Identify the Y-INTERCEPT of the graph from the following equation. Write your answer in coordinate pair form with parentheses * y = -3(x-4)2 + 1

Answer:

Negative Reciprocals

Step-by-step explanation:

Consider two slopes being perpendicular to each other:

\(\displaystyle \large{m_1\cdot m_2=-1}\)

You will either receive:

\(\displaystyle \large{m_1=-\dfrac{1}{m_2}}\)

or:

\(\displaystyle \large{m_2=-\dfrac{1}{m_1}}\)

Say, you want to find perpendicular slope of 4. You have first slope as 4 and another as unknown which is assigned as m variable:

\(\displaystyle \large{4m=-1}\\\displaystyle \large{m=-\dfrac{1}{4}}\)

Therefore, 4 and -1/4 are perpendicular to each other. See that one slope is positives while another is negative. If you have negative slope then the perpendicular slope is positive.

Hence, they are indeed reciprocal but also negative as well.

Answer:

83 kids total

Step-by-step explanation:

There are 54 girls on the playground. There are 25 fewer boys than girls on the playground. How many kids are on the playground?

girls = 54

boys = 54 - 25 = 29

54 + 29 = 83 kids total

kids that are on the playground are 83.

Merging objects and identifying them since one big bunch is done through addition. In arithmetic, addition is the technique of adding two or more integers together. The product can meet are the quantities that are included, and the outcome of the operation, or the final response, is referred to as the sum.

The total number of girls that are present is 54

The data given is that there are

25 fewer boys taht are4 present

The total number of boys will be

boys = 54 - 25 = 29

The number of kids that are present will be the total of boys and girls that are present.

Kids = boys + girls

54 + 29 = 83 kids total

The quantity of kids that are present in the playground is 83.

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The angle measures for this problem are given as follows:

The sum of the measures of the internal angles of a triangle is of 180º.

The triangle in this problem is ABC, hence the measure of a is obtained as follows:

a + 68 + 50 = 180

a = 180 - (68 + 50)

a = 62º.

c and d are corresponding angles to angle a, as they are on the same position relative to parallel lines, hence their measures are given as follows:

Angle b is a corresponding interior angle with angle a, hence they are supplementary and it's measure is given as follows:

a + b = 180

62 + b = 180

b = 118º.

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The area of the shaded part is: 42.14 ft² .

Area = s²

Area = 1/4πr²

Thus:

Area of the shaded part of the figure = area of square - area of quarter circle

Area of shaded part = s² - 1/4πr²

s = 14 ft

r = 14 ft

Substitute

Area of shaded part = 14² - 1/4(3.14)(14²)

= 42.14 ft²

Therefore, the area of the shaded part is: 42.14 ft² .

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Answer:

1/5x

Step-by-step explanation:

1/5x

The percentage of sugars in the carbohydrate in Fitade is 64%.

The percentage refers to the ratio or proportion of one value (numerator) compared with another (denominator).

Percentages are fractional values, which can also be expressed as decimals, fractions, or ratios.

Nutritional Information    per 100 ml     per bottle

Energy (kilocalories)               28               112 (28 x 4)

Carbohydrate (grams)              6.25          25

   of which sugars (grams)       4                16

Salt (grams)                               0.1 (0.4)      0.4

Sugar in Carbohydrate = 4/6.25

= 64% (4/6.25 x 100)

= 0.64

or 64% (16/25 x 100)

Thus, we can conclude that sugar is 64 percent of the carbohydrate in Fitade.

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Answer:

Option C.

Step-by-step explanation:

From the table attached,

Pre-image coordinates J(-8, 2) → Image coordinates J'(-22, 5.5)

J(-8, 2) → J'(-22, 5.5)

Since, rule for the dilation of a point is,

(x, y) → (kx, ky) [Here k = scale factor of dilation]

Therefore, kx = -22

k(-8) = -22

k = \(\frac{-22}{-8}\)

k = 2.75

So the scale factor should be 2.75

From the given options,

Option A.

(x, y) → \(\frac{4}{11}(x, y)\)

       → 0.36(x, y)

But value of k should be 0.36

Therefore, Incorrect option.

Option B.

(x, y) → \(\frac{3}{22}(x, y)\)

       → 0.14(x, y)

k = 0.14

But the value of k should be 2.75

Incorrect option.

Option C.

(x, y) → \(\frac{11}{4}(x, y)\)

       → 2.75(x, y)

k = 2.75

Therefore, this option is correct.

Option D.

(x, y) → \(\frac{22}{3}(x, y)\)

       → 7.33(x, y)

k = 7.33

But the scale factor should be 7.33

Incorrect option.

Each letter should be matched to its correct term as follows;

1. A ⇔ Efficiency.

2. B ⇔ Impossible.

3. C ⇔ Inefficiency.

In Economics and Mathematics, a production possibilities curve (PPC) can be defined as a type of graph that is typically used for illustrating the maximum and best combinations of two (2) products that can be produced by a producer (manufacturer) in an economy, if they both depend on the following two (2) factors;

Based on the production possibilities curve shown in the image attached above, we can reasonably infer and logically deduce that each of the letters represent the following terminologies;

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The key features of the given quadratic functions are listed below.

In Mathematics and Geometry, the graph of any quadratic function would always form a parabolic curve because it is a u-shaped. Based on the first quadratic function, we can logically deduce that the graph is an upward parabola because the coefficient of x² is positive and the value of "a" is greater than zero (0) i.e 3 > 0.

For the quadratic function y = 3x² - 5, the key features are as follows;

Axis of symmetry: x = 0.

Vertex: (0, -5).

Domain: [-∞, ∞]

Range: [-5, ∞]

For the quadratic function y = -2x² + 12x - 15, the key features are as follows;

Axis of symmetry: x = 3.

Vertex: (3, 3).

Domain: [-∞, ∞]

Range: [-∞, 3]

For the quadratic function y = -x² + 1, the key features are as follows;

Axis of symmetry: x = 0.

Vertex: (0, 1).

Domain: [-∞, ∞]

Range: [-∞, 1]

For the quadratic function y = 2x² - 16x + 30, the key features are as follows;

Axis of symmetry: x = 4.

Vertex: (4, -2).

Domain: [-∞, ∞]

Range: [-2, ∞]

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Answer: NOW

Step-by-step explanation:

Total amount of money in the account will be $456.

Simple interest is an interest charge that borrowers pay lenders for a loan. It is calculated using the principal only and does not include compounding interest.

The formula for simple interest is: Simple Interest = Principal × Rate × Time

Principal (P) is $300

Rate (R) is 6.5%

Time (T) is 8 years.

Simple Interest = $300 × 0.065 × 8

Simple Interest = $156

Total Amount = Principal + Simple Interest

Total Amount = $300 + $156

Total Amount = $456.

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The function f(x) = x² + 6x + 7 is increasing over the interval x > -3 and decreasing over the interval x < -3.

An equation is an expression that shows the relationship between two or more numbers and variables.

Given the function f(x) = x² + 6x + 7. This is a quadratic equation,that is of degree two.

The function f(x) = x² + 6x + 7 is increasing over the interval x > -3 and decreasing over the interval x < -3.

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Answer:

29

Step-by-step explanation:

=5+5×5–1(5÷5=1)

Multiplication

=5+25–1(5×5=25)

Addition

=30–1

(25+5=30)

Subtraction

=29

(30-1=29)

Answer:

4(h+3)

Step-by-step explanation:

4h+12

Rewriting as

4h+4*3

Factor out the 4

4(h+3)

Answer:

4(h+3)

Step-by-step explanation:

Answer:

\( z = \frac{500-520}{\frac{90}{\sqrt{100}}}= -2.22\)

And we can find this probability using the normal standard distribution and we got:

\( P(z<-2.22) =0.0132\)

Step-by-step explanation:

For this case we have the foolowing parameters given:

\( \mu = 520\) represent the mean

\( \sigma =90\) represent the standard deviation

\( n = 100\) the sample size selected

And for this case since the sample size is large enough (n>30) we can apply the central limit theorem and the distribution for the sample mean would be given by:

\( \bar X \sim N(\mu , \frac{\sigma}{\sqrt{n}}) \)

And we want to find this probability:

\( P(\bar X <500)\)

We can use the z score formula given by:

\( z = \frac{500-520}{\frac{90}{\sqrt{100}}}= -2.22\)

And we can find this probability using the normal standard distribution and we got:

\( P(z<-2.22) =0.0132\)

Is there anything else that goes with the question or is that it?

The table can be summarized as follows:

|          | Has a dog | Does not have a dog |

|----------|-----------|---------------------|

| Has a cat     | 2         | 3                   |

| Does not have a cat | 12        | 10                  |

To find the probability that a student chosen randomly from the class has a cat, we need to find the total number of students who have a cat (regardless of whether or not they have a dog), and divide it by the total number of students in the class.

The number of students who have a cat is 2 (those who have a dog and a cat) + 3 (those who have a cat but do not have a dog) = 5.

The total number of students in the class is the sum of all four categories: 2 (has a cat and a dog) + 3 (has a cat, does not have a dog) + 12 (does not have a cat, has a dog) + 10 (does not have a cat, does not have a dog) = 27.

So, the probability that a student chosen randomly from the class has a cat is 5/27.

The value of ABP is 120°

The value of PQX is 60°

A hexagon, also known as a sexagon, is a six-sided polygon that forms the shape of a cube in geometry. Any simple hexagon has 720° of internal angles in total.

To find their values:

Recall that in a regular hexagon, (6-2) x 180°/ 6 = 120°

Also, (5-2) x 180°/5 = 108°

With these values, we would find that the value of ABP is 120°

<PQX = 120°/2 = 60°

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1. Answer (a) Positive. The leading coefficient of the polynomial on the right is positive.

Answer (b) 3, the highest power of the variable is 3, so the minimum degree of the polynomial is 3.

2. Answer (a) 2, Answer (b) 1

3. Answer (a) 3, Answer (b) 1 and 5

A polynomial is an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables. Polynomials can have constants and variables, and they usually have multiple terms that are separated by addition or subtraction.

1. The leading coefficient of a polynomial is the coefficient of the highest degree term. In the graph, the highest degree term is x3, and it is positive. Therefore, the leading coefficient of the polynomial on the right is positive.

The degree of a polynomial is the highest power of the variable in the equation. In the graph, the highest power of the variable is 3, so the minimum degree of the polynomial is 3.

2. The number of real zeros of a polynomial is the number of times the polynomial crosses the x-axis. In the graph, the polynomial crosses the x-axis twice, so it has 2 real zeros.

The number of imaginary zeros of a polynomial is the number of times the polynomial bounces off the x-axis. In the graph, the polynomial bounces off the x-axis once, so it has 1 imaginary zero.

3. The polynomial p(x) bounces off the x-axis at x=3 because the polynomial changes direction at this point.

The polynomial p(x) crosses the x-axis at x=1 and x=5 because the polynomial intersects the x-axis at these points.

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Answer:

A

Step-by-step explanation:

Answer:

27

Step-by-step explanation:

Because if it is halfway, that means

halfway=1/2

1/2=1/2 of 54

54/2 or 1/2 of 54=27

PLS MARK ME BRAINLIEST I NEED IT PLEASE

The center of the sign will be 27 feet apart from both ends of the bridge.

Given that,
A footbridge has a span of 54 feet. A sign is to be placed exactly halfway across the bridge. How far will the center of the sign be from each end of the bridge is to be determined.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,

Here,

Since the bridge is 54 feet long,
Now at the center of the bridge, a sign is placed,
So the distance of sign from both ends is equal to half of the total length of the bridge. i.e.
= 54 / 2
= 27

Thus, the center of the sign will be 27 feet apart from both ends of the bridge.

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Answer:

\(r \geqslant - 16\)

Step-by-step explanation:

\( \frac{ - 10 + r}{2} \geqslant - 13\)

multiply both sides by 2:

\( - 10 + r \geqslant - 26\)

add 10 on both sides:

\(r \geqslant - 16\)

Answer:

\(r \ge -16\)

Step-by-step explanation:

To solve any equation/inequality:

1. get the variable to show up exactly once

2. isolate it

\(\frac{-10+r}{2} \ge -13\)

Multiply both sides by 2 and simplify (note that we're multiplying by a positive, not a negative, so the direction of the inequality stays the same, whereas multiplying or dividing by a negative would have changed the direction of the inequality)

\(\frac{-10+r}{2} *2 \ge -13 *2\)

\(-10+r \ge -26\)

Add 10 to both sides, and simplify

\((-10+r)+10 \ge (-26)+10\)

\(r \ge -16\)

Answer:

Inverse Property of Addition

Step-by-step explanation:

Answer:

The 90% confidence interval for the mean time that the drug will take to reduce all fevers for all people is between 304 minutes and 336 minutes

Step-by-step explanation:

We have the standard deviation for the sample, so we use the t-distribution to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 40 - 1 = 39

90% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 39 degrees of freedom(y-axis) and a confidence level of \(1 - \frac{1 - 0.9}{2} = 0.95\). So we have T = 1.685

The margin of error is:

\(M = T\frac{s}{\sqrt{n}} = 1.685\frac{60}{\sqrt{40}} = 16\)

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 320 - 16 = 304 minutes

The upper end of the interval is the sample mean added to M. So it is 320 + 16 = 336 minutes

The 90% confidence interval for the mean time that the drug will take to reduce all fevers for all people is between 304 minutes and 336 minutes

The misleading about the data shown on the figure is the clas width

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

The histogram

On the histogram, we have the following readings

From the above, we can see that

The above readings are not consistent i.e. the class widths are not equal

Hence, the misleading about the data shown on the figure is the clas width

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Each consecutive element of the series has one less blue points than the before element, with that, we conclude that the correct option is D, where there is only one blue point.

Here we can see a series of 3 elements.

the first element is a circle with 4 blue points on its circumference, such that the points are connected to form a rectangle.

The next element is a circle with 3 blue points on it, such that when the points are connected a triangle is formed.

The third element is a circle, this time with 2 points, and the connection forms a segment.

So what we can see is that in each consecutive element the number of blue points on the circumference of the circles decreases by one, so the logical conclusion is that the next element will have only one point on its perimeter, then the correct option is D, where we can see only one blue point on the perimeter of the circle.

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1. The average rates of change found in Exercise 3 represent the average speed at which the rim of the tire is moving

towards or away from the street between two specific time intervals.

2. The instantaneous rate of change, which is typically found by taking the derivative of the function and evaluating it at the desired point (t=3 sec in this case).

In past mathematics classes, you may have encountered expression (1) in the context of finding the slope of a secant

line between two points on a curve, which represents the average rate of change of a function.

1. The average rates of change found in Exercise 3 represent the average speed at which the rim of the tire is moving

towards or away from the street between two specific time intervals.

2. Using the average rate of change is an approximation but not exact at the instant t=3sec because it considers the

change over an interval of time rather than at a specific instant.

To find the exact rate at which the rim of the tire is

approaching the street at t=3 sec, we need to calculate the instantaneous rate of change, which is typically found by

taking the derivative of the function and evaluating it at the desired point (t=3 sec in this case).

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a)There are 286 ways to select any three people from the group of 13.

b)There are 35 ways to select three women from the group of seven women.

c) The probability that the selected group consists of all women is 0.122 or approximately 12.2%

What is probability?

Probability is the measure of the likelihood or chance that an event will occur, expressed as a number between 0 (impossible) and 1 (certain), or as a percentage between 0% and 100%. It is used to quantify uncertainty and make predictions in various fields such as mathematics, statistics, physics, engineering, economics, and social sciences

a. The total number of ways to select three people from a group of 13 is given by the combination formula,

C(13, 3) = 13! / (3! × (13 - 3)!) = 286

Therefore, there are 286 ways to select any three people from the group of 13.

b. The number of ways to select three women from a group of seven women is given by the combination formula,

C(7, 3) = 7! / (3! × (7 - 3)!) = 35

Therefore, there are 35 ways to select three women from the group of seven women.

c. To find the probability that the selected group consists of all women, we need to find the number of ways to select three women from the group of seven women and divide it by the total number of ways to select three people from the group of 13:

P(all women) = C(7, 3) / C(13, 3) = 35 / 286 = 0.122

Therefore, the probability that the selected group consists of all women is 0.122 or approximately 12.2%.

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