Which of the following is true about the relationship between the slopes of the lines whose equations are 8x - 9y = 5 and 9x - 8y = 1?

They are equal.
They are reciprocals.
They are opposites.

Answer:

f(g(x)) = x² + 2x +1

Step-by-step explanation:

The given functions are:

f(x) = 4x²

g(x) = x+1

 f(x) = 4x²

(fog)(x) = f(g(x))

f(g(x)) = 4(x+1)²                 [f(x) = x² ]

 we know that (a+b)² = a² + b² + 2ab

f(g(x))  = 4(x²+1²+2(x)(1))

f(g(x))  = 4(x² + 1 + 2x )

f(g(x)) = 4x² + 8x +4

Answer:

Step-by-step explanation:

Use PEMDAS:

P Parentheses first

E Exponents (ie Powers and Square Roots, etc.)

MD Multiplication and Division (left-to-right)

AS Addition and Subtraction (left-to-right)

[tex]\dfrac{1}{2}\times\underbrace{(6\times4)}_{1}+3+2\\\\=\underbrace{\dfrac{1}{2}\times24}_{2}+3+2\\\\=12+3+2=17[/tex]

Answer:

$0.08 (rounded to nearest hundredth, 2 decimals)

Step-by-step explanation:

This is very easy if we setup a unitary method ratio.

" If 12.8 pesos equal 1 dollar, 1 peso is HOW MANY (let it be x) dollars?"

We translate the above sentence in ratio and solve for x:

[tex]\frac{Peso}{Dollar}=\frac{12.8}{1}=\frac{1}{x}\\12.8x=1\\x=\frac{1}{12.8}\\x=0.08[/tex]

Thus, it is worth about $0.08

Answer:

Step-by-step explanation:

The slope-intercept form of an equation of a line:

y = mx + b

m - slope

b - y-intercept (0, b)

We have the slope m = -9 and the y-intercept (0, -2) → b = -2.

Substitute:

y = -9x + (-2) = -9x - 2

The slope-intercept equation of a line with a slope of -9 and a y-intercept of (0, -2) is y = -9x - 2.

The slope-intercept equation of a line is in the form y = mx + b, where m is the slope and b is the y-intercept.

Given a slope of -9 and a y-intercept of (0, -2), the slope-intercept equation is y = -9x - 2.

Therefore, the slope-intercept equation of the line is y = -9x - 2.

Hello there!

X = 67°

Answer and work are provided in the image attached.

For this case we must find an expression equivalent to:

[tex](x ^ {\frac {4} {3}} * x ^ {\frac {2} {3}}) ^ {\frac {1} {3}}[/tex]

By definition of power properties we have to:

[tex](a ^ n) ^ m = a ^ {n * m}[/tex]

So, rewriting the expression we have:

[tex]x ^ {\frac {4} {3 * 3}} * x ^ {\frac {2} {3 * 3}} =[/tex]

[tex]x ^ {\frac {4} {9}} * x ^ {\frac {2} {9}} =[/tex]

By definition of multiplication of powers of the same base, we put the same base and add the exponents:

[tex]x ^ {\frac {4} {9} + \frac {2} {9}} =\\x ^ {\frac {4 + 2} {9}} =\\x ^ {\frac {6} {9}} =\\x ^ {\frac {2} {3}}[/tex]

Answer:

Option B

Answer:

[tex]x^{2/3}[/tex]

Step-by-step explanation:

The question is on rules of rational exponents

Here we apply the formulae for product rule where;

[tex]= a^{n} *a^{t} = a^{n+t} \\\\\\\\=(x^{4/3} *x^{2/3} ) = x^{4/3 + 2/3} = x^{6/3} = x^{2} \\\\\\=(x^2)^{1/3} \\\\\\=\sqrt[3]{x^2}[/tex]

[tex]=x^{2/3}[/tex]

Answer:

g=6

Step-by-step explanation:

[tex]g^{2} -12=-36\\g^{2} -12+36\\ (g-6)(g-6)\\ g-6=0\\ g=6[/tex]

Answer:

In this case, you can use the concept of cosine to calculate y, and things are even easier when you have one of the special angles which is a 45° angle.

So we know that: cos45° = √2/2

This fact will always be true. In our case, we have:

cos45° = 7/y

Therefore, we have the equation:

7/y = √2/2

⇔ 14 = y√2

⇔ y   = 14/√2

⇔ y   = √196/√2 = √(196/2) = √98 = 7√2

So y is equal to 7√2

Answer:

7√2

Step-by-step explanation:

By observation, we can determine that because this is a right angle triangle with one of the internal angles = 45°, that the remaining unknown angle is also 45°, which makes this an isosceles triangle.

This means that x = 7

we can find y by using the Pythagorean equation:

y² = x² + 7²

y² = 7² + 7²

y² = 98

y = √98 = 7√2

Answer:

Part 1) [tex]m=0[/tex]

Part 2) The slope is undefined

Step-by-step explanation:

we know that

The formula to calculate the slope between two points is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

Part 1

we have

[tex]A(-2,-5)\ B(8,-5)[/tex]

Substitute the values

[tex]m=\frac{-5+5}{8+2}[/tex]

[tex]m=\frac{0}{10}[/tex]

[tex]m=0[/tex]  ----> is a horizontal line (parallel to x-axis)

Part 2

we have

[tex]A(4,9)\ B(4,-7)[/tex]

Substitute the values

[tex]m=\frac{-7-9}{4-4}[/tex]

[tex]m=\frac{-16}{0}[/tex]   ----> is a vertical line (parallel to y-axis)

The slope is undefined

Answer:  The correct answer is:  " 5% increase " .

_________________________________________

Step-by-step explanation:

_________________________________________

Note:  The particular "percentage change" is a "percent increase" ; since we are going from "20" to "21" which is an "increased value of "1" .

_________________________________________

Note the formula for "percent increase" ; as follows:

_________________________________________

Percent increase = [(new value - original value)/original value] * 100 ;

_________________________________________

So;  let us "plug in" our known values; to solve for the "percentage change"    

                 →  [i.e. "percent increase" (in this case)] :

_________________________________________

 Percent increase  =  [(21 - 20)/20] * 100 ;

                                =  [1/20] * 100 ;

                                = [100/20] ;

                                = 5.

_________________________________________

The correct answer is:  " 5 % increase" .

_________________________________________

Hope this helps!

  Best wishes to you!

_________________________________________

Answer:

100 Degrees

Step-by-step explanation:

It's correct for Acellus! :-)

Answer:

1/6

Step-by-step explanation:

To find the common ratio, you compare a few pairs of consecutive terms, by dividing an element by its predecessor.

12 / 72 = 1/6

2 / 12 = 1 / 6

1/3 / 2 = 1 / 6

The ratio is constant... so that's your common ratio to go from one term to the next.  

To go from one term to the next, you have to multiply by 1/6.

Answer:

y = x - 6.

Step-by-step explanation:

Do the division:

x + 2 ) x^2 - 4x + 8 (  x - 6 <------- Quotient.

          x^2 + 2x

                    -6x + 8

                    -6x - 12

                     ----------

                              20

The volume of the space outside the pyramid but inside the prism is 250 cubic centimeters.

To find the volume of the space outside the pyramid but inside the prism, we first need to determine the volumes of both the prism and the pyramid.

The prism has a height of 12 centimeters and a square base with sides measuring 5 centimeters. The volume of a rectangular prism is calculated by multiplying the base area by the height. In this case, the base area is 5 cm * 5 cm = 25 square centimeters. Therefore, the volume of the prism is 25 cm² * 12 cm = 300 cubic centimeters.

The pyramid has the same square base as the prism, with sides measuring 5 centimeters. However, its height is half that of the prism, which is 12 cm / 2 = 6 centimeters. The volume of a pyramid is calculated by multiplying the base area by one-third of the height. In this case, the base area is 25 cm², and one-third of the height is 6 cm / 3 = 2 centimeters. Therefore, the volume of the pyramid is 25 cm² * 2 cm = 50 cubic centimeters.

To find the volume of the space outside the pyramid but inside the prism, we subtract the volume of the pyramid from the volume of the prism: 300 cubic centimeters - 50 cubic centimeters = 250 cubic centimeters.

Know more about volume here:

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Answer: 60 and 80

Step-by-step explanation: Start off with the highest number, which is 10. The numbers between 49 and 95 that can be divided by 10 are 50, 60, 70, 80, and 90. Next, figure out what can be divided by 5. All of them can. Next, find out what numbers can be divided by 4. 50, 70, and 90 can’t because they would end up as a decimals. 60 and 80 can be divided by 4, 5, and 10.

Answer:

Step-by-step explanation:

sqrt(28): sqrt(4*7)

sqrt(4) = 2;

sqrt28)=2*sqrt(7)

sqrt(343): sqrt(7 * 7 * 7) = 7 * sqrt(7)

Note: the rule is if you have 3 equal primes under the root sign, you leave one, you throw one away, and you put one outside the root sign.

2 sqrt(63) = 2 sqrt(3*3*7)  The above rule gets modified to throw 1 three away and take the other one outside the root sign.

2sqrt(63) = 2*3 sqrt(7)

Numerator: 2*sqrt(7) + 7sqrt(7) = 9sqrt(7)

9sqrt(7)

======

6 sqrt(7)

3/2

Note without brackets I cannot be certain that I have interpreted this correctly. The division only apply to sqrt(343) / 2 sqrt(63). If this is so please leave a note.

Answer:

The answer is the second figure and the vertices of Δ R'S'T' are:

R' = (-6 , 6) , S' = (-3 , -6) , T' = (0 , 3)

Step-by-step explanation:

* Lets revise some transformation

- If point (x , y) reflected across the x-axis

 ∴ Its image is (x , -y)

- If point (x , y) reflected across the y-axis

 ∴ Its image is (-x , y)

- If point (x , y) reflected across the line y = x

 ∴ Its image is (y , x)

- If point (x , y) reflected across the line y = -x

 ∴ Its image is (-y , -x)

- Now we can solve the problem

∵ R = (6 , 6) , S = (3 , -6) , T = (0 , 3), they are the vertices of ΔRST

- The triangle RST is reflected over the y-axis

- According to the rule above the signs of x-coordinates will change

∵ R = (6 , 6)

∴ Its image is (-6 , 6)

∵ S = (3 , -6)

∴ Its image is (-3 , -6)

∵ T = (0 , 3)

∴ Its image is (0 , 3)

* Now lets look to the figure to find the correct answers

- The image of Δ RST is ΔR'S'T'

∵ The vertices of the image of ΔRST are:

  R' = (-6 , 6) , S' = (-3 , -6) , T' = (0 , 3)

* The answer is the second figure

Answer:

54°

Step-by-step explanation:

Since the triangle is right use the cosine ratio to solve for angle

cos? = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{26}{44}[/tex], hence

? = [tex]cos^{-1}[/tex] ( [tex]\frac{26}{44}[/tex] ) ≈ 54° ( nearest degree )

Answer: alternate exterior angles

Step-by-step explanation:

Evaluate 2(x + 1) - 3 when x = 6.

First, plug in x value.

2(6 + 1) -3   ParenthesisEMDAS

2(7) - 3       PEMultiplyDAS

14 - 3          PEMDASubtract

11 ←

Answer:

11

Step-by-step explanation:

just took test

Answer:

6

Step-by-step explanation:

Plug in 3 into both expressions

Then add those results

2(3)+21=6+21=27

3-24             =-21

                    -------

                         6  is the sum of 27 and -21

Answer:

10r(d - 6).

Step-by-step explanation:

The GCF is 10r.

So the answer is:

10r(d - 6).

Answer:

13.9 containers or 14 rounded

Step-by-step explanation:

2/7 of a pound is 0.28571429 in decimal form. To solve you have to know how many 2/7 of a pound will go into 4 pounds. So you divide 2/7 of a pound by 4 pounds, and the answer is 14.

Answer:

14

Step-by-step explanation:

He will need 14 containers. 4 times 7/2 is 28/2. You then have to simplify it and will get 14.

Answer:

[tex](x+3)^{2}+(y+5)^{2}=36[/tex]

Step-by-step explanation:

we know that

The equation of a circle in standard form is equal to

[tex](x-h)^{2}+(y-k)^{2}=r^{2}[/tex]

In this problem we have

[tex](h,k)=(-3,-5)[/tex]

[tex]r= 6\ units[/tex]

substitute

[tex](x+3)^{2}+(y+5)^{2}=6^{2}[/tex]

[tex](x+3)^{2}+(y+5)^{2}=36[/tex]

Answer:

V≈4.19ft³

Step-by-step explanation:

The volume of a sphere with a radius of 1 foot is 4.19ft³.

In order to find this:

V=4

3πr3=4

3·π·13≈4.18879ft³

[tex]V=\dfrac{4}{3}\pi r^3\\\\V=\dfrac{4}{3}\cdot3.14\cdot 1^3\approx4.19\text { ft}^3[/tex]

Answer:

2.4

Step-by-step explanation:

tanB = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{AC}{BC}[/tex] = [tex]\frac{12}{5}[/tex] = 2.4

Answer:  2.4

Step-by-step explanation:

[tex]tan\theta=\dfrac{opposite}{adjacent}\\\\\\tan\angle B=\dfrac{12}{5}\\\\\\tan\angle B=2.4[/tex]

Answer:

B

Step-by-step explanation:

Area of a triangle is given by the formula:

[tex]A=\frac{1}{2}bh[/tex]

Now, we need to solve for b. We multiply the right side, cross multiply, and follow rules of algebra to isolate b. Shown below:

[tex]A=\frac{1}{2}bh\\A=\frac{bh}{2}\\2A=bh\\b=\frac{2A}{h}[/tex]

Thus, b is 2 times A over h, the answer choice B is right.

Answer:

The Answer is B. b equals two times A over h

Hope This Helps!

Step-by-step explanation:

a = x^2 - 1

b = 2x

c = x^2 + 1

The Pythagorean theorem states

a^2 + b^2 = c^2

Let's find a^2 and b^2 and add them to get a^2 + b^2:

a^2 = (x^2 - 1)^2 = x^4 - 2x^2 + 1

b^2 = (2x)^2 = 4x^2

a^2 + b^2 = x^4 - 2x^2 + 1 + 4x^2 = x^4 + 2x^2 + 1

Now let's find c^2:

c = x^2 + 1

c^2 = (x^2 + 1)^2 = x^4 + 2x^2 + 1

We see that both a^2 + b^2 and c^2 equal x^4 + 2x^2 + 1, so we have shown that the triangle is a right triangle.

We can see that a² + b² = c² = x⁴ + 2x² + 1, indicating that the triangle is a right triangle.

It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometric function.

According to Pythagoras, the sum of the squares of two sides equals the square of the longest side.

Given data;

a = x² - 1

b = 2x

c = x² + 1

According to the Pythagorean theorem;

[tex]\rm a^2 + b^2 = c^2[/tex]

Let's find a^2 and b^2 and add them to get a^2 + b^2:

[tex]\rm a^2 = (x^2 - 1)^2 \\\\ a^2 = x^4 - 2x^2 + 1 \\\\ b^2 = (2x)^2 \\\\ b^2 = 4x^2\\\\[/tex]

Left hand side:

[tex]\rm a^2 + b^2 = x^4 - 2x^2 + 1 + 4x^2 \\\\ a^2 + b^2 =x^4 + 2x^2 + 1[/tex]

Right hand side:

[tex]\rm c^2 = (x^2 + 1)^2 \\\\ c^2 = x^4 + 2x^2 + 1[/tex]

L.HS.=R.H.S

Hence,the given triangle is a right angled triangle.

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Answer:

slope is -5

y-intercept is -5

Step-by-step explanation:

Solve for y to write in y=mx+b

m is slope

b is y-intercept

5x+y=-5

Subtract 5x on both sides

    y=-5x-5

slope is -5

y-intercept is -5

Answer:

[tex]x^3+1[/tex]

Step-by-step explanation:

[tex] 26(x^3+1)^2-22(x^3+1)-3=0 [/tex]

Comparing to

[tex] A(u)^2+B(u)+C =0 [/tex]

Where A,B,C are constants

You should see that we need to substitute the [tex]x^3+1[/tex] with u.