Solve for x.

−4.5(x+3.21)=−33.21
Responses

x = 4.17
x, = 4.17
x = 6.67
x, = 6.67
x = 8.09
x, = 8.09
x = 10.59

Factoring a trinomial when the leading coefficient (a) is not equal to 1 requires a different approach compared to factoring a trinomial when a = 1. The difference lies in the initial steps of factoring, but both methods aim to express the trinomial as a product of two binomials. The similarity between the two cases is that both involve finding factors that multiply to give the constant term (c) and add up to give the coefficient of the linear term (b).

When factoring a trinomial with a leading coefficient (a) not equal to 1, the process involves identifying factors of the product of the leading coefficient (a) and the constant term (c) that add up to the coefficient of the linear term (b). This means that the factoring may involve more steps and calculations.

In contrast, when factoring a trinomial with a leading coefficient (a) equal to 1, the process simplifies as the coefficients of the linear and constant terms are the same. This allows for a simpler approach where we only need to find factors of the constant term that add up to the coefficient of the linear term.

Despite the difference in the initial steps, both methods ultimately aim to express the trinomial as a product of two binomials. The factors obtained in either case represent the terms within the binomials, allowing us to rewrite the trinomial in factored form.

In summary, the main difference in factoring trinomials lies in the initial steps, but the ultimate goal of expressing the trinomial as a product of binomials remains the same in both cases.

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for a confidence interval, decreasing the sample size will have no effect on the width of the confidence interval

Value of Confidence Interval is from 0% to 100% as probability value lies from 0 to 1 for a given set of data values.

Value of Confidence Interval  does not depend upon the Sample Size .It is always from 0% to 100% , whatever the width of sample size is.

As the sample size​ decreases, the width stays the same.

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Answer:

Step-by-step explanation:

so by "exact" they mean leave in the \(\sqrt{x}\) parts.... sooo

they tell us the Hypotenuse  ( Hyp) and one  angle and want that side Opposite ( Opp)  of the angle... sooo use the mnemonic

SOH CAH TOA  

to help remember how the sin , cos, and tan functions fit on a triangle

there problems b/c easy A's when you get this.  :P so learn it, know it, live it  :D

Sin = Opp / Hyp

Cos = Adj / Hyp

Tan = Opp / Adj

now look at which one of the above formulas have the things we know and want to find

Sin looks like a good choice b/c it's got  Opp, which we want to find, and Hyp which we know and also an angle which we can plug into the function

Sin(45) = Opp / 6

see how I got that?

\(\sqrt{2}\) / 2 = Opp / 6

6 ( \(\sqrt{2}\) / 2 ) = Opp

3\(\sqrt{2}\)  = Opp

the problem says leave it exact.. so don't try to reduce \(\sqrt{2}\)  just leave it

there is  your answer

X  = 3\(\sqrt{2}\)

Answer:

Option A

Step-by-step explanation:

Angular velocity of an object is defined by,

Angular velocity (w) = \(\frac{\triangle \theta}{\triangle t}\)

Here, Δθ = Change in angle of rotation

Δt = Duration or time

In this question Δθ = \(\frac{7\pi }{2}\) radians and Δt = 24 seconds

Therefore, angular velocity = \(\frac{\frac{7\pi }{2} }{24}\)

                                              = \(\frac{7\pi }{48}\) radians per second

Option A is the answer.

The graph meets the vertical line test requirement, it must represent a function (C) The vertical line test shows that the graph is correct, hence the answer is yes.

According to the function, every value in the domain is associated to exactly one value in the range, and they have a predefined domain and range. It is characterized as a certain kind of relationship.

Please refer to the image instead of the graph, which is related to it.

The graphic displays a graph.

A parabola is seen on the graph.

The vertical line test determines if a graph can be a function, as is common knowledge.

The graph passes the vertical line test option, indicating that it does in fact represent a function (C) The vertical line test shows that the graph is correct, hence the answer is yes.

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Answer:

$1,962.00

Step-by-step explanation:

Same explanation as the previous problem

Answer: option d because it still has a negative sign from the numerator.

Step-by-step explanation:

I apologize if I am wrong I am a bit rusty with these problems

I guess you can report my answer if you want to but just letting you know that I am a little rusty

Answer:

i think answer is 5

Step-by-step explanation:

since you could think what are factors of 36
1x36
2x18
3x12
4x9 and
6x6

Answer:

3/4 miles

Explanation:

To know how long the road's total section, we need to multiply the number of workers by the miles that each one resurfaces. So:

Therefore, the total section was 3/4 miles

Notice that the slope of the line is equal to the speed

hence, the speed = 5 miles / hour

The steps to graph the function are

From the question, we have the following function that can be used in our computation:

f(x) = -(x + 4)² - 6

The above function is a quadratic function

A quadratic function has its parent function to be

f(x) = x²

First, we have the transformation to be:

From f(x) = x² to f(x) = (x + 4)²

This means the function is translated left by 4 units

Next, we have the transformation to be:

From f(x) = (x + 4)² to f(x) = -(x + 4)²

This means the function is reflected across the x-axis

Lastly, we have

From f(x) = -(x + 4)² to f(x) = -(x + 4)² - 6

This means the function is translated down  by 6 units

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Answer:

scale factor P to Q: 4/5   scale factor Q to P: 5/4

Step-by-step explanation:

Divide original length over new length and you'll get the scale factor.

We can conclude that it is extremely unlikely to obtain a sample mean greater than 904.8 minutes if the design engineer's claim about the population variance and mean is true.

We can use the Central Limit Theorem to approximate the distribution of the sample means.

Under the given assumptions, the mean of the sampling distribution of the sample means is equal to the population mean, which is 886886 minutes, and the standard deviation of the sampling distribution of the sample means is equal to the population standard deviation divided by the square root of the sample size, which is\(\sqrt{84648464/145145} = 41.77\) minutes.

Therefore, we can standardize the sample mean using the formula:

\(z = (\bar{x} - \mu) / (\sigma / \sqrt{n } )\)

where \(\bar{x}\)  is the sample mean, \(\mu\)  is the population mean, sigma is the population standard deviation, and n is the sample size.

Plugging in the values we get:

z = (904.8 - 886886) / (41.77) = -21115.47

The probability of getting a sample mean greater than 904.8 minutes can be calculated as the area under the standard normal curve to the right of z = -21115.47.

This probability is essentially zero, since the standard normal distribution is symmetric and nearly all of its area is to the left of -6.

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Answer:

1 = -9

Step-by-step explanation:

Just substitute 3 for g

then 3/3 = 1

a) Using the Law of Cosines for this triangle, we can write the equation:
d² = (36)² + (3s)² - 2(36)(3s)cos(60°)

b) The second ship must travel at approximately 4.24 miles per hour to be 42 miles apart from the first ship at noon.

(a) To write an equation that relates the speed s and the distance d between the two ships at noon using the Law of Cosines, we first need to determine the distance each ship has traveled by noon. Since they leave at 9 a.m. and we're interested in the distance at noon, they travel for 3 hours.

Ship 1:
Speed: 12 miles per hour
Distance traveled: 12 miles/hour * 3 hours = 36 miles

Ship 2:
Speed: s miles per hour
Distance traveled: s miles/hour * 3 hours = 3s miles

Now, we can form a triangle where Ship 1 travels 36 miles, Ship 2 travels 3s miles, and the distance between them (d) is the third side. The angle between Ship 1 and Ship 2 is 180° - (53° + 67°) = 60°.

Using the Law of Cosines for this triangle, we can write the equation:
d² = (36)² + (3s)² - 2(36)(3s)cos(60°)

(b) To find the speed s that the second ship must travel so that the ships are 42 miles apart at noon, we can plug d = 42 into our equation from part (a) and solve for s.

42² = (36)² + (3s)² - 2(36)(3s)cos(60°)

Solving for s, we get:
s ≈ 4.24 miles per hour (rounded to two decimal places)

So, the second ship must travel at approximately 4.24 miles per hour to be 42 miles apart from the first ship at noon.

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Differences with in number of volunteers can explain  60.01% of the variation in the amount of trash bags collected.

The coefficient of correlation (r) between both the number of volunteers x and also the number of trash bags collected y is 0.775.

To calculate the percentage of variation for one derivative contract by the other, simply square the correlation coefficient.

Here, r = 0.775

Squaring both side.

r² = 0.775²

r² = 0.600625

Simply multiply with 100 to get the percent.

r² = 60.0625

r² = 60.01

Thus, differences in the number of volunteers can explain 60.01% of the variation in the number of trash bags collected.

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Answer:

The numbers are 16 and 20

Step-by-step explanation:

Let the multiples be: x+4 and x+8

Sum is 36, so we can make an equation:

x+4+x+8=36

2x=36-12

x=12

The numbers are 12+4=16, 12+8=20.

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As we move from the top layer (crust) to the bottom layer (lower mantle), the density of the Earth generally increases.

We have,

The table provided shows the density values for different layers of the Earth, specifically the crust, upper mantle, and lower mantle.

From the given data, we can observe that the density increases as we move from the top layer (crust) to the bottom layer (lower mantle).

The crust has the lowest density, ranging from 2.2 to 2.9 g/cm³.

As we move downwards to the upper mantle, the density increases to a range of 3.4 to 4.4 g/cm³.

Finally, in the lower mantle, the density further increases to a range of 4.4 to 5.6 g/cm³.

This pattern suggests that the materials present in the lower layers of the Earth are denser than those in the upper layers.

This aligns with the understanding that the Earth's interior becomes progressively denser towards the core, as different materials with varying densities and compositions are found at different depths.

The variation in density is attributed to the different compositions of rocks and minerals present in each layer.

The denser materials in the lower layers likely consist of heavier elements and compounds, contributing to the overall increase in density.

Therefore,

Based on the information in the table, we can conclude that there is a general trend of increasing density as we move deeper into the Earth's layers, from the crust to the upper mantle and then to the lower mantle.

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The complete question:

                           Density

Layer                top    bottom

crust                 2.2      2.9

upper mantle   3.4      4.4

lower mantle   4.4       5.6

You have learned that different types of rocks are found in Earth’s layers. Their composition affects their densities. What can you conclude based on the information in the table?

Answer:

the average cost if you go to ten classes plus the 200 plus 100 it will equal 300

Step-by-step explanation:

200 annual fee then 10+10+10+10+10+10+10+10+10+10 equal 100   so 200+100 equal 300 for the 10 classes plus the annual fee.

In linear equation, 15.2% did the total number of students on the honor roll decrease.

What in mathematics is a linear equation?

50 × 24% = 12

50 × 14%= 7

12+ 7 = 19

50+75 = 125

19 ÷125= 15.2%

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Answer:

Volume of the given pyramid = 1122.37 cubic feet

Step-by-step explanation:

Volume of the regular hexagonal pyramid = \(\frac{1}{3}(\text{Area of the base})(\text{Base})\)

Measure of internal angle of a polygon = \(\frac{(n-2)\times 180}{n}\)

Here, n = number of sides of the polygon

For a hexagon, n = 6

Measure of interior ∠C = \(\frac{(6-2)\times 180}{6}\)

                                       = 120°

Measure of ∠BCD = \(\frac{120}{2}\)

                              = 60°

By applying tangent rule in ΔCED,

tan(∠ECD) = \(\frac{\text{Opposite side}}{\text{Adjacent side}}\)

tan(60°) = \(\frac{DE}{CE}\)

\(\sqrt{3}=\frac{DE}{6}\)

DE = \(6\sqrt{3}\) feet

And cos(60°) = \(\frac{EC}{CD}\)

\(\frac{1}{2}=\frac{6}{CD}\)

CD = 12 feet

Area of ΔBCD = \(\frac{1}{2}(\text{Base})(\text{Height})\)

                        =  \(\frac{1}{2}(6\sqrt{3})(12)\)

                        = \(36\sqrt{3}\) feet

Area of hexagonal Base of the pyramid = \(6(36\sqrt{3})\)

                                                                  = 216√3 square feet

Since, lateral height of the pyramid (AC) = 15 feet

By applying Pythagoras theorem in ΔADC,

AC² = AD² + CD²

(15)² = AD² + (12)²

AD = \(\sqrt{225-144}\)

AD = 9 feet

Volume of the given pyramid = \(\frac{1}{3}(216\sqrt{3})(9)\)

                                                 = 648√3 cubic feet

                                                 = 1122.37 cubic feet

Multiply both sides by -2 to get p > 32. The inequality sign will flip because we are multiplying both sides by a negative number.

The graph of p > 32 has an open hole at 32 and shading to the right to indicate all values greater than 32. The open hole means we don't include 32 itself as a solution.

The line graph first represents the solution to the inequality (-1/2)p < -16 option first is correct.

It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.

We have an inequality:

(-1/2)p < -16

After removing negative signs on both sides.

(1/2)p > 16  (inequality sign changes)

p > 32

p ∈ (32, ∞)

Thus, the line graph first represents the solution to the inequality (-1/2)p < -16 option first is correct.

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Answer:

x=30

Step-by-step explanation:

90+130+x+10+x+x+x=360

230+3x=360

3x=90

x=30

It is important to note that the values of a, b, and c in a quadratic equation can be used to determine the nature of its solutions, whether they are real or imaginary, and whether they are distinct or equal. These properties of a quadratic equation can be useful in various applications, such as in physics, engineering, and finance.

To determine the values of a, b, and c in the quadratic equation 3x^2 - 7t + 4 = 0, we need to understand the general form of a quadratic equation, which is ax^2 + bx + c = 0.

In this equation, a represents the coefficient of the x^2 term, b represents the coefficient of the x term, and c represents the constant term. Therefore, we can identify the values of a, b, and c in our given equation by comparing it to the general form of a quadratic equation.

From our given equation, we can see that:

a = 3
b = -7t
c = 4

Therefore, the correct values of a, b, and c in the quadratic equation 3x^2 - 7t + 4 = 0 are:

a = 3
b = -7t
c = 4

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The perimeter measures around 36 metre.

The perimeter refers to the area surrounding an object. For instance, your house has a fenced-in yard. The perimeter is the length of the fence. If the yard is 50 feet by 50 feet, your fence is 200 feet long.

While 12.74 rounds up to 13, 5.45 rounds down to 5. Recatangle created a total of four sides, two of which are identical in length to the other two (which is a poor way to explain it). There are two sides that are 13 inches long and two sides that are 5 inches long, which is the solution to this question. When added together, the perimeter would be 13+13+5+5.

As an expression,

2(13)+2(5)

=26+10

=36.

The perimeter is approximately 36 meters.

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