What is the measure of angle PSQ?

Final answer:

The roots of the equation 5x³ + 45x² + 70x = 0 are -7 and -2.

Explanation:

This expression is a quadratic equation of the form at² + bt + c = 0, where the constants are a = 5, b = 45, and c = 70. To find the roots of the equation, we can use the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

Plugging in the values, we get:

x = (-45 ± √(45² - 4(5)(70))) / (2(5))

Simplifying further gives us:

x = (-45 ± √(2025 - 1400)) / 10

And finally, calculating the square root and applying the ± gives us the two roots:

x = (-45 ± √625) / 10

x = (-45 ± 25) / 10

which can be further simplified to:

x = -7 or x = -2

Step 1

Find the slope of the line

Let

[tex]A(0,1)\\B(2,5)[/tex]

the slope is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

substitute

[tex]m=\frac{5-1}{2-0}[/tex]

[tex]m=\frac{4}{2}[/tex]

[tex]m=2[/tex]

Find the equation of the line

we know that

the equation of the line into slope-intercept form is

[tex]y=mx+b[/tex]

where

m is the slope

b is the y-intercept

in this problem we have

[tex]m=2[/tex]

[tex]b=1[/tex] ------> the y-intercept is the point A

substitute

[tex]y=2x+1[/tex]

Step 2

Find the equation of the inequality

we know that

the solution is the shaded area above the dotted line

so

above dotted line---------> represent the symbol ([tex]>[/tex])

the inequality is

[tex]y>2x+1[/tex]

therefore

the answer is

[tex]y>2x+1[/tex]

The correct option is [tex]\boxed{\bf option (c)}[/tex] i.e., [tex]\boxed{y>2x+1}[/tex].

Further explanation:

The linear equation of the line is [tex]y=mx+b[/tex] where, [tex]m[/tex] is the slope of the line and [tex]c[/tex] is the [tex]y[/tex]-intercept of the line.

Suppose the line passes through the two points [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex].

Therefore, the slope of the line can be calculated as follows:

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

The symbol [tex]>[/tex] represents the solution set lies above the dotted line and the symbol [tex]<[/tex] represents the solution set below the dotted line.

Given:

The linear inequalities are  given as follows:

[tex]\boxed{\begin{aligned}y&>2x+2\\ y&\geq x+1\\ y&>2x+1\\ y&\geq x+2\end{aligned}}[/tex]

Calculation:

First we will find the equation of the line.

The line cuts the [tex]y[/tex]-axis on the coordinate [tex](0,1)[/tex] as shown in the Figure 1 (attached in the end).

Therefore, the [tex]y[/tex]-intercept is [tex]1[/tex].

Kindly refer the Figure attached to the question.

From the figure 1 (attached in the end) we can see that the line passes through the points [tex](-2,-3)\text{ and }(1,3)[/tex].

The slope of the line can be calculated as follows:

[tex]\begin{aligned}m&=\dfrac{3-(-3)}{1-(-2)}\\&=\dfrac{6}{3}\\&=2\end{aligned}[/tex]    

Therefore, the value of [tex]m[/tex] is [tex]m=2[/tex] and the value of [tex]b[/tex] is [tex]b=1[/tex].

Substitute [tex]2[/tex] for [tex]m[/tex] and [tex]1[/tex] for [tex]b[/tex] in the equation of the line [tex]y=mx+b[/tex].

Second we will find the equation of the inequality.

The shaded region is shown in Figure 1 above the dotted line .  

Therefore, the solution set of the line lie above the dotted line and it will represented by the symbol [tex]>[/tex].

Thus, the inequality [tex]y>2x+1[/tex] satisfies the given graph.

Therefore, the correct option is [tex]\boxed{\bf option (c)}[/tex] i.e., [tex]\boxed{y>2x+1}[/tex].

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Answer details:

Grade: Middle school

Subject: Mathematics

Chapter: Linear inequalities

Keywords:  Linear equations, linear inequality, equation, line, slope, intercept, dotted line , coordinate, shaded region, solutions set, graph, curve.

The value of the derivatives is A'(12) = 24.

We have,

To find the derivative of the area function A(x) with respect to x, we can differentiate the equation for the area of a square:

A(x) = x^2

Using the power rule, we differentiate A(x) with respect to x:

A'(x) = 2x

To find A'(12), we substitute x = 12 into the derivative equation:

A'(12) = 2 * 12 = 24

Therefore,

The value of the derivatives is A'(12) = 24.

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Final answer:

To find A'(12), the rate at which the area A(x) changes when the side length x changes, take the derivative of A(x), which is 2x, and evaluate it at x = 12. The derivative of A(x) is 2x, so A'(12) = 2(12) = 24.

Explanation:

To find the rate at which the area A(x) changes with respect to a change in x, we need to take the derivative of A(x) with respect to x. In this case, A(x) represents the area of a square wafer of silicon with a side length x. The derivative with respect to x is A'(x), which represents the rate of change of the area.

We want to find A'(12), which means we want to find the rate of change of the area when the side length is 12 mm. To do this, we need to take the derivative of A(x) and then evaluate it at x = 12.

Since the side length of the wafer is very close to 12 mm, we can assume x = 12.

Let's find the derivative of A(x):

A(x) = x^2

A'(x) = 2x

Now we can evaluate A'(12):

A'(12) = 2(12) = 24

Answer:

6.5 km

Step-by-step explanation:

1:50,000

13 cm on a map, multiply both sides by 13 which leaves us with:

13:650,000

However, we need to calculate the distance in kilometers, not centimeters. To do that, we have to divide 650,000 by 100,000 which leaves us with 6.5 km

Final answer:

Norma can expect the spinner to land on section A 4 times after spinning it 16 times, based on the probability of [tex]\frac{1}{4}[/tex].

Explanation:

The question asks about the expected number of times Norma can anticipate the spinner to land on section A after spinning it 16 times, given that the probability of landing on A is [tex]\frac{1}{4}[/tex]. To find this, we use the concept of expected value, which in this context is the probability of an event happening multiplied by the number of trials. Since the probability of landing on A is [tex]\frac{1}{4}[/tex] and there are 16 spins, the expected number of times landing on A is calculated as [tex]\frac{1}{4}[/tex] multiplied by 16.

Expected number of landings on A = Probability of landing on A × Number of spins = [tex]\frac{1}{4}[/tex] × 16 = 4.

Therefore, Norma can expect the spinner to land on section A four times after spinning it 16 times.

Answer-

[tex]\boxed{\boxed{QR=12}}[/tex]

Solution-

Triangle Midpoint Theorem-

The line segment connecting the midpoints of two sides of a triangle is parallel to the third side and is congruent to one half of the third side.

As given in the question,

QV = SV, so V is the mid point of QS,

SU = RU, so R is the mid point of RS.

Hence, UV is the line joining the midpoints of QS and RS.

Applying Triangle Midpoint Theorem,

[tex]\Rightarrow UV=\dfrac{1}{2}QR[/tex]

[tex]\Rightarrow QR=2UV[/tex]

[tex]\Rightarrow QR=2\times 6[/tex]

[tex]\Rightarrow QR=12[/tex]

Therefore, the side length of QR is 12 units.

To solve for the measure of the central angle (x) in the arc length formula, rearrange the formula such that [tex]x = (L/2\pi r) * 360.[/tex] This method allows you to determine the degree measure of the arc once you know the arc length (L) and the radius (r) of the circle.

Given that the formula for finding the length of an arc in a circle is [tex]L=2\pi r(x/360)[/tex], you can solve for x if L and r are known. In this formula, r stands for the radius of the circle and x represents the measure of the central angle of the arc in degrees. So, to isolate x, you would need to rearrange the formula, giving us: [tex]x = (L/2\pi r) * 360.[/tex]

This effectively means that the degree measure of the arc (x) is equivalent to the ratio of the arc length to the circumference (which is 2πr) times 360 degrees.

For instance, let's consider a circle where r=5 and the arc length L has a value of 10 units. We would substitute these values into our newly rearranged formula thus: [tex]x = (10/2\pi *5) * 360 = 36[/tex] degrees. This tells us that the central angle for this particular arc on a circle with a radius of 5 units is 36 degrees.

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Apprentice will take [tex]1\frac{1}{2}[/tex] days  to finish the wall.

" Work is defined as when force is applied to move an object in the direction of displacement."

According to the question,

Number of days taken by Vella to build a brick = 4 days

Work done by Vella in 1 day = [tex]\frac{1}{4}[/tex]

Work done  by Vella in 3 days = [tex]\frac{3}{4}[/tex]

Number of days taken by apprentice to build same brick = 6 days

Total days taken by apprentice to complete 3/4 of work =  [tex]\frac{3}{4} of 6[/tex]

                                                     = [tex]\frac{3}{4}[/tex] × 6

                                                     =[tex]\frac{9}{2}[/tex]

                                                     = [tex]4\frac{1}{2}[/tex] days

Number of days apprentice take to finish the wall is = 6 - [tex]4\frac{1}{2}[/tex]

                                                                                       = [tex]1\frac{1}{2}[/tex]

Hence, apprentice will take [tex]1\frac{1}{2}[/tex] days  to finish the wall.

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To find two consecutive integers whose product is 5 less than the square of the smaller number, let the smaller number be x and use algebraic equations to solve for x.

To find two consecutive integers whose product is 5 less than the square of the smaller number, we can let the smaller number be x. The larger number would then be x + 1. The product of the two consecutive integers is x(x + 1) and the square of the smaller number is x^2. According to the problem, x(x + 1) = x^2 - 5. We can solve this equation to find the values of x and x + 1.

Expanding x(x + 1) gives us x^2 + x. So, the equation becomes x^2 + x = x^2 - 5. We can simplify this equation by canceling out x^2 on both sides, which leaves us with x = -5.

So the consecutive integers are -5 and -4.

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Answer:

Step-by-step explanation:

If all were chickens, there would be 26 legs. There are 14 legs more than that. Each pig contributes 2 additional legs, so there must be 14/2 = 7 pigs. The remaining 6 animals are chickens.

___

Check

7×4 + 6×2 = 28 +12 = 40 . . . . total legs

Answer:

easy! 27

Step-by-step explanation:

13- 40 = 27

or 13 + 27 =40

just add up 13 and 27 you'll get 40 in all

edit; btw I'm not the brightest

Answer:

Option C is the answer.

Step-by-step explanation:

Option A. [tex]y=\sqrt{x-5}+3[/tex]

For domain of this function

(x - 5) ≥ 0

x ≥ 5

For range of the function

for every value of x ≥ 0

y ≥ 3

Opttion B. [tex]y=\sqrt{x+5}-3[/tex]

For Domain

(x + 5) ≥ 0

x ≥ (-5)

and for every value of x ≥ (-5) range of the function will be

y ≥ (-3)

Option C.

y = -√(x -5) + 3

For domain

x - 5 ≥ 0

x ≥ 5

For range

y ≤ 3

Option D. [tex]y=-\sqrt{x+5}-3[/tex]

For domain (x + 5) ≥ 0

x ≥ -5

For range

y ≤ (-3)

Therefore option C will be the answer.

According to the Five-pan strategy ,

For given problem :

Step 1. 48 pounds of sand are used to fill 12 bags.

To find : how many pounds of sand should she find each bag will hold?

Step 2. We need to divide the total amount of sand require to fill 12 bags by 12.

Step 3. Amount of sand require to fill one bag = (amount of sand require to fill 12 bags) ÷ 12

= (48) ÷ 12

= 4 pounds

Step 4. Checking our answer as

Amount of sand require to fill 12 bags = 12 x (Amount of sand require to fill one bag)

= 12 x 4 = 48 pounds which is given, thus our answer is correct.

Step 5. She should fill 4 pounds of sand in each bag.

The required months are x = 0.60 months where at the cost become same.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,

Here,
Let the total cost be y and the month be x
Apartment A has a $1000 security deposit and costs $1200 each month.
y = 1200x +1000 - - - - - (1)
Apartment B has $1500 and costs $1175 each month.
y = 1175x + 1500
From equation 1
1200x + 1000 = 1175x + 1500

1200x - 1175x = 500
825x = 500
x = 500 / 825
x = 0.60 months,
y = 1200*0.60 + 1000
y = 1,720

Thus, the required months are x = 0.60 months where the cost becomes the same.

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An open sentence is a mathematical sentence that has an unknown.

The solution set for t is (a) Null set

The equation is given as:

[tex]\mathbf{2t - t = 0}[/tex]

The set is given as:

[tex]\mathbf{\{1,2,3,4\}}[/tex]

First, we solve for t in: [tex]\mathbf{2t - t = 0}[/tex]

[tex]\mathbf{t = 0}[/tex]

The above equation implies that, the value of t is 0

0 is not represented in the given set, [tex]\mathbf{\{1,2,3,4\}}[/tex]

Hence, the solution set for t is (a) Null set

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Answer:

Fourth-degree trinomial  

Step-by-step explanation:

9x^4 – 3x + 4 is a trinomial expression because it has three parts: 9x^4, –3x and 4, and is a fourth-degree expression because four is the highest exponent applied to the variable x (the other exponents are one and zero).