WILL GIVE BRAINLIEST AND 35 POINTS Solve this system of equations. \(\left \{ {{3x+y=-21} \atop {y=4x}} \right.\)

\(~~~~~2x^2 -3 =0\\\\\implies 2x^2 = 3\\\\\implies x^2 =\dfrac 32\\\\\implies x = \pm\sqrt{\dfrac 32 }\)

Answer:

Number of elements in set = n(B) = 3 . Therefore, Number of elements in power set = 2^n(B) = 2^3 = 8 . Hope helped!

Step-by-step explanation:

Answer:

201

Step-by-step explanation:

3.14*8*8=201

sin(x) is a mathematical function that calculates the sine of angle x, where x is in radians.

In mathematics, angles are measured in radians or degrees. The symbol π represents the mathematical constant pi, which is approximately equal to 3.14159.

When we say π/2, it means half of the circumference of a circle, which corresponds to 90 degrees.

The inequality "π/2 < 0" suggests that π/2 is less than zero, implying that the angle of 90 degrees is negative. However, this is incorrect.

In the standard coordinate system, angles are measured counterclockwise from the positive x-axis.

Thus, π/2 or 90 degrees lies in the positive direction. The correct relationship should be "π/2 > 0" to indicate that the angle is greater than zero.

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Answer:

8 / 5

Step-by-step explanation:

Since 2/5 gallons cover 1/4 of the deck you would have to multiply 2/5 times 4 to so how much it would take to cover the whole deck so your answer is 8/5 gallons

Answer:

x= -8/41

y= 27/41

Step-by-step explanation:

7y=2x+5

3x+10y=6

maybe divide all parts of first equation by 7 to leave y by itself: y=2/7x+5/7

Then plug that in for y in the second equation:

3x+10(2/7x+5/7)=6

Then just solve for x:

x= -8/41

Substitute value of x into first equation:

7y=2(-8/41)+5

Solve for y:

y=27/41

In systems of equations, the values of x and y are -8 and 3, respectively.

Given systems of equations are:

7y=-2x+5 .....(i)

3x+10y=6 .....(ii)

We want both equations to be in standard form (Ax + By = C) so we need to fix the first equation.

For the equation (i), simply add 2x from both sides, so that x & y are on the same side of the equal sign

2x + 7y = 5 .....(i)

3x + 10y = 6 .....(ii)

To get the same x value in both equations (i) and (ii), we must now multiply equation (i) by 3 and equation (ii) by 2.

3(2x + 7y = 5) .....(i)

2(3x + 10y = 6) .....(ii)

Simplify.

6x + 21y = 15 .....(i)

6x + 20y = 12 .....(ii)

Now, subtract equations (ii) from (i)

y = 3

Now, substitute value of y = 3 in equation (i).

2x + 7y = 5 .....(i)

2x + 7(3) = 5

2x + 21 = 5

Then, subtract 21 from both sides.

2x + 21 - 21  = 5 - 21

2x = - 16

Divide both sides by 2.

2x / 2 = - 16 / 2

x = -8

So, x = -8 & y = 3

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The equation is P(x) = (x²  - 2x -1 )(x -1)

The given parameters are

Zeros of the polynomial = 1 - √2, 1, 1 + √2

The sum of multiplicities of the polynomial equation must be equal to the degree.

This means that the multiplicity of the zeros 1 - √2, 1, 1 + √2 is 1

The equation of the polynomial is then calculated as

P(x) = (x - zero)^ multiplicity

So, we have

P(x) = (x - (1 - √2)) * (x - (1 + √2)) * (x - 1)

This gives

P(x) = (x² - (1 - √2)x - (1 + √2)x + (1 - √2)(1 + √2))(x -1)

So, we have

P(x) = (x²  - 2x -1 )(x -1)

Hence, the equation of the polynomial is P(x) = (x - 4)(x - 6)(x + 3)²

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Answer:

3,696

Step-by-step explanation:

7x24x22 equals 3,696

24x7=168

168x22=3,696

The tangent of angle R is given as follows:

\(\tan{R} = \frac{\sqrt{47}}{17}\)

The three trigonometric ratios are the sine, the cosine and the tangent of an angle, and they are obtained according to the formulas presented as follows:

For the angle R, we have that:

Hence the tangent is given as follows:

\(\tan{R} = \frac{\sqrt{47}}{17}\)

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This representation describes the part of the plane z = x + 2 that lies inside the cylinder x^2 + y^2 = 9.

To find a parametric representation for the surface, we can express x, y, and z in terms of a parameter, let's say u.

Given:

Plane equation: z = x + 2

Cylinder equation: x^2 + y^2 = 9

Let's express x and y in terms of the parameter u:

x = 3cos(u)

y = 3sin(u)

Substituting these expressions into the plane equation, we have:

z = 3cos(u) + 2

Therefore, a parametric representation for the surface is:

x = 3cos(u)

y = 3sin(u)

z = 3cos(u) + 2

This representation describes the part of the plane z = x + 2 that lies inside the cylinder x^2 + y^2 = 9.

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Answer:

60

Step-by-step explanation:

Note that angle ZXY is the bisected angle which was split into angle 1 and 2

Also note that bisectors split angles into to separate congruent angles ( So if angle ZXY was bisected into angle 1 and angle 2 then angle 1 = angle 2 )

If angle 2 = 30 then angle 1 also = 30

Like stated multiple times angle ZXY is made up of angle 1 and 2

Hence, Angle ZXY = Angle 1 + Angle 2

Angle ZXY = 30 + 30 = 60

Answer:

0.2m x 0.12m

Step-by-step explanation:

A scale drawing is a reduced form in terms of dimensions of an original image / building / object

the scale drawing is usually reduced at a constant dimension

scale of the drawing = original dimensions / dimensions of the scale drawing

Scale of drawing = (10 / 50) x (6/50) = 0.2m x 0.12m

Answer:

\(1 + { \sin} \theta\)

Step-by-step explanation:

\( \frac{ { \cos}^{2} \theta}{1 - \sin \theta} \\ \\ = \frac{ { \cos}^{2} \theta}{(1 - \sin \theta)} \times \frac{(1 + \sin \theta)}{(1 + \sin \theta)} \\ \\ = \frac{{ \cos}^{2} \theta(1 + { \sin} \theta)}{(1 - { \sin}^{2} \theta)} \\ \\ = \frac{{ \cancel{ \cos}^{2} \theta}(1 + { \sin} \theta)}{ \cancel{{ \cos}^{2} \theta}} \\ \\ = 1 + { \sin} \theta\)

Let's see

\(\\ \rm\Rrightarrow \dfrac{cos^2\theta}{1-sin\theta}\)

\(\\ \rm\Rrightarrow \dfrac{1-sin^2\theta}{1-sin\theta}\)

\(\\ \rm\Rrightarrow \dfrac{(1-sin\theta)(1+sin\theta)}{1-sin\theta}\)\)

\(\\ \rm\Rrightarrow 1+sin\theta\)

Option A

Answer:

7 km

Step-by-step explanation:

2 hours 20 minutes is 2 and 1/3 hours. 3 * 2 and 1/3 = 3 * 7/3 = 7km.

Answer: 7 km

Step-by-step explanation:

In 1 hour, he did 3 km

In 2 hours, he will do 6 km

20 minutes = 20/60 = 1/3

In 20 minutes, he will do 1/3 x 3 = 1 km

So total distance travelled = 7 km

Answer:

- 22719559.

Step-by-step explanation:

Answer:

infinity or any number

Step-by-step explanation:

we need to distribute first because we cannot combine the things inside of the parentheses

-10 - 12x < 48 -12x

now we need to combine like numbers!

0 (this is -12x + 12x) < 58 (this is 48 + 10)

oh no! x is not given to us in this equation! don't worry though, because this means that x can be any single number. why?

x could be any number and this equation will be true!

Answer:Step by step is answer

Step-by-step explanation:

To find the correlation coefficient and interpret the relationship between the two variables (temperature and heaters sold), we can use statistical software or a graphing calculator. Here is the table of the data with the calculated mean, standard deviation, and correlation coefficient:

Month Temp. (C) Heaters Sold

Jan -5 98

Feb -7 100

Mar 5 75

Apr 10 67

May 18 24

Jun 22 26

Jul 28 25

Aug 25 27

Sep 16 40

Oct 10 55

Nov 2 88

Dec -3 95

Mean: 10.5 - 53.5

Standard Deviation: 11.64 - 27.54

Correlation Coefficient: -0.76

The correlation coefficient, which ranges from -1 to +1, indicates the strength and direction of the linear relationship between the two variables. In this case, the correlation coefficient is negative, which means that as the temperature increases, the number of heaters sold decreases. The closer the correlation coefficient is to -1 or +1, the stronger the relationship is. In this case, the correlation coefficient of -0.76 suggests a moderate negative linear relationship between temperature and heaters sold.

Given the line of best fit for men's weight based on height:

f(x) = 1.9x + 40

(i) The coefficient 1.9 represents the slope of the line, which indicates the rate at which the weight changes with respect to height. Specifically, for every 1 inch increase in height, the predicted weight increases by 1.9 pounds.

(ii) To find the predicted weight of a man who is 71 inches tall, we can plug in x=71 into the equation and evaluate:

f(71) = 1.9(71) + 40 = 193.9

Therefore, the predicted weight of a man who is 71 inches tall is approximately 193.9 pounds.

The equation to solve the height of the trapezoid is 45h = 1,575

Given data ,

Let the area of the trapezoid be A

Now , the value of A = 1,575 cm²

And , the Top(base2) = 63cm and  Bottom(base1) = 27 cm

Area of Trapezoid = ( ( a + b ) h ) / 2

where , a = shorter base of trapezium

b = longer base of trapezium

h = height of trapezium

On simplifying , we get

1,575 = (63 + 27) / 2 x h

1575 = 45h

Hence , the equation is 1575 = 45h

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The complete question is attached below :

The trapezoid has an area of 1,575 cm2, Which equation could you solve to find the height of the trapezoid?

A 850.5h = 1,575

B 1,701h = 1,575

C 90h = 1,575

D 45h = 1,575

Top(base2) = 63 cm

Bottom(base1) = 27 cm

Answer:

17

Step-by-step explanation:

First, find the sides by looking at how many squares are filled. Using that you add to find the perimeter. (In this case, it was 8.5) Take the perimeter and multiply it by 2. Then you have your answer. (17.) If it was the other way around you would multiply by 1/2.

Using L'Hopital's rule, we can find that the limit is equal to (g(0) - 3)/2.

Since the line tangent to g at (0,3) has slope 2, we know that g(0) - 3 = 2(0) = 0. Therefore, the limit is 0/2 = 0. Based on the given information, we have a twice-differentiable function g(x) and its tangent line at the point (0,3). To find the value of the limit as x approaches 0 for g(x)e^(-x) - 3x^2 - 2x, we can use L'Hopital's rule since it involves indeterminate forms of the type 0/0 or ∞/∞.  Apply L'Hopital's rule twice on the given expression. Then, evaluate the resulting expression at x=0. This will give you the value of the limit for the given expression. Make sure to check if the conditions for using L'Hopital's rule are met before applying it.

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Answer:

Step-by-step explanation:

It will take 48 minutes to make 140 airplanes. 35 × 4 = 140 airplanes. So take 12 × 4 = 48 minutes.

Answer:

(2)

Step-by-step explanation:

slope:-1/2

y-intercept:1   (because the function passes (0,1))

The slope of the linear function is -2 and the y-intercept is 2. Therefore, the correct answer is: slope: -2; y-intercept: 2.

A linear function is a type of function where the rate of change of the dependent variable (y) with respect to the independent variable (x) is constant. In other words, the graph of a linear function is a straight line.

To determine the slope and y-intercept of the linear function graphed, we can use the slope-intercept form of a linear equation, which is:

y = mx + b

Where m is the slope and b is the y-intercept.

Looking at the graph, we can see that the line passes through the y-axis at the point (0, 2), which means that the y-intercept is 2. To find the slope, we can choose any two points on the line and use the formula:

slope = (change in y) / (change in x)

For example, we can choose the points (-1, 0) and (1, -4) which lie on the line. The change in y is -4 - 0 = -4, and the change in x is 1 - (-1) = 2. Therefore, the slope is:

slope = (change in y) / (change in x) = -4 / 2 = -2

Hence, the slope of the linear function is -2 and the y-intercept is 2. Therefore, the correct answer is:

slope: -2; y-intercept: 2

Thus, the answer is slope: -2; y-intercept: 2.

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Answer:

30

Step-by-step explanation:

Answer:

x = 30

Step-by-step explanation:

The equation modelling the statement is

\(\frac{x}{3}\) - 1 = 2 ( \(\frac{x}{4}\) - 3 ) ← distribute parenthesis by 2

\(\frac{x}{3}\) - 1 = \(\frac{x}{2}\) - 6 ( multiply through by 6 to clear the fractions )

2x - 6 = 3x - 36 ( subtract 2x from both sides )

- 6 = x - 36 ( add 36 to both sides )

30 = x

The required equation is m - 15 = 52

To translate the sentence "15 less than Matt's savings is 52" into an equation using the variable "m" to represent Matt's savings, we need to express the concept of "15 less than." When we subtract 15 from Matt's savings, it should equal 52. Therefore, the equation can be written as

m - 15 = 52.

In this equation, "m" represents Matt's savings. We subtract 15 from "m" to indicate "15 less than." The equal sign represents the relationship of equality, indicating that the result of the subtraction should be equal to 52. By setting up this equation, we can solve for the value of "m" and find out the exact amount of Matt's savings that satisfies the given condition.

Therefore, the required equation is m - 15 = 52

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Given question is incomplete, the complete question is below

Translate this sentence into an equation.

15 less than Matt's savings is 52.

Use the variable m to represent Matt's savings.

Answer:

A. 7 and 3

&

B. 1 and 5

Step-by-step explanation:

Corresponding angles are a pair of angles each of which is on the same side of one of two lines cut by a transversal and on the same side of the transversal.

The answers are:

•8 and 4

•5 and 1

•7 and 3

•6 and 2

I hope this helps! I'm sorry if it's wrong.

F(3) is equal to 9, based on the given table and the corresponding values of x and f(x). Option D.

To find the value of F(3) based on the given table, we look at the corresponding x-value of 3 and find its corresponding f(x) value.

From the table, we see that when x = 3, f(x) = 9. Therefore, F(3) = 9.

The table shows the values of x and their corresponding f(x) values. We can see that when x increases by 1, f(x) also increases by 3. This indicates that the function has a constant rate of change, where the change in f(x) is always 3 units for every 1 unit change in x.

Given that F(3) represents the value of the function when x = 3, we look at the x-values in the table and find the corresponding f(x) value. In this case, when x = 3, f(x) = 9.

Therefore, the value of F(3) is 9. Option D is correct.

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Answer

I don’t quite understand what your asking but I hope this helps

y=3x-13

Step-by-step explanation:

Answer:

The difference in width is 2000 cm.

Step-by-step explanation:

The wideness of Fernando’s lawn = 30 meters

Neighbour’s lawn = 50 meters

Now we have to find the difference in width that can easily find out by subtracting the width of Fernando’s lawn from the neighbor’s lawn.

The difference in width = neighbor's lawn - Fernando's lawn

The difference in width = 50 - 30

The difference in width = 20 meters

The difference in width = 20 meters ×100 = 2000 cm.

When two variables have a relationship of inverse variation, their product remains constant. In the given relationship, the product of xy is constant, indicating that the relationship is an inverse variation.

Inverse variation is a relationship between two variables where the product of their values remains constant. In this relationship, one variable increases while the other decreases.

For example, if y is inversely proportional to x, then the product xy is constant. The question asks to determine whether the given relationship is an inverse variation or not. Given: y 424 280 210 x 2 3 4

The product xy can be calculated as follows: 2 * 424 = 8483 * 280 = 8404 * 210 = 840.

Since the product of xy is constant, we can conclude that the relationship between x and y is an inverse variation.

Therefore, the answer is "The product xy is constant, so the relationship is an inverse variation."

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