Factor the expression completely
[tex] { \times }^{2} - 2x - 63 [/tex]
​

Answer:  The correct option is

(B)  g(x) has a greater slope.

Step-by-step explanation:  We are given the following two functions :

[tex]f(x)=2x-5~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

and

x                    2                      4                    6

g(x)                0                      5                     10

Comparing equation (i) of f(x) with the slope-intercept form y = mx+c, we get

[tex]\textup{slope, m}=2.[/tex]

Now, we know that if a linear function contains two points (a, b) and (c, d), then its slope is given by

[tex]m=\dfrac{d-b}{c-a}.[/tex]

Since (2, 0) and (4, 5) are two points on g(x), so its slope will be

[tex]m=\dfrac{5-0}{4-2}=\dfrac{5}{2}=2.5.[/tex]

Therefore, slope of f(x) = 2 and slope of g(x) = 2.5.

Thus, slope of g(x) is greater.

Option (B) is CORRECT.  

Answer:

a) false

b) false

c) true

d) true

e) false

f) false

Step-by-step explanation:

hope this helps :)

Answer:

#7: (p, r) = (0, -2) #8: (z,w) = z, [tex]\frac{8}{3}[/tex] + [tex]\frac{4}{3}[/tex]z), ∈R  #9: (c,d) = (3,3) #10: (u,x) ∈∅ #11: (a,b) = (-1, 2) #12:

Step-by-step explanation:

#7

Solve for 2p

2p - 3r = 6

2p = -6 -3r

substitute the given value of 2p into equation 2p - 3r = 6

-6 - 3r - 3r = 6

solve for r

r= -2

substitute value of r in equation

2p = -6 - 3x (-2)

solve for p

p=0

solution is ordered pair (p,r) = (0, -2)  

#8

Solve for w

w= [tex]\frac{8}{3}[/tex] + [tex]\frac{4}{3}[/tex]z

substitute the given value of w into equation

6 ([tex]\frac{8}{3}[/tex] + [tex]\frac{4}{3}[/tex]z) - 8z = 16

solve for z

z ∈ R

The statement is true for any value of z and w that satisfy both equations from the system. Therefore, the solution is in parametric form.

(z,w) = z, [tex]\frac{8}{3}[/tex] + [tex]\frac{4}{3}[/tex]z)

#9

Solve for c

c + d = 6

c = d

substitute the given value of c into equation c + d = 6

d + d = 6

solve for d

d=3

substitute value of d in equation

c=3

solution is ordered pair (c,d) = (3,3)

#10

Solve for u

u= 3-2x

substitute the given value of c into equation

2 (3-2x) +4x = -6

solve for x

x ∈∅

Since the system has no solution for x the answer is  

(u,x) ∈∅

#11

Solve for b

b= 5+3a

substitute the value of b into equation

3a + 5 + 3a+ b = -1

solve for a

a= -1

substitute the value of a into equation

b= 5 + 3x (-1)

solve for b

b=2

solution is ordered pair (a, b) = (-1, 2)

Final answer:

The system of equations leads to a true statement when added together, indicating that the two equations represent the same line and thus have infinitely many solutions. There's no unique solution for the variables but rather a relationship where each value of p corresponds to a specific value of r.

Explanation:

To solve the system of equations by substitution, let's first identify the given equations and the unknown variables. The two given equations are 2p - 3r = 6 and -2p + 3r = -6. We need to solve for the unknown variables p and r. Notice that adding these two equations together will eliminate both p and r, giving us an identity 0 = 0, which indicates the system has infinitely many solutions or the equations represent the same line.

Here's the process to verify this:

First equation: 2p - 3r = 6

Second equation: -2p + 3r = -6

Add the two equations: (2p - 3r) + (-2p + 3r) = 6 - 6

This simplifies to: 0 = 0

Since we have derived a true statement that does not involve the variables p and r, it is clear that these two equations are dependent and represent the same line. Therefore, there isn't a unique solution for p and r, but rather an infinite number of solutions where each value of p corresponds to a specific value of r that will satisfy both equations.

To check if the answer is reasonable, we can take any point that lies on this line and see if it satisfies both original equations, confirming that it is indeed a solution.

Answer:

A. $301

B. $721

Step-by-step explanation:

Let $x be the amount of money they raised.

Rowena tried to put the $1 bills into two equal piles and found one left over at the end, then

[tex]x=2q_1+1[/tex]

Polly tried to put the $1 bills into three equal piles and found one left over at the end, then

[tex]x=3q_2+1[/tex]

Frustrated, they tried 4, 5, and 6 equal piles and each time had $1 left over, then

[tex]x=4q_3+1\\ \\x=5q_4+1\\ \\x=6q_5+1[/tex]

Finally Rowena put all the bills evenly into 7 equal piles, and none were left over, then

[tex]x=7q_6[/tex]

This means [tex]x-1[/tex] is divisible by 2, 3, 4, 5 and 6 without remainder, so

[tex]x-1=2\cdot 3\cdot 2\cdot 5n=60n[/tex]

Hence,

[tex]x=60n+1, \ n\in N[/tex]

The smallest amount of money they could have raised is $301, because

[tex]x=60\cdot 5+1=301[/tex] is divisible by 7.

Now, the number [tex]x=60n+1[/tex] should be divisible by 7 and must be greater than 500.

So,

[tex]60n+1>500\\ \\60n>499\\ \\n>8[/tex]

When n = 9,

[tex]x=60\cdot 9+1=541[/tex] is not divisible by 7.

When n = 10,

[tex]x=60\cdot 10+1=601[/tex] is not divisible by 7.

When n = 11,

[tex]x=60\cdot 11+1=661[/tex] is not divisible by 7.

When n = 12,

[tex]x=60\cdot 12+1=721[/tex] is divisible by 7.

B. The least amount of money they could have raised is $721

Answer:

A:301 and b: 721

The square with a side length of  [tex]2\frac{1}{2}[/tex] inches has a larger area of 6.25 square inches, compared to the area of the rectangle which is 5.25 square inches.

To determine which shape has a larger area, let's calculate the area of both the rectangle and the square. The rectangle measures 7 inches by 3/4 inch, so its area is calculated by multiplying these dimensions:

Area of the rectangle = length ×width = 7 inches × [tex]\frac{3}{4}[/tex] inch = [tex]\frac{21}{4}[/tex] square inches or 5.25 square inches.

The square has a side length of [tex]2\frac{1}{2}[/tex] inches, which is equivalent to 2.5 inches. Hence, the area of the square is:

Area of the square = side ×side = 2.5 inches × 2.5 inches = 6.25 square inches.

Comparing the two, we can see that the square with a side length of [tex]2\frac{1}{2}[/tex] inches has a larger area of 6.25 square inches compared to the rectangle's area of 5.25 square inches.

Answer:

equilateral triangle

Step-by-step explanation:

all sides are equal

Hey!

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

Answers:

Equilateral

Acute

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Explanation:

The lines on each side show that all the sides are the same length. Acute angles are angles that are less than 90 degrees. Each angle is less than 90 degrees.

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

Hope This Helped! Good Luck!

Answer:

[tex]\boxed{18. \, -3 \leq x \leq \dfrac{16}{9};\quad 22. \text{ $x \leq -19$ or $x \geq -5$}}[/tex]

Step-by-step explanation:

Q18

[tex]\left |\dfrac{3x - 5}{2} \right | \leq 7[/tex]

Multiply each side by 2

[tex]|3x - 5| \leq 14[/tex]

Apply the absolute rule:

If |x| ≤ a, then -a ≤ x ≤ a

This gives

-14 ≤ 3x - 5 ≤ 14

Separate into two inequalities

[tex]\begin{array}{cc}-14 \leq 3x - 5 & 3x - 5 \leq 14 \\-9 \leq 3x & 3x\leq 19 \\-3 \leq x & x \leq \dfrac{19}{3} \\\end{array}[/tex]

Merge the overlapping intervals

[tex]\boxed{\mathbf{-3 \leq x \leq \dfrac{16}{9}}}[/tex]

Q22

-5|x + 12| ≤ -35

Divide each side by -5

This reverses the sign of the inequality.

|x + 12| ≥ 7

Apply the absolute rule

If |x| ≥ a, then -a ≥ x or x ≥ a

-7 ≥ x + 12 or x + 12 ≥ 7

Separate into two inequalities

[tex]\begin{array}{cc}-7 \geq x + 12 & x + 12 \geq 7 \\-19 \geq x & x\geq -5 \\\end{array}[/tex]

Combine the intervals

[tex]\boxed{\textbf{$x \leq -19$ or $x \geq -5$}}[/tex]

Answer:

950,000

Take the placement before the placement you need to round and round.

Answer:

irrational

Step-by-step explanation:

Answer: 2400

Step-by-step explanation:

for every pound there is 300 gallons, so

300 x 8 = 2400

Hope this helps!

Simplifying

64 + -12w = 6w

Solving

64 + -12w = 6w

Solving for variable 'w'.

Move all terms containing w to the left, all other terms to the right.

Add '-6w' to each side of the equation.

64 + -12w + -6w = 6w + -6w

Combine like terms: -12w + -6w = -18w

64 + -18w = 6w + -6w

Combine like terms: 6w + -6w = 0

64 + -18w = 0

Add '-64' to each side of the equation.

64 + -64 + -18w = 0 + -64

Combine like terms: 64 + -64 = 0

0 + -18w = 0 + -64

-18w = 0 + -64

Combine like terms: 0 + -64 = -64

-18w = -64

Divide each side by '-18'.

w = 3.555555556

Simplifying

w = 3.555555556

Answer:

x represents Jane's initial amount of money in her bank account.

Step-by-step explanation:

x - 135 = 650

650 + 135 = x

x = 785

Step-by-step explanation:

Look at the picture

a. 5pk → 5

b. f = 1f → 1

c. -9t → -9

d. -j = -1j → -1

Answer: She needs to walk 5 miles an hour

There's two numbers 2.5 miles and 0.5 hours, you divide that, and you get the number 5, so that means, 5 miles an hour

She needs to walk at a speed of 4 miles/hour to reach the destination in 45 minutes.

Speed is the ratio of the total distance covered by an object and the required time to cover that by that object. It is also called Velocity.

[tex]Velocity=\frac{Distance}{Time}[/tex]

Velocity is the measurement which shows an object is how fast.

In this given problem,

The total distance Danielle needs to cover by walking is 3 miles.

She needs to reach the destination in 45 minutes

We know that,

60 minutes = 1 hour

1 minute = [tex]\frac{1}{60}[/tex] hour

45 minutes [tex]=\frac{45}{60}=\frac{3}{4}[/tex] hours

So she has to have the velocity/speed of [tex]=\frac{3}{\frac{3}{4}}=3\times\frac{4}{3}=4[/tex] miles/hour

Hence she needs to walk 4 miles/hour.

Learn further about Speed here -

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Answer:

corresponding

Step-by-step explanation:

Answer:congruent because they are corresponding angles.

Step-by-step explanation:

[tex]4^{2}[/tex] – 2(3 • 5 + 1) = -16

The 2 is a superscript which was the first person's mistake

Answer:

no .8 9 10 are false statement

Step-by-step explanation:

8.angle 3 and angle 5 are not vertical angles because the two lines do not intersect

9 angle 3 and angle 4 are not complementary angle because their non common arms are two opposite rays.

10.angle 1 and angle 2 are not supplementary angles because their non common arms are not two opposite rays.

The answers for #8-10 involve finding the derivative of a function, solving a system of equations, and finding the slope of a line.

For question #8, you need to find the derivative of the given function. This involves using the power rule and the chain rule. For question #9, you are given a system of equations and you need to solve for the values of x and y. This can be done using substitution or elimination. Finally, for question #10, you are asked to find the slope of a line given two points. You can use the formula (y2 - y1) / (x2 - x1) to find the slope.

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Lucy ate 56 pretzels and Matt ate 16 pretzels.

To find out how many pretzels Matt ate, we need to use the information given in the question. Let's represent the number of pretzels Matt ate as 'x'. According to the question, Lucy ate 56 pretzels, which is 8 more than three times the number of pretzels Matt ate. So we can write the equation: 56 = 3x + 8. We must place x on one side of the equation alone in order to solve for it.  Subtracting 8 from both sides, we get 56 - 8 = 3x, which simplifies to 48 = 3x. Finally, dividing both sides by 3, we find that x = 16.

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[tex]\text{Hello there!}\\\\\boxed{\text{This would not be an arithmetical sequence}}\\\\\text{This is not an arithmetic sequence because the common number is}\\\text{not adding.}\\\\\text{The sequence in the question would be known as a geometric sequence}\\\\\text{A geometric sequence multiplies by a common ratio, and that's what the}\\\text{sequence is doing}\\\\\text{The sequence is being multiplied by a common ratio of 3}[/tex]

Final answer:

The sequence is not arithmetic; the terms are increasing by multiplying the previous term by 3.

Explanation:

This sequence does not follow an arithmetic pattern. In an arithmetic sequence, each term is found by adding a constant difference to the previous term. However, in this sequence, the terms are increasing by multiplying the previous term by 3. For example:

Term 1: 4

Term 2: 4 x 3 = 12

Term 3: 12 x 3 = 36

Term 4: 36 x 3 = 108

Since the terms are not increasing by a constant difference, this sequence is not arithmetic.

2.485

2.463

2.90

hope this helps

Answer:

2.90, 2.463, 2.485

Step-by-step explanation:

I'm pretty sure when you do this you need to find the number that's closest to one (2.90). The bigger the number the less it's closer to one. If that makes sense.

I'm pretty sure I did this right. If i'm wrong I do apologize.

(I haven't done greatest to least for decimals in awhile. So seriously i'm sorry if this is wrong)

Answer:

U'(3, -6), V'(8, -1), W'(3, -1)

Step-by-step explanation:

According to the 180°-rotation rule, you take the OPPOSITE of both the y-coordinate and x-coordinate:

Extended Rotation Rules

270°-clockwise rotation [90°-counterclockwise rotation] >> (x, y) → (-y, x)

270°-counterclockwise rotation [90°-clockwise rotation] >> (x, y) → (y, -x)

180°-rotation >> (x, y) → (-x, -y)

I am joyous to assist you anytime.

Answer:

[tex]10^{2}[/tex]

one hundred

Step-by-step explanation:

10 × 10 = 100

100 square feet can be written in exponent form as 10^2, which is read as 'ten squared'. The word form of this is 'one hundred'.

The area of the closet is given as 100 square feet. This can be written in exponent form as 102. The '^' symbol denotes an exponent, which means 'raised to the power of'. Here, '10' is the base and '2' is the exponent, indicating that 10 is multiplied by itself once. In word form, this can be referred to as 'ten squared' or 'one hundred'.

Learn more about Exponent Form here:

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Answer:

1

Step-by-step explanation:

The last part of the line starts from (1,3) and goes to (4,0)

We have two points, so we figure out the equation of this line with the formula:

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

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

m = [tex]\frac{0-3}{4-1}=\frac{-3}{3}=-1[/tex]

So we can now write  y = -x + b

Plugging in a point (1,3), we get:

3 = -1 + b

b = 3+1 = 4

The equation is y = -x + 4

To find h(3), we substitute 3 into x and find the value of y:

y = -x + 4

y = -3 + 4

y = 1

Thus, h(3) = 1

Answer:

Step-by-step explanation:

f(x)=10-2^x,

f(7) = 10 - 2^7     but : 2^7 = 128

so : f(7) = 10 - 128 = - 118

Final answer:

To find the coordinates of point B, use the midpoint formula and solve the equations.

Explanation:

To find the coordinates of point B, we can use the formula for finding the midpoint of a line segment. The midpoint of AB is given as (6,8), and the coordinates of A are (3,2). Let's call the coordinates of B as (x,y).

According to the midpoint formula, the x-coordinate of the midpoint is the average of the x-coordinates of A and B, and the y-coordinate of the midpoint is the average of the y-coordinates of A and B.

So, we can set up the following equations:

(3+x)/2 = 6 and (2+y)/2 = 8

Solving these equations, we find that x = 9 and y = 14.

Therefore, the coordinates of point B are (9,14).

Answer:

Vertex of parabola (-1, -10)

Step-by-step explanation:

For a given quadratic y = ax² + bx + c, the vertex (h, k) is found by computing h = –b/2a, and then evaluating y at h to find k. If you've already learned the Quadratic Formula, you may find it easy to memorize the formula for k, since it is related to both the formula for h and the discriminant in the Quadratic Formula: k = (4ac – b2) / 4a.

Good luck I’m actually looking for answers just like this

Answer:

Step-by-step explanation:

As the object is falling from a fixed Distance, so Speed increases as time increases.

Both speed and time are Directly proportional to each other if distance remains constant.

S = k T

When , T=0, S=0

T=1 s, S=1 m/s

T=2 s, S= 2 m/s

\frac{dS}{dT}=k=Change in speed(Average Speed), if it is Change in Velocity then it will be equal to =a (Acceleration).

Answer:

A on edge 2021

Hey!

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Solution:

y² = 81

To solve just take the square root of 81.

√81 = 9

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Check:

(9)² = 81

81 = 81

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Answer:

x = 9

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Hope This Helped! Good Luck!