What is an equation for the line that passes through (-2,-3) with a slope of -1/2?
A) 4y+2x=7
B) 4y-2x=-12
C) 4y+2x=-16
D) 5y-4x=12

Answer:

f(-10) = -19

f(2) = 4

f(-5) = -9

f(-1) = 1

f(8) = -5

Step-by-step explanation:

This is relatively simple if you understand the concept. All you have to do is take each number and then look at each inequality to see where it fits.

For example, if you take 2 and look at the first inequality, you see that 2 is not less than or equal to 5. Now if you look at the second inequality, you see that 2 is both greater than -5 and less than 5. Since 2 fits in the second inequality, you plug it into the second equation.

These functions where you have to see where the x-value fits are called piecewise functions and you will see them a lot in higher level math.

(disclaimer: I evaluated the numbers quickly, so I would doublecheck it, but I am pretty sure I didn't mess up)

Answer:

f(-10) = -19

f(2) = 4

f(-5) = -9

f(-1) = 1

f(8) = -5

Step-by-step explanation:

The domain for x is all real numbers (without restrictions). For instance, if f(x) = x^2, on -5 < x < 5, on negative x, you must use f(x) = (-1)^2 to get 1.

If x is >= 5, then the range is 3 - x, so f(x) = 3 - x, if x >= 5.

If x is <= -5, then the range is 2x + 1, so f(x) = 2x + 1, if x <= -5.

Answer:   [tex]\bold{\dfrac{-5\pm 2\sqrt{10}}{3}}[/tex]

Step-by-step explanation:

[tex]5-10x-3x^2=0\quad \rightarrow \quad a=-3,\ b=-10,\ c=5\\\\\\\text{Quadratic formula is: }x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}\\\\\\x=\dfrac{-(-10)\pm \sqrt{(-10)^2-4(-3)(5)}}{2(-3)}\\\\\\.\ =\dfrac{10\pm \sqrt{100+60}}{2(-3)}\\\\\\.\ =\dfrac{10\pm \sqrt{160}}{2(-3)}\\\\\\.\ =\dfrac{10\pm 4\sqrt{10}}{2(-3)}\\\\\\.\ =\dfrac{-5\pm 2\sqrt{10}}{3}[/tex]

The central angle is described by angle AOC

What is the central angle?

A central angle is an angle formed by two radii (lines from the center of a circle) that intersect at a point on the circle's circumference.

It is called "central" because it originates from the center of the circle.

In this case, the radii are AO and CO

Central angles are essential in geometry

Answer:

Step-by-step explanation:

DG=x+20

DG=2x+17+8+2

x+20=2x+27

20=x+27

-7=x

DG=13

Answer:

DG = 20

Step-by-step explanation:

We are given a straight line DG with point E and F on it and we are to find the length of DG.

We have [tex] D E = 2 x + 7 [/tex], [tex] E F = 8 [/tex],  [tex] F G = 2 [/tex] and [tex] D G = x + 20 [/tex].

So we can write it as:

[tex] DG = DE + EF + FG [/tex]

[tex]x+20 = 2x+17+8+2[/tex]

[tex]2x-x=20-17-8-2[/tex]

[tex]x=-7[/tex]

Substituting this value of [tex]x[/tex] to find DG:

DG = [tex]+x+20 = -7+20[/tex] = 13

The area is greater because you multiply 10 by 10. The perimeter is all the sides added together so that would be 40 units. All sides of the square are the same. Area is length times width

The area of a square with a side of 10 units is 100 square units, which is greater than its perimeter of 40 units, because the area measurement squares the side's length, whereas the perimeter is a sum of side lengths.

To determine which is greater between the area of a square and its perimeter, we start by understanding that the area of a square is calculated by squaring the length of one side. In this case, the square's side is 10 units, so the area is 10 units  imes 10 units = 100 square units. The perimeter of a square is the sum of all its sides, which is 4 times the length of one side. Hence, the perimeter is 10 units times 4 = 40 units.

As a result, the area, which is 100 square units, is greater than the perimeter, which is 40 units. This demonstrates that while the perimeter is a measure of the distance around the square, the area represents the entire space enclosed within it, leading to larger numerical values when the sides of the square are squared as opposed to simply multiplied by four.

Answer:

29*sqrt(5)

Step-by-step explanation:

Start with sqrt (45). You must reduce it to it's prime factors.

45: 9 * 5            9 is not prime so reduce it.

45: 3 * 3 * 5  

When you write √45, you should replace it with √(3*3*5)

The rule is

Rule: when you have a pair of equal prime factors under a root sign, you can take one out and throw one away.

Rule 2: If there are an odd number of equal primes one of them will be left underneath the root sign.

√45 = 3√5

11sqrt(45) - 4 sqrt(5)              Substitute for 45

11*3*sqrt(5) - 4sqrt(5)            Take out sqrt(5) using the distributive property.

(11*3 - 4)*sqrt(5)                      Combine 11 * 3  

(33- 4) * sqrt(5)                       Do the subtraction

29 * sqrt(5)                             Answer

The correct answer is 29[tex]\sqrt{5}[/tex]

The third option.

Answer:

[tex]d = \sqrt{14} = 3.74...[/tex]

Step-by-step explanation:

To find the distance between (8, -3, 4) and (6, -4, 1), use the distance formula for (x,y,z) points. It is very similar to (x,y) points.

[tex]d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2 + (z_2 - z_1)^2} \\d = \sqrt{(8 - 6)^2 + (-3--4)^2 + (4-1)^2} \\d = \sqrt{(2)^2 + (1)^2 + (3)^2} \\d = \sqrt{4 + 1 + 9}\\ d = \sqrt{14} = 3.74...[/tex]

Answer:

the answer is probably 6x:8y

Step-by-step explanation:

Answer:

vertex = (- 5, - 8)

Step-by-step explanation:

Given a quadratic in standard form : ax² + bx + c = 0 : a ≠ 0

Then the x- coordinate of the vertex is

[tex]x_{vertex}[/tex] = - [tex]\frac{b}{2a}[/tex]

Given x² + 10x = - 17 ( add 17 to both sides )

x² + 10x + 17 = 0 ← in standard form

with a = 1, b = 10, c = 17, then

[tex]x_{vertex}[/tex] = - [tex]\frac{10}{2}[/tex] = - 5

Substitute x = - 5 into the quadratic for the corresponding value of y

y = (- 5)² + 10(- 5) + 17 = 25 - 50 + 17 = - 8

Hence vertex = (- 5, - 8)

The answer is:

C. [tex]\frac{x-\sqrt{5x}}{x-5}[/tex]

Since we have rational numbers on both numerator and denominator, we need to rationalize (simplify) using the conjugate method on the denominator, for this case, the conjugate will be the same expression changing the positive sign "+" to a negative sign "-". Conjugate method means that we need to multiply and divide for the same term in order to not affect the expression.

Also, for solving this problem, we need to remember the following:

[tex]a^{2}-b^{2}=(a+b)(a-b)[/tex]

And,

[tex]\sqrt[n]{a}*\sqrt[n]{b}=\sqrt[n]{a*b}[/tex]

So, the conjugate for the expression will be:

[tex]\sqrt{x}-\sqrt{5}[/tex]

Applying the conjugate for the expression, we will have:

[tex]\frac{\sqrt{x} }{\sqrt{x}+\sqrt{5}}*\frac{\sqrt{x}-\sqrt{5}}{\sqrt{x}-\sqrt{5}}=\frac{\sqrt{x}*\sqrt{x} -\sqrt{x}*\sqrt{5}}{(\sqrt{x})^{2}-\sqrt{x}*\sqrt{5}+\sqrt{5}*\sqrt{x}-(\sqrt{5})^{2}}\\\\\frac{(\sqrt{x})^{2}-\sqrt{5x}}{x-5}=\frac{x-\sqrt{5x}}{x-5}[/tex]

So, the rationalized form of the expression is:

[tex]\frac{x-\sqrt{5x}}{x-5}[/tex]

Have a nice day!

Answer:

1. 15

2. 26.6666666667

3. 26.6666666667

4. 15

5. 8

Step-by-step explanation:

Answer:

George is 12, Mary Lou is 24 and Kate is 10.

Step-by-step explanation:

To find these, start by setting George's age as x. This means that we can model Mary Lou's age as 2x, since she is twice as old. We can also model Kate's age as x - 2 since she is two years younger. Now we can add these 3 together and set equal to 46

x + 2x + x - 2 = 46

4x - 2 = 46

4x = 48

x = 12

This means that George is 12.

Mary Lou = 2x

Mary Lou = 2(12)

Mary Lou = 24

Kate = x - 2

Kate = 12 - 2

Kate = 10

Answer:

G 12 Mary L 24 and kate is 10

Step-by-step explanation:

Answer:

they need to sell 15,000 because 42 percent of 15,00 is 6,300+2500=800

the inequality should be. 2500+0.42s≥8,800

and the number line should have a closed point on 15,000 with the line pointing to the right

Answer:

11.02 = a, rounded to the nearest 10th

Step-by-step explanation:

The length of the ladder (13 ft) forms the hypotenuse of the triangle when leaned against the house.  The distance the ladder goes up the wall is the side opposite to the angle we are working with, so we can use the sine function to solve.  

Sin X = (opposite side)/(hypotenuse)

Sin 58 = a/13

     13(Sin 58) = a

              11.02462525 = a

                  11.02 = a, rounded to the nearest 10th    

A 13-foot ladder making a 58-degree angle with the ground will reach approximately 6.9 feet up a wall when we use the cosine function to calculate the height.

To find how many feet up a wall a 13-foot ladder will reach when it makes a 58-degree angle with the ground, we can use trigonometric functions, specifically the cosine function for adjacent and hypotenuse in a right-angled triangle.

The formula we will use is:

cosine(angle) = [tex]\frac{height}{hypotenuse}[/tex]

Re-arranging the equation to solve for the adjacent side, we get:

adjacent side = cosine(angle) * hypotenuse

Now plug in the values:

adjacent side = [tex]cosine(58 ^0) * 13 feet[/tex]

We can calculate the cosine of 58 degrees using a calculator and multiply it by 13, which will give us the height the ladder reaches on the wall. Let's calculate:

adjacent side = 0.5299 * 13 feet

adjacent side = 6.8887 feet

Therefore, a 13-foot ladder at a 58-degree angle with the ground will reach approximately 6.9 feet up a wall.

The answer for your question is:

C: Rectangle

If a parallelogram is inscribed in a circle, then it must be a Rectangle

Any quadrilateral in which opposites sides are parallel is called a parallelogram.

Any 2 dimensional figure bounded by 3 sides and sum of all the angles is 180° is called a triangle.

A parallelogram with four equal sides and sometimes one with no right angles is called a rhombus.

A rectangle is a four sided quadrilateral, having all the internal angles equal to 90 degrees and opposite sides are equal.

A trapezoid is a quadrilateral with one pair of opposite sides parallel.

This follows the characteristics features of a circle.

So the required parallelogram will be a rectangle.

Option C is correct.

So, options A , B, D are incorrect.

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Answer:

your answer is 0.001

Step-by-step explanation:

you multiply by 100

move the decimal two places to the right

~~→hope this helps← ~~

║bangtanboys7║

Answer:

you get 0.001

Step-by-step explanation:

Convert the percentage to a fraction by placing the expression over  100 . Percentage means 'out of  100 '.

[tex]\frac{0.01}{100}[/tex]

Convert the decimal number to a fraction by shifting the decimal point in both the numerator and denominator. Since there are  2  numbers to the right of the decimal point, move the decimal point  2  places to the right.

[tex]\frac{1}{0000}[/tex]

Convert the fraction to a decimal by dividing the numerator by the denominator. then you get 0.001 as your answer

Hope This Helps

Have A Nice Day/Night (·❛ᴗ❛·)

Stay Safe,Stay Positive, Stay Gold ⭐

                                ~susu

answer: 1 over 165 step by step: #1 Evaluate the power 5 to the power of 1= 5 because any expression raised to the power of 1 if u asking what's is an expression the expression is five and together is 5 to the power of 1) #2 if a term like five doesn't have a exponent the exponent is 1) #3 remove the parathesis ) #4 subtract 1 and -2 u get 1 over 5 to the power of -4 and 5 to the power of negative four is 1 over 165) the second I don't know

Answer:

you need to list the sets of data.

Step-by-step explanation:

Flora's car is 79/100 meters longer than Trevor's car after adding the separate differences between Flora's car and Sally's and Sally's car and Trevor's.

To find out how much longer Flora's car is than Trevor's, we need to add the two differences mentioned:

Flora's car is 59/100 meters longer than Sally’s car.

Sally’s car is 2/10 of a meter (20/100 when having a common denominator with 59/100) longer than Trevor’s car.

First, we express 2/10 as 20/100 to have a common denominator with 59/100 for easier addition:

59/100 + 20/100 = 79/100

Now we add the two lengths to determine how much longer Flora’s car is than Trevor's.

79/100 meters

Therefore, Flora's car is 79/100 meters longer than Trevor's car.

It would be D because 45.60-.01 would mean you subtract the .01 from the .60

Answer:

D)4.193

Step-by-step explanation:

If one angle in a parallelogram is 90°, all four angles are 90°, making the parallelogram a rectangle.

When dealing with a parallelogram, it is important to remember certain properties about its angles. A parallelogram has opposite angles that are equal and consecutive angles that are supplementary (add up to 180 degrees). If one angle is 90°, then the opposite angle must also be 90°. Since one pair of opposite angles are right angles, this parallelogram is actually a rectangle. This means the other two angles in the parallelogram must also be 90° each.

So, in conclusion, if a parallelogram has one angle that measures 90 degrees, the measures of the other three angles in the parallelogram are also 90 degrees each. This is because a parallelogram with all right angles is a rectangle, and by definition, a rectangle has all angles measuring 90 degrees.

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In a parallelogram with one angle measuring 90°, the other three angles also measure 90°, making the parallelogram a rectangle.

In a parallelogram, opposite angles are equal, and adjacent angles are supplementary (sum to 180°). Since one angle measures 90°, its opposite angle must also be 90°. Therefore, the adjacent angles must each be 180° - 90° = 90°.

Since one angle in a parallelogram measures 90°, the other three angles must also be 90°, making this parallelogram a rectangle.

Answer: C

Explanation:

If a store paid x dollars to buy the computer and they sold it for 10 percent extra, it would be x+.1x. We can use the distributive property to get that x+.1x=x(1+.1) to get 1.1x, or C

Answer: c.1.1x

Step-by-step explanation:

Hi, the correct option is c.1.1x.

Since the price they paid for the computer is 100%, if they sell them for 10% more:

100%+10% =110% (sales percentage)

So, for a price x, to obtain the selling price we have to multiply the price (x) by the sales percentage in decimal form (110/100= 1.1)

The final expression is:

1.1x

Answer:

D. 53.2 ft.

Step-by-step explanation:

As you can see in the diagram, Farimah, Helio, and the kite are making a triangle. We know from our problem that the distance from Farimah to Helio is 15 ft, the distance from Farimah to the kite is 57 ft, and the angle of elevation from Farimah to the kite is 68°. From this situation, we can infer that we have two sides of the triangle and the angle between those sides; therefore, we can use the law of cosines to find the third side, which is the distance form Helio to the kite:

[tex]c^2=a^2+b^2-2abcos(C)[/tex]

[tex]c^2=57^2+15^2-2(57)(15)cos(68)[/tex]

[tex]c=\sqrt{57^2+15^2-2(57)(15)cos(68)}[/tex]

[tex]c=53.2[/tex]

We can conclude that Helio is 53.2 ft from the kite.

Answer:

D. 53.2

You can use the Law of Cosines to solve.

Answer:

[tex]\large\boxed{(f-g)(x)=-3x^2-x-4}[/tex]

Step-by-step explanation:

[tex](f-g)(x)=f(x)-g(x)[/tex]

[tex]f(x)=-4x^2-6x-1,\ g(x)=-x^2-5x+3\\\\(f-g)(x)=(-4x^2-6x-1)-(-x^2-5x+3)\\\\(f-g)(x)=-4x^2-6x-1-(-x^2)-(-5x)-3\\\\(f-g)(x)=-4x^2-6x-1+x^2+5x-3\qquad\text{combine like terms}\\\\(f-g)(x)=(-4x^2+x^2)+(-6x+5x)+(-1-3)\\\\(f-g)(x)=-3x^2-x-4[/tex]

Answer: 3,520 feet

Step-by-step explanation:

To solve this exercise you must apply the proccedure shown below.

You know that 1 miles is equal to 5,280 feet.

1 mile=5,280 feet (This is the conversion factor that you should use)

Then, keeping the above on mind, you can convert 2/3 miles to feet as following:

[tex](\frac{2}{3}miles)(\frac{5,280feet}{1mile})=3,520feet[/tex]

Answer:

One eighth is one part of eight equal sections. Two eighths is one quarter and four eighths is a half. It's easy to split an object, like a cake, into eighths if you make them into quarters and then divide each quarter in half.

There are two eighths of an inch in a quarter of an inch.

The student is asking how many eighths of an inch are in 1/4 of an inch. To get the answer, you have to ask "how many 1/8's fit into 1/4". Since 1/4 is the same as 2/8, there are two eighths in one quarter.The student is asking how many eighths of an inch are in 1/4 of an inch. To get the answer, you have to ask "how many 1/8's fit into 1/4". Since 1/4 is the same as 2/8, there are two eighths in one quarter.The student is asking how many eighths of an inch are in 1/4 of an inch. To get the answer, you have to ask "how many 1/8's fit into 1/4". Since 1/4 is the same as 2/8, there are two eighths in one quarter.

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Answer:

If point a and point b split the circle in 2 arcs.

One of the point take up way more space than the other one.

Answer:  Measure of ∠BAM is 30°.

Step-by-step explanation:  As shown in the attached figure, points A and B split the circle with center O into two arcs. Major of the minor arc is 150°. And, the point M splits the major arc in the ratio 2 : 5.

We are to find the measure of ∠BAM.

Since the measure of minor arc AB is 150°, so the measure of major arc AB will be

360° - 150° = 210°.

Also, point M divides the major arc AB in the ratio 2 : 5, so we have

[tex]\textup{arc }BM:\textup{arc }{MA}=2:5.[/tex]

Therefore, the measure of ∠BOM is given by

[tex]m\angle BOM=\dfrac{2}{2+5}\times 210^\circ=\dfrac{2}{7}\times210^\circ=2\times30^\circ=60^\circ.[/tex]

We know that the measure of the angle subtended at the center by an arc is equal to twice the measure of the angle subtended at the circumference by the same arc.

That is, for arc BC, we get

[tex]m\angle BOM=2\times m\angle BAM\\\\\\\Rightarrow m\angle BAM=\dfrac{m\angle BOM}{2}\\\\\\\Rightarrow m\angle BAM=\dfrac{60^\circ}{2}\\\\\\\Rightarrow m\angle BAM = 30^\circ.[/tex]

Thus, the measure of ∠BAM is 30°.

Answer: 3

Step-by-step explanation:

1. Convert the mixed number to fraction:

- Multiply the denominator of the fraction by the whole number.

- Add the product obtained and the numerator of the fraction.

- Write the sum obtained as the numerator and rewrite the original denominator of the fraction.

Then:

[tex]1\ 1/2=\frac{(1)(2)+1}{2}=\frac{3}{2}[/tex]

2. Multiply the numerators.

3. Multiply the denominator.

4. Reduce the fraction.

Then:

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

Answer:

21. Option d

22. Option b

23. Option b

Step-by-step explanation:

The formula to calculate the binomial probability is represented as follows.

[tex]P(X=x) = \frac{n!}{x!(n-x)!}p^x(1-p)^{n-x}[/tex]

The formula to calculate the binomial probability is represented as follows.

In this formula x represents the number of successes, n represents the number of times the experiment is repeated, p represents the probability of success.

1. First we are asked to calculate the probability of obtaining 3 successes, with n = 6 and p = 0.35.

Then we substitute the values in the formula [tex]P(X=3) = \frac{6!}{3!(6-3)!}(0.35)^3(1-0.35)^{6-3}\\\\P(3) = 0.2354[/tex]

Option d.

2. Second we are asked to calculate the probability of obtaining 5 successes, with n = 20 and p = 60%, p = 0.6.

[tex]P(X=5) = \frac{20!}{5!(20-5)!}(0.6)^5(1-0.6)^{20-5}\\\\P(5) = 0.00129[/tex]

option b

3. Third we are asked to calculate the probability of obtaining 2 successes, with n = 10 and p = 1/2, p = 0.5.

[tex]P(X=2) = \frac{10!}{2!(10-2)!}(0.5)^2(1-0.5)^{10-2}\\\\P(2) = 0.04394[/tex]

option b

Answer:

R = PV / nT

Step-by-step explanation:

PV = nRT solve for R

rewrite

nRT = PV

Divide both sides by nT

nRT / nT = PV / nT

Simplifying

R = PV / nT

First option is the answer