Suppose x = 5 is a solution to the equation 4x − 3(x + a) = 2. Find the value of a that makes the equation true.
a. -25

b. 2

c. 3

d. 1

The term that can be added to the list so that the greatest common factor of the three terms  12h3 36h3, 12h6, is 48h5

A group of numbers' greatest common factor (GCF) is the biggest factor that all the numbers have in common. For instance, 12, 20, and 24 all share two characteristics.

The term that  can fit in to the list so the GCF is 12h3 would be 48h5, this is so because 48 is first divisible by 12  without any  fraction, and we can remove upon dividing 3 h's from this term as it contains a total of 5 h's.

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Answer:

the answer of the question is 256m^2

Answer:

S=288

Step-by-step explanation:

Let’s solve the equation x^2 - 4x = 5 by factoring:

First, we’ll move all the terms to one side of the equation:

x^2 - 4x - 5 = 0

Now, we’ll factor the left side of the equation. We’re looking for two numbers that multiply to -5 and add to -4. Those numbers are -5 and 1. So we can write:

(x - 5) (x + 1) = 0

Now we’ll use the zero-product property to solve for x. This property states that if the product of two numbers is zero, then at least one of the numbers must be zero. So we have:

x - 5 = 0 or x + 1 = 0

Solving each equation separately, we find that x = 5 or x = -1.

So, the solutions to the equation x^2 - 4x = 5 are x = 5 and x = -1.

Answer:

Step-by-step explanation:

Let x be the number of miles you and your friend travel.We know that the cost of the bus ride is 60 cents per mile, so the total cost of the trip is 60 * x.This can be written as an equation as follows:Cost = 60 * xOr, more simply:Cost = 60xThis equation represents the relationship between the number of miles you and your friend travel and the cost of the trip. As the number of miles increases, the cost of the trip also increases at a rate of 60 cents per mile.

Answer: the last option is correct

Step-by-step explanation:Using the formulas for converting Cartesian coordinates to polar coordinates:

r = √(x^2 + y^2)

θ = atan2(y, x)

where x and y are the Cartesian coordinates, r is the distance from the origin to the point, and θ is the angle between the positive x-axis and the line connecting the origin to the point.

Given the Cartesian coordinates (x, y) = (-7√3/2, 7/2), we can substitute these values into the formulas:

r = √((-7√3/2)^2 + (7/2)^2)

θ = atan2(7/2, -7√3/2)

Simplifying the expressions:

r = √(147/4 + 49/4) = √(196/4) = √49 = 7

θ = atan2(7/2, -7√3/2)

Using a calculator or reference table to find the arctangent of 7/2 divided by -7√3/2, we get:

θ ≈ 5π/6

So the correct answer is: (7, 5π/6), which is option (6).

The correct answer is d. There are 10 letters from a to j. Taking 4 slips at a time will give a sample space with C(10,4) = 210 elements. S = { abcd, aefg, aeij,..}.

What is an illustration of slips?

Slips happen when people plan to do one thing but wind up doing something else, frequently something similar. An I instead of a "o" on a keyboard qualifies as a slip, as does accidently placing liquid hand soap on someone's toothbrush instead of toothpaste.

What does the term slides past mean?

The act of hiding something or concealing a truth in order to avoid drawing attention to it; sneaking anything past a process or examination. Your trick won't work since no prisoner has managed to trick Officer Smith in a long time.

To form codes of four letters each, we need to select 4 slips out of 10. The order in which the slips are selected does not matter, so we can use combinations to calculate the number of possible outcomes. The formula for the number of combinations of n objects taken r at a time is C(n,r) = n! / (r!(n-r)!), where n! denotes the factorial of n (i.e., n! = n × (n-1) × (n-2) × ... × 2 × 1).

So, the number of ways to select 4 slips out of 10 is C(10,4) = 10! / (4!(10-4)!) = 210. Therefore, the sample space has 210 elements. It is not practical to enumerate all the elements of the sample space, but we can describe a few sample points, such as abcd, aefg, aeij, and so on.

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Answer:

68

Step-by-step explanation:

Given triangle is an isoceless 56=56

So

X+56+56=180

X=180-112

X=68

So value is X is 68

Answer:

Step-by-step explanation:

You want the slopes of the lines parallel and perpendicular to 7x -6y = -3.

The slope is the x-coefficient when the equation is in slope-intercept form:

  y = mx +b

Solving for y gives ...

  -6y = -7x -3

  y = 7/6x +1/2 . . . . . divide by -6

The slope of the given line is 7/6.

A parallel line will have the same slope: 7/6.

A perpendicular line will have opposite reciprocal slope: -6/7.

The question that Diondra would ask that does not allow for variability is A. Which movie did her best friend like the most?

The other three questions ("How many awards did each movie win?", "What is the total dollar amount that each movie made from ticket sales?", and "How many weeks did each movie play in the theater?") all offer metrics by which a movie's popularity could be measured, and those measurements could vary from movie to movie.

However, the question about her best friend's favorite movie depends solely on the opinion of one individual, not a variable measure, and therefore doesn't allow for variability.

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The quadrilateral PQRS is a parallelogram since opposite sides PQ and SR have the same lengths and slopes.

To determine the correctness of the statements and calculate the lengths and slopes of the given quadrilateral PQRS, let's perform a coordinate proof.

Length and slope of PQ:

The coordinates of points P and Q are P(0, 2) and Q(3, -4), respectively.

Length of PQ: √[(x₂ - x₁)² + (y₂ - y₁)²]

= √[(3 - 0)² + (-4 - 2)²]

= √[9 + 36]

= √45

= 3√5 (approx.)

Slope of PQ: (y₂ - y₁) / (x₂ - x₁)

= (-4 - 2) / (3 - 0)

= -6 / 3

= -2

Therefore, the length of PQ is approximately 3√5, and its slope is -2.

Length and slope of SR:

The coordinates of points S and R are S(-2, 1) and R(1, -5), respectively.

Length of SR: √[(x₂ - x₁)² + (y₂ - y₁)²]

= √[(1 - (-2))² + (-5 - 1)²]

= √[9 + 36]

= √45

= 3√5 (approx.)

Slope of SR: (y₂ - y₁) / (x₂ - x₁)

= (-5 - 1) / (1 - (-2))

= -6 / 3

= -2

Therefore, the length of SR is approximately 3√5, and its slope is -2.

Length and slope of SP:

The coordinates of points S and P are S(-2, 1) and P(0, 2), respectively.

Length of SP: √[(x₂ - x₁)² + (y₂ - y₁)²]

= √[(0 - (-2))² + (2 - 1)²]

= √[4 + 1]

= √5

Slope of SP: (y₂ - y₁) / (x₂ - x₁)

= (2 - 1) / (0 - (-2))

= 1 / 2

Therefore, the length of SP is √5, and its slope is 1/2.

Length and slope of HQ:

The coordinates of points H and Q are H(0, 2) and Q(3, -4), respectively.

Length of HQ: √[(x₂ - x₁)² + (y₂ - y₁)²]

= √[(3 - 0)² + (-4 - 2)²]

= √[9 + 36]

= √45

= 3√5 (approx.)

Slope of HQ: (y₂ - y₁) / (x₂ - x₁)

= (-4 - 2) / (3 - 0)

= -6 / 3

= -2

Therefore, the length of HQ is approximately 3√5, and its slope is -2.

Based on the calculations, we can conclude that both statements are correct:

The quadrilateral PQRS is a parallelogram since opposite sides PQ and SR have the same lengths and slopes.

The quadrilateral PQRS is not a rectangle since the lengths of the adjacent sides PQ and SP are not equal.

Summary:

Length of PQ is approximately 3√5, and its slope is -2.

Length of SR is approximately 3√5, and its slope is -2.

Length of SP is √5, and its slope is 1/2.

Length of HQ is approximately 3√5, and its slope is -2.

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Answer:

2x^3-5x^2-28x+15 -------------------------expanded

2x^3-5x^2-28x+15--------------------simplified

Step-by-step explanation:

\left(2x-1\right)\left(x+3\right)\left(x-5\right)

=2x^2x+2x^2\left(-5\right)+5xx+5x\left(-5\right)-3x-3\left(-5\right)

simplyfied

\left(2x^2+5x-3\right)\left(x-5\right)

=2x^2x+2x^2\left(-5\right)+5xx+5x\left(-5\right)-3x-3\left(-5\right)

=2x^3-5x^2-28x+15

Answer:

8

Step-by-step explanation:

4x2

Answer:

B

Step-by-step explanation:

The description best fits the distribution of the data shown in the histogram is option D which is approximately Bell shaped .

What is bell shaped histogram ?

A bell-shaped histogram is a type of histogram that displays data that is normally distributed, also known as a Gaussian distribution. It is a common way to visually represent data that follows this particular pattern.

In a bell-shaped histogram, the x-axis represents the range of values being measured, while the y-axis represents the frequency or number of occurrences of each value. The histogram is named after its characteristic shape, which resembles a bell curve with a symmetrical peak in the middle and gradually tapering off on either side.

The bell-shaped histogram is useful because it provides a visual representation of the distribution of data, allowing us to see how the data is clustered around the mean or average value. It also allows us to identify outliers or values that fall outside of the typical range of values.

Bell-shaped histograms are commonly used in many fields, including statistics, finance, and scientific research. They can be used to analyze data from experiments, surveys, and other sources, and can help researchers make predictions about future outcomes based on past data.

Overall, a bell-shaped histogram is a powerful tool for understanding and interpreting data that is normally distributed, and can provide valuable insights into patterns and trends that might not be immediately apparent from raw data alone.

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Answer: A null hypothesis is a statistical hypothesis that is tested for possible rejection under the assumption that it is true.

Step-by-step explanation:

The null hypothesis\((H_0)\) and alternative hypothesis\((H_a)\) both are statements as per the researcher's claim that involves population parameter .

Null hypothesis has  ≤,≥ ,= signs

Alternative hypotheses has < , > , ≠ signs.

A null hypothesis is a statistical hypothesis that is tested for possible rejection under the assumption that it is true.

Answer:

why is brainlys ask a tutor not free anymore I really needed help so I pressed the button and all it said was pay for tutor plus

Answer:182.524

Step-by-step explanation:28.98•12.6=365.148 365.148 divided by 2=182.524

Answer:

b

Step-by-step explanation:

Answer:

B. $137.20

Step-by-step explanation:

Answer:

length l = 32.25 m

width w = 8223.75 m

height h = 12.5 m

diagonal d = 8223.82273 m

total surface area Stot = 736831.875 m2

lateral surface area Slat = 206400 m2

top surface area Stop = 265215.938 m2

bottom surface area Sbot = 265215.938 m2

volume V = 3315199.22 m3

Step-by-step explanation:

You would write AB with a horizontal line segment over the letters A and B

So you would write this \(\overline{AB}\)

If you cannot draw that on your computer, then I would stick to saying "segment AB".

line segment is used to name a segment that has an endpoint at point A and another endpoint at point B

A line segment is a part of line that is bounded by two distinct end points , and contains every point on the line that is in between its endpoint  .

since , in question it is given that their are two end points A and B then, it will form a line segment named AB

the answer is line segment

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For the system of equations x² + y² = 100 and y = x + 2, the solution is obtained as (-8, -6) and (6, 8).

What is an equation?

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").

We can solve this system of equations using substitution.

First, we can solve the second equation for y in terms of x -

y - x = 2

y = x + 2

Now we can substitute this expression for y into the first equation -

x² + y² = 100

x² + (x + 2)² = 100

Expanding the square -

x² + x² + 4x + 4 = 100

Combining like terms -

2x² + 4x - 96 = 0

Dividing both sides by 2 -

x² + 2x - 48 = 0

Factorizing the quadratic equation -

x² + 8x - 6x - 48 = 0

x(x + 8) - 6(x + 8) = 0

(x + 8)(x - 6) = 0

This gives us two possible values for x - x = -8 or x = 6.

If x = -8, then y = x + 2 = -8 + 2 = -6.

If x = 6, then y = x + 2 = 6 + 2 = 8.

Therefore, the solutions to the system are (-8, -6) and (6, 8).

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The given sequence is

To find the explicit formula, first, we have to find the difference by subtracting two consecutive terms.

As you can observe, the difference is 4.

From the sequence, we observe that the first term is -7.

The formula for arithmetic sequences is

Now, let's replace the values we've got.

Then, we simplify.

The factors of the original expression, u and v to produce a sum of simpler terms, the derivative of y with respect to x is: y' = -2x⁴ - x² - 10x + 15

Given the expression y = (3 - x²) (x³ - 5x + 5),

We need to find the derivative of y with respect to x.

We can find y' using two methods:

Method 1: Applying the Product RuleIf y = uv, then we know that y' = u'v + uv'Applying this formula to the given expression, We get:

y = (3 - x²) (x³ - 5x + 5)u = (3 - x²) and v = (x³ - 5x + 5)

Differentiating u and v, we get:u' = -2x and v' = 3x² - 5

Substituting these values into the formula for y', we get:

y' = u'v + uv' = (-2x) (x³ - 5x + 5) + (3 - x²) (3x² - 5)

Simplifying this expression, we get:

y' = -2x⁴ + 10x² - 10x - 3x² + 15 = -2x⁴ - x² - 10x + 15

Method 2: Multiplying the Factors to Produce a Sum of Simpler Terms to Differentiate

Expanding the given expression, we get:

y = 3x³ - 15x + 15 - x⁵ + 5x³ - 5x - 3x² + 15x² - 15x

Differentiating this expression, we get: y' = 9x² - 15 + 0 - 5x⁴ + 15x² - 5 - 6x + 30x - 15

Simplifying this expression, we get:

y' = -2x⁴ - x² - 10x + 15

Therefore, the derivative of y with respect to x is:y' = -2x⁴ - x² - 10x + 15

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Answer:

2.1

Step-by-step explanation:

Answer:

\(50-1.64\frac{15}{\sqrt{30}}=45.509\)    

\(50+1.64\frac{15}{\sqrt{30}}=54.491\)    

The 90% confidence inverval for the mean will be 45.509 and 54.491

Step-by-step explanation:

Information given

\(\bar X= 50\) represent the sample mean

\(\mu\) population mean (variable of interest)

\(\sigma= 15\) represent the sample standard deviation

n= 30 represent the sample size  

Confidence interval

The confidence interval for the mean is given by the following formula:

\(\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}\)   (1)

Since the Confidence is 0.90 or 90%, the value of \(\alpha=0.1\) and \(\alpha/2 =0.05\), the critical value would be \(z_{\alpha/2}=1.64\)

Now we have everything in order to replace into formula (1):

\(50-1.64\frac{15}{\sqrt{30}}=45.509\)    

\(50+1.64\frac{15}{\sqrt{30}}=54.491\)    

The 90% confidence inverval for the mean will be 45.509 and 54.491

Answer:

25

Step-by-step explanation:

x+7 = 32 (similar triangles)

x = 25

The coordinates of the midpoints of the given line segment is:

(3.5, 1.5)

The midpoint of a line segment is simply referred to as the center of that specific line segment.

Thus, the coordinates at that point will be referred to as the coordinates of the midpoint.

The coordinates of the endpoints of the line are:

(4,6) and (3,-3)

The formula to find the coordinates of the midpoint of the line is:

(x, y) = (x₁ + x₂)/2, (y₁ + y₂)/2

Thus, we have:

(x, y) = (4 + 3)/2, (6 - 3)/2

= (3.5, 1.5)

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Answer:

you forgot the pic

Step-by-step explanation:

Answer:6.8

Step-by-step explanation:

i dont know how to explain.