Which is the standard form of the equation of a parabola with a focus of (8, 0) and directrix x = –8?​

Answer:

y - 5 = 3(x - 2)

Step-by-step explanation:

Point Slope Form: y – y1 = m(x – x1)

y1 represents the y-coordinate

x1 represents the x-coordinate

m represents the slope

The area of this rectangle is 18 square units. What is the unit of measurement?

Answer:

Step-by-step explanation:so first you need to find the sides 6*3 so it is 24

Answer:

The two real solutions are [tex]x=\frac{12}{18} = 0.6667[/tex]  and [tex]x=-\frac{12}{18} =-0.6667[/tex]

Step-by-step explanation:

The equation [tex]9x^{2} -4=0[/tex] is a quadratic function of the form [tex]ax^{2} +bx+c=0[/tex] that can be solved by using the Quadratic Formula.

[tex]x=\frac{-b±\sqrt{b^{2} -4ac} }{2a}[/tex]

The plus and minus mean that the equation has two solution.

In order to identify is the equation has two real solutions we use the discriminant equation [tex]b^{2} -4ac[/tex]. Depending of the result we got:

1. If the discriminant is positive, we get two real solutions.

2. if the discriminant is negative, we get complex solutions.

3. If the discriminant is zero, we get just one solution.

Solution:

The equation [tex]9x^{2} -4=0[/tex] has a=9, b=0, and c=-4

Using the discriminant equation to know if the quadratic equation has two real solutions:

[tex]b^{2} -4ac[/tex]

[tex]0^{2} -4(9)(-4)=144[/tex] The discriminant is positive which mean we get two real solutions.

Using the Quadratic Formula

[tex]x=\frac{-b±\sqrt{b^{2} -4ac} }{2a}[/tex]

[tex]x=\frac{-0±\sqrt{0^{2} -4(9)(-4)} }{2(9)}[/tex]

[tex]x=\frac{±\sqrt{144} }{18}[/tex]

[tex]x=±\frac{12}{18}[/tex]

then

[tex]x=\frac{12}{18} = 0.6667[/tex]  and [tex]x=-\frac{12}{18} =-0.6667[/tex]

To solve the equation 9x^2-4=0, we simplify and take the square root of both sides, resulting in two real solutions: x = 2/3 and x = -2/3.

To find two real solutions to the equation 9x^2-4=0, we can approach this by simplifying it into a form that can use the square root method for solving. Here are the steps:

Therefore, the two real solutions are x = 2/3 and x = -2/3.

Answer:

degree of vertex B = 2

degree of vertex g = 4

Step-by-step explanation:

Using given picture we need to find about what is the degree of vertex B and G.

In graph theory, we know that the degree (or valency) of a vertex of a graph is the number of edges incident to the vertex.

So we just need to count how many edges are incindent on vertex B and G.

From picture we see that number of edges incident on vertex B = 2

Hence degree of vertex B = 2

From picture we see that number of edges incident on vertex G = 4

Hence degree of vertex g = 4

Answer:

1600

Step-by-step explanation:

first, 1.6 m is 160 cm.

160 cm is 1 in 1:100

converting the proportion into a fract., it is 1/100.

160=1/100x

1600=x

To find the width of the model car in centimeters, we need to follow a different approach, because the information given doesn't include the width of the actual car or the ratio of length to width. Since only the scale of the model and the length of the model car are given, without additional information about the actual car or its dimensions, we cannot directly calculate the width of the model car.
However, I can explain the general process of how to calculate the width of the model car if the necessary information was provided:
1. **Find the width of the actual car**: If the width of the actual car (in meters or any other units) is given, we could proceed to the next step. Without this information, we cannot continue, so let's assume hypothetically that this information is available.
2. **Convert the width of the actual car to centimeters**: Since the dimensions of the model car are sought in centimeters, we need to convert the actual car's width from meters to centimeters by the following conversion:
  \[ \text{width in centimeters} = \text{width in meters} \times 100 \].
3. **Apply the scale ratio**: After converting the actual car's width to centimeters, we need to apply the scale ratio to calculate the width of the model car. The scale is 1:100, which means that one unit of measurement on the model represents 100 of the same units on the actual car.
4. **Calculate the width of the model car**: Divide the width of the actual car in centimeters by the scale ratio (which is 100 in this case) to calculate the width of the model car in centimeters:
  \[ \text{width of model car in centimeters} = \frac{\text{width of actual car in centimeters}}{100} \].
If we suppose that the actual car is twice as long as it is wide, and we have the model's length (1.6 m), we could assume that the actual car's length is 160 m (since 1.6 m times the scale factor of 100). With an assumption of the actual car being twice as long as wide, we can deduce that the actual car's width would be 80 m (160 m divided by 2). Converting that to centimeters would be 8000 cm (since 80 m times 100 cm/m). Dividing that by 100 (scale factor) would yield a result of 80 cm for the width of the model car.
However, please note, without the essential information about the actual car's width or its length-to-width ratio, this is just a hypothetical scenario. To proceed with a real calculation, you would need to clarify the actual width of the car or provide the proportional dimensions.

The solution to the equation by using quadratic formula is [tex]x = \dfrac{1 + 2\sqrt{2}}{2} \ or \ \dfrac{1 - 2\sqrt{2}}{2}[/tex]

Solving quadratic equation using formula.

Quadratic equation can be solved by using the quadratic formula [tex]x = \dfrac{-b \pm \sqrt{b^2 -4ac}}{2a}[/tex]

The given equation (2x - 1)² = 8 can be written as 4x² - 4x - 7 = 0. where:

Replacing the values into the quadratic formula, we have:

[tex]x = \dfrac{-(-4) \pm \sqrt{(-4)^2 -4(4)(-7)}}{2(4)}[/tex]

[tex]x = \dfrac{4 \pm \sqrt{16 + 112}}{8}[/tex]

[tex]x = \dfrac{4 \pm \sqrt{128}}{8}[/tex]

[tex]x = \dfrac{4 \pm 8\sqrt{2}}{8}[/tex]

Divide the right hand side by 4;

[tex]x = \dfrac{1 \pm 2\sqrt{2}}{2}[/tex]

[tex]x = \dfrac{1 + 2\sqrt{2}}{2} \ or \ \dfrac{1 - 2\sqrt{2}}{2}[/tex]

Answer:

B

Step-by-step explanation:

Since the probability of an animal being blue isn't affected by the animal having two heads, the two events are independent.

Step-by-step explanation:

To find the answer you have to put it into y=mx+b format.

This means that it will be 5y=-30x+15

So it will simplify to y=-6x+3

This means that:

If y=2

You substitute then…

2=-6x+3

So x would equal 1/6.

The rate of change in y per unit change in x for the function 30x+5y=15 is 1/6.

Suppose that the considered linear equation is of the form y=mx+c

Then, when we change x by 1 unit, then:

[tex]y + \delta y = m(x + 1) + c\\mx + c + \delta y = mx + c + m\\\delta y = m[/tex]

where[tex]\delta[/tex] y  shows the change in y as x changes by 1 unit. We found that this change is the value of 'm'. It is called slope of the line this equation represents (each linear equation represents a line).

To find the answer we have to put it into y=mx+b format.

Given the function 30x+5y=15

This means that it will be;

5y = -30x+15

So it will simplify and gives;

y=-6x+3

If y=2

substitute then;

2=-6x+3

x  =1/6

Thus x would equal 1/6.

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Answer:

Expression for the total cost is $1J.

Step-by-step explanation:

Given that each granola bar costs $1.

Now we need to write an expression that shows the total costs of the granola bars using the variable J.

So let's assume that the number of granola bars = J

then total cost of g granola bars = (J)($1) = $1J

Hence required expression for the total cost is 1J dollars.

Answer:

interest earned= 1436.143

the future value of an annuity= 2836.143

Step-by-step explanation:

Given Data:

Interest rate= 4%

time,t = 18 years

Annual payment, P= 1400

At the end of 18 years, final investment A= ?

As per the interest formula for interest

A= P(1+r)t

Putting the values in above equation

= 1400(1+0.04)^18

= 2836.143

Interest earned = A-P

                           = 2836.143-1400

                          = 1436.143 !

Answer:

A=2(wl+hl+hw)

2·(4·7+15·7+15·4)

386

Step-by-step explanation:

Final answer:

The sum of the absolute deviations for the given data set is 14.

Explanation:

To find the sum of the absolute deviations of a data set, you need to find the absolute value of the difference between each data point and the mean, and then add them up. Here is the calculation for the given data set:

Absolute deviations: |8-10| + |5-10| + |15-10| + |12-10| + |10-10| = 2 + 5 + 5 + 2 + 0 = 14

So, the sum of the absolute deviations for this data set is 14.

To evaluate 16+j⋅4 for j=8, substitute j with 8, multiply the result by 4, and add it to 16 to get the final result of 48.

To evaluate 16+j⋅4 for j=8, follow these steps:

16 + j * 4 = 16 + 8 * 4 = 16 + 32 = 48

After performing these steps, we find that the expression 16+j⋅4 for j=8 is equal to 16+32, which is 48.

Answer:

6x + 1

3x + 3

6x + 9

Step-by-step explanation:

1)

To find the missing number, compare both sides of the equation. If the variable terms are the same and the constant terms are different, then the equation has no solutions.

2x + 9 + 3x + x  = _x +_

6x + 9 = _x + _

6x + 9 = 6x + 1

2)

To find the missing number, compare both sides of the equation. If the variable terms are the different and the constant terms are either different or same, then the equation has one solution.

2x + 9 + 3x + x = _x + _

6x + 9 = _x + _

6x + 9 = 3x + 3

3)

When equation is true for every possible value of x.

To find the missing number, compare both sides of the equation. If the variable terms are the same and the constant terms are same, then the equation has no solutions.

2x + 9 + 3x + x = _x + _

6x + 9 = _x + _

6x + 9 = 6x + 9

6x = 6x +9 -9

6x = 6x

6x/6 = x

x = x

The value of x is 60.

The Midpoint theorem states that :

The line segment in a triangle joining the midpoint of two sides of the triangle is said to be parallel to its third side and is also half of the length of the third side

By Midpoint theorem

DE = 30

AC = x

DE = [tex]\frac{1}{2}[/tex] AC

30 = [tex]\frac{x}{2}[/tex]

x = 60

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Answer:

Step-by-step explanation:

The first step will be to make y the subject of the formula, by multiplying both sides of the equation by -1.

y = x - 1

This is simply the equation of a line with a slope of 1 and y-intercept (0,-1)

To determine the three points that solve the equation, we can let x be;

0, 1, 2

When x =0, y = 0-1 = -1

When x = 1, y = 1-1 = 0

When x = 2, y = 2 - 1 = 1

Therefore, we have the following three sets of points that can be used to graph the given linear equation;

(0, -1)

(1, 0)

(2, 1)

Find the attached for the graph

Answer:

"The x-intercepts are where the graph crosses the x-axis, and the y-intercepts are where the graph crosses the y-axis."

Step-by-step explanation:

:)

Final answer:

The y-intercept is the point where a graph crosses the y-axis, while the x-intercept is the point where a graph crosses the x-axis.

Explanation:

The y-intercept is the point where a graph crosses the y-axis. It is represented by the coordinate (0, b), where b is the y-coordinate of the intercept. The y-intercept can be found by analyzing the equation of the line y = mx + b, where b is the y-intercept.

The x-intercept, on the other hand, is the point where a graph crosses the x-axis. It is represented by the coordinate (a, 0), where a is the x-coordinate of the intercept. To find the x-intercept, set y equal to 0 in the equation y = mx + b and solve for x.

Answer:

Option C. 6

Step-by-step explanation:

we know that

If NM bisects the angle ENL

then

∠MNL=∠MNE

In the right triangle MLN

sin(∠MNL)=ML/MN -----> equation A

In the right triangle MEN

sin(∠MNE)=6/MN -----> equation B

equate equation A and equation B

ML/MN=6/MN

Simplify

ML=6

Answer:

The answer is C.

Step-by-step explanation:

Just go to Desmos.com and plug it in.

For this case we have:

Let k> 0:

To graph[tex]y = f (x) + k,[/tex] the graph k units is moved up.

To graph [tex]y = f (x) -k[/tex], the graph moves k units down.

Let h> 0:

To graph [tex]y = f (x-h)[/tex], the graph moves h units to the right.

To graph [tex]y = f (x + h),[/tex] the graph moves h units to the left.

So, we have:

[tex]y = f (x) = \sqrt [3] {x}[/tex]

Shifted 1 unit down and 4 to the left means:

[tex]k = 1\\h = 4[/tex]

[tex]y = f (x) = \sqrt [3] {x + 4} -1[/tex]

Answer:

Option D

Question: 6^x = 1 (finding x)

Answer: x = 0

Explanation: Any non-zero expression raised to the power of 0 equals 1. Since we are trying to find 1, 0 would be an appropriate vale for x.

A dilation with a scale factor greater than 1 and then a translation is correct.

Dilation of a figure will leave its sides to get scaled (multiplied) by the same number. That number is called the scale factor of that dilation.

Its also called scaling of a figure, but due to the involvement of coordinates, it involves a center of a dilation, which is like a pinned point that stays at the same place after dilation.

It's like we enlarge or shorten the size of the figure (or keep it same, when scale factor = 1).

Dilation totally depends on the scale factor.

We need to find the composition of similarity transformations maps A

LMN to AL'M'N'.

If the absolute value of the scale factor is more than 1, then it represents the enlargement and if the absolute value of the scale factor lies between 0 to 1, then it represents the compression.

Therefore, a dilation with a scale factor greater than 1 and then a translation is correct.

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Answer:

D.a dilation with a scale factor greater than 1 and then a translation.

Answer:

[tex]\boxed{ -2}[/tex]

Step-by-step explanation:

On a number line

Using the number line,

Add 3 + (-5)

Step 1. Find 3 on the number line  

Start at 0 and move three units to the right (see Image below).

This takes you to 3.

Step 2. Add (-5)

Start at 3 and move five units to the left.

This takes you to -2.

[tex]\boxed{\textbf{3 + (-5) = -2}}[/tex]

The value of the expression 3 + (-5) is - 2

Given the value :

3 + (-5)

From the operation rule :

+ and - = -

Hence,

3 + (-5) = 3 - 5 = - 2

Using the number line analogy :

Positive values (+) lies to the right of a number line while negative (-) are positioned on the left.

To perform 3 + (-5) using a number line ;

From +3 taking 5 points backwards to the left (-5) ; takes us to the point - 2

Hence, the value of the expression 3 + (-5) = - 2

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Answer:

The correct answer option is: True.

Step-by-step explanation:

Its true that if there is no linear equation to start with, you can isolate and substitute a variable that is squared in both the equation.

For example, for the given non linear equation, start by dividing both sides by coefficient of the variable.

Once you do that and isolate a variable, continue solving by substituting that variable into the other equation.

Answer: true

Step-by-step explanation: A pex

Answer:

4x²  +  12x  +  18

Step-by-step explanation:

This would be the trinomial.

Answer:

if you mean to factor it, it would be, (2x + 3)(2x + 3) but if you do mean the trinomial, that is already the answer.

Step-by-step explanation:

4x^2 + 12x + 9

you can split 12x into 6x + 6x so now it's

4x^2 + 6x + 6x + 9

then simplify it into:

2(2x + 3) + 3(2x + 3)

then into:

(2x + 3)(2x + 3)

Answer:

The answer is D

Step-by-step explanation:

In D, all of the multiplacative parts of the problems add up to the factoring of 185 • 12, and the others don't. I really hope this helps!

Answer:

D. [tex]12\cdot 100 + 12 \cdot 80 + 12 \cdot 5[/tex]

Step-by-step explanation:

A possible solution of the expression is:

[tex]12\cdot (185)[/tex]

[tex]12\cdot (100 + 80 + 5)[/tex]

[tex]12\cdot 100 + 12 \cdot 80 + 12 \cdot 5[/tex]

The right answer is D.

Answer:the awnser is:B the mean will decrease

Step-by-step explanation:

The effect it would have on the dot plot graph is that: B. The mean will decrease.

The mean of a dot plot is found by simply adding up all data points on the dot plot and divide by the number of data points we have on the dot plot.

Mean of the first 10 monologues = (1.5 + 1.5 + 2 + 2.5 + 2.5 + 2.5 + 3 + 3.5 + 3.5 + 4)/10 = 2.65

Mean of the first 10 monologues + 0.5 minutes = (1.5 + 1.5 + 2 + 2.5 + 2.5 + 2.5 + 3 + 3.5 + 3.5 + 4 + 0.5)/11 = 2.45

Therefore, the effect it would have on the dot plot graph is that: B. The mean will decrease.

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Answer:

[tex]\large\boxed{\text{The domain is the set of all real numbes}\to x\in\mathbb{R}}[/tex]

Step-by-step explanation:

[tex]f(x)=x^2-1,\ g(x)=2x-3\\\\(f\circ g)(x)-\text{instead of x in the function equation f(x) put}\ 2x-3:\\\\(f\circ g)(x)=(2x-3)^2-1\qquad\text{use}\ (a-b)^2=a^2-2ab+b^2\\\\(f\circ g)(x)=(2x)^2-2(2x)(3)+3^2-1=4x^2-12x+9-1\\\\(f\circ g)(x)=4x^2-12x+8\\\\\text{the domain is the set of all real numbes}\to x\in\mathbb{R}[/tex]

Answer:

32 m²

Step-by-step explanation:

V(cylinder) = Area(base)*height

288 = Area(base)*9

Area(base)= 288/9=32 m²

Answer: [tex]32\pi\ m^2[/tex]

Step-by-step explanation:

We know that the volume of cylinder is given by :-

[tex]\text{Volume}=\text{Area of base * height}[/tex]

Given: The volume of cylinder = [tex]288\pi\text{ cubic meters}[/tex]

Height of the cylinder= 9 meters

[tex]\Rightarrow\ 288\pi=\text{Area of base }\times9\\\\\Rightarrow\ \text{Area of base }=\dfrac{288\pi}{9}=32\pi[/tex]

Hence, the area of the base = [tex]32\pi\ m^2[/tex]

Answer:

[tex]x^2 + y^2 =18[/tex]

Step-by-step explanation:

The standard equation of a circumference has the following formula.

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

Where the point (h, k) is the center of the circle and r is the radius.

If in this case we know that the circle has center at point (0,0), then its equation will have the following form

[tex]x ^ 2 + y ^ 2 = r ^ 2[/tex]

The radius of the circumference will be the distance from the center of the circumference to the point where the circumference is tangent to the line [tex]Ax + Bx + C = 0[/tex]

The radio is:

[tex]r=\frac{|Ah + Bk +C|}{\sqrt{A^2+B^2}}[/tex]

In this case, the line is

[tex]x + y = 6[/tex]

And the center of the circumference is (0, 0)

So

[tex]A = 1\\B = 1\\C = -6\\h = 0\\k = 0[/tex]

The radio is:

[tex]r=\frac{|1*0 + 1*0 -6|}{\sqrt{1^2+1^2}}\\\\r=\frac{|-6|}{\sqrt{1^2+1^2}}\\\\r=\frac{6}{\sqrt{2}}[/tex]

Finally the equation of the circumference is:

[tex]x^2 + y^2 =(\frac{6}{\sqrt{2}})^2\\\\x^2 + y^2 =18[/tex]

Final answer:

The standard form equation of the circle centered at (0, 0) and tangent to the line x + y = 6 is x² + y² = 18, after determining the radius using the distance formula.

Explanation:

The question asks for the standard form equation of a circle centered at (0, 0) that is tangent to the line x + y = 6. To find the standard form of the circle, we first need to determine the radius of the circle, which is equal to the distance from the center of the circle to the tangent line. Since the center of the circle is at the origin (0,0), we can use the distance formula for a point to a line:

d = |Ax + By + C| / √(A² + B²), where A, B, and C are the coefficients from the line equation Ax + By + C = 0.

In this case, the line x + y = 6 can be rewritten as x + y - 6 = 0 (A = 1, B = 1, C = -6). Plugging these into the distance formula we get:

d = |1 · 0 + 1 · 0 - 6| / √(1² + 1²) = 6 / √2 which simplifies to √18.

The standard form equation of a circle with center at (h, k) and radius r is (x - h)² + (y - k)² = r². With a center at (0, 0) and a radius of √18, the equation becomes:

x² + y² = 18.

This is the standard form equation of the circle which is tangent to the line x + y = 6 at one point.

Answer:

2 2/5

Step-by-step explanation:

First, lets convert these all to decimals.

2 2/3 = 8/3 = 2.66666666.....

2.45 = 2.45

2 2/5 = 12/5 = 2.4

Thus, the smallest decimal here is 2.4, or, 2 2/5.

I hope this helps!

Answer:

the least value is 2 2/5

Step-by-step explanation: