If g(x) = x3 + 2x – 5, find the value.
a) 8(2)=
b) 8(-2) =

Help plzzz

Answer:

C: 2 Quarts

Step-by-step explanation:

Since 1 gallon is 4 quarts, 1 1/4 gallons is 5 quarts. (Just multiply by 4)

Now just subtract, 5-3=2

The solution of the system of equation is (-7, -2).

The system of the equations;

\(\rm y^2 + x^2 = 53 \\\\y -x = 5\)

From equation 1

\(\rm y -x=5\\\\y = 5+x\)

Substitute the value of y in equation 1

\(\rm y^2+x^2=53\\\\(5+x)^2+x^2=53\\\\25+x^2+10x+x^2=53\\\\2x^2+10x+25-53=0\\\\2 x^2 + 10x - 28 = 0 \\\\Divide \ by \ 2 \ both \ side \ the \ equation\\\\x^2 + 5x - 14 = 0\\\\x^2-7x+2x-14=0\\\\x(x-7) + 2(x-7) =0\\\\(x-7) \ (x+2)=0\\\\x-7=0 \ \ x = 7\\\\x +2 =0 \ \ x=-2\)

The value of x= 2 is rejected because x = 2 not satisfy the equation.

Substitute 2 for the value of x in equation II

y − x = 5

y – 2 = 5

y = 5 +2

y = 7 (x =2, y =7) … Not included in the options

If x = -7

Substitute the value of x = -7 in the equation

\(\rm y -x=5\\\\y - (-7)=5\\\\y +7= 5\\\\y = 5-7\\\\y = -2\)

Hence, the solution of the system of equation is (-7, -2).

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2.67 pints of red paint to be added to the paint Mixer in order to achieve the desired 75% red and 25% yellow mixture.

The number of pints of red paint that need to be added to the paint mixer, we need to calculate the amount of paint in the mixer currently and find the difference between that amount and the desired 75% red mixture.

Currently, the paint mixer contains 4 pints of equal amounts of yellow and red paint. Since the yellow and red paint are in equal amounts, we can say that there are 2 pints of red paint in the mixer.

Now, let's calculate the amount of red paint required for the desired mixture. We want the final mixture to be 75% red, which means that 75% of the total mixture should be red.

the total mixture required is X pints. Since 75% of the mixture should be red, we have:

0.75X pints of red paint.

Since the current amount of red paint in the mixer is 2 pints, we can subtract this from the desired amount to find the additional pints of red paint needed:

0.75X - 2 pints.

We want the additional pints of red paint to equal 0, so we set up the equation:

0.75X - 2 = 0.

Solving this equation, we find:

0.75X = 2.

X = 2 / 0.75.

X ≈ 2.67.

Therefore, we need approximately 2.67 pints of red paint to be added to the paint mixer in order to achieve the desired 75% red and 25% yellow mixture.

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Developing strategies for remembering facts is essential for children before they engage in drill and practice activities to develop fluency. By establishing these strategies, children can effectively learn, retain, and recall information, ultimately enhancing their performance during practice sessions.

Yes, it is important for children to develop strategies for remembering facts before engaging in drills and practice to develop fluency. By doing so, children can enhance their ability to recall information more quickly and accurately, making it easier for them to perform well on tests and assignments. Strategies such as visualizing, chunking, and using mnemonic devices can help children remember information more effectively. Once these strategies are established, drill and practice can then be used to further reinforce their understanding and speed up their recall time. This approach can ultimately lead to improved academic performance and a stronger foundation for learning.

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The length of the midsegment of the trapezoid is 8 units

Trapezoid

A trapezoid, also known as a trapezium, is a flat closed shape having 4 straight sides, with one pair of parallel sides. The parallel sides of a trapezium are known as the bases, and its non-parallel sides are called legs.

The midsegment of a trapezoid is the segment connecting the midpoints of the two non-parallel sides of the trapezoid and is parallel to the pair of parallel sides.

In this problem

The two non-parallel sides of the trapezoid are AD and BC

Step 1

Find the midpoint side of AD

Let

E the midpoint AD

A ( 2,4 ) D (-2,-1)

Find the x-coordinate of the midpoint AD

\(x = \frac{2-2}{2} = 0\)

Find the y-coordinate of the midpoint AD

\(y = \frac{4 - 1}{2} = 1.5\)

the point E is equal to (0, 1.5 )

Step 2

Find the midpoint side of BC

Let

F the midpoint BC

\(B ( 7,4) C ( 9, -1)\)

Find the x-coordinate of the midpoint BC

\(x = \frac{9+2}{7} = 8\)

Find the y-coordinate of the midpoint BC

\(y = \frac{4 - 1}{2} = 1.5\)

The point F is equal to ( 8 , 1.5 )

Step 3

Find the distance EF

Know that

The formula to calculate the distance between two points is equal to

\(d = \sqrt{(y2 - y1)^{2}+ (x2 -x1)^{2} }\)

we have

E ( 0 ,1.5) F ( 8, 1.5)

substitute the values

\(d = \sqrt{(1.5 - 1.5)^{2} + (8-0 )^{2} }\)

d = 8 units

Therefore

The length of the midsegment of the trapezoid is 8 units

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Answer:

It actually depends on where the point of letter is

The angle swept out by Natalie can be calculated by dividing the distance she has traveled (d) by the radius of the Ferris wheel (12), so the expression is d/12 in radians.

Natalie's height above the center of the Ferris wheel can be calculated using the sine function. The angle she has swept out in radians (d/12) is the angle between the radius of the Ferris wheel and the line connecting the center of the Ferris wheel to her position. The sine of this angle is equal to the opposite side (her height above the center of the Ferris wheel) divided by the hypotenuse (the radius of the Ferris wheel), so the expression is d(sin(d/12)) in radius lengths. To convert the radius lengths to meters, we need to multiply by the radius of the Ferris wheel (12), so the expression for Natalie's height above the center of the Ferris wheel in meters is 12sin(d/12) meters.

Finally, to find Natalie's height above the ground, we need to add the height of the center of the Ferris wheel (16) to her height above the center of the Ferris wheel, so the expression is 16 + 12sin(d/12) meters.

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The independent variable is h, the number of hours Vincent spends reading every day, and the dependent variable is d, the number of days it will take Vincent to finish reading the book.

The independent variable is the variable that can be changed by the experimenter. In this case, Vincent can change the number of hours he spends reading every day. The dependent variable is the variable that is affected by the independent variable. In this case, the number of days it will take Vincent to finish reading the book depends on the number of hours he spends reading every day. For example, if Vincent spends 2 hours reading every day, it will take him 15 days to finish the book. If he spends 3 hours reading every day, it will take him 10 days to finish the book. The number of hours he spends reading every day (the independent variable) determines the number of days it will take him to finish the book (the dependent variable).

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Answer:

f(50) = 31928.24 thousands

Therefore, it means that the US population in year 1850 is 31928.24 thousands

Step-by-step explanation:

Given the function;

f(x)=165.6x^1.345

Where;

f(x) is in thousand and

x is the number of year after 1800

To determine f(50), we will substitute x = 50 into the function of f(x);

f(50)=165.6(50)^1.345

f(50) = 31928.24 thousands

Since f(50) is the US population in year 1800+50 = 1850

Therefore, the US population in year 1850 is 31928.24 thousands

Answer:

The circumference of the circle A = 110 cm and the circumference of the circle B = 132 cm

Step-by-step explanation:

Circumference of circle A = 2πr = 110

[2×(22/7)×r ]= 110

r = (7×5)/2 = 17.5 cm.

Circumference of circle B = 2πR = 132

Answer:You should have learnt this in kindergarten yet you're in high school, the answer is 86

Answer:

I only

Step-by-step explanation:

All numbers are rational.

Not all numbers are whole or integers.

Answer: I only

we can solve the given equation by taking log to get answer as x = log₈(25)

what is  an equation ?

An equation is a mathematical statement that contains an equal sign, indicating that two expressions have the same value. It is a way of expressing the relationship between different variables or quantities.

In the given question,

Taking the logarithm of both sides with base 8, we get:

log₈(8ˣ) = log₈(25)

Using the logarithmic property that logₐ(b^c) = c logₐ(b), we can simplify the left-hand side to:

x log₈(8) = log₈(25)

Since log₈(8) = 1, we have:

x = log₈(25)

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Answer:

X Intercept is 3,0 and y intercept is 0, 5/2

Step-by-step explanation:

the 5/2 Is a Fraction

The total number of ways to select 4 baseball players and 4 basketball players from 8 baseball players and 13 basketball players is 70 × 715 = 50,050.

The number of ways to select 4 baseball players and 4 basketball players from 8 baseball players and 13 basketball players is equal to the number of combinations without repetition (denoted as C(n,r) n≥r) of 8 baseball players taken 4 at a time multiplied by the number of combinations without repetition of 13 basketball players taken 4 at a time.

The number of ways to select 4 baseball players from 8 baseball players = C(8,4)

= 8!/4!(8-4)!

= (8×7×6×5×4!)/(4!×4!)

= 8×7×6×5/(4×3×2×1)

= 2×7×5

= 70

The number of ways to select 4 basketball players from 13 basketball players = C(13,4)

= 13!/(13-4)!4!

= (13×12×11×10×9!)/(9!×4!)

= (13×12×11×10)/(4×3×2×1)

= 13×11×5

= 715

Therefore, the total number of ways to select 4 baseball players and 4 basketball players from 8 baseball players and 13 basketball players is 70 × 715 = 50,050.

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The value of x in the triangle is 6√5

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

The triangle

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

x/20 = 9/x

Cross multiply the equation

so, we have the following representation

x^2 = 180

TAke the square root of hoth sides

This gives

x = 6√5

Hence, the solution of x is  6√5

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Answer:

B. No, Hannah should have used the ratio \( \frac{adjacent}{opposite} \)

Step-by-step explanation:

✍️The formula for calculating cotangent of an angle is given as:

\( cot = \frac{adjacent}{opposite} \).

The ratio, \( \frac{opposite}{adjacent} \), used by Hannah is the formula for calculating tangent of an angle.

Therefore, Hannah did not calculate the cotangent of the angle correctly.

She should have used, the ratio, \( \frac{adjacent}{opposite} \) instead.

Answer:

12

Step-by-step explanation:

12 is the most number in the equation

Answer:

Mean Age: 13 years

Step-by-step explanation:

To find the mean or average in mathematics, add up all data in a set, and divide by the amount of individual values there are in the set.

Here's what I mean:

12+14+12+15+14+13+12+12 = 104 / 8 different ages in the set = 13

Hope this helped :) .

Answer:

27

Step-by-step explanation:

bc m1=31 and m2=29 you subtract 31-29and it is 27

Answer:

576.97

Squared

The z statistic of 2.41 indicates that the test is measuring a difference that is 2.41 standard deviations away from the mean. The correct option is a.

To determine if this difference is statistically significant, we need to compare it to the critical values for our chosen level of significance (α).

If the critical value for α=0.05 is less than 2.41, but the critical value for α=0.01 is greater than 2.41, then the test is statistically significant at α=0.05 but not at α=0.01. This means that there is evidence to support the alternative hypothesis at a less strict level of significance (α=0.05), but not at a more strict level of significance (α=0.01).

On the other hand, if both the critical value for α=0.05 and the critical value for α=0.01 are less than 2.41, then the test is statistically significant at both levels of significance. This means that there is strong evidence to support the alternative hypothesis even at a very strict level of significance (α=0.01).

In summary, we need to compare the z statistic to the critical values for α in order to determine if the test is statistically significant. Depending on the values of the critical values for α, the test may be statistically significant at both levels of significance, only at α=0.05, or not statistically significant at either level of significance. The correct option is a.

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(a)

The gradient of f at the point P = (2,-2) is given by:

∇f(x, y) = [∂f/∂x, ∂f/∂y]

Taking partial derivatives of f with respect to x and y, we get:

∂f/∂x = y^2

∂f/∂y = 2xy

Substituting x = 2 and y = -2, we get:

∂f/∂x = (-2)^2 = 4

∂f/∂y = 2(2)(-2) = -8

Therefore, the gradient of f at the point P = (2,-2) is:

∇f(2, -2) = [∂f/∂x, ∂f/∂y] = [4, -8]

(b)

The maximal and minimal rates of change in f at the point (2,-2) are given by the magnitudes of the gradient vector ∇f(2, -2).

The maximal rate of change is the magnitude of the gradient vector, which is:

|∇f(2, -2)| = sqrt(4^2 + (-8)^2) = 8

The minimal rate of change is the negative of the magnitude of the gradient vector, which is:

-|∇f(2, -2)| = -8

(c)

To find an equation for the plane tangent to the graph z = f(x,y) at the point (2,-2, f(2,-2)), we need a point on the plane and a normal vector to the plane.

The point on the plane is (2, -2, f(2,-2)), and the normal vector to the plane is the gradient vector ∇f(2, -2), which we already found in part (a).

Therefore, an equation for the plane tangent to the graph z = f(x,y) at the point (2,-2, f(2,-2)) is:

4(x - 2) - 8(y + 2) + [f(2,-2) - V1] = 0

where V1 is the constant term in the expression for f(x,y).

(d)

The level curve f(x, y) = f(2,-2) is the set of points (x, y) in the domain of f where f(x, y) takes on the same value as f(2,-2).

Substituting f(2,-2) into the expression for f(x,y), we get:

f(x, y) = V1 + xy^2 = V1 + 2y^2

To find the equation for the line tangent to this level curve at the point (2,-2), we need a point on the line and a direction vector for the line.

The point on the line is (2,-2), and the direction vector for the line is the gradient vector ∇f(2, -2), which we already found in part (a).

Therefore, an equation for the line tangent to the level curve f(x, y) = f(2,-2) at the point (2,-2) is:

(x, y) = (2, -2) + t[∂f/∂x, ∂f/∂y] = (2, -2) + t[4, -8] = (2 + 4t, -2 - 8t)

where t is a parameter.

Thus,

a)

The gradient of f at the point P = (2,-2) is ∇f(2, -2) = [∂f/∂x, ∂f/∂y] = [4, -8].

b)

The minimal rate of change is the negative of the magnitude of the gradient vector, which is -|∇f(2, -2)| = -8.

c)

An equation for the plane tangent to the graph z = f(x,y) at the point (2,-2, f(2,-2)) is 4(x - 2) - 8(y + 2) + [f(2,-2) - V1] = 0.

d)

An equation for the line tangent to the level curve f(x, y) = f(2,-2) at the point (2,-2) is (2 + 4t, -2 - 8t).

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From 1976 until 1987, red M&Ms were removed from packets owing to a research associating the food dye used to color them to cancer.

Arithmetic is defined as working with numbers through addition, subtraction, multiplication, and division. Adding two and two to produce four is an example of arithmetic. Arithmetic is a fundamental branch of mathematics that studies the characteristics of classical operations on numbers such as addition, subtraction, multiplication, division, exponentiation, and root extraction. Arithmetic (derived from the Greek word arithmos, "number") relates to the fundamental components of number theory, arts of mensuration (measuring), and numerical computing (that is, the processes of addition, subtraction, multiplication, division, raising to powers, and extraction of roots).

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Answer:

Step-by-step explanation:

He has $500 to start with, and he takes $25 out of the account each week. But he wants more than 200 in his account by the end of summer. 25 goes into 500 20 times. But if he wanted more than 200 left, like 300-400, he could spend 4 week's worth of money to have 400 left, or 8 weeks to have 300 left. This is the best-case scenario.