Find the value of k so that the equation has the solution set {-3}

3(2x-1) = x(2-k)

Solve ( x – 3)( x + 2) > 0.

Solve ( x – 3)( x + 2) = 0. By the zero product property, 

Make the boundary points. Here, the boundary points are open circles because the original inequality does not include equality (see Figure 1).

Select points from the different regions created (see Figure 2).

See whether the test points satisfy the original inequality.

Since x = –3 satisfies the original inequality, the region x < –2 is part of the solution. Since x = 0 does not satisfy the original inequality, the region –2 < x < 3 is not part of the solution. Since x = 4 satisfies the original inequality, the region x > 3 is part of the solution.

Represent the solution in graphic form and in solution set form. The graphic form is shown in Figure 3.

The solution set form is { x| x < –2 or x > 3}.

6/3 =2

15/3 =5

6/15 = 2/5

8/4 =2

20/4 =5

8/20 = 2/5

answer is B 2/5

Answer:

15 baskets

Step-by-step explanation:

In order to solve this question, first we need to know the amount of hours that Nim was able to work.

If Nim worked Monday through Friday, 8 hours a day, then:

Monday to Friday = 5 days

1 day = 8 hours

5 days * 8 hours = 40 hours

Out of these forty hours, Nim needs 2 2/3 hours to weave a basket. Therefore:

40 / (2 2/3) =

40 / (8 /3) =

40 * 3/8 =

120/8 = 15

Answer:

D

Step-by-step explanation:

Quadrilateral ABCD is inscribed in a circle. Let the measure of arc BAD be a°. Arcs BCD and BAD form a circle  and a circle measures 360°, then  measure of arc BCD is 360°-a°.

The inscribed angle theorem states that an angle  inscribed in a circle is half of the central angle  that subtends the same arc on the circle.

Because of the Inscribed angle theorem,

[tex]m\angle A=\dfrac{a^{\circ}}{2};[/tex]

[tex]m\angle C=\dfrac{360^{\circ}-a^{\circ}}{2}.[/tex]

The sum of the measures of angles A and C is

[tex]\dfrac{a^{\circ}}{2}+\dfrac{360^{\circ}-a^{\circ}}{2}=180^{\circ}.[/tex]

Therefore, angles A and C are supplementary, because their measures add up to 180°.

Angles B and D are supplementary, because the sum of the measures of the angles in a quadrilateral is 360°.

m∠A + m∠C + m∠B + m∠D = 360°,

and using substitution,

180° + m∠B + m∠D = 360°, so m∠B + m∠D = 180°.

Answer: inscribed angle theorem

Answer:A

Step-by-step explanation:

Inscribed angle

Power is the result of multiplying two numbers together. The solution of the x²=144 is ±12. The correct option is C.

Power is the result of multiplying two numbers together such that both numbers are equal to each other. Power is typically expressed by a base number and an exponent. The base number indicates the number being multiplied. The exponent, which is a little number printed above and to the right of the base number, indicates the number of times the base number is multiplied.

The solution of the given expression can be written as,

x² = 144

x² = 12×12  or -12×-12

x = √(12×12)  or √(-12×-12)

x = 12 or -12

x = ±12

Thus, the solution of the x²=144 is ±12. This is because the multiplication of two positive numbers is positive, also, the sum of the two negative numbers is positive.

Hence, the solution of the x²=144 is ±12

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Answer:

45

Step-by-step explanation:

I can confirm, the first guy is right (I did the test)

What is the question? If you are only trying to expand the expression then the answer would be:

1/4 (5y-3)+ 1/16 (12y+17)

(5y/4) – (3/4) + (12y/16) + (17/16)

1.25y – 0.75 + 0.75y + 1.0625

2y + 0.3125

If you are trying to find for y, then you forgot to equate it to 0, that is:

2y + 0.3125 = 0

2y = -0.3125

y = 0.15625

Final answer:

To rewrite 56 + 32 as the product of the GCF and a sum, calculate the GCF, which is 8. Then, express the sum as 8 times the sum of the numbers obtained by dividing 56 and 32 with the GCF. The rewritten expression is 8 × 11.

Explanation:

To rewrite the expression 56 + 32 as the product of their greatest common factor (GCF) and a sum, we first need to find the GCF of 56 and 32. The factors of 56 are 1, 2, 4, 7, 8, 14, 28, and 56. The factors of 32 are 1, 2, 4, 8, 16, and 32. The common factors are 1, 2, 4, and 8. The largest common factor is 8, which is the GCF.

Next, we divide both 56 and 32 by the GCF to find the other factor:

56 ÷ 8 = 7

32 ÷ 8 = 4

Now, we represent the original sum as the product of the GCF and the sum of the results from the division:

56 + 32 = 8 × (7 + 4)

When we simplify the sum inside the parentheses, we get:

8 × 11

Therefore, the expression rewritten as the product of the GCF and a sum is 8 × 11.

Answer:

(B)

Step-by-step explanation:

From the given figure, we can see that the opposite sides of the given quadrilateral are congruent but they do not meet at right angles because there is no right angle marked on the given figure, thus the given quadrilateral cannot be rectangle (by the definition).

Therefore,  No, it is not a rectangle because the sides of the parallelogram do not meet at right angles.

Also, only one diagonal of measure 28 is given, no other diagonal is given, thus rest of the options do not hold.

Slope is Undefined because it's just a vertical line and it's not angled...

R is the midpoint of QS, if QR=2x and RS=x+3, then, the value of RS is:

RS is 6 units.

Here, we have that, R is the midpoint of QS, if QR=2x and RS=x+3.

Since R is the midpoint of QS, we know that QR is equal to RS.

Given that,

QR = 2x, and RS = x + 3,

we can set them equal to each other:

2x = x + 3

Now, let's solve for x:

2x - x = 3

x = 3

Now that we have the value of x, we can find RS:

RS = x + 3

RS = 3 + 3

RS = 6

So, RS is 6 units.

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It will indeed take Bill 1.5 hours to finish the remaining [tex]\( \frac{3}{16} \)[/tex] signs.

Work done by Bill, Bob, and Barry collectively take the working efficiency in a defined time interval.

Barry's work in 3 hours:

[tex]\(3 \times \frac{1}{6} = \frac{3}{6} = \frac{1}{2} \text{ sign}\)[/tex]

Bob's work in 3.5 hours:

[tex]\(3.5 \times \frac{1}{4} = \frac{7}{8} \text{ sign}\)[/tex]

Bill's work for the same time until Bob leaves (3.5 hours):

[tex]\(3.5 \times \frac{1}{8} = \frac{3.5}{8} = \frac{7}{16} \text{ sign}\)[/tex]

Total work done by all three in the first 3.5 hours:

[tex]\[ = \frac{1}{2} + \frac{7}{8} + \frac{7}{16}\\= \frac{8}{16} + \frac{14}{16} + \frac{7}{16} \\= \frac{29}{16} \text{ signs} \][/tex]

Remaining work to be done:

[tex]\[ = 2 - \frac{29}{16} \\= \frac{32}{16} - \frac{29}{16} = \frac{3}{16} \text{ signs} \][/tex]

Time for Bill to complete remaining work:

Bill’s rate: [tex]\( \frac{1}{8} \text{ signs per hour}\)[/tex]

Time to paint [tex]\( \frac{3}{16} \text{ signs}\):[/tex]

[tex]\[ =\frac{\frac{3}{16}}{\frac{1}{8}} \\= \frac{3}{16} \times 8 = \frac{24}{16} = 1.5 \text{ hours} \][/tex]

Thus, It will indeed take Bill 1.5 hours to finish the remaining [tex]\( \frac{3}{16} \)[/tex] signs. This confirms that the correct answer is 1.5 hours.

The answers are PT−→−  and PY−→−