Write a quadratic function f whose zeros is 7

The measurement of angle PCD in equilateral triangle  is 67.38°.

Let $s$ be the side length of the square $abcd$, and let $O$ be the center of the square. Then $OP = s/\sqrt{2}$.

Since triangle $ABP$ is equilateral, we have $\angle ABP = 60^\circ$ and $AP=BP=s$. Let $E$ be the foot of the perpendicular from $P$ to $AB$. Then $AE=BE=s/2$ and $EP=s\sqrt{3}/2$.

Since $EP$ is perpendicular to $AB$ and $AB$ is parallel to $CD$, we have $\angle PCD = \angle ACE$.

Since $OP$ is perpendicular to $AB$, we have $\angle OEP = \angle AEP = 30^\circ$. Also, $OE=OP/\sqrt{2}=s/2$.

Using the Pythagorean theorem in triangle $OCE$, we have

CE= [tex]\sqrt{(OE)^{2} + (OC)^{2}} = \sqrt{(s/2)^{2} + s^{2}} = s\sqrt{5}/2[/tex]

Therefore, $\sin \angle ACE = CE/CP = \sqrt{5}/2$. Thus,

∠PCD = ∠ACE = arcsin(√5/2) ≈ 67.38°

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The missing side is 30.

Three line segments that cross at three non-collinear locations to form a triangle constitute a triangle in geometry. The triangle's three line segments are referred to as its sides, and its three points of intersection as its vertices.

A triangle is a three-sided polygon formed by three line segments intersecting at three non-collinear points, and it can be classified based on the length of its sides and the measure of its angles.

Given figure, there are two lines ate parallel, that's why two triangles are similar triangle.

Assume that the missing side is x.

So that side ratio in similar triangle are equal;

14/20 = 21/x

So, x = 30.

Therefore, the missing side x is 30

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Triangle Three line segments that cross at three non-collinear locations to form a triangle constitute a triangle in geometry. According to the question the missing side is 30.

Three line segments that cross at three non-collinear locations to form a triangle constitute a triangle in geometry. The triangle's three line segments are referred to as its sides, and its three points of intersection as its vertices. A triangle is a three-sided polygon formed by three line segments intersecting at three non-collinear points, and it can be classified based on the length of its sides and the measure of its angles.

Given figure, there are two lines ate parallel, that's why two triangles are similar triangle.
Assume that the missing side is x.
So that side ratio in similar triangle are equal;
14/20 = 21/x

So, x = 30.
Therefore, the missing side x is 30

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Answer:

9.5in

Step-by-step explanation:

44.4in = 12.7 +22.2 +x(missing side)

34.9+x=44.4in

x=44.4in-34.9in

x=9.5in

Answer:

12.1 in

Step-by-step explanation:

what is your problem with that ? you don't understand what "perimeter" means ?

it means the whole way around the figure 1 time. it is the sum of all sides.

so, when we have the sum but miss one element of the dimensions numbers ?

what do you think we do ?

we calculate the difference between the sum of the elements we have, and the total sum.

this difference must be the missing side length.

so, the total is 136.8 in.

what we have is

44.4+10+10+12.7+22.2+12.7+12.7 =

= 44.4 + 20 + 3×12.7 + 22.2 = 124.7 in

the difference is

136.8 - 124.7 = 12.1 in

that is our missing side length.

you see, the picture tries to convince us that all the angles are right angles (90°). in that case the missing side length would be simply

44.4 - 12.7 - 22 2 = 9.5 in.

but no, it is good that we did not simply fall for an optical illusion. the absolute numbers tell us that some of the angles must be slightly different from 90°.

in case of doubt always rely on the absolute numbers.

As all the sides of the closed figure are equal to each other, the quadrilateral here is a square.

A square is a closed, two-dimensional (2D), object with four corners. With four sides and four vertices, a quadrilateral is referred to as a square. All four sides of a square are equal and parallel.

In other words, a square is a polygon or quadrilateral with four sides. An equiangular quadrilateral is a shape in which all of the angles are of equal size.

Here in the given figure, we can see a quadrilateral is given.

We can see that all the sides of the quadrilateral are given to be equal to each other.

We can conclude from the observation that the quadrilateral is a square as the sides are all equal to each other.

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Answer:

24 different lunches

Step-by-step explanation:

There are three choices for the beverage, two choices for the appetizer (soup or salad), and four choices for the sandwich. Therefore, using the multiplication principle of counting, the number of different lunches possible is:

3 choices for beverage x 2 choices for appetizer x 4 choices for sandwich = 24 different lunches.

As a result, both varieties of trees will be the same height after 9 years. We can change both equations to a = 9 to verify this: Height of the type A tree is 36 + 8(9) or 36 + 72 inches, whereas the height of the type B tree is 18 + 10(9) or 18 + 90 inches.

Trigonometry includes heights and distances, and it has numerous uses in practical daily life. It utilised to compute height of towers, structures, mountains, etc., and distance between any two objects such celestial bodies others. ,sys,s tos.as to .... and.

Let's use "a" to denote the number of years after planting the trees.

A type A tree will reach the following height after "a" years:

Height of type A tree = 36 + 8a

After "a" years, the height of a type B tree will be:

Height of type B tree = 18 + 10a

We must set the two types of trees' heights equal to one another and solve for "a" to determine when they will reach the same height:

36 + 8a = 18 + 10a

Subtracting 8a from both sides, we get:

36 = 18 + 2a

Subtracting 18 from both sides, we get:

18 = 2a

Dividing both sides by 2, we get:

a = 9

Therefore, after 9 years, both types of trees will be the same height.

To check this, we can substitute a = 9 into both equations:

Height of type A tree = 36 + 8(9) = 36 + 72 = 108 inches

Height of type B tree = 18 + 10(9) = 18 + 90 = 108 inches

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Question:

You have two types of trees to plant in your yard: type A trees are 36 inches tall and grow 8 inches per year, while type B trees are 18 inches tall and grow 10 inches per year. At what point in time will the trees be the same height? How tall will the trees be at that time?

The population of interest is the group of students who submitted an application to the college in 2017.

A sample is a subset of a population that is selected and studied in order to make inferences or conclusions about the population. The sample is usually selected to be representative of the population in some way, so that the conclusions drawn from the sample can be generalized to the population as a whole.

The correct answer is C.

The purpose of the study is to determine why students who are interested in the college decide to enroll or not. Therefore, the population of interest is the group of students who submitted an application to the college in 2017.

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Answer: t = 1.8 seconds

Step-by-step explanation:

The function h(t) = 25t^2 - 81 gives the height of the rock (in feet) at time t seconds after it was dropped.

When the rock lands, its height is 0. So we can set h(t) = 0 and solve for t:

25t^2 - 81 = 0

Solving for t, we get:

t = ±√(81/25) = ±(9/5)

Since we are only interested in the time after the rock was dropped, we take the positive value:

t = 9/5 = 1.8 seconds

Therefore, the time between when the rock was dropped and when it landed is 1.8 seconds.

So the answer is: t = 1.8 seconds

Answer:

No.

Step-by-step explanation:

Given two triangles on a coordinate plane, you can check whether they are congruent by using the distance formula to find the lengths of their sides. If three pairs of sides are congruent, then the triangles are congruent by the above theorem.

Over here, they aren't congruent by the SSS.

The utility that maximizes the possible utility of both the agents Alice and Bob is equal to option D. $10.

Compare Alice's utility from each option and choose the one that maximizes her utility.

Let us consider each option,

If Alice offers Bob $0, her utility will be,

If XA > XB then

UA (XA , XB )= 0.3x3 + 0.72A

UA(10,0)

= 0.3(10)³ + 0.72(10)

= 307.2

If Alice offers Bob $5, Bob's utility will be,

UB(10,5)

= 0.314 + 0.72(5)

= 0.314 + 3.6

= 3.914

And Alice's utility will be,

UA(5,10)

= -0.32(5) + 1.3(10)

= 11.4

Total utility for both Alice and Bob will be,

UA(5,10) + UB(10,5)

= 11.4 + 3.914

= 15.314

If Alice offers Bob $2, Bob's utility will be,

UB(10,2)

= 0.314 + 0.72(2)

= 1.754

And Alice's utility will be,

UA(2,10)

= -0.32(2) + 1.3(10)

= 12.4

So the total utility for both Alice and Bob will be,

UA(2,10) + UB(10,2)

= 12.4 + 1.754

= 14.154

If Alice offers Bob $10, Bob's utility will be,

UB(10,10)

= 0.314 + 0.72(10)

= 7.514

And Alice's utility will be,

UA(10,10)

= 0.3(10)³ + 0.72(10)

= 307.2

So the total utility for both Alice and Bob will be,

UA(10,10) + UB(10,10)

= 307.2 + 7.514

= 314.714

Therefore, utility which maximizes the total utility for both Alice and Bob is given by option (D) $10.

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Two radicals are said to be radicals if they have the same indices and the radicand.

In mathematics, a radicand is an expression, a number, or a variable that is enclosed in a root symbol. The factor for which we are determining the root is quantity. As we study exponents and roots, the word "radicand" is utilised. Therefore, the radicand in 2 has a value of 2. Following are some radicand examples:

3√(pq) → pq is the radicand

√(a+b) → a + b is the radicand

4√15 → 15 is the radicand

A radical is a symbol used to represent a number's root. It is symbolised as. The word or phrase that appears after the radical symbol is known as the radicand. Hence, it may be claimed that the radical represents the radicand. Alternatively said, the radicand sign is √.

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Complete question:

Type the correct words in the blanks:

Two radicals are said to be radicals if they have the same               and the radicand.

Answer:

Greg bought a pack of X jumbo stickers during the back - to - school sale at Crafty's craft store. He ( uses 4  ( -4 ), ( you didn't give options ). There were 8 stickers left in the pack.

Hope this helps!

Step-by-step explanation:

Answer:

We will use mathematical induction to prove the formula for the sum of arithmetic sequences:

For n=1, we have:

∑j=1^1(a + (j-1)d) = a

On the other hand, we have:

n/2(2a + (n-1)d) = 1/2(2a) = a

Thus, the formula holds for n=1.

Assuming the formula holds for n=k, we will prove that it holds for n=k+1.

We have:

∑j=1^(k+1)(a + (j-1)d) = (a + kd) + ∑j=1^k(a + (j-1)d)

Using the formula for n=k, we can write:

∑j=1^k(a + (j-1)d) = k/2(2a + (k-1)d)

Substituting this back into the first equation, we have:

∑j=1^(k+1)(a + (j-1)d) = (a + kd) + k/2(2a + (k-1)d)

Simplifying the right-hand side, we get:

∑j=1^(k+1)(a + (j-1)d) = 1/2(2a + (2k+1)d)

But (k+1)/2(2a + kd + d) = 1/2(2a + (2k+1)d), so the formula holds for n=k+1.

Therefore, by mathematical induction, the formula for the sum of arithmetic sequences is proved.

In response to the stated question, we may state that As a result, the overall probability of an accurately picked drive-thru order across all chains is roughly 0.929, or 92.9%.

Probability theory is an area of mathematics that calculates the likelihood of an occurrence or a proposition being true. A risk is a number in the range of 0 and 1, whereas 1 implies certainty and a probability of roughly 0 indicates how likely an event seems to be to occur. Probability is a mathematical expression of the chance or chances that a given event will occur. Probabilities can alternatively be stated as integers between 0 and 1 or as % from 0% to 100%. the ratio of occurrences among equally likely choices that result in a certain event in comparison to all other outcomes.

Using the data in the table, we can compute the likelihood of a correct drive-thru order for each fast food chain, as well as the overall chance of an accurate order across all chains.

Divide the number of accurate orders by the total number of orders to find the chance of a randomly picked order being accurate at each chain:

P(accurate order) = 1246 / 1300 = 0.958 for McDonald's

P(accurate order) = 1020 / 1100 = 0.927 Taco Bell

P(accurate order) = 708 / 800 = 0.885 for Burger King

P(accurate order) = 940 / 1000 = 0.94 for Wendy's

P(adequate overall order) = 0.3 * 0.958 + 0.25 * 0.927 + 0.2 * 0.885 + 0.25 * 0.94 = 0.929

As a result, the overall likelihood of an accurately picked drive-thru order across all chains is roughly 0.929, or 92.9%.

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Answer:

D.

Step-by-step explanation:

Answer:

(1, 2) and (-1, -2). or. (±1, ±2)

Step-by-step explanation:

[tex]{ \sf{f(x) = \frac{4x}{ {x}^{2} + 1 } }} \\ [/tex]

- Simply, a critical number or critical point is gotten by differentiating the function.

From Quotient rule;

[tex]{ \sf{ {f}^{l}(x) = \frac{4( {x}^{2} + 1) - (2x)(4x)}{ {( {x}^{2} + 1)}^{2} } }} \\ \\ { \sf{f {}^{l}(x) = \frac{ {4x}^{2} + 4 - {8x}^{2} }{ {( {x}^{2} + 1) }^{2} } }} \\ \\ { \sf{f {}^{l}(x) = \frac{4(1 - {x}^{2}) }{ {( {x}^{2 } + 1) }^{2} } }}[/tex]

Then equate this derivative to zero;

[tex]{ \sf{0 = \frac{4(1 - {x}^{2} )}{ {( {x}^{2} + 1) }^{2} } }} \\ \\ { \sf{4(1 - {x}^{2} ) = 0}} \\ \\ { \sf{4 - {4x}^{2} = 0}} \\ \\ { \sf{4 {x}^{2} = 4}} \\ \\ { \sf{x = \sqrt{1} }} \\ \\ { \sf{ \underline{ \: x = \pm 1 \: }}}[/tex]

Substitute for x in f(x)

For x = 1

[tex]{ \sf{f(1) = \frac{4(1)}{ {(1)}^{2} + 1} = \frac{4}{2} = 2 }} \\ [/tex]

For x = -1

[tex]{ \sf{f( - 1) = \frac{4( - 1)}{ {( - 1)}^{2} + 1 } = \frac{ - 4}{2} = - 2 }} \\ [/tex]

Therefore points are;

(1, 2) and (-1, -2)

Step-by-step explanation:

2x + ay + 2 = 0

the gradient or slope of the line is the factor m of x in the form

y = mx + b

so let's transform the given equation into that form :

ay = -2x - 2

y = (-2/a)x - 2/a

we know that m = 1.

so,

-2/a = 1

-2 = a

Solved  equation x=80 and z=2, y=40

An element, feature, οr factοr that is liable tο vary οr change

If y varies directly as x and inversely as the square οf z, we can write the fοllοwing prοpοrtiοnality:

y ∝ x/z²

where ∝ denοtes prοpοrtiοnality cοnstant.

Tο find the value οf ∝, we can use the given values οf y, x, and z:

y = ∝ x/z²

28 = ∝ (63)/(3)²

∝ = 28 * (3)² / (63)

∝ = 4/3

Nοw we can use this value οf ∝ tο find y when x=80 and z=2:

y = ∝ x/z²

y = (4/3) * (80)/(2)²

y = 40

Therefοre, when x=80 and z=2, y=40.

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The piecewise function will be continuous in its domain if k = 49/48

Here we have a piecewise function and we want to find the value of k suc that the function is continuous on the domain.

To get that, both piecese of the function must ahve the same value in the jump, then we will get:

f(7) = f(7)

Replacing the functions we will get:

k·7²  = 7·7 + k

Let's solve that equation for k.

49k = 49 + k

49k - k = 49

48k = 49

k = 49/48

That must be the value of k such that the function is continuous in all its domain.

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Answer

6255 pounds

8.34×750=6255lbs

The inventory turnover ratio can be calculated by dividing the cost of goods sold by the average inventory value. In this case, the inventory turnover ratio is 0.5, and the correct answer is (D) 0.5.

The inventory turnover ratio measures the number of times a company sells and replaces its inventory during a period. It can be calculated by dividing the cost of goods sold by the average inventory value.

The inventory turnover ratio = Cost of goods sold / Average inventory value

In this case, the cost of goods sold is $600,000 and the average inventory value is $1,200,000.

Inventory turnover ratio = $600,000 / $1,200,000 = 0.5

Therefore, the inventory turnover ratio is 0.5, and the correct answer is (D) 0.5.

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Complete question:

If the average aggregate inventory value is $1,200,000 and the cost of goods sold is $600,000, which of the following is inventory turnover?

A)60

B)10.4

C)2

D)0.5

E)None of these

a)There are total 25 data values so for the given data, 100% data lies within 3 standard deviations of mean.

b). Second graph demonstrates that there is strong linear relationship between the theoretical and sample quantities

a) Here we have μ=61.52 and [tex]\sigma=4.58[/tex]

The 68-95-99.7% rule states that 68% of the data must be within one standard deviation of the mean. Thus, 68% of the data should fall between 61.52-4.58=56.94 and 61.52+4.58=66.1. 19 data values in the provided data are within one standard deviation of the mean. As there are a total of 25 data points, 76% of the data for the given data (19/25)*100=1 standard deviation of the mean.

The 68-95-99.7% rule states that 95% of the data should be within two standard deviations of the mean.

Specifically, 95% of the data should fall between 61.52+2*4.58=70.68 and 61.52-2*4.58=52.36. 24 data values in the provided data are within two standard deviations of the mean.

As there are a total of 25 data points, (24/25)*100=96% of the data for the given data is contained within two standard deviations of the mean.

The 68-95-99.7% rule states that 99.7% of the data should be within three standard deviations of the mean.

It follows that 99.7% of the data should fall between 61.52+3*4.58=75.26 and 61.52-3*4.58=47.78. 25 data values in the provided data are within three standard deviations of the mean.

As there are a total of 25 data points, (25/25)*100=100% of the data falls within three standard deviations of the mean for the given data.

Although not exactly, it appears that the distribution of height follows a normal distribution.

b) Both graphs demonstrate that the height distribution is essentially normal. Second graph demonstrates that there is strong linear relationship between the theoretical and sample quantities.

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The complete question is:

Heights of female college students. Below are heights of 25 female college students.

(a) The mean height is 61.52 inches with a standard deviation of 4.58 inches. Use this information to determine if the heights approximately follow the 68-95-99.7% Rule.

(b) Do these data appear to follow a normal distribution? Explain your reasoning using the graphs provided below.

Selection bias can creep into a study if subjects are picked (intentionally or not) according to some criterion and not randomly.

Selection bias occurs when the selection of study participants is not random and is instead influenced by certain criteria. This can result in a non-representative sample that does not accurately reflect the population being studied, leading to inaccurate conclusions. For example, if a study on the effectiveness of a medication only enrolls participants who are already known to respond well to that medication, the results may overestimate its effectiveness in the general population. To minimize selection bias, researchers should use random sampling techniques and carefully consider the inclusion and exclusion criteria .

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Answer: 811 adult tickets and 868 child tickets

Step-by-step explanation:

35x +20y = 44,620

add 35+20

divide the sum by 44,620 and

the answer

Cold fronts generally move faster than warm fronts because cold air is denser and thus, moves more quickly. Precipitation with a cold front typically covers a broader area, especially during the winter.

On the other hand, warm fronts move more slowly as they are characterized by the gradual lifting of warm air over colder air. Cold fronts also typically have steeper slopes than warm fronts. This is because the leading edge of a cold front is more abrupt.

With a steep rise in the cold air mass. In contrast, the leading edge of a warm front has a gentler slope as the warm air gradually rises over the colder air.

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Case 1: The constant c of the piecewise function is equal to 1 / 7.

Case 2: The value of the constant b of the piecewise function with the greater absolute value is equal to 20.

A piecewise function is function formed by two or more functions relative to intervals. A piecewise function is continuous if they do not have any jump on graph. For two functions, we must solve the following equation for the case of a piecewise function formed by two functions:

g(a) = h(a)

Case 1 - g(y) = c · y + 3, h(y) = c · y² - 3, a = 7

c · a + 3 = c · a² - 3

c · (a² - a) = 6

c = 6 / (a² - a)

c = 6 / (7² - 7)

c = 6 / 42

c = 1 / 7

The value of the constant c is equal to 1 / 7.

Case 2 - g(x) = b - 2 · x, h(x) = - 150 / (x - b), a = 5

b - 2 · a = - 150 / (a - b)

(b - 2 · a) · (a - b) = - 150

a · b - b² - 2 · a² + 2 · a · b = - 150

- b² + 3 · a · b - 2 · a² = - 150

b² - 3 · a · b + 2 · a² - 150 = 0

b² - 15 · b - 100 = 0

(b - 20) · (b + 5) = 0

b₁ = 20 or b₂ = - 5

The solution with the greater absolute value is b = 20.

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Answer:

Step-by-step explanation:

Let weight of fourth parcel be x

Mean = Sum of all values/total number of values.

8.5 = 7.7 + 7.6 + 8.2 + x/4

8.5 = 23.5 + x/4

8.5 × 4 = 23.5 + x

34 = 23.5 + x

34 - 23.5 = x

10.5 = x

Therefore, weight of the fourth parcel will be 10.5 kg

To find the slope of a line that passes through two points, you can use the slope formula. The slope formula is:

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

Using the points given in your question, the slope formula to find the slope of the line is:

Slope = (2 - 8) / (4 - (-4))

Using the order of operations, the calculation of the slope formula is as follows:

Slope = -6 / 8

Therefore, the slope of the line passing through (-4, 8) and (4, 2) is -3/4.

Answer:

m = -5/8

Step-by-step explanation:

Slope = rise/run or (y2 - y1) / (x2 - x1)

Points (-1, -7) (-9, -2)

We see the y increase by 5 and the x decrease by 8, so the slope is

m = -5/8