write the equation of the lines that passes through the points (-3, -2) and (0, -3)

Answer:

-1

Step-by-step explanation:

The product of the slopes of perpendicular lines is always   -1    .

Answer:

The new function is (x + 7)² - 47 ⇒ the 3rd answer

Step-by-step explanation:

* Lets put the function f(x) in the vertex form at first and then make

 the translation

∵ The general form of the quadratic function is

  f(x) = ax² + bx + c

∵ The x-coordinate of the vertex of the function is -b/2a

∵ The y-coordinate of the vertex of the function is f(-b/2a)

- Lets find a , b from the function two find the vertex point

∵ f(x) = x² + 22x + 58

∴ a = 1 , b = 22 , c = 58

∵ x-coordinate of the vertex = -b/2a

∴ x-coordinate of the vertex = -22/2(1) = -11

∵ y-coordinate of the vertex = f(-11)

∴ f(-11) = (-11)² + 22(-11) + 58 = 121 - 242 + 58 = -63

∴ The vertex point is (-11 , -63)

- The vertex form of the quadratic function is f(x) = (x - h)² + k , where

  (h , k) are the coordinates of the vertex point

∵ The vertex point is (-11 , -63)

∴ h = -11 , k = -63

∴ f(x) = (x - -11)² + -63

∴ f(x) = (x + 11)² - 63

* lets revise the rules of the translation

- If the function f(x) translated horizontally to the right  

 by m units, then the new function g(x) = f(x - m)

- If the function f(x) translated horizontally to the left  

 by m units, then the new function g(x) = f(x + m)

- If the function f(x) translated vertically up  

 by n units, then the new function g(x) = f(x) + n

- If the function f(x) translated vertically down  

 by n units, then the new function g(x) = f(x) – n

∵ f(x) will translate 4 units to the right

∴ m = 4

∵ f(x) ⇒ f(x - m)

∴ (x + 11)²  ⇒ (x + 11 - 4)² = (x + 7)²

∵f(x) will translate 16 units up

∴ -63 will add by 16

∴ n = 16

∴ f(x) ⇒ f(x) + n

∵ -63 + 16 = -47

∴ The new function is (x + 7)² - 47

Answer:

(x + 7)^2 - 47

Step-by-step explanation:

just answered this on my class

The numbers are 10 and 3.

Step-by-step explanation:

STEP 1: Based on the problem, two equations can be set up:

First, "one number is seven less than another." This can be expressed mathematically:

Let x = first number

      y = second number

[tex]x \ - 7 = \ y[/tex]

The second equation is based on "their sum is thirteen."

[tex]x \ + \ y \ = 13[/tex]

STEP 2: Solve for the variables.

In this step, substitute the value of y from Equation 1 into Equation 2:

[tex]x \ + \ (x \ - \ 7) \ = \ 13\\2x \ - \ 7 \ = 13\\[/tex]

Next, solve for x by manipulating the equation:

[tex]2x \ = \ 13 \ + \ 7\\2x \ = \ 20\\\boxed {x \ = \ 10}[/tex]

Now that the value of x is known, it can be used to determine the value of y.

To do this, use the calculated value for x and plug it into Equation 1:

[tex]y \ = \ x \ - 7\\y \ = 10 \ - 7\\\boxed {y = \ 3}[/tex]

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Keywords: two equations, two variables

To find the two numbers where one is seven less than the other and their sum is thirteen, a system of equations is set up and solved, revealing that the only possible combination is 10 (larger number) and 3 (smaller number).

To solve the problem where one number is seven less than another and their sum is thirteen, let's set up some equations.

Let x be the larger number and y be the smaller number. We can express the two conditions in the following way:

y = x - 7  (the smaller number is seven less than the larger number)

x + y = 13 (their sum is thirteen)

Substituting the first equation into the second gives us:

x + (x - 7) = 13

Simplifying, we get:

2x - 7 = 13

Adding 7 to both sides, we have:

2x = 20

Dividing both sides by 2, we find:

x = 10

Now we substitute x back into the first equation to find y:

y = 10 - 7

y = 3

So the larger number is 10 and the smaller number is 3. There is only one possible combination of numbers that fit the given conditions.

Answer:

The answer on edge is C: 0.39 seconds.

Step-by-step explanation:

At t = 0.39 seconds the object is 4 inches below the rest position option third is correct.

It is defined as the function which is sinusoidal in nature, and it has a domain of all real numbers and lies between the [a, a]where is a amplitude of the function.

We have:

The motion of a weight that hangs from a spring is represented by the equation:

h = -5sin[(3π/4)t]

Plug h = -4

-4 = -5sin[(3π/4)t]

Or

-4 = -5sin[135t]

135t = 53.13

t = 0.39 seconds

Thus, at t = 0.39 seconds the object is 4 inches below the rest position option third is correct.

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Answer: 0.2

Explainations: 1/5 = 0.2

Answer:

Number would be [tex]\frac{x^{2}}{5}[/tex].

Step-by-step explanation:

Given  : One fifth of the square of a number.

To find : Expression .

Solution ; We have given One fifth of the square of a number.

According to question :

Let the number = x .

Square of the number = x².

One fifth of the square of the number = [tex]\frac{x^{2}}{5}[/tex].

Therefore, Number would be [tex]\frac{x^{2}}{5}[/tex].

Answer:

54

Step-by-step explanation:

2x^0y^-2

Let x =2 and y =3

2 * (2)^0 3^(3)

2 to the zero power is 1

2 * 1 *27

54

Answer:The answer is 1/9!

Step-by-step explanation:

Have a good day!

Answer:

C. Rhombus or Kite

Step-by-step explanation:

1/2 d1d2 is the formula for a rhombus or kite.

Answer:

Rhombus or Kite

Step-by-step explanation:

learning about it rn

Divide the number of cans by the number of sheets to find the constant.

36 cans / 2 sheets = 18 cans per sheet.

180 cans / 10 sheets = 18 cans per sheet.

The proportionality constant is 18 cans per sheet.

Answer:

Function.

Step-by-step explanation:

A relation is a function every x that in your domain only gets assigned to exactly one number in your range.

Basically if you have a set of points and you see that the same x is being used more than once, then it isn't a function (unless for some reason they repeated the same point).

So the x's I see in the order that your points are is 3,1,-1,-2.  All of these x's are different so it is a function.

Answer: Yes, it is a function.

Step-by-step explanation:

Usually we denote the input value as 'x' and the output value as 'y'.

The given relation: {(3, −5), (1, 2), (−1, −4), (−2, 2)}

Here , each input value corresponds an unique output value.

Therefore , the given relation is a function.

The answer is A.

Because both angles of triangles are equal to 42° that means the distance of UV is equal to the distance of XY.

Hope this helps.

r3t40

Answer:

nope its actaually 46 degrees

Step-by-step explanation:

Answer:

Part 1) The area of the base of the rectangular prism is [tex]18\ cm^{2}[/tex]

Part 2) The height of the rectangular prism is equal to [tex]6\ cm[/tex]

Part 3) The volume of the rectangular prism is [tex]108\ cm^{3}[/tex]

Step-by-step explanation:

Part 1) What is the area of the base of the rectangular prism?

we know that

The base of the rectangular prism is the rectangle ABCD

so

AD=BC and AB=DC

The area B of the rectangle is equal to

[tex]B=AD*DC[/tex]

substitute

[tex]B=(9)(2)=18\ cm^{2}[/tex]

Part 2) What is the height of the rectangular prism?

The height of the rectangular prism is equal to the segment line AW (segment perpendicular to the base)

we have that

[tex]H=AW=BX=DY=CZ=6\ cm[/tex]

Part 3) What is the volume of the rectangular prism?

we know that

The volume of the rectangular prism is equal to

[tex]V=BH[/tex]

where

B is the area of the base of the prism

H is the height of the prism

we have

[tex]B=18\ cm^{2}[/tex]

[tex]H=6\ cm[/tex]

substitute

[tex]V=(18)(6)=108\ cm^{3}[/tex]

The area of the base of the rectangular prism is 18 cm² and its volume is 108 cm³.

Prism is a three dimensional shape with two identical shapes called bases facing each other.

From the diagram:

Area of base = length * width = 9 cm * 2 cm = 18 cm²

Volume = height * length * width = 6 * 9 * 2 = 108 cm³

The area of the base of the rectangular prism is 18 cm² and its volume is 108 cm³.

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Answer:

Step-by-step explanation:

It's the definition of an altitude.

Answer: Altitude

Step-by-step explanation:

Answer:

r = 5.35

Step-by-step explanation:

The radius of a circle with an area of 90 inches is 5.35.

Use the formula: A=πr2

r=A

π=90

π≈5.35237

Answer:

x = 8

Step-by-step explanation:

We can see that this is using power of a point or PoP! So we immediately know that 5x = 4*10.

So solving for x (by dividing by 5 on both sides) we get:

x = 8

Answer : The value of 'x' is, 8

Step-by-step explanation :

According to the theorem, if two chords intersect inside a circle then the product of the lengths of the one chord equals to the length of another chord.

That means in the given figure,

AO × OB = CO × OD

Given:

Length AO = 10

Length OB = 4

Length CO = x

Length OD = 5

Now put all the given values in the above expression, we get:

AO × OB = CO × OD

10 × 4 = x × 5

40 = x × 5

x = 8

Therefore, the value of 'x' is, 8

Answer:

[tex]\sin(\frac{\pi}{7}+x)[/tex]

Step-by-step explanation:

We are going to use the identity

[tex]\sin(a+b)=\sin(a)\cos(b)+\cos(a)\sin(b)[/tex]

because this identities right hand side matches your expression where

[tex]a=\frac{\pi}{7}[/tex] and [tex]b=x[/tex].

So we have that [tex]\sin(\frac{\pi}{7})\cos(x)+\cos(\frac{\pi}{7})\sin(x)[/tex] is equal to [tex]\sin(\frac{\pi}{7}+x)[/tex].

The given expression is written as sin(π/7 + x). Using sine of compound angle identity it is obtained.

A compound angle is the sum of two or more angles. Consider A and B are two angles. Where their compound angle becomes A + B. So, the sine and cosine of this compound angle are

1) sin (A + B) = sin A cos B + cos A sin B

2) sin (A - B) = sin A cos B - cos A sin B

3) cos (A + B) = cos A cos B - sin A sin B

4) cos (A - B) = cos A cos B + sin A sin B

The given expression is sin(π/7) cos(x) + cos(π/7) sin(x)

This is in the form of sin A cos B + cos A sin B

where A = π/7 and B = x

So, using the above identity we can write,

sin(π/7) cos(x) + cos(π/7) sin(x) = sin(π/7 + x)

Thus, the given expression is expressed in the angle of sine. I.e., sin(π/7 + x).

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Answer:

163

Step-by-step explanation:

0 judges - [tex]C^8_0=1[/tex] way to vote

1 judge - [tex]C^8_1=8[/tex] ways to vote

2 judges-

[tex]C^8_2=\dfrac{8!}{2!(8-2)!}=\dfrac{6!\cdot 7\cdot 8}{2\cdot 6!}=\dfrac{56}{2}=28[/tex]

ways to vote for 2 different judges

3 judges-

[tex]C^8_3=\dfrac{8!}{3!(8-3)!}=\dfrac{5!\cdot 6\cdot 7\cdot 8}{2\cdot 3\cdot 5!}=\dfrac{6\cdot 56}{6}=56[/tex]

ways to vote for 3 different judges

4 judges-

[tex]C^8_4=\dfrac{8!}{4!(8-4)!}=\dfrac{4!\cdot 5\cdot 6\cdot 7\cdot 8}{4!\cdot 4!}=\dfrac{5\cdot 6\cdot 7\cdot 8}{2\cdot 3\cdot 4}=5\cdot 7\cdot 2=70[/tex]

ways to vote for 4 different judges

In total, there are

[tex]1+8+28+56+70=163[/tex]

different ways to vote.

Since m = 4.5 and b = 21 the desired formula is:

T=4.5x+21

Answer:

1 / x^8

Step-by-step explanation:

We know that a^b / a^c = a^ (b-c)

x^7 / x^ 15 = x^ (7-15) = x^-8

We also that that a^-b = 1/ a^b

x^-8 = 1 / x^8

Answer:

1/(x^8)

Step-by-step explanation:

Simplify by the following steps. To make it easier, I will expand them:

First, expand each of the powers out:

[tex]\frac{x^7}{x^{15} } = \frac{x* x * x * x * x * x * x}{x * x * x * x * x * x * x * x * x * x * x * x * x * x * x}[/tex]

When dividing with the same variables with different powers, you are effectively subtracting the powers. Your answer will look like:

[tex]\frac{x^7}{x^(15)} = x^{7 - 15} = x^{-8}[/tex]

Next, simplify. Note that if there is a negative sign in the power, you must change the sign into a positive by flipping the fraction.

[tex]x^{-8} = \frac{1}{x^{8} }[/tex]

1/(x^8) is your answer.

~

Answer:

(-2,6)

Step-by-step explanation:

If b is (6,4) and we have b' is the image that follows from the translation

(x-8,y+2).

Basically the image of (x,y) is (x-8,y+2).

So the image of (6,4) is (6-8,4+2).

Simplify:

(6-8,4+2)

(-2,6).

b' is (-2,6).

Answer:

[tex]Z=2.99999999999995[/tex]

Step-by-step explanation:

We can write the proportionality equation as:

[tex]Z=k\frac{X}{Y}[/tex]

Note: Directly proportional goes top and top, multiplied. And inversely proportional goes top bottom, divided. Also, k is the proportionality constant.

When X is 3, Y is 19, Z is 0.94736842105263. Plugging these, we figure out k:

[tex]Z=\frac{kX}{Y}\\0.94736842105263=\frac{k(3)}{19}\\k=\frac{0.94736842105263*19}{3}\\k=5.99999999999999[/tex]

Now we put X = 13 and Y = 26 and k = 5.99999999999999, to find Z:

[tex]Z=\frac{kX}{Y}\\Z=\frac{(5.99999999999999)(13)}{26}\\Z=2.99999999999995[/tex]

Answer:

27/35

Step-by-step explanation:

(f/g)(5) means f(5)/g(5).

So we will need to find both f(5) and g(5).

f(5) means replace x with 5 in f. This gives us 7+4×5.

Let's simplify 7+4×5:

7+4×5

7+20

27.

g(5) means replace x with 5 in g. This gives us 7×5.

Simplifying 7×5 gives us 35.

(f/g)(5)=f(5)/g(5)=27/35.

Answer:

3^x -2x +14

Step-by-step explanation:

I will assume you mean 3^x in the function f(x)

f(x) = 3^x+ 10

g(x) = 2x - 4

(f - g)(x) =  3^x+ 10  - (2x - 4)

       Distribute the minus sign

              =  3^x+ 10  - 2x + 4

              = 3^x -2x +14

Hi !

Answer:

Begin with a line segment on the paper and fold the paper so that the segment's endpoints lie on top of each other.

The method used in paper folding to form the midpoint of a line segment is called bisecting a line segment. This involves drawing the line segment, folding the paper so the endpoints of the line segment meet, and marking the point of intersection which forms the midpoint.

The method that can be used in paper folding to form the midpoint of a line segment is called bisecting a line segment. Here's how you can do it:

That point of intersection is the midpoint of the line segment. You've now bisected the line segment into two equal halves using paper folding.

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Answer:

[tex]\angle 12 \cong \angle 8\\\angle 4 \cong \angle 8[/tex]

Step-by-step explanation:

When two parallels lines are crossed by a transversal, certain pair of angles are called corresponding angles, specifically, those that are placed in the same side of the transversal, on inside the parallels and the other outside the parallels. The image attached shows an example of corresponding angles.

So, we observe in the given image that all corresponding angles with angle 8 are

[tex]\angle 12\\\angle 4[/tex]

These angles are form corresponding angle with [tex]\angle 8[/tex], that means they are congruent, that is

[tex]\angle 12 \cong \angle 8\\\angle 4 \cong \angle 8[/tex]

Answer: 3(2)^2 + 4(3)^2

Step-by-step explanation:

First do what is replacing the variables by changing X to 2 and Y to -3

3(2)^2 + 4(-3)^2 = 3(4) + 4(9) = 12 + 36 = 48

Answer: The value is 48

Step-by-step explanation:

Given the following expression:

[tex]3x^2+4y^2[/tex]

You need to substitute the values of each variables provided in the exercise into this expression. You can observe that the value of the variable "x" and  the value of the variable "y" are:

[tex]x=2 \\ y=-3[/tex]

Therefore, substituting values, you get:

[tex]3x^2+4y^2=3(2)^2+4(-3)^2=3(4)+4(9)=12+36=48[/tex]

Answer:

6x^2+2x-6

Step-by-step explanation:

In the expression (2x)(x2)+(2x)(x)+(2x)(-2)+(3)(x2)+(3)(-2) take each set of two and solve those individually. The expression then becomes 4x^2+2x^2-4x+6x-6 the combining like terms you get 6x^2+2x-6.

[tex]\bf 9x^2-49\implies 3^2x^2-7^2\implies \stackrel{\stackrel{\textit{difference of}}{\textit{squares}}}{(3x)^2-7^2}\implies (3x-7)(3x+7)[/tex]

Answer:

16

Step-by-step explanation:

If you have a 12-inch board and you are making 3/4 inch long sections, and you want to know many times you can do that here.

You just need to take 12 and divide it by the 3/4, to see how many sections you can have.

[tex]12 \div \frac{3}{4}[/tex]

Change division to multiplication by taking the reciprocal (the flipping) of the second number:

[tex]12 \cdot \frac{4}{3}[/tex]

Write 12 as a fraction:

[tex]\frac{12}{1}\cdot \frac{4}{3}[/tex]

To multiply fractions, multiply straight across on top and straight across on bottom:

[tex]\frac{(12)(4)}{(1)(3)}[/tex]

[tex]\frac{48}{3}[/tex]

16

Final answer:

By dividing the 12-inch board length by the section length of 3/4 inches, we find that 16 sections can be made.

Explanation:

The question asks how many sections of 3/4 inches can be made from a 12-inch board. To find this, divide the total length of the board by the length of each section. Calculate by dividing 12 inches by 3/4 inches (which is the same as 12 divided by 0.75 in decimal form).

Therefore, you can cut 16 sections that are 3/4 inches long each from a 12-inch board.

Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}\dfrac{1}{3}x+\dfrac{1}{4}y=1&\text{multiply both sides by 12}\\2x-3y=-30\end{array}\right\\\left\{\begin{array}{ccc}12\!\!\!\!\!\diagup^4\cdot\dfrac{1}{3\!\!\!\!\diagup_1}x+12\!\!\!\!\!\diagup^3\cdot\dfrac{1}{4\!\!\!\!\diagup_1}y=12\cdot1\\2x-3y=-30\end{array}\right\\\left\{\begin{array}{ccc}4x+3y=12\\2x-3y=-30&\text{multiply both sides by (-2)}\end{array}\right\\\underline{+\left\{\begin{array}{ccc}4x+3y=12\\-4x+6y=60\end{array}\right}\qquad\text{add both sides of the equations}[/tex]

[tex].\qquad9y=72\qquad\text{divide both sides by 9}\\.\qquad y=8[/tex]

Answer:

8

Step-by-step explanation: