Indicate the equation of the given line in standard form. The line containing the longer diagonal of a quadrilateral whose vertices are A (2, 2), B(-2, -2), C(1, -1), and D(6, 4).

Answer:

Number of Black grapes = 32

Step-by-step explanation:

This is a problem related to ratio and proportion. We are given the number of Green Grapes and the ration of Green Grapes to the Black Grapes

The ratio is 3:4

This means

[tex]\frac{G_g}{G_b} = \frac{3}{4}[/tex]

Now assume that the number of Black Grapes = x

Given that [tex]G_g[/tex]=24

Substituting these values in [tex]\frac{G_g}{G_b} = \frac{3}{4}[/tex]

[tex]\frac{24}{x} = \frac{3}{4}[/tex]

[tex]24*4 = 3*x\\x=\frac{24*4}{3}\\x=\frac{8*4}{1}\\x=32[/tex]

Hence the number of Black Grapes are 32

Answer:

32

Step-by-step explanation:

If 3:4 then 24:x (x represent the unknown)

So you have to divide 24 by 3 and the answer you get, which is 8, you multiply with four to get 32.

So we can say that both types of grapes are 8 times the amount that they originally were.

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]

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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ANSWER

Last option

EXPLANATION

The given equation is

[tex]4 {x}^{5} - 12 {x}^{4} + 6x = 5 {x}^{3} - 2x[/tex]

We can form a system of equations by equating each side of the equation to y.

Equating the left hand side to y, we get

[tex]y = 4 {x}^{5} - 12 {x}^{4} + 6x...(1)[/tex]

Equating the right hand side to y gives

[tex]y= 5 {x}^{3} - 2x...(2)[/tex]To find the solution to

[tex]4 {x}^{5} - 12 {x}^{4} + 6x = 5 {x}^{3} - 2x[/tex]

We graph the two equations and locate the x-values of their points of intersection.

The last option is the correct answer

Answer:

D

Step-by-step explanation:

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:

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:

A

Step-by-step explanation:

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

Answer:

25 percent.

Step-by-step explanation:

1,000 would be 20% of 5,000

250 is 5% of 5,000

20+5=25

25% of Emma's monthly income goes towards rent.

To calculate the percentage of Emma's monthly pay that goes towards rent, we need to divide the amount spent on rent by the total monthly income, and then multiply that result by 100 to convert it to a percentage.

Emma spends $1,250 a month on rent and earns $5,000 per month. The calculation is as follows:

Divide the monthly rent by the monthly income: $1,250 / $5,000 = 0.25.

Convert the decimal to a percentage: 0.25 * 100 = 25%.

Therefore, 25% of Emma's monthly income goes towards rent.

[tex]\bf 3x+y=15\implies y=-3x+15\impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{perpendicular lines have \underline{negative reciprocal} slopes}} {\stackrel{slope}{-3\implies -\cfrac{3}{1}}\qquad \qquad \qquad \stackrel{reciprocal}{-\cfrac{1}{3}}\qquad \stackrel{negative~reciprocal}{\cfrac{1}{3}}}[/tex]

A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The slope of a line perpendicular to 3x + y =15 is 1/3. Thus, the correct option is C.

A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of a line is given by,

y =mx + c

where,

x is the coordinate of the x-axis,

y is the coordinate of the y-axis,

m is the slope of the line, and

c is the y-intercept.

In the given equation 3x + y =15, the slope of the line will be,

3x + y = 15

y = 15 - 3x

y = -3x + 15

Thus, the slope of the equation is -3.

Now, the product of the slope of two perpendicular lines is always equal to -1. Therefore, the product can be written as,

-3 × m = -1

m = -1/-3

m = 1/3

Hence, the slope of a line perpendicular to 3x + y =15 is 1/3. Thus, the correct option is C.

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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

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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ANSWER

x=-2

EXPLANATION

The given polynomial function is:

[tex]f(x) = {(x - 5)}^{3} {(x + 2)}^{2} [/tex]

The polynomial has two factors, one with an odd multiplicity which is

[tex] {(x - 5)}^{3} [/tex]

and the other with an even multiplicity which is

[tex] {(x + 2)}^{2} [/tex]

The graph does not cross the x-axis at where the multiplicity is even.

Therefore the graph touches the x-axis at

[tex]x = - 2[/tex]

We got this by solving

[tex]{(x + 2)}^{2} = 0[/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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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:

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:

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

Answer:

Another point is (3,1) and the vertex is (0,0)

Step-by-step explanation:

The vertex is still (0,0) since the parabola has only been stretched some way and not shifted from the parent function f(x)=x^2.

Enter in any x you like like 3 (I chose 3 because I see I'm going to multiply by 1/3). Anyways

g(3)=(1/3*3)^2=(1)^2=1  so another point on the parabola is (3,1)... Now just use the fact that all parabolas are symmetrical to graph it.

Answer:

f(x) = 10² + 3 = 100 + 3 = 103

Final answer:

Without a specific definition of ƒ(x), we can't provide a precise evaluation at x = 10. However, if ƒ(x) is a constant function such as ƒ(x) = 20 for the range of 0 to 20, then ƒ(10) would be 20.

Explanation:

To evaluate the function ƒ(x) when x = 10, we need to know the specific form of the function. However, based on the information provided, which seems fragmented and from different contexts, I can assume that ƒ(x) is defined for certain ranges. There’s reference to a horizontal line graph representation of a function, which suggests that ƒ(x) could potentially be a constant function within a certain range. If the function ƒ(x) is indeed a constant function, such as ƒ(x) = 20 for 0 ≤ x ≤ 20, then evaluating it at x = 10 would simply give the constant value, which is 20.

From the other contexts provided, it's implied that there could be scenarios where ƒ(x) represents different mathematical or physics concepts, such as force, probability distribution, or equations of motion. Without a direct specification of ƒ(x) for the x value in question, the remaining information cannot be used to definitively evaluate ƒ(x) at x = 10.

[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:

100

Step-by-step explanation:

When being asked what is x% more than y (y is something), you can use the formula 25% * y + y. However, you must convert the percent into a decimal for it to be used mathematically.

25% = 0.25

Now we can plug all of the numbers in.

0.25 * 80 + 80

20 + 80

100

[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:

[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]

this is what the graph look like

ANSWER

See attachment.

EXPLANATION

The given function is

[tex]f(x) = {x}^{3} + {x}^{2} + 4[/tex]

The degree of this function is odd and the leading coefficient is positive.

The graph of this function rises on the left and keeps rising on the right.

The y-intercept of this graph is 4.

The graph intersects the y-axis at 4.

The graph of this function is the one shown in the attachment.

Answer:

48

Step-by-step explanation:

Multiply 16 and 3 together! This isn't usually the case but for this question it is. Hope this helps and have a nice day!

Answer:

48

explanation:

prime factorisation of 16 and 3.

[tex]16 = 2 \times 2 \times 2 \times 2 = {2}^{4} [/tex]

[tex]3 = 1 \times 3[/tex]

taking the greatest power from both the equation for multiplication

[tex]2 \times 2 \times 2 \times 2 \times 3 = 48[/tex]

hence the L.C.M of 16 and 3 is "48"

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.

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

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