Explanation:
10. Jack and Jill were working on their homework together but ended up with two different
answers to the same problem. The problem asked for a new line, parallel to y=2x+3, and
containing the point (-2,-2). Who got the problem correct? Explain your reasoning?
Jack:
y-2 = 2(x - 2)
y-2 = 2x - 4
y = 2x - 2
Jill:
y + 2 = 2(x + 2)
y + 2 = 2x + 4
y = 2x + 2
Answer:
Explanation:

Answer:

Step-by-step explanation:

2(3x+5) = 4(2x - 3)

First expand the terms

That's

6x + 10 = 8x - 12

6x - 8x + 10 = - 12

- 2x + 10 = - 12

Subtract 10 from both sides

That's

- 2x + 10 - 10 = - 12 - 10

- 2x = - 22

Divide both sides by - 2

We have the final answer as

Hope this helps you

Answer:

this is a correct answer

Answer:

θ  = [tex]30^{0}[/tex]

Step-by-step explanation:

Since the vertical height of the mountain is 800 feet, and the distance from the top to its base is 1600 feet. Let the angle of elevation be represented by θ, applying the required trigonometric function;

Sin θ = [tex]\frac{opposite}{hypotenuse}[/tex]

Sin θ = [tex]\frac{800}{1600}[/tex]

        = 0.5

θ = [tex]Sin^{-1}[/tex] 0.5

θ  = [tex]30^{0}[/tex]

Thus, the angle of elevation from the base to the top of the mountain is [tex]30^{0}[/tex].

Answer: The equations are y = 4x-3  and y= 3x -1

Step-by-step explanation:

So lets say both equations will have positive slopes. Using that, we can input any slope  and solve for the y intercept using the coordinates.We will use the formula, y=mx + b  where m is the slope and b is the y-intercept

Let's say the slope is 3.

5 = 3(2) + b

5= 6 + b

-6  -6  

b= -1  

We can now come up with the equation, y= 3x -1  

We need to find another equation that will intersect with it at the point (2,5)

For lines to intersect, they need to have different slopes and different y-intercepts.

We need to come up with a new slope, the slope of the second equation could be 4. Now using the formula, use the coordinates so solve for the y intercept.

5= 4(2) + b

5 = 8 + b

-8   -8

b = -3

The equation will be   y = 4x -3  

We now have the equations y=4x -3   and  y = 3x -1  

To find that their solution is (2,5)  substitute one of the y-values into the other and solve for x then solve for y.  

4x -3 = 3x -1

    +3        +3

4x = 3x + +2

-3x   -3x

1x = 2

x = 2  

We know now that the value of x is true because the value of x is 2.Input it into one of the equations and solve for y.

y = 4(2) - 3

y = 8-3

y = 5

The solution is indeed (2,5) .

Answer: 20 green pencils

Step-by-step explanation:

given data:

cost of red pencils = 3 for 10¢.

cost of green pencils = 2 for 5¢.

cost of blue pencils = 5¢/each.

Greatest number of pencils one can buy for 50¢ By choosi any color is 20pencils which is green

red pencils 50¢ = 15 pencils

green pencils 50¢  = 20 pencils

blue pencils 50¢  = 10 pencils

Answer:

20

Step-by-step explanation:

Answer:

The answer is A. (3x^4-5x^3+5x+2) =(x-2)

Step-by-step explanation:

we see that the polynomial that gives the remainder as 20 is

(3[tex]x^{4}[/tex] - 5x³ + 5x + 2) ÷ (x - 2)

Option A is our correct answer.

The remainder theorem states that when a polynomial p(x) is divided by

(x - a), then the remainder = f(a).

We have,

(3[tex]x^{4}[/tex] - 5x³ + 5x + 2) ÷ (x - 2) ____(1)

We can directly find the remainder as:

x - 2 = 0

x = 2

Putting x = 2 in (1) we get,

= 3 x 16 - 5 x 8 + 5 x 2 + 2

= 48 - 40 + 10 + 2

= 20

The remainder is 20.

(3x³ + 7x² + 5x + 2) ÷ (x - 2) ) _______(2)

x - 2 = 0

x = 2

Putting x = 2 in (2) we get,

= 3 x 8 + 7 x 4 + 5 x 2 + 2

= 24 + 28 + 10 + 2

= 64

The remainder is 64.

(x³ + 5x² - 4x + 6) ÷ (x + 5) ______(3)

x + 5 = 0

x = -5

Putting x = -5 in (3) we get,

= - 125 + 5 x 25 - 4 x (-5) + 6

= -125 + 125 + 20 + 6

= 20 + 6

= 26

The remainder is 26.

([tex]x^{4}[/tex] - 8x² + 16) ÷ (x + 4) _______(4)

x + 4 = 0

x = -4

Putting x = -4 in (4) we get,

= 256 - 8 x 16 + 16

= 256 - 128 + 16

= 144

The remainder is 144.

Thus we see that the polynomial that gives the remainder as 20 is

(3[tex]x^{4}[/tex] - 5x³ + 5x + 2) ÷ (x - 2)

Option A is our correct answer.

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Answer:

[See Below]

Step-by-step explanation:

✦ Solve:

  ✧ -2.6 + 5.8 = 3.2

✦ Sometimes in math simplify could mean just solve and get the smallest version of that number. That's what it means in this case. So the simplified version would be 3.2.

~Hope this helps Mate. Feel free to message me if you need anything.

Answer: 0.81

Step-by-step explanation: Think about all the way to the 100.

Answer:

$6650

Step-by-step explanation:

→ Calculate the decimal multiplier

100 - 30 = 70

70 ÷ 100 = 0.7

→ Multiply the decimal multiplier by the cost

9500 × 0.7 = 6650

Answer:

$6,650

Step-by-step explanation:

This is called percentage decrease:

(100 - 30)% = 70%

9500 × 70/100

= $6,650

Answer:105

Step-by-step explanation:

first find f(7)

(7)^2 + 1

=50

then put the answer for f(7) in g of x

2(50) + 5

=105

Answer:

True

Step-by-step explanation:

the parent function f(x) = 1/x has a vertical asymptote at x = 0 and a horizontal asymptote at y = 0

Answer:

Step-by-step explanation:

4(2x-1)=3x+5-x

8x-4=3x+5-x

8x-4=2x+5

6x-4=5

6x=9

x=3/2

Answer: x=1.3

Explanation: Just simplify the equation so there is a variable on one side and a number on the other.

Answer:

C

Step-by-step explanation:

Given

[tex]\frac{-m}{2}[/tex] - [tex]\frac{5}{4}[/tex] ≤ [tex]\frac{5m}{12}[/tex] - [tex]\frac{7}{6}[/tex]

Multiply through by 12 to clear the fractions

- 6m - 15 ≤ 5m - 14 ( subtract 5m from both sides )

- 11m - 15 ≤ - 14 ( add 15 to both sides )

- 11m ≤ 1

Divide both sides by - 11, reversing the symbol as a result of dividing by a negative quantity

m ≥ - [tex]\frac{1}{11}[/tex] → C

The value of the given expression (7m - 2m²n)² = 34,596 at m = -6 and n = 2.

An expression consists of variables, constants, and operators. Based on the number of terms in an expression, they are named linear, binomial, and so on.

The given expression is (7m - 2m²n)²

It is given that m = -6 and n = 2

To evaluate the given expression, the given values are substituted in it.

On substituting these values,

(7m - 2m²n)² = (7(-6) - 2(-6)²(2))²

⇒ (-42 - 4(36))²

⇒ (-42 - 144)²

⇒ (-186)²

∴ (7m - 2m²n)² = 34,596

Therefore, the required value of the given expression is 34,596.

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Answer:

00304761

Step-by-step explanation:

Answer:

$18.15

Step-by-step explanation:

Exact form is N=49/12 mixed number form is N=4 1/12

Step-by-step explanation:you have to simplify both sides and then isolate the variable.

Answer:

n=49/12 or 4 1/12

Step-by-step explanation:

n-5•2/3=3/4

n-10/3=3/4

n=3/4+10/3

n=49/12 or 4 1/12

Answer:

x=-5

Step-by-step explanation:

x=10/5 - 7

x=2-7

x=-5

Answer:

Perpendicular line through a point off a line

Step-by-step explanation:

Based on the markings in the diagram, we have;

Marking points E and F along AB extended forms two points equidistant from the point C on the line AB

Construction of the line HI by using equal arc lengths from E and F creates two points equidistant from E and F on either side of the line AB such that HI passes through C forming a perpendicular bisector from C to AB.

Therefore, a perpendicular line has been constructed from the point C off the line AB to the line AB

Hence the correct option is the construction of a perpendicular line through a point off a line.

Answer:

C. Perpendicular line through a point off a line (its off not on)  Took the test and got it right

Step-by-step explanation:

Answer:

-396

Step-by-step explanation:

Plug it into a calculator

4 x 33 = 132

132 x -3 = -396

4 x 33 x -3= 132 x -3= -396

Answer:

it should be 2nd option, 3rd, and 5th.

Step-by-step explanation:

From the given options

options I, III and IV  are Arithmetic sequences.

Given :

we are given with sequences. we need to check which one is arithmetic sequence.

A sequence is arithmetic when the consecutive terms have common difference.

Lets check one by one

[tex]-8.6, -5.0, -1.4, 2.2, 5.8,......\\-5-(-8.6)=3.6\\-1.4-(-5)=3.6\\2.2+1.4=3.6\\[/tex]

Its arithmetic because common difference is same 3.6

2, –2.2, 2.42, –2.662, 2.9282, …

-2.2-2=-4.2

2.42+2.2=6.62

Its not arithmetic

5, 1, –3, –7, –11, …

1-5=-4

-3-1=-4

-7+3=-4

-11+7=-3

Common difference is -4. So it Arithmetic

–3, 3, 9, 15, 21, …

3+3=6

9-3=6

15-9=6

Its Arithmetic

–6.2, –3.1, –1.55, –0.775, –0.3875, …

-3.1+6.2=3.1

-1.55+3.1=1.55

Its not Arithmetic

So, options I, III and IV  are Arithmetic sequences.

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Answer:

[tex]x = 7[/tex]

Step-by-step explanation:

Given

[tex]\frac{4}{3}x - \frac{1}{3} = 9[/tex]

Required

Solve for x

[tex]\frac{4}{3}x - \frac{1}{3} = 9[/tex]

Add [tex]\frac{1}{3}[/tex] to both sides

[tex]\frac{4}{3}x - \frac{1}{3} + \frac{1}{3} = 9 + \frac{1}{3}[/tex]

[tex]\frac{4}{3}x = 9 + \frac{1}{3}[/tex]

Take LCM

[tex]\frac{4}{3}x = \frac{27 + 1}{3}[/tex]

[tex]\frac{4}{3}x = \frac{28}{3}[/tex]

Multiply both sides by [tex]\frac{3}{4}[/tex]

[tex]\frac{3}{4} * \frac{4}{3}x = \frac{3}{4} *\frac{28}{3}[/tex]

Evaluate the left hand side

[tex]x = \frac{3}{4} *\frac{28}{3}[/tex]

[tex]x = \frac{28}{4}[/tex]

Divide 28 by 4

[tex]x = 7[/tex]

Answer:

x=7 we are both correct

Step-by-step explanation:

Answer: 145

Step-by-step explanation:

Answer: 145

Step by step explanation:

Answer:

h(x) = 2x² - 2x - 8

Step-by-step explanation:

Step 1: Write out equation

h(x) = 2(x + 1)(3x - 4)

Step 2: FOIL

h(x) = 2(x² - 4x + 3x - 4)

Step 3: Combine like terms (x)

h(x) = 2(x² - x - 4)

Step 4: Distribute

h(x) = 2x² - 2x - 8

Answer:

A)

The simplest way to solve A is by checking 1st digit one-by-one.

selecting 1 as 1st digit, we have 2 ways

1324 and 1423

selecting 2 as 1st digit, we have 3 ways

2143, 2314, and 2413

selecting 3 as 1st digit, we have 3 ways

3142, 3241, and 3412

selecting 4 as 1st digit, we have 2 ways

4132 and 4231

=> 2 +3 + 3 + 2 = 10 ways in total.

B)

Use the same strategy as A)

selecting 1st digit that is greater than 6, there are 3 digits: {9, 8, 7}

selecting 9 as 1st digit => 967, 968

selecting 8 as 1st digit => 867, 869

selecting 7 as 1st digit => 768, 769

=> 3 x 2 = 6 ways

selecting 1st digit that is smaller than 6, there are 5 digits: {5, 4, 3, 2, 1}

selecting 5 as 1st digit => 565, 564, 563, 562, 561, 560

similarly, selecting 4, 3, 2, 1, there are 6 ways to select that last digit

=> 5 x 6 = 30 ways

=> 30 + 6 = 36 ways in total

C)

a 7-digit snakelike number starts with digit 9 (the largest digit)

=> 2nd digit is smaller than 9

=> 3rd digit is larger than 2nd digit

=> 4th digit is smaller than 3rd digit

=> 5th digit is larger than 4th digit

=> 6th digit is smaller than 5th digit

=> 7th digit is larger than 6th digit (this is impossible because 0 is smallest digit)

Answer:

r = - 2

Step-by-step explanation:

Use the slope formula to find m then equate to - 1

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (6, r) and (x₂, y₂ ) = (9, - 5)

m = [tex]\frac{-5-r}{9-6}[/tex] = [tex]\frac{-5-r}{3}[/tex]  = - 1 ( multiply both sides by 3 )

- 5 - r = - 3 ( add 5 to both sides )

- r = 2 ( multiply both sides by - 1 )

r = - 2

Answer:

the answer for number 38 is H

Step-by-step explanation:

(f-g)(x) = f(x) - g(x).

When x = 2, f(2) - g(2) = 3(2)^2 + 1 - (1 - 2) = 12 + 1 + 1 = 14.