Select the correct answer.
Which equation represents the line that is perpendicular to y = and passes through (-6,-9)?
OA. x = -9
B. X=-6
OC. y=-9
OD. y=-4

Answer:

6. perfect squares 5 and 6

7. between integers 5 and 6

Step-by-step explanation:

[tex]\sqrt[3]{141} = 35.62\\[/tex]

Answer:

A) [tex]x = -5[/tex]

Step-by-step explanation:

[tex](x + 3)^2 = | x + 1 |\\\to x^2 + 6x + 9 = | x + 1|[/tex]

Case 1: x + 1 is positive

[tex]x^2 + 6x + 9 = x + 1\\\to x^2 + 5x + 8 = 0\\\to \text{No solutions.}[/tex]

Case 2: x + 1 is negative

[tex]-x^2 - 6x - 9 = x + 1\\\to 0 = x^2 + 7x + 10\\\to 0 = (x + 5)( x + 2)\\\to x = -5 \text{ or } x = -2[/tex]

The interest rate is the amount a lender charges a borrower and is a percentage of the principal—the amount loaned. Athena's will be charged $74.77 for interest.

The interest rate is the amount a lender charges a borrower and is a percentage of the principal—the amount loaned.

Given,

Athena's credit card has an APR of 32.99%.

We need to convert the percentage to decimal.

32.99%=32.99/100

=0.3299

The amount will she be charged for interest is

=(2719.83*0.3299)/12

=897.27/12

=74.77

Therefore Athena's will be charged $74.77 for interest.

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Answer:

A D B C E

Step-by-step explanation:

That is the order of steps in the solution

By using algebra and trigonometry properties, the expression (cot² t + 1) · (sin² t + 1) is equivalent to the expression cot² t + 2.

In this problem we find an equivalence between two trigonometric expressions. This can be done by transforming the expression at one side by using algebra and trigonometry properties until the expression of the other side is found. The procedure is now presented and explained:

(cot² t + 1) · (sin² t + 1)                              Given

(cot² t + 1) · sin² t + (cot² t + 1)                 Distributive property

cot² t · sin² t + sin² t + cot² t + 1              Distributive property

cos² t + sin² t + cot² t + 1                         cot t = cos t / sin t / Associative and commutative properties / Existence of multiplicative inverse / Modulative property

1 + cot² t + 1                                              cos² t + sin² t = 1

cot² t + 2                                                  Commutative and associative properties / Definition of addition

Thus, the expression (cot² t + 1) · (sin² t + 1) is equivalent to the expression cot² t + 2.

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Two or more expressions with equal sign is equation, if the equation 5k^2−20k=15 then 1 and 3 are exact values of the solutions.

Two or more expressions with equal sign is called as Equation.

The given equation 5k^2−20k=15,

let us make it a QE by taking 15 to left.

5k^2−20k-15

a=5, b=-20, c=-15

k=-b±√b^2-4ac/2a

=20±√(-20)^2-4(5)(-15)/2(5)

=20±√400-300/10

=20±√100/10

=20±10/10

k=20+10/10 or k=20-10/10

k=3, or k=1

Therefore the solutions of equation 5k^2−20k=15 are 1 and 3.

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Step-by-step explanation:

the slope of a line is always the factor of x, and it is defined as ratio (y coordinate change / x coordinate change) when going from one point to another on the line.

in that sense it is y/x.

the perpendicular slope turns that ratio upside-down and flips the overall sign.

so, in our case, the original slope is 3 = 3/1.

the perpendicular slope is then -1/3.

so, now, we have the slope and a point, and we can start with the point-slope form of the line equation :

y - y1 = a(x - x1)

"a" being the slope, (x1, y1) being the point.

y - 1 = -1/3 × (x - 9) = -x/3 + 3

y = -x/3 + 4

and that is the usual slope-intercept form

y = ax + b

"a" is again the slope, "b" is the y-intercept (the y value when x = 0).

Answer:

A'(12,9), B'(12,3), C'(-1,5)

Step-by-step explanation:

A is 6 units from the line y=3, so it will map to be 6 units away on the other side of y=3, to the point (12, 9).

Similarly, B' has coordinates (12,3) and C' has coordinates (-1, 5)

Pamela is 1 year old now.

How to solve problems on ages ?

Age after n years = X +n

Age n years ago = X - n

n times the present age = nX

If ages in the numerical are mentioned in the ratio A : B, then A : B will be AX and BX.

Age of Y = Ratio of Y / Sum of ratios x sum of ages

Age of Y = q/ (p +q) x A  

In the given statement is:

Debra is 7 years younger than Pamela. In 6 years, Pamela will be twice as old as Debra.

To find the how old is Pamela now.

Now, Based on the given conditions,

Formulate:

Let x be the Pamela's age

6 + 7 + x = 2(6 + x)

13 + x = 12 + 2x

x - 2x = 12 - 13

-x = -1

x = 1

Hence, Pamela is 1 year old now.

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Amos says that the opposite and the absolute value of a number are always the same. This is true.

It should be noted that from the information, Amos says that the opposite and the absolute value of a number are always the same.

For example, given the number 23, the opposite will be -23 and the absolute value is also -23. This implies that they are the same.

Therefore, Amos says that the opposite and the absolute value of a number are always the same. This is true.

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Amos says that the opposite and the absolute value of a number are always the same. True or false.

Answer: Rate of tree's height per year = 0.275 m per year.

Rate of tree's trunk per year = 0.025 m per year.

Step-by-step explanation:

Given data,

Exactly 120 years​ ago, students planted a tree in front of their school

Since​ then, the tree has grown 33 meters taller

The distance around the trunk has increased by 3 meters.

Define Unit rate :

A unit rate means a rate for one of something. We write this as a ratio with a denominator of one. For example, if you ran 70 yards in 10 seconds, you ran on average 7 yards in 1 second. Both of the ratios, 70 yards in 10 seconds and 7 yards in 1 second, are rates, but the 7 yards in 1 second is a unit rate.

So, we can write,

There are 2 various unit rates in this:

The increase of the tree's height per year

The increase of the tree's trunk per year

Let us assume,

The increase of the tree's height per year = x

The increase of the tree's trunk per year = y

we can solve it :

Rate of tree's height per year x = 33m / 120 years

                                                x = 0.275 m per year.

Rate of tree's trunk per year y = 3m / 120 years

                                              y = 0.025 m per year.

Therefore,

Rate of tree's height per year = 0.275 m per year.

Rate of tree's trunk per year = 0.025 m per year.

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The product of 3/6×5/4 is equal to the product of 3/4×5/6.

What is simplification?

Here,

3/6×5/4 = 3 * 5 / 6* 4

            = 15 / 24

3/4×5/6 = 3 * 5 / 4 * 6

            = 15 / 24

Thus, The product of 3/6×5/4 is equal to the product of 3/4×5/6.

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Answer: wdym

Step-by-step explanation:

Elise doesn't like sorbet.

(Assuming we fix the grammar???)

Answer:

No solution

Step-by-step explanation:

Answer:5 per  Gallone

Step-by-step explanation:

Answer:

Gas in India is $3.88 per gallon.

This is MORE expensive than $2.36 per gallon.

Step-by-step explanation:

Use the conversion factors given to change rupees to dollars and liters to gallons. See image.

(and btw, this question has very outdated information. Gas is $5.90 per gallon today in this poster's City, State, USA)

Answer: No veo lo que estás mirando. Pero aquí hay un consejo para ayudarte. Un paralelogramo es una figura con cuatro lados en los que los lados opuestos son paralelos.

¡Espero que esto ayude! :)

The probability that an NBA player who makes 80% of his free throws makes 2 of his next 3 free throws is 0.384

Probability is the extent to which an event is likely to occur, measured by the ratio of the favorable cases to the whole number of cases.

Now it is given that,

The proportion of free throws the player makes, p = 80% = 0.8

The number of throws, n = 3

The throws the player makes, r = 2

Since the probability is given as,

P(r) = nCr x p^r x (1 - p)^(n-r)

So, the probability that an NBA player makes 2 of his next 3 free throws

Putting the values we get,

P(2) = ³C₂ x (0.8)^2 x (1 - 0.8)^(3-2)

Solving we get,

P(2) = 3 x 0.64 x (0.2)^(1)

Thus we get,

P(2) = 3 x 0.64 x 0.2

Multiplying we get,

P(2) = 0.384

this is the required probability that an NBA player makes 2 of his next 3 free throws.

Thus, the probability that an NBA player who makes 80% of his free throws makes 2 of his next 3 free throws is 0.384

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The value of the two numbers are 30 and 20.

According to the statement

We have to find that the value of the two numbers.

So, For this purpose, we know that the

A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept.

From the given information:

The larger of two numbers is 10 less than the smaller number. The sum of the two numbers is 50.

Then

Let the first number be x and the second number y

Then

y = x -10

And

x+y = 50

Then

Substitute the value then

x+x-10 = 50

2x = 50+10

2x = 60

x =30

Then

y = x -10

y = 30 -10

y = 20

So, The value of the two numbers are 30 and 20.

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Answer:

a. [tex]\frac{10}{3}[/tex]

b. [tex]\frac{4}{3}[/tex]

c.[tex]4\frac{2}{3}[/tex]

Step-by-step explanation:

a.

[tex]\mathrm{Convert\:mixed\:numbers\:to\:improper\:fraction:}\:a\frac{b}{c}=\frac{a\cdot \:c+b}{c}[/tex]

[tex]3\frac{1}{2}=\frac{3\cdot 2+1}{2}=\frac{7}{2}[/tex]

b.

reciprocal is technically the opposite

c.

[tex]\mathrm{Convert\:mixed\:numbers\:to\:improper\:fraction:}\:a\frac{b}{c}=\frac{a\cdot \:c+b}{c}[/tex]

[tex]=\frac{7}{2}\div \frac{3}{4}[/tex]

[tex]\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{a}{b}\div \frac{c}{d}=\frac{a}{b}\times \frac{d}{c}[/tex]

[tex]=\frac{7}{2}\times \frac{4}{3}[/tex]

[tex]\mathrm{Cross-cancel\:common\:factor:}\:2[/tex]

[tex]=\frac{7}{1}\times \frac{2}{3}[/tex]

[tex]\mathrm{Multiply\:fractions}:\quad \frac{a}{b}\times \frac{c}{d}=\frac{a\:\times \:c}{b\:\times \:d}[/tex]

[tex]\frac{7\times \:2}{1\times \:3}[/tex]

[tex]\mathrm{Multiply\:the\:numbers:}\:7\times \:2=14[/tex]

[tex]=\frac{14}{1\times \:3}[/tex]

[tex]\mathrm{Multiply\:the\:numbers:}\:1\times \:3=3[/tex]

[tex]=\frac{14}{3}[/tex]

[tex]\mathrm{Convert\:improper\:fraction\:to\:mixed\:numbers}[/tex]

[tex]4\frac{2}{3}[/tex]

An equation and number line which shows that a number and its opposite are additive inverses is: 2 + (-2) = 0 in graph B.

A number line can be defined as a type of graph with a graduated straight line which contains both positive and negative numerical values that are placed at equal intervals along its length.

An additive inverse can be defined as a number (n) which when added to another number (a) makes it equal to zero (0). This ultimately implies that, an additive inverse is the opposite of another number (a).

Mathematically, an additive inverse can be represented by the following expressions:

a + n = 0

a = -n

In this context, we can reasonably infer and logically deduce that an equation and number line which shows that a number and its opposite are additive inverses is 2 + (-2) = 0 in graph B (see attachment).

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The weight average of the coordinates is 9

Given,

The coordinate 6 has a weight of 2

The coordinate 9 has a weight of 2

The coordinate 15 has a weight of 1

We have to find the weight average:

The weight average is then calculated as:

Weight average = Sum of (Weight * Coordinate)/Sum of Weights

So, we have:

Weight average = ( (6 x 2) + (9 x 2) + (15 x 1) ) / (2 + 2 + 1)

= (12 + 18 + 15) / 5

= 45 / 5

= 9

Hence, the weight average of the coordinates is 9

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Answer:

the last choice

Step-by-step explanation:

u will minus 3 from each side. that's the point

The distance of the running is 15 miles and the distance of the bicycling is 27 miles.

According to the statement,We have to find that the distance of the run and the bicycle race.

So, For this purpose, we know that the

The distance between two points is that the length of the trail connecting them.

From the given information:

you have entered a 42-mile biathlon that consists of a run and a race. During your run, your average velocity is 5 miles per hour, and through your race, your average velocity is 27 miles per hour. You finish the race in 4 hours.

Then

Total distance of the race = 42 miles

The average velocity of the running = 5 miles per hour

The average velocity of the bicycling = 27 miles per hour

Then

If let he covers 27 miles with the cycles then

The distance he runs = 42-27

The distance he runs = 15.

Then it means he runs for a 3 hours.

So, The distance of the running is 15 miles and the distance of the bicycling is 27 miles.

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Ms. Cody needs 45.05 yards of fabric to make 17 pillow.

For the given question;

Ms. Cody needs 2.65 yards of fabric to make one pillow.

For finding yards for 17 pillows, simply multiply the given yards by 17.

For 17 pillows = 17×2.65

For 17 pillows = 45.05

Thus, 45.05 yards of fabric is required to Ms.Cody to make 17 pillows.

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The equation that is parallel and perpendicular are y + 4  = 7/5(x-35) and y+4 = -5/7(x - 35) respectively.

A line is defined as the shortest distance between two points. The formula for finding the equation of a line in point slope form is:

y - y₁ = m(x-x₁) (Parallel lines)

y - y₁ = -1/m(x-x₁) (Perpendicular lines)

Given the following parameters;

Point = (35, -4)

Given the equation 7x-5y = 0

5y = 7x

y = 7/5x

Slope = 7/5

Substitute the slope and point into the equation

y + 4  = 7/5(x-35) (Parallel lines)

y +4 = -1/(7/5)(x-35) (Perpendicular lines)

y+4 = -5/7(x - 35)(Perpendicular lines)

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Answer:

Brahmagupta in 628

Step-by-step explanation:

Answer:

Zero and its operation are first defined by Brahmagupta in 628. He developed a symbol for zero: a dot underneath numbers.