If $c$ is a constant such that $9x^2+10x+c$ is equal to the square of a binomial, then what is $c$?

The factors in this algebraic expression are:

14 And (18 - 3x)

An algebraic expression can also be written as a list of its constituent parts. Variables, constants, and operators are the components of an algebraic expression. Terms are separated from one another in an algebraic equation by the addition operation.

Algebraic Expressions can be factorized using many methods. The most common methods used for factorization of algebraic expressions are:

Factorization using common factors

Factorization by regrouping terms

Factorization using identities

The algebraic expression written by Aaron to represent the product of 14 and the difference of 18 and 3x is:

14 * (18 - 3x)

The factors in this expression are:

14

(18 - 3x)

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Yes, we can solve Curious Georgia's math problem using the concept of combinations.

There are 924 different paths we can take from our apartment to the math classroom, each of which is exactly 12 blocks long and does not backtrack or go out of the way.

We have,

Yes, we can solve Curious Georgia's math problem using the concept of combinations.

Since we cannot backtrack or go out of our way, we need to take exactly 6 blocks to the north and 6 blocks to the east to reach the math classroom.

This means that we need to choose 6 out of the 12 blocks to go north, and the remaining 6 blocks will be used to go east.

The total number of paths we can take is the number of ways we can choose 6 blocks out of the 12 blocks.

This can be calculated using the combination formula:

[tex]^nC_r[/tex] = n! / r!(n-r)!

where n is the total number of objects, r is the number of objects to choose, and ! represents the factorial function

In this case,

we have n = 12 and r = 6.

The number of paths.

= [tex]^{12}C_6[/tex]

= 12! / 6!(12-6)!

= 924

Therefore,

There are 924 different paths we can take from our apartment to the math classroom, each of which is exactly 12 blocks long and does not backtrack or go out of the way.

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Answer:

need better photos

Step-by-step explanation:

Answer: Line of best fit refers to a line through a scatter plot of data points that best expresses the relationship between those points.

Step-by-step explanation:

Line of best fit refers to a line through a scatter plot of data points that best expresses the relationship between those points.

For the pattern A, the terms are 6, 11, 16 and 21

For the pattern B, the terms are 24, 20, 16, 12

To determine the consecutive terms of the sequence, we need to take note of the rule of each.

From the information given, we have that;

For the Pattern A

Each term is the previous term plus 5

This is represented as;

Pattern A = a + 5,

The first term = 1

Second term = 1 + 5 = 6

Third term = 6 + 5 = 11

Fourth term = 11 + 5 = 16

Fifth term = 16 + 5 = 21

For Pattern B = a - 4

Second term = 28 - 4 = 24

Third term = 24 - 4 = 20

Fourth term = 20 -4 = 16

Fifth term = 16 - 4 = 12

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If the hiker is 6 feet tall, then the height of the waterfall will be: 32.57 feet.

We can solve this problem using similar triangles. Let us call the height of the waterfall "h". Then, the distance from the base of the waterfall to the mirror is also "h" (since the mirror reflects the top of the waterfall down to the hiker's eye).

Using similar triangles, we can set up the following proportion:

(h + 6 feet) / 45 feet = 6 feet / 7.5 feet

Cross-multiplying and simplifying, we get:

h + 6 feet = 270 feet / 7

h + 6 feet = 38.57 feet

h = 32.57 feet

So, the correct height given the variables is 32.57 feet.

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Answer:

36 ft

Step-by-step explanation:

We can use the concept of similar triangles to solve this problem. The ratio of the heights of the hiker and the waterfall is the same as the ratio of their distances to the mirror.

Given:

Distance from mirror to waterfall = 45 feet

Distance from mirror to hiker = 7.5 feet

Hiker's height = 6 feet

Let's set up a proportion:

(Hiker's height) / (Hiker's distance to mirror) = (Waterfall's height) / (Waterfall's distance to mirror)

Substitute the given values:

6 / 7.5 = (Waterfall's height) / 45

Now solve for the height of the waterfall:

Cross-multiply:

6 * 45 = 7.5 * (Waterfall's height)

270 = 7.5 * (Waterfall's height)

Divide by 7.5:

Waterfall's height = 270 / 7.5

Waterfall's height = 36 feet

So, the height of the waterfall is 36 feet.

Among the provided options, the correct answer is:

a) 36 ft

The proof of cot²(x) - tan²(x) = csc²(x) - sec²(x) is the help of trigonometry

identity and Pythagorean identity .

A trigonometric identity is an equation that is true for all values of the variables in the equation, where the variables are trigonometric functions such as sine, cosine, tangent, cotangent, secant, or cosecant.

The Pythagorean identity is a fundamental trigonometric identity that relates the three basic trigonometric functions: sine, cosine, and tangent, in terms of the unit circle or right triangle.

The identity you provided, cot²(x) - tan²(x) = csc²(x) - sec²(x), is a trigonometric identity that can be derived from the Pythagorean identity and the reciprocal identities. Here's one way to prove it:

Start with the Pythagorean identity:

sin²(x) + cos²(x) = 1

Divide both sides by sin²(x):

1 + cos²(x)/sin²(x) = 1/sin²(x)

Recall that cot(x) = cos(x)/sin(x) and tan(x) = sin(x)/cos(x):

1 + cot²(x) = csc²(x)

Subtracting sec²(x) from both sides:

cot²(x) - tan²(x) = csc²(x) - sec²(x)

Therefore, cot²(x) - tan²(x) = csc²(x) - sec²(x) is a valid trigonometric identity.

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You will need 38/1.17 ≈ 32.48 stone pavers to go around the patio. Rounding to the nearest whole number, you will need 32 stone pavers.

Explain whole numbers

Whole numbers are a set of numbers that includes all natural numbers (positive integers) and zero. They are represented by the symbol "W" and do not include any fractions or decimals. Whole numbers are used in counting, measuring, and representing quantities of discrete objects or entities, and are a fundamental concept in mathematics.

According to the given information

First, let’s convert the length of the stone paver from inches to feet: 14 inches = 14/12 feet = 1.17 feet.

The perimeter of the patio is (12 + 14 + 12) feet = 38 feet. Since each stone paver is 1.17 feet long, you will need 38/1.17 ≈ 32.48 stone pavers to go around the patio. Rounding to the nearest whole number, you will need 32 stone pavers.

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The range of 1 year performance is more than 1 Day performance.

We have,

1 year performance: -30%, -20%, -10% 0%, 10%, 20%, 30%

1 Day performance : -3%, -2%, -1%, 0, 10%, 20%, 30%

Now, the range of 1 year performance

= Highest - lowest

= 30 - (-30)

= 60

and, the range of 1 Day performance

= Highest - lowest

= 30 - (-3)

= 33

Thus, the range of 1 year performance is more than 1 Day performance.

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a) Jill receives £45

b) Jack receives £20 the following Christmas

c) Jack will be 5/4 years old, which is equivalent to 1 year and 3 months when he receives £25 from Uncle Fred.

Explain the term years

Years are a unit of time measurement used to quantify the duration of one complete orbit of the Earth around the sun. A year consists of 365 days, except in a leap year when an extra day is added. The concept of a year is used in various fields, including astronomy, geology, and history.

According to the given information

(a) Let's first find the total ratio of their ages:

1 + 3 = 4

So Jack's share will be:

1/4 x £60 = £15

And Jill's share will be:

3/4 x £60 = £45

Therefore, Jill receives £45.

(b) The next Christmas, Jack will be 2 and Jill will be 4. We can use the same ratio to find Jack's share:

2/6 x £60 = £20

So Jack receives £20.

(c) Let x be the age of Jack when he receives £25 from Uncle Fred. We know that:

1/4 x £60 = £25

Multiplying both sides by 4/60, we get:

x = 5/4

So Jack will be 5/4 years old, which is equivalent to 1 year and 3 months, when he receives £25 from Uncle Fred.

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This study uses blocking: True. The study randomly assigns each child to one of the four treatment groups, which helps to control for individual differences that could affect the results.

This study uses blinding: It is not mentioned in the scenario whether the study uses blinding or not in individual.

This study uses a control group: True. The first group, with no screen time, serves as the control group. By comparing the results of the other groups to the control group, the scientists can see the effects of different amounts of screen time.

This study uses a repeated measures design: True. Each subject experiences each of the four treatments, so the study design is repeated measures.

This study uses random sampling: True. The study randomly selects group of 100 children for the experiment.

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Answer:

See below!

Step-by-step explanation:

Length = x + 4 cm

Width = 2x - 7 cm

Perimeter:

Put the given data.

36 = 2(x + 4) + 2(2x - 7)

36 = 2x + 8 + 4x - 14

36 = 2x + 4x + 8 - 14

36 = 6x - 6

36 + 6 = 6x

42 = 6x

42/6 = x

7 = x

OR

Area = (x + 4)(2x - 7)

Put x = 7

Area = (7 + 4)(2(7) - 7)

Area = 11(14 - 7)

Area = 11(7)

[tex]\rule[225]{225}{2}[/tex]

Answer: (a) x=7

(b) area of this rectangle = 77[tex]cm^{2}[/tex]

Step-by-step explanation:

(a) the perimeter of a rectangle = 2 * [  l + b ]

36 = 2 * [ (x + 4) + (2x - 7) ]

36 / 2 = x + 4 + 2x - 7

18 = 3x -3

18 + 3 = 3x

21 = 3x

x = 7

(b) the area of a rectangle = l * b

l = x + 4 = 11cm

b = 2x -7 = 7cm

therefore, 11cm * 7cm = 77[tex]cm^{2}[/tex]

The amount of chalk that is greater is yellow.

Michelle is correct because more than 1/2 the chalk in the bucket is blue.

In order to determine the amount of chalk that is greater between the amount of yellow chalk and amount of green chalk, we would have to find the difference between them as follows;

Difference = 2/6 - 3/12

Difference = (4 - 3)/12

Difference = 1/12 (positive value)

Similarly, we can determine the greater amount of chalk as follows;

2/6 × 2/2 = 4/12

4/12 > 3/12

Total number of chalks = 2/6 + 5/12 + 3/12

Total number of chalks = (4 + 5 + 3)/12

Total number of chalks = 12/12

Total number of yellow and green chalks = 2/6 + 3/12

Total number of yellow and green chalks = (4 + 3)/12

Total number of yellow and green chalks = 7/12 chalks.

1 - 7/12 = 5/12

7/12 - 1/2 = 6/12 (Michelle is correct).

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Thus, the value of b over a for the given logarithmic function is obtained as: b/a = 1 + √2.

The logarithm is exponentiation's opposite function in mathematics. This indicates that the exponent with which b must be raised in order to obtain a number x is the logarithm of x to the base b.

A base must still be raised to a certain exponent or power, or logarithm, in order to produce a specific number. If bˣ = n, then x is the logarithm of n to the base b, which is expressed mathematically as x = logb n.

Given that:

log9(a) = log15(b) = log25(a + 2b)

Let ,  log9(a) = log15(b) = log25(a + 2b) = x

Then,

log9(a) = x (taking antilog)

log3²(a) = x

a = 3²ˣ

log15(b) = x  (taking antilog)

log(3*5)(b) = x

b = 3ˣ.5ˣ

log25(a + 2b) = x   (taking antilog)

log5²(a + 2b) = x

a + 2b = 5²ˣ

Now,

b²/a = a + 2b

(b/a)² = 1 + 2*(b/a)

If t = b/a, then t² - 2t -1 = 0

On factorization:

t = 1 ± √2 ( a and b are positive integer)

b/a = 1 + √2

Thus, the value of b over a for the given logarithmic function is obtained as: b/a = 1 + √2.

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The statement cos(theta) = √3/2 is correct.

Angles are the angles formed by 2 bisecting lines or surfaces at or near their intersection.

The following information has been provided:

The angle (theta) = [tex]\frac{2\pi }{3}[/tex] measurement has been given to us.

We must determine which propositions are true by determining the measure of angle (theta) =  [tex]\frac{2\pi }{3}[/tex]

cos(theta) = [tex]\frac{\sqrt{3} }{2}[/tex]

= cos30

theta = 30

tan(theta)= [tex]-\sqrt{3} = tan(90 + 30)[/tex]

tan(theta) = tan120

theta = 120

sin(theta) = [tex]-\frac{1}{2}[/tex] = [tex]cos(90 + 30)[/tex]

sin(theta) = sin120

theta = 120

Therefore the correct statement is cos(theta) = √3/2

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Complete question:

The measure of angle(theta) Is 2pi/3, which statements are true?

cos(theta) = √3/2

The measure of the reference angle is 30°.

The measure of the reference angle is 45°.

The measure of the reference angle is 60°.

tan(theta) = -√3

sin(theta)=-1/2​

The wi-fi router shall not be strong enough to cover the area of the house.

According to the statement, we must determine if a wi-fi router can cover all the area of a house, described by a rectangle. The area formula of rectangle is introduced below:

A = b · h

Where:

Now we proceed to determine the area of the house:

A = (50 ft) · (50 ft)

A = 2500 ft²

The wi-fi router shall not cover the entire area of the house.

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Answer:

x = -14 and x = 12

Step-by-step explanation:

Let x be the width of the rectangular room in feet. Then, according to the problem, the length of the room is 2 feet longer than the width, or x + 2 feet.

The area of a rectangle is given by the formula A = length × width, so we have:

A = (x + 2) × x = x^2 + 2x

We are also given that the area of the room is 168 square feet, so we set A = 168 and get:

x^2 + 2x = 168

This is a quadratic equation in standard form, where 1x^2 + 2x - 168 = 0. We can solve this equation by factoring or using the quadratic formula. This will give us the value(s) of x, which represents the width of the room. Once we have the width, we can find the length by adding 2 feet to it.

And x is :  -14 and 12

No. The reported return rate appears lower than expected.

To determine whether the reported rate of return is reasonable or not, we can calculate the expected rate of return based on the investment amount and the ending value of the account.

First, we need to calculate the total number of quarters that have elapsed between the initial investment and the current quarter. Let's assume that the investment has been held for n quarters.

Then, we can use the following formula to calculate the expected rate of return:

Expected rate of return = (Ending value / Initial investment) ^ (1/n) - 1

Plugging in the given values, we get:

n = 1 (since we are only given information for a single quarter)

Initial investment = 26,245

Ending value = 26,292

Expected rate of return = (26,292 / 26,245) ^ (1/1) - 1 = 0.18%

Comparing the expected rate of return of 0.18% with the reported rate of return of -0.02%, we can see that they are quite different. However, it's important to note that a single quarter's rate of return may not be indicative of the overall performance of the investment.

Therefore, while the reported rate of return seems lower than expected, we would need to consider the performance over a longer period of time to make a more informed assessment of the investment's performance.

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I will be finding the minimum of this parabolic function.

The function y = x^2 - 9 is a parabola that opens upwards, since the coefficient of the x^2 term is positive. Therefore, the minimum value of the function occurs at the vertex of the parabola.

To find the x-coordinate of the vertex, we can use the formula -b/2a, where the quadratic function is in the form y = ax^2 + bx + c. In this case, a = 1 and b = 0, so the x-coordinate of the vertex is -b/2a = -0/(2*1) = 0.

To find the corresponding y-coordinate of the vertex, we can substitute x = 0 into the function, which gives y = 0^2 - 9 = -9.

Therefore, the minimum value of the function y = x^2 - 9 is -9, which occurs at x = 0.

~~~Harsha~~~

The minimum point of this function is located at (0, -9).

So from plain sight we can tell we're looking for a maximum point, because the coefficient of x² is positive, it's 1. If the function was y=-x²-9, we would be looking at a minimum point.

The vertex if the exact point where a quadratic or any pair exponent function will start to either decay or increase, therefore, it will be the minimum or maximum point.

Formula for "x" value of vertex: [tex]\sf x_{Vertex} =\dfrac{-b}{2a}[/tex].

In this equation, a and b are coefficients extracted when the formula is expressed on its standard form.

Standard form of a quadratic equation: ax² + bx + c = 0

➔ You need to substitute the "y" by a "0", and the formula should look like this:

[tex]\sf 0=x^2-9[/tex]

➔ Reorganizing...

[tex]\sf x^2-9=0[/tex]

Let's expand the previous expression:

[tex]\sf x^2+0x_{} -9=0[/tex]

The coefficients are:

a= 1, beacuse "x²" is being multiplied by 1, which is implicit.

b= 0, because "x" doesn't really exist on the simplified equation.

c= -9.

Now let's calculate the "x" position of the vertex using the formula from step 2:

[tex]\sf x_{Vertex} =\dfrac{-b}{2a}=\dfrac{-(0)}{2(1)}=0[/tex]

Now, the "y" value can be obtained just by substituting "x" by 0 on the argument of the function:

[tex]\sf y=(0)^2-9\\ \\y=-9[/tex]

Therefore, the vertex, or minimum point of this function is located at (0, -9).

Check out the attached image to verify this information with the graph.

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Answer:

7

Step-by-step explanation:

[4x2+(5+1)] ÷ 2

[8+(6)] ÷ 2

14 ÷ 2

7

For the given right angled triangle cosine of angle B is 5√89/89.(option A).

What is right angled triangle?

It is a particular type of triangle having one angle is 90° or right angle. The adjacent sides of the right angle are called base and the perpendicular and the opposite side of 90° is called hypotenuse.

The given triangle is the right angled triangle. The three sides of a right angled triangle are called base, perpendicular and hypotenuse.

In the given figure base=  5 inches and perpendicular = 8 inches

By Pythagoras theorem at first we will find out the hypotenuse. Let the hypotenuse= c inches

For any right angled triangle,

(perpendicular)² +(base)²= (hypotenuse)²

⇒ (8)² + (5)² = (c)²

⇒ 64+ 25 = c²

⇒ c² =89

⇒ c= ±√89

As hypotenuse cannot be negative

So hypotenuse = √89 inches.

Now to find cosine of angle B that is cos B we will use the trigonometric function.

cos B= Adjacent side/ hypotenuse

         = 5/√89

        = 5√89/89 [ Multiplying the numerator and the denominator by √89 ]

Hence, cosine of angle B is 5√89/89.

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The sequences that show that the two figures are similar, but not congruent, are:

This sequence includes a dilation with a different scale factor for each figure and reflections, which preserve the shape of the figures but not their size or orientation.

In conclusion, the correct options are A and C

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Answer:

the missing y coordinate is 2/5

Step-by-step explanation:

You are basically solving for y since you are missing the y coordinate

Since x=5 plug that in and you will get 5+5y=7

subtract 5 on both sides and you will get 5y=2

divide 5 on both sides and you will get 2/5

The correct values to fill in the missing information are:

Claim: The claim is that the proportion of American adults who eat salad once per week is different from 50%, which corresponds to the null hypothesis H0: p = 0.5.

Opposite: The opposite of the claim is that the proportion of American adults who eat salad once per week is equal to 50%, which corresponds to the alternative hypothesis H1: p = 0.5 (Note that in this case, the alternative hypothesis is the opposite of the claim since we are testing for a difference from 50% in the claim).

Therefore, the claim is H0: p ≠ 0.5 (two-tailed test), and the opposite is H1: p = 0.5 (two-tailed test).

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The interest he earns in 10 years =  $395.42.

What is compound interest?

The interest that is calculated using both the principal and the interest that has accrued during the previous period is called compound interest.

Here the Principal P = $500

Rate of interest= 6% = 6/100 = 0.06

Number of years t= 10 years.

Now using  compound interest formula then,

=> Amount = [tex]P(1+r)^t[/tex]

=> Amount = 500[tex](1+0.06)^{10[/tex] = [tex]500\times1.06^{10[/tex]

=> Amount = $895.42.

Now interest = $895.42 - $500 = $395.42

Hence the interest he earns in 10 years =  $395.42.

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Answer:

$23.30

Step-by-step explanation:

We Know

You paid $6.99

The shirt was 70% off

$6.99 = 30%

What was the original price of the shirt?

We Take

(6.99 ÷ 30) x 100 = $23.30

So, the original price is $23.30

Answer:the median is  Q2 aka 105

Step-by-step explanation:

Option B

One dimensional objects

Answer:

B. One-dimensional objects

A line segment can "grow" from one-dimensional objects. A line segment is a one-dimensional figure that has two endpoints and connects them with a straight path. One-dimensional objects include lines and curves, and a line segment can be a part of a longer line or curve.

Three-dimensional objects (A) are made up of length, width, and height and cannot "grow" into a line segment, but a line segment can be a part of a three-dimensional object, such as an edge or a diagonal.

Zero-dimensional objects (C) are points, which do not have any length, width, or height. A line segment cannot "grow" from a point, but a point can be one of the endpoints of a line segment.

Answer: 195 adult tickets and 262 children tickets

Step-by-step explanation:

     Let a be adult tickets and c be children tickets.

We know there are 457 seats.

     a + c = 457

We also know the cost of the tickets and how much money was made.

     $54a + $17c = $14,984

Now, we have a system of equations we can use to solve.

     a + c = 457

     $54a + $17c = $14,984

Lastly, we will graph this system, see attached. The point of intersection, or where the lines intersect, is our answer.

     195 adult tickets and 262 children tickets.

Answer:

Chidden tickets were 262 and adult tickets were 195 tickets

Step-by-step explanation:

Let x = the number of children tickets

Let y = the number of adult tickets.

x + y = 457

17x + 54y = 14984

Use substitution

x + y = 457 Solve for y

y = 457 -x  Substitute 457 -x for y in the equation 17x + 54y = 14984

17x + 54y = 14984

17x + 54(457 -x) = 14984  Solve for x  Distributer the 54

17x + 24678 - 54x = 14984  Combine like terms

-37x = -9694   Divide both sides by -37

x = 262

The number of children tickets.

x + y = 457  Substitute 262 for x and solve for y

262 + y = 457  Subtract 262 from both sides

y = 195

The number of adult tickets.

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