Write an equation that represents each diagram and find the value of x.

Answer:

Step-by-step explanation:

[tex]\begin{cases}9x-9y=-9&\left(1 \right) \\ 3x+9y=-15&\left( 2\right) \end{cases}[/tex]

[tex]\Longleftrightarrow \begin{cases}9x-9y=-9&\left( 1\right) \\ 12x=-24&\left( 1\right) +(2)\end{cases}[/tex]

[tex]\Longleftrightarrow \begin{cases}x-y=-1&\left( 1\right) \\ x=-2&\left( 1\right) +(2)\end{cases}[/tex]

[tex]\Longleftrightarrow \begin{cases}y=x+1=-2+1=-1&\left( 1\right) \\ x=-2&\left( 1\right) +(2)\end{cases}[/tex]

Answer:

The amount y is depends on what x's value is. It is helpful to make a table or graph so we can see how the y value changes like the x value :)

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If you want the type of relationship between 'x' and 'y'

  ⇒ they are a linear relationship as in they form a straight line together

If you want to describe how the value of x correlates to y

 ⇒ as x increases, y increases thus it is a direct variation.

Hope that helps!

Answer:

a. All of the whole - 10/10

b. A tenthof the whole - 1/10

Step-by-step explanation:

Step-by-step explanation:

a. since the entire whole represents a 100% , the number of whole that makes up for 100% is the 10 of the ten parts divided by 10 which is equal to 10.

b. since a whole equals 100% , if divided by 10 the entire 100% becomes 10% each for 10 parts. hence a single part equivalent to 1/10 is 10%

Answer:

X intercepts: (0,12)

Y intercepts: (-32,88)

Answer:

=> 7√3

Step-by-step explanation:

Given :

∠ Q = 30°

RS/QR = tan 30°

7/QR = 1/√3

QR = 7√3

Answer: 97 degrees

Step-by-step explanation:

Answer:

After adding the numbers the result obtained is called the sum.

Answer:

y=-4/3x-4

Step-by-step explanation:

The equation of the line that is perpendicular to the line which has a slope of 3 / 4 and passes through the point ( 0, - 4 ) is equals to [tex]y= \frac{-4}{3} x-4[/tex]

" Equation of line is defined as the equation which represents the set of points using slope."

Formula used

[tex]y=mx+c[/tex]

m = slope of the line

c = y-intercept

Product of the Slopes of perpendicular lines  = -1

According to the question,

Slope of the given line = [tex]\frac{3}{4}[/tex]

Using condition for slope of perpendicular lines we have,

Slope of the line perpendicular to the given line 'm' = [tex]\frac{-4}{3}[/tex]

From given point (0, -4)

Y- intercept 'c' = -4

Substitute the value in the formula to get equation of required line,

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

Hence,  equation of the line that is perpendicular to the line which has a slope of 3 / 4 and passes through the point ( 0, - 4 ) is equals to [tex]y= \frac{-4}{3} x-4[/tex].

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[tex]~~~~~~\cos B = \dfrac{\text{Base}}{\text{hypotenuse}}\\\\\\\implies \cos B = \dfrac{BC}{AB}\\\\\\\implies \cos B = \dfrac{12}{13}[/tex]

Answer:

85 ft^2

Step-by-step explanation:

Base = 5 x 5 = 25 ft^2

FOUR triangles   4  *   1/2 * b * h  = 4 * 1/2 * 5 * 6 = 60 ft^2

added together = 85 ft^2

Answer:

490 miles

Step-by-step explanation:

7/1.4 = 5

98*5 = 490

Answer:

792 cm²

Step-by-step explanation:

Surface Area (Cylinder)

⇒ 2πrh + 2πr²

⇒ 2πr (h + r)

Here, r = 9 cm and h = 5 cm.

⇒ 2π × 9 (5 + 9)

⇒ 18π × 14

⇒ 252 x 22/7

⇒ 36 x 22

⇒ 792 cm²

Answer:

-24/16, -√2, 21/51, 0.42

Step-by-step explanation:

Look at the signs of the numbers. Negative numbers will be on the left, while positive numbers will be on the right. That means -√2 and -24/16 will be on the left, while 0.42 and 21/51 will be on the right.

Part 1:

We can change the negative numbers to decimals to compare them.

-√2 ≈ -1.41

-24/16 = -1.5

-1.5 is smaller, which means the first number in the sequence will be -24/16 and then -√2.

Part 2:

We can also change the positive numbers to decimals to compare them.

0.42 = 0.42

21/51 ≈ 0.41

21/51 is a bit smaller, so the third number in the sequence will be 21/51 and then 0.42.

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Answer:

simultaneous equations are used to solve for 2 variable

First, find the mode, median, and mean of the given set of numbers.

Mode

The mode is the number that shows up frequently within the given set. In this case, it will be 10, as it shows up 4 times, 3 times more than any other number.

Mode: 10

~

Median

The median is the number that is in the middle of the given set. In this case, there are 9 numbers, and so the 5th given number is your median:

10 , 10 , 10 , 10 , 11 , 12 , 13 , 15 , 17

Median: 11

~

Mean

The mean is combining all numbers within the given set and dividing by the amount of numbers in that said set:

(10 + 10 + 10 + 10 + 11 + 12 + 13 + 15 + 17)/9 = 108/9 = 12

Mean: 12

Answer:

$8.95

Step-by-step explanation:

If Ari spent $35.80 for 4 posters and each of the poster price was the same therefore if we want the price for one poster we have to divide $35.80 by four to see the cost for one poster which will be $8.95. If you want to know if the price of each poster was the same you can just multiply $8.95 by 4 and you'll actually see that you got back the same money that Ari used to spend for the four posters .

The probability that at least one of the sides of the triangle is also a side of the octagon is 5/7

A regular octagon has 8 sides, and a triangle has 3 sides

Assume that there is a point on the triangle.

Then we select (3 - 1) points from the (8 - 1) sides.

8 - 1 = 7

3 - 1 = 2

So, the total number of selection is:

Selection = 7C2

Evaluate the combination expression

Selection = 21

Adjacent triangles have 5 lines (one line in common).

So, we have:'

n = 5 - 1

n = 4

The number of ways this points can be selected is:

Selection = 4C2

Evaluate

Selection = 6

The probability that the triangle and the octagon do noth have the same side is:

P= 6/21

The probability that at least one of the sides of the triangle is also a side of the octagon is calculated using the following complement rule

P = 1 - 6/21

Evaluate the difference

P = (21 -6)/21

P = 15/21

Reduce fraction

P = 5/7

Hence, the probability that at least one of the sides of the triangle is also a side of the octagon is 5/7

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Answer:

[tex]\frac{x}{2} *\sqrt{x^{2} +4}[/tex] +[tex]\frac{1}{2}[/tex]*LN(|[tex]\frac{x+\sqrt{x^{2} +4} }{2}[/tex]|) +C

Step-by-step explanation:

we will have to do a trig sub for this

use x=a*tanθ for sqrt(x^2 +a^2) where a=2

x=2tanθ, dx= 2 sec^2 (θ) dθ

this turns [tex]\int\limits {\sqrt{x^{2}+4 } } \, dx[/tex] into integral(sqrt( [2tanθ]^2 +4) * 2sec^2 (θ) )dθ

the sqrt( [2tanθ]^2 +4) will condense into 2sec^2 (θ) after converting tan^2(θ) into sec^2(θ) -1

then it simplifies into integral(4*sec^3 (θ)) dθ

you will need to do integration by parts to work out the integral of sec^3(θ) but it will turn into (1/2)sec(θ)tan(θ) + (1/2) LN(|sec(θ)+tan(θ)|) +C

then you will need to rework your functions of θ back into functions of x

tanθ will resolve back into [tex]\frac{x}{2}[/tex] (see substitutions) while secθ will resolve into [tex]\frac{\sqrt{x^{2} +4} }{2}[/tex]

sec(θ)=[tex]\frac{\sqrt{x^{2} +4} }{2}[/tex]  is from its ratio identity of hyp/adj where the hyp. is [tex]\sqrt{x^{2} +4}[/tex]  and adj is 2 (see tan(θ) ratio)

after resolving back into functions of x, substitute ratios for trig functions:

= [tex]\frac{x}{2} *\sqrt{x^{2} +4}[/tex] + [tex]\frac{1}{2}[/tex]*LN(|[tex]\frac{x+\sqrt{x^{2} +4} }{2}[/tex]|) +C

Answer:

See below ~

Step-by-step explanation:

The given polynomial : -2x + 1 + 2x² needs to be written in the form :

On rewriting in this asked format,

Step-by-step explanation:

thats the answer i think

Answer:

C.

Step-by-step explanation:

when you put it in a graphing calculator it would show the standard graph of an exponential decay function.

Answer: B

Step-by-step explanation:

Answer:

1/4

Step-by-step explanation:

There are 8 sections and skating is on 2 of the 8;  the probability is 2/8 = 1/4. It does not matter how many times it has appeared on previous spins.

Answer:

Step-by-step explanation:

Could you show two points need to be calculated? A and D are the same in this case

Using it's concept, it is found that there is a 0.004 = 0.4% probability of a game console buyer buying a defective Suny Playcom.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem, 40% of the consoles bought are of the Suny Playcom series, and of those, 1% are defective, hence the probability is given by:

p = 0.4 x 0.01 = 0.004

0.004 = 0.4% probability of a game console buyer buying a defective Suny Playcom.

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Answer:

x > 2

Graph in picture

Step-by-step explanation:

Given:

7x + 10 < 11x + 2

To Find:

Solve and graph on a number line. Show your work in the box below.

Solve:

Subtract 10 from both sides

7x + 10 -10 < 11x + 2-10

Simplify

-4x < - 8

Multiply both sides by -1 which reverse the inequality

Simplify

4x > 8

Now, Divide both sides by 4

4x ÷ 4 > 8 ÷ 4

Simplify

x > 2

Solution: x > 2

Now graphing:

> means greater than

that means x is greater than 2

Thus, the line is going to the right.

Graph below:

Answer: x > 2

Step-by-step explanation:

7x+ 10 < 11x + 2

7x+10-10 < 11x + 2 -10

subtract the numbers

7x < 11x -8

7x < 11x -8

7x - 11x < 11x -8 - 11x

-4x < -8

-4x < -8

-4x/-4 > -8/-4

x > 2

Answer:

D. [tex]\frac{12x+20}{5y^3}[/tex]

Step-by-step explanation:

When multiplying 2 fractions, you multiply the numerators and denominators, so we have:

[tex](\frac{3x+5}{y^6})(\frac{4y^3}{5}) = \frac{(3x+5)\cdot 4y^3}{y^6\cdot 5} = \frac{(3x+5)\cdot 4}{y^3 \cdot 5} = \frac{12x + 20}{5y^3}[/tex]

Answer:

4th option

Step-by-step explanation:

[tex]\frac{3x+5}{y^6}[/tex] × [tex]\frac{4y^3}{5}[/tex] ( cancel y³ and [tex]y^{6}[/tex] on numerator/denominator by y³ )

= [tex]\frac{3x+5}{y^3}[/tex] × [tex]\frac{4}{5}[/tex]

= [tex]\frac{4(3x + 5)}{5y^3}[/tex]

= [tex]\frac{12x+20}{5y^3}[/tex]

Answer:

See below ~

Step-by-step explanation:

Using PEMDAS

Our equation

1. Simplifying Parentheses

2. Simplifying Exponents

3. Multiplying

4. Adding (As division without simplifying isn't correct)

5. Subtracting

6. Dividing

Deducing from the considered box plot, the number of crates that weigh more than 99.5 pounds is 330 approx.

A box plot has 5 data description.

When we get data which can be compared relatively with each other, for finding quartiles, we arrange them in ascending or descending order.

Quartiles are then selected as 3 points such that they create four groups in the data, each groups approximately possessing 25% of the data.

Left to right is said in assumption that data was arranged increasingly from left to right

We're specified here that:

Total 440 crates is being shipped by company.

The box plot is defined by the points 84, 99.5, 113, 143, 170

The point 99.5 is the first quartile.

There are 75% observations on its right, so 75% of 440 is the number of crates which weigh greater than 99.5 pounds.

We get this value as:

[tex]\dfrac{440}{100} \times 75=330[/tex]

Thus, deducing from the considered box plot, the number of crates that weigh more than 99.5 pounds is 330 approx.

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