What is the slope of the line that passes through the points (-6, 8) and (-9, 7)? Write your answer in simplest form.

Answer:

Given system of equations:

[tex]\begin{cases}f(x)=-x^2+2x+3\\g(x)=-2x+3\end{cases}[/tex]

To solve by substitution, equate the equations and solve for x:

[tex]\begin{aligned}f(x) & = g(x)\\\implies -x^2+2x+3 & = -2x+3\\-x^2+4x & = 0\\x^2-4x & = 0\\x(x-4) & = 0\\\implies x & = 0\\\implies x-4 & = 0 \implies x=4\end{aligned}[/tex]

Therefore, the x-values of the solution are [tex]x = 0[/tex] and [tex]x = 4[/tex].

To find the y-values of the solution, substitute the found values of x into the functions:

[tex]f(0)=-(0)^2+2(0)+3=3[/tex]

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

[tex]f(4)=-(4)^2+2(4)+3=-5[/tex]

[tex]g(4)=-2(4)+3=-5[/tex]

Therefore, the solutions to the given system of equations are:

[tex](0, 3)[/tex] and [tex](4, -5)[/tex]

eden must run 2 3/8 laps to complete the race.

To calculate the laps that Eden is missing, we must perform the following operation:

We must take into account that he has already completed 7 laps and a segment of the eighth lap that is equivalent to 5/8, that is to say that he has 3/8 to complete the eighth lap.

On the other hand, once he completes the eighth lap, he will have 2 full laps left to finish the race. Due to the above, it can be stated that it is missing 2 3/8 laps.

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The solution to the quadratic equation 2x² - 4x - 3 = 0 is x = 1 ± √2.5

An equation is an expression that shows the relationship between two or more numbers and variables.

Solving the polynomial using completing the square:

2x² - 4x - 3 = 0

First divide through by 2:

x² - 2x - 3/2 = 0

add 3/2 to both sides:

x² - 2x - 3/2 + 3/2 = 0 + 3/2

x² - 2x = 3/2

add the square of half the coefficient x to both sides:

x² - 2x + 1 = 3/2 + 1

(x - 1)² = 2.5

taking square root:

x - 1 = ±√2.5

x = 1 ± √2.5

The solution to the quadratic equation 2x² - 4x - 3 = 0 is x = 1 ± √2.5

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Answer: Step 3

Step-by-step explanation: this is the right answer on the edge, hope this helps!

Answer:

the answer would be 6,600ft

Step-by-step explanation:

I hope this helps!!

Answer:

\frac{9}{20} (or 9/20, if this doesn't show up the right way in my answer.)

Step-by-step explanation:

Fist what we'll do here is divide 1000 by 450. 1000÷450=2\frac{2}{9} (2/9, if this doesn't show up the right way either).

Then, we'll apply the inverse formula. In case you've forgotten, the inverse of a number is what you have to multiply a number by to get 1. The inverse of 2/9 (too lazy to put it in that form anymore) is 0.45, or 9/20.

If that doesn't work, I might be interpreting this incorrectly.

Here.

Answer:

0.05, or 1/20

Step-by-step explanation:

So, we have the fraction. we can simplify it to 20/9, making the numerator 20. As previously stated, the inverse of a number is what you have to multiply a number by to get 1. So, 1÷20=0.05

Let me know which one works!

Warmest regards,

Sanjana

Professional 6th grader and quantum physics lover

Answer:

F and D

Step-by-step explanation:

there 2 out of the other lead

Step-by-step explanation:

A department has five employees with five jobs to be performed. the time in hours each man will take to perform each jobs is given in the effectiveness matrix .

Answer:

BOD = 189 °

Step-by-step explanation:

that is the answer above

The highest common factor of the numbers 210 and 308 is 4.

The highest factor of the two numbers which divides both the numbers is called as greatest common factor or HCF.

The highest common factor will be calculated by finding the factors of the two numbers. The factors of the two numbers are as follows:-

308   =  2 x  2   x  7  x  11

210   =  2  x  2   x  3  x  17

We can see that the 2  x  2  =  4 is the highest factor which is common between the two numbers 210 and 308. So 4 is the HCF which can divide both the numbers 210 and 308.

Therefore the highest common factor of the numbers 210 and 308 is 4.

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Answer:

Horizontal lines have a slope of zero, and run parallel to the x axis. Vertical lines have a undefined slope, and run parallel to the y axis. The equation for a horizontal line equals y=c, and the equation for a vertical line equals x=c. If a horizontal line crosses a vertical line the two lines would be perpendicular to one another.

Step-by-step explanation:

Use this:

A Horizontal Line is a line that goes straight from left to right (or right to left)  parallel to the x-axis of the coordinate plane. All of the points on the line will have the same y-coordinates.

A Vertical Line is a line that goes straight up and down Parallel to the y-axis of the coordinate plane. All of the points on the line will have the same x-coordinates.

Answer:

third one passes through the slope .

Answer:

Step-by-step explanation:

y - 1 = 1/2(x - 5)

y - 1 = 1/2x - 5/2

y - 2/2 = 1/2x - 5/2

y = 1/2x - 3/2

Option 3

Answer:

Step-by-step explanation:

Since ,AB is the mid segment of triangle LMN

Then

[tex]\Longleftrightarrow AB=\frac{MN}{2}[/tex]

[tex]\Longleftrightarrow x+8=\frac{5x+4}{2}[/tex]

[tex]\Longleftrightarrow 2\times(x+8)=5x+4[/tex]

[tex]\Longleftrightarrow 2x+16=5x+4[/tex]

[tex]\Longleftrightarrow 16-4=5x-2x[/tex]

[tex]\Longleftrightarrow 3x=12[/tex]

[tex]\Longleftrightarrow x=\frac{12}{3}=4[/tex]

The function that has a greater slope will be B. The broccoli function has the greater slope, which shows that the cost per pound of broccoli is greater than the cost per pound of cauliflower.

It should be noted that a linear function simply means a function whose graph is a straight line.

From the information given, the slope will be:

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

= (3.6 - 3)/(3 - 2.5)

= 1.2

The slope for broccoli is 1.2

The slope of the cauli flower will be:

= (3.20 - 2.75)/(3.20 - 2.75)

= 1

Therefore, the broccoli function has the greater slope, which shows that the cost per pound of broccoli is greater than the cost per pound of cauliflower.

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Answer:

B

Step-by-step explanation:

right on 2022 edg

A parallelogram in which adjacent sides are perpendicular to each other is called a rectangle. The width of the rectangle is 10ft , while the length of the rectangle is 24ft.

A parallelogram in which adjacent sides are perpendicular to each other is called a rectangle. A rectangle is always a parallelogram and a quadrilateral but the reverse statement may or may not be true.

Let the width of the rectangle be represented by x.

The length of the rectangle is (2x+4), therefore, the area is,

Area = x(2x+4)

240 ft² = 2x² + 4x

2x² + 4x - 240 = 0

x² + 2x - 120 = 0

x = -12, 10

Since the width can not be negative, the width of the rectangle is 10, while the length of the rectangle is 24.

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Answer:

64 × [tex]10^{6}[/tex]

Step-by-step explanation:

(8 × 10³)² = (8 × 10³)(8 × 10³)
               = 8 × 10³ × 8 × 10³
               = 64 × [tex]10^{6}[/tex]

Answer:

Step-by-step explanation:

Find the value of (8 × 10³)²

(8 × 10³)² =

(8 × 1000)² =

8000² =

64000000

Answer:

-q^2-q+72

Step-by-step explanation:

We can use the FOIL (First Outer Inner Last) method for this. First, multiply 9*8 (72). Then, multiply 9*-q(-9q). After that, multiply q*8 (8q). Finally, multiply q*-q(-q^2). Arrange the different terms:

-q^2-9q+8q+72

Finally, combine like terms:

-q^2-q+72

Hope this helps!

The mean, median, standard deviation, and interquartile range for each data set is given below.

When arranged from lowest to highest, the IQR represents the central 50% of values.

Find the median (middle value) of the lower and higher half of the data to get the interquartile range (IQR).

These are the quartile 1 (Q1) and quartile 3 (Q3) values (Q3). The difference between Q3 and Q1 is the IQR.

Using the statistical tool, the following were arrived at:

Using the statistical tool, the following were arrived at:

See the respective Histograms attached.

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Using translation concepts, it is found that the coordinates of the image of the origin under the same translation are given by:

3. (-2,1).

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

A translation maps A(1,2) onto A'(-1,3), hence the rule is given by:

(x,y) -> (x - 2, y + 1).

Then the image of the origin (0,0) is given by:

(0,0) -> (0 - 2, 0 + 1) = (-2,1)

Which means that option 3 is correct.

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[tex] \rm \: {2x}^{2} + x - 6[/tex]

[tex] \rm \: {2x}^{2} + 4x - 3x - 6[/tex]

[tex] \rm \: {2x} \times (x + 2)- 3x \times (x + 2)[/tex]

[tex] \rm \: (x + 2) \times (2x - 3)[/tex]

Answer:

it’s b

Step-by-step explanation:

the answer is 2x3x3x5, but it’s the same thing when you put an exponent of two on a 3.

Hope it helps

Sry if I’m wrong

Answer:

A

Step-by-step explanation:

has more arrows coming out

the reason it's not D is because it is going in a red-blue pattern not red-red

hope that helps :)

Answer:

A

Step-by-step explanation:

red blue red ??? and 1 arrow, 3 arrows, 5 arrows so next is blue 7 arrows

Step-by-step Explanation:

the volume of a pyramid is:

volume = (1/3) • base_area • height

(area = length • width)

(area) • (height) = (volume)³

Example:

area = 12cm² (12 cm squared)

height = 4cm

12 • 4 = 48cm³ (48 cm cubed)

Answer:

area: 6 • 8 = 48(1/2) = 24cm²

height: 12

volume: 24 • 12 = 288cm³(1/3) = 96cm³

Answer:

28

Step-by-step explanation:

[tex]7+7\times 3 = 7(1+3)= 7 \times 4 = 28[/tex]

Answer:

28

Step-by-step explanation:

When we find the product of 2 or more numbers, we multiply them.

so

product of 7 and 3 = 7 x 3 = 21

7 + 21 = 28

Hope this helps. I attempted to make it as simple as possible.

- profparis

Answer:

6x = 16

Step-by-step explanation:

Given:

[tex]\displaystyle \large{6:2 = 8:x}[/tex]

The equation can be rewritten as:

[tex]\displaystyle \large{\dfrac{6}{2}=\dfrac{8}{x}}[/tex]

Multiply both sides by 2x.

[tex]\displaystyle \large{\dfrac{6}{2}\cdot 2x=\dfrac{8}{x}\cdot 2x}[/tex]

Simplify the equation in simplest form.

[tex]\displaystyle \large{6x=8\cdot 2}\\\\\displaystyle \large{6x=16}[/tex]

Therefore, the answer to this question is 6x = 16.

Please let me know if you have any questions regarding my answer or explanation!

Answer:

[tex] x = \dfrac{c + d}{a - b} [/tex]

Step-by-step explanation:

ax - c = bx + d

ax - bx = c + d

x(a - b) = c + d

[tex] x = \dfrac{c + d}{a - b} [/tex]

Answer:  B.   5/13

This is the same as writing [tex]\frac{5}{13}[/tex]

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

Reason:

We have two given sides of this right triangle. Use the pythagorean theorem to find the missing side.

a = 5 and b = 12 are the two known legs; c is the unknown hypotenuse

[tex]a^2+b^2 = c^2\\\\c = \sqrt{a^2+b^2}\\\\c = \sqrt{5^2+12^2}\\\\c = \sqrt{25+144}\\\\c = \sqrt{169}\\\\c = 13\\\\[/tex]

The hypotenuse is exactly 13 units long. This is a 5-12-13 right triangle.

Now we can compute sine of theta

[tex]\sin(\text{angle}) = \frac{\text{opposite}}{\text{hypotenuse}}\\\\\sin(\theta) = \frac{5}{13}\\\\[/tex]

This points us to choice B as the final answer.

----------------

Extra Info (optional)

Answer:

Step-by-step explanation:

Studio A rents for $75 plus $75 an hour .

Studio B rents for $150 and $50 an hour.

Let t = the number of hours and c = cost.

Part A

Write a system of equations to represent the cost at each studio.

Studio A: c = 75 +75·t

Studio B: c = 150 +50·t

Part B

Solve the system of equations from Part A. Explain your method.

We solve the system of equation using substitution method, where we substitute c in the first equation with 150 +50t.

150 +50·t = 75 +75·t, subtract 75 and 50t from both sides

   150 -75 = 75t -50t, combine likes terms

           75 = 25t, divide both sides by 25

             3 = t

Now we know that t = 3 so we find c by substituting t with 3 in the second equation.

c = 150 +50·t

c = 150 +50·3

c = 300

The solution of the system of equations is c = 300 and t = 3

Part C

Explain what the solution to the system means in terms of where your band will rent a studio.

The solution of the system of equation tells us that if we rent either studio A or B for 3 hours will pay the same price $300.

The price will be different if we rent studio A then studio B if we rent it for a different amount of time than 3 hours.

Given:

The equation of the circle is

We need to determine the center and radius of the circle.

Center:

The general form of the equation of the circle is

where (h,k) is the center of the circle and r is the radius.

Let us compare the general form of the equation of the circle with the given equation  to determine the center.

The given equation can be written as,

Comparing the two equations, we get;

(h,k) = (0,-4)

Therefore, the center of the circle is (0,-4)

Radius:

Let us compare the general form of the equation of the circle with the given equation  to determine the radius.

Hence, the given equation can be written as,

Comparing the two equation, we get;

Thus, the radius of the circle is 8

Answer:

  A

Step-by-step explanation:

The solution matrices shown are the result of reducing the augmented coefficient matrix to "reduced row-echelon form". Many calculators and spreadsheets have functions specifically for that purpose.

The attachment shows the result of a TI-84 work-alike calculator's reduction of the coefficient matrix. It matches the first choice.

__

Additional comment

When the equations are written in the form shown here, with the variables in the same order, and the constant on the right side of the equal sign, the augmented matrix is simply the matrix of the numbers. It is shown as the argument of the RREF function in the attachment.

The left-right order of the variables on the left side of the equal sign matches the top-down order of the solution values in the rightmost column of the reduced matrix. That is, ...

  a = 2, b = -2, c = 0.