Graph the solution of the following inequality and answer the questions below

hello

to solve this question, we need to plot the graph of this equation

Problem

Which of the following equations represents a line that passes through the

points (-3, -14) and (0, –2)?

Solution

For this case we want to create an equation with this general form:

y= mx+b

We can calculate the slope with this operation:

And the intercept can be founded with the second point:

-2= 4(0)+b

b= -2

And the equation would be:

y= 4x -2

If we analyze the second option given we can see that we can write like this:

y-6 = 4(x-2)

y-6= 4x-8

y-6+8 =4x

y+2= 4x

y= 4x-2

So then the best option would be:

II. y-6 = 4(x-2)

Answer:

Please see the enclosed screenshot.

Step-by-step explanation:

Please see the enclosed screenshot.

The distances that the footballs travel before hitting the ground is 50 yards.

For the given question;

The football is kicked by the player.

The second kick is modeled by f(x) = -0.051x(x - 50).

Where, f is the height (in yards) and x is the horizontal distance (in yards).

For calculating the distances that the footballs travel before hitting the ground, Put f(x) = 0.

As, the ball will reach the ground the height of ball above ground will be zero, thus f(x) = 0.

f(x) = -0.051x(x - 50) = 0

Simplifying;

-0.051x² + 2.25x = 0

Or, divide wole equation by x.

0.051x = 2.25

x = 50 yards.

Thus, the distances that the footballs travel before hitting the ground is 50 yards.

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The value of g(x) will be expressed as g(x) = (x + 5)

A function may be defined as an expression in which for one value of input variable x there is only one value of output variable y. The input variable is called as independent variable and output variable is called dependent variable. Composite functions are the functions which are written as combination of two functions. A function f(x) may be defined as composite function of another function g(x) when it can be written as either f(g(x)) or g(f(x)). We know that f(x) = x⁹ and the composite function H(x) = f(g(x)) = (x + 5)⁹. So, from this we can say that the function g(x) will be given as (x + 50 as we put (x + 5) as x in the function H(x).

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Answer:

  y = -7/8x -2

Step-by-step explanation:

You want the slope-intercept equation of the line through the points (8, -9) and (0, -2).

The slope of the line through points (x1, y1) and (x2, y2) is given by the formula ...

  m = (y2 -y1)/(x2 -x1)

For the given points, the slope of the line is ...

  m = (-2 -(-9))/(0 -8) = -7/8

The y-intercept of the line is the y-value when x = 0. The point (0, -2) tells you the y-intercept is -2.

The slope-intercept equation is ...

  y = mx +b . . . . . . where m is the slope, and b is the y-intercept

For a slope of -7/8 and a y-intercept of -2, the equation is ...

  y = -7/8x -2

Answer:7719

Step-by-step explanation:

The most appropriate choice for Vertically opposite angle will be given by-

b =  126°, c = 54°

What is Vertically opposite angle?

At first we need to understood what is angle

Angle

When two straight lines intersect, an angle is formed. The point of intersection is called the vertex of the angle and the lines are called the arms of the angle.

Vertically opposite angle

The angle formed by two intersecting straight lines and are opposite to one another at a specific vertex is called vertically opposite angle.

Vertically opposite angles are equal.

Here,

∠b = 126° [Vertically Opposite Angle]

∠c = 180° - 126° [Angle on a straight line]

    = 54°

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The rate at which the area of this square increases when the area of the square is 9 cm is 24 cm²/s.

The rate of change is a type of function that describes the average rate at which a quantity decreases or increases with respect to another quantity.

Mathematically, the area of a square can be calculated by using this formula;

A = s²

Where:

Next, we would determine the side length of a square by making s the subject of formula as follows:

A = s²

s = √A

s = √9

s = 3 cm.

By applying chain rule of differentiation, the rate of change (da/dt) in area of this square with respect to time is given by:

dA/dt = 2 × s(t) × ds/dt

dA/dt = 2 × 3 × 4

dA/dt = 24 cm²/s.

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Answer:

Solution

verified

Verified by Toppr

Given, A={1,2,3,4}, B={2,4,6,8} and C={3,4,5,7}.

Now, B∩C={4}.

The  A−(B∩C)={1,2,3}.

Answer:

B-C=(2,4,6,8)-(3,4,5,6)

=(2,8)

because we have to remove only maching number from B or any other.

IN THE PLACE OF x PLYG IN 4 AND SOLVE.

[tex]f(4) = - (4)^{2} - 8 \\ f(4) = - (16) - 8 \\ f(4) = - 16 - 8 \\ f(4) = - 24[/tex]

HOPE THIS HELPS

Answer:

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

Solve by substitution

The linear inequality that is represented by the graph is y ≤ x/3 - 4. The correct option is the second option y ≤ x/3 - 4

From the question, we are to determine the linear inequality that is represented by the graph

First, we will determine two points on the line

The line in the graph passes through (0, -4) and (3, -3)

Using the equation,

(y - y₁)/(x - x₁) = (y₂ - y₁)/(x₂ - x₁)

(y - -4)/(x - 0) = (-3 - (-4))/(3 - 0)

(y + 4)/x = (-3 + 4)/3  

(y + 4)/x = 1/3

y + 4 = 1/3x

y = 1/3x - 4

y = x/3 - 4

This is the equation of the line

In the given graph, the line is a solid line and the solution of the inequality is below the line

Thus,

The inequality becomes y ≤ x/3 - 4

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Let

x -----> the number of milliliters of the 3.5% solution

y ----> the number of milliliters of the 6% solution

we have that

3.5%=3.5/100=0.035

6%=6/100=0.06

5%=5/100=0.05

so

0.035x+0.06y=0.05(500) -------> equation A

and

x+y=500 -----> x=500-y ------> equation B

solve the system of equations

substitute equation B in equation A

0.035(500-y)+0.06y=0.05(500)

solve for y

17.5-0.035y+0.06y=25

0.025y=25-17.5

0.025y=7.5

y=300

Find out the value of x

x=500-300=200

therefore

To find the slope of the line that passes through (9, 10) and (6, 12)

We will use the formula;

From the points given;

x₁ = 9 y₁=10

x₂ = 6 y₂=12

Substitute the values into the formula;

Evaluate;

Answer:

Solutions below.

Step-by-step explanation:

This question tests on the concept of graph reading.

To find the slope of a line, we have to use the following formula:

[tex] \frac{y2 - y1}{x2 - x1} [/tex]

Now, we can pick 2 random points on the line to substitute the values in to find the slope.

We will pick

(0, 3) as (x1, y1)

and

(2,0) as (x2, y2)

Therefore the slope will be:

[tex] \frac{0 - 3}{2 - 0} \\ = \frac{ - 3}{2} \\ = - \frac{3}{2} [/tex]

Now to find the y-intercept, as the name suggests, it is the point where the line intercepts the y-axis (vertical axis) , in this case, it is 3.

The point of this intercept is (0,3).

Answer:

Step-by-step explanation:

You want the slope and the y-intercept of the line shown in the graph.

The slope is the ratio of "rise" to "run". It is best found by identifying points on the graph where the line crosses grid intersections. The attachment shows two of those: (0, 3), (3, -2).

You can count grid squares or use the slope formula to find the slope.

  slope = rise/run = (y2 -y1)/(x2 -x1)

  slope = (-2 -3)/(3 -0)

  slope = -5/3

The y-intercept is the y-value of the point where the line crosses the y-axis. We have already found that to be 3, at one of the points used to find the slope.

  y-intercept = 3 . . . . point (0, 3)

__

Additional comment

The slope-intercept form equation for the line would be ...

  y = -5/3x +3

The standard-form equation would be ...

  5x +3y = 9

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Given the following question:

The principal wants to estimate the percentage of students in the school who play video games, which is a good number of students. Selecting 30 random students and asking them if they play video games can represent the entire school. Asking 30 random students keeps it from being biased for example option B, asking 30 students who take coding classes is biased because they are in one specific class, they do not represent the majority of the school unless the school is a coding school.

The answer is the first option because it is a random sample of people to represent a population of people. This keeps the results from being biased so asking 30 random students is the way to go.

Given:

A figure is given.

Required:

To find the area of the given figure.

Explanation:

The given figure is made up of three figures. So we will find the area of the three figures.

Area of square

Area of the triangle

Answer:

4+3(×+23)=5×-2

Step-by-step explanation:

4+3×+69=3×from here you will group like terms 4+69=3×-3×

=73=×

this implies that ×=73

To reflect the figure, we have to draw the new vertex at the same distance from the line x = -4, the image below shows this reflection.

Notice that the new figure has the same distance from x = -4 as the pre-image.

Answer:

Im unsure what your asking but the answer is 6 1/2 in fraction form and 6.5 in decimal form :/

Step-by-step explanation:

math

When 117 is divided by 18 we get 117/18 in fraction form.

To divide 117 by 18, we perform long division.

We start with the first digit of the dividend (1) and divide it by the divisor (18).

Since 18 is larger than 1, the quotient for this step is 0.

We then bring down the next digit (1) and place it next to the previous result.

Again, since 18 is larger than 11, the quotient for this step is 0.

Therefore, the result of dividing 117 by 18 is 0 with a remainder of 117.

In fraction form, this can be expressed as 117/18.

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You have a figure (black lines) with the following points:

C(-4,0)

G(-5,-2)

Q(-2,-5)

I(-1,0)

After a translation, the figure becomes the red one, with the following points:

C'(1,2)

G'(0,-1)

Q'(3,-4)

I'(4,1)

You can notice that each x' coordinate of the new figure is respecto the previous figure:

x' = x + 5

Furthermore, for y':

y' = y +1

That is, the transformation applied to the figure (black lines), is:

T<5,1>

In fact, for each point you have:

T<5,1>C(-4,0) => C'(-4+5 , 0 + 1) = C'(1 , 1)

T<5,1>G(-5,-2) => G'(-5 + 5 , -2 + 1) = G'(0 , -1)

T<5,1>Q(-2,-5) => Q'(-2 +5 , -5 + 1) = Q'(3 , -4)

T<5,1>I(-1,0) => I'(-1 + 5 , 0 + 1) = I'(4 , 1)

We need to examine each expression at a time.

(A) x^2 + x - 6

notice the -6 has factors 3 and -2 which could be used to reverse the FOIL method:

x^2 + x - 6 = x^2 + 3 x - 2 x - 6 = x( x + 3) - 2 (x + 3) = (x+ 3) (x - 2)

(B) In this cubic expression we cannot use the reverse FOIL to extract factors.

(C) 4 x^2 - 2 x + 1 We cannot reverse the FOIL property either.

(D) x^2 + 8 x + 12

We notice that 12 has factors 2 and 6 which can be used to factor out this expression as shown below:

x^2 + 2 x + 6 x + 12 = x (x + 2) + 6 (x + 2) = (x + 2) (x + 6)

Therefore we were able to use the reverse of the FOIL property in expressions (A) and (D).

The measure of angle TRS would be of 37º.

The vertices of the triangle can be attributed freely, hence we attribute as is in the drawing.

The altitude RT bisects the triangle forming a right angle, with R and T, hence the internal angles of the triangle TRS are as follows:

The sum of the measures of the internal angles of a triangle is of 180º, hence the measure of the missing angle TSR can be found as follows:

43 + 90 + x = 180

133 + x = 180

x = 180 - 133

x = 47º -> m<TSR = 47º.

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Answer:

what is the problem text me

I can probably

Step-by-step explanation:

SOLUTION

In a photograph, a skyscraper measures 5.8 in, tall

The scale of the photo to the actual skyscraper is 1 : 245

That is 1 : 245 = 1 / 245 = 5. 8 / x

Cross- multiply we have:

1 X x = 5 . 8 X 245

x = 1421 inches in feet = 118.4167 feet

⇒First step is to find the gradient

[tex]m=\frac{y_{2} -y_{1} }{x_{2}-x_{1} } \\m=\frac{8-(-3)}{-5-2} \\m=\frac{8+3}{-7} \\m=-\frac{11}{7}[/tex]

In the general equation y=mx+c let us find the value of c by plugging in the known values

I will use the point (-5,8) Note you can use any .You will get the same value of c.

[tex]8=-\frac{11}{7} (-5)+c\\8=\frac{55}{7} +c\\c=8-\frac{55}{7} \\c=\frac{1}{7}[/tex]

The equation now is:

[tex]y=-\frac{11}{7} x+\frac{1}{7}[/tex]

The domain is

and the range

Then, the answer is d)

Noted that the Diagonals of a parallelogram bisect each other. Here in PQSR, it does bisect PT =ST and QT = TR). Hence, PQSR is a parallelogram.

Note that IGHJ is a parallelogram. This is because the opposite sides of a parallelogram are congruent. Here, H = I and G = J. Hence, IGHJ is a parallelogram.

It is correct to state that CABD is a parallelogram because of the alternative interior angles ACB = CBD and ABC = BCD.

VWYX is NOT a parallelogram. The rule states that if opposites sides are congruent then the quadrilateral is a parallelogram. In this case, clearly, line VW ≠ XY and VX ≠ WY.

A parallelogram (which could be a rhombus, rectangle, or square) is a quadrilateral with congruent and parallel opposing sides.

There are six critical parallelogram characteristics to note. They are:

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