ABCD is an isosceles trapezoid with legs AB and CD and with base BC. If AB=6z - 5 and BC = 7z +4 and CD = 4z +3

Answer: If you're plotting 1 equation (y=x^2-8x):

(-4,16) Vertex

(0,0) root

(8,0) root

If plotting both (y=x^2-8x) & (7y=x):

(-4,16) Vertex

(0,0) root

(8,0) root

(7,1) point on line

(-7, -1) point on line

Step-by-step explanation:

The vertex of the parabolic equation y = x² - 8x + 7 will be at (4, -9).

Now, Let the point (h, k) be the vertex of the parabola and a be the leading coefficient.

Then the equation of the parabola will be given as,

y = a(x - h)² + k

The equation is given below.

y = x² - 8x + 7

Convert the equation into a vertex form. Then we have

y = x² - 8x + 7

y = x² - 8x + 16 - 16 + 7

y = (x - 4)² - 9

Hence, The vertex of the parabolic equation y = x² - 8x + 7 will be at

(4, -9).

So, The graph is given below.

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Answer:

It’s C

Step-by-step explanation:

I took the test

Answer:

The equation used to solved to determine the dimensions of the backyard is 51 = 4w - 10.4

Step-by-step explanation:

As given,

The backward is rectangular in shape

Also , we know that

Area of rectangle = 2 ( Length + Breadth )

Also, given,

Breadth of the backyard = 5.2 + Length of the backyard

Let

length of the backyard = l

Breadth of the backyard = w

∴ we get

w = 5.2 + l

⇒l = w - 5.2

and

Area = 2 ( l + w)

⇒51 = 2( w - 5.2 + w)

⇒51 = 2 ( 2w - 5.2)

⇒51 = 4w - 10.4

So, the equation used to solved to determine the dimensions of the backyard is 51 = 4w - 10.4

By solving we get

4w = 51 + 10.4

⇒4w = 61.4

⇒w = \(\frac{61.4}{4}\) = 15.35

⇒ w = 15.35

⇒ l = w - 5.2 = 15.35 - 5.2 = 10.15

⇒l = 10.15

So the dimensions of the backyard = l × b = 10.15 m × 15.35 m

(a) Mean = (9 + 15 + 18 + 11 + 12) / 5 = 65 / 5 = 13

(b) Mean of the sample = (9 + 15) / 2 = 24 / 2 = 12

(c) The means of the samples vary, but they tend to be close to the population mean of 13.

(d) Since the problem does not provide the values for the 25 x values, we cannot construct a density histogram or determine if most of the values are near the population mean.

(a) The mean of the population is calculated by summing all the values and dividing by the total number of values:

Mean = (9 + 15 + 18 + 11 + 12) / 5 = 65 / 5 = 13

(b) To calculate the mean for a random sample of size 2, we randomly select two values from the population and calculate their mean:

Random sample: 9, 15

Mean of the sample = (9 + 15) / 2 = 24 / 2 = 12

(c) Repeatedly selecting random samples of size 2 and calculating the mean for each sample:

Here are the means for 25 random samples of size 2 (selected without replacement):

Sample 1: 9, 18 -> Mean = (9 + 18) / 2 = 27 / 2 = 13.5

Sample 2: 11, 9 -> Mean = (11 + 9) / 2 = 20 / 2 = 10

Sample 3: 15, 12 -> Mean = (15 + 12) / 2 = 27 / 2 = 13.5

...

Sample 25: 12, 15 -> Mean = (12 + 15) / 2 = 27 / 2 = 13.5

The means of the samples vary, but they tend to be close to the population mean of 13.

(d) Constructing a density histogram using the 25 x values:

Since the problem does not provide the values for the 25 x values, we cannot construct a density histogram or determine if most of the values are near the population mean.

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Complex numbers can be represented in GeoGebra using the complex number constructors, specifically the complexnumber(real,imaginary) command.

This command creates a complex number with the given real and imaginary components. For example, a complex number with a real part of 3 and an imaginary part of 4 can be written as complexnumber(3,4). This will create a complex number with a real part of 3 and an imaginary part of 4, represented as 3+4i. GeoGebra also contains other commands for manipulating complex numbers, such as the conjugate(z) command, which produces the conjugate of the given complex number z, and the re(z) and im(z) commands, which extract the real and imaginary components of the given z, respectively. Together, these commands allow GeoGebra to effectively represent and manipulate complex numbers.

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Answer:

Step-by-step explanation:

19  .m= (64*7)/8=56  

20.a= (36*7) /28=9

12*у=15у-40

12у-15у=-40

У=40/3

Answer:

(i) a = 2

   b = -1

   c = -1

(ii) x= 1

Step-by-step explanation:

Step 1: Factorise

\(f(x) = 2(x^{2} -2x+\frac{1}{2})\)  

Step 2: Use the complete square method.

\(f(x)=2(x^{2} -2x+(\frac{-2}{2})^{2} + \frac{1}{2} - (\frac{-2}{2})^{2} )\)  

Step 3: Have it to \(a(x+b)^{2} +c\)

\(f(x)=2((x-1)^{2} -\frac{1}{2} )\\ = 2(x-1)^{2} -1\)

Line of symmetry:  

To find line of symmetry, we use -b/2a formula.

Based from \(2x^{2} -4x+1\):

a=2, b=-4

-b/2a = -(-4)/2(2) = 1

Answer:

First option

Step-by-step explanation:

First, Solve the inequality:

Find the inequality that matches the solution:

Answer:

91 people

Step-by-step explanation:

(a) A nonzero vector orthogonal to the plane through the points P, Q, and R is (9, -17, 35). (b) The area of triangle PQR is \(\sqrt\)(811) / 2.

(a) To determine a nonzero vector orthogonal to the plane through the points P, Q, and R, we can first find two vectors in the plane and then take their cross product. Taking vectors PQ and PR, we have:

PQ = Q - P = (5, 1, -2) - (-4, 0, 0) = (9, 1, -2)

PR = R - P = (6, 4, 1) - (-4, 0, 0) = (10, 4, 1)

Taking the cross product of PQ and PR, we have:

n = PQ x PR = (9, 1, -2) x (10, 4, 1)

Evaluating the cross product gives n = (9, -17, 35). Therefore, (9, -17, 35) is a nonzero vector orthogonal to the plane through points P, Q, and R.

(b) To determine the area of triangle PQR, we can use the magnitude of the cross product of vectors PQ and PR divided by 2. The magnitude of the cross product is given by:

|n| = \(\sqrt\)((9)^2 + (-17)^2 + (35)^2)

Evaluating the magnitude gives |n| = \(\sqrt\)(811).

The area of triangle PQR is then:

Area = |n| / 2 = \(\sqrt\)(811) / 2.

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Let:

x = pounds of sands

y = pounds of cement

32 pounds of sand are needed

So, the z-scores are approximately 1.34 and 2.08.

Therefore, the probability that the sample mean will be between 66.6 and 68.4 is approximately 0.4115, or 41.15% (rounded to two decimal places).

To calculate the probability that the sample mean falls between 66.6 and 68.4, we need to find the z-scores corresponding to these values and then use the z-table or a statistical calculator.

a) Calculate the z-scores:

The formula for calculating the z-score is:

z = (x - μ) / (σ / √n)

For the lower value, x = 66.6, μ = 63.3, σ = 16.0, and n = 35:

z1 = (66.6 - 63.3) / (16.0 / √35) ≈ 1.34

For the upper value, x = 68.4, μ = 63.3, σ = 16.0, and n = 35:

z2 = (68.4 - 63.3) / (16.0 / √35) ≈ 2.08

b) Find the probability:

To find the probability between these two z-scores, we need to find the area under the standard normal distribution curve.

Using a z-table or a statistical calculator, we can find the probabilities corresponding to these z-scores:

P(1.34 ≤ z ≤ 2.08) ≈ 0.4115

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Answer:

Jack's final bank account amount will be $54,782.50, earning $7,459.31 in interest.

General Formulas and Concepts:
Algebra I

Compounded Interest Rate Formula: \(\displaystyle A = P \bigg( 1 + \frac{r}{n} \bigg) ^{nt}\)

Step-by-step explanation:

Step 1: Define

Identify given variables.

P = $47,323.15

r = 0.05

n = 1

t = 3

Step 2: Find Interest

∴ Jack will gain $7,459.31 and have a net balance of $54,782.50.

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Topic: Algebra I

Answer:

3053.62806

Step-by-step explanation:

d=18 so r=9

(check attachement)

Parallel lines have equal slopes, but different y intercepts.

For example, y = 2x+5 and y = 2x+7 are parallel lines with the same slope m = 2, but the y intercepts are different (5 and 7) to ensure we aren't talking about the same line.

The actual distance between Beitbridge and Musina is 3,900,000 kilometers.

To calculate the actual distance between Beitbridge and Musina, given the scale of the map and the measured distance on the map, we can use the concept of scale.

The scale of the map is given as 1:3,000,000, which means that 1 cm on the map represents 3,000,000 cm in real life.

The measured distance on the map between Beitbridge and Musina is 1.3 cm.

To find the actual distance, we can set up a proportion using the scale:

1 cm on the map / 3,000,000 cm in real life = 1.3 cm on the map / x km in real life.

Simplifying the proportion, we have:

1 / 3,000,000 = 1.3 / x.

Cross-multiplying, we get:

x = (1.3 * 3,000,000) / 1.

x = 3,900,000 / 1.

x = 3,900,000 km.

The actual distance between Beitbridge and Musina is 3,900,000 kilometers.

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The eigenvalues of a are 2, 2, 5, then a is invertible matrix .

The eigenvalues are 2, 2, 5.

(A) First check the matrix is certainly invertible.

The matrix is invertible when the product of eigenvalues does not equal to zero.

invertible of A = 2*2*5

invertible of A = 20 ≠ zero.

So the matrix is certainly invertible.

(B) Now we check the matrix is certainly diagonalizable.

We note that the eigen value 2 has an algebraic multiplicity of 2 (number of repetitions), but we are unsure if the accompanying eigen vectors likewise have a count of two (geometric multiplicity)

The sum of the algebraic multiplicities must equal the sum of the geometric multiplicities in order for A to be diagonalizable.

In this instance, there is no evidence to support the geometric multiplicity of the eigenvalue 2. Therefore, we are unable to affirm that A is diagonalizable

So A can not be diagonalizable.

(C) Now we check the matrix is certainly not diagonalizable.

If the homogeneous equation from (A-⋋I)x=0 when the eigen value ⋋=2 is substituted x+y+z=0, then the solution set is x=-k-m where y=k, z=m are the parameters.

So it can be written as

\(\left[\begin{array}{ccc}x\\y\\z\end{array}\right] = k\left[\begin{array}{ccc}-1\\1\\0\end{array}\right] + m \left[\begin{array}{ccc}-1\\0\\1\end{array}\right]\)

Putting k=1 and m=1, then the corresponding eigen vectors for ⋋=2 are  

\(\left[\begin{array}{ccc}-1\\1\\0\end{array}\right] , \left[\begin{array}{ccc}-1\\0\\1\end{array}\right]\)

So the geometric multiplicity of the eigen value ⋋=2 is 2.

The algebraic multiplicity = Geometric multiplicity we can see the given matrix A is diagonalizable.

So the statement is false.

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Answer:

Step-by-step explanation:

It's helpful to draw it out, but you need a calculator for this.

You have the values of line b, line c, and angle C.

You can use sinC / c since you have C and c.

Solve for sinB by doing sinB/5.7 = sinC/8.6

you'll get the value of sinB, use inverse trig to solve for B (sin^-1)

Then you'll have the angle values for C and B. Add them, and subtract by 180 to find the angle measure of A.

Use the steps above to find a:

sinA (which u just found) / a = sinC (125) / c (8.6)

Hope this helps.

To map polygon ABCDE onto polygon A'B'C'D'E', the following tranformations will take place:

A Dilation with a scale factor of 2 and a translation of 8 units to the right

Therefore the series of transformation are:

Dilation with a scale factor of 2

Translation of 8 units to the right

ANSWER:

Dilation with a scale factor of 2

Translation of 8 units to the right

Answer:

5 ≥ d^2 ≤ q

Step-by-step explanation:

let d= # of dimes

let q= # of quarters

hope this is right. does it look familiar?

Answer:

the answer is 78.36 sir

Step-by-step explanation:

lol its a troll

Using concepts of Mean, we got Paired samples test for the difference between two means is the type of test researcher is using.

The test procedure, called the two-sample t-test, is correct when the following conditions are met:

If the sample findings are not in favour, given the null hypothesis, the researcher rejects the null hypothesis. Typically, this will involves comparing the P-value to the significance level, and rejecting null hypothesis when the P-value is smaller than the significance level.

Hence, the test type which researcher is using Paired samples test for the difference between two means.

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Answer:

Step-by-step explanation:

If WY and XZ are the diagonals (I think they are), then the equation to find it is 16x + 2 = 36x - 6 --> 8 = 20x --> x = 0.4

16(0.4) + 2 = WY = XZ --> 6.4 + 2 = 8.4 are the diagonal lengths.

Answer:

2.99 = 3

2.999 = 3

Step-by-step explanation:

To round 2.99 to the nearest tenth consider the hundredths’ value of 2.99, which is 9 and equal or more than 5. Therefore, the tenths value of 2.99 increases by 1 to 0.

2.99 rounded to the nearest tenth = 3.0

Now

To round 2.999 to the nearest hundredth consider the thousandths’ value of 2.999, which is 9 and equal or more than 5. Therefore, the hundredths value of 2.999 increases by 1 to 0.

2.999 rounded to the nearest hundredth = 3.00

So, If you would round it to the nearest tenth which is the third nine, you'd see that it would add up to the whole number 3. So the answer is 3!!

The candy store will use 103 grams of sugar in 10 hours.

To find out how many grams of sugar the store will use in 10 hours, we can simply multiply the amount of sugar used in one hour (10.3 grams) by the number of hours (10).

To solve the problem, we use a simple multiplication formula: the amount used per hour (10.3 grams) multiplied by the number of hours (10) to find the total amount of sugar used in 10 hours.

We can interpret this problem using a rate equation: the rate of sugar usage is 10.3 grams/hour, and the time period is 10 hours. Multiplying the rate by the time gives the total amount of sugar used.

So the calculation would be:

10.3 grams/hour x 10 hours = 103 grams

Therefore, the candy store will use 103 grams of sugar in 10 hours.

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To calculate the annual payment required to pay off a five-year, $25,000 loan at an interest rate of 3.50 percent EAR, we can use the formula for calculating the equal annual payment for an amortizing loan.

The formula is: A = (P * r) / (1 - (1 + r)^(-n))

Where: A is the annual payment,

P is the loan principal ($25,000 in this case),

r is the annual interest rate in decimal form (0.035),

n is the number of years (5 in this case).

Substituting the given values into the formula, we have:

A = (25,000 * 0.035) / (1 - (1 + 0.035)^(-5))

Simplifying the equation, we can calculate the annual payment:

A = 6,208.61

Therefore, the annual payment required to pay off the five-year, $25,000 loan at an interest rate of 3.50 percent EAR is $6,208.61.

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Answer:

the right answer would be A: dilate by a scale factor of 2 and reflect over the x-axis

Step-by-step explanation:

you can clearly see the triangle reflect over the axis, not going down by 2 unit. the scale got bigger not smaller so it cant be dilate by a scale factor of 1/2.

have a nice day.

Answer:

D. Undefined

Step-by-step explanation:

4-4 = 0, 10-6 = 4

Change of x = 0

Change of y = 4

Since the change of x is 0 (a horizontal line), it is undefined.

Answer:

Step-by-step explanation:

recall that powers rule says that we can combine powers

\(5^{6}\)*\(5^{9}\) = \(5^{6+9}\)

\(5^{6+9}\) = \(5^{15}\)

Answer:

The first one

Step-by-step explanation:

Answer:

Impractical

Step-by-step explanation:

It's not practical to have a ship hold up for so long also new technology will arrive in the next 100 years no need to use outdated technology