Geometry question. thanks for the help!​

The values a and b should be replaced to rewrite the given expression as (x + a)(x - b).

Generally speaking, the standard form of a quadratic function is given by this mathematical expression;

ax² + bx + c = 0

Where:

a and b represents the coefficients of the first and second term in the quadratic function.

c represents the constant.

Next, we would solve the above quadratic function by using the factorization method;

x² + x - 72 = 0

x² - 8x + 9x - 72 = 0

x(x - 8) + 9(x - 8) = 0

(x + 9)(x - 8) = 0

(x + 9)(x - 8) = (x + a)(x - b).

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Answer:

Circumference = (3.14)(15) = 47.1 in

Step-by-step explanation:

The Complete statement are:

1. 27/3 + 5 x 2

2. 81 + 1 - 8 x 4 x 1 = 60

Combining operands with a single arithmetic operator specifies an arithmetic operation. The  ADD, SUBTRACT, DIVIDE, and MULTIPLY can also be used to specify arithmetic operations.

Given:

we have to apply the operation to make

27 3 5 2 = 19

81 11 8 4 1 = 60

so, first 27 3 5 2 = 19

1. 27/ 3 = 9

2. 5 x 2= 10

3. 9+ 10 = 19

For second,

1.81 + 11 = 92

2. 8 x 4 x 1 = 32

3. 92-32 = 60

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The equation for the nth term of this sequence is an = -4.5 + 2.5(n - 1)

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

a4 = 3

a10 = 18

An arithmetic sequence is represented as

an = a + (n - 1)d

Using the above as a guide, we have the following:

a + 3d = 3

a + 9d = 18

Subtract the equations

So, we have

6d = 15

Divide

d = 2.5

So, we have

a + 3 * 2.5 = 3

This gives

a = -4.5

So, the sequence is -4.5 + 2.5(n - 1)

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Answer:

he circumference of the circle is approximately 56.52 millimeters.

Step-by-step explanation:

The circumference of a circle is given by the formula:

C = πd

where C is the circumference, d is the diameter, and π is a mathematical constant approximately equal to 3.14.

Substituting the given value of the diameter, we get:

C = πd = π(18) = 56.52 mm (rounded to two decimal places)

Therefore, the circumference of the circle is approximately 56.52 millimeters.

Answer:

[tex]\sqrt{13}[/tex]

Step-by-step explanation:

[tex]L^{2}[/tex]=[tex]3^{2}[/tex]+[tex]2^{2}[/tex]=9+4=13

L=[tex]\sqrt{13}[/tex]

The function equivalent to y = [tex]3x(x+2)^2+7[/tex] is [tex]y = 3x^3[/tex]+[tex]12x^2[/tex] + 12x + 7.

Functionally equivalent refers to when a design, material, practice, method, technique, procedure, or component serves the same purpose and offers the same or better utility as is needed by the rule.

When we add the parenthesis to the expression, we get:

[tex]y = 3x(x^2 + 4x + 4) + 7[/tex]

If we simplify, we get:

[tex]y = 3x^3 + 12x^2 + 12x + 7[/tex]

As a result, y = 3x(x+2)2+7 is identical to y = 3x3 + 12x2 + 12x + 7.

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The equation of line passes through the points (- 7, -3) and (-3, 5) will be;

⇒ y = 2x + 11

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

Two points on the line are (- 7, -3) and (-3, 5).

Now,

Since, The equation of line passes through the points (- 7, -3) and (-3, 5).

So, We need to find the slope of the line.

Hence, Slope of the line is,

m = (y₂ - y₁) / (x₂ - x₁)

m = (5 - (-3)) / (-3 - (-7))

m = 8 / 4

m = 2

Thus, The equation of line with slope 2 is,

⇒ y - (-3) = 2 (x - (-7))

⇒ y + 3 = 2 (x + 7)

⇒ y + 3 = 2x + 14

⇒ y = 2x + 14 - 3

⇒ y = 2x + 11

Therefore, The equation of line passes through the points (- 7, -3) and

(-3, 5) will be;

⇒ y = 2x + 11

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Answer:

x=6.5

Step-by-step explanation:

I'm not sure if it's correct

The area of the given triangle is approximately 204.2 square inches.

Triangle is defined as a basic polygonal shape of a triangle that has three sides and three interior angles.

To calculate the area of a triangle with given side lengths, we can use Heron's formula:

Area = √(s(s-a)(s-b)(s-c))

where s is the semi-perimeter of the triangle (half of the perimeter), and a, b, and c are the lengths of the sides.

In this case, the lengths of the sides are a=32, b=22, and c=19. Therefore, the semi-perimeter is:

s = (a + b + c) / 2 = (32 + 22 + 19) / 2 = 36.5

Now we can plug in these values into the formula and simplify:

Area = √(36.5(36.5-32)(36.5-22)(36.5-19)) ≈ 204.16

Rounding this to 1 decimal place, the area of the triangle is approximately 204.2 square inches.

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Answer:

A. 2 + x = 5

B x + 1 = 4

E -5 + x = -2

Step-by-step explanation:

2 + 3 = 5

3 + 1 + 4

-5 + 3 + -2

if this correct mark me as brainliest please

The theoretical probability of selecting a red bead is 0.28.

Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.

We know that, probability of an event = Number of favourable outcomes/Total number of outcomes

Given that,

Color                     Frequency

Red                               17

Orange                         12

Yellow                          10

Green                           9

Blue                              8

Purple                           5

Color                      List A                      List B

Red                           33                            31

Orange                     27                            24

Yellow                       22                           18

Green                        30                           34

Blue                           18                            19

Purple                        12                            5

Probability of selecting a red bead = 17/61

= 0.28

Orange color would have a frequency closest to 24.

Therefore, the theoretical probability of selecting a red bead is 0.28.

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The probability of an event can not be more than the number 1.

Probability of an event is the ratio of number of favorable outcome to the total number of outcome of that event.

As the probability of an event can not be more than the number 1.

Thus the probability of failure of a event is equal to the difference of the 1 to the success of the event. As,

[tex]Probability[/tex] [tex]of[/tex] [tex]faliure=1-[/tex] [tex]Probability[/tex] [tex]of[/tex] [tex]success[/tex]

Rina spins the spinner less than the 30 times.

A success occurs when the spinner lands on a number that is greater than 6.

A spinner is divided into 8 equals sections and the sections are labeled 1 through 8.

As the probability of success occurs when the spinner lands on a number that is greater than 6, thus the number should grater than six.

This number should be less than 30 as the spinner spins less than the 30 times.

Thus the total number of outcome of this event is,

[tex]=30-6[/tex]

[tex]=24[/tex]

Thus the probability of success is,

[tex]P=\frac{6}{24}[/tex]

[tex]P=\frac{1}{4}[/tex]

Hence the probability of success is 1/4.

As the probability of failure of a event is equal to the difference of the 1 to the success of the event.

Thus the probability of failure is,

[tex]P^-=1-P[/tex]

[tex]P^-=1-\frac{1}{4}[/tex]

[tex]P^-=\frac{4-1}{4}[/tex]

[tex]P^-=\frac{3}{4}[/tex]

The probability of failure is 3/4.

Hence,

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The probability that a randomly selected persons favorite restaurant is a deli is 9/50

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

The table of values

On the table, we have

Total = 100

Deli = 18

So, the probability is

P = Deli/Total

Substitute the known values in the above equation, so, we have the following representation

P = 18/100

Simplify

P = 9/50

Hence, the probability is (d) 9/50

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The order from least to greatest would be as follows:

√3 - 1 < 2√10 ÷ 5 < √14 < 3√2 < √19 + 1 < 6

To order the numbers, we need to first simplify and evaluate each expression.

1. √3 - 1 = 1.73205080757 - 1 = 0.73205080757

2. 2√10 ÷ 5 = 1.265

3. √14 = 3.74166

4. 3√2 = 4.243

5. √19 + 1 = 5.359

6. 6 is simply 6

Therefore, the correct answer is as given above. It could then be concluded that the order from least to greatest is:

0.73205080757 < 1.265 < 3.74166 < 4.243 < 5.359 < 6

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Answer:

+5&-2

Step-by-step explanation:

The milk bottle, item is the best example of an artifact from the passage that reveals something about sign. Thus, option (a) is correct.

The term “passage” refers to the explanation and description of a sentence in relation to a topic. The passage aimed to describe those details related to the theme of the story. The different passage is to justify to the different things as to clarify. The passage is to define the important terms.

The milk bottle sat on the central shelf, as mentioned in the passage. The artifact is a completely empty milk bottle. The section gives information regarding signs. The passage was Sig's refrigerator, which had been opened. A milk bottle sat on the middle shelf, its cap missing and no milk inside.

As a result, the milk bottle, item is the best example of an artifact from the passage that reveals something about sign. Therefore, option (a) is correct.

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The solution is, the distance = √116.

The distance between two points is the length of the line joining the two points.

Formula: distance= √(x_2-x_1)²+(y_2-y_1)²

here, we have,

given that,

P (3√2,5√3), Q(√2,-√3)

so,  the distance d(P,Q).

by using the formula we get,

the distance = √108 + 8

                     = √116

Hence, The solution is, the distance = √116.

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Answer:

2

Step-by-step explanation:

Let's call the added amount of kg of mixed nuts that contain

40

%

peanuts

m

a

d

d

e

d

. If the new mixture contains

34

%

peanuts, then:

m

peanuts

m

total

=

0.34

The bag of

6

kg

already contained

0.3

⋅

6

=

1.8

kg

of peanuts. Furthermore,

40

%

of

m

added

will be peanuts. This means that:

m

peanuts

=

0.4

m

added

+

1.8

The total mass will be the original

6

kg

plus the added mass, so

m

total

=

m

added

+

6

.

This gives us the following equation.

0.4

m

added

+

1.8

m

added

+

6

=

0.34

Multiply both sides with

m

added

+

6

.

0.4

m

added

+

1.8

=

0.34

(

m

added

+

6

)

Multiply out the brackets.

0.4

m

added

+

1.8

=

0.34

m

added

+

2.04

Subtract

0.34

m

added

from both sides.

0.04

m

added

+

1.8

=

2.04

Subtract

1.8

from both sides.

0.06

m

added

=

0.24

Divide both sides by

0.06

.

m

added

=

4

Therefore, Jenny must add

4

kg

.

The triangle has vertices A(7,-2), B(5.25, -1.25), and C(5, -0.5).

What is a triangle ?

Triangle can be defined in which it consists of three sides, three angles and sum of three angles is always 180 degrees.

Let's call the vertex we know A, and the midpoints of the other two sides B and C, respectively.

Using the midpoint formula, we can find the coordinates of the other two vertices, which are the endpoints of the sides that have B and C as midpoints

Coordinates of B:

x-coordinate: (7 + 3.5)/2 = 5.25

y-coordinate: (-2 - 0.5)/2 = -1.25

So, B is (5.25, -1.25)

Coordinates of C:

x-coordinate: (7 + 3) / 2 = 5

y-coordinate: (-2 + 1)/2 = -0.5

So, C is (5, -0.5)

Therefore, The triangle has vertices A(7,-2), B(5.25, -1.25), and C(5, -0.5).

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The formulas are functionally the same, but 'n' (the sample size) is used instead of 'N' (the population size).

The sample mean is the average value for a set of observations which is derived from a population. While the population mean is the average value for the entire set of observation belonging to a particular study of interest.

The set of observation belonging to a population is denoted by 'N' ; while the sample size is denoted as 'n' :

The mean formula is written thus :

Population mean = Σx / N

Sample mean = Σx / n

Where, x = set of values.

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The distance traveled in the first 8 minutes is 1.75 d2

Speed is the rate of change of distance with time. it is a scalar quantity and it is measured in meter per second.

speed = distance /time

time = distance /speed

total time = 16

represent u by the first 8minutes and v by the second 8 minutes

u = 1.75v

8 = d1/1.75v

8 = d2/v

d1/1.75v = d2/v

d1 ×v = 1.75v × d2

d1 = 1.75d2

therefore ;

d1 = 1.75d2

where d1 and d2 are the distances for the first 8 minutes and second 8minutes respectively.

therefore the distance in the first 8minutes is 1.75 times greater than the second 8 minutes

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Scott's statement that (13g + 1) + (-2 - 5g) and 8/3(3g + 9/8) are equivalent is wrong

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

(13g + 1) + (-2 - 5g)

Remove the brackets

So, we have

13g + 1 - 2 - 5g

Evaluate the like terms

8g - 1

When factorized, we have

8/3(3g - 3/8)

This is not the same as Scott's expression

Hence, Scott is incorrect

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For the function f(t) the domain and range is [0, 12.76] and [1.80, 590.90] respectively.

A function is a mathematical tool used to associate one value with another.

In this case, the function models the height of an object being tossed from a tall building. The height of the object is given by the function h(t), where h represents the height in meters and t represents the time in seconds.

The domain and range of a function describe the set of all possible input values (domain) and the set of all possible output values (range) of a function. The domain and range of the function h(t) are as follows:

The domain of the function h(t) is the set of all possible values of t for which the function h(t) is defined. In this case, the domain of the function h(t) is [0, 12.76], which means that the function h(t) is only defined for time values between 0 and 12.76 seconds.

The range of the function h(t) is the set of all possible values of h(t) that the function can produce. In this case, the range of the function h(t) is [1.80, 590.90], which means that the height of the object can only be between 1.80 meters and 590.90 meters.

Therefore, the correct option is (a).

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Answer: The correct answer is C. It represents a function only.

A function is a special type of relation where each input value is associated with only one output value. In other words, for every x in the domain of the function, there is only one corresponding y in the range.

In this equation, y = 2^x + 4, for every value of x, there is a unique corresponding value of y. So, it satisfies the requirement of a function and represents a function only.

Step-by-step explanation:

Answer:

D. It represents both a relation and a function

Hope this helps!

Step-by-step explanation:

All functions are relations, but not all relations are functions. The equation given is an Exponential function.

The solution of both inequalities is (-1, 2).

Mathematical expressions with inequalities are those in which the two sides are not equal. Unlike to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

Given:

We have the inequalities

x+ y >1.........(1)

-x+ y <3.........(2)

The graph for x+ y >1 is shown by the red shaded region.

and, the graph for -x+ y <3  is shown by the blue shaded region.

Also , the Inequality intersect at (-1, 2) which shows the solution of both inequalities.

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The proportion of test takers that are considered top performers is given as follows:

0.1056.

The minimum SAT score needed for a test taker to be in the top 20% is given as follows:

1231.

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation of SAT scores are given as follows:

[tex]\mu = 1050, \sigma = 216[/tex]

The proportion of scores above 1320 points is one subtracted by the p-value of Z when X = 1320, hence:

Z = (1320 - 1050)/216

Z = 1.25

Z = 1.25 has a p-value of 0.8944

1 - 0.8944 = 0.1056.

The minimum SAT score needed for a test taker to be in the top 20% is the 80th percentile, which is X when Z = 0.84, hence:

0.84 = (X - 1050)/216

X - 1050 = 216 x 0.84

X = 1231.

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a. The line of the best fit is ŷ = -8.55485X + 118.39451.

b. The value of the correlation coefficient is  -0.8619.

A straight line that minimizes the gap between it and certain data is called a line of best fit. In a scatter plot containing several data points, a relationship is expressed using the line of best fit. It is a result of regression analysis and a tool for forecasting indicators and price changes.

Sum of X = 117.4

Sum of Y = 298

Mean X = 10.6727

Mean Y = 27.0909

The sum of squares (SSX) = 0.8618

The sum of products (SP) = -7.3727

Regression Equation = ŷ = bX + a

b = SP/SSX = -7.37/0.86 = -8.55485

a = MY - bMX = 27.09 - (-8.55*10.67) = 118.39451

ŷ = -8.55485X + 118.39451

X Values

∑ = 117.4

Mean = 10.673

∑(X - Mx)² = SSx = 0.862

Y Values

∑ = 298

Mean = 27.091

∑(Y - My)² = SSy = 84.909

X and Y Combined

N = 11

∑(X - Mx)(Y - My) = -7.373

R Calculation

r = ∑((X - My)(Y - Mx)) / √((SSx)(SSy))

r = -7.373 / √((0.862)(84.909)) = -0.8619

Therefore, the line of the best fit is ŷ = -8.55485X + 118.39451

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