Use the Distributive Proper
10
9. 2(-3x + 5)

If we are told that ab=0, then we can infer that either a or b (or both) must be equal to 0.

This is because when the product of two numbers is 0, at least one of the numbers must be 0 according to the zero product property.

One of the most crucial concepts for pupils to understand in maths and science is the zero product property.

The greatest educators, mathematicians, and recognized scientists in the fields of physics and chemistry have worked with Vedantu to provide their insights on the subject.

Their suggestions helped us develop materials for your understanding that would make it simple for you to put these ideas into practice.

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Answer:  x > _5

Step-by-step explanation:

The seat is 99 feet off the ground when it is at the top of the Ferris

wheel.

The height of a seat on a Ferris wheel can be modeled by the function H(t) = 47 sin((π/30)t + (3π/2)) + 52, where t is the time in seconds and H(t) is the height in feet.

To find how far off the ground the seat is when it is at the top of the Ferris wheel, we need to find the maximum value of the function. We know that the sine function has a maximum value of 1, which occurs when the input to the function is (π/2) + kπ, where k is an integer.

Since the input to our function is ((π/30)t + (3π/2)), we need to solve for t when this expression is equal to (π/2) + kπ.

((π/30)t + (3π/2)) = (π/2) + kπ

Multiplying both sides by 30, we get:

πt + 45π = 15π + 30kπ

Subtracting 15π from both sides and simplifying, we get:

t = 30k - 30

This means that the function H(t) will have a maximum value every 30 seconds. To find the maximum height, we can substitute t = 30k - 30 into the function:

H(30k - 30) = 47 sin((π/30)(30k - 30) + (3π/2)) + 52

Simplifying, we get:

H(30k - 30) = 47 sin(kπ - π/2) + 52

Since sin(kπ - π/2) =\((-1)^k\), we can write:

H(30k - 30) =\(52 - 47(-1)^k\)

When k is even, H(30k - 30) is at its maximum height of 99 feet (52 + 47).

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There are two main methods to determine if it is a rainy day at a given location: measuring rainfall using weather instruments, and using radar and satellite imagery.

Measuring rainfall using weather instruments involves setting up a rain gauge, an instrument that measures the amount of rainfall in a specific location. These instruments measure the amount of rainfall at a given time and provide more accurate readings than radar or satellite imagery.

Using radar and satellite imagery is another way to measure if it is a rainy day at a given location. Radar and satellite imagery show precipitation patterns, cloud types, and the movement of the clouds. These images can help identify where it is raining and how much rainfall is expected in the near future.

Both methods are useful for predicting rain or other types of precipitation. Rainfall measurements from weather instruments provide more accurate data, while radar and satellite imagery offer a bigger picture of the overall weather patterns in a given area.

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The measures of KM, KQ, LK, LR, NK and PM are 2, 2, 4, 4, 6 and 2 respectively.

1) KM: Since N is the midpoint of QR, we know that QN = NR, so QN + NR = QN + QN = 2QN = 26 = 12. Therefore, KM = KR - QN = (PK+KQ) - QN = 4 - 6 = -2.

2) KQ: Since PK = 4 and KM = -2, we have KQ = PK + KM = 4 + (-2) = 2.

3) LK: The median of a triangle connects a vertex to the midpoint of the opposite side, and it's length is 2/3 the length of the hypotenuse of the right triangle formed by the median and the two segments from the vertex to the endpoints of the median.

In this case, LK = (2/3)(PQ) = (2/3)(4+2) = (2/3)*6 =4

4)LR: In this case, LR = LK = 4

5) NK: NK = QN = 6

6) PM: PM = PK - KQ = 4 - 2 = 2

Please note, that in order to be able to calculate all these lengths and measures, it is assumed that the triangle PQR is a valid triangle i.e, the sum of the lengths of any two sides of the triangle is greater than the length of the third side.

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To confirm this, we can see that if Marco buys 2 bags of him, in total he inequality gets 2x2 + 3 = 7 embers for his tetras. This is the maximum number of fish he can have in his tank.

An inequality in mathematics is a relationship between two expressions or values ​​that are not equal. Imbalance therefore leads to inequality. An inequality establishes a connection between two values ​​that are not equal in mathematics. Equality is different from inequality. The inequality sign () is most commonly used when two values ​​are not equal. Various inequalities are used to contrast values, no matter how small or large. Many simple inequalities can be solved by changing both sides until only variables remain. But many things contribute to inequality. Negative values ​​on both sides are divided or added. Swap left and right.  

Let's start by defining a variable representing the number of bags Ember Tetra Marco can buy. Let's call this variable "x"

Each bag contains 2 of his Embertetras, so the total number of his Embertetras Marco can add to the tank is 2x.

However, he cannot put 10 fish in Marco's tank. He already has his 3 Ember tetras, so you can add up to 7 to your tank. Therefore, we can write the following inequality:

\(2x + 3 ≤ 7\)

To solve for x, first subtract 3 from both sides to separate the variables on one side of the inequality

\(2x ≤ 4\)

Then divide both sides by 2.

\(×≤2\)

So Marco can buy up to 2 bags of carassin for his aquarium.

To confirm this, we can see that if Marco buys 2 bags of him, in total he gets \(2x2 + 3 = 7\) embers for his tetras. This is the maximum number of fish he can have in his tank.

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After rationalization, (√3-√6)/(√3-√6) the expression becomes (4+√2)3.

The expression given for rationalizing is (√3-√6)/(√3-√6).

Rationalization means that we have to remove the root from the term in the denominator of the expression.

So, we will multiply and divide the denominator term in the expressions with the changes middle operator. This is how we do it,

= (√3-√6)/(√3-√6) x (√3-√6)/(√3+√6)

= (√3-√6)²/(√3-√6)(√3+√6)

= (√3-√6)²/(3+6)

= (3+9+2√18)/9

= (12+√18)/(9)

= (12+3√2)/9

= (4+√2)3

So, after we rationalize, the expression is  (4+√2)3.

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Answer:

hope this is correct

Answer:

108

Step-by-step explanation:

The p-value for testing the hypothesis that the proportion of unemployed people in Karachi city is not equal to 30%, based on a sample of 55 unemployed individuals out of a sample of 100 people, is approximately 0.1539 (rounded to four decimal places).

To calculate the p-value, we use the z-test for proportions. Given the null hypothesis that the proportion of unemployed people is 30%, the alternative hypothesis is that it is not equal to 30%. We compare the sample proportion to the hypothesized population proportion using the standard normal distribution.

Using the formula for the z-statistic:

z = (sample proportion - hypothesized proportion) / sqrt((hypothesized proportion * (1 - hypothesized proportion)) / sample size)

z = (55/100 - 0.30) / sqrt((0.30 * 0.70) / 100)

z = (0.55 - 0.30) / sqrt(0.21 / 100)

z = 0.25 / 0.0458

z = 5.4612

To calculate the two-tailed p-value, we find the area under the standard normal curve beyond the observed z-value. In this case, the p-value is the probability of observing a z-value as extreme or more extreme than 5.4612.

Using a standard normal distribution table or statistical software, we find that the two-tailed p-value for a z-value of 5.4612 is approximately 0.1539.

Therefore, the p-value for this hypothesis test is approximately 0.1539.

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Each bird would receive 1/9 cup of bird food.

A quotient is defined as the outcome of dividing an integer by any divisor that can be said to be a quotient. The dividend contains the divisor a specific number of times.

We have been given an area model with 12 shaded parts and 6 unshaded parts. The shaded part is labeled two-thirds. Adela divided Two-thirds of a cup of bird food equally among 6 birds.

The dividend would be

⇒ 2/3

The divisor would be

⇒ 6

The division expression would be

⇒ 2/3

Divided by 6

Rewrite the division expression to get

⇒ 2/3 × 1/6

⇒ 2 / 18

⇒ 1/9

Therefore, each bird would receive 1/9 cup of bird food.

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Step-by-step explanation:

ok so its basically like addition the top + the bottom.

3x + 3y = 12

6x + 11y = 14

9x + 15y = 26

now u wat to cancel out

9x + 15y = 26

9                

15y = 26     y = 1.7

9x = 26      x = 2.8

i think this is right i hopw this helps

Answer:

y= -2

x= 6

there you go

I used elimination method!

Hope It Helps!!!!

When operating under Instrument Flight Rules (IFR) with a Visual Flight Rules (VFR) on-top clearance, the altitude to be maintained depends on the specific clearance and regulations in place.

Generally, when flying VFR-on-top, the pilot is authorized to operate in VFR conditions above a layer of clouds or other obscuring phenomena. In terms of altitude, the pilot is expected to maintain a cruising altitude appropriate for the direction of flight and comply with the relevant airspace regulations. This typically involves flying at the appropriate altitude for the specific airspace class, as defined by the Federal Aviation Regulations (FARs) or the applicable regulatory authority. It's important for pilots to review and understand the specific requirements and altitude restrictions outlined in their VFR-on-top clearance, as well as any additional instructions provided by air traffic control.

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Answer:

This relation is a function.

Step-by-step explanation:

This relation is a function because a there should be no repeating x-coordinates in the relation for it to be a function and that is exactly what happens in this relation.

Answer:

It is a function.

Step-by-step explanation:

no two different outputs, y, have the same input, x, meaning it passes the vertical line test.

sorry for the lousy explanation

using calculator

Area right to the right of the 2=2.12

P(Z > 2.12)

• P(Z < -2.12)

= 0.0170

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Answer:

The range of this quadratic function is

-infinity < y ≤ 2.

The rectangular pyramid rises 7 feet in height.

Pyramids are three-dimensional objects with triangle-shaped faces and an all-encompassing polygonal base. It is referred to as a rectangular pyramid if the base of the structure is rectangular. Although all pyramids have a rectangular foundation, they all have triangular edges.

How is the height of the rectangular pyramid determined?

First, we understand that a rectangular pyramid's volume is determined by:

                         \(V=B * H / 3\)

The height H is determined by the base B.

When we know the volume is 56 \(ft^{3}\) and the base is 24 \(ft^{2}\), we can then swap out those two numbers in the volume calculation to get:

                          \(56 f t^{3}=24 f t^{2} * H / 3\)

When we solve it for H, we get:

                          \(H=3 *\left(56 f t^{\circ} / 24 f t^{2}\right)=7 f t\)

The rectangular pyramid rises 7 feet in height.

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An linear equation is formed of two equal expressions. The maximum height reached by a rocket, to the nearest tenth of a foot is 883.3 feet.

What is a linear equation in mathematics?

A linear equation in algebra is one that only contains a constant and a first-order (direct) element, such as y = mx b, where m is the pitch and b is the y-intercept.

                         Sometimes the following is referred to as a "direct equation of two variables," where y and x are the variables. Direct equations are those in which all of the variables are powers of one. In one example with just one variable, layoff b = 0, where a and b are real numbers and x is the variable, is used.

To find the maximum height through which the rocket will reach, we need to differentiate the given function, therefore, we can write,

y=-16x²+228x+71

dy/dx = -16(2x)+228

Substitute the value of dy/dx as 0, to get the value of x,

0 = -32x + 228

228 = 32x

x =7.125

Substitute the value of x in the equation to get the maximum height,

y=-16x²+228x+71

y=-16(7.125²)+228(7.125)+71

y=883.3feet

Hence, the maximum height reached by the rocket, to the nearest tenth of a foot is 883.3 feet.

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To find σg(X)^2, we need to calculate the variance of the function g(X) = 4X^2 + 2, where X is a random variable with a given density function. The density function is defined as f(x) = (3/2)(x + 1) for 0 ≤ x and 0 elsewhere. By calculating the variance of g(X), we can determine the value of σg(X)^2.

To calculate the variance of g(X), we first need to find the mean of g(X), denoted as E[g(X)]. For a continuous random variable, the mean is calculated as the integral of the function multiplied by the density function. In this case, we have:

E[g(X)] = ∫(4X^2 + 2) * f(x) dx

Substituting the given density function, we have:

E[g(X)] = ∫(4X^2 + 2) * (3/2)(X + 1) dx

After simplifying and evaluating the integral, we can find the value of E[g(X)].

Next, we calculate the variance of g(X), denoted as Var[g(X)]. The variance is calculated as the expectation of the squared difference between g(X) and its mean, E[g(X)]^2. In mathematical terms:

Var[g(X)] = E[(g(X) - E[g(X)])^2]

By substituting the values of g(X) and E[g(X)], we can evaluate this expression and find the value of Var[g(X)].

Finally, to find σg(X)^2, we take the square root of Var[g(X)], i.e., σg(X) = √Var[g(X)]. After calculating Var[g(X)], we can determine the value of σg(X) to three decimal places as needed.

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angle of F is 134, why? Because each triangle is 180 degrees altogether.

Step-by-step explanation:

The value of k is 6

In this question, we have been given In a high school, 20% of the students own a supercharged Greased Lightning 409 car while the other 80% own a feeble Milquetoast car. Last year the students owning a 409 received 60 speeding tickets while the students owning a Milquetoast received 10 speeding tickets.

A student owning a 409 was k times more likely to receive a ticket than a student owning a Milquetoast.

We write this statement in mathematical expression form as,

60 = 10 * k

We need to find the value of k

Consider above equation,

60 = 10 * k

k = 60/10

k = 6

Therefore, the value of k is 6

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No, it is not safe to assume that the sampling distribution of the sample means is about normal given the sample size.

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Answer:

Step-by-step explanation:

Answer:

\(y = 2x + 2\)

Step-by-step explanation:

The equation of any (non-vertical) line can take the form

y = ax + b where a is the slope and b is the y intercept. We know that in this case, the y intercept is 2. So we can substitute b = 2:

\(y = ax + 2.\)

Now, to find the x intercept, simply put y = 0 (since every point on the x axis has y = 0) and x = -1, since that is the given x intercept:

0 = -a + 2, so we see that a = 2. The equation is then:

y = 2x + 2

Brand B is the better buy because it offers the most ounces for the lowest price.

To compare the prices of the three brands, we need to convert them to a common unit of measurement. Brand A is priced at $4.89 for 54 ounces, Brand B is priced at $3.91 for 16 ounces, and Brand C is priced at $3.10 for 910 grams. Since 16 ounces is equivalent to 1 pound and 1 pound is equivalent to 453.59 grams, we can convert the weight of Brand B and C to ounces. 910 grams is equivalent to 2.01 pounds, which is equivalent to 32.16 ounces.

A.

54oz, convert to lb

54/16=3.375lb

find per lb

4.89/3.375=$1.4488888 per lb

B.

2 and 3/4=2.75, 3.91/2.75=$1.42181 per lb

C. 910/453.59=2.00621lb

3.10/2.00621=$1.545 per lb

compare

A: $1.4488888 per lb

B: $1.42181 per lb

C: $1.545 per lb

It is observed from the above calculation that Brand B have lowest price per unit on ounce.

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Answer:

84mm

Step-by-step explanation:

square = LxW = 6x6 =36

triangle = bxh/2 = 6x8/2 =24

add together 24x2+36=84

663.

i found out what 35% of 1020 is and then subtracted that by 1020.

Answer:

(x + 1)² = 4(y + 10)

Step-by-step explanation:

Equation of parabola:

(x - h)² = 4a(y - k)

with vertex(h, k) and focus (h, k + a)

vertex(h, k) = (-1, -10)

⇒h = -1 and k = -10

focus (h, k + a) = (-1, -9)

⇒ k + a = -9

⇒ -10 + a = -9

⇒ a = 10 - 9

⇒ a = 1

Equation of parabola:

(x - h)² = 4a(y - k):

(x - (-1))² = 4(1)(y - (-1))

= (x + 1)² = 4(y + 10)

Answer:

57?

Step-by-step explanation:

I'M NPT SURE IF IT'S CORRECT but I added them both and subtracted 180

Answer:

supplement angle : 107

complement angle : 17

Step-by-step explanation:

supplement :

180 - 73 = 107

complement :

90 - 73 = 17