Which of the following points lies on the graph of f(x) = -x 2?

(-4, 2)
(-2, -4)
(-2, 4)
(4, -2)

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:

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:

5/2 or 5:2

Step-by-step explanation:

Answer:

6*5=30 to 2*6=12

Step-by-step explanation:

6:5 and 2:6 for smaller hexagon

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

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:

400mL/3l

Is the correct answer

Step-by-step explanation:

To find the quotient of 6 liters by 27 liters and 600 milliliters, convert both to milliliters and divide. The quotient is approximately 0.21739.

To find the quotient of 6 liters (L) divided by 27 liters and 600 milliliters (mL), we first need to convert the amounts to the same unit. Since there are 1,000 milliliters in a liter, we can convert 27 liters into milliliters:

27 L × 1,000 mL/L = 27,000 mL

Now we add the 600 mL:

27,000 mL + 600 mL = 27,600 mL

Rewrite the problem with both measurements in milliliters:

6,000 mL / 27,600 mL

We now divide 6,000 by 27,600:

6,000 mL / 27,600 mL = 0.21739 (rounded to five decimal places)

So, the quotient is approximately 0.21739.

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.

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:

[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:

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.

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:

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:

[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:

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

To evaluate the expression (9.08 × 10⁶) - (2.25 × 10⁵), align the exponents and then subtract the base numbers, resulting in (8.855 × 10⁶) expressed in scientific notation.

To evaluate the expression (9.08 × 10⁶) - (2.25 × 10⁵) and express the result in scientific notation, we will align the exponents and then subtract the base numbers. Since the exponents are not the same, we need to adjust the smaller exponent to match the larger one.

First, we rewrite (2.25 × 10⁵) with a base of 10⁶, which becomes (0.225 × 10⁶). Now we can subtract:

(9.08 × 10⁶) - (0.225 × 10⁶) = (9.08 - 0.225) × 10⁶

Performing the subtraction, we get:

(8.855 × 10⁶)

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:

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

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.

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:

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

We have

[tex]\dfrac{x^4+2x^3-7x^2-8x+12}{x-2}=x^3+4x^2+x-6[/tex]

The rational root theorem suggests that other possible roots may be -6, 6, -3, 3, -2, 2, -1, and 1. It turns out that [tex]x=-2[/tex] is a root, since [tex](-2)^3+4(-2)^2+(-2)-6=0[/tex], so [tex]x+2[/tex] is also a factor and we have

[tex]\dfrac{x^4+2x^3-7x^2-8x+12}{(x-2)(x+2)}=x^2+2x-3[/tex]

Finally, we can factorize the remaining quotient easily:

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

so the other factors are [tex]x+2[/tex], [tex]x+3[/tex], and [tex]x-1[/tex].

Answer:

About 609,000 Cowboy stadiums could fit inside of Mount Everest

Step-by-step explanation:

we have

The estimate volume of Mount Everest is at around [tex]2,413\ km^{3}[/tex]

The Dallas Cowboys Stadium has a volume of [tex]140,000,000\ ft^{3}[/tex]

step 1

Convert ft³ to km³

we know that

1 km=3,280.84 ft

so

[tex]140,000,000\ ft^{3}=140,000,000*(1/3,280.84)^{3}=0.003964\ km^{3}[/tex]

step 2

To find how many Cowboy stadiums could fit inside of Mount Everest, divide the volume of Mount Everest by the volume of the Dallas Cowboys Stadium

[tex]2,413/0.003964=608,729[/tex]

Round to the nearest Thousands

[tex]608,729=609,000[/tex]

The volume of Mount Everest is about 609,000 times greater than the volume of the Dallas Cowboys Stadium

To estimate how many Dallas Cowboys stadiums could fit inside Mount Everest, we converted the volume of the stadium to cubic kilometers and then divided Mount Everest's volume by this number, resulting in approximately 608,845 stadiums.

Calculating the Volume of Mount Everest Compared to the Dallas Cowboys Stadium

To estimate how many Dallas Cowboys stadiums could fit inside of Mount Everest, we need to convert the volume of both structures to the same units and then perform a division.

We have the volume of Mount Everest as approximately 2,413 cubic kilometers. To convert the volume of the Dallas Cowboys Stadium from cubic feet to cubic kilometers, we use the conversion factor of 1 cubic kilometer equals 35.3147 million cubic feet:

Cowboys Stadium volume in cubic kilometers = 140 million cubic feet × (1 cubic kilometer / 35.3147 million cubic feet) = 3.9642 × 10-3 cubic kilometers.

Now, we can find how many Cowboys stadiums fit into Mount Everest:

Mount Everest volume / Cowboys Stadium volume = 2,413 cubic kilometers / 3.9642 × 10-3 cubic kilometers ≈ 608,845.

Therefore, approximately 608,845 Dallas Cowboys stadiums could fit inside of Mount Everest's volume.

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.

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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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:

[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]

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:

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: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:

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