end{gathered}[/tex]

now solve for r^2 dividing 20pi on both sides

[tex]\begin{gathered} \frac{320\pi}{20\pi}=r^2 \\ \\ r^2=16 \\ \end{gathered}[/tex]

and solve for r using roots

[tex]\begin{gathered} r=\sqrt[]{16} \\ \\ r=4 \end{gathered}[/tex]

the value of the radious is 4ft and the diameter double, then

[tex]\begin{gathered} d=2\times4 \\ d=8 \end{gathered}[/tex]

diameter of the cylinder is 8 ft then rigth option is C

I Wills Send You A Picture

Related Questions

0.2x + 0.21x - 0.04 = 8.16Solve for "x".

Answers

Given the folllowing equation:

[tex]0.2x+0.21x-0.04=8.16​[/tex]

You need to solve for "x" in order to find its value. To do this, you can follow the steps shown below:

1. You can apply the Addition property of equality by adding 0.04 to both sides of the equation:

[tex]\begin{gathered} 0.2x+0.21x-0.04+(0.04)=8.16​+(0.04) \\ 0.2x+0.21x=8.2 \end{gathered}[/tex]

2. Now you need to add the like terms on the left side of the equation:

[tex]0.41x=8.2[/tex]

3. Finally, you can apply the Division property of equality by dividing both sides of the equation by 0.41:

[tex]\begin{gathered} \frac{0.41x}{0.41}=\frac{8.2}{0.41} \\ \\ x=20 \end{gathered}[/tex]

The answer is:

[tex]x=20[/tex]

(2i) - (11+2i) complex numbers

Answers

= -11
Hope this helps :)

Can someone help me with this math question. I just need to see the work.
pic of question below

Answers

The polar coordinates for each point are given as follows:

a. [tex](r, \theta) = \left(2\sqrt{5}, \frac{7\pi}{4}\right)[/tex]

b. [tex](r, \theta) = \left(6, \frac{\pi}{3}\right)[/tex]

Polar coordinates

Suppose we have a point with Cartesian coordinates given as follows:

(x,y).

The polar coordinates will be found as follows:

r² = x² + y².θ = arctan(y/x).

For item a), the Cartesian coordinates are as follows:

(-4, 4).

Hence the polar coordinates will be given as follows:

r² = (-4)² + (4)² -:> r =  sqrt(32) = 2sqrt(5).θ = arctan(-4/4) = arctan(-1) = -45º = 2pi - pi/4 = 7pi/4.

For item a), the Cartesian coordinates are as follows:

(3, 3sqrt(3)).

Hence the polar coordinates will be given as follows:

r² = (3)² + (3sqrt(3))² = 9 + 27 = 36 -> r = sqrt(36) = 6.θ = arctan(3sqrt(3)/3) = arctan(sqrt(3)) = 60º = pi/3.

More can be learned about polar coordinates at https://brainly.com/question/7009095

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Find the volume of this triangular prism.Be sure to include the correct unit in your answer.8 cm7 cm→5 cm

Answers

The formula to find the volume of a triangular prism is the following:

[tex]V=\frac{1}{2}h\cdot b\cdot w[/tex]

where:

h - height

b - base length

w - width

for this problem:

h = 8 cm

b = 5 cm

w = 7 cm

then

[tex]V=\frac{1}{2}8\cdot5\cdot7[/tex]

solving this, we obtain that the volume of the triangular prism is 140 cm^3 or cubic centimeters

(Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.) And determine the quadrants of A+B and A-B.

Answers

Given that:

[tex]\cos A=\frac{5}{13}[/tex]

Where:

[tex]0And:[tex]\cos B=\frac{3}{5}[/tex]

Where:

[tex]0You need to remember that, by definition:[tex]\theta=\cos ^{-1}(\frac{adjacent}{hypotenuse})[/tex]

Therefore, applying this formula, you can find the measure of angles A and B:

[tex]A=\cos ^{-1}(\frac{5}{13})\approx67.38\text{\degree}[/tex][tex]B=\cos ^{-1}(\frac{3}{5})\approx53.13\text{\degree}[/tex]

(a) By definition:

[tex]\sin \mleft(A+B\mright)=sinAcosB+cosAsinB[/tex]

Knowing that:

[tex]\sin \theta=\frac{opposite}{hypotenuse}[/tex]

You can substitute the known values into the equation in order to find the opposite side for angle A:

[tex]\begin{gathered} \sin (67.38\text{\degree)}=\frac{opposite}{13} \\ \\ 13\cdot\sin (67.38\text{\degree)}=opposite \\ \\ opposite\approx12 \end{gathered}[/tex]

Now you know that:

[tex]\sin A=\frac{12}{13}[/tex]

Using the same reasoning for angle B, you get:

[tex]\begin{gathered} \sin (53.13\text{\degree)}=\frac{opposite}{5} \\ \\ 5\cdot\sin (53.13\text{\degree)}=opposite \\ \\ opposite\approx4 \end{gathered}[/tex]

Now you know that:

[tex]\sin B=\frac{4}{5}[/tex]

Substitute values into the Trigonometric Identity:

[tex]\begin{gathered} \sin (A+B)=sinAcosB+cosAsinB \\ \\ \sin (A+B)=(\frac{12}{13})(\frac{3}{5})+(\frac{5}{13})(\frac{4}{5}) \end{gathered}[/tex]

Simplifying, you get:

[tex]\begin{gathered} \sin (A+B)=\frac{36}{65}+\frac{20}{65} \\ \\ \sin (A+B)=\frac{36+20}{65} \end{gathered}[/tex][tex]\sin (A+B)=\frac{56}{65}[/tex]

(b) By definition:

[tex]\sin \mleft(A-B\mright)=sinAcosB-cosAsinB[/tex]

Knowing all the values, you get:

[tex]\begin{gathered} \sin (A-B)=(\frac{12}{13})(\frac{3}{5})-(\frac{5}{13})(\frac{4}{5}) \\ \\ \sin (A-B)=\frac{36-20}{65} \\ \\ \sin (A-B)=\frac{16}{65} \end{gathered}[/tex]

(c) By definition:

[tex]\tan (A+B)=\frac{\tan A+\tan B}{1-\tan A\cdot\tan B}[/tex]

By definition:

[tex]\tan \theta=\frac{opposite}{adjacent}[/tex]

Therefore, in this case:

- For angle A:

[tex]\tan A=\frac{12}{5}[/tex]

- And for angle B:

[tex]\tan B=\frac{4}{3}[/tex]

Therefore, you can substitute values into the formula and simplify:

[tex]\tan (A+B)=\frac{\frac{12}{5}+\frac{4}{3}}{1-(\frac{12}{5}\cdot\frac{4}{3})}[/tex][tex]\tan (A+B)=\frac{\frac{56}{15}}{1-\frac{48}{15}}[/tex][tex]\tan (A+B)=\frac{\frac{56}{15}}{-\frac{11}{5}}[/tex][tex]\tan (A+B)=-\frac{56}{33}[/tex]

(d) By definition:

[tex]\tan (A-B)=\frac{\tan A-\tan B}{1+\tan A\cdot\tan B}[/tex]

Knowing all the values, you can substitute and simplify:

[tex]\tan (A-B)=\frac{\frac{12}{5}-\frac{4}{3}}{1+(\frac{12}{5}\cdot\frac{4}{3})}[/tex][tex]\tan (A-B)=\frac{\frac{16}{15}}{\frac{21}{5}}[/tex][tex]\tan (A-B)=\frac{16}{63}[/tex]

(e) Knowing that:

[tex]\sin (A+B)=\frac{56}{65}[/tex][tex]\tan (A+B)=-\frac{56}{33}[/tex]

Remember the Quadrants:

By definition, in Quadrant II the Sine is positive and the Tangent is negative.

Since in this case, you found that the Sine is positive and the Tangent negative, you can determine that this angle is in the Quadrant II:

[tex]A+B[/tex]

Draw the following vectors using the scale 1 cm = 50 km/h. Plant the tail at the origin. A. 200 km/h on a bearing of 020° B. 75 km/h S 10° W C. 350 km/h NE

Answers

Solution

a)

200 km/h on a bearing of 020°

Scale 1 cm = 50 km/h.

[tex]Length\text{ = }\frac{200}{50}\text{ = 4cm}[/tex]

b)

B. 75 km/h S 10° W

[tex]Lenght\text{ = }\frac{75}{50}\text{ = 1.5cm}[/tex]

C. 350 km/h NE

[tex]Length\text{ = }\frac{350}{50}\text{ = 7cm}[/tex]

Find the product. Write your answer in scientific notation. (6.5 X 10^8) X (1.4 x 10^-5) =

Answers

Evaluate the product of the expression.

[tex]\begin{gathered} (6.5\times10^8)\cdot(1.4\times10^{-5})=6.5\cdot1.4\times10^{8-5} \\ =9.1\times10^3 \end{gathered}[/tex]

So answer is 9.1X10^3.

I need these answers quickly. If I don't get them by midnight ill cry.

Answers

The answer is the second option, “The tank has 200 gallons in it when Jack opens the valve.”

This is because the y intercept represents how much water is in the tank when the time = 0 minutes, and at 0 minutes Jack hasn’t opened the valve yet and no water has been lost.

Slope of Linear EquationsWhich description best compares the graph given by the following equations:23-5y = 82Y == -6Choose one. 4 pointsO parallelO perpendicularintersecting but not perpendicularO coinciding

Answers

Answer:

The two lines are parallel.

Explanation:

We have the equations:

[tex]\begin{gathered} 2x-5y=8 \\ y=\frac{2}{5}x-6 \end{gathered}[/tex]

Let's solve the first one for y, so we get the same formatting on both euqations:

[tex]\begin{gathered} 2x-5y=8 \\ 5y=2x-8 \\ y=\frac{2}{5}x-\frac{8}{5} \end{gathered}[/tex]

SInce the two lines have the same slope, 2/5, the two lines are parallel.


*Statistical question: Is the proportion of inner-city families living on a subsistence income: 20%? Two hundred families were randomly selected for the survey
and 38 were found to have income at the subsistence level. Use the formal critical value method at 5% level of significance.
List the assumptions pertaining to this procedure.


Answers

Since the critical value of the test is greater than the absolute value of the test statistic, there is not enough evidence to conclude that the proportion is different of 20%.

Hypothesis tested and critical value

At the null hypothesis, it is tested if the proportion is of 20%, that is:

[tex]H_0: p = 0.2[/tex]

At the alternative hypothesis, it is tested if the proportion is different of 20%, hence:

[tex]H_1: p \neq 0.2[/tex]

We have a two-tailed test, as we are testing if the mean is different of a value, with a significance level of 0.05, hence the critical value is of:

|z| = 1.96.

Test statistic

The test statistic is given by the rule presented as follows:

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

In which:

[tex]\overline{p}[/tex] is the sample proportion.p is the proportion tested at the null hypothesis.n is the sample size.

In the context of this problem, the parameters are given as follows:

[tex]p = 0.2, n = 200, \overline{p} = \frac{38}{200} = 0.19[/tex]

Hence the test statistic is:

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

[tex]z = \frac{0.19 - 0.2}{\sqrt{\frac{0.2(0.8)}{200}}}[/tex]

z = -0.35.

|z| < 1.96, hence there is not enough evidence to conclude that the proportion is different of 20%.

More can be learned about the use of the z-distribution to test an hypothesis at https://brainly.com/question/13873630

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Four research teamed each used a different method to collect data on how fast a new strain of maize sprouts. Assume that they all agree on the sample size and the sample mean ( in hours). Use the (confidence level; confidence interval) pairs below to select the team that has the smallest sample standard deviation

Answers

We need to identify the team that has the smallest sample standard deviation.

In order to do so, we need to find the stand deviation of each experiment based on the confidence level and confidence interval of each of them.

A. A confidence level of 99.7% corresponds to a confidence interval of 3 standard deviations above and 3 standard deviations below the mean.

Thus, for the confidence interval 42 to 48, the mean is 45. And the standard deviation is given by:

[tex]\begin{gathered} 3\sigma=48-45=3 \\ \\ \sigma=\frac{3}{3} \\ \\ \sigma=1 \end{gathered}[/tex]

B. A confidence level of 95% corresponds to a confident interval of 2 standard deviations above and 2 standard deviations below the mean.

Thus, for the confidence interval 43 to 47, the mean is 45. And the standard deviation is given by:

[tex]\begin{gathered} 2\sigma=47-45=2 \\ \\ \sigma=\frac{2}{2} \\ \\ \sigma=1 \end{gathered}[/tex]

C. A confidence level of 68% corresponds to a confident interval of 1 standard deviation above and 1 standard deviation below the mean.

Thus, for the confidence interval 44 to 46, the mean is 45. And the standard deviation is given by:

[tex]\begin{gathered} \sigma=46-45 \\ \\ \sigma=1 \end{gathered}[/tex]

D. Again, we have a confidence level of 95%, which corresponds to 2 standard deviations.

Thus, for the confidence interval 44 to 46, the mean is 45. And the standard deviation is given by:

[tex]\begin{gathered} 2\sigma=46-45=1 \\ \\ \sigma=\frac{1}{2} \\ \\ \sigma=0.5 \end{gathered}[/tex]

Therefore, the team that has the smallest sample standard deviation is:

Answer

I need help finding 5 points. the vertex, 2 to the left of the vertex, and 2 points to the right of the vertex.

Answers

Let's convert the given equation first into a vertex form.

[tex]y=a(x-h)^2+k[/tex]

where (h, k) is the vertex.

The vertex form of the equatio that we have is:

[tex]y=-2(x-0)^2+0[/tex]

Hence, the vertex of the equation is at the origin (0, 0).

Since "a" is negative, our parabola is opening downward.

Let's identify two points to the left of the vertex. Let's say at x = -1. Replace "x" with -1 in the equation.

[tex]\begin{gathered} y=-2(-1)^2 \\ y=-2(1) \\ y=-2 \end{gathered}[/tex]

Hence, we have a point to the left of the parabola at (-1, -2).

Let's say x = -2. Replace "x" with -2 in the equation.

[tex]\begin{gathered} y=-2(-2)^2 \\ y=-2(4) \\ y=-8 \end{gathered}[/tex]

Hence, we also have another point to the left of the parabola at (-2, -8).

If our x is to the right of the vertex, say, x = 1. Replace "x" with 1 in the equation.

[tex]\begin{gathered} y=-2(1)^2 \\ y=-2(1) \\ y=-2 \end{gathered}[/tex]

We have a point to the right of the parabola at (1, -2).

If x = 2, let's replace "x" with 2 in the equation.

[tex]\begin{gathered} y=-2(2)^2 \\ y=-2(4) \\ y=-8 \end{gathered}[/tex]

Hence, we also have another point to the right of the parabola at (2, -8).

The graph of this equation is:

An observer in a lighthouse 350 ft above sea level observes two ships directly offshore. The angles of depression to the shops are 4 degree and 6.5 degree. How far apart are the ships?

Answers

Answer:

The two ships are 1933.32 ft apart

Explanation:

Given:

The height of the lighthouse = 350 ft

The angles of depression to the ships are 4 degree and 6.5 degree

To find:

the distance between the two ships

To determine the distance, we will use an illustration of the situation

First we will find the value of y as we need to know this value to get x

To get y, we will apply tan ratio (TOA)

[tex]\begin{gathered} tan\text{ 6.5\degree = }\frac{opposite}{adjacent} \\ opp\text{ = 350 ft} \\ adj\text{ = y} \\ tan\text{ 6.5\degree = }\frac{350}{y} \\ y(tan\text{ 6.5\degree\rparen= 350} \\ y\text{ = }\frac{350}{tan\text{ 6.5}} \\ y\text{ = 3071.9106 ft} \end{gathered}[/tex]

Next is to find x using tan ratio (TOA):

[tex]\begin{gathered} angle\text{ = 4\degree} \\ tan\text{ 4\degree= }\frac{opposite}{adjacent} \\ \\ opposite\text{ = 350 ft} \\ adjacent\text{ = y + x} \\ tan\text{ 4\degree= }\frac{350}{y\text{ + x}} \end{gathered}[/tex][tex]\begin{gathered} tan\text{ 4 = }\frac{350}{3071.9106+x} \\ \frac{350}{tan\text{ 4}}\text{ = 3071.9106 + x} \\ 5005.2332\text{ = 3071.9106 + x} \\ x\text{ = 1933.3226} \\ \\ The\text{ ships are 1933.32 ft apart \lparen nearest hundredth\rparen} \end{gathered}[/tex]

You want to build a sandbox that can hold50,445 cubic inches of sand. If the sandbox is to be59 in. long and57 in. wide, how tall will it need to be?

Answers

Volume of sandbox (to be built) = 50,445 cubic inches

A sandbox is the shape of a cuboid and is calculated by the formula

[tex]\text{volume = length }\cdot\text{ wi}\differentialD tth\text{ }\cdot\text{ height }\Rightarrow\text{ v = l }\cdot\text{ w }\cdot\text{ h}[/tex]

Volume = Length * Width * Height

Volume = 50,445 cubic inches, Length = 59 in. Width = 57 in, Height = ?

50,445 = 59 * 57 * h

Make h the subject of the formula, we have:

h = 50445 / (59 * 57) = 15 in

**Determine the x-value at which the-following function touches but does not cross the x-axis:3x^3- 182 + 27x

Answers

Okay, here we have this:

We need to identify the x-value at which the-following function touches but does not cross the x-axis in the following function: 3x^3- 18^2 + 27x. So, considering that if is a zero with even multiplicity, the graph touches the x-axis and bounces off of the axis. And if it is a zero with odd multiplicity, the graph crosses the x-axis at a zero.

According with this let's

I don't understand please explain in simple words the transformation that is happeningwhat is the function notation

Answers

We have the next functions

[tex]f(x)=5^x^{}[/tex][tex]g(x)=2(5)^x+1[/tex]

Function notation

[tex]g(x)=2(f(x))+1[/tex]

Describe the transformation in words

we have 2 transformations, the 2 that multiplies the function f(x) means that we will have an expansion in the y axis by 2, the one means that we will have a shift up by one unit

Use the change of base formula and a calculator to evaluate the logarithm

Answers

The change of base formula states that:

[tex]\log _bx=\frac{\ln x}{\ln b}[/tex]

this means that we can caculate any logarithm using the natural logarithm if we make the quotient of the natural logarithm of the original value and the natural logarithm of the original base.

In this case we have:

[tex]\begin{gathered} x=14 \\ b=\sqrt[]{3} \end{gathered}[/tex]

Then, using the change of base formula, we have:

[tex]\log _{\sqrt[]{3}}14=\frac{\ln 14}{\ln \sqrt[]{3}}[/tex]

Once we have the expression we just evaluate the expression on the right to get the appoximation we need:

[tex]\log _{\sqrt[]{3}}14=\frac{\ln14}{\ln\sqrt[]{3}}\approx4.804[/tex]

What is the seventy-seven is forty-six more than r

Answers

Answer: 77 = 46 + r, r = 31

Step-by-step explanation:

      We will write an equation to represent this situation. Then, we will solve for r by isolating the variable.

  Seventy-seven is forty-six more than r.

77 is forty-six more than r.

77 = forty-six more than r.

77 = 46 more than r.

  77 = 46 + r

  77 = 46 + r

(77) - 46 = (46 + r) - 46

31 = r

  r = 31

write 2500g in appropriate prefix pls.​

Answers

Answer: 2.5kg

Step-by-step explanation:

I am assuming you mean to simplify it. So 2.5kg

1g=1000kg

2500/1000=2.5

I need help question 10 b and c

Answers

Part b.

In this case, we have the following function:

[tex]y=5(2.4)^x[/tex]

First, we need to solve for x. Then, by applying natural logarithm to both sides, we have

[tex]\log y=\log (5(2.4^x))[/tex]

By the properties of the logarithm, it yields

[tex]\log y=\log 5+x\log 2.4[/tex]

By moving log5 to the left hand side, we have

[tex]\begin{gathered} \log y-\log 5=x\log 2.4 \\ \text{which is equivalent to} \\ \log (\frac{y}{5})=x\log 2.4 \end{gathered}[/tex]

By moving log2.4 to the left hand side, we obtain

[tex]\begin{gathered} \frac{\log\frac{y}{5}}{\log2.4}=x \\ or\text{ equivalently,} \\ x=\frac{\log\frac{y}{5}}{\log2.4} \end{gathered}[/tex]

Therfore, the answer is

[tex]f^{-1}(y)=\frac{\log\frac{y}{5}}{\log2.4}[/tex]

Part C.

In this case, the given function is

[tex]y=\log _{10}(\frac{x}{17})[/tex]

and we need to solve x. Then, by raising both side to the power 10, we have

[tex]\begin{gathered} 10^y=10^{\log _{10}(\frac{x}{17})} \\ \text{which gives} \\ 10^y=\frac{x}{17} \end{gathered}[/tex]

By moving 17 to the left hand side, we get

[tex]\begin{gathered} 17\times10^y=x \\ or\text{ equivalently,} \\ x=17\times10^y \end{gathered}[/tex]

Therefore, the answer is

[tex]f^{-1}(y)=17\times10^y[/tex]

Write the equation of the circle centered at (−4,−2) that passes through (−15,19)

Answers

In this problem, we are going to find the formula for a circle from the center and a point on the circle. Let's begin by reviewing the standard form of a circle:

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

The values of h and k give us the center of the circle, (h,k). The value r is the radius. We can begin by substituting the values of h and k into our formula.

Since the center is at (-4, -2), we have:

[tex]\begin{gathered} (x-(-4))^2+(y-(-2))^2=r^2 \\ (x+4)^2+(y+2)^2=r^2 \end{gathered}[/tex]

Next, we can use the center and the given point on the circle to find the radius.

Recall that the radius is the distance from the center of a circle to a point on that circle. So, we can use the distance formula:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Let

[tex](x_1,y_1)=(-4,-2)[/tex]

and let

[tex](x_2,y_2)=(-15,19)[/tex]

Now we can substitute those values into the distance formula and simplify.

[tex]\begin{gathered} r=\sqrt{(-15-(-4))^2+(19-(-2))^2} \\ r=\sqrt{(-11)^2+(21)^2} \\ r=\sqrt{562} \end{gathered}[/tex]

Adding that to our equation, we have:

[tex]\begin{gathered} (x+4)^2+(y+2)^2=(\sqrt{562})^2 \\ (x+4)^2+(y+2)^2=562 \end{gathered}[/tex]

Use the information given to find the equation of the line using the point-slope formula (y-y_1=m(x-x_1)). Then convert your answer to slope-intercept form (y=mx+b).(0,3) with a slope of 4The point slope form is (y-Answer)=Answer(x-Answer)Converting it to slope intercept form gives us y=Answerx+Answer

Answers

we have

m=4

point (0,3)

y-y1=m(x-x1)

substitute given values

y-3=4(x-0) ----> equation in point slope form

Convert to slope-intercept form

y=mx+b

y-3=4x

adds 3 both sides

y=4x+3 ----> equation in slope-intercept form

what is 0.024 ÷ 0.231​

Answers

Answer:

0.10389610389

Step-by-step explanation:

Hi!

I plugged it into a calculator:

0.024 ÷ 0.231​ = 0.10389610389

Have a great day! :)

The points (1,7) and (7,5) fall on a particular line. What is its equation in point-slope form?
Use one of the specified points in your equation. Write your answer using integers, proper fractions, and improper fractions. Simplify all fractions.

Answers

Answer:

[tex]y-7=-\dfrac{1}{3}(x-1)[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{4.4cm}\underline{Slope Formula}\\\\Slope $(m)=\dfrac{y_2-y_1}{x_2-x_1}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ \\are two points on the line.\\\end{minipage}}[/tex]

To find the equation of a line that passes through two given points, first find its slope by substituting the given points into the slope formula.

Define the points:

(x₁, y₁) = (1, 7)(x₂, y₂) = (7, 5)

Substitute the points into the slope formula:

[tex]\implies m=\dfrac{5-7}{7-1}=\dfrac{-2}{6}=-\dfrac{1}{3}[/tex]

Therefore, the slope of the line is -¹/₃.

[tex]\boxed{\begin{minipage}{5.8 cm}\underline{Point-slope form of a linear equation}\\\\$y-y_1=m(x-x_1)$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $(x_1,y_1)$ is a point on the line.\\\end{minipage}}[/tex]

To find the equation in point-slope form, simply substitute the found slope and one of the given points into the point-slope formula:

[tex]\implies y-7=-\dfrac{1}{3}(x-1)[/tex]

Need help figuring out if the following is Real or Complex Question number 10

Answers

Explanation:

We have the expression:

[tex]i^3[/tex]

where i represents the complex number i defined as follows:

[tex]i=\sqrt{-1}[/tex]

To find if i^3 is real or complex, we represent it as follows:

[tex]i^3=i^2\times i[/tex]

And we find the value of i^2 using the definition of i:

[tex]i^2=(\sqrt{-1})^2[/tex]

Since the square root and the power of 2 cancel each other

[tex]\imaginaryI^2=-1[/tex]

And therefore, using this value for i^2, we can now write i^3 as follows:

[tex]\begin{gathered} \imaginaryI^3=\imaginaryI^2\times\imaginaryI \\ \downarrow \\ \imaginaryI^3=(-1)\times\imaginaryI \end{gathered}[/tex]

This simplifies to -i

[tex]\imaginaryI^3=-\imaginaryI^[/tex]

Because -i is still a complex number, that means that i^3 is a complex number.

Answer: Complex

What is the first operation that should be performed to calculate (3 + 2) × 6÷5 - 4?

A) addition
B) division
C) subtraction
D) multiplication

Answers

Answer: A) addition

Step-by-step explanation:

because of BODMAS, you need to do the bracket first

addition is first
(3+2)

Sara spent 35 minutes on math homework and 20 minutes on reading homework. Mia spent a total of 40
minutes on reading and math homework. How much longer did Sara spend on her homework than Mia?

Answers

Sara spent 15 minutes longer than (the difference is 15 min) Mia in her homework.

According to the question,

We have the following information:

Sara spent 35 minutes on math homework and 20 minutes on reading homework. Mia spent a total of 40 minutes on reading and math homework.

So, it means that the total time spent by Sara in her homework is:

35+20 minutes

55 minutes

So, the differences between their time spent in her homework (will give us the more time taken by Sara) is:

Time spent by Sara in her homework-time spent by Mia in her homework

(55-40) minutes

15 minutes

Hence, Sara spent 15 more minutes than Mia.

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Find 2 given that =−4/5 and < < 3/2

Answers

Find 2 given that =

−4/5 and < < 3/2

we know that

sin(2x) = 2 sin(x) cos(x)

so

step 1

Find the value of cos(x)

Remember that

[tex]\sin ^2(x)+\cos ^2(x)=1^{}[/tex]

we have

sin(x)=-4/5

The angle x lies on III quadrant

that means

cos(x) is negative

substitute the value of sin(x)

[tex]\begin{gathered} (-\frac{4}{5})^2+\cos ^2(x)=1^{} \\ \\ \frac{16}{25}+\cos ^2(x)=1^{} \\ \\ \cos ^2(x)=1-\frac{16}{25} \\ \cos ^2(x)=\frac{9}{25} \\ \cos (x)=-\frac{3}{5} \end{gathered}[/tex]

step 2

Find the value of sin(2x)

sin(2x) = 2 sin(x) cos(x)

we have

sin(x)=-4/5

cos(x)=-3/5

substitute

sin(2x)=2(-4/5)(-3/5)

sin(2x)=24/25

Enter a rule for each function f and g, and then compare their domains, ranges, slopes, and y-intercepts.The function f(x) has a slope of -2 and has a y-intercept of 3. The graph shows the function g(x).

Answers

The rule of the function f(x) is : -2x + 3

To find the rule of the function g(x) let's calculate the slope of the line

[tex]m=\frac{y2-y1}{x2-x1}=\frac{-11-5}{4-0}=\frac{-16}{4}=-4[/tex]

The slope of the line is -4 and the intercept is 5 ( from the graph).

The rule of the function g(x) is : -4x + 5

The domains of f(x) and g(x) is All real numbers, because there is not any number of x which doesn't have a corresponding y-coordinate.

The ranges of f(x) and g(x) is All real numbers, because there is not any number of y which doesn't have a corresponding x-coordinate.

The slope of f(x) is greater than g(x) (-2 is greater than -4)

The y-intercept of f(x) is less than the y-intercept of g(x).(3 is less than 5)

How to find the area of a regular hexagon with a radius of 12 inches? Please help

Answers

[tex]\begin{gathered} In\text{ this case, as a regular hexagon} \\ \text{radius = side} \\ Area\text{ =}3\cdot\frac{\sqrt[]{3}side^2}{2} \\ \text{side}=12in \\ side^2=144in^2 \\ Area\text{ =}3\cdot\frac{\sqrt[]{3}\cdot(144in^2)}{2} \\ \\ \text{Area}=374.1in^2 \\ \text{The regular hexagon's area is }374.1in^2 \end{gathered}[/tex]

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