The diameter of a circle is 9 in. Find its area to the nearest tenth.




schoology

When two straight lines or rays intersect at a single endpoint then an angle is created. The vertex of an angle is that location where two points are come together.

The sum of angles equal to 180° is called Supplementary Angle.

Complementary Angle, Sum of the angle is equal to 90°.

a. (10x + 7) + (4x + 5) = 180 ( Supplementary angle )

14x + 12 = 180

14x = 180 -12

x = 12

10x + 7 = 127°

4x + 5 = 53°

c. (5x -11) + (8x -3) = 90 ( Complementary Angle )

13x - 14 = 90

13x = 90 + 14

x = 8

5x - 11 = 29°

8x - 3 = 61°

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1) a. 6     b. 5 - i     c. 1 + 4i    d.  -0.5 + 2.5i

2) x^3 - (7 - 3i)x^2 + (14 - 6i)x - (8 - 24i).

(1)
(a) 2 + 3i + 4 - 3i = 6 + 0i = 6

(b) (3 + 2i)(1 - i) = 3 + 2i - 3i - 2i^2 = 3 - i + 2 = 5 - i

(c) 2 + 3i - (1 - i) = 2 + 3i - 1 + i = 1 + 4i

(d) 2+3i / 1-i = (2+3i)(1+i) / (1-i)(1+i) = (2+2i+3i+3i^2) / (1-i+i-i^2) = (2+5i-3) / (1+1) = (-1+5i) / 2 = -0.5 + 2.5i

(2)

If x = 1 – 3i, x = 2, and x = 4 are roots of f(x),

then we can write f(x) as:
f(x) = (x - (1 - 3i))(x - 2)(x - 4)

Multiplying these factors out, we get:

f(x) = (x^2 - (1 - 3i)x - 2x + 2(1 - 3i))(x - 4)
f(x) = (x^2 - (3 - 3i)x + 2 - 6i)(x - 4)
f(x) = x^3 - (7 - 3i)x^2 + (14 - 6i)x - (8 - 24i)
So, the polynomial f(x) is x^3 - (7 - 3i)x^2 + (14 - 6i)x - (8 - 24i).

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To find the hypotenuse of a right triangle, we can use the Pythagorean theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the other two sides. The formula for the Pythagorean theorem is:
c^2 = a^2 + b^2
Where c is the hypotenuse, and a and b are the other two sides of the triangle.

In this case, we are given the lengths of the two legs of the triangle, 11 inches and 24 inches.
We can plug these values into the formula and solve for the hypotenuse:
c^2 = 11^2 + 24^2
c^2 = 121 + 576
c^2 = 697
c = √697
c ≈ 26.4 inches

Therefore, the hypotenuse of the triangle is approximately 26.4 inches.

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The function  f(g(x)) = x/(3+2x)-2 and g(f(x)) = (-x+2)/(1-2x) after simplifying.

The composition of two functions f and g is denoted by (f∘g)(x) and is defined as f(g(x)). In other words, we apply the function g to the input x, and then apply the function f to the result.

For the first part of the question, let f(x)=2x+2 and g(x)=2x²+2x. To find (f∘g)(x), we apply g(x) to the input x and then apply f(x) to the result:

(f∘g)(x) = f(g(x)) = f(2x²+2x) = 2(2x²+2x)+2 = 4x^2+4x+2

So, (f∘g)(x) = 4x^2+4x+2 after simplifying.

For the second part of the question, let f(x)=1/x-2 and g(x)=3/x+2. To find f(g(x)), we apply g(x) to the input x and then apply f(x) to the result:

f(g(x)) = f(3/x+2) = 1/(3/x+2)-2 = 1/(3+2x)/x-2 = x/(3+2x)-2

To find g(f(x)), we apply f(x) to the input x and then apply g(x) to the result:

g(f(x)) = g(1/x-2) = 3/(1/x-2)+2 = 3x/(1-2x)+2 = (3x+2-4x)/1-2x = (-x+2)/(1-2x)

So, f(g(x)) = x/(3+2x)-2 and g(f(x)) = (-x+2)/(1-2x) after simplifying.

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Answer:

See explanation below

Step-by-step explanation:

S has x-coordinate of 6 => the distance from origin to x-coordinate is 6 units, which is one leg of the right triangle

Pythagorean theorem states that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse.

c^2 = a^2 + b^2

with c = 10, a = 6

10^2 = 6^2 + b^2

b^2 = 100 - 36 = 64

b = √64 = 8

Point S can have 2 y-coordinates, one (+) and one (-) depending on the location of point S, so S can be either (6,8) or (6,-8)

The relative frequency for the total number of boys in this survey, rounded to the nearest hundredth, is 0.43.

What is frequency ?

In statistics, frequency refers to the number of times a particular observation or value occurs in a given dataset or sample. It is often represented in a frequency table, which organizes the data by category or value and shows the number of occurrences for each.

To find the relative frequency for the total number of boys in this survey, we need to divide the number of boys who prefer math or social studies by the total number of students in the survey, which is 120.

Relative frequency of boys who prefer math = 43/52 ≈ 0.83

Relative frequency of boys who prefer social studies = 9/52 ≈ 0.17

Relative frequency of total number of boys = 52/120 ≈ 0.43

Therefore, the relative frequency for the total number of boys in this survey, rounded to the nearest hundredth, is 0.43.

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They are not the best factors to use because 12 cannot be simplified further into a perfect square. It is better to factor 48 into perfect squares and simplify each square root separately.

Factors can be classified as prime or composite. A prime factor is a factor that is a prime number, meaning it is only divisible by 1 and itself. For example, the prime factors of 12 are 2 and 3. A composite factor is a factor that is not a prime number, meaning it has more than two factors. For example, 4, 6, and 12 are composite factors of 12.

Let's examine the factors 4 and 12 to see if they can be used to simplify the square root of 48:

4 is a perfect square, and its square root is 2. However, 12 is not a perfect square, and its square root cannot be simplified further.

We can write 48 as 4 x 12, so the square root of 48 can be simplified as the product of the square root of 4 and the square root of 12, or 2√12.

However, this is not the simplest form of the square root of 48. We can further simplify √12 by factoring it into perfect squares: √12 = √(4 x 3) = √4 x √3 = 2√3.

Therefore, the simplest form of the square root of 48 is 2√3, not 2√12.

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Answer:

Let's assume that Mia's present age is x.

According to the problem, Rosie is 6 years older than Mia, so Rosie's present age is x + 6.

In 4 years, Mia's age will be x + 4, and Rosie's age will be (x + 6) + 4 = x + 10.

The problem also states that Rosie's age in 4 years will be three times Mia's present age, so we can write the equation:

x + 10 = 3x

Simplifying this equation, we can subtract x from both sides to get:

10 = 2x

Dividing both sides by 2, we get:

x = 5

Therefore, Mia is currently 5 years old. To check, we can verify that in 4 years, Rosie will be three times Mia's age:

Rosie's age in 4 years = (5 + 6) + 4 = 15

Mia's age in 4 years = 5 + 4 = 9

Rosie's age in 4 years is indeed three times Mia's age, so our solution is correct.

The  true about the volumes of the triangular prism and the triangular pyramid is D; triangular pyramid has a volume one-third the volume of the triangular prism.

Suppose a triangle. Now, strech it up so as to make a stack of triangles up above another. This new 3d object is called a triangular prism.

Usually, about triangular prism, we talk about the triangular prism, whose stack goes straight up, thus, we talk about a right triangular prism.

In order for us to know the volume of the triangular pyramid, first we need to know the ratio of the volume of triangular prism and the volume of the triangular pyramid.

Take a traingle as a base then take 3 triangles such that each of them are connected to one-one side of the first traingle and when they're taken together, they form a closed object, called as a triangular pyramid.

Volume of the pyramid = 1/3 volume of the prism.

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The triangular pyramid has a volume one-third the volume of the triangular prism .

Correct option is D.

Volume is the measure of the capacity that an object holds. Volume can also be defined as the amount of space occupied by a 3-dimensional object. The volume of a solid like a cube or a cuboid is measured by counting the number of unit cubes it contains. The best way to visualize volume is to think of it in terms of the space enclosed/occupied by any 3-dimensional object or solid shape.

Given,

A triangular prism and a triangular pyramid have the same base and height.

Let the height be h unit and area of base be x square unit

Volume of triangular prism

= base area × height

= Ah cubic unit

Volume of triangular pyramid

= (1/3)× base area × height

= (1/3)Ah

= (1/3) volume of triangular prism

Hence, volume of triangular pyramid is one-third of  volume of triangular prism.

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Precise and accurate in your construction, using the ruler and compass correctly to create the desired lines.

To make a ruler-and-compass construction of the lines tangent to a given circle that pass through a given point, follow these steps:

1. Draw the given circle using a compass.
2. Mark the given point on the paper with a pencil.
3. Place the point of the compass at the given point and extend the compass until it touches the edge of the circle.
4. Draw a circle with the compass. This circle will intersect the given circle at two points.
5. Use a ruler to draw a line from the given point to each of the intersection points. These lines are the tangent lines to the given circle that pass through the given point.
6. Label the tangent lines and the given point for clarity.

By following these steps, you can create a ruler-and-compass construction of the lines tangent to a given circle that pass through a given point. Remember to be precise and accurate in your construction, using the ruler and compass correctly to create the desired lines.

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The experimental probability of spinning a number less than 3 is given as follows:

0.38.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

The outcomes for this problem are given as follows:

Hence the experimental probability of spinning a number less than 3 is given as follows:

p = 38/100

p = 0.38.

The bars are given as follows:

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The sample size of N=120 and significance level of α=0.01 would be the most likely to lead to the highest power.

To maximize statistical power, we want to select the sample size and importance degree in order to maximize the likelihood of detecting a real effect if one exists. Better pattern size and a decreased importance degree each tend to increase statistical energy.

Assuming a -tailed test and equal variances, we will use a power analysis to determine the sample size needed to acquire a favored degree of power. Based totally on the impact size we count on to examine, we will estimate the minimum sample size required for the take look to have 80% energy (that is regularly considered acceptable).

For instance, if we count on a small impact length (d=0. 2) and an importance level of α=0. 05, we might need a pattern size of about n=128 to reap 80% power. Growing the sample length in addition would retain increased strength, however, the marginal returns could diminish.

As for significance level, lower alpha degrees tend to cause higher strength due to the fact they lessen the possibility of a type I error (false wonderful), which frees up extra of the kind I error rate for detecting genuine outcomes. However, excessively low alpha tiers can boom the chance of kind ii errors (fake negatives), which decreases strength.

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Answer:

yes

Step-by-step explanation:

there is a theorem that states that two sides of a triangle should be greater than its third which is true in this case

1+11=12  (12>11)

11+1=12  (12>11)

11+11=22 (22>1)

a) When the number of chirps per minute, c = 110, then the outdoor temperature is 67.5°F.

b) If outdoor temperature is, f at least 55° F, then 60 chirps we can expect to hear in a minute at that temperature.

c) The graph for linear function, f = (1/4)c + 40, is present above.

d) The cofficient of linear function/ equation represents the slope of linear equation.

A function is a relationship that exists between two variables, where one variable depends on the other.

The linear equation is f = (1/4)c + 40 ----(1)

where, c--> the number of chirps per minute, that the tree cricket makes is linearly dependent on f.

f--> the temperature in Fahrenheit.

a) When number of chirps per minute,c = 110. We have to determine the outdoor temperature in degrees Fahrenheit. Substitute the value c = 110 in equation (1),

=> f = 1/4×110 + 40

=> f = 27.5 + 40

=> f = 67.5

So, required value is 67.5° F.

b) The outdoor temperature is, f at least 55° F, i.e., f = 55° F

Substitute f value in equation (1),

=> 55 = (1/4)c + 40

=> 55 - 40 = (1/4)c

=> (1/4)c = 15

=> c = 4× 15

=> c = 60

c) On the coordinate plane, graph that represents the relationship between the number of chirps, c and the temperature, f is attached in above figure.

d) The cofficient 1/4 in linear equation represents the slope of equation, df/dc that is change in outdoor temperature (°F) per crickets chirp in minutes. Hence, the required cofficient represents slope.

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Complete question:

In places where there are crickets, the outdoor temperature can be predicted by the rate at which crickets chirp. One equation that models the relationship between chirps and outdoor temperature is f = (1/4)c + 40, where c is the number of chirps per minute and f is the temperature in degrees Fahrenheit.

a). Suppose 110 chirps are heard in a minute. According to this model, what is the outdoor temperature?

b) The equation is only a good model of the relationship when the outdoor temperature is at least 55∘F. (Below that temperature, crickets aren't around or inclined to chirp.) How many chirps can we expect to hear in a minute at that temperature?

c) On the coordinate plane, draw a graph that represents the relationship between the number of chirps and the temperature.

d) Explain the cofficient 1/4 in equation tells us about relationship.

Answer:

u>36

Step-by-step explanation:

u>36

9×4=36

so u>36

When solving a polynomial equation by factoring, we can apply the zero-product property to the factors that are equal to zero.

The zero-product property states that if the product of two or more factors is equal to zero, then at least one of the factors must be equal to zero. For example, if (x-2)(x+3) = 0, then either (x-2) = 0 or (x+3) = 0.

In the case of a polynomial equation, we can apply the zero-product property to the factors that are equal to zero in order to find the values of x that make the equation true.

For example, if we have the equation x^2 - 5x + 6 = 0, we can factor the left-hand side of the equation to get (x-2)(x-3) = 0. We can then apply the zero-product property to find that either (x-2) = 0 or (x-3) = 0, which means that x = 2 or x = 3 are the solutions to the equation.

In summary, when solving a polynomial equation by factoring, we can apply the zero-product property to the factors that are equal to zero in order to find the values of x that make the equation true.

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The answer to the quadratic equation -9d^(2)+6=-6d is 11/20 and -11/20. To solve the given quadratic equation f -9d^(2)+6=-6d, we need to rearrange the terms and use the quadratic formula.

Step 1: Rearrange the terms to get the equation in the standard form of ax^(2) + bx + c = 0
-9d^(2) + 6d + 6 = 0

Step 2: Identify the values of a, b, and c.
a = -9
b = 6
c = 6

Step 3: Use the quadratic formula to find the solutions for d.
The quadratic formula is given by:

d = (-b ± √(b^(2) - 4ac))/(2a)

Substitute the values of a, b, and c into the formula:

d = (-(6) ± √((6)^(2) - 4(-9)(6)))/(2(-9))

Step 4: Simplify the expression inside the square root:

d = (-(6) ± √(36 + 216))/(-18)

d = (-(6) ± √(252))/(-18)

Step 5: Simplify the expression further:

d = (-(6) ± 15.87)/(-18)

Step 6: Solve for d using both the positive and negative values inside the square root:

d = (-(6) + 15.87)/(-18) = 0.55

d = (-(6) - 15.87)/(-18) = -0.55

So, the solutions for d are 0.55 and -0.55 or 11/20 and -11/20 using the quadratic formula to solve the given quadratic equation.

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Answer: 8

Step-by-step explanation:

2*3= 6
[tex]\frac{2}{3}[/tex]*3= 2

Answer:

the quotient of 100 and the sum of B and 24

Step-by-step explanation:

The word expression is: "the quotient of 100 and the sum of B and 24"

The algebraic expression is: 100 / (B + 24)

To evaluate this expression for the values 1, 6, and 13.5, we substitute each value in turn for B and simplify:

When B = 1:

100 / (1 + 24) = 100 / 25 = 4

When B = 6:

100 / (6 + 24) = 100 / 30 = 3.33...

When B = 13.5:

100 / (13.5 + 24) = 100 / 37.5 = 2.666...

Therefore, the values of the expression for B = 1, 6, and 13.5 are approximately 4, 3.33, and 2.67, respectively.

Alex want to subtract 196 from . So here we have to know about basic mathematical calculation.

What is calculation?

Calculation is a mathematical process we take one or more input to get one or more output. For this we uses various operations like Addition , Subtraction, Multiplication, Division, Percentage etc.

In addition we add one or more no to other and get output.

Example : 5 + 4 + 6 = 15

In addition we subtract smaller by the bigger no.

Example : 5 -4 = 1

In Multiplication we multiply two or more number to get output.

Example : 5 x 4 x 6 = 120

In division we divide smaller number by the big one to take output.

Example : 12 / 6 = 2

So , In question, [tex]50^{2} - 48^{2} =196[/tex]

So, My answer is 196.

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Using Poisson distribution, the probability of each scenario is attached below.

(a) The probability of receiving 0 complaints in a 3-day period is given by the Poisson distribution:

P(X=0) = (λ^x * e^(-λ)) / x!

where λ is the expected number of complaints per day, and x is the number of complaints in the time period of interest.

In this case, λ = 1.1 complaints per day, and x = 0 complaints in 3 days.

P(X=0) = (1.1^0 * e^(-1.1 * 3)) / 0! = 0.037

So the probability of receiving 0 complaints in a 3-day period is 3.7%.

(b) The probability of receiving 1 complaint in a 3-day period is:

P(X=1) = (1.1^1 * e^(-1.1 * 3)) / 1! = 0.041

So the probability of receiving 1 complaint in a 3-day period is 4.1%.

(c) The probability of receiving 2 complaints in a 3-day period is:

P(X=2) = (1.1^2 * e^(-1.1 * 3)) / 2! = 0.022

So the probability of receiving 2 complaints in a 3-day period is 2.2%.

(d) The probability of receiving 3 complaints in a 3-day period is:

P(X=3) = (1.1^3 * e^(-1.1 * 3)) / 3! = 0.008

So the probability of receiving 3 complaints in a 3-day period is 0.8%.

(e) The probability of receiving 4 complaints in a 3-day period is:

P(X=4) = (1.1^4 * e^(-1.1 * 3)) / 4! = 0.0022

So the probability of receiving 4 complaints in a 3-day period is 0.22%.

(f) The probability of receiving less than or equal to 4 complaints in a 3-day period is:

P(X ≤ 4) = P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4) = 0.1102

So the probability of receiving less than or equal to 4 complaints in a 3-day period is 11.02%.

(g) The probability of receiving more than 4 complaints in a 3-day period is:

P(X > 4) = 1 - P(X ≤ 4) = 1 - 0.1102 = 0.8898

So the probability of receiving more than 4 complaints in a 3-day period is 88.98%.

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The sum of the squares of n standard gaussians is known as a Chi square and denoted by x2. In other words, if Z1, Z2, ..., Zn are independent N(0, 1) then x2 = Z1^2 + Z2^2 + ... + Zn^2.  to use the Central Limit Theorem (CLT) to find P(x2 > 30). The closest value is (C) 0.20 The correct option is C) 0.20

The CLT states that the sum of a large number of independent and identically distributed random variables will be approximately normally distributed. In this case, the sum of the squares of n standard gaussians (x2) will be approximately normally distributed with mean n and variance 2n.

Therefore, we can standardize x2 to find the probability that it is greater than 30:

Z = (x2 - n) / sqrt(2n)

We want to find P(x2 > 30), which is equivalent to P(Z > (30 - n) / sqrt(2n)). Using the standard normal table, we can find the closest value to this probability. The closest value is (C) 0.20. Therefore, the answer is (C) 0.20.

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Answer:

the paper is too blurry i would help if i could.

Step-by-step explanation:

The statement g(5) = 33.75 represents total cost of $33.75 when the purchase of a stuffed giraffe added to 5 accessories to it, the total cost

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

g(x) = the cost of a stuffed giraffe.

The giraffe costs $15 and accessories cost $3.75 each.

This means that

g(5) = 33.75

Using the above as a guide, we have the following:

The statement g(5) = 33.75 means that if we purchase a stuffed giraffe and add 5 accessories to it, the total cost will be $33.75.

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The least common denominator of the two fractions (2x)/(7x-21) and (1)/(2x-6) is 14(x-3).

To find the least common denominator of the two fractions (2x)/(7x-21) and (1)/(2x-6), we need to find the least common multiple of the denominators 7x-21 and 2x-6.

Step 1: Factor the denominators.
7x-21 = 7(x-3)
2x-6 = 2(x-3)

Step 2: Identify the common factors.
Both denominators have the factor (x-3).

Step 3: Multiply the unique factors together.
7 * 2 * (x-3) = 14(x-3)

Step 4: The least common denominator is 14(x-3).

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The number of miles travelled by Juan is 28 miles.

An equation is a mathematical statement that shows that two mathematical expressions are equal.

For example, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

Given that, a taxi fare is given by an expression, F = 2.25+0.20(m-1), where F is the taxi fare and m is the number of miles traveled,

We need to find the number of miles if the taxi fare is $7.65

Put F = 7.65 in equation given to find the value of m,

7.65 = 2.25+0.20(m-1)

5.4 = 0.20(m-1)

m-1 = 5.4 / 0.2

m-1 = 27

m = 28

Hence, the number of miles travelled by Juan is 28 miles.

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The answer is A: Yes B: Yes C: Yes D: Yes E: Yes F: Yes. Each point is correctly placed on the coordinate plane.

A coordinate plane is a two-dimensional plane consisting of two axes (x and y) which intersect at a point called the origin. The x-axis, which runs horizontally, is referred to as the abscissa and the y-axis, which runs vertically, is referred to as the ordinate. The origin, which is the point of intersection of the two axes, is the point (0, 0).The coordinate plane is also known as the Cartesian plane, named after mathematician René Descartes.

Yes, Point A is located correctly on the coordinate plane at (4, –2). Yes, Point B is located correctly on the coordinate plane at (2 1/2, 2). Yes, Point C is located correctly on the coordinate plane at (2 1/2, –2). Yes, Point D is located correctly on the coordinate plane at (1, 3). Yes, Point E is located correctly on the coordinate plane at (–1, 1). Yes, Point F is located correctly on the coordinate plane at (–2, –2 1/2).

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The expression b^(2)-7b+1 evaluates to -9 when b=5.

To evaluate the expression when b=5, we simply need to substitute the value of b into the expression and then simplify.

Here's how we do it step-by-step:

Step 1: Substitute the value of b into the expression:

b^(2)-7b+1 = (5)^(2)-7(5)+1

Step 2: Simplify the expression by following the order of operations (PEMDAS):

= 25-35+1

Step 3: Combine like terms:

= -9

So, the final answer is -9.

Therefore, the expression b^(2)-7b+1 evaluates to -9 when b=5.

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The solutions to the quadratic equation are x = -1/3 and x = -8.

To solve the quadratic equation 3x^2 + 1 = -25x - 7 by factoring, we first need to rearrange the equation so that all the terms are on one side of the equal sign:

3x^2 + 25x + 8 = 0

Next, we need to find two numbers that multiply to give us 8 (the constant term) and add to give us 25 (the coefficient of the x term). These numbers are 20 and 1, so we can factor the trinomial as follows:

(3x + 1)(x + 8) = 0

Now we can use the zero product property to set each factor equal to zero and solve for x:

3x + 1 = 0 or x + 8 = 0

x = -1/3 or x = -8

So the solutions to the quadratic equation are x = -1/3 and x = -8.

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