Write a polynomial function of least degree with integral coefficients that has the given zeros

"Copy an angle" construction has been performed.

What is an angle?

Two lines intersect at a location, creating an angle. An "angle" is the term used to describe the width of the "opening" between these two rays.  Angles are frequently expressed in degrees and radians, a unit of circularity or rotation. We encounter angles frequently in life. Angles are used in the design of buildings, roadways, and sports venues by engineers and architects.

Observe that angles BAC and TSR are same.

This means, construction is done to copy the angle BAC.

So, "copy an angle" construction has been performed.

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The image created by the scale factor of 1 will be same as the pre-image

The scale factor of the image = 1

The ratio between the new size of the figure and the original figure = 1 : 1

The scale factor is the ratio between the dimensions of the new figure and the dimensions of the original figure.

The image in the dilation is the new/final figure and the pre-image is the original figure before dilation

Here, the size of the image and pre-image will be same because the ratio is 1 : 1, image and pre-image has same dimensions

Therefore, the image and the pre-image will be same

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The domain, range and asymptotes of the exponential function y = -2^(-x+2)+1 are given as follows:

The function in this problem is defined as follows:

y = -2^(-x+2)+1.

It is an exponential function, hence it has no restrictions, meaning that:

The range of the function is the set that is composed by all the output values of the function.

Due to the multiplication by the negative number, the function is reflected over the x-axis, and the addition by 1 means that the function is shifted up 1 unit, thus:

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The flour will last for about 11 days.

What is equation ?

The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equal. Consider the equation 3x + 5 = 14, where 3x + 5 and 14 are two expressions that are separated by the symbol "equal."

An equals sign is a part of a mathematical expression referred to as an equation. A lot of equations include algebra. In math, algebra is employed when you don't know the precise amount to calculate.

Suppose, the flour will last for x days.

She uses 15 pounds of flour each day.

So, the total amount of flour used in x days 15x pounds.

Given that, she has 157.86 pound of flour.

So, the equation will be

15 x = 157.86

x = 157.86 / 15

 = 10.524

 ≈ 11

Thus, the flour will last for about 11 days.

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The expression equivalent to the statement raise p to the 7th power, then add q to the result is p⁷ + q

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

raise p to the 7th power, then add q to the result

When p is raised to the power of 7, we have the following representation

p⁷, then add q to the result

When q is added to p⁷ above, we have

p⁷ + q

Hence, the expression is p⁷ + q

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Answer: 175

Step-by-step explanation: So the formula for finding the area of a rhombus is A= 1/2 d1+d2. So, we multiply 14 x 25 to get 350, then we divide by 2, and get 175!  I hoped this helped you solve your problem :)

The domain and the range are {0.5, 1.25, 2.0, 2.5} and {50, 100, 200, 225, 300}

The relation is not a function

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

Time (in minutes)      (x)  0.5   1.25   2.0   2.0   2.5

Distance (in meters) (y)   50   100   200  225  300

The domain is the list of the x values (without repetition)

So, we have

Domain = {0.5, 1.25, 2.0, 2.5}

The range is the list of the y values (without repetition)

So, we have

Range = {50, 100, 200, 225, 300}

For a relation to be a function, the x values must not be repeated for different y values

From the table, we have: (2.0, 200) and (2.0, 225)

The x value 2.0 is repeated for y values 200 and 225

Hence, the relation is not a function

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The Interest Rates are 2% and 5% respectively

What is Simple Interest?

Simple interest is a quick and straightforward way to calculate the interest on a loan. Simple interest is calculated by multiplying the daily interest rate by the principle multiplied by the number of days between payments.

Solution:

Let, the lesser interest rate be x

Simple Interest = Principal*Time*Rate/100

Total Interest = $166

166 = 2300*x*1/100 + 2400*(x + 3)*1/100

166 = 2300x + 2400x + 7200 / 100

16600 = 4700x + 7200

9400 = 4700x

x = 2%

and the Higher Interest Rate = 5%

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Jamall's salary when he made no sales is $3400

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

y = 3400 + 0.05x

When he made no sales, the value of x is 0

So, we have the following representation

y = 3400 + 0.05 x 0

Evaluate

y = 3400

Hence, the salary is $3400

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Three types of infinitives in Spanish are the word that ends with the letters -er , -ar, and -ir.

Explanation:

Infinitive : In general sense infinitive represent the action or the purpose.

Infinitive in Spanish are generally non -conjugated verbs and they are ending with -er , -ar , -ir.

Basically infinitive in Spanish classified into three groups.

-er : Aprender meaning camping.

-ar : Acampar meaning Camping and so on.

Therefore, the three types of Spanish infinitives are word ends with -er , -ar, and -ir.

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Rhombus is 4 pairs of congruent sides.

Congruent triangles are triangles that are precisely the same size and shape. The word congruent has the sign ≅. When the three sides and three angles of one triangle match the same dimensions as the three sides and three angles of another triangle, two triangles are said to be congruent.

A rhombus is a parallelogram with four congruent sides.

All the characteristics of a parallelogram are present in a rhombus, plus the following: The diagonals intersect at right angles.

Square and rhombus are the only two quadrilateral shapes that consistently have four congruent sides. Note that congruent sides refer to sides that are of the same length. A quadrilateral having four equal sides and four equal angles is called a square (90 degrees). It combines a rhombus and a right-angled rectangle ( equal side ).

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The kinematic equation of the motion of the paintbrush dropped 35 feet height from the ground and the 1.85 seconds reaction time of the 6 feet person standing directly below, indicates that they will be hit  by the paintbrush before they can move out of the way.

The kinematic equation of motion describe the motion of a body that moves under constant acceleration, without consideration of the forces causing the body to move.

The height from which the paintbrush is dropped from the roof to the ground = 35 feet

Height of the person standing directly below where the brush falls = 6 feet

The reaction time of the person = 1.85 seconds

The kinematic equation of motion of free fall of an object is presented as follows;

s = u·t + 0.5·g·t²

Where; s = The height through which the paintbrush falls

u = The initial velocity of the paintbrush = 0

g = The acceleration due to gravity ≈ 32.1741 ft/s²

The height the paintbrush falls before meeting the 6 feet tall person, s = 35 feet - 6 feet = 29 feet

Therefore, we get;

29 = 0 × t + 0.5 × 32.1741 × t²

t² = 29 ÷ (0.5 × 32.1741) ≈ 1.803

The time it takes the paintbrush to fall 29 feet, t, is therefore;

t = √(29 ÷ (0.5 × 32.1741)) ≈ 1.343

It takes the paintbrush to reach the height of the person standing directly below in just about 1.3 seconds after it is dropped, before the person can react to move away in 1.85 seconds, therefore, they will be hit by the paintbrush before they can move out of the way.

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The probability that the sample mean will be less than 318 is 0.0011.

Mean is defined as the average of given numbers i.e. sum of all numbers divided by the total number of numbers. The Mean is denoted as m or μ. Standard deviation is the measure which it shows the variation from the mean exists or not. The standard deviation is denoted as σ.

We know that,

                 P ( x  <  n  )   =   P (   z     <     x  -  μ / ( σ / √n )   )    →   1  

where,     z   =       x - μ / ( σ / √n )  

As per the given question,

                                    P ( x  <  318 ) = ?

Substitute the values in 1,

P ( x < 318 )   =   P ( z < x - μ / ( σ / √n ) )

                      =   P ( z  <   318 - 330 / ( 35 / √80 )

                      =   P ( z < -12 / ( 35 / 8.94 )

                      =   P ( z < -12 / 3.91 )

                      =   P ( z < -3.069 )

                      =   P ( z < -3.07 )

P ( x < 318 )   =   0.0011

Therefore, 0.0011 is the probability that the sample mean will be less than 318. Hence Option a is correct.

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The complete question is

A certain brand of electric bulbs has an average life of 330 hours with a standard deviation of 35. A random sample of 80 bulbs is tested. What is the probability that the sample mean will be less than 318?

a.) 0.0011

b.) 0.9989

c.) 0.0006

d.) 0.0127

By using testing of hypothesis, it can be concluded that

There is a systematic error in atleast one of the methods

First option is correct

What is testing of hypothesis?

Suppose there is a data at hand and there is a hypothesis to be tested. Testing of hypothesis determines whether the given hypothesis can be supported with the data at hand.

A t test can be used to compare results from two different methods.

Here, the difference in the results is significant, it means that

So the null hypothesis has to be rejected

There is a systematic error in atleast one of the methods

First option is correct

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Complete Question

The complete question has been attached

Answer: x=45 degrees

Step-by-step explanation:

125+x+10=180

all triangles add up to 180 degrees

135+x=180

x=45

Answer:

Step-by-step explanation:

Gradient of a line that is perpendicular to another line is always the negative reciprocal.

So:

the gradient perpendicular to -0.25x is 4

to find the y-intercept (c), you need to substitute x and y into the equation:

5 = 2(4) + c

5 = 8 + c

c = -3

hence:

y = 4x -3

Answer:3

Step-by-step explanation:

The width at the instant the width is decreasing at .5 units/sec is increasing 5 units per/sec.

How to find change in length or width?

Given:

Area of triangle = 100 units²

Area of triangle = Length * Width

Length * Width = 100

dl / st = 2 unit/sec

a) Find length

when dw/dt = -0.5 unit/sec

l * w = -0.5

l dw/dt + w dl/dt = 0

100/w (-0.5) + w(2) = 0

(- 50+ 2w²) / w = 0

2w² = 50

w² = 25

w = 5

Hence, the width at the instant the width is decreasing at .5 units/sec is increasing 5 units per sec.

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Answer: 400 points

Step-by-step explanation:

500 x 80 =  40,000

40,000/100 = 400 points

The coordinates of the point on the directed line segment from (−3,4) to (3,8) partitions the segment into a ratio of 1 to 3 is given as follows:

(-1.5, 1).

The coordinates of the point are applied using proportions, as the fact that the point partitions the segment into a ratio of 1 to 3 means that the following equation is built:

Point - Initial Coordinate = 1/4(Final Coordinate - Initial Coordinate).

This equation is used to find both the x-coordinate and the y-coordinate of the point.

The x-coordinate of the point is obtained as follows:

x + 3 = 1/4(3 + 3)

x + 3 = 1.5

x = -1.5.

The y-coordinate of the point is obtained as follows:

y - 4 = 1/4(-8 - 4)

y - 4 = -3

y = 1.

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A function formula y = f(x) defines the relation between input values and output values.

We know that the function defines relation between the input values and the output values. A relation is a function if and only of for each input there is exactly one output.

A mathematical equation which involves x and y, i.e., a function, can be written in the form y = an expression involving x

y = f (x).

The function formulas are used for calculating the x-intercept, y-intercept and slope in any function.

We can find the x-intercept of a function by substituting the value of f(x) as 0. Similarly, the y-intercept of a function by substituting the value of x is 0. We can calculate the slope of a linear function by rearranging the function to the form, f(x) = mx + c; where m is the slope and c is the y-intercept.

Therefore, the function formulas are used to determine the x-intercept, y-intercept and slope in any function.

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Answer:

4.125 rounded to 4.13 = the price of tax.

4.13 + 55 = 59.13

The sample space for this experiment contains a total of 120 possible outcomes. This is because there are 10 possible balls to be drawn, and each of them can be chosen in 3 different ways. Thus, 10 x 10 x 10 = 1,000 possible combinations. However, since the order of the selected numbers does not matter, the number of possible outcomes is reduced to 1,000 / 6 = 120.

Mathematical explanations of the likelihood that an event will occur or that a statement is true are referred to as probabilities. A value between 0 and 1 represents the likelihood of an event, with 0 basically denoting impossibility and 1 generally indicating certainty.

Subtract the total number of events from the total number of outcomes. Divide the total number of ways the event could occur by the total number of possible outcomes once the probability event has been identified and its corresponding consequences have been determined.

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It will be less than 26 °C as water has a relatively higher specific heat than sand is true statement about the final temperature of water.

Temperature is a unit used to represent hotness or coolness on any of a number of scales, including Fahrenheit and Celsius. According to temperature, heat energy will naturally move from a hotter (body with a higher temperature) to a colder (body with a lower temperature) (one at a lower temperature).

Given,

In an experiment, equal amounts of water and sand were heated under a lamp. The initial and final temperatures of each were recorded. A partial record of the temperature is shown.

Experimental Record

Substance Initial Temperature Final Temperature

Sand 20 °C 26 °C

Water 20 °C

The quantity of heat energy absorbed by one unit of a substance when its temperature rises by one unit is measured as the substance's specific heat.

This allows you to calculate the equation for a substance's specific heat:

Specific heat equals heat / (mass Δ T)

Given that both samples have the same amount (mass) and that all of the heat from the lamp is applied to them, you can assume that the specific heat of the samples will be as follows:

particular heat is equal to constant / ΔT.

Therefore, the two quantities are inversely connected.

Since sand has a lower specific heat than water, the sand on the shore of a beach is warmer during the day. When walking on a sandy beach on a bright day, your feet get scorched since it's hotter than the ocean.

When equal amounts of water and sand are heated as per the experiment's instructions, water will increase in temperature more slowly and, as a result, reach a lower end temperature than sand. This is because water has a higher specific heat than sand. This is the second option; because water has a substantially higher specific heat than water, the end temperature of water is less than 26°C.

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Assuming that the population proportion of blue eyes is accurately reflected in each sample, about 380 of the 400 confidence intervals should cover the population proportion.

The confidence interval for the proportion of blue eyes in the population is calculated as follows:

Proportion of blue eyes in the population = sample mean +/- (1.96* Standard Error)

Where Standard Error = sqrt[(proportion of blue eyes in the population)*(1-proportion of blue eyes in the population)/sample size]

At a 95% confidence level, the confidence interval should cover the population proportion 95% of the time. Therefore, 95% of the 400 confidence intervals should cover the population proportion, which is approximately 380 intervals.

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To find the average rate of change of a function over an interval, we need to calculate the slope of the secant line connecting the points on the function at the two endpoints of the interval.

The equation of a line in slope-intercept form is y = mx + b, where m is the slope of the line and b is the y-intercept. In the case of a secant line, we can calculate the slope by using the formula:

m = (y2 - y1) / (x2 - x1)

For the function y = x^2 + 4x - 1, we can plug in the values of x and y at the two endpoints of the interval, (-4 and 1), to find the slope of the secant line:

m = [(1)^2 + 4(1) - 1] - [(-4)^2 + 4(-4) - 1] / (1 - (-4))

Simplifying this expression, we get:

m = (1 + 4 - 1) - (16 + 16 - 1) / (-3)

This simplifies to:

m = -20 / -3

Therefore, the average rate of change of the function y = x^2 + 4x - 1 over the interval -4 ≤ x ≤ 1 is 6.5.

Answer:

100 km

Step-by-step explanation:

Using the t-distribution, it is found that the p-value is of 0.

[tex]H_{0\\}[/tex] : μ₁ - μ₂ ≥ 0

[tex]H_{1}[/tex] : μ₁ - μ₂ < 0

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Answer:

A credit report is not useful for lenders and borrowers because it does not provide detailed information about a person's financial history.

The proof of  AB ≅ CD is given below.

What is triangle?

Three vertices make up a triangle, a three-sided polygon. The triangle's angles are formed by a point where the three sides are joined end to end. The triangle's three angles add up to a total of 180 degrees.

Given:  BD and AC bisect each other.

So, AE = AC  and BE = ED

Consider the triangles  ΔAEB and , ΔECD

Given,

AE = EC                         ...S

BE = ED                         ....S

Here, lines BC and AD intersects at point E, so

 m ∠AEB = m ∠DEC               ....A

Therefore, from SAS congruency,

ΔAEB ≅ ΔECD

Hence,  AB ≅ CD

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