What is the distance between the points (-6, 7) and
(-1, 1)? Round to the nearest whole unit.

Answer:

Part 1) The ratio of the areas of triangle TOS to triangle TQR is [tex]\frac{4}{25}[/tex]

Part 2) The ratio of the areas of triangle TOS to triangle QOP is [tex]\frac{4}{9}[/tex]

Step-by-step explanation:

Part 1) Find the ratio of the areas of triangle TOS to triangle TQR

step 1

Find the scale factor

we know that

If two figures are similar, then the ratio of its corresponding sides is equal to the scale factor

The scale factor is equal to

TS/TR

substitute the values

6/(6+9)

6/15=2/5

step 2

Find the ratio of the areas of triangle TOS to triangle TQR

we know that

If two figures are similar, then the ratio of its areas is equal to the scale factor squared

so

[tex](\frac{2}{5})^{2}=\frac{4}{25}[/tex]

Part 2) Find the ratio of the areas of triangle TOS to triangle QOP

step 1

Find the scale factor

we know that

If two figures are similar, then the ratio of its corresponding sides is equal to the scale factor

The scale factor is equal to

TS/QP

substitute the values

6/9

6/9=2/3

step 2

Find the ratio of the areas of triangle TOS to triangle QOP

we know that

If two figures are similar, then the ratio of its areas is equal to the scale factor squared

so

[tex](\frac{2}{3})^{2}=\frac{4}{9}[/tex]

Answer:

44.238

Step-by-step explanation:

50.441-6.203=44.238

Answer:

At x=-2, y=16

At x=0, y=1

At x=3, y=1/64

Step-by-step explanation:

As we know that the function is given by:

[tex]y=(\frac{1}{4})^{x}[/tex]

The table represents the output values on given inputs.

So, when the input is -2:

[tex]y=(\frac{1}{4} )^{-2}\\y= \frac{(1)^{-2}}{(4)^{-2}}[/tex]

To convert the power in positive:

[tex]y=\frac{(4)^{2}}{(1)^{2} }\\y=16[/tex]

So the output for x=-2 is 16.

For x=0

[tex]y=(\frac{1}{4})^{0}[/tex]

Anything whose exponent is zero equals to 1, so y=1

For x=3, output is incomplete.

To complete,

[tex]y=(\frac{1}{4})^{3}\\y=\frac{(1)^{2} }{(4)^{2} }\\y=\frac{1}{64}[/tex] ..

Answer:

- (- 10)

Step-by-step explanation:

Point A is positioned at - 10 on the number line.

The opposite is the negative of the value

That is the opposite of - 10 is - (- 10)

Alright (so what I did was type this into desmos and it was the exact same line but it was the other way around so it is) C

Changing from y = -3x + 5 to y = 2x + 5 would make the slope steeper.

The slope of the new graph would become steeper.

When changing from y = -3x + 5 to y = 2x + 5, the original slope of -3 increases to 2, making the new graph steeper.

Therefore, the correct answer is D. The slope of the new graph would become steeper.

To calculate the GPA, convert each grade to its numerical equivalent, add these up, and then divide by the total number of grades given. For example, the GPA for grades 'A', 'A', 'B', 'C', and 'D' would be 2.8.

To find the grade point average (GPA), you add up all the grade points and then divide by the total number of grades. Let's imagine you received the following grades: 'A', 'A', 'B', 'C', and 'D'.

So your GPA would be 2.8.

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Final answer:

To calculate your grade point average (GPA), assign numerical values to each letter grade and average them. In this case, the GPA would be 2.5 for the given grades.

Explanation:

To calculate your grade point average (GPA), you need to assign the respective numerical value to each letter grade and then average them. In the given scenario, an 'A' is equal to 4.0, a 'B' is 3.0, a 'C' is 2.0, a 'D' is 1.0, and an 'F' is 0.0. Let's assume the grades for your first semester are A, B, C, and D. To calculate your GPA, add up the numerical values of the grades and divide by the number of grades you have.

So, the calculation would be: (4.0 + 3.0 + 2.0 + 1.0) / 4 = 2.5.

Therefore, your grade point average for the first semester would be 2.5.

Answer:

An interpolation has a result which lies within the scatterplot’s cluster of data points. An extrapolation lies outside the cluster. An interpolation is more reliable than an extrapolation.

Step-by-step explanation:

Interpolations and extrapolations are both methods used to estimate values based on a scatterplot, but they differ in their approach.

Interpolations and extrapolations are both methods used to estimate values based on a scatterplot, but they differ in their approach.

Interpolations involve estimating values within the range of the given data points, while extrapolations involve estimating values beyond the range of the given data points.

For example, if we have a scatterplot of temperature measurements at different times throughout a day, interpolation would involve estimating the temperature at a specific time between the given measurements, while extrapolation would involve estimating the temperature at a time outside of the given measurements, such as predicting the temperature at midnight.

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ANSWER

The common ratio is -3.

EXPLANATION

In general, the common ratio of a Geometric Sequence is given by:

[tex] r = \frac{a_{n+1}}{a_{n}} [/tex]

We can find the common ratio using any two consecutive terms of the geometric sequence by dividing the subsequent term by the previous term.

The given sequence is -2,6,-18,54

Using the first two terms the common ratio is

[tex]r = \frac{6}{ - 2} = - 3[/tex]

We could also used the second and third terms to get

[tex]r = \frac{ - 18}{6} = - 3[/tex]

and so on and so forth.

Therefore the common ratio is -3.

1.

Cubic Polynomial--

A cubic polynomial is a polynomial of degree three.

2.

End behavior--

The end behavior of a function is it's behavior when x tends to infinity in both the directions i.e. when x tends to minus infinity and when x tends to plus infinity.

3.

Irreducible--

A polynomial is said to be irreducible if it can't be reduced i.e. it cannot be factored.

4.

Leading coefficient--

It is the coefficient of the highest degree term existing in the expression.

5.

Leading term--

It is the term with the highest degree.

6.

quartic polynomial-

A quadratic polynomial is a polynomial of degree 4.

7.

Zeros of polynomial--

The zeros of a polynomial are all the possible values of x at which the polynomial expression is equal to zero.

To find the area of a rhombus, multiply the two diagonals together then divide by 2.

Area = 20 *15 = 300 / 2 = 150 sq. units.

Answer:

x(t)=-t/4

y(t)=-t-2

(answer can vary)

Step-by-step explanation:

Many different ways to do... you are just introducing a different variable, t, to rewrite x and y.  We are rewriting x and y as functions of t.

So if we let -4x=t  then x=t/-4 or x=-t/4

So if -4x=t then t+y=-2 so y=-t-2

So you could write the following:

x(t)=-t/4

y(t)=-t-2

Answer: the answer is a)x=t,y=4t-2

Step-by-step explanation: I guessed and got it right so sorry i do not know how to explain anything but hopefully it helps someone in the future at least

[tex]|\Omega|=6^2=36\\|A|=1\cdot5\cdot2+1=11\\\\P(A)=\dfrac{11}{36}\approx30.6\%[/tex]

Answer:

[tex]P=\frac{13}{36}=0.361[/tex]

Step-by-step explanation:

There are six possible outcomes when rolling a die. Therefore the probability of obtaining a 3 is a given is

[tex]P = \frac{1}{6}[/tex].

When throwing the two dice together, the probability of obtaining a 3 is the same:

[tex]P_1 = \frac{1}{6} * \frac{5}{6} + \frac{5}{6} * \frac{1}{6}=\frac{5}{18}[/tex]

Since the events are independent then the probability of obtaining a three in both dice is:

[tex]P_2 = \frac{1}{6} * \frac{1}{6} = \frac{1}{12}[/tex].

Finally the probability of obtaining a 3 on a given or both is equal to the sum of the probabilities [tex]P_1[/tex] and [tex]P_2[/tex]

[tex]P=\frac{1}{12}+\frac{5}{18}=\frac{13}{36}=0.361[/tex]

Answer:  84

Step-by-step explanation:

Set up a proportion as follows: [tex]\dfrac{\text{students that practice everyday}}{\text{total students}}[/tex]

[tex]\dfrac{7}{12}=\dfrac{x}{144}[/tex]

Cross multiply: 12x = 7 × 144

Divide by 12:         x = 7 × 12

Simplify:                x = 84

Answer:

66

Step-by-step explanation:

We know x = -4. To solve, we just need to plug in -4 for x.

6 (-4 + 15) =

6 (11) =

66

Answer:

66

Step-by-step explanation:

x= -4  

6(x + 15)

Substitute x =-4 into the second equation

6(-4+15)

6(11)

66

Power = Current *Voltage  

You already have the current, but not the voltage.  

But you are given resistance, and you know that  

Voltage=Current*Resistance  

Therefore  

V=I*R=4*12=48V  

So you have 48V  

Now you can figure out the Power  

P=I*V=4*48=192W  

Therefore you have 192W.

hope this helps

The total power in a circuit is 192W.

Power exists at the time rate of excess or absorbing energy. The power delivered or absorbed by an element exists as the product of the current flowing through the component and the voltage across the element. Power exists estimated in watts. If the power exists positive then it exists absorbed by the component and if it exists negative then it is supplied by the element.

Power = Current [tex]*[/tex] Voltage

We have the current, but not the voltage.

But you are given resistance, and you know that

Voltage = Current [tex]*[/tex] Resistance

Therefore,

[tex]V=I*R=4*12=48V[/tex]

So you have 48V

Thus, we get the Power

[tex]P=I*V=4*48=192W[/tex]

Therefore, the total power in a circuit is 192W.

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His average pay was:

Answer:

£1350

----------- = £8.44/hr   based upon  160 work hours per week

160 hr

Step-by-step explanation:

We must assume that Han works a standard 40-hour week, and that there are 4 weeks in each month.  That comes to 160 hours.

Then his average hourly pay rate was

£1350

--------- = £8.44

160 hr

The graph at option 4 represents the given equation y = -4x - 3 correctly. This is obtained by calculating the slope and finding the y-intercept.

The slope of a line given by

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

The ratio of the difference between y-coordinates of two points on the line to the difference of their x coordinates.

The equation is y = -4x - 3

On comparing the equation with the slope-intercept form y = mx + c,

m = -4 and y-intercept c = -3.

Since the y-intercept is -3, the graphs at options 1 and 2 do not represent this equation. So, the remaining graphs may represent the given equation.

The graph at option 3 has a line with two points (2, 5) and (0, -3)

So, the slope is

m = [tex]\frac{-3-5}{0-2}[/tex]

   = 4

Thus, it is not the same as the slope of the given equation.

The graph at option 4 has a line with two points (-2, 5) and (0, -3)

So, the slope is

m = [tex]\frac{-3-5}{0+2}[/tex]

   = -4

Thus, the line shown in the graph at option 4 has a slope of -4 and the y-intercept is -3. These are the same as the given equation. So, option 4 is correct.

Therefore, the graph at option 4 is the correct representation of the given equation.

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y = –16(x – 2)² + 68 is the equation which models the motion of the ball.

Two or more expressions with an Equal sign is called as Equation.

Given that Ryan throws a tennis ball straight up into the air.

The ball reaches its maximum height at 2 seconds.

The approximate height of the ball x seconds after being thrown is shown in the table.

We need to find the equation of the motion of the ball.

Let us take a point (0, 4) from the table.

The right equation is the point in which the equation satisfies.

y=-17(0)(0-4)

4=0

So y = –17(x)(x – 4) is false.

y = –16(x – 2)² + 68

4=-16(4)+68

The point (0, 4 ) satisfies the equation y = –16(x – 2)² + 68

Hence, y = –16(x – 2)² + 68 is the equation which models the motion of the ball.

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Slope formula: y2-y1/x2-x1

Plug in: -15-0/-11-3 = -15/-14 = 15/14 = slope

For this case we have by definition, the slope of a line can be found by the following formula:

[tex]m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}}[/tex]

Two points are needed through which the line passes.

According to the data we have:

[tex](x_ {1}, y_ {1}) :( 3,0)\\(x_ {2}, y_ {2}): (- 11, -15)[/tex]

Substituting we have:

[tex]m = \frac {-15-0} {- 11-3} = \frac {-15} {- 14} = \frac {15} {14}[/tex]

ANswer:

The slope is [tex]\frac {15} {14}[/tex]

Answer:

x^2 -2x-8

Step-by-step explanation:

f(x) = x + 2

g(x) = x – 4

(f*g) (x) = (x+2) (x-4)

    FOIL

first x*x = x^2

outer  -4*x = -4x

inner 2*x = 2x

last = -4*2 = -8

Add them together

x^2 -4x+2x -8

x^2 -2x-8

Answer:

C on ed

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

The standard form of a quadratic equation is

ax² + bx + c = 0 : a ≠ 0

Express the equations in this form and extract the coefficients

1

4 - 2x + 3x² = 0 , that is

3x² - 2x + 4 = 0 ← in standard form

with a = 3, b = - 2 and c = 4

2

x(x + 5) - 2x = 0 ← distribute parenthesis

x² + 5x - 2x = 0

x² + 3x = 0 ← in standard form

with a = 1, b = 3 and c = 0

3

x² - 2x(x - 2) + 5 = 0 ← distribute parenthesis and simplify

x² - 2x² + 4x + 5 = 0

- x² + 4x + 5 = 0 ← in standard form

with a = - 1, b = 4 and c = 5

Step-by-step explanation:

[tex]f(x)=\dfrac{2}{x}\ and\ g(x)=\dfrac{2}{x}\\\\(f\circ g)(x)=f(g(x))\to\text{substitute}\ 2-3x\ \text{instead}\ x\ \text{in}\ f(x):\\\\(f\circ g)(x)=\dfrac{2}{\frac{2}{x}}=2\cdot\dfrac{x}{2}=x[/tex]

Each line on the graph is one unit.

AB = 15 units long

Answer:

15 units

Step-by-step explanation:

Since A and B are along the same horizontal line, we count count the number of units to determine the distance

The horizontal distance from A to B is 15 units

Answer:

A

Step-by-step explanation:

ABC to CAB, use that method to help you. You can research more on it.

Answer:

[tex]\large\boxed{\text{sixth term is equal to}\ \dfrac{1}{1024}}[/tex]

Step-by-step explanation:

The explicit formula for a geometric sequence:

[tex]a_n=a_1r^{n-1}[/tex]

[tex]a_n[/tex] - n-th term

[tex]a_1[/tex] - first term

[tex]r[/tex] - common ratio

[tex]r=\dfrac{a_2}{a_1}=\dfrac{a_3}{a_2}=...=\dfrac{a_n}{a_{n-1}}[/tex]

We have

[tex]a_1=-1,\ a_2=\dfrac{1}{4},\ a_3=-\dfrac{1}{6},\ ...[/tex]

The common ratio:

[tex]r=\dfrac{\frac{1}{4}}{-1}=-\dfrac{1}{4}\\\\r=\dfrac{-\frac{1}{6}}{\frac{1}{4}}=-\dfrac{1}{6}\cdot\dfrac{4}{1}=-\dfrac{2}{3}\neq-\dfrac{1}{4}[/tex]

If [tex]a_3=-\dfrac{1}{16}[/tex] then the common ratio is [tex]r=\dfrac{-\frac{1}{16}}{\frac{1}{4}}=-\dfrac{1}{16}\cdot\dfrac{4}{1}=-\dfrac{1}{4}[/tex]

Put to the explicit formula:

[tex]a_n=-1\left(-\dfrac{1}{4}\right)^{n-1}[/tex]

Put [tex]a_n=\dfrac{1}{1024}[/tex] and solve for n :

[tex]-1\left(-\dfrac{1}{4}\right)^{n-1}=\dfrac{1}{1024}\qquad\text{use}\ a^n:a^m=a^{n-m}\\\\-\left(-\dfrac{1}{4}\right)^n:\left(-\dfrac{1}{4}\right)^1=\dfrac{1}{1024}\\\\-\left(-\dfrac{1}{4}\right)^n\cdot(-4)=\dfrac{1}{1024}\\\\(4)\left(-\dfrac{1}{4}\right)^n=\dfrac{1}{1024}\qquad\text{divide both sides by 4}\ \text{/multiply both sides by}\ \dfrac{1}{4}/\\\\\left(-\dfrac{1}{4}\right)^n=\dfrac{1}{4096}\\\\\dfrac{(-1)^n}{4^n}=\dfrac{1}{4^6}\qquad n\ \text{must be even number. Therefore}\ (-1)^n=1[/tex]

[tex]\dfrac{1}{4^n}=\dfrac{1}{4^6}\iff n=6[/tex]

Answer: A. It would be shifted up.

Step-by-step explanation: the only thing that is changing in the two equations is the last number. The last number is not there in the second equation because the y-intercept is 0. The y-intercept in the first equation is -2 and shifts up 2 to y-intercept if 0. Therefore, your answer would be A. It would shift up.

The graph of the new equation compared with the original graph is the new graph would be shifted up.

Option A is the correct answer.

We have,

If the equation y = 12x - 2 were changed to y = 12x, the graph of the new function would be different from the original.

The original equation y = 12x - 2 represents a linear function with a slope of 12 and a y-intercept of -2.

The graph of this equation would be a straight line that is steep (with a slope of 12) and shifted downward by 2 units (due to the y-intercept of -2).

However, if we change the equation to y = 12x, the new equation represents a linear function with the same slope of 12 but with no y-intercept (it passes through the origin).

The graph of this equation would still be a straight line, but it would be shifted up compared to the original equation since the y-intercept has been removed.

Therefore,

It would be shifted up.

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[tex]\bf \textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=\stackrel{altitude}{height}\\ \cline{1-1} r=3\\ h=9 \end{cases}\implies V=\cfrac{\pi (3)^2(9)}{3}\implies V=27\pi \implies V\approx 84.8[/tex]

Answer:

A and D

Step-by-step explanation:

The remainder after division is 8, that is the 8 at the end of 2 - 4 8

Given f(x) divided by (x + h)

Then if (x + h) is a factor the remainder = 0

Hence (x + 7) is not a factor since remainder is 8

and f(- h) = remainder

that is f(- 7) = 8 → D

A and D are the correct statements.

In option  A f(-7) is the remainder which gives the value 8.

So, option A is correct.

When we put x = 7 in the function it is coming 99

So, option B and C are wrong.

So options D is correct

So, option E is wrong.

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