For a project in her Geometry class, Victoria uses a mirror on the ground to measure the height of her school’s football goalpost. She walks a distance of 12.35 meters from the goalpost, then places a mirror on flat on the ground, marked with an X at the center. She then steps 1.25 meters to the other side of the mirror, until she can see the top of the goalpost clearly marked in the X. Her partner measures the distance from her eyes to the ground to be 1.75 meters. How tall is the goalpost? Round your answer to the nearest hundredth of a meter.

If one of the zeros in the quadratic polynomial is 4, then the value of k is 3.

A polynomial is a mathematical expression made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables. x2 4x + 7 is an illustration of a polynomial with a single indeterminate x. A polynomial is a mathematical expression that only uses the operations addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Variables are also known as indeterminates in mathematics.

Here,

4 is a root/zero of polynomial

P(x)  =   (k-2) x²  - 2 x  - (k+5)

P(4) = 0

(k - 2) 4²  - 2 * 4 - (k+5)  = 0

15 k - 45 = 0  

k = 3

The value of k if 4 is one of the zeros of the quadratic polynomial is 3.

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Complete question:

If one of the zeros of a quadratic polynomial(k-2)x^2-2x-(k+5) is 4 , find value of k.

The multiplicative inverse of p/q is q/p

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

Expression = p/q

The multiplicative inverse of an expression a is represented as

1/a

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

The multiplicative inverse of p/q is q/p

Hence, the multiplicative inverse of p/q is q/p

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Given,

The equation of the curve are,

Taking the equation first as,

Taking the equation second as,

We know that,

This is the required rectangular equation.

Hence, option c is correct.

Answer:

2/9 and 4/9

Step-by-step explanation:

There are 3 * 3 = 9 possible outcomes of spinning the spinners. Out of those, there are only 2 ways to achieve a product of 6 (2 and 3 or 6 and 1) so the answer to B is 2/9. For C, there are 4 ways for the total to be greater than 10 (12, 18, 20, 30) so the answer is 4/9.

Answer:

b=2/9

c=4/9

Step-by-step explanation:

b: 2/3(there are two options you can land on that have a pair that multiplies to six)*1/3(each only has one pair)= 2/9

c: 2/3(6 or 4)*2/3(3 or 5) =4/9

Answer:

f(x)=9^(x)

Plugging in m+n+p=x, we have

f(m+n+p) = 9^(m+n+p)

Using the properties of exponential a^(b+c) = a^b*a^c, we have

f(m+n+p) = 9^(m)*9^(n)*9^(p)

f(m+n+p) = f(m)*f(n)*f(p)

Given:

The system of the equation is,

Draw the lines on the graph, the point at which the lines intersects. That point will be the solution of the system.

The points on the line 2x+5y=0 are,

And the points on the line x+6y=14

The graph of the lines is,

As the point of intersection is ( -10,4).

The solution of the given system of equation is x = -10, y = 4.

Answer: 0.875 or 56/49

Step-by-step explanation:

x = -8

3x = 3 · (-8) = -24

.......

The fallout in the process could potentially be reduced by a factor of \($10^{1.276} \approx 19.7$\) if the process were corrected to operate at the nominal specification.

To estimate the potential capability, we first need to calculate the process capability index, which is given by:

\($C_{p k}=\min \left(\frac{U S L-\bar{x}}{3 s}, \frac{\bar{x}-L S L}{3 s}\right)$\)

where \($\bar{x}$\) is the sample mean, \($s$\) is the sample standard deviation, and \($USL$\) and \($LSL$\) are the upper and lower specification limits, respectively. In our case, we have:

\($\bar{x} = 100$\)

\($s = s_{\bar{x}} = \frac{s}{\sqrt{n}} = \frac{1.05}{\sqrt{5}} \approx 0.469$\)

\($USL = 105$\), \($LSL = 95$\)

\($C_{p k}=\min \left(\frac{105-100}{3(0.469)}, \frac{100-95}{3(0.469)}\right) \approx 0.426$\)

The potential capability is therefore approximately 0.426.

\($\frac{105+95}{2}-100=0$\)

In other words, there is no mean shift. Therefore, the actual capability is the same as the potential capability, which is approximately 0.426.

If the process were corrected to operate at the nominal specification of 100, the upper and lower specification limits would be 100 ± 10. Plugging these values into the formula for \($C_{pk}$\), we get:

\($C_{p k}=\min \left(\frac{110-100}{3(0.469)}, \frac{100-90}{3(0.469)}\right) \approx 1.702$\)

Therefore, the process capability would be significantly improved if it were corrected to operate at the nominal specification. The difference in capability can be quantified by taking the difference between the new and old values of \($C_{pk}$\):

\($\Delta C_{p k}=C_{p k, \text { new }}-C_{p k, \text { old }}=1.702-0.426 \approx 1.276$\)

To estimate the actual capability, we need to take into account the process mean shift, which is the difference between the actual mean and the target value. In our case, the target value is 100, and the process specifications are at 95 ± 10. This means that the actual mean is shifted by:

Plugging these values into the formula, we get:

This means that the fallout in the process could potentially be reduced by a factor of \($10^{1.276} \approx 19.7$\) if the process were corrected to operate at the nominal specification.

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Answer:

6

Step-by-step explanation:

6 is the most common lol

Answer:

I'll say 5

Step-by-step explanation:

Hoped this helped!

Answer:

g= -20,17

Step-by-step explanation:

i used symbolab plus i just worked this in class

The study design described is a cross-sectional study.

The study design in this scenario is a cross-sectional study. The study aims to examine the relationship between family status and school performance. The sample is selected by randomly choosing every 5th child from the list of children at the ABC elementary school. Data is collected from the school record for each child, and family status is operationalized by whether the child lives in a single-parent household, dual-parent household, or has a non-parent guardian in the household. The school performance is measured by administering a student math test and a student reading test to the child in April, with each test including 20 questions and each correct answer being worth five points.

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Answer:

8 :)

Step-by-step explanation:

Answer:

y = 5x-1

Step-by-step explanation:

parallel lines have the same slope.

y intercept: -1

slope: 5

- 1 is the same as +-1

so, y = 5x-1

Answer:

The annual net income is $2770

Step-by-step explanation:

The annual net income on the rental property is the yearly rental minus the yearly annual expenses which consist mortgage interest,taxes, repairs,insurance as well as annual depreciation totaling $8,750

Annual rental =monthly rental* 12 months=$960*12=$ 11,520.00  

Annual net income=$ 11,520.00-$8,750.00=$2,770

The annual net income is the gain that accrues to Anne Deno for purchasing the rental property and the subsequent letting to tenants

Answer:

163 degrees

Step-by-step explanation:

because the whole circle is 360 degrees and the other side would be 163 as it's the same angle.

Answer:

x>=9

Step-by-step explanation:

so, we can plot this on a number line

the point at 9 is a solid dot, since brackets (not parenthasis) indicates that we including the number. the shaded part of the line extends all the way to positive infinity. the shaded part means that it is a solution, while the un-shaded parts aren't solutions to [9,infinity) it is x>=9 and not x>9 because 9 is included.

x>=9 is the answer

Answer:

Step-by-step explanation:

Multiply the constants and the variables

(4*5)(x*y) = 20xy

Step-by-step explanation:

you can just put in some values to check.

I actually used p =2 and q=3

the It will be

2^3-1 + 3^2-1 = 1 (mod 2×3)

2^2 +3^1 = 1 (mod 6)

4+3= 1 (mod6)

7= 1 (mod6)

which is true.

therefore p^(q-1) + q^( p-1) = 1 ( mod pq) is true

To show that p^(q-1) + q^(p-1) = 1 (mod pq), we can use Fermat's Little Theorem, which states that if p is a prime number and a is an integer not divisible by p, then a^(p-1) = 1 (mod p). Using this theorem, we can first show that p^(q-1) = 1 (mod q), since q is a prime number and p is not divisible by q. Similarly, we can show that q^(p-1) = 1 (mod p), since p is a prime number and q is not divisible by p.

Therefore, we can write:

p^(q-1) + q^(p-1) = 1 (mod q)
p^(q-1) + q^(p-1) = 1 (mod p)

By the Chinese Remainder Theorem, we can combine these two equations to obtain:

p^(q-1) + q^(p-1) = 1 (mod pq)

Thus, we have shown that p^(q-1) + q^(p-1) = 1 (mod pq).
We'll use Fermat's Little Theorem to show that p^(q-1) + q^(p-1) = 1 (mod pq).

Fermat's Little Theorem states that if p is a prime number and a is an integer not divisible by p, then:
a^(p-1) ≡ 1 (mod p)

Step 1: Apply Fermat's Little Theorem for p and q:
Since p and q are prime numbers, we have:
p^(q-1) ≡ 1 (mod q) and q^(p-1) ≡ 1 (mod p)

Step 2: Add the two congruences:
p^(q-1) + q^(p-1) ≡ 1 + 1 (mod lcm(p, q))

Step 3: Simplify the congruence:
Since p and q are prime, lcm(p, q) = pq, so we get:
p^(q-1) + q^(p-1) ≡ 2 (mod pq)

In your question, you've mentioned that the result should be 1 (mod pq), but based on Fermat's Little Theorem, the correct result is actually:
p^(q-1) + q^(p-1) ≡ 2 (mod pq)

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If q is an odd number and the median of q consecutive integers is 120, then the largest of these integers is option (A) (q-1) / 2 + 120

The number q is an odd number

The median of q consecutive integers = 120

Consider the q = 3

Then three consecutive integers will be 119, 120, 121

The largest number = 121

Substitute the value of q in each options

Option A

(q-1) / 2 + 120

Substitute the value of q

(3-1)/2 + 120

Subtract the terms

=2/2 + 120

Divide the terms

= 1 + 120

= 121

Therefore, largest of these integers is (q-1) / 2 + 120

I have answered the question in general, as the given question is incomplete

The complete question is

if q is an odd number and the median of q consecutive integers is 120, what is the largest of these integers?

a) (q-1) / 2 + 120

b) q/2 + 119

c) q/2 + 120

d) (q+119)/2

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The expression where the greatest common factor (GCF) is factored completely is \(2x^3y + 18xy - 10x^2y - 90y = 2y(x^3 + 9x - 5x^2 - 45)\)

The expression completely factored in is

\(2y(x^3 + 9x - 5x^2 - 45) = 2y[x(x^2 - 5) + 9(x^2 - 5)]\\= 2y(x - 5)(x^2 + 9)\)

Please refer below for the remaining answers.

We have,

Part A:

To rewrite the expression 2x³y + 18xy - 10x²y - 90y so that the greatest common factor (GCF) is factored completely, we can factor out the common terms.

GCF: 2y

\(2x^3y + 18xy - 10x^2y - 90y = 2y(x^3 + 9x - 5x^2 - 45)\)

Part B:

To completely factor the expression, we can further factor the quadratic term.

\(2y(x^3 + 9x - 5x^2 - 45) = 2y[x(x^2 - 5) + 9(x^2 - 5)]\\= 2y(x - 5)(x^2 + 9)\)

Now,

Part A:

To determine the length of each side of the square given the area expression (9x² + 24x + 16), we need to factor it completely.

The area expression (9x² + 24x + 16) can be factored as (3x + 4)(3x + 4) or (3x + 4)².

Therefore, the length of each side of the square is 3x + 4.

Part B:

To determine the dimensions of the rectangle given the area expression (16x² - 25y²), we need to factor it completely.

The area expression (16x² - 25y²) is a difference of squares and can be factored as (4x - 5y)(4x + 5y).

Therefore, the dimensions of the rectangle are (4x - 5y) and (4x + 5y).

Now,

f(x) = 2x² - 5x + 3

Part A:

To find the x-intercepts of the graph of f(x), we set f(x) equal to zero and solve for x.

2x² - 5x + 3 = 0

The quadratic equation can be factored as (2x - 1)(x - 3) = 0.

Setting each factor equal to zero:

2x - 1 = 0 --> x = 1/2

x - 3 = 0 --> x = 3

Therefore, the x-intercepts of the graph of f(x) are x = 1/2 and x = 3.

Part B:

To determine if the vertex of the graph of f(x) is maximum or minimum, we can examine the coefficient of the x^2 term.

The coefficient of the x² term in f(x) is positive (2x²), indicating that the parabola opens upward and the vertex is a minimum.

To find the coordinates of the vertex, we can use the formula x = -b / (2a), where a and b are the coefficients of the quadratic equation.

For f(x),

a = 2 and b = -5.

x = -(-5) / (2 x 2) = 5/4

To find the corresponding y-coordinate, we substitute this x-value back into the equation f(x):

f(5/4) = 25/8 - 25/4 + 3 = 25/8 - 50/8 + 24/8 = -1/8

Therefore, the vertex of the graph of f(x) is at the coordinates (5/4, -1/8), and it is a minimum point.

Part C:

To graph f(x), we can start by plotting the x-intercepts, which we found to be x = 1/2 and x = 3.

These points represent where the graph intersects the x-axis.

Next,

We can plot the vertex at (5/4, -1/8), which represents the minimum point of the graph.

Since the coefficient of the x² term is positive, the parabola opens upward.

We can use the vertex and the symmetry of the parabola to draw the rest of the graph.

The parabola will be symmetric with respect to the line x = 5/4.

We can also plot additional points by substituting other x-values into the equation f(x) = 2x² - 5x + 3.

By connecting the plotted points, we can draw the graph of f(x).

The steps to graph f(x) involve plotting the x-intercepts, the vertex, and additional points, and then connecting them to form the parabolic curve.

The answer in part A (x-intercepts) and part B (vertex) are crucial in determining these key points on the graph.

Thus,

The expression where the greatest common factor (GCF) is factored completely is \(2x^3y + 18xy - 10x^2y - 90y = 2y(x^3 + 9x - 5x^2 - 45)\)

The expression completely factored in is

\(2y(x^3 + 9x - 5x^2 - 45) = 2y[x(x^2 - 5) + 9(x^2 - 5)]\\= 2y(x - 5)(x^2 + 9)\)

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Answer:

6a + 6b

Step-by-step explanation:

Its simplified

The constant of proportionality is the ratio of the number of guests to the food prepared is 0.8.

What are the ratio and proportion?

The ratio is the division of the two numbers.

For example, a/b, where a will be the numerator and b will be the denominator.

Proportion is the relation of a variable with another. It could be direct or inverse.

As per the given table,

Suppose the number of guest ∝ food prepared.

Take the first data,

12 ∝ 15

12 = k(15)

k = 12/15 = 0.8

Hence "The constant of proportionality is the ratio of the number of guests to the food prepared is 0.8".

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The length of the leg in the triangle is 11.6 units

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

The length of the other leg using Pythagorean Theorem is

Other Leg = √(Hypotenuse² - One Leg²)

So, we have

Orher Leg = √(16² - 11²)

Evaluate

Other leg = 11.6

Hence, the other leg is 11.6 units

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Answer:

Alright, lets get started.

Angle 3 and angle 4 are adjacent angles because they are having the common side.

They both are on straight line, so, their addition will be 180°.

Suppose angle 4 is x , hence

angle 4 + angle 3 = 180

Subtracting 89 from both sides

°

Hence angle 4 is 91°. : Answer

Hope it will help :)

Step-by-step explanation:

Answer:

91 degrees

Step-by-step explanation

trust the lord

A key requirement for the process of testing hypotheses in the scientific method is experimentation. A hypothesis is an idea or explanation for a phenomenon that is grounded in existing knowledge or observations, and the scientific method involves testing those hypotheses through experimentation.

The process of testing hypotheses requires the development of a testable hypothesis, the design of experiments to test the hypothesis, and the collection and analysis of data from those experiments to evaluate the hypothesis. The experiments must be designed carefully, with appropriate controls and variables to ensure that the results are reliable and valid. Scientists also need to communicate their findings to the scientific community, which involves publishing their results in scientific journals and presenting their work at conferences.

This helps to ensure that other scientists can replicate their experiments and validate their findings, which is a critical part of the scientific process. Ultimately, the process of testing hypotheses is essential for advancing scientific knowledge and understanding how the world works.

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Answer:

x= -3 y=2 (-3,2) this should be the answer for the system of equations Hope this helps!

The probability that Julian will roll a 3 on the next roll is approximately 16.67%. The probability of rolling a 3 on a normal 6-sided die is independent of the previous rolls. This means that regardless of the outcomes of Julian's previous rolls, the probability remains the same.

Explanation

On a 6-sided die, there is 1 favorable outcome for rolling a 3 (the number 3 itself) out of 6 possible outcomes (1, 2, 3, 4, 5, and 6).

To find the probability, you can use the formula:

Probability = (Number of favorable outcomes) / (Total number of outcomes)

In this case:

Probability of rolling a 3 = 1 (favorable outcome) / 6 (total outcomes)

Probability of rolling a 3 = 1/6 ≈ 0.1667 or 16.67%

So, the probability that Julian will roll a 3 on the next roll is approximately 16.67%.

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