1. What is the slope of the line that passes through (-2, 6) and (8, 1)?
a. -1/2
b. 1/2
c. -2
d. 2

Answer:

There are two possible values for r (area):  r =-7 or r=3

Step-by-step explanation:

Given the rectangular rug area is:

[tex]r^{2} -4r -21[/tex]  

We have to convert the above equation into factored form.

So two numbers whose product is -21r² and sum is -4r

<=> [tex]r^{2} -4r -21[/tex]  

= [tex]r^{2} -7r + 3r -21[/tex]

= r (r -7) + 3(r -7)

= (r-7)(r+3)

We set  [tex]r^{2} -4r -21[/tex]   = 0

<=> (r-7)(r+3) = 0

<=> (r-7) = 0 or (r+3)  = 0

<=> r =-7 or r=3

So, there are two possible values for r (area):  r =-7 or r=3

Final answer:

The possible dimensions of the rectangular rug with the given area trinomial r²-4r-21 are 7 by 3 or 3 by 7.

Explanation:

The possible dimensions of the rectangular rug with area given by the trinomial r²-4r-21 can be found by factoring the trinomial.

Factoring r²-4r-21 results in (r-7)(r+3). Therefore, the dimensions could be 7 by 3 or 3 by 7.

Step-by-step explanation:

[tex]y = 2x - 3 \\ plug \: x = - 1 \\ y = 2( - 1) - 3 = - 2 - 3 = - 5 \neq1 \\ hence \: ( - 1, \: 1) \: does \: not \: lie \: on \: the \: \\ graph \: of \: y = 2x - 3. \\ \\ y = 2x - 3 \\ plug \: x = 1 \\ y = 2 \times 1- 3 = 2 - 3 = - 1 \\ hence \: ( - 1, \: 1) \: lie \: on \: the \: graph \: of \: \\ y = 2x - 3. \\ \\ [/tex]

Answer: 1/16

Do Keep Change Flip (KCF)

Keep: 1/2

Change: ÷ into ×

Flip: 8/1 into 1/8

Your New Problem Should Be: 1/2×1/8

Multiply

1/2 × 1/8 = 1/16

The amount of pasta each would get is 1/16

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. Unitary method is a technique by which we find the value of a single unit from the value of multiple devices and the value of more than one unit from the value of a single unit. It is a method that we use for most of the calculations in math.

Do Keep Change Flip (KCF)

Keep: 1/2

Change: ÷ into ×

Flip:

8/1 into 1/8

= 1/2×1/8

Multiply,

1/2 × 1/8 = 1/16

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Answer:

1<y≤8

Step-by-step explanation:

step 1

The number is y and it is greater than one.

The sign for greater than in mathematics is '>'

Therefore, we can write

y>1

And it means 1 is less than y

Less than = <

1<y

Step 2

y is less than or equal to 8. In mathematics, the 'less than or equal to' sign is '≤'

Therefore, we can write

y≤8

Step 3

We then combine these two inequalities

1<y≤8

Final answer:

The inequality 1 < y ≤ 8 represents a number y that is greater than 1 and less than or equal to 8.

Explanation:

An inequality representing the statement 'A number y is greater than 1 and is less than or equal to 8' can be expressed as:

1 < y ≤ 8

This inequality signifies that y is greater than 1 (1 < y) and at the same time, less than or equal to 8 (y ≤ 8), fulfilling both conditions simultaneously.

The value of  (-3/4[tex])^{-4[/tex] is 256/81.

Exponents and powers are ways used to represent very large numbers or very small numbers in a simplified manner.

For example, if we have to show 3 x 3 x 3 x 3 in a simple way, then we can write it as [tex]3^4[/tex], where 4 is the exponent and 3 is the base. The whole expression 34 is said to be power.

We have to find the value of (-3/4[tex])^{-4[/tex]

First of all make the power positive by reciprocate the number

= (-3/4[tex])^{-4[/tex]

= (-4/ 3 [tex])^4[/tex]

Now, expanding the number we get

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

= 256 / 81

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Answer:

10 ^(R-15)/3   -2=  a

Step-by-step explanation:

R = 3 log (a+2) +15

Subtract 15 from each side

R-15 = 3 log (a+2) +15-15

R-15 = 3 log (a+2)

Divide each side by 3

(R-15)/3 = 3/3 log (a+2)

(R-15)/3 =  log (a+2)

The opposite of log is to raise each side to the power of 10

10 ^(R-15)/3 = 10 ^ log (a+2)

10 ^(R-15)/3 =  (a+2)

Subtract 2 from each side

10 ^(R-15)/3   -2=  (a+2-2)

10 ^(R-15)/3   -2=  a

Answer:

10 ^(R-15)/3   -2=  a

Step-by-step explanation:

i answered this on edge

1.Total cost of the computer: Let's represent the original price as $x. After an 80% sale, it's 0.8× x.

2. Amount Leona saved: $102.50.

3. Remaining amount needed: Total cost - Amount saved = 0.8 × x - $102.50.

So, Leona needs $102.50 more to afford the computer after her savings.

let's break it down step by step:

1. Find the total cost of the computer: Let's say the original price of the computer is $x, and it's currently on sale. Since Leona saved $102.50, this means the amount she has saved is a part of the total cost of the computer.

2.Calculate the remaining amount needed: We subtract the amount Leona saved from the total cost of the computer to find out how much more money she needs to save.

So, let's go through these steps:

1. Total cost of the computer: Let's represent the original price of the computer as $x. Since the computer is on sale, let's say it's now priced at 80% of its original price.

  So, the total cost of the computer after the sale = 0.8 ×x.

2. Amount Leona saved = $102.50.

3. Remaining amount needed = Total cost of the computer - Amount Leona saved.

Let's perform the calculation

Total cost of the computer = 0.8 × x

Amount Leona saved = $102.50

Remaining amount needed = Total cost of the computer - Amount Leona          = 0.8 × x - $102.50

So, Leona needs to save $102.50 more to buy the computer.

Answer:

45/4 or    11.25   or   11 1/4

Step-by-step explanation:

Answer:

Step-by-step explanation:-15/4

-15/4

Answer:

210

Step-by-step explanation:

multipy the percent of the won skating competitions by the total amout of competions to get the result of how mant he won. 84% x 250 competitions= 210 competitions won!

Answer:

the answer above is incorrect im sorry i dont know the answer i wish i could help more god bless have a wonderful day

Step-by-step explanation:

Answer:

x = - 191/28

Step-by-step explanation:

14 (8x + 56) = 20

112x + 784 = 20

112x = 20 - 784

112x = - 764

x = - 764/112

x = - 191/28

Answer:

Here are a few equivalent equations:

112x + 784 = 20

112x = -764

x = -6.82

Step-by-step explanation:

14(8x + 56) = 20

Multiply

112x + 784 = 20

Subtract 784 from both sides of the equation

112x = -764

x = -6.82

Hope this was useful to you!

Answer:

2.331 = (2.33 × 100)(1 × 100) = 233100. As the numerator is greater than the denominator, we have an IMPROPER fraction, so we can also express it as a MIXED NUMBER, thus 233100 is also equal to 233100 when expressed as a mixed number.

Step-by-step explanation:

or mutilpy by 100

Answer:

2.33 * 100 because

2.33*100=233

Answer:

6 ft = 72 inches

72*1/3=24

24

They will get 24 slices if they cut the 6 foot hero into 1/3 inch slices.

A fraction is a numerical figure that represents a portion of a total.

Total length of the hero = 6 foot

1 foot = 12 inches

Total length of hero = 72 inches

Length of the slice cut = 1/3 inch

Total no. of slices = (1/3 * 72) = 24 slices

Hence the total no. of slices they will get is 24.

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Answer:

x^2 + (y – 3)^2 = 36

Step-by-step explanation:

The standard equation of a circle with center at (h, k) and radius r is

(x - h)^2 + (y - k)^2 = r^2.

If the center lies on the y-axis, then h = 0:  (x - 0)^2 + (y - k)^2 = r^2

If the circle diameter is 12, then the circle radius is 6, and so r^2 = 36

So, among the given equations, your

x^2 + (y – 3)^2 = 36 is correct (but only if you use " ^ " for exponentiation).

The equations that represent circles with a diameter of 12 units and a center on the y-axis are x² + (y - 6)² = 36 and x² + (y + 6)² = 36.

The equations that represent circles with a diameter of 12 units and a center on the y-axis are:

To determine if an equation represents a circle, we need to check if the equation follows the standard form of a circle equation, which is (x - h)² + (y - k)² = r², where (h, k) is the center and r is the radius. In this case, since the center lies on the y-axis, the x-coordinate of the center is 0, and we only need to consider the y-coordinate.

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The amount of money that remained from Takuya's presence during month n is expressed as an=120-20n and the sequence is an arithmetic sequence.

The arithmetic sequence is the sequence where the common difference remains constant between any two successive terms. Let us recall what is a sequence. A sequence is a collection of numbers that follow a pattern. The general form of an arithmetic sequence is an=a+(n-1)d.

If Takuya's parents gave him $100 as a birthday gift and she spent $20 each month on board games until his money ran out, this means he keeps spending $20 every month and his money keeps reducing by the same amount each month until his money ran out, the following can be inferred;

initial amount = $100

If he spends $20 each month,

Balance at the end of 1st month = $100-$20 = $80

Balance at the end of 2nd month = $80-$20 = $60

Balance at the end of  3rd month = $60-$20 = $40 and so on

Since the amount keeps reducing by the same value i.e $20, then the sequence formed is an arithmetic sequence.

a is the first term of the sequence = 100

d is the common difference = 80-100 = 60-80 = 40-60 = -20

n is the number of terms

Substituting the given values in the formula we have; an=100+(n-1)(-20)

⇒an=100+(-20n+20)

⇒an=100-20n+20

⇒an=120-20n

Therefore, the amount of money that remained from Takuya's presence during month n is expressed as an=120-20n and the sequence is an arithmetic sequence.

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1) Option (A) arithmetic sequence.

2) The recursive formula is f(n) = f(n-1) - 20 with an initial condition of f(1) = 100.

3) The explicit formula is f(n) = 120 - 20n.

Let's address Takuya's birthday gift scenario step by step.

1. Type of Sequence

The sequence described is an arithmetic sequence because the same amount of money, $20, is spent each month, leading to a consistent decrease in the balance.

2. Recursive Formula

Initially, he had $100. So,

f(1) = 100

Given the monthly spending of $20, the recursive formula is: f(n) = f(n-1) - 20

3. Explicit Formula

To find the explicit formula of the arithmetic sequence, we use the initial value and the common difference:

f(n) = 100 - 20(n-1)

Simplifying gives us:

f(n) = 120 - 20n

Thus, the balance remaining after n months can be calculated using this explicit formula.

Complete question:

Takuya's parents gave him $100dollar as a birthday gift. Since he loves board games, he spent $ 20 dollars out of his present on board games at the end of each month until his money ran out. Let f(n) be the amount of money that remained from Takuya's present during month n, where n=1 represents the month he received his present.

1) f is a sequence. What kind of sequence is it?

Choose 1 answer:

A ) Arithmetic sequence

B) Geometric sequence

2) Complete the recursive formula for f(n).

f(1) = □

f(n) = □

3) Find the explicit formula.

Answer:

the graph that's got long lines in the top right and bottom left

Answer: 10

Step-by-step explanation:

Answer: the answer is 10

Answer: 5/2 meters

Step-by-step explanation:

You can find the area of a rectangle using this equation:

A = bh, where b is the base (length) and h is the height.

So, your rectangle is:

[tex]\frac{35}{4} = \frac{7}{2}h[/tex]

You can then divide both sides by 7/2 to find h.

[tex]\frac{\frac{35}{4}}{\frac{7}{2}}[/tex]

To divide, you can flip the fraction in the denominator to multiply:

[tex]\frac{35}{4}*\frac{2}{7}[/tex]

So, your width is 70/28. You can divide both sides by 14 to get 5/2.

Answer:

Step 1:  Find the x

2x + 5:  Solve

[tex]2x + 5 - 5 = 0 - 5[/tex]

[tex]2x / 2 = -5 / 2[/tex]

[tex]x = -5/2[/tex]

3x + 15:  Solve

[tex]3x + 15 - 15 = 0 - 15[/tex]

[tex]3x / 3 = -15 / 3[/tex]

[tex]x = -5[/tex]

Answer:

144 yards

Step-by-step explanation:

Multiply 12 yd by 12 yd =

144 yards

Answer: The answer is 144yd squared

Step-by-step explanation:

Answer:

Step-by-step explanation:

It will be 6855 because it’s telling you the difference of them so you subtract to see

The difference in meters between the highest and lowest elevation points 7065 meters.

Integers include all whole numbers and negative numbers. This means if we include negative numbers along with whole numbers, we form a set of integers.

An integer is a number with no decimal or fractional part and it includes negative and positive numbers, including zero. A few examples of integers are: -5, 0, 1, 5, 8, 97, and 3,043. A set of integers, which is represented as Z, includes:

Positive Numbers: A number is positive if it is greater than zero. Example: 1, 2, 3 . . .

Negative Numbers: A number is negative if it is less than zero. Example: -1, -2, -3 . . .

Zero is defined as neither a negative number nor a positive number. It is a whole number.

Z = {... -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, ...}

Given:

highest point= 6960 meters above sea level.

lowest point = 105 meters below sea level.

Considering integers

highest points= +6960

lowest point= -105

So, difference in meters between the highest and lowest elevation points

= 6960 - (-105)

=6960+ 105

= 7065 meters

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It would be A or < since 54 is positive and -26 isn't, that makes 54 greater than -26.

Answer:

Segments parallel to XT: YU, ZV, WS

Segments parallel to ZY: VU, WX

Segments parallel to ZS: None

Plane parallel to plane STU: WXY

Plane parallel to plane UVZ: TSW

All segments skew to SW: WX, ST

All segments skew to UT: UY, TX

Step-by-step explanation:

Let's begin by explaining the following:

Two line segments are parallel only if their slopes are identical, allowing them to never intersect.

Hence, according to this definition we have:

Segments parallel to XT: YU, ZV, WS

Segments parallel to ZY: VU, WX

Segments parallel to ZS: None

Now, if we go to the three-dimensional space, two planes are parallel, when they do not share any line, which allows them to never cross in space.

Hence, according to this definition we have:

Plane parallel to plane STU: WXY

Plane parallel to plane UVZ: TSW

Two lines are skew if and only if they are not in the same plane (also known as not coplanar). So, if two lines are not coplanar, they are not parallel and cannot intersect, either.

Hence, according to this definition we have:

All segments skew to SW: WX, ST

WZ and SV do not match the condition, since they are in the same plane where SW is,

All segments skew to UT: UY, TX

UV and  ST do not match the condition, since they are in the same plane where UT is.

The following answers can be given as the solution to the given questions:

a) All segments parallel to XT:  YU, ZV, WS

b) All segments parallel to ZY:  VU, WX

c) All segments parallel to ZS:  YT

d) A plane parallel to plane STU: WXY

e) A plane parallel to plane UVZ:  TSW

f) All segments skew to SW:  ZY, VU, XY, UT

g) All segments skew to UT:  SW, WX, VZ, ZY

To give the appropriate answers to the given questions, the following terms must be understood.

i. Parallel lines: Two or more lines are parallel if and only if they do not meet even when extended to infinity.

ii. Skew lines: Two or more skew lines are lines that are neither parallel nor intersecting.

iii. Plane: This is flat surface which can either be in x-axis, y-axis or z-axis.

Therefore, the answers to each of the questions are:

a) All segments parallel to XT:  YU, ZV, WS

b) All segments parallel to ZY:  VU, WX

c) All segments parallel to ZS:  YT

d) A plane parallel to plane STU: WXY

e) A plane parallel to plane UVZ:  TSW

f) All segments skew to SW:  ZY, VU, XY, UT

g) All segments skew to UT:  SW, WX, VZ, ZY

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Answer:

y = (-¼)x + 1

Step-by-step explanation:

y = 4x + 1

Slope of the perpedicular:

m = -¼

Equation:

y = (-¼)x + 1

4y = -x + 4

Answer:

-0.14

Step-by-step explanation:

First eliminate the parenthesis:

6( 4x + 5) = 3(x + 8) + 3 =>

24x + 30 = 3x + 24 + 3

Then group x terms on the left and constants on the right

24x - 3x = 24 + 3 - 30

21x = -3

Divide by 21 and simplify:

x = -3/21 = -1/7 ≈ -0.14

Answer:

- 1/7

Step-by-step explanation:

6(4x + 5) = 3(x + 8) + 3

Expand the brackets

6 X 4x + 6 x 5 = 3 X x + 3 X 8 + 3

24x + 30 = 3x + 24 + 3

24x + 30 = 3x + 27

Subtract 30 from both sides to eliminate 30 on the left side

24x + 30 - 30 = 3x + 27 - 30

24x = 3x - 3

Subtract 3x from both sides to eliminate bring all variables to one side

24x - 3x = 3x - 3x - 3

21x = -3

Divide both sides by 21 to isolate x

21x/21 = -3/21

x = -1/7

x = - 1/7