Solve for x
5x – 7 = 18

Answer:

the answer is 3x+2y=2

you can find this simply by replacing the points from the graph in each of equations.And if they are false statements then we remove as possibilities to be the correct one. I replaced points (0,1) and (2,-2)

Answer:

Step-by-step explanation:

To find Jonas's total score after 9 holes of golf, we add up all the individual scores:

+2 + 1 - 1 + 0 + 0 - 1 + 3 + 4 - 1 = 7

Jonas's total score after 9 holes is 7.

Since the total score is positive (above zero), Jonas's score is above par.

The only possible value for "a" that satisfies the given conditions (opens downward and wider than f(x) = x²) is -3.

To determine the possible value of "a" in the equation f(x) = ax², given that the graph opens downward and is wider than the graph of f(x) = x², we need to analyze the properties of quadratic functions.

When the graph of a quadratic function opens downward, the coefficient of x² (a) must be negative. This ensures that the parabola opens in the opposite direction.

When comparing two quadratic functions, the coefficient of x² determines the width of the parabola. A larger absolute value of the coefficient will result in a narrower parabola, while a smaller absolute value will result in a wider parabola.

Based on these properties, let's analyze the given options:

Option -½: If a = -½, the coefficient of x² is negative, satisfying the condition for the graph to open downward. However, the absolute value of -½ is smaller than 1, indicating that the graph would be narrower than the graph of f(x) = x². Therefore, -½ is not a possible value for "a" in this case.

Option -3: If a = -3, the coefficient of x² is negative, satisfying the condition for the graph to open downward. Moreover, the absolute value of -3 is greater than 1, suggesting that the graph would be wider than the graph of f(x) = x². Thus, -3 is a possible value for "a."

Option ¾: If a = ¾, the coefficient of x² is positive, which contradicts the condition that the graph should open downward. Therefore, ¾ is not a possible value for "a" in this case.

Option 5: If a = 5, the coefficient of x² is positive, which contradicts the condition that the graph should open downward. Therefore, 5 is not a possible value for "a" in this case.

In conclusion, the only number for "a" that meets the requirements (opens downward and is broader than f(x) = x2) is -3.

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Answer:

B 4.4

Step-by-step explanation:

There is 1 gallon in 3.7 liters so you would divide 16.5 by 3.7

The tank has a capacity of 58.90 liters of gas.

Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions.

The operator that performs the arithmetic operation is called the arithmetic operator.

Operators which let do a basic mathematical calculations.

+ Addition operation: Adds values on either side of the operator.

For example 4 + 2 = 6

- Subtraction operation: Subtracts right-hand operand from the left-hand operand.

for example 4 -2 = 2

* Multiplication operation: Multiplies values on either side of the operator

For example 4*2 = 8

Given that the gas tank in Sharon’s car can hold up to 16.5 gal of gas

Since one  gallon is 4 quarts

Volume in quarts as:

16.5 gallons = 16.5 x 4 quarts = 66 quarts

So quarts = 0.946

66 quarts = 0.946 x 66 = 62.436

So Volume = 62.436q

Volume in liters as:

Given as one litre = 1.06qt

If one liter is 1.06, Then 62.436 will be = 62.436/1.06 = 58.90

The volume in liters of 58.90

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The function h(x) = 5 square root x e^-x is increasing on the interval (0, ∞) and decreasing on the interval (-∞, 0).

1. Calculate h'(x) = 5 (1/2 x^-1/2 e^-x - x^1/2 e^-x)

2. Set h'(x) = 0 to find the critical points.

3. Since h'(x) < 0 for x < 0 and h'(x) > 0 for x > 0, h(x) is decreasing for x < 0 and increasing for x > 0.

4. Therefore, h(x) is increasing on the interval (0, ∞) and decreasing on the interval (-∞, 0).

The derivative of h(x) = 5 square root xe^-x is h'(x) = 5 (1/2 x^-1/2 e^-x - x^1/2 e^-x). Setting h'(x) = 0 gives the critical points of the function. Since h'(x) is negative for x < 0 and positive for x > 0, this tells us that the function is decreasing for x < 0 and increasing for x > 0. So, h(x) is increasing on the interval (0, ∞) and decreasing on the interval (-∞, 0). We can also conclude from the graph of the function that it is concave down for x < 0 and concave up for x > 0.

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By definition of linear independence, the vectors in the set {a, b, c} are independent if

\(k_1\vec a+k_2\vec b+k_3\vec c=\vec0\)

can only be obtained with the choice of k₁ = k₂ = k₃ = 0.

This vector equation corresponds to the system of linear equations

\(\begin{cases}k_1 - 2k_3 = 0 \\ 2k_1 + k_2 = 0 \\ k_1 + 2k_3 = 0\end{cases}\)

The first equation says k₁ = 2 k₃, while the third one says k₁ = -2 k₃. This can only be possible if k₁ = k₃ = 0, and from the second equation it follows that k₂ = 0. So the given set is linearly independent (and *not* dependent).

The equation of a circle with diameter endpoints of (13, -1) and (15, 9) will be x² + y² - 28x - 8y + 186 = 0.

Given that:

Endpoints of diameter, (13, -1) and (15, 9)

The equation of the circle when endpoints of diameter are given is written as,

(x - x₁)(x - x₂) + (y - y₁)(y - y₂) = 0

The equation of the circle is calculated as,

(x - 13)(x - 15) + (y + 1)(y - 9) = 0

x² - 28x + 195 + y² - 8y - 9 = 0

x² + y² - 28x - 8y + 186 = 0

The equation of a circle with diameter endpoints of (13, -1) and (15, 9) will be x² + y² - 28x - 8y + 186 = 0.

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Answer:

Range: 9. Mean: 16. Hope it helps:)

Step-by-step explanation:

Answer:

Step-by-step explanation:

17 + 21 + 14 + 17 + 12 + 15 + 16 = 112

= 112 / m₇

= 16

Hope this helps!

The two triangles exist congruent if they contain two congruent corresponding sides and their contained angles exist congruent.

Let \($&\overline{A B} \cong \overline{D E} \\\) and \($&\overline{A C} \cong \overline{D F}\)

Angle between \($\overline{A B}$\) and \($\overline{A C}$\) exists \($\angle A$\).

Angle between \($\overline{D E}$\) and \($\overline{D F}$\) exists \($\angle D$\).

Therefore, \($\triangle A B C \cong \triangle D E F$\) by SAS, if \($\angle A \cong \angle D$$\).

Given:

\($&\overline{A B} \cong \overline{D E} \\\) and

\($&\overline{A C} \cong \overline{D F}\)

According to the SAS congruence property, two triangles exist congruent if they contain two congruent corresponding sides and their contained angles exist congruent.

Let \($&\overline{A B} \cong \overline{D E} \\\) and \($&\overline{A C} \cong \overline{D F}\)

Angle between \($\overline{A B}$\) and \($\overline{A C}$\) exists \($\angle A$\).

Angle between \($\overline{D E}$\) and \($\overline{D F}$\) exists \($\angle D$\).

Therefore, \($\triangle A B C \cong \triangle D E F$\) by SAS, if \($\angle A \cong \angle D$$\).

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Answer:

y = -7

Step-by-step explanation:

3(-4) = y - 5

-12 = y - 5

y = -12 + 5

y = -7

Answer:

A

Step-by-step explanation:

if these are fractions than its A.

2x-4=2

4x-5=5/4

2200 because all 200 stocks dropped 11$ equaling 2200

The sequence that shows the numbers in order from least to greatest is D. 2.14 < 2.8 < 3.16227766017.

The sequence that shows the numbers in order from least to greatest is D. 2.14 < 2.8 < 3.16227766017.What is the meaning of the inequality symbols?The inequality symbols are mathematical symbols that are used to compare two values.

They indicate the relationship between two values that are not equal to each other. Here are the inequality symbols:

< (less than)≤ (less than or equal to)> (greater than)≥ (greater than or equal to)What is the meaning of the sequence?

A sequence is a set of numbers arranged in a particular order. The order of the numbers in a sequence can be from smallest to largest or largest to smallest.

The sequence D. 2.14 < 2.8 < 3.16227766017 is arranged from smallest to largest because the first number in the sequence, 2.14, is the smallest, and the last number in the sequence, 3.16227766017, is the largest.

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Answer:

13 gallons

Step-by-step explanation:

Answer:

i hope this helpes

Step-by-step explanation:

a) A group of 16 pays $40 + ($2 x (16 - 10)) = $40 + $6 = $46.

b) The cost function can be represented as C(x) = 40 + 2(x - 10) for x > 10 and C(x) = 40 for x <= 10, where x is the number of people in the group and C(x) is the cost for the group.

c) The domain of the cost function is all non-negative real numbers less than or equal to 50 (0 <= x <= 50), since the maximum group size is 50. The range of the cost function is all non-negative real numbers greater than or equal to 40 (C(x) >= 40), since the minimum charge for a group is $40.

Answer:

a) $52

b) C(x) = 40 + 2x, if x > 10 and x ≤ 50

C(x) = 40, if x ≤ 10

c) Domain = {x ≥ 1 and x ≤ 50}

Range = { from 40 to 140}

The characteristics of the undefined geometric terms are as follows;

Across

2. Planes can also be labeled with a capital letter that isn't connected to a point.

6 Points that are not on the same line are non–colinear

7 Points, lines, and planes are undefined terms

8 A portion of a line containing two endpoints that can be measured is a segment.

9 Direction matters when labelling this geometric figure. A ray

12 These are always measured using one capital letter. A point.

13. These pair of lines have the same slope value. Parallel lines

14 A plane is usually labeled with this number of points. Three points

15 Lines and points sharing the same plane are coplanar lines and points.

Down

1 The symbols of a segment has arrows on each end. False

2 These intersect at either endpoints and resemble a line. Rays

3 Points that are on the same line are considered this. Colinear points

4 This line pair form a 90° angle when they intersect. Perpendicular lines

5 When two lines intersect they form a point. False

10 These can be labeled with one lower case letter. A plane

11. When two of these intersect they form a line. Rays

Undefined terms are terms in geometry which are only given an elucidation or a description. Other terms can be defined using the undefined terms.

Across

2 The methods of naming a plane includes;

6 When points are not on the same line or on the same plane, they are known as non–colinear or non–coplanar respectively.

7 undefined terms includes, points lines and planes

8 A segment has two endpoints and represents a portion of a line.

9 A ray is labeled by including the letter representing the endpoints first and then a letter representing any other point on the ray.

12 A point is labeled by using a capital letter

13 Parallel lines extends continuously without meeting, therefore they form the same corresponding angles with a common transversal and have the same slope

14 The labels of three points in space can be used to label the plane which the points are located.

15 The term used to describe lines and points sharing the same plane are coplanar lines and coplanar points respectively

Down

1 The symbol of a segment has a dot marking at each end.

2 When the endpoints of two parallel rays intersect, the geometric figure formed resembles a line

3 Colinear points are points that are on a line

4 Perpendicular lines are lines oriented 90 degrees relative to each other

5 An angle is formed by the intersection of two lines

10 A line can be labeled with one lower case letter

11 When the endpoints of two parallel rays facing opposite directions intersect, they form a line

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A physical quantity with both magnitude and direction is called a vector quantity.

A vector quantity is a physical quantity that has both magnitude and direction. One example of a vector quantity is velocity, which is defined as the rate of change of an object's position with respect to time. Velocity is a vector quantity because it has both a magnitude (speed) and a direction (the object's motion). For instance, if an object is moving with a speed of 20 meters per second to the north, its velocity would be 20 meters per second north. If the object's direction changes to east, its velocity would become 20 meters per second east. Therefore, velocity is a vector quantity because its value depends not only on the speed of the object but also on the direction in which it is moving.

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Complete Question

Write down a vector quantity and explain your response.

The value of x for the equation to have infinite solution is 12

For an equation to have infinite solution, the expression on both sides must be equal

Given the expression below

3x–18=3(x–10)+ x

expand

3x - 18 = 3x - 30 + x

Equate

-18 = -30 + x

x = -18 + 30

x = 12

Hence the value of x for the equation to have infinite solution is 12

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The x-coordinate of the other end point as described in the question is; 4 + 4√5

The distance between two points in line geometry is given as follows;

In this scenario;

Therefore, the x-coordinate of this end point is;

4 + 4√5

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Answer:

4+4/5 AND 4-4/5

Step-by-step explanation:

just took the test and they want both of those included in your answer

Using the expression 5x/12 = 20, the amount that A originally had was $48.

We have,

Let x be the amount of money that A originally had.

Then, A gave away 1/2 x 1/3 = 1/6 of the amount, which is equal to x/6.

The amount received by B is 1/2 of the remaining amount,

which is (x - x/6)/2 = 5x/12.

We know that 5x/12 = 20,

Solving for x.

5x/12 = 20

5x = 240

x = 48

Therefore,

The amount that A originally had was $48.

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Answer:

9 inches wide

Step-by-step explanation:

so in the text it tells you that the rectangle is 3 inches wide by 4 inches long

then it gives you the final length but you need the width. so what i did is find out how much the increase of the length was, the length was4 at the start then ended at 12 to find out how much it increased i divided 12 by 4 and got 3. that shows that the object is 3 times larger so then I multiplied the original width by 3 which would be 3*3 which equals 9. so 9 is the width of the enlarged shape.

\(~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ A(\stackrel{x_1}{8}~,~\stackrel{y_1}{7})\qquad B(\stackrel{x_2}{x}~,~\stackrel{y_2}{y}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ x +8}{2}~~~ ,~~~ \cfrac{ y +7}{2} \right) ~~ = ~~\stackrel{\textit{\LARGE M}}{(1~~,~~4)} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ x +8}{2}=1\implies x+8=2\implies \boxed{x=-6} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ y +7}{2}=4\implies y+7=8\implies \boxed{y=1}\)

The most appropriate choice for equation of line in slope intercept form will be given by-

\(y = -\frac{1}{2}x - 4\)  is the required equation of line

What is equation of line in slope intercept form?

The most general form of equation of line in slope intercept form is given by y = mx + c

Where m is the slope of the line and c is the y intercept of the line.

Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.

If \(\theta\) is the angle that the line makes with the positive direction of x axis, then slope (m) is given by

m = \(tan\theta\)

The distance from the origin to the point where the line cuts the x axis is the x intercept of the line.

The distance from the origin to the point where the line cuts the y axis is the y intercept of the line.

Here,

The given equation of line is y = 2x-5

Slope of this line = 2

Slope of the line perpendicular to this line = \(-\frac{1}{2}\)

The line passes through (2 , -5)

Equation of the required line = \(y - (-5) = \frac{1}{2}(x - 2)\)

                                                    \(y +5=-\frac{1}{2}x+1\\y = -\frac{1}{2}x +1 -5\\y = -\frac{1}{2}x -4\)

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Answer:

D) 180 inches²

SEE NOTE*

Step-by-step explanation:

Base = 10x10=100

Each triangle = 1/2x10x4=20

20x4=80

100+80=180

* This may be a trick question.  This pyramid CANNOT exist.  If the base is 10 inches, the height of the triangles cannot be 4 inches.  They must be more than 5.  

The value of v is -12.5 when u = 15, t = 8, and s = 40.

According to the question,

We have the following expression:

s = (u+v)\(t^{2}\)

We have the following values:

u = 15, t = 8, s = 40

Now, we can easily find the value of v by putting all these values in the given expression.

So, we have the following expression:

40 = (15+v)8*8

40 = (15+v)16

Multiplying 16 into the bracket:

40 = 15*16+16v

40 = 240+16v

Subtracting 240 from both sides:

40-240 = 16v

-200 = 16v

Dividing by 16 on both sides:

-200/16 = v

v = -12.5

Hence, the value of v is -12.5 when u = 15, t = 8, and s = 40.

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Answer:

\( (x, y) = (2, 1) \)

Step-by-step explanation:

Given vertices of a triangle:

\( (x_1, y_1) = (-4, -2) \)

\( (x_2, y_2) = (1, 0) \)

\( (x_3, y_3) = (9, 5) \)

Using the centroid formula:

\( (x, y) = (\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}) \)

Plug in the values into the formula

\( (x, y) = (\frac{-4 + 1 + 9}{3}, \frac{-2 + 0 + 5}{3}) \)

\( (x, y) = (\frac{6}{3}, \frac{3}{3}) \)

\( (x, y) = (2, 1) \)

Answer:

The area of the garden is

797

f

t

2

.

Explanation:

First, let's find the area of the rectangle.

We know that the area of a rectangle is the length times width, or

20

⋅

32

in this example:

20

⋅

32

=

640

So the area of the rectangle is

640

f

t

2

.

You may not know the area of a semicircle, but that's fine

−

we know the area of a circle, or

π

r

2

.

Since the area of a semicircle is half the area of a circle, we just do the area of the circle divided by

2

:

So the area of a semicircle is

π

r

2

2

.

The question asks for

π

to just be

3.14

, so instead the equation is

A

=

3.14

r

2

2

The picture gives the diameter of the circle.

To find the radius, or

r

, we divide the diameter by

2

:

20

2

=

10

Now we can solve for the area of the semicircle:

3.14

(

10

)

2

2

3.14

(

100

)

2

314

2

157

f

t

2

Now that we now the areas of the rectangle and semicircle, we can add them up to find the area of the rose garden:

640

+

157

=

797

f

t

2

Step 1: Isolate the Sin Operator

\(8 sin(\frac{\pi }{6} x)=2\\sin(\frac{\pi }{6} x)=0.25\\\\\)

Step 2: Use Inverse Sin(arcsin) to isolate the term with the x variable

Note that since trig functions have 2 general solutions, this will give us one of our general solutions.

\(x=\frac{6 arcsin(0.25)}{\pi } =0.48\)

x₁= 0.48

Solving for x₂

Use the period identity for Sin Functions

\(sin(x)=sin(\pi -x)\)

X in this case is arcsin(0.25)

\(\frac{\pi }{6} x=\pi -arcsin(0.25) = 5.52\)

So our two general solutions are 0.48 and 5.52

Step 3: Period

Trig Functions have periodic behavior and this function period is

\(\frac{2\pi }{1} (\frac{6}{\pi } )= 12\)

So our general solutions are

0.48±12k, where k is an integer

5.52±12k, where k is an integer

Let k=1, and we get our next set of solutions:

12.48 and 17.52

So our answer is 0.48,5.52,12.48,17.52

Answer:

1.504

Step-by-step explanation:

0.47×100 = 47

3.2×100 = 320

47×320 = 15040

15040÷10000 = 1.504

Answer:

The range of g(x) = -2x + 33 is D. (Negative infinity, positive infinity)

Step-by-step explanation:

The function g(x) is a linear line, so all values of x are included in the domain. If all values of x in the domain works, then there are infinite amount of values for both x and y. Therefore, your answer is D.