for f(x)=5x-2 and g(x)=2x+1,find(f+g(x)

Answer:  The required solution set of the given equation is [tex]\{4\sqrt5,-4\sqrt5\}.[/tex]

Step-by-step explanation:  We are given to determine the solution set of the following quadratic equation :

[tex]x^2-80=0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

Since the given equation does not contain the term involving x, so we will use the method of square root to solve the given equation.

The solution of equation (i) is as follows :

[tex]x^2-80=0\\\\\Rightarrow x^2=80\\\\\Rightarrow x=\pm\sqrt{80}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~[\textup{taking square root on both sides}]\\\\\Rightarrow x=\pm\sqrt{16\times5}\\\\\Rightarrow x=\pm4\sqrt5.[/tex]

Thus, the required solution set of the given equation is [tex]\{4\sqrt5,-4\sqrt5\}.[/tex]

they can drive 45 miles on 1 gallon, so divide 500 by 45

500/45 = 11.11

 they would need 11.11 gallons of gas

Answer:  The required co-ordinates of the point are (0.5, 5.5).

Step-by-step explanation:  We are given to find the co-ordinates of the point that splits CD in half if point C is located at (-2,4) and point D is located at (3,7).

The point that splits the line segment CD in half will be the mid-point of the segment CD.

We know that

the co-ordinates of the mid-point of a line segment with endpoints (a, b) and (c, d) are given by

[tex]\left(\dfrac{a+c}{2},\dfrac{b+d}{2}\right).[/tex]

Therefore, the co-ordinates of the given point that splits CD in half are given by

[tex]\left(\dfrac{-2+3}{2},\dfrac{4+7}{2}\right)=\left(\dfrac{1}{2},\dfrac{11}{2}\right)=(0.5,5.5).[/tex]

Thus, the required co-ordinates of the point are(0.5, 5.5).

The rational equation [tex]x^2 - 36 / (x+6)[/tex], when x is not -6, simplifies to x - 6. The correct answer is D.) x - 6.

This is a Mathematics problem related to algebraic expressions and rational expressions. Given the equation [tex]x^2 - 36 / (x+6)[/tex], when x is not equal to -6, we can simplify this equation by factoring. Note that x^2 - 36 is a difference of two squares, which factors into (x-6)(x+6). So we now have [tex](x-6)(x+6) / (x+6).[/tex]

Since x is not -6, we can cancel out the (x+6)s, leaving us with x-6. Therefore, the answer is D.) x - 6. It's important to be careful with the conditions given in the problem, as they can affect the result.

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its 69---------------------------------

Answer:

35

Step-by-step explanation:

The volume of a pyramid with a base area of 15 square inches and a height of 7 inches is 35 cubic inches.

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

Suppose the base of the pyramid has length = L units and width = W units, slant height = K units, and the height of the pyramid is of H units.

Then the volume of the pyramid will be

V = (L × B × H) / 3

V = (Base area x H) / 3

The volume of a pyramid varies jointly with the base area of the pyramid and its height.

The volume of one pyramid is 24 cubic inches when its base area is 24 square inches and its height is 3 inches.

Then the volume of a pyramid with a base area of 15 square inches and a height of 7 inches will be

V = (15 x 7) / 3

V = 35 cubic inches

Hence, the volume of a pyramid with a base area of 15 square inches and a height of 7 inches is 35 cubic inches.

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Answer:

The correct answer is A, "f(n) = 2n + 35."

Step-by-step explanation:

I got it correct on the test. I hope this helps!

The side that is parallel to side s is side q. The equation of side q is: y = -x + 9.

We can represent the equation of a line as, y = mx + b, where m is the slope of the line and b is the y-intercept.

The side that is parallel to side s is q.

Slope (m) of q = change in y / change in x = (6 - 3) / (3 - 6) = 3/-3 = -1.

Substitute m = -1 and (3, 6) = (a, b) into y - b = m(x - a):

y - 6 = -1(x - 3)

y - 6 = -x + 3

y = -x + 3 + 6

y = -x + 9

Equation of the side that is parallel to side s is: y = -x + 9.

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A conditional statement that correctly describes each Venn diagram include the following;

I. If m∠A = 40, then it represent acute angles.

II. If 2x = 4, then x is equal to 2.

In Mathematics, a conditional statement is a type of statement that can be written to have both a hypothesis and conclusion. This ultimately implies that, a conditional statement typically has the form "if P then Q."

Where:

P and Q represent sentences or statements.

Part I.

Based on the Venn diagram shown in the image above, we can logically deduce the following conditional statement;

"If m∠A = 40, then it represent acute angles."

All acute angles are less than 90 degrees.

Part I.

Based on the Venn diagram shown in the image above, a conditional statement that correctly describes it can be written as follows;

"If 2x = 4, then x is equal to 2."

Proof:

2x = 4

x = 4/2

x = 2

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2.11*7 = 14.77

2.11*9 = 18.99

 the answer is y=2.11x

The volume the hemisphere is 56. 55 cubic feet

what is the volume of the hemisphere ?

The volume of a hemisphere is the space occupied by the hemisphere.

Formula used to find volume of  the hemisphere is :

V = 2/3 × π × r ^3

Given : diameter = 6 feet

r = d/2 = 3 feet

V = 2/3 × π × 3 ^3

⇒ 2/3 × 22/7 × 27

V = 56.5486 cubic feet

round off to nearest hundredth is :

V = 56. 55 cubic feet

Hence , the volume of hemisphere is 56. 55 cubic feet .

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Answer:

C.

Step-by-step explanation:

the triangle shown in the middle is a 45-90-45 degree triangle ( the orange lines on the legs mean legs are equal)

 so if you were to mirror it there would be 90 degrees between A & B

 answer is 90 degrees

Without additional details, this question can't be answered accurately. Typically, one uses properties of an isosceles trapezoid, such as base angles or diagonal lengths, to find unknown variables. More information would allow a more precise answer.

Without a visual or additional information about the isosceles trapezoid, it would be challenging to accurately identify the value of X. However, typically in a problem like this, you would use the properties of an isosceles trapezoid, such as its base angles or the lengths of its diagonals, to find the value of an unknown variable. If given the measures of the other sides, it might be possible to calculate the remaining length. An example would be a problem like this: If the bases of an isosceles trapezoid are 10 and 20 units long, respectively, and the non-parallel sides (legs) are equal and represented by X, then based on specific conditions, X could potentially be calculated.

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The expression [tex](a^8)^4[/tex] is equivalent to  [tex]a^{32}[/tex].

The correct option is [tex]a^{32}[/tex].

To simplify the expression [tex](a^8)^4[/tex], we need to apply the exponent rule for raising a power to a power. According to this rule, when we have an exponent raised to another exponent, we multiply the exponents together.

In this case, [tex](a^8)^4[/tex]  can be simplified as [tex](a^8)^4[/tex], which equals [tex]a^{32}[/tex]. Therefore, the expression [tex](a^8)^4[/tex] is equivalent to  [tex]a^{32}[/tex].

To understand why we multiply the exponents, think of it this way: [tex](a^8)^4[/tex] means we have the base a raised to the 8th power, and that whole expression is raised to the 4th power. When we multiply the exponents, 8 x 4, we get 32. This tells us that we have a multiplied by itself 32 times, which is represented by  [tex]a^{32}[/tex].

Therefore, the correct answer is  [tex]a^{32}[/tex].

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