If QS bisects PQT, SQT=(8x- 25),PQT=(9x+34), and SQR=112, find each measure.

Answer:

x=1

Step-by-step explanation:

If y=6x+1, we can substitute that into the original equation, so it would look like 3x+6x+1=10.

Now we just solve for x. Add 3x and 6x to get 9x, and subtract 1 from both sides of the equation, now we have

9x=9, divide both sides by 9 and we end up with x=1.

PS. sorry for the bad handwriting but i attached a photo of how i solved it.

To calculate the 99% confidence interval for the amount of aspirin in a single analgesic tablet, we can use the following formula:

Confidence Interval = Sample Mean ± (Z * (Standard Deviation / √Sample Size))

Given the information:

Population mean (μ) = 230mg

Population variance (σ^2) = 23mg^2

To obtain the standard deviation, we take the square root of the variance:

Population standard deviation (σ) = √(23mg^2) ≈ 4.796mg

The confidence level is 99%, which means the significance level (α) is 1 - (confidence level) = 1 - 0.99 = 0.01. This is a two-tailed test, so we need to find the critical value for α/2 = 0.01/2 = 0.005.

Using a standard normal distribution table or a calculator, the critical value corresponding to a significance level of 0.005 is approximately 2.576.

Assuming we have a sample size large enough for the Central Limit Theorem to hold, the sample mean will be an unbiased estimator of the population mean.

Therefore, the 99% confidence interval for the amount of aspirin in a single analgesic tablet is:

Confidence Interval = Sample Mean ± (2.576 * (4.796mg / √Sample Size))

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The 99% confidence interval for the amount of aspirin in a single analgesic tablet, drawn from a population with a mean μ of 230mg and a variance σ^2 of 23mg^2, can be calculated as (225.369mg, 234.631mg).

To calculate the confidence interval, we use the formula:

CI = (X- z ( σ/√n), X+ z ( σ/√n))

Here, X represents the sample mean, z is the z-score corresponding to the desired confidence level (99% confidence corresponds to a z-score of 2.576), σ represents the population standard deviation, and n represents the sample size.

Since we are given the population variance (σ^2), we can take the square root to obtain the standard deviation σ. We also assume that the sample size is large enough for the Central Limit Theorem to hold.

Substituting the given values into the formula, we have:

CI = (230 - 2.576 (√ (23)/√n), 230 + 2.576 (√(23)/√n))

Since the sample size is not provided, the confidence interval cannot be calculated precisely. However, using the given information, we can determine that the confidence interval will be of the form (230 - k, 230 + k), where k depends on the sample size.

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Answer: -5/3

Step-by-step explanation:

Answer: m = -4/3

Step-by-step explanation:

If you're given two different coordinates, and you want to find the slope, the general rule is that you subtract the first coordinates from the first. The formula for these kinds of problems is \(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\) .

Answer:

Step-by-step explanation:

x = 4

3x^2

3(4)^2

3(16)= 48

The value of the expression given is 10.

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Given that, the expression 5·x³/x², where x = 2, we need to find the value of the expression,

5·x³/x²

= 5·x·x·x / x·x

= 5x

Put x = 2

5x = 5·2

= 10

Hence, the value of the expression given is 10.

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Answer: 3x^3 + 6x^2 - 15x

Answer:

(-4, 4)

Step-by-step explanation:

x can be either negative 4 or positive 4.  A negative number squared is a negative number times a negative number, which will be a positive number.

Answer:

yeeeeeeeeeeeet

Step-by-step explanation:

thx for points

Answer:

B. isolate the \(x^{2}\) by using inverse operations.

Step-by-step explanation:

Hope this helps! Brainliest would be much appreciated! Have a great day! :)      

Answer:

hi this is my alt, the answer is b

Step-by-step explanation:

Answer:

Step-by-step explanation:

You want the value of the piecewise function for various values of x.

The first step in evaluating a piecewise function is determining which domain is applicable to the value of x you have. Then you use the corresponding function, evaluating it in the usual way.

For x = -5, the applicable domain is x < -3, so the function is ...

  h(-5) = -4(-5) -18 = 20 -18

  h(-5) = 2

For x = 0, the applicable domain is -3 ≤ x < 1, so the function is ...

  h(0) = 1

For x = 1 or 4, the applicable domain is x ≥ 1, so the function is ...

  h(1) = 1 +2 = 3

  h(4) = 4 +2 = 6

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the answer is no symmetry

Answer:

kml

Step-by-step explanation:

got it right

Answer:

triangle KML or answer C is corrreeeccttt

Step-by-step explanation:

edgee

Answer:

-------------------------

AB is the missing hypotenuse of the right triangle with shown legs.

Find AB using Pythagorean theorem:

Find the perimeter:

A polygon will be dilated on a coordinate grid to create a smaller polygon. The polygon is dilated using the origin as the center of dilation. The rule that could represent this dilation is G. (x, y) → (0.9x, 0.9y).Step-by-step explanation:The center of dilation is a point from which we take measurements of how much we should increase or decrease the original polygon to get the dilated polygon.

When the center of dilation is the origin, the rules of dilation are simple. In this case, we multiply the coordinates of each vertex of the original polygon by a scale factor to get the coordinates of the vertices of the dilated polygon. This is because the scale factor tells us how much we should stretch or shrink each side of the original polygon to get the sides of the dilated polygon. We should also note that the scale factor should always be positive, and it should be greater than 1 for enlargement and less than 1 for reduction.So, from the given options, the rule that could represent this dilation is G. (x, y) → (0.9x, 0.9y). This is because when we multiply the coordinates of each vertex of the original polygon by a scale factor of 0.9, we get the coordinates of the vertices of the dilated polygon.

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The first-order autonomous equation dx/dt = x²(4 – x²) represents a system with critical points. To find these points, we set dx/dt = 0 and solve for x. The critical points are x = 0, x = ±2. By analyzing the sign changes in the equation, we can classify the critical points as stable, unstable, or semi-stable.

1. In this case, x = 0 is a semi-stable critical point, while x = ±2 are unstable critical points. A phase diagram can be drawn to illustrate the behavior of the system.

2. To find the critical points, we set dx/dt = 0 and solve for x. In this case, the equation becomes x²(4 – x²) = 0. The solutions are x = 0 and x = ±2. These are the critical points of the system.

3. Next, we analyze the stability of these critical points. We can determine the stability by examining the sign changes in the equation dx/dt = x²(4 – x²). For x < -2 or -2 < x < 0, the term x²(4 – x²) is positive, indicating that dx/dt is positive and the system is moving away from the critical points. Therefore, x = ±2 are classified as unstable critical points.

4. For 0 < x < 2, the term x²(4 – x²) is negative, indicating that dx/dt is negative and the system is moving towards the critical point x = 0. However, for x > 2, the term x²(4 – x²) becomes positive again, implying that dx/dt is positive and the system is moving away from x = 0. Hence, x = 0 is considered a semi-stable critical point.

5. A phase diagram can be constructed to visualize the behavior of the system. The x-axis represents the values of x, while the y-axis represents the values of dx/dt. The critical points x = ±2 are represented as unstable points where the system moves away from them. The critical point x = 0 is represented as a semi-stable point where the system approaches it for 0 < x < 2 but moves away for x > 2. The phase diagram provides a clear visual understanding of the system's dynamics.

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The specific name of the quadrilateral is trapezoid

The measure of the missing angle is 55 degrees

To determine the measure of the angle, we need to know the following;

The properties of a trapezoid are listed as;

From the information given, we have that;

125 + x = 180

collect the like terms, we have;

x = 180 - 125

subtract the values, we get;

x = 55 degrees

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The population size of the protozoa after seven days, starting with an initial population of five members and a constant relative growth rate of 0.469 per member per day, can be calculated using the formula\(P(t) = 5 * e^{(0.469 * 7)\).

Part 1 of the question establishes that the relative growth rate of the protozoa population is 0.469 per member per day. This information helps us define the differential equation that represents the growth: dP/dt = 0.469P.

Part 2 introduces the exponential growth formula for population growth, which states that \(P(t) = P(0)e^{kt\) where P(t) is the population size at time t, P(0) is the initial population size, k is the growth rate, and e is the base of the natural logarithm.

To find the population size after seven days, we substitute the given values into the formula: \(P(t) = 5 * e^{(0.469 * 7)\). Evaluating this expression yields the final answer, which represents the population size of the protozoa after seven days.

Note: The calculation itself is not included in the answer as the model response is limited to explaining the approach.

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I'm uploading a picture because it thought it had innapropriate words for some reason.

The transformation of a shape includes rotating and reflecting the shape;

(a) Image of BC after \(120^o\) rotation

First, we calculate the angle of rotation, to make the hexagon lie onto itself

\(\alpha = \frac{\theta}{n}\)

Where:

\(\theta = 360^o\) --- angle at the center of the hexagon and the circle

\(n = 6\) -- sides of hexagon

So, we have:

\(\alpha = \frac{360^o}{6}\)

\(\alpha = 60^o\)

This means that a \(60^o\) rotation would make the hexagon lie onto itself.

We have that:

\(120^o = 60^o \times 2\)

This means that the shape can be rotated \(60^o\)  twice to achieve the \(120^o\) rotation.

The image of BC at the first \(60^o\) rotation is AB

The image of BC at the next \(60^o\) rotation is FA

Hence, the image of BC after \(120^o\) is FA

(b) Image of BC after reflection over line FC

Line FC divides the hexagon into equal halves.

So, when reflected over line FC, each segment would be flipped on the opposite segment.

The opposite of segment BC is DC.

Hence, the image of BC reflecting over FC is DC.

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Answer:

Step-by-step Explanation:

In a Cartesian plane, we learn many such terms which represent a point, or a line, or cooridnates of some points etc\(.\)

Such terms are:

The type of reading a student does varies by season, as it "Depends on it."

The temperature starts to warm up in the spring, and plants and trees start to sprout new leaves. The warmest time of year features lengthy, typically bright days in the summer. The climate cools down in the fall and many different kinds of trees begin to drop their leaves. The shortest days and coldest weather are in winter.

The type of reading is dependent on the season because the observations are dependent and two matched populations are compared. The observations were conducted with the same pupils. The observations from the school year and the summer are matched.

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The complete question should be:

Does the type of reading a student does vary by season? To find out, a communication specialist interviewed a sample of 10 children regarding the number of books they had read during two times of the year. First, she had them rate the books they read during the summer for how much they liked each one on a scale of 1 to 10 for fun. Then she compared this to the ratings of the books these same children had read during the school year for fun. How would we find out if there is a difference in rating of the books read by the students during the summer for pleasure and those read for pleasure during the school year? What statistical test?

Independent t

One way ANOVA

Dependent t

The factor of the expression will be (x + 1) and (x + 1). Then the product of two binomials will be (x + 1) and (x + 1).

It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.

The expression is given below.

⇒ x² + 2x + 1

Factorize the expression, then the factor of the expression will be

⇒ x² + x +  x + 1

⇒ x(x + 1)x + 1(x + 1)

⇒ (x + 1)(x + 1)

⇒ (x + 1)²

The product of two binomials will be (x + 1) and (x + 1).

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Answer:

3x+1

Step-by-step explanation:

(2x+x+3+6x)/3

9x+3/3

3x+1

The final result is a simplified algebraic expression 3x + 1 that represents the average of 2x, x + 3, and 6x.

Expressions are defined as mathematical statements that have a minimum of two terms containing variables or numbers.

The average of 2x, x + 3, and 6x can be represented by the algebraic expression (2x + (x + 3) + 6x)/3.

This expression takes the sum of 2x, x + 3, and 6x, and then divides that sum by 3, which is the number of terms being averaged.

Alternatively, the average can be represented by (2x + x + 6x + 3) / 3 = (9x + 3) / 3 = 3x + 1.

In either case, the final result is a simplified algebraic expression that represents the average of 2x, x + 3, and 6x.

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The measurement that gives you the difference between the points on the scatterplot and the prediction line for the same value of x is the residual. Therefore, the correct answer is C. Residual.

In regression analysis, the residual represents the vertical distance between the observed data points and the corresponding predicted values on the regression line. It is calculated by taking the difference between the actual observed value and the predicted value for a specific value of the independent variable (x). The residuals provide a measure of how well the regression line fits the data, with smaller residuals indicating a better fit.

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Answer:

a.\(-7 < x < 7\)
b.\(-12 < x < 6\)
c. Two answers are: y < -3 or y > 19
d. Two answers are x ≤ -17/3 or x ≥ 19/3
e. -4 ≤ y ≤ 5/2

Step-by-step explanation:

Given the following questions:

Question one:

\(|x| < 7\)
x is less than 7
\(=-7 < x < 7\)

Question two:

\(|x+3| < 9\)
\(x+3 > -9\)
\(3-3=0\)
\(-9+-3=-12\)
\(x > -12\)

\(x+3 < 9\)
\(3-3=0\)
\(9-3=6\)
\(x < 6\)
x is greater than -12, while less than 6
\(-12 < x < 6\)

Question three:

\(|y-8| > 11\)
\(y-8 < -11\)
\(-8+8=0\)
\(-11+8=-3\)
\(y < -3\)

\(y-8 > 11\)
\(-8+8=0\)
\(11+8=19\)
\(y > 19\)
Two answers are: y < -3 or y > 19

Question four:

|3x - 1| ≥ 18
3x - 1 ≤ -18
-1 + 1 = 0
-18 + 1 = -17
3x ≤ -17
x ≤ -17/3

3x - 1 ≥ 18
-1 + 1 = 0
18 + 1 = 19
3x ≥ 19
x ≥ 19/3
Two answers are: x ≤ -17/3 or x ≥ 19/3

Question five:

|4y + 3| ≤ 13
|4y + 3| ≤ 13 = -13 ≤ 4y + 3 ≤ 13
-13 ≤ 4y + 3 ≤ 13
4y + 3 ≥ -13
3 - 3 = 0
-13 + - 3 = -16
4y ≥ -16
4 ÷ - 16 = -4
y ≥ -4

4y + 3 ≤ 13
3 + -3 = 0
13 - 3 = 10
4y ≤ 10 = 10/4 ÷ 2 = 5/2
y ≤ 5/2
-4 ≤ y ≤ 5/2

Hope this helps.

The equation for the length of the diagonal of a right rectangular prism is: d = √(\(l^{2} + w^{2} + h^{2}\)) = √(\(9^{2} + 10^{2} + 6^{2}\)) units = 14.73 units

Here, d = length of the diagonal, l = length of the rectangular base of the prism, w = width of the rectangular base of the prism, and h = height of the prism.

Allow us to track down the diagonal of a right rectangular prism with a length of 9 units, the width of 10 units, and the height of 6 units.

The equation for the length of the diagonal of a right rectangular prism =

√(\(l^{2} + w^{2} + h^{2}\)) units.

Substitute the value in the equation,

= √(\(9^{2} + 10^{2} + 6^{2}\)) units

= 14.73 units

In this way, the recipe for the length of the diagonal of a right rectangular prism is √(\(l^{2} + w^{2} + h^{2}\)), where l is the length, b is the expansiveness and h is the height of a right rectangular prism.

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Answer:

C=0

Step-by-step explanation:

115.5  is the total amount of interest paid by this investment at the end of 5 years

percentage, a relative value indicating hundredth parts of any quantity.

Given,

Samantha invested $660 into an account that paid 3.5% interest compounded annually.

We need to find  total amount of interest paid by this investment at the end of 5 years

A=P(1+rt)

A is final amount

P is principal amount

r is rate of interest

t is time

A=?,P=660,r=3.5%=0.035, t=5

A=660(1+0.035(5))

=660(1+0.175)

=660(1.175)

A=775.5

To check the total amount of interest paid by this investment at the end of 5 years

We need to find difference between initial amount and final amount

775.5-660

115.5

Hence 115.5  is the total amount of interest paid by this investment at the end of 5 years

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Answer:

The answer is first one.

Hope it helps uh!

Answer:

0.5

Step-by-step explanation:

Look at the decimal go down. It goes down 0.5 each time or 1/2

The common difference in the arithmetic sequence 5.0, 4.5, 4.0, 3.5 will be 0.5.

Let a₁ be the first term and d is the common difference between the terms. Then the nth term will be given as

\(\rm a_n = a_1 + (n - 1)d\)

The arithmetic sequence is given below.

5.0, 4.5, 4.0, 3.5

Then the common difference will be

d = 5.0 – 4.5 = 0.5

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