1. Given the functions f(x)=3x-4 and g(x)=4x+10, find the value of x for which f(x) = g(x)
A. 2
B. -2
C. -6
D. -14

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:

P = -2600/3 t + 25600/3

P = -8200/3

Step-by-step explanation:

t is the time in years since 1990, so two points on the line are (5, 4200) and (8, 1600).

Using the points to find the slope:

m = (y₂ − y₁) / (x₂ − x₁)

m = (1600 − 4200) / (8 − 5)

m = -2600/3

Now writing the equation in point-slope form:

P − 4200 = -2600/3 (t − 5)

Converting to slope-intercept form:

P − 4200 = -2600/3 t + 13000/3

P = -2600/3 t + 25600/3

In 2003, t = 13:

P = -2600/3 (13) + 25600/3

P = -8200/3

The linear formula for the moose population is P = -800t + 8200. The moose population predicted by this model for the year 2003 is 2,400.

In this question, we are given that in 1995 the moose population was 4200 and by 1998 it was 1600. This change in population mimics a linear relationship. We are asked to find the formula for this line and then predict the moose population in 2003.

We know that 1995 corresponds to t = 5 (since t is the years since 1990) and 1998 corresponds to t = 8. Therefore we can find the slope of the line (m) as (4200- 1600) / (5 - 8) = -800 per year. Since we know that the line crosses the point (5,4200), we can find the y-intercept, denoted as (b), using the formula y = mx + b.

Substitute m = -800, x = 5, and y = 4200 into the equation and solve for b

4200 = -800 * 5 + b

This simplifies to b= 4200 + 4000 = 8200

Therefore, the formula is P = -800t + 8200

To predict the moose population in 2003, simply substitute t = 13 into the formula (since 2003 is 13 years since 1990). Therefore,

P = -800 * 13 + 8200 = 2400

Therefore, the model predicts that the moose population in 2003 would be 2400.

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Answer:

B. 68%.

Step-by-step explanation:

We have been given that driving times for students' commute to school is normally distributed, with a mean time of 14 minutes and a standard deviation of 3 minutes.

First of all, we will find z-score of 11 and 17 using z-score formula.

[tex]z=\frac{x-\mu}{\sigma}[/tex]

[tex]z=\frac{11-14}{3}[/tex]

[tex]z=\frac{-3}{3}[/tex]

[tex]z=-1[/tex]

[tex]z=\frac{17-14}{3}[/tex]

[tex]z=\frac{3}{3}[/tex]

[tex]z=1[/tex]

We know that z-score tells us a data point is how many standard deviations above or below mean.

Our z-score -1 and 1 represent that 11 and 17 lie within one standard deviation of the mean.

By empirical rule 68% data lies with in one standard deviation of the mean, therefore, option B is the correct choice.

Answer: 68%

Step-by-step explanation: ya boy just took le test :-)

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:

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:

[tex]\large\boxed{A=54\ m^2}[/tex]

Step-by-step explanation:

The formula of an area of a trapezoid:

[tex]A=\dfrac{b_1+b_2}{2}\cdor h[/tex]

b₁, b₂ - bases

h - height

We must use the Pythagorean theorem:

[tex]x^2+8^2=10^2[/tex]

[tex]x^2+64=100[/tex]              subtract 64 from both sides

[tex]x^2=36\to x=\sqrt{36}\\\\x=6\ m[/tex]

We have b₁ = 6 + 6 = 12m, b₂ = 6m and h = 8m.

Substitute:

[tex]A=\dfrac{12+6}{2}\cdot6=\dfrac{18}{2}\cdot6=(9)(6)=54\ m^2[/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

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:

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:

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

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:

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:

(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:

[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]

Answer:

False

Step-by-step explanation:

It would be at -3,9.

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:

{-0.36, 8.36) to the nearest hundredth.

Step-by-step explanation:

x^2 - 8x = 3

(x - 4)^2 - 16 = 3

(x - 4)^2 = 19

Taking square roots:

x - 4 = +/- √19

x =  4 +/- √19

x = {-0.36, 8.36} to nearest 1/100.

For this case we have the following expression:

[tex]x ^ 2-8x = 3[/tex]

We must complete squares.

So:

We divide the middle term between two and we square it:

[tex](\frac {-8} {2}) ^ 2[/tex], then:

[tex]x ^ 2-8x + (\frac {-8} {2}) ^ 2 = 3 + (\frac {-8} {2}) ^ 2\\x ^ 2-8x + (- 4) ^ 2 = 3 + 16[/tex]

We have to, by definition:

[tex](a-b) ^ 2 = a ^ 2-2ab + b ^ 2[/tex]

Then, rewriting:

([tex](x-4) ^ 2 = 19[/tex]

To find the roots, we apply square root on both sides:

[tex]x-4 = \sqrt {19}[/tex]

We have two solutions:

[tex]x_ {1} = \sqrt {19} +4\\x_ {2} = - \sqrt {19} +4[/tex]

Answer:

([tex](x-4) ^ 2 = 19\\x_ {1} = \sqrt {19} +4\\x_ {2} = - \sqrt {19} +4[/tex]

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:

4√3.

Step-by-step explanation:

√48

= √(16 * 3)

= √16 * √3

= 4√3.

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:

(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:

20 sweets.

Step-by-step-explanation:

Let Colin have x sweets.

The Henry gets x+15 sweets

Then according to the ratios:

5/2 = x+15/x

5x = 2x + 30

3x = 30

x = 10.

So Colin has 10 sweets.

The ratio of Brian's sweets to Colin's  sweets  is  4: 2 or 2:1.

So Brian has 2 * 10 = 20 sweets.

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:

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:

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:

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:

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.