Which of the following statements must be true

Answer:

The equation of the parallel line will be y = -2.5x - 8.

Step-by-step explanation:

First things first, let's rearrange the line equation provided into a more standard form:

[tex]5x + 2y = 14[/tex]

[tex]5x - 14 = -2y[/tex]

[tex]\frac{5x - 14}{-2} = y[/tex]

[tex]y = -2.5x + 7[/tex]

Therefore, we can see that this line has a slope (the coefficient preceding x) of -2.5. The parallel line must therefore also have a slope of -2.5.

Now, let us set the y-intercept of the parallel line to be (0, a) (since it must be on the y-axis).

If we factor in all of this, we get the equation:

[tex]\frac{a-(-3)}{0-(-2)} = -2.5[/tex]

Remember, the slope is found by dividing the vertical difference with the horizontal difference.

[tex]a - (-3) = -2.5(0+2)[/tex]

[tex]a + 3 = -5[/tex]

[tex]a = -8[/tex]

Hence, the equation of the parallel line will be y = -2.5x - 8.

Hope this helped!

Answer:

[tex]x \approx 2.278863[/tex]

Step-by-step explanation:

Required

The positive root of [tex]3\sin(x) = x[/tex]

Equate to 0

[tex]0 = x -3\sin(x)[/tex]

So, we have our function to be:

[tex]h(x) = x -3\sin(x)[/tex]

Differentiate the above function:

[tex]h'(x) = 1 -3\cos(x)[/tex]

Using Newton's method of approximation, we have:

[tex]x_{n+1} = x_n - \frac{h(x_n)}{h'(x_n)}[/tex]

Plot the graph of [tex]h(x) = x -3\sin(x)[/tex] to get [tex]x_1[/tex] --- see attachment for graph

From the attached graph, the first value of x is at 2.2; so:

[tex]x_1 = 2.2[/tex]

So, we have:

[tex]x_{n+1} = x_n - \frac{h(x_n)}{h'(x_n)}[/tex]

[tex]x_{1+1} = x_1 - \frac{h(x_1)}{h'(x_1)}[/tex]

[tex]x_{2} = 2.2 - \frac{2.2 -3\sin(2.2)}{1 -3\cos(2.2)} = 2.28153641[/tex]

The process will be repeated until the digit in the 6th decimal place remains unchanged

[tex]x_{3} = 2.28153641 - \frac{2.28153641 -3\sin(2.28153641)}{1 -3\cos(2.28153641)} = 2.2788654[/tex]

[tex]x_{4} = 2.2788654 - \frac{2.2788654 -3\sin(2.2788654)}{1 -3\cos(2.2788654)} = 2.2788627[/tex]

[tex]x_{5} = 2.2788627 - \frac{2.2788627-3\sin(2.2788627)}{1 -3\cos(2.2788627)} = 2.2788627[/tex]

Hence:

[tex]x \approx 2.278863[/tex]

Answer:

The area of the circle in terms of π is:

Step-by-step explanation:

To find the area of that circle, you can use the equation:

Where:

Now, we can replace the given measurement in the equation:

That result is the same that to write:

By this reason, the result is 9/64 π in^2, giving the result in terms of π.

Answer:

59.44

Step-by-step explanation:

Nine employees If an electronic company retired last year

The retirement ages are listed below

56, 65, 62, 53, 68, 58, 65, 52, 56

The mean retirement age can be calculated as follows

= 56+65+62+53+68+58+65+52+56/9

= 535/9

= 59.44

Hence the mean retirement age is 59.44

Answer:

1/6

Step-by-step explanation:

10x = 1.6666....

100x =16.6666...

90x = 16.6666... - 1.6666...

90x = 15

x = 15/90

x = 1/6

Answer:

the answer is 84.... .....

Answer:

136 general admission tickets were​ purchased, and 300 upper reserved tickets were purchased.

Step-by-step explanation:

This question is solved using a system of equations.

I am going to say that:

x is the number of general admission tickets purchased.

y is the number of reserved tickets purchased.

There were 436 tickets purchased for a major league baseball game.

This means that [tex]x + y = 436[/tex], or also, [tex]x = 436-y[/tex]

The general admission tickets cost ​$6.50 and the upper reserved tickets cost ​$8.00. The total amount of money spent was ​$3284.00.

This means that [tex]6.5x + 8y = 3284[/tex]. Since [tex]x = 436-y[/tex]

[tex]6.5(436-y) + 8y = 3284[/tex]

[tex]1.5y = 450[/tex]

[tex]y = \frac{450}{1.5}[/tex]

[tex]y = 300[/tex]

And:

[tex]x = 436 - y = 436 - 300 = 136[/tex]

136 general admission tickets were​ purchased, and 300 upper reserved tickets were purchased.

Answer:

Answer B

Step-by-step explanation:

Answer:

49

81

Step-by-step explanation:

Probability = number of possible outcome.

number of total outcome.

= orange counters = 81 - 32 = 49

49

81

Answer:

[tex]65.4[/tex]

Step-by-step explanation:

In any right triangle, the cosine of an angle is equal to its adjacent side divided by the hypotenuse, or longest side, of the triangle.

Therefore, we have:

[tex]\cos 61^{\circ}=\frac{y}{135},\\t=135\cos 61^{\circ}=65.4492987333\approx \boxed{65.4}[/tex]

Answer:

a) 3/5 < 4/5

b) In general if two fractions have the same denominator, then whichever fraction has the numerator closer to its denominator will be the largest fraction.

c)  [tex]\frac{7}{10} > \frac{9}{15}[/tex]  or  [tex]\frac{7}{10}<\frac{9}{15}[/tex]

Step-by-step explanation:

a) 3/5 < 4/5

Flip the sign and the placement of the fraction so 3/5 is less then 4/5.

b) In general if two fractions have the same denominator, then whichever fraction has the numerator closer to its denominator will be the largest fraction.

c) We need to change the denominators to a common denominator to compare the size of the two fractions:

[tex]\frac{7}{10}[/tex] × [tex]\frac{3}{3}[/tex] = [tex]\frac{21}{30}[/tex]

[tex]\frac{9}{15}[/tex] ×  [tex]\frac{2}{2}[/tex] = [tex]\frac{18}{30}[/tex]

The common denominators of the two fractions is 30. Comparing the two fractions:

[tex]\frac{21}{30} >\frac{18}{30}[/tex]  or  [tex]\frac{18}{30}<\frac{21}{30}[/tex]

so we get:  [tex]\frac{7}{10} > \frac{9}{15}[/tex]  or  [tex]\frac{7}{10}<\frac{9}{15}[/tex]

Answer:its d

Step-by-step explanation:

Answer:

volume of the cube=15×15×15

=3375 in³

volume of the cylinder=πr²h

=π×7²×14

=686π

volume of the figure=3375+686π

the answer is first option

Answer:

16% of GMAT scores are 647 or higher.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

The average GMAT score is 547 (Magoosh website). Assume that GMAT scores are bell-shaped with a standard deviation of 100.

This means that [tex]\mu = 547, \sigma = 100[/tex]

What percentage of GMAT scores are 647 or higher?

The proportion is 1 subtracted by the p-value of Z when X = 647. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{647 - 547}{100}[/tex]

[tex]Z = 1[/tex]

[tex]Z = 1[/tex] has a p-value of 0.84.

1 - 0.84 = 0.16

0.16*100% = 16%

16% of GMAT scores are 647 or higher.

Answer:

eeeeeee

Step-by-step explanation:

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Answer:

1. Paralleogram

2. Trapeziod

3. Square

4. Rhombus

5. Rectangle

6. I don't know

7. Rectangle

8. can't see it

9. Trapeziod

Answer:

(x+3)^2+(y−3)^2=9

Step-by-step explanation:

The equation for a circle is given by

(x−h)^2+(y−k)^2=r^2  where (h,k) is the center and r is the radius

(x− -3)^2+(y−3)^2=3^2

(x+3)^2+(y−3)^2=9

Answer:

37.7

Step-by-step explanation:

EF and ED define the Tangent of D

Tan(37) = side opposite D / side adjacent to D

Opposite means a line (FE) that is not connected to the angle. It is never the longest line (hypotenuse) in a Right Triangle

Adjacent means the leg that is connected to the angle, but is not the hypotenuse.

Tan(D) = opposite over adjacent

Opposite = x

Adjacent = 50

Tan(37) = 0.7536 rounded to 4 places, but I've kept the exact value in my calculator.

0.7536 = x / 50     Multiply both sides by 50

0.7536*50 = x

x = 37.6777

The nearest 1/10 is 37.7

Answer:

[tex]\boxed {\boxed {\sf B. \ 324 \ cm^3}}[/tex]

Step-by-step explanation:

The volume of a triangular prism is the product of the area of the triangular cross-section (B) and the height (h).

First, let's find the area of the triangular cross-section/the end of the triangle. The area of a triangle is:

[tex]B= \frac{1}{2} b*h[/tex]

The base of the triangle base (not the prism) is 6 centimeters and the height is 9 centimeters.

[tex]B= \frac{1}{2} (6 \ cm)(9 \ cm)[/tex]

Multiply the numbers in parentheses.

[tex]B= \frac{1}{2}(54 \ cm^2)[/tex]

Multiply by 1/2 or divide by 2.

[tex]B= 27 \ cm^2[/tex]

Now we know the area of the cross-section or base is 27 square inches. The height of the prism is 12 centimeters.

Substitute the values into the volume formula for a triangular prism.

[tex]V= 27 \ cm^2 * 12 \ cm[/tex]

Multiply.

[tex]V= 324 \ cm^3[/tex]

The volume of the prism is 324 cubic centimeters and choice B is correct.

The volume of the triangular prism is 324 cubic centimeters, and choice B is correct.

The volume of a triangular prism is determined by multiplying the area of the triangular cross-section (B) by the height (h). In this case, the base (b) of the triangular cross-section is given as 6 centimeters, and the height (h) is given as 9 centimeters.

To find the area of the triangular cross-section (B), we can use the formula for the area of a triangle: B = (1/2) * base * height.

Substituting the values:

B = (1/2) * 6 * 9 = 27 square centimeters.

Next, we multiply the area of the cross-section (B) by the height (h) to find the volume (V) of the prism:

V = B * h = 27 * 12 = 324 cubic centimeters.

Therefore, the volume of the triangular prism is 324 cubic centimeters, and choice B is correct.

To know more about triangular prism:

https://brainly.com/question/27102803

#SPJ6

Answer:

16/33

Step-by-step explanation:

Tổng của cả 4 tấm thẻ là một số lẻ khi:

Có 1 thẻ là lẻ, 3 thẻ còn lại là chẵn, có: 6C1.5C3=60 cách

Có 3 thẻ là lẻ, 1 thẻ là chẵn, có: 5C1.6C3=100 cách

Suy ra có 160/11C4=16/33 cách

Answer:

why you just don't put the question up

Step-by-step explanation:

Answer:

At this pace the country will have only 237.6 million acres of forest left in 44 years.

Step-by-step explanation:

Given that a certain country has 586.08 million acres of forest, and every year, the country loses 7.92 million acres of forest mainly due to deforestation for farming purposes, to determine, if this situation continues at this pace, how many years later will the country have only 237.6 million acres of forest left, the following calculation must be performed:

Current amount - (amount lost per year x number of years) = 237.6

586.08 - (7.92 x X) = 237.6

586.08 - 7.92X = 237.6

-7.92X = 237.6 - 586.08

-7.92X = -348.48

X = -348.48 / -7.92

X = 44

Therefore, at this pace the country will have only 237.6 million acres of forest left in 44 years.

Answer:

297

Step-by-step explanation:

5.5x4.5x12=297

Answer:

Let's define A as the area given by the integral:

[tex]\int\limits^1_{-1} {3x^4} \, dx[/tex]

Which is the area between the curve y = 3*x^4 and the x-axis between x = -1 and x = 1

To find the volume of a revolution around the x-axis, we need to multiply the area by 2*pi (a complete revolution)

where pi = 3.14

First, let's solve the integral:

[tex]\int\limits^1_{-1} {3x^4} \, dx = \frac{3}{5}(1^5 - (-1)^5) = \frac{3*2}{5} = \frac{6}{5}[/tex]

Then the volume of the solid is just:

V = (6/5)*2*3.14 = 7.536

Answer:

Step-by-step explanation:

Answer:

the function g because the graphs the graphs of f and g are symmetrical about the line y=x

Step-by-step explanation:

Inverse functions are symmetrical to each other about the line y=x. This means that if you flip a function over y=x, that will be its inverse function. It makes sense because inverse functions turn the input of the original function (x) into the output of the inverse function (y), so y=x and x=y. Take the point (-6,0) on f, it becomes (0,-6) on g.

Answer:

option4 : 0.4

Step-by-step explanation:

[tex]Sin N = \frac{Opposite}{hypotenuse}[/tex]

[tex]sin 7 = \frac{x}{3.4}\\\\3.4 \times sin 7 = x \\\\3.4 \times 0.122 = x \\x = 0.41[/tex]