A cuboid with a volume of 374cm^3 has dimensions 2cm,(x+3)cm and (x+9)cm
Please help me get the full 7 marks

Answer:

x = 30

Step-by-step explanation:

x/2 = 12 + 3

x = 2(12+3)

x = 30

Applying the angles of intersecting secants theorem, the measures of the arcs are:

m(KL) = 20°; m(MJ) = 80°.

When two secants intersect and form an angle outside the circle, the measure of the angle formed is half the positive difference of the measures of the intercepted arcs.

Given the following:

m∠MEJ = 1/2(MJ - KL)

30 = 1/2(MJ - KL)

60 = MJ - KL

KL = MJ - 60

m∠MFJ = 1/2(MJ + KL)

50 = 1/2(MJ + MJ - 60)

100 = 2MJ - 60

2MJ = 100 + 60

2MJ = 160

MJ = 160/2

MJ = 80°

KL = MJ - 60 = 80 - 60

KL = 20°

Thus, applying the angles of intersecting secants theorem, the measures of the arcs are:

m(KL) = 20°; m(MJ) = 80°.

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The fraction is 5/2

The decimal is 2.5

Answer:

8 days per 1 pound

Step-by-step explanation:

Using the calculator enter 1 divided by .125

Thats all :)

Answer:

[tex]y=\frac{1}{10}x + 7[/tex]

Step-by-step explanation:

Hi there!

We are given the points (-20, 5) and (-10, 6)

We want to write the equation of the line in slope-intercept form

Slope-intercept form can be written as y=mx+b, where m is the slope, and b is the y intercept

First, let's find the slope of the line

The formula for the slope (m) calculated from 2 points is [tex]\frac{y_2-y_1}{x_2-x_1}[/tex], where [tex](x_1, y_1)[/tex]and [tex](x_2, y_2)[/tex] are points

We have everything we need to find the slope, but let's label the values of the points to avoid confusion and mistakes

[tex]x_1=-20\\y_1=5\\x_2=-10\\y_2=6[/tex]

Substitute these values into the formula to find the slope

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

m=[tex]\frac{6-5}{-10--20}[/tex]

Simplify

m=[tex]\frac{1}{-10+20}[/tex]

m=[tex]\frac{1}{10}[/tex]

The slope (m) of the line is 1/10

We can substitute this value into the formula y=mx+b

y = [tex]\frac{1}{10}x[/tex] + b

Now we need to solve for b

As the equation passes through the points (-20, 5) and (-10, 6), we can use either point to solve for b.

Taking (-20, 5) for instance:

Substitute -20 as x and 5 as y:

5=[tex]\frac{1}{10}(-20)[/tex] + b

Multiply

5=-2+b

Add 2 to both sides

7=b

Substitute 7 as b.

y=[tex]\frac{1}{10}x + 7[/tex]

Hope this helps!

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The amplitude of a periodic graph of a function is 2 because the amplitude of the function is half of the difference between the maximum and minimum values of a function.

It is defined as a special type of relationship and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have a graph of a function(refer to attached picture)

We know the amplitude of the function is given by:

[tex]\rm Amplitude \ of \ f \ = \frac{1}{2} |max \ f -min \ f|[/tex]

As we can see in the graph the maximum value is 0 and

the minimum value of a function is -4, thus the amplitude

[tex]\rm Amplitude \ of \ f \ = \frac{1}{2} |0 -(-4)|[/tex]

The amplitude of f = 2

Thus, the amplitude of a periodic graph of a function is 2 because the amplitude of the function is half of the difference between the maximum and minimum values of a function.

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Answer:

5 3/12 cm^2

Step-by-step explanation:

I just put it in the calculator.

The amount Dempsey can expect to receive from the sale of the bonds is $424,578.27.

The amount that would be recieved from the sale of the bond is the present value of the bond. Present value is the sum of discounted cash flows.

Present value can be determined using a financial calcualtor:

PV = $424,578.27

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Answer:

refrence attached

Step-by-step explanation:

Answer:

Around x = 3 y = 6

Step-by-step explanation:

I'm not sure if you need to round to the nearest whole or hundreth or tenth

Answer: There are no answer choices but an example of a true statement would be that spending on a debit card will NOT count towards your credit score.

Step-by-step explanation:

The form that the null and alternative hypothesis should take if the investigator is concerned only about salary discrimination include U = $82000 and U < $82000.

The alternative hypothesis is the claim of the test. Here, the investigator wants to test whether the average salary of females is less than $82500.

Assuming the hypothesis test supports the conclusion of salary discrimination against female members, the 0.01 level of significance will be recommended.

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Answer: x=12

Step-by-step explanation:

The two angles provided are on a straight line

A straight line is 180 degrees, so we can add the two angles to make 180 and solve for x

[tex]10x-20+6x+8=180[/tex]

Simplify

[tex]10x-20+6x+8=180\\10x+6x-20+8=180\\16x-12=180[/tex]

Add 12 on both sides

[tex]16x-12=180\\16x-12+12=180+12\\16x=192[/tex]

Divide both sides by 16 to isolate x

[tex]16x=192\\\frac{16x}{16} =\frac{192}{16} \\x=12[/tex]

Answer:

i think there was a discount of 40

Step-by-step explanation:

Answer:

The answer is: 40% Off Discount

Step-by-step explanation:

$100 - $60 = 40%

Answer:

1/6

Step-by-step explanation:

1/3 divided by 2

Answer:

x = 47°

Step-by-step explanation:

First see that Angle W is 90°. Either because T is the center and LS is a diameter. Or because Arc LCS is 180° so Angle W is half that = 90°

Then, see Triangle WSL. The angles in a triangle add up to 180°

90° + x + x-4 = 180°

Subtract 90°

x + x - 4 = 90

Combine the x's

2x - 4 = 90

Add 4

2x = 94

Divide by 2.

x = 47

coefficient of 5r² is 5

hope it helps...!!!

PART A: 100 wolves population

PART B: 6/5

Answer:

Part A: 100 wolves population.

Part B:6/5

Step-by-step explanation:.

The solution to the system of inequalities y > -2x+7, y ≤ 3x-8 is the set of points ( (x,y) pairs ) in the intersection of the regions these inequalities are true for, as shown in the graph by the intersection of the blue and red colors.

When mathematical expressions are compared, with non-strict equality, then such mathematical statements are called mathematical inequalties.

A collection of inequalities for which we consider common solution for all inequalities is called a system of inequalities.

Suppose there is inequality given as: y ≥ f(x)

The region it covers is the region of value pairs (x,y) for which this inequality holds true.

We've to draw the region covered by it.

For a function y = f(x), there is y > f(x) on one side of the graph of the function y = f(x) in XY plane, and on other side there is y < f(x).

We just need to figure out this fact at 1 point on either side of the graph of the function y = f(x) , and then the area where y > f(x) is true, along with the curve of the function y = f(x) is included in the region covered by inequality y ≥ f(x)

For this case, the inequalities given are:

y > -2x+7, y ≤ 3x-8

Their solution is the points lying in the intersection of the regions these inequalities are true for, as shown in the graph by the intersection of the blue and red colors.

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Answer:

See below

Step-by-step explanation:

[tex] \sec \: I = \frac{HI}{IJ} \\ \\ \implies \: \sec \: I = \boxed{\frac{89}{39} }[/tex]

Answer:

Step-by-step explanation:

To find the vertex from the given table look when the values of x or y start to switch the pattern. For example look at y value they get lower and lower 15,8,3,0,-1 then they get greater and greater 0, 3,8,15,24,...

So the he vertex is at (-2, -1) because here is where the pattern changed.

Y-intercept of the parabola is where the parabola intersects the y-axis so the x must be 0 there. Look in the table where is x=0 and see is at y=3.

Y-intercept point is at (0, 3)

X-intercept of the parabola is where the parabola intersects the x-axis so the y must be 0 there. Look in the table where is y = 0 and see is at x= -1 and also at x= -3.

X-intercept points are at (-1, 0) and (-3, 0)

Equation of the parabola in factored form is in general

y= (x- x intercept1)(x- x intercept 2), and for our problem is:

y = (x +1)(x +3)

The equation for the axis of symmetry is x = -2 because we have a vertical parabola (since x is squared in the equation) and the vertex is as we said previously at (-2, -1).

Answer:

27/462

OR

.058

Step-by-step explanation:

the probability that the first student, selected at random, is a nursing student is 3/22.

the probability that the second student, selected at random from the remaining students, is an accounting major is 9/21.

the probability the first student chosen is a nursing student and the second student chosen is an accounting major is therefore 3/22 * 9/21 = 27/462.

Answer:

NF = 16

Step-by-step explanation:

Since N is the incenter of ΔABC then ND = NE = NF

ND = NE ⇔ 6x - 2 = 3x + 7 ⇔ 6x - 3x = 7 + 2 ⇔ 3x = 9 ⇔ x = 3

Now , we calculate ND:

ND = 6(3) - 2 = 18 - 2 = 16

and because NF = ND then NF is also equal to 16

Answer:

The answer is 105 degrees

Step-by-step explanation:

Answer:6

Step-by-step explanation:

Look at the number 16 on the y side and then go to the dot that is on the 16 line then go all the way down and look at the number of people.

The right answer would be 216

1) 6*6=36

2)36*6=216

Answer:

6561*27/9

Step-by-step explanation:

3^8=6561

6561*27=177,147

177,147/9=19,683