7 × (–3) × (–2)2 = ?

Answer:

b = -9

Step-by-step explanation:

As we go from M(4, 3) to N(7, 12), x increases by 3 and y increases by 9.  Thus, the slope of the line segment connecting these two points is m = rise / run = m = 9/3, or just m = 3.

Subbing the coordinates of M into y = mx + b, we get:

3 = 3(4) + b, or 3 = 12 + b, so that b = -9.

Answer:

-9

Step-by-step explanation:

Answer:

Discontinuities are created when the denominator of the rational expression equals zero (because division by zero is undefined). Graphically, this is usually represented by a dashed vertical line indicating a vertical asymptote.

Answer:

[tex]\large\boxed{1.\ V=\dfrac{80\pi}{3}\ cm^3\approx83.73\ cm^3}\\\boxed{2.\ V=\dfrac{28\pi}{3}\ cm^3\approx29.31\ cm^3}\\\boxed{3.\ V=36\pi\ in^3\approx113.04\ cm^3}[/tex]

Step-by-step explanation:

The formula of a volume of a cone:

[tex]V=\dfrac{1}{3}\pi r^2H[/tex]

r - radius

H - height

[tex]\pi\approx3.14[/tex]

[tex]\bold{1.}\\\\r=4cm,\ H=5cm\\\\V=\dfrac{1}{3}\pi(4^2)(5)=\dfrac{1}{3}\pi(16)(5)=\dfrac{80\pi}{3}\ cm^3\approx\dfrac{(80)(3.14)}{3}=83.73\ cm^3[/tex]

[tex]\bold{2.}\\\\r=2cm,\ H=7cm\\\\V=\dfrac{1}{3}\pi(2^2)(7)=\dfrac{1}{3}\pi(4)(7)=\dfrac{28\pi}{3}\ cm^3\approx\dfrac{(28)(3.14)}{3}=29.31\ cm^3[/tex]

[tex]\bold{3.}\\\\r=6in,\ H=3in\\\\V=\dfrac{1}{3}\pi(6^2)(3)=\dfrac{1}{3}\pi(36)(3)=36\pi\ in^3\approx(36)(3.14)=113.04\ in^3[/tex]

Answer:

Choice A. Segment LM is congruent to segment LO.

Step-by-step explanation:

Triangles LMX and LOX are right triangles since we see that each one has a right angle.

Segment LX is congruent to itself. Segment LX is a side of both triangles. It is a leg of both triangles, so we already have a leg of one triangle congruent to a leg of the other triangle.

For the HL theorem to work, we need a leg and the hypotenuse of one triangle to be congruent to the corresponding parts of the other triangle. Since we already have a pair of legs, we need a pair of hypotenuses.

The hypotenuses of the triangles are segments LM and LO.

Answer: A. Segment LM is congruent to segment LO.

Answer:

The quotient is 1/4

Step-by-step explanation:

1/3 ÷ 4/3

The first step you have to do is change the division sign into multiplication. So that the denominator of 2nd term will become numerator and the numerator will become denominator.

Like:

1/3 * 3/4

Now you can cancel out 3 by 3

1 * 1/4

1/4

Thus the quotient is 1/4 ....

For this case we must find the quotient of the following expression:

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

If we apply double C we have:

[tex]\frac {3 * 1} {3 * 4} =[/tex]

We cancel similar terms in the numerator and denominator and finally we have the quotient is:

[tex]\frac {1} {4}[/tex]

Answer:

[tex]\frac {1} {4}[/tex]

Answer: 3 - [tex]\frac{c}{4}[/tex]

Step-by-step explanation:

2c - 8f = 24

2(c - 4f) = 2(12)

c - 4f = 12

4f = 12 - c

F = 3 - [tex]\frac{c}{4}[/tex]

Answer:

16

Step-by-step explanation:

х2 + 8x = 4

Take the coefficent of the x term, 8

Divide it by 2. 8/2 =4

Then square it, 4^2 = 16

Add this to both sides of the equation

x^2 +8x+16 = 4+16

Answer:

[tex]\large\boxed{D.\ a^2+2ah+h^2+3a+3h+5}[/tex]

Step-by-step explanation:

[tex]f(x)=x^2+3x+5\\\\f(a+h)\to\text{exchange x to (a + h)}:\\\\f(a+h)=(a+h)^2+3(a+h)+5\\\\\text{use}\ (a+b)^2=a^2+2ab+b^2\ \text{and the distributive property}\\\\f(a+h)=a^2+2ah+h^2+3a+3h+5[/tex]

Multiply the total number of slices by the fraction he ate:

12 slices x 1/6 = 12/6 = 2

He ate 2 slices.

Answer:

2

Step-by-step explanation:

1/6 of 12 =

= 1/6 * 12

= 1/6 * 12/1

= (1 * 12)/(6 * 1)

= 12/6

= 2

Answer:

B.

Step-by-step explanation:

If f(-x)=f(x), then f is even.

If f(-x)=-f(x), then f is odd.

To determine if f(x)=3x^4+5x^2+1 is even or odd plug in -x like so:

f(x)=3x^4+5x^2+1

f(-x)=3(-x)^4+5(-x)^2+1

f(-x)=3x^4+5x^2+1

f(-x)=f(x)

So f is even.

You should keep in mind the following:

(-x)^odd=-(x^odd)

(-x)^even=x^even

Examples:

(-x)^81=-(x^81) since 81 is odd

(-x)^10=x^10 since 10 is even

Anyways, the student is right and f(-x)=f(x).

Answer:

The student's claim is true, because for any input of x, f(x)=f(−x).

Step-by-step explanation:

If a student says that the function f(x)=3x^4+5x^2+1 is an even function, the student's statement true  because for any input of x, f(x)=f(−x).

f(-x)=f(x) is even.

f(-x)=-f(x) is odd

Answer:

(8,10)

Step-by-step explanation:

If we reflect a point over the y-axis, the x becomes opposite while the y stays the same.

So the rule here is (a,b)->(-a,b) if we are reflecting over y-axis.

So if you reflect (-8,10) over the y-axis you get (8,10).

Answer:

x < -2

Step-by-step explanation:

2|x| > 3x + 10

Divide both sides by 2.

|x| > 1.5x + 5

********************************************************

An absolute value inequality of the form

|X1| > X2

where X1 and X2 are expressions in x is solved by solving the compound inequality

X1 > X2 or X1 < -X2

********************************************************

Back to your problem.

|x| > 1.5x + 5

x > 1.5x + 5   or   x < -(1.5x + 5)

-0.5x > 5     or   x < -1.5x - 5

x < -10   or    2.5x < -5

x < -10    or    x < -2

Since x < -10 is included in x < -2, the solution is

x < -2

Answer:

Step-by-step explanation:

The slope-intercept of an equation of a line:

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

m - slope

b - y-intercept

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

=========================================

[tex]f(x)=2x-5\to m=2[/tex]

From the table of function g(x) we have:

x = 2 → y = 0

x = 4 → y = 5

Calculate the slope:

[tex]m=\dfrac{5-0}{4-2}=\dfrac{5}{2}=2.5[/tex]

The slope of f(x) is equal to 2.

The slope of g(x) is equal to 2.5.

2 < 2.5

Answer:

B. g(x) has a greater slope

Step-by-step explanation:

Given the function f(x) =2x-5 and g(x), g(x) has a greater slope.

f(x) = 2

g(x) = 2.5

Answer:

[tex]\large\boxed{5x\times(3x^2-5)=15x^3-25x}[/tex]

Step-by-step explanation:

[tex]5x\times(3x^2-5)\qquad\text{use the distributive property:}\ a(b+c)=ab+ac\\\\=(5x)(3x^2)+(5x)(-5)\\\\=15x^3-25x[/tex]

The resulting product of the functions using the distributive property is

15x³ - 25x.

Product is an operation carried out when two or more variables, numbers, or functions are multiplied together.

Given the expression 5x(3x² - 5)

Taking the product:

5x(3x² - 5)

Expand using the distributive property

= 5x(3x²) - 5x(5)

= (5×3)(x × x²) - 25x

= 15x³ - 25x

Hence the resulting function is 15x³ - 25x.

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Answer:

(5,1)

(5,0)

Step-by-step explanation:

Vertical lines contain the same x-coordinate per any point on it's line.

So the x-coordinate of (5,-2) is 5.

We are looking for points that have the x-coordinate being 5.

(5,1)

(5,0)

Actually the equation for this line is x=5.

[tex]\huge{\boxed{\text{(5, 1)}}}\ \huge{\boxed{\text{(5, 0)}}}[/tex]

[tex]\text{A vertical line is a line where all of the x values (the first values) are the same.}[/tex]

[tex]\text{In this case, all answers with an x value of 5 are correct.}[/tex]

Answer:

please could you send graphics A,B,C. you just sent D.

Answer:

6/16 or 0.375 ..

Step-by-step explanation:

Each time the coin has two possible outcomes so tossing the coin four times

The sample space will be: 2^4 = 16

The sample space is: {HHHH, HTHH, THHH, HTHT , HHHT, HTTH, TTHH, THTH, HHTT, HHTH, TTTH, THHT ,HTTT, TTTT, TTHT, THTT}

Let A be the event that there are exactly two heads

A = {HTHT, HTTH, TTHH, THTH, HHTT, THHT}

n(A) = 6

So the probability of exactly two heads is:

P(A) = 6/16 or 0.375 ..

Answer:

3/8

Step-by-step explanation:

The person up there answered it right they just went too high with the numbers.

Answer:

13 square units

Step-by-step explanation:

First of all, you need to identify that ABCD is a rectangle (AB=CD and AD=BC).

The area of a rectangle is calculated by multiplying the length and the width.

Secondly, we use the Pythagoras’s theorem to calculate side CD and AD (the length and width). I’ve added some labels to your original diagram (see picture attached) so that it’s easier to understand.

The Pythagoras’s theorem is a^2 + b^2 = c^2 (c is the hypotenuse).

So, for side CD:

3^2 + 1^2 = (CD)^2

9 + 1 = (CD)^2

CD = √ 10

and for side AD:

4^2 + 1^2 = (AD)^2

16 + 1 = (AD)^2

AD = √17

Lastly, to calculate the area:

√10 x √17 = 13.04

Your answer is 13 square units.

Hope this helped :)

Answer:

Option B. 13 square units

Step-by-step explanation:

Area of a parallelogram is defined by the expression

A = [tex]\frac{1}{2}(\text{Sum of two parallel sides)}[/tex] × (Disatance between them)

Vertices of A, B, C and D are (3, 6), (6, 5), (5, 1) and (2, 2) respectively.

Length of AB = [tex]\sqrt{(x-x')^{2}+(y-y')^{2}}[/tex]

                      = [tex]\sqrt{(5-6)^{2}+(6-3)^{2}}[/tex]

                      = [tex]\sqrt{10}[/tex]

Since length of opposite sides of a parallelogram are equal therefore, length of CD will be same as [tex]\sqrt{10}[/tex]

Now we have to find the length of perpendicular drawn on side AB from point D or distance between parallel sides AB and CD.

Expression for the length of the perpendicular will be = [tex]\frac{|Ax_{1}+By_{1}+C|}{\sqrt{A^{2}+B^{2}}}[/tex]

Slope of line AB (m) = [tex]\frac{y-y'}{x-x'}[/tex]

                                 = [tex]\frac{6-5}{3-6}=-(\frac{1}{3} )[/tex]

Now equation of AB will be,

y - y' = m(x - x')

y - 6 = [tex]-\frac{1}{3}(x-3)[/tex]

3y - 18 = -(x - 3)

3y + x - 18 - 3 = 0

x + 3y - 21 = 0

Length of a perpendicular from D to side AB will be

= [tex]\frac{|(2+6-21)|}{\sqrt{1^{2}+3^{2}}}[/tex]

= [tex]\frac{13}{\sqrt{10}}[/tex]

Area of parallelogram ABCD = [tex]\frac{1}{2}(AB+CD)\times (\text{Distance between AB and CD})[/tex]

= [tex]\frac{1}{2}(\sqrt{10}+\sqrt{10})\times (\frac{13}{\sqrt{10} } )[/tex]

= [tex]\sqrt{10}\times \frac{13}{\sqrt{10} }[/tex]

= 13 square units

Option B. 13 units will be the answer.

Answer:

4√3.

Step-by-step explanation:

√48

= √(16 * 3)

= √16 * √3

= 4√3.

Answer:

(4/7) + x  = (11/12)

(11/12) -(4/7) = x

We need to convert BOTH denominators to 84

(11/12) * 7 = 77 / 84

(4 / 7) * 12 = 48 / 84

77 / 84  -(48 / 84) = 29 / 84

Step-by-step explanation:

Answer:

There is only 1 plane that contains all 3 points.

Step-by-step explanation:

According to the three point postulate, three non-collinear points are in one plane. Therefore, your answer would be there is only 1 plane that contains all 3 points.

Let's analyze each statement regarding the three non-collinear points:
1. "The intersection of 2 planes would contain all 3 points."
This statement is false. The intersection of two planes in three-dimensional space is a line, and there is no guarantee that a line resulting from the intersection of two arbitrary planes will contain all three non-collinear points. In fact, the likelihood of this happening by chance is zero.
2. "They will be contained in the same line."
This statement is false as well. Since the points are non-collinear, by definition, they do not all lie on a single line. A line can only contain two of the points at a time, but not all three if they are non-collinear.
3. "There is only 1 plane that contains all 3 points."
This statement is true. Given any three non-collinear points in space, there is exactly one plane that contains all three. This is because any three points that are not on the same line can define a plane by being unique points in a two-dimensional subspace of three-dimensional space.
4. "Only one line can be drawn containing any 2 of the points."
This statement is true as well. For any two distinct points, there exists exactly one line that connects them. This is one of the fundamental principles of geometry: through any two points, there is exactly one straight line.
In summary, the third and fourth statements are true, while the first and second are false.

Answer:

-3

Step-by-step explanation:

-9+6

=6-9

=-3

Answer:

-3

Step-by-step explanation:

-9+6

- + = -

So this expression will be subtracted.

-9+6 = -3

The answer is negative because greater value has a negative sign....

Answer:

Because they are both infinitely long.

Step-by-step explanation:

A ray goes on to infinity from a given point in one direction, whereas a line goes on to infinity in both directions.

Final answer:

A line or ray cannot have a perpendicular bisector because they extend infinitely without definite endpoints, thus lacking a midpoint for bisecting. Only a line segment, which has two endpoints, can have a perpendicular bisector that divides it into two equal parts at a right angle.

Explanation:

The question why a line or ray can't have a perpendicular bisector can be explained through geometric principles. A ray, by definition, is a line that starts at a point and extends infinitely in one direction. It doesn't have a midpoint or an end, and therefore cannot be bisected. Similarly, a line extends infinitely in both directions and does not have a midpoint for bisection. The concept of a perpendicular bisector requires a line segment, which has two endpoints, allowing for a midpoint to be determined and a line to be drawn at a 90-degree angle, equally dividing it into two equal parts.

Considering Euclidean geometry, it's understood that two perpendiculars cannot be parallel to the same line as they would then be parallel to each other, contradicting the definition of perpendicular lines. Moreover, a perpendicular bisector is defined in the context of a line segment within a plane, where the extremities of the segment are known, and there's a definite length to bisect.

Using Hyperbolic Geometry, it's also noted that if there were two common perpendiculars, a rectangle would form, which is not possible in that geometry. This further establishes the distinct properties between lines, rays, and line segments regarding the possibility of establishing perpendicular bisectors.

Answer:

False

Step-by-step explanation:

It would be at -3,9.

The graph of the quadratic parent function, y = x^2, is indeed a parabola and lies in quadrants I and II. It is not a straight line and doesn't occupy quadrants I and III.

The graph of the quadratic parent function, which is y = x^2, has specific characteristics, namely:

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Answer:

Efficiency is the ratio of output work to input work.

Machine efficiency is the percent ratio of output work to input work, calculated by (Wout / Win) * 100, and accounts for real-world energy losses, making it always less than 100 percent.

The ratio of output work to input work expressed as a percent is known as the efficiency of a machine. This efficiency (Eff) can be calculated using the equation Eff = (Wout / Win) * 100, where Wout is the output work and Win is the input work. In the context of simple machines, work (W) is defined as the force (F) applied over a distance (d), thus W = F * d. While ideal mechanical advantage (IMA) does not consider losses like friction and is calculated using specific equations for each type of machine, efficiency takes into account real-world factors and is always less than 100 percent due to these energy losses.

Answer:

5 : 3

Step-by-step explanation:

Five A's

Three B's

Therefore, 5 : 3

You would not include the letters because a ratio is just a number.

Answer:

[tex]\Large \boxed{Y=5}[/tex]

Step-by-step explanation:

[tex]\textnormal{First, divide by 90 from both sides of the equation.}[/tex]

[tex]\displaystyle \frac{90y}{90}=\frac{450}{90}[/tex]

[tex]\textnormal{Solve to find the answer.}[/tex]

[tex]\displaystyle 450\div90=5[/tex]

[tex]\displaystyle y=5[/tex], which is our answer.

Hope this helps!

The value of Y in the equation '90 x Y = 450' can be found by isolating Y. This is done by dividing both sides of the equation by 90. Hence, Y equals 5.

In the mathematical equation

90 x Y = 450

, we are being asked to solve for Y. To solve for Y, we can use the basic algebraic principle of isolating the variable on one side of the equation. In this case, since we have 90 multiplied by Y equals 450, we want to isolate Y. We can do that by dividing both sides of the equation by 90. The equation now becomes

Y = 450/90

. By performing the division, we find that

Y equals 5

.

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