What are the solutions to the system of equations? y = 1/2 * x ^ 2 - 4; y = x - 4 Graph the system of equations to solve. (0, - 4) and (2, - 2); (- 2.75, 0) and (2.75, 0); (2, - 2) and (4, 0); (4, 0) and (0, - 4)

The required equation in slope intercept form is equal to y = -2x - 21.

In Mathematics, the slope-intercept form of a line can be calculated by using this linear equation:

y = mx + c

Where:

Based on the information provided about the line, it is represented by this equation;

2x - y = -21

Making y the subject of formula in the above equation, we have the following:

y = -2x - 21

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Answer: y/x = k, where k is the constant of proportionality.

Step-by-step explanation:

The proportional connection is represented by the linear equation y equals two-thirds times x.

A proportionate connection is a two-variable relationship in which one variable is a constant multiple of the other. In other words, if y is proportional to x directly, then y = kx for some constant k. This can alternatively be written as y/x = k, where k is the proportionality constant.

The proportionate connection is represented by the linear equation y = 2/3x.

It demonstrates a direct connection since the coefficient of x (2/3) is constant and there is no constant term (y-intercept) to break the proportionality.

The other equations do not have a proportionate connection because they feature a variable coefficient or a constant term.

Answer:

y/x = k, where k is the constant of proportionality.

Step-by-step explanation:

To find the zeroes (also known as roots) of a polynomial, we can set the polynomial equal to zero and solve for the variable. The solutions to the equation are the zeroes of the polynomial.

What is a polynomial?

A polynomial is a mathematical expression that is a sum of powers in one or more variables (indeterminates) with non-negative integer exponents and real or complex coefficients. The degree of a polynomial is the highest power of the variable. For example, the polynomial 3x^2 + 2x - 1 is a polynomial of degree 2, and the polynomial 5 is a polynomial of degree 0.

To find the zeroes (also known as roots) of a polynomial, we can set the polynomial equal to zero and solve for the variable. The solutions to the equation are the zeroes of the polynomial.

For example, to find the zeroes of the polynomial 3x^2 + 2x - 1, we set the polynomial equal to zero:

3x^2 + 2x - 1 = 0

Then we can factor the polynomial or use the quadratic formula to find the solutions:

x = (-2 +/- sqrt(2^2 - 43(-1)) ) / (2*3) = (-2 +/- sqrt(4 + 12))/6 = (-2 +/- sqrt(16))/6 = (-1 +/- sqrt(4))/3 = (-1 +/- 2i)/3

The zeroes of the polynomial 3x^2 + 2x - 1 are x = (-1 + 2i)/3 and x = (-1 - 2i)/3, which are complex numbers.

Hence, To find the zeroes (also known as roots) of a polynomial, we can set the polynomial equal to zero and solve for the variable. The solutions to the equation are the zeroes of the polynomial.

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A p-value of 0.04 obtained from a two-tailed t-test means that there is a 4% chance that the obtained results are due to chance. Given the conventional significance level, you would accept that the alternative hypothesis is correct.

The P=0.04 defines that if the null hypothesis is true and if you perform the study a large number of times and in exactly the same manner.

Drawing random samples from the population on each occasion, then, on 4% of occasions, you would get the same or greater difference between groups.

In statistical hypothesis testing, we need to express the null hypothesis, which is the no statistical difference within the groups, and the alternative hypothesis, which is the statistical difference.

Then, we determine the test statistic, which is a standardized quantitative measure of the group difference.

The null hypothesis predicts that the test statistic value will be small, but there is a slight possibility that it will be big by chance. We utilize the test statistic to compute the p-value once we determine the test statistic.

The p-value is described as the calculated probability of determining the observed result from the value of the test statistic, or larger, under the null hypothesis.

Therefore, we can conclude that the value of the definition of the p-value is the probability that we would see a test statistic this extreme or more if the null hypothesis were true.

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The value of x and y of the first parallelogram is x = 7 and y = 9

The value of x and y of the second parallelogram is x = 3 and y = 6

A parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure

The four types are parallelograms, squares, rectangles, and rhombuses

Properties of Parallelogram

Opposite sides are parallel

Opposite sides are congruent

Opposite angles are congruent.

Same-Side interior angles (consecutive angles) are supplementary

Each diagonal of a parallelogram separates it into two congruent triangles

The diagonals of a parallelogram bisect each other

Given data ,

a)

Let the first parallelogram be ABCD

Now , the opposite sides are parallel and opposite sides are congruent

So , The measure of AB = measure of CD

And , the measure of AD = measure of BC

Substituting the values in the equation , we get

3x - 5 = 2x + 2   be equation (1)

On simplifying the equation , we get

Subtracting 2x on both sides of the equation , we get

x - 5 = 2

Adding 5 on both sides of the equation , we get

x = 7

Now , 2y - 6 = y + 3   be equation (2)

On simplifying the equation , we get

Subtracting y on both sides of the equation , we get

y - 6 = 3

Adding 6 on both sides of the equation , we get

y = 9

Therefore , the value of x and y of the parallelogram is 7 and 9 respectively

b)

Let the second parallelogram be ABCD

Now , the the diagonals of a parallelogram bisect each other

Let O be the point of intersection of diagonals

So , The measure of AO = measure of CO

And , the measure of DO = measure of BO

Substituting the values in the equation , we get

2x + 5 = 11   be equation (1)

On simplifying the equation , we get

Subtracting 5 on both sides of the equation , we get

2x = 6

Divide by 2 on both sides of the equation , we get

x = 3

Now , y + 4 = 2x + 4   be equation (2)

On simplifying the equation , we get

Substitute the value of x = 3 in the equation , we get

y + 4 = 2 ( 3 ) + 4

y + 4 = 10

Subtracting 4 on both sides of the equation , we get

y = 6

Therefore , the value of x and y of the parallelogram is 3 and 6 respectively

Hence , the measures of parallelogram is solved

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[tex] \large \frak{ \green 5 + \red{w }= \green 8}[/tex]

[tex] \: [/tex]

[tex] \ \: \large \frak{ \red{w }= \green 8 { -} \green5}[/tex]

[tex] \: [/tex]

[tex] \underline{ \boxed{ \large \frak{ \: \red{w }= \green 3 \: }}}[/tex]

[tex] \: [/tex]

hope it helps!

Answer:

see below

Step-by-step explanation:

b = √3

then move t to the end you'll see

m= -0.4√13

It is revealed through completing the task that the graph of y = sin x + cos x is periodic, having a maximum point at x 0.94 and y 2.24. We've also noted that changing the values of A and B causes the graph to move to the left, with the highest point at x 0.44 and y 2.84. This demonstrates that the ratio of A and B determines the greatest point of the graph.

This activity has demonstrated the effect of changing the coefficients of sine and cosine functions when combined. For example, when A and B are both 1, the graph of y = sin x + cos x creates a wave-like shape with a maximum point at (π/2, 2). When A is increased to 2 and B is kept at 1, the maximum point moves to the right and increases in y-value to (2π/3, 3). When B is increased to 2 and A is kept at 1, the maximum point moves to the left and increases in y-value to (π/3, 3). This shows that when the coefficient of the sine term is increased, the maximum point moves to the right, and when the coefficient of the cosine term is increased, the maximum point moves to the left. This also shows that the maximum point of the graph y = A sin x + B cos x increases in y-value as A and B increase.

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Answer:

I honestly hv iyiu u ughu ugvjug uyvbuyg uugbjug niyhnig mhyij. umnninji. oh jiuh

the angle between the diagonal of a cube and its edge is equal to 35.2 degrees.

Let us consider a cube with side length = a.

Length of diagonal of cube on one of its faces = a√2

Length of diagonal of cube = a√3

To find the angle between the, use law of cosines.

The law of cosines is given by.

⇒ [tex]c^2=a^2+b^2-2abcosC[/tex]

Where c = length of side c, b = length of side b, a = length of side a

C = angle opposite to c

⇒ [tex]c^2=(a\sqrt{2})^2+(a\sqrt{3})^2-2a\sqrt{2}a\sqrt{3}[/tex]

On simplification,

[tex]cosC=\frac{2a^2}{a^2\sqrt{2}\sqrt{3}} \\cosC=\sqrt\frac{2}{3} \\[/tex]

C=35.2 degree

Therefore, the angle between the diagonals is 35.2°

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Answer:

D

Step-by-step explanation:

Option A has a dot on -25 and the arrows point from there to the left of the number line, going down from there. Representing x<-25.

Option B has a dot on -25 and the arrow goes to the right from there meaning it goes up. Representing x>-25

Option C has a dot on 25 and an arrow pointing to the left going down. Representing x<25

Finally, option D has a dot on 25 and an arrow pointing to the right meaning the number is going upward as intended by the question.

the expression for the apparent nth term an of the sequence is 3*2^(n-1) + 1.

the expression for the apparent nth term an of the sequence is 3*2^(n-1) + 1.

an = 3*2^(n-1) + 1

The sequence appears to follow a pattern of 3*2^n + 1

Therefore, the expression for the apparent nth term an of the sequence is 3*2^(n-1) + 1. (Note that n begins with 1, so we subtract 1 from n.)

The nth term an of the sequence 3, 10, 29, 66, 127, can be expressed as 3*2^(n-1) + 1. This follows a pattern of multiplying the previous term by 2 and then adding 1. For example, the second term 10 is 3*2^1 + 1, and the third term is 3*2^2 + 1. This pattern continues for each term in the sequence, which begins at n=1. Therefore, the expression for the apparent nth term an of the sequence is 3*2^(n-1) + 1.

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The probability that the student owns a credit card given that they are a freshman is 0.350  (3 d.p.)

[tex]Probability\: of\: an\: event\: occurring = \frac{Number\: of \:ways\:it\:can\:occur}{Total\:no.\:of\:possible\:outcomes}[/tex]

Let P(A) = probability that the student is a freshman

Let P(B) = probability that the student owns a credit card

Use the given table to calculate the probability that the student is a freshman:

[tex]= > P(A)=\frac{60}{100} =0.6[/tex]

And the probability that the student is a freshman and owns a credit card:

[tex]= > P(A \cap B)=\frac{21}{100}=0.21[/tex]

To find the probability that the student owns a credit card given that they are a freshman, use the conditional probability formula:

Conditional Probability Formula

The probability of B given A is:

[tex]P(B |A)=\frac{P(A\cap B)}{P(A)}[/tex]

Substitute the found values into the formula:

[tex]P(B|A)=\frac{0.21}{0.6} =0.35[/tex]

Therefore, the probability that the student owns a credit card given that they are a freshman is 0.35.

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The complete question is:

A group of students was asked if they carry a credit card. the responses are listed in the table. if a student is selected at random, find the probability that he or she owns a credit card given that the student is a freshman. round your answer to three decimal places.

The answer to column 4 is a circle pattern that is shifted one unit up. This pattern consists of a series of overlapping circles that expand outward in a vertical direction.

To replace the question mark in column 4, you need to identify the pattern that is shifted one unit up. To do this, start by looking at the pattern in column 3 and imagining it shifted upwards one unit. This will give you the pattern for column 4. The pattern is a series of overlapping circles which expand outward in a vertical direction. To create the pattern, start by drawing a circle in the center of the column. Then, draw circles around the center circle that are slightly larger than the previous one. Repeat this process until the circles reach the edge of the column. This will create the circle pattern that is shifted one unit up. Finally, connect the circles with straight lines to create the full pattern. This pattern will replace the question mark in column 4.

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The complete question: which pattern should replace the question mark in column 4? this question is required. * circle pattern up one circle pattern down one

the data suggests that the difference in average tension bond strengths is greater than 0. In other words, the polymer latex modified mortar has a higher tension bond strength than the unmodified mortar.

a) The rejection region for this one-tailed hypothesis test is z ? z > 2.33.

The test statistic value is z = 2.76.

Therefore, the conclusion is that we reject H0. The data suggests that the difference in average tension bond strengths is greater than 0.

For this one-tailed hypothesis test, we must reject the null hypothesis (H0: m1 - m2 = 0) if the test statistic is greater than 2.33. Our test statistic value is 2.76, which is greater than 2.33, so we reject H0. This indicates that the data suggests that the difference in average tension bond strengths is greater than 0. In other words, the polymer latex modified mortar has a higher tension bond strength than the unmodified mortar.

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The expression for the total number of pages Millie and Lee read each day is 225 + 155.

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

Mille = 225 pages

Lee = 155 pages

The expression to find the total number of pages Millie and Lee read each day is given by the sum of the individual pages

i.e. p = 225 + 155

So, the expression to find p is p = 225 + 155.

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5329 Sq meters  is the maximum area that can be enclosed.

What is a rectangle, exactly?

A rectangle is a sort of quadrilateral with parallel sides that are equal to one another and four vertices that are all 90 degrees apart. It is also known as an equiangular quadrilateral for this reason.

                          The term "parallelogram" can also be used to describe a rectangle because the opposing sides are equal and parallel.

Perimeter of Rectangle: 2W + 2L

One L is the river so we have 3 sides

220m/3 = 73m

Area of Rectangle is WL

73 × 73 =  5329 Sq meters

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Choosing a white rose at random first and then again at a later time are separate actions. based on the information provided White roses in a vase total four.

All potential results are gathered in a random experiment's sample space. A portion of the sample space is made up of an event connected to a random experiment. A value between 0 and 1 represents the chance of any result. All possible outcomes have a cumulative probability of 1.

A random experiment's sample space, or S, is referred to as the collection of all potential results. The results, often referred to as sample points, in a random experiment are exclusive (i.e., they cannot occur simultaneously). Sample space is the collection of all outcomes that can be found in a random experiment. The S sign stands in for it. the sample space is (S) = (HH), (HT), for two coin tosses, for instance (TT) .

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The number of quarters in the bowl is 14.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x+ 3 = 9 is an equation.

We have,

Dimes = x

Quarters = y

10 dimes = $1

1 dime = $0.1

4 quarters = $1

1 quarter = $0.25

Now,

0.1x + 0.25y = 5 _____(1)

x + y = 29 _____(2)

Solve for y from (1) and (2),

x = 29 - y

Substitute in (1) we get,

0.1 (29 - y) + 0.25y = 5

2.9 - 0.1y + 0.25y = 5

2.9 + 0.15y = 5

0.15y = 5 - 2.9

y = 2.1/0.15

y = 14

Thus,

There are 14 quarters in the bowl.

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The linear transformation a must be an involution, meaning it must be its own inverse, such that a^2 = 1. In order for the probability density functions (PDFs) of x and y to be equal, the linear transformation a must satisfy a certain property.

In order for the probability density functions (PDFs) of x and y to be equal, the linear transformation a must satisfy a certain property. To determine this property, we can look at the two-dimensional transformation above, where y = ax + b. In order for the PDFs of x and y to be the same, the linear transformation a must be an involution, meaning it must be its own inverse, such that a^2 = 1. The linear transformation a must be an involution, meaning it must be its own inverse, such that a^2 = 1.In order for the probability density functions (PDFs) of x and y to be equal, the linear transformation a must satisfy a certain property.

The complete question is : g as a generalization of the two-dimensional transformation above, what property must the linear transformation a satisfy if the pdfs for x and y, where y = ax + b, are to be the same?

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Nick has failed to meet the condition that n p hat greater-than-or-equal-to 10 and n (1 minus p hat) greater-than-or-equal-to 10.

In order for the Central Limit Theorem to be applied and for the sample proportion to be approximately normally distributed, the sample size must be at least 30. This means that the sample size must be large enough so that the sample proportion of healthy breakfast eaters (p hat) and the sample proportion of non-healthy breakfast eaters (1-p hat) are both greater than or equal to 10. In this case, since the sample proportion of healthy breakfast eaters is 20/25 = 0.8, the sample proportion of non-healthy breakfast eaters is 5/25 = 0.2. Since 5 is less than 10, this condition is not met, and Nick cannot construct a confidence interval for p.

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The remainder when the sum Σ 2017 m=2 Q(m) is divided by 1000 is 448.

448

Q(m) is the least positive integer such that for every n ≥ Q(m), there is a perfect cube k^3 in the range n < k^3 ≤ m.

For example, Q(2) = 1 since 1^3 is in the range 1 < 1^3 ≤ 2.

Similarly, Q(3) = 2 since 2^3 is in the range 2 < 2^3 ≤ 3, and Q(4) = 3 since 3^3 is in the range 3 < 3^3 ≤ 4.

We are asked to find the remainder when the sum Σ 2017 m=2 Q(m) is divided by 1000.

To do this, we can calculate the sum of the first 2017 terms of the sequence.

Q(2) + Q(3) + Q(4) + ... + Q(2017) = 448

Since 448 is divisible by 1000, the remainder when the sum is divided by 1000 is 0.

The remainder when the sum Σ 2017 m=2 Q(m) is divided by 1000 is 448.

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Answer:

£362.1

Step-by-step explanation:

6.5% =

6.5 / 100 =

65 / 1000 = 0.065

£340 * 0.065 = £22.1  => £22.1 is the pay raise in terms of English pounds(£)

Now add the pay raise to the earnings per week to get the total earnings after the raise:

£22.1 + £340 =

£22.1 + £340.0 = £362.1

The triangle with the side lengths and the angle is drawn by the image given at the end of the answer.

The area of the triangle is given as follows:

1.68 inches squared.

The area of a triangle, given two side lengths a and b, and the angle θ between them, is given as follows:

A = ab x sin(θ).

The parameters for this problem are given as follows:

The angle is of 50º, hence the area is given as follows:

A = 1.25 x 1.75 x sin(50º)

A = 1.68 inches squared.

The problem asks for the area of the triangle.

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The length of side LN is equal to 44 units. (Correct choice: A)

Two triangles are similar when these triangles have congruent angles but non-congruent though proportional sides. Triangles LMN and NUV are similar. Therefore, we can determine the length of side LN of geometrical system by means of following relationship:

NV / LN = NU / MN

LN = NV × MN / NU

If we know that NV = 11, MN = 32 and NU = 8, then the length of side LN is:

LN = 11 ×  (32 / 8)

LN = 11 × 4

LN = 44

The side LN has a length of 44 units.

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Answer:

Step-by-step explanation:

we first have to remove the 3 years as it is the difference

then when we divide it we get the age of yeboah=10

as akua is 3 years older we add the3 to the 10= 13

the product is = 10×13=130

The interval notation, which describes a set of numbers by using values enclosed in brackets, can be used to express the domain and range. When writing intervals, we place a square bracket around the endpoint when it is part of the set and a parenthesis around it if it is not or if the interval is unbound.

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The correct option is e. (Necessarily False) It required by the court to seek counselling

Because it is given as a fact that the child was "required by the court to seek counselling" ; and there is already P -> Q statement; where P : A child is released with no charges. and Q : Child is NOT required by the court to seek counseling. Taking the negation of this [tex]$\sim Q \Longrightarrow \sim P$[/tex]

[tex]$\sim P:$[/tex]Child is released with some charge.

If your child is arrested for a criminal offence and they are under 18, the police must tell you as soon as possible. The police should not interview your child until you are present, unless a delay would mean an immediate risk of harm to someone or serious loss of, or damage to, property.

Legal Counselling is the process by which a lawyer communicates advice to a client. I cannot emphasize anymore over the fact that it is the duty of an advocate to fearlessly uphold the interests of his client by all fair and honorable means without regard to any unpleasant consequences to himself or any other.

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