six more than twice a number is ten. find the number 8th grade math
write the equation
solve for the variable

Answer:

True, a cone has an apex which is the point where the sides of the cone meet to form a tip.

Answer:

  71.6°

Step-by-step explanation:

The angle can be found from the dot product of PQ and PR.

  PQ·PR = |PQ|×|PR|×cos(α)

where α is the angle between the two segments.

  cos(α) = (Q -P)·(R -P)/(|Q -P|×|R -P|)

  = ((0, 1, 0) -(1, 0, 0))·((0, 0, 2) -(1, 0, 0))/(|Q -P|×|R -P|)

  = (-1, 1, 0)·(-1, 0, 2)/(√(((-1)² +1²)((-1²) +2²)) = (1+0+0)/√10

  α = arccos(1/√10) ≈ 71.6°

The angle at P is about 71.6°.

_____

Additional comment

The side lengths of the triangle are √2, √5, √5. As we have seen, the angle at P is bounded by the sides of length √2 and √5. The law of cosines can also be used to arrive at the angle between these sides.

Answer:

15

Step-by-step explanation:

The solutions to the linear function are;

1. The soccer team makes more money per car ($8) than the French club ($5).

2. The graph that demonstrates Arnold's journey is graph 3

3. The graph that demonstrates Francisco's journey is graph 1

4. The graph that demonstrates Celia's journey is graph 2

To determine which group makes the most money per car, we can calculate the slope of the linear function representing the amount earned per car washed for both the French club and the soccer team. The slope of a linear function is the change in the dependent variable (y) divided by the change in the independent variable (x).

Let's calculate the slope for the soccer team. We can choose any two points to calculate the slope. Let's use the points (3, 24) and (6, 48):

Slope (m) = (change in y) / (change in x) = (48 - 24) / (6 - 3) = 24 / 3 = 8

The soccer team earns $8 per car washed.

We can choose any two points to calculate the slope for the French club. Let's use the points (2, 10) and (4, 20):

(20 - 10) / (4 - 2) = 10 / 2 = 5

The French club earns $5 per car washed

The above answer is dependent on the questions below;

The french club and soccer team are washing cars to earn money. The amount earned, (y) dollars for washind (x) cars is a linear function.  Which group makes the most money per car? explain

                                      French club

Number of cars (x)                       Amount earned (y)

2                                                         10

4                                                          20

6                                                          30

8                                                         40

10                                                         50

Soccer team

Number of cars (x)                       Amount earned (y)

3                                                      24

6                                                       48

9                                                      72

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Answer:

\(h'(1) = 23\)

Step-by-step explanation:

Let be \(h(x) = (x^{2}+8)\cdot g(x)\), where \(r(x) = x^{2} + 8\). If both \(r(x)\) and \(g(x)\) are differentiable, then both are also continuous for all x. The derivative for the product of functions is obtained:

\(h'(x) = r'(x) \cdot g(x) + r(x) \cdot g'(x)\)

\(r'(x) = 2\cdot x\)

\(h'(x) = 2\cdot x \cdot g(x) + (x^{2}+8)\cdot g'(x)\)

Given that \(x = 1\), \(g (1) = -2\) and \(g'(1) = 3\), the derivative of \(h(x)\) evaluated in \(x = 1\) is:

\(h'(1) = 2\cdot (1) \cdot (-2) + (1^{2}+8)\cdot (3)\)

\(h'(1) = 23\)

Answer:

The area of this trapezoid is equal to 240 \(m^{2}\)

Step-by-step explanation:

The area of a trapezoid can be found by using the following formula...

\(Area = \frac{(a + b)h}{2}\)   (in this formula a and b are the bases of the trapezoid and h is

                         the height of the trapezoid).

Now we just substitute the values and get...

\(Area = \frac{(a + b)h}{2} = \frac{(9 + 15)(20)}{2} = \frac{480}{2} = 240m^{2}\)

The lateral surface area of a prism is the sum of the areas of all its rectangular faces.

Surface area is a two-dimensional measure that refers to the total area of a surface, such as the area of a two-dimensional shape, a three-dimensional solid, or a combination of both. It is the sum of the areas of all the faces of a solid object. It is also referred to as the area of the boundary of a three-dimensional object. It can be used to calculate the volume of an object, and is also used in other calculations like area of the base of a triangle, area of a circle, and more.

It is calculated by multiplying the perimeter of the base by the height of the prism. For example, if the base of a prism is a square with side length s and the height is h, then the lateral surface area of the prism can be calculated as 4sh. If the base of the prism is a rectangle with length l and width w, then the lateral surface area of the prism can be calculated as 2lw + 2wh.

The lateral surface area of a prism can also be calculated by adding the areas of the triangular faces. If the base of the prism is a triangle with side lengths a, b, and c, then the lateral surface area of the prism can be calculated as a + b + c.

It is important to note that the lateral surface area of a prism is different from its surface area. The surface area of a prism is the sum of the areas of its lateral faces and its two bases.

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Complete question:

How to find the lateral surface area of the prism?

Answer:

78.3333333333

Step-by-step explanation:

77 + 78 + 80 = 235

235 ÷ 3 = 78.3333333333

Answer:

78.3333

Step-by-step explanation:

add all the numbers and divide by 3(as there are three numbers)

\( \sf{\blue{«} \: \pink{ \large{ \underline{A\orange{N} \red{S} \green{W} \purple{E} \pink{{R}}}}}}\)

Expression: \(\displaystyle\sf (6-2x) +(15-3x)\)

Substituting \(\displaystyle\sf x=0.2\):

\(\displaystyle\sf (6-2(0.2)) +(15-3(0.2))\)

Simplifying the expression inside the parentheses:

\(\displaystyle\sf (6-0.4) +(15-0.6)\)

\(\displaystyle\sf 5.6 +14.4\)

Calculating the sum:

\(\displaystyle\sf 20\)

Therefore, \(\displaystyle\sf (6-2x) +(15-3x)\) evaluated at \(\displaystyle\sf x=0.2\) is equal to \(\displaystyle\sf 20\).

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

Answer:

  86.75

Step-by-step explanation:

Given test scores of 63.5, 76, and 87 that each count for 20% of your grade, you want to know the fourth test score needed for an average of 80, if the fourth test is worth 40% of your grade.

The grade for the course, with fourth test score x, will be ...

  0.20(63.5 +76 +87) +0.40x = 80

  0.40x +45.3 = 80

Solving for x, we get ...

  0.40x = 34.7 . . . . subtract 45.3

  x = 86.75 . . . . . . . divide by 0.4

The minimum score you need on the fourth test is 86.75.

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The best interpretation of the slope of the linear regression equation is given as follows:

For each increase of one degree of latitude, the average low temperature decreases by 0.70 degrees Fahrenheit.

The slope represents the rate of change of the output variable relative to the input variable of a linear relation.

Hence, it can be said that the slope states by how much the output variable y changes when the input variable x is increased by 1.

The variables in this problem are given as follows:

The negative slope of -0.7 means that for each increase of one degree of latitude, the average low temperature decreases by 0.70 degrees Fahrenheit.

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Answer:

B

Step-by-step explanation:

The height of the cone in figure 2 is 4.5 centimeters.

Two figures are said to be similar if they have the same shape and the ratio of their corresponding sides are in the same proportion.

From the diagram, the two cone are similar. Let h represent the height of the cone in figure 2, hence:

h/3 = 12/8

h = 4.5 cm

The height of the cone in figure 2 is 4.5 centimeters.

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Answer:

4.5

Step-by-step explanation:

The slope of the line passing through the points (-6, 1) and (8, -7) is -4/7.

Slope is simply expressed as change in y over the change in x.

Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given the data in the question;

Point A: ( -6,1 )

x₁ = -6

y₁ = 1

Point B: ( 8,-7 )

x₂ = 8

y₂ = -7

Now, plug the given x and y values into the slope formula above and simplify:

\(Slope\ m = \frac{y_2 - y_1}{x_2 - x_1} \\\\Slope\ m = \frac{-7 - 1}{8 - (-6)} \\\\Slope\ m = \frac{-7 - 1}{8 + 6} \\\\Slope\ m = \frac{-8}{14} \\\\Slope\ m = -\frac{4}{7}\)

Therefore, the slope of the line is -4/7.

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Answer:22

Step-by-step explanation:

Add

Multiply

Divide

Answer:

3x + 9

Step-by-step explanation:

Answer:

it's equal to 21 when I say it's equal to 21

In order to find the solution of this inequality, first let's find its roots:

The roots are 1 and -6.

Since the concavity of this function is upwards (because a > 0), we have that the function is negative for value of x between the roots and positive for the other values (x < -6 or x > 1).

Since the inequality has the symbol "greater than or equal", we want the positive values, including zero, therefore the answer is x ≤ -6 or x ≥ 1 (option B).

Answer:

\(x < - 6 \ \text{and} \ x > 1\)

Step-by-step explanation:

We are given an inequality:

\(7x^2 + 35x > 42\)

We are asked to find the solution to this inequality.

First, treat this as a quadratic equation. Get the inequality to quadratic form:

\(ax^2+bx+c > 0\\\\7x^2+35x > 42\\\\7x^2+35x-42 > 42-42\\\\7x^2+35x-42 > 0\)

Then, divide both sides by 7:

\(\displaystyle 7x^2+35x-42 > 0\\\\\frac{7x^2+35x-42}{7} > \frac{0}{7}\\\\x^2+5x-6 > 0\)

Then, separate 5x to create a factorable expression. Ask yourself: what two numbers will add up to -6 and multiply to create -6?

\(x^2+5x-6 > 0\\\\x^2+6x-x-6 > 0\)

Then, group the terms together:

\(x^2+6x-x-6 > 0\\\\(x^2+6x)(-x-6) > 0\)

Then, factor out x from the inequality:

\((x^2+6x)(-x-6) > 0\\\\x(x+6)(-x-6) > 0\)

Then, factor out the negative sign from the second part of the expression:

\(x(x+6)(-x-6) > 0\\\\x(x+6)-(x+6) > 0\)

Then, factor out x + 6 from the inequality:

\(x(x+6)-(x+6) > 0\\\\(x+6)(x-1) > 0\)

Then, separate the factors and create two separate inequality sets:

\((x+6)(x-1) > 0\\\\\displaystyle \left \{ {{x+6 > 0} \atop {x-1 > 0}} \right. \\\\\left \{ {{x+6 < 0} \atop {x-1 < 0}} \right.\)

Then, solve the inequalities for x:

\(x+6 > 0\\\\x+6-6 > 0-6\\\\x > -6\\---------------\\x-1 > 0\\\\x-1+1 > 0+1\\\\x > 1\\---------------\\x+6 < 0\\\\x+6-6 < 0-6\\\\x < -6\\---------------\\x-1 < 0\\\\x-1+1 < 0+1\\\\x < 1\)

Then, test each value in the inequality:

\(7x^2+35x > 42\\\\7(-5)^2+35(-5) > 42\\\\7(25)-175 > 42\\\\175-175 > 42\\\\0 \ngtr 42\\\\\text{x} > \text{-6 is not a solution.}\\---------------\\7x^2+35x > 42\\\\7(2)^2+35(2) > 42\\\\7(4)+70 > 42\\\\28+70 > 42\\\\98 > 42\\\\\text{x} > \text{1 is a solution.}\\---------------\)

\(\\7x^2+35x > 42\\\\7(-7)^2+35(-7) > 42\\\\7(49)-245 > 42\\\\343-245 > 42\\\\98 > 42\\\\\text{x} < \text{-6 is a solution.}\\---------------\\7x^2+35x > 42\\\\7(-1)^2+35(-1) > 42\\\\7(1)-35 > 42\\\\7-35 > 42\\\\-28\ngtr42\\\\\text{x} < \text{1 is not a solution.}\)

Therefore, the solutions are x > 1 and x < -6. This means that answer choice A is correct.

Answer:

210°  

Step-by-step explanation:

To change from radians to degrees, multiply 7π/6 by 180/π

That will give 210°  

Would appreciate a Brainliest if this helped :)

The representations of the inequality is  an open circle is at 1 and a bold line starts at 1 and is pointing to the right.

An inequality compares two values, showing if one is less than, greater than, or simply not equal to another value e.g. 5 < 6, x ≥ 2, etc.

Since our answer is x > 1.  An open circle will be at 1 and a bold line starts at 1 and is pointing to the right (>). Check the attached image.

Note: You only shade up if you have ≤ (less than or equal) or ≥ (greater than or equal).

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The best represents the statement C(5) = 15 is the cost of renting a bicycle for 5 hours is 15 dollars.

What is a function?

A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

Here, we have

Given the function C(x) represents the cost, in dollars, of renting a bicycle for x hours.

So, the best statement that represents the given statement C(5) = 15 is the cost of renting a bicycle for 5 hours is 15 dollars.

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The answers are:

B. The graph of f(x) is shifted up 50 units

E. The graph of f(x) is shifted right 10 units

F. The graph of f(x) is reflected over the x-axis

The given function is f(x) = x²

This is an upward-facing vertical parabola.

The vertex is the smallest.

The vertex's origin is at (0, 0).

g(x) = –5x² + 100x – 450

This is an open downhill vertical parabola.

The vertex is the greatest

The first thing to notice is that fx) opens up whereas g(x) opens down, indicating that a reflection across the x-axis was used.

Find the g(x) vertex.

change the form to vertex

g(x) = –5x² + 100x – 450

Complete the square

g(x) = -5(x² - 20x) - 450

g(x) = -5(x² - 20x + 100) - 450 + 500

g(x) = -5(x² - 20x + 100) + 50

g(x) = -5( x - 10)² + 50

The vertex is located at (10, 50).

To the vertex from (0,0) to (10,50)

The translational principle is

(x,y) ------> (x+10,y+50)

This implies ----> The translation is 50 units up and 10 units to the right.

The adjustments are

The f(x) graph is moved forward by 50 units.

The f(x) graph is 10 units to the right.

Over the x-axis is a reflection of the f(x) graph.

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The complete question is,

Which transformations have been applied to the graph of f(x) = x² to produce the graph of g(x) = –5x² + 100x – 450? Check all that apply.

A.The graph of f(x) = x² is shifted up 25 units.

B.The graph of f(x) = x² is shifted up 50 units.

C.The graph of f(x) = x² is shifted down 950 units.

D.The graph of f(x) = x² is shifted left 10 units.

E.The graph of f(x) = x² is shifted right 10 units.

F.The graph of f(x) = x² is reflected over the x-axis.

The values of a and b using the factor theorem for the polynomial f(x), we set f(1) and f(-1) equal to zero. Solving the resulting system of equations, we find that a = 12 and b = -1.

To find the values of a and b using the factor theorem, we need to use the given factors (x - 1) and (x + 1) and the fact that they are roots of the polynomial f(x).
The factor theorem states that if (x - c) is a factor of a polynomial, then f(c) = 0. Therefore, we can set x = 1 and x = -1 in the polynomial f(x) to get two equations.
First, let's substitute x = 1 into f(x):
f(1) = (1)^3 + a(1)^2 + b(1) - 12
f(1) = 1 + a + b - 12
Next, let's substitute x = -1 into f(x):
f(-1) = (-1)^3 + a(-1)^2 + b(-1) - 12
f(-1) = -1 + a - b - 12
Since (x - 1) and (x + 1) are factors, f(1) and f(-1) must equal zero. Therefore, we can set the two equations equal to zero and solve for a and b:
1 + a + b - 12 = 0
-1 + a - b - 12 = 0
Rearraning the equations, we have:
a + b = 11
a - b = 13
Now, we can solve this system of equations. Adding the two equations, we get:
2a = 24
a = 12
Substituting the value of a into one of the equations, we find:
12 - b = 13
b = -1
Therefore, the values of a and b are 12 and -1 respectively.

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Answer:

c) 13

Step-by-step explanation:

\( {a}^{2} + {b}^{2} = {c}^{2} \\ {5}^{2} + {12}^{2} = {c}^{2} \\ 25 + 144 = {c}^{2} \\ 169 = {c}^{2} \\ c = 13\)

Answer:

C) 13

Step-by-step explanation:

Using the formula: \(a^{2} +b^{2}=c^{2}\), we can plug in 5 into a and 12 into b, since c is always the hypotenuse. Plug those numbers into the formula: \(5^{2} + 12^{2} =c^{2}\) and you get 25 + 144 = \(c^{2}\) or 169 = \(c^{2}\). You can then get rid of the square on the c by finding the square root of both sides. So, the square root of 169 would give you the answer of 13.

The probability of obtaining exactly 2 frozen rains after defeating 20 Frigid Elements in the video game is approximately 0.2713 or 27.13%.

q = 1 - p

q = 1 - 0.019

q = 0.981

X: The number of successful outcomes.

In this scenario, we can model the situation using a binomial distribution. Let's determine the values of n, p, q, and X:

n: The number of trials or attempts.

In this case, the number of trials is the number of Frigid Elements defeated, which is given as 20.

n = 20

p: The probability of success on a single trial.

The probability of a frozen rain item dropping after defeating a Frigid Element is given as 1.9%, which can be expressed as 0.019.

p = 0.019

q: The probability of failure on a single trial.

The probability of failure is the complement of the probability of success. Therefore:

q = 1 - p

q = 1 - 0.019

q = 0.981

X: The number of successful outcomes.

We want to find the probability of 2 frozen rains dropping, so X is 2.

X = 2

Now that we have determined the values, we can calculate the probability using the binomial distribution formula. The formula for the probability mass function of the binomial distribution is:

P(X = x) = \((nCx) * (p^x) * (q^(n-x))\)

where nCx represents the binomial coefficient, which is the number of ways to choose x successes out of n trials.

Using this formula, we can substitute the values into the equation:

P(X = 2) = \((20C2) * (0.019^2) * (0.981^(20-2))\)

Calculating the binomial coefficient:

(20C2) = (20!)/(2!(20-2)!)

= (20 * 19 * 18!)/(2 * 18!)

= (20 * 19)/(2 * 1)

= 190

Now substituting the values:

P(X = 2) = \(190 * (0.019^2) * (0.981^18)\)

Now we can calculate the probability:

P(X = 2) ≈ 0.2713 or 27.13% (rounded to two decimal places)

Therefore, the probability of obtaining exactly 2 frozen rains after defeating 20 Frigid Elements in the video game is approximately 0.2713 or 27.13%.

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The key features of the given quadratic functions are listed below.

In Mathematics and Geometry, the graph of any quadratic function would always form a parabolic curve because it is a u-shaped. Based on the first quadratic function, we can logically deduce that the graph is an upward parabola because the coefficient of x² is positive and the value of "a" is greater than zero (0) i.e 3 > 0.

For the quadratic function y = 3x² - 5, the key features are as follows;

Axis of symmetry: x = 0.

Vertex: (0, -5).

Domain: [-∞, ∞]

Range: [-5, ∞]

For the quadratic function y = -2x² + 12x - 15, the key features are as follows;

Axis of symmetry: x = 3.

Vertex: (3, 3).

Domain: [-∞, ∞]

Range: [-∞, 3]

For the quadratic function y = -x² + 1, the key features are as follows;

Axis of symmetry: x = 0.

Vertex: (0, 1).

Domain: [-∞, ∞]

Range: [-∞, 1]

For the quadratic function y = 2x² - 16x + 30, the key features are as follows;

Axis of symmetry: x = 4.

Vertex: (4, -2).

Domain: [-∞, ∞]

Range: [-2, ∞]

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Answer:

60 feet

Step-by-step explanation:

Answer:

27

Step-by-step explanation:

If n = 4, all we need to do is substitute the number into the equation.

6n + 3

= 6(4) + 3

= 24 + 3

= 27

I recommend checking out a few more problems like these to get the gist of it. You'll be using this a lot in the future! I recommend taking a look on Kahn Academy for more learning.

Good luck!