What are the steps for using a compass and straightedge to construct the bisector of ∠G? Two rays share a common endpoint labeled G, forming an obtuse angle. One ray is horizontal and points right. The second ray is inclined to horizontal in upward-left direction. Drag the steps and drop them in order from start to finish. Without changing the opening of the compass, place the point of the compass on point J and draw another arc in the interior of the angle.Use the straightedge to draw GK−→−.Place the point of the compass on point H and draw an arc in the interior of the angle.Label the intersection of the arcs in the interior of the angle as point K.Place the point of the compass on point G and draw an arc that intersects the sides of ∠G. Label the points of intersection as points H and J.

the answer is -4

hope it helpsss

5^-4 is 5 to power of negative 4

Answer:

4.038 < 4.08 < 4.3 < 4.803

Step-by-step explanation:

We are given four decimal numbers and we have to arrange them in increasing order:

The numbers are 4.08, 4.3, 4.803, 4.038

The expanded form of these decimal numbers are:

[tex]4.08 = 4 + \displaystyle\frac{8}{100}[/tex]

[tex]4.3 = 4 + \displaystyle\frac{3}{10}[/tex]

[tex]4.803 = 4 + \displaystyle\frac{8}{10} + \displaystyle\frac{3}{1000}[/tex]

[tex]4.038 = 4 + \displaystyle\frac{3}{100} + \displaystyle\frac{8}{1000}[/tex]

Thus, the increasing order is:

4.038 < 4.08 < 4.3 < 4.803

Answer:

30 workers are required.

Step-by-step explanation:

If the site measured 30 acres and was completed in 10 days, then it can be said that on average [tex]\frac{30}{10} = 3\frac{acres}{day}[/tex] were made.

Then, 24 workers completed 3 acres / day.

Then, [tex]\frac{24.workers}{\frac{3acres}{day}} = \frac{8..Workers * days}{acre}[/tex]

8 workers can complete 1 acre per day

Now to know how many workers are needed to complete 45 acres in 12 days, we multiply:

[tex]8\frac{Workers * days}{acre}*\frac{45}{12} \frac{acres}{days} = 30.workers[/tex].

Finally, 30 workers are required.

To solve this problem it was assumed that everyone worked at the same pace, which may not be true, the fact that some work at a slower or faster pace than another could alter the result, causing them to finish less or more acres by day.

It’s the product of three and nine.

the solution of the equation x²+27 = 0 is 3√3 i

What are real and imaginary roots ?

A real root to an equation is a real number. A complex root to an equation is an imaginary root represented as complex numbers.

In other words real roots can be represented in a number line where as imaginary roots can not.

In order to determine the simplification, we have to know the rule of the imaginary numbers.

The imaginary numbers are the same than real numbers, but they add just one term more, which is :

√-1 = i

So, to implicate this term, we have to use the rules of the roots:

given equation is :

x²+27 = 0

solving for x by Subtracting 27 from both sides

x²+27 -27 = -27

x² = -27

To remove square root , take square root on both sides

√x² = √-27

x = √-27

The value of √-1 is 'i' therefore,

x = i√27

x =3√3 i

Therefore, The solution of the equation x²+27 = 0 is 3√3 i

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The quadratic function is given by the equation [tex]h(t)=-0.075t^2+0.6t+2.5.[/tex]

The maximal height will be at vertex. Find t-coordinate of the parabola vertex:

[tex]t_{vertex}=-\dfrac{b}{2a}=-\dfrac{0.6}{2\cdot (-0.075)}=4\text{ seconds.}[/tex]

At t=4,

[tex]h(4)=-0.075\cdot 4^2+0.6\cdot 4+2.5=-1.2+2.4+2.5=3.7\text { feet. }[/tex]

Answer: it will take 4 seconds for the ball to reach the maximal height of 3.7 feet.

Answer:

D

Step-by-step explanation:

The longest side is twice as long as the shortest side because lets suppose I have a triangle that has vertices with angles 30 and 60, the last one has to be 90 because the total is 180 degrees. Now for a 30 60 triangle, if the hypotenuse has a length of 2, the following ratios will hold true for the other two sides. The side that shares the 90 degrees and 60 degrees corners will be of length 1 and the side that shares the 30 degrees and 90 degrees corners (vertices) will be of length sqrt(3). This is true all the time. In this case the correct answer is that the longest side is twice as long as the shortest side because the longest side is the hypotenuse with length 2 and the shortest side will be the one that shares the 90 degrees and 60 degrees corners and is of length 1.

Answer:

A

Step-by-step explanation:

The slope-intercept form:

[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]

We have the points (-1, 1) and (2, 13). Substitute:

[tex]m=\dfrac{13-1}{2-(-1)}=\dfrac{12}{3}=4[/tex]

Therefore the equation of a line is

[tex]y=4x+b[/tex]

Put the coordinates of the point (2, 13) to the equation of a line:

[tex]13=4(2)+b[/tex]

[tex]13=8+b[/tex]     subtract 8 from both sides

[tex]5=b\to b=5[/tex]

Final answer:

To estimate the division of 771 by 3.6, round 3.6 to 4 and divide 771 by 4 to get an approximate result of 192.75.

Explanation:

To estimate 771 divided by 3.6, we can round 3.6 to the nearest whole number, which is 4. The estimation calculation would then be 771 ÷ 4. Dividing 771 by 4 can be done by breaking down 771 into 760 + 11. Now, 760 ÷ 4 equals 190, and 11 ÷ 4 is approximately 2.75. Adding these two results, we get an estimated total of 192.75. Therefore, the estimated result of 771 ÷ 3.6 is approximately 192.75.

Answer: 40 cups

If you have 2.5 gallons and need to convert it to cups, you first need to know how these two units of liquid volume compare to each other in size.

There are 16 customary cups in one gallon. To find how many cups are in 2.5 gallons, you'd multiply 2.5 (the number of gallons you have) by 16 (the number of cups in one gallon).

2.5 x 16 equals 40. This tells you that 2.5 gallons is equivalent to 40 cups

Question: If one gallon is the same amount as 16 cups, how many cups equal 2.5 gallons? (Only input whole numbers.)

Explantion: 16(number of cups per gallon)×2.5(amount of gallons)

The equation would be [tex]16*2.5[/tex] and that equals 40.

Answer: 40 cups

ANSWER TO QUESTION 1

Check attachment for long division.

From our long division we can write the following;

[tex]\frac{8x^4-6x^3+7x^2-11x+10}{2x-1} =4x^3-x^2+3x-4+\frac{6}{2x-1}[/tex]

Since the polynomial

[tex]8x^4-6x^3+7x^2-11x+10[/tex] leaves a non zero  remainder of [tex]6[/tex] when divided by [tex]2x-1[/tex], we conclude that [tex]2x-1[/tex] not a factor of the dividend,

ANSWER TO QUESTION 2

We want to factor

[tex]f(x)=x^4+x^3-8x^2+6x+36[/tex]

The possible rational roots are;

[tex]\pm1, \pm 2,\pm 3, \pm 4,\pm 6,\pm 9, \pm18, \pm 36[/tex]

We found

[tex]f(-2)=(-2)^4+(-2)^3-8(-2)^2+6(-2)+36[/tex]

[tex]f(-2)=16+-8-32+-12+36[/tex]

[tex]f(-2)=-36+36[/tex]

[tex]f(-2)=0[/tex]

and

[tex]f(-3)=(-3)^4+(-3)^3-8(-3)^2+6(-3)+36[/tex]

[tex]f(-3)=81-27-72-18+36[/tex]

[tex]f(-3)=-36+36[/tex]

[tex]f(-3)=0[/tex].

This means that [tex](x+2)[/tex] and [tex](x+3)[/tex] are factors of the polynomial.

This also means that

[tex](x+2)(x+3)=x^2+5x+6[/tex] is also a factor of the polynomial

So we apply long division to obtain the remaining factors as shown in the attachment.

[tex]\Rightarrow f(x)=x^4+x^3-8x^2+6x+36=(x+2)(x+3)(x^2-4x+6)[/tex]

We factor further to obtain;

[tex]\Rightarrow f(x)=x^4+x^3-8x^2+6x+36=(x+2)(x+3)(x-(2-\sqrt{2}i))(x-(2+\sqrt{2}i))[/tex]

The answer of this expression is - 4 1/6

22a. False

22b. True

22c. True

22d. False

For each scenario, we multiply Rachel's daily earnings ($21) by the number of days worked to find her total earnings.

In 22a, Rachel earns 21 × 20 = $420, not $421 as stated.

In 22b, Rachel indeed earns 21 × 15 = $315, making the statement true.

Similarly, in 22c, Rachel earns 21 × 13 = $273, confirming the statement as true.

However, in 22d, Rachel's earnings for 13 days amount to 21 × 13 = $273, not $250, rendering the statement false.

Therefore, the true statements are 22b and 22c, while 22a and 22d are false.

Complete Question:

The answer would be -5 because:

-6-(-1)

Keep Change Flip

-6 + 1

Different signs Subtract..so the answer would be 5 but then you add the negative to it because -6 is greater than the positive 1

Given dimensions of a rectangular garden are:

length = 2(x+6) feet

width = 3.5x feet

using the distributive property on length we get, length = 2x+12

Perimeter of a rectangle is 2(length+width)

So, P = 2(2x+12+3.5x)

Solving it we get,

P = 2(5.5x +12)   ..............adding like terms

P = [tex](2\times5.5)+(2\times12)[/tex] .............multiplying and adding

P = 11x+24

So, perimeter is 11x+24 feet. This value of fencing will be needed.

Answer:

C. [tex]2\times 10^7[/tex] is 5 times larger than [tex]4\times 10^6[/tex]

Step-by-step explanation:

We want to compare [tex]4\times 10^6[/tex] and [tex]2\times 10^7[/tex].

In order to determine how many times

[tex]2\times 10^7[/tex]

is larger than

[tex]4\times 10^6[/tex],

we need to divide [tex]2\times 10^7[/tex] by  [tex]4\times 10^6[/tex] to obtain;

[tex]\frac{2\times 10^7}{4\times 10^6} =\frac{10}{2} =5[/tex]

Therefore we can see that;

[tex]2\times 10^7[/tex] is 5 times larger than [tex]4\times 10^6[/tex]

The correct answer is C.

Answer:  C. -20

Hope this helps!!  Please mark me brainliest??

This is actually quite easy.  

Britt=4c+12 because 4 boxes and 12 extra

Jim=3c+5 because 3 boxes and 5 extra

Final answer:

The total number of CDs that Britt and Jim have is represented by the expression 7c + 17, where c is the number of CDs in each full box.

Explanation:

The total number of CDs that Britt and Jim have can be expressed using the variable c, which represents the number of CDs in each full box. Britt has 4 full boxes and 12 extra CDs, so her total is given by the expression 4c + 12. Jim has 3 full boxes plus 5 extra CDs, so his total is 3c + 5. To find the combined total number of CDs for both Britt and Jim, we add their individual totals:

Total CDs = Britt's CDs + Jim's CDs

Total CDs = (4c + 12) + (3c + 5)

By combining like terms, we get:

Total CDs = 7c + 17

This expression represents the total number of CDs that Britt and Jim have together in terms of c, the number of CDs per box.

Answer: The perimeter is 17.52

Step-by-step explanation:

1. You can plot the points, as you can see in the graph attached.

2. As you can see in the graph, the points are:

[tex]A(-2,-2)\\B(-2,3)\\C(2,4)\\D(3,1)\\E(0,-2)[/tex]

And the lenghts AB and EA are:

[tex]AB=5[/tex]

[tex]EA=2[/tex]

3. To find the other lenghts, you can apply the formula for calculate the distance between two points:

[tex]distance=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}[/tex]

4. Thefore, you have:

[tex]BC=\sqrt{(2-(-2))^{2}+(4-3)^{2}}=4.12\\CD=\sqrt{(2-3)^{2}+(4-1)^{2}}=3.16\\DE=\sqrt{(3-0)^{2}+(1-(-2))^{2}}=4.24[/tex]

5. The perimeter is:

[tex]P=AB+CD+DE+EA\\P=5+4.12+3.16+4.24+2\\P=17.52[/tex]

The perimeter of the polygon is 18.64 units.

To find the perimeter of a polygon, we need to sum the lengths of all its sides. Let's calculate the distance between each consecutive pair of vertices and add them up.

The distance between (-2, -2) and (-2, 3) is 5 units.

The distance between (-2, 3) and (2, 4) is 4.24 units (rounded to the nearest tenth).

The distance between (2, 4) and (3, 1) is 3.16 units (rounded to the nearest tenth).

The distance between (3, 1) and (0, -2) is 4.24 units (rounded to the nearest tenth).

The distance between (0, -2) and (-2, -2) is 2 units.

Adding up these distances, the perimeter of the polygon is 5 + 4.24 + 3.16 + 4.24 + 2 = 18.64 units (rounded to the nearest tenth).

no it would not be congruent

Hello!

No, these shapes would not be considered congruent. In geometry, figures would only be congruent if they have the same size and shape. In the above image, the two figures have the same shapes, but they do not have the same size.

4x - 2x + 8 = 6(x + 4)   Given

(4x - 2x) + 8 = 6(x + 4)

2x + 8 = 6(x + 4)     Combine like terms

2x + 8 = (6)(x) + (6)(4)

2x + 8 = 6x + 24    Distributive Property

2x - 6x + 8 = 6x - 6x + 24

-4x + 8 = 24      Subtraction Property of Equality

-4x + 8 - 8 = 24 - 8

-4x = 16    Subtraction Property of Equality

-4x : (-4) = 16 : (-4)

x = -4       Division Property of Equality

On the number line, smaller numbers are located to the left of larger numbers, which are located on the right.

So, if you have two numbers x and y on the number line, the smaller of the two will be on the left, the larger one on the right.

So, -13 is located to the right of -15, because it's larger.

For the same reason, -11 is located to the right of -13.

On the number line, you would have something like

<--------(-15)-------(-13)--------(-11)---------->

On a number line, negative values decreases as we move to the left while positive values increases to the right. Hence,

Starting from 0 to the left, we have - 1, - 2, - 3,... which continues in that sequence as decreases as we move to the left of the number line.

Moving towards the left, - 13 appears before - 15 ; Hence - 13 is located relative to the right of - 15 on the number line

Similary, - 11 appears before - 13 ; Hence - 11 is located relative to the right of - 13 on the number line.

Therefore, - 13 and - 11 are located to the right of - 15 and - 13 respectively on the number line.

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12*7 = 84

84 Pumpkin Plants

Answer: Independent variable

Step-by-step explanation:

The variable usually on the x-axis, which is used to predict y-values, is called the Independent variable.

Discussion:

In most mathematical relations including linear programming problems; we usually have a combination of two variables namely;

The variable whose value determines the value of other variables is termed the independent variable and is usually plotted on the x-axis.

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Im pretty sure its y = 3x - 17

Answer:

- 28 - 40i

note that i² = (√-1)² = - 1

expand product of factors using FOIL

= - 6 - 6i - 14i - 14i² - 20i + 36i²

= - 6 - 6i - 14i + 14 - 20i - 36

= - 28 - 40i

Step-by-step explanation:

Got right on PLATO

The solution to the complex expression (3+7i) (-2-2i) -4i(5-9i) is -28 - 40i

A complex number is a number of the form a + bi, where a and b are real numbers, and i = √-1

i² = (√-1)² = -1

Given the expression:

(3+7i) (-2-2i) -4i(5-9i)

= -6 - 14i -6i + 14 - 4i(5 - 9i)

= 8 - 20i - 20i - 36

= -28 - 40i

The solution to the complex expression (3+7i) (-2-2i) -4i(5-9i) is -28 - 40i

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Answer:

Option B is the correct choice.

Step-by-step explanation:

Since we know that polynomials are closed under addition, subtraction and multiplication but not under division because division of two polynomials is not necessarily a polynomial.

Dividing a binomial by a trinomial will result in a rational expression and it will have negative exponent. Negative exponents are not allowed in polynomials.

Therefore, option B is the correct choice.  

Assuming that the inequality you were going for was a ≤, set both polynomials less than or equal to 0.

x - 3 ≤ 0

x + 5 ≤ 0

For the first equation add 3 to both sides of the inequality. For the second, subtract 5 from both sides.

x ≤ 3

x ≤ - 5

These would be your solutions I guess, however, if you want to expand upon that, your actual answer is (- ∞, - 5] because if you were to plot these two inequalities on a number line, that is where the overlap would occur.

12 links long because 5 + 7 = 12