Question 1
Let f(x) = 2x^2 - 3x - 4 and g(x) = x + 5. Find (fg)(x).

Answer:

Height of the triangle = 12 feet

Base of the triangle = 19 feet

Step-by-step explanation:

Let the height of the triangle be x feet

-> Base of the triangle = (x + 7) feet

[tex]A(\triangle)= 114\: ft^2[/tex]

[tex]\because A(\triangle)=\frac{1}{2}(base)(height) [/tex]

[tex]\implies 114=\frac{1}{2}(x+7)(x) [/tex]

[tex]\implies 114\times 2= x^2+7x[/tex]

[tex]\implies 228= x^2+7x[/tex]

[tex]\implies x^2+7x-228=0[/tex]

[tex]\implies x^2+19x-12x-228=0[/tex]

[tex]\implies x(x+19)-12(x+19)=0[/tex]

[tex]\implies (x+19)(x-12)=0[/tex]

[tex]\implies (x+19)=0,\:\:(x-12)=0[/tex]

[tex]\implies x =-19,\:\:x=12[/tex]

x represents the height of the triangle.

-> x can not take negative value.

[tex]\implies x\neq -19[/tex]

[tex]\implies x = 12[/tex]

[tex]\implies x +7= 12+7=19[/tex]

Thus,

Height of the triangle = 12 feet

Base of the triangle = 19 feet

Answer:

i believe its A

Step-by-step explanation:

Answer:

B. The graph is not a function.

Step-by-step explanation:

We are given the graph of a relation. It is required to determine whether the graph represents a function or not. 'If a vertical line passing through the graph of the relation cuts the graph at at-most one point, then the given graph represents a function else not'. So, if we plot the vertical line 'x = 3' in the figure, we see that, The vertical line drawn crosses the graph at two points A and B as shown below. Thus it would be B

We are given the equation of circle (x - 7)² + (y - 3)² = 64² , but let's recall the standard equation of circle i.e (x - h)² + (y - k)² = r², where (h, k) is the centre of the circle and r being the radius ;

So, consider the equation of circle ;

[tex]{:\implies \quad \sf (x-7)^{2}+(y-4)^{2}=(64)^{2}}[/tex]

On comparing this equation with the standard equation of Circle, we will get, centre and radius as follows

Answer:

looking at the straight line, it touches the axis at (-2,0) and (6,0)

Step-by-step explanation:

Answer:

m = 5[tex]\sqrt{5}[/tex]

Step-by-step explanation:

To find the measure  of m we use the following Euclidian theorem:

m^2 = 5*(5+20)

m^2 = 125 find the root for both sides

m = 5[tex]\sqrt{5}[/tex]

Answer:

19

Step-by-step explanation:

(Assuming that each cube is 1 unit), the volume is 5 + 6 + 8 which equals 19

Yes :- true

as in the diagram 6 units in between the 20° and 90° and third angle will be 180-110 = 70°

Triangle with angle 90 and 20 degree possible as it Satisfies the angle sum property.

The total of a triangle's three internal angles is 180 degrees, as stated by the angle sum feature of a triangle. A closed shape with both inner and exterior angles, a triangle is created by three line segments.

Given:

angles= 20 and 90 degree

Using Angle Sum property

20 + 90 + <3 =180

<3 = 180 - 110

<3 =70

Hence, the Triangle with angle 90 and 20 degree possible as it Satisfies the angle sum property.

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Right now, Scott is 5.
His Aunt Mary is 4*5 = 20

We can solve this algebraically if your teacher requires to.
In x years, Scott will be half as old as his Aunt right now (which is 20).

5+x= 20/2
5+x=10
x=5

In 5 years Scott will be half as old as his aunt was.

Step-by-step explanation:

1) [tex] \Rightarrow \: \sf \: 4x + 8 - 2x + 7[/tex]

Combine like terms

[tex] \rightarrow \: \sf \: ( 4x - \textcolor{green}{2}x) + (7 + \textcolor{green}{8})[/tex]

Add 4x and 2x , 7 + 8

[tex] \rightarrow \sf \: 2x + 15[/tex]

~Done~

2) [tex] \Rightarrow \sf 2n ×5 ×2a[/tex]

[tex] \rightarrow \sf \:( 2n) (5) (2a)[/tex]

[tex] \rightarrow \sf \: 20an[/tex]

~Done~

Answer:

A=lw+l(w

2)2+h2+w(l

2)2+h2=30·20+30·(20

2)2+282+20·(30

2)2+282≈2127.25933

Your answer is 2127.259

I think it will help you

If "s" represents the slant height in the rectangular pyramid with dimensions l = 30, w = 20, and h = 28, then the length of "s" is approximately 29.75 units.

To find the length of "s" in the rectangular pyramid, we first need to understand the terminology used to describe the different dimensions of a pyramid.

In a rectangular pyramid, "l" usually represents the length of the base, "w" represents the width of the base, and "h" represents the height of the pyramid (the perpendicular distance from the base to the apex or top vertex of the pyramid).

However, there is no standard notation for the length of the slant height (s) in a rectangular pyramid. In this context, the term "s" could represent either the slant height or some other unknown dimension of the pyramid.

If "s" represents the slant height of the pyramid, we can use the Pythagorean theorem to find its value. The slant height, "s," is the hypotenuse of a right triangle formed by one of the triangular faces of the pyramid and the height and half the width of the base.

Using the given dimensions:

l = 30 (length of the base)

w = 20 (width of the base)

h = 28 (height of the pyramid)

Let's find the value of "s" using the Pythagorean theorem:

[tex]s^2 = h^2 + (w/2)^2\\s^2 = 28^2 + (20/2)^2\\s^2 = 28^2 + 10^2\\s^2 = 784 + 100\\s^2 = 884\\[/tex]

Now, take the square root of both sides to find the value of "s":

s ≈ √884

s ≈ 29.75 (rounded to two decimal places)

So, if "s" represents the slant height in the rectangular pyramid with dimensions l = 30, w = 20, and h = 28, then the length of "s" is approximately 29.75 units.

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Answer:

a.15 feet

Step-by-step explanation:

150 divided by 20 is 7.5

7.5 times 2 is 15

[tex]\text{Radius of circle, r} =\dfrac 62 = 3~ m \\\\\text{Area of circle} = \pi r^2 = \pi \cdot 3^2 = 3.14 \times 9 =28.26~m^2[/tex]

Answer:

a∥b, Converse of the Alternate Interior Angles Theorem

Answer:

N = 9  & P = 4

Step-by-step explanation:

N* N = 81

N * N = 9*9

N = 9

N * P = 36

Substitute N = 9,

9* p = 36

    P = 36 ÷ 9

  P = 4

Answer:

Bridget flew 4100 miles.

Step-by-step explanation:

L + K + B = 7800

1500+2200+B=7800

3700 + B = 7800

Subtract 3700.

B = 4100

Bridget flew 4100 miles.

Answer: I am pretty sure it's 18 feet.

Step-by-step explanation:

Answer:

125x 12 and divide the answer

Step-by-step explanation:

Answer:

125x 12 and divide the answer

Step-by-step explanation:

There are several ways to reduce how much does it cost to run an air conditioner. The two main ones are:Buying an air conditioner with a high energy efficiency rating (EER, SEER, CEERratings are valid specifications).Reducing the number of hours per day that you use a given air conditioner.Note: It’s recommended to estimate how much electricity does an air conditioner use before buying a specific unit.On average, running an air conditioner costs between $0.06 and $0.88 per hour. Let’s calculate how much does air conditioning cost per month (running 8h per day):

Answer:

D.)25 children and 75 adults

Equation 1: a + c = 100

Equation 2: 3a + 2c = 275

Step-by-step explanation:

A team t-shirt costs $3 per adult and $2 per child.

Let the number of children be = c

Let the number of adults be = a

A team t-shirt costs $3 per adult that is 3a and $2 per child that is 2c, also given is that the total money collected is $275, so equation becomes:

On a certain day, the total number of adults (a) and children (c) who bought shirts was 100, equation becomes:

Now to know the number of children and adult, we can check by plugging in the values from options provided.

25 children and 75 adults  = 25(2)+75(3)=50+225 =275

Answer:

  1 1/2 inches

Step-by-step explanation:

To find how much more a second number is than a first number, the first is subtracted from fhe second. Here, we want to know how much more the second week total is than the first, so we subtract the first week's total from the second week's total.

__

We find the second week's total by adding up the values associated with the different days in the second week.

  second week's total = 1 7/8 +2 3/4 = (1 +2) +(7/8 +6/8) = 3 13/8 = 4 5/8

Then the difference is ...

  second week's total - first week's total

  = 4 5/8 -3 1/8 = (4 -3) +(5/8 -1/8) = 1 4/8 = 1 1/2

It rained 1 1/2 inches more this week than last week.

The required point that could have been one of the points that Tom graphed is (-3,-7) lies in Quadrant III. The correct answer would be an option (A).

A quadrant is defined as an area contained by the x and y axes, which there are four quadrants in a graph.

A point that could have been one of the points that Tom graphed is (-3,-7). This is because it lies in Quadrant III of the coordinate grid. In Quadrant III, the x-coordinate is negative and the y-coordinate is negative.

Point A has a negative x-coordinate and a negative y-coordinate, so it satisfies the requirement of being in Quadrant III.

Hence, the correct answer would be option (A).

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[tex]\text{R.H.S}\\\\=4\sin 45^{\circ} \cos 15^{\circ} \\\\=4\sin 45^{\circ} \cos (45^{\circ}-30^{\circ})\\ \\=4 \sin 45^{\circ} \left(\cos 45^{\circ} \cos 30^{\circ} +\sin 45^{\circ} \sin 30^{\circ} \right)\\\\=4 \left(\sin 45^{\circ} \cos 45^{\circ} \cos 30^{\circ} +\sin^2 45^{\circ} \sin 30^{\circ} \right)\\[/tex]

[tex]=4\left[\dfrac 1{\sqrt 2} \cdot \dfrac 1{\sqrt 2} \cdot \dfrac{\sqrt 3}2 +\left( \dfrac 1{\sqrt 2} \right)^2 \cdot \dfrac 12 \right]\\ \\=4\left(\dfrac{\sqrt 3}4 +\dfrac 14\right)\\\\=4\cdot \dfrac 14 \left(1+\sqrt 3\right)\\\\=1+\sqrt 3\\\\=\text{L.H.S}[/tex]

[tex]\text{Area of equilateral triangle ABC}\\ \\=\dfrac{\sqrt 3}{4} BC^2\\\\=\dfrac{\sqrt 3}4 \cdot 12^2\\\\=\dfrac{144\sqrt 3}{4}\\\\=36\sqrt 3[/tex]

Answer: $7401.22

Step-by-step explanation: it’s right just trust me

Answer:

9×4 - 10 fours - 26 fours

Step-by-step explanation:

9×4 - 10 fours - 26 fours

[tex]======================================[/tex]

In order to solve this equation, we should first subtract 3 from both sides:

[tex]\pmb{2x=12-3}[/tex]

Which equals

[tex]\pmb{2x=9}[/tex]

Divide both sides by 2

[tex]\pmb{x=\displaystyle\frac{9}{2} }[/tex]

[tex]======================================[/tex]

Hope everything is clear; if you need any more explanation/clarification, kindly let me know, and I will comment and/or edit my answer :)

Answer:

If you are trying to find slope this is how you solve it.

Step-by-step explanation:

2x+3=12

-2x       -2x

3=-2x+12

÷3  ÷3   ÷3

y=-2/3x+4

So if you are trying to find the slope it is -2/3x and the y intercept is 4.

Step-by-step explanation:

Given point are: P(at², 2at)

Q(a/t², 2a/t)

S(0, 0)

Now, the distance between A(x₁y₁) and B(X₂, y₂)

then AB = √{(x₂ - x₁)² + (y₂ - y₁)²} units

(i) The distance between S and P:

(x₁, y₁) = (0, 0) ⇛x₁= 0, y₁ = 0

(x₂, y₂ ) = (at², 2at) ⇛x₂ = at², y₂ = 2at

SP = √{at² - 0)² + (2at - 0)²}

= √{(at²)² + (2at)²}

= √{a²t²*² + 4a²t²}

= √{a²t⁴ + 4a²t²}

= √{a²t²(t²+4)}

SP = at√(t² + 4)→→→Eqn(1)

(ii) The distance between S and Q :

(x₁, y₁) = (0, 0) ⇛x₁= 0, y₁ = 0

(x₂, y₂ ) = (a/t², 2a/t) ⇛x₂ = a/t², y₂ = 2a/t

SQ = √[{(a/t²) - 0} + {(2a/t) - 0}

= √{(a/t²)² + (2a/t)²}

= √{(a²/t²*²) + (4a²/t²)}

= √{(a²/t⁴) + (4a²/t²)}

= √{(a² + 4a²t²)/t⁴}

= √[{a²(1 + 4t²)}/t⁴]

SQ = (a/t²)√(1 + 4t²) →→→ Eqn(2)

Now,

(1/SP) + (1/SQ) = [1/{at√(t² + 4)}] + [1/{(a/t²)√(1 + 4t²)}]

= (1/at)[1/{√(t² + 4)}] + (t²/a)[1/{(√1 + 4t²)}]

= (1/a)[[1/{t√(t² + 4)}] + [t²/{√(1 + 4t²)}]]

(1/SP) + (1/SQ) = 1/a is not independent of 't'

If suppose S = (a, 0) then

SP = √{(at² - a)² + (2at - 0)²}

= √{a²(t² - 1)² + (2at)²}

= a√{(t² - 1)² + 4t²}

= a√{(t² + 1)²}

SP = a(t² + 1)

1/SP = 1/{a(t² + 1)} →→→Eqn(1)

And

SQ = √[{(a/t²) - a}² + {(2a/t) - 0}²]

= √[a²{(1/t²) - 1}² + a²(2/t)²]

= a√[{(1 - t²)²/t⁴} + (4/t²)]

= a√[{(1 - t²)² + 4t²}/t⁴]

( a/t²)√(1 + t²)²

SQ = (a/t²)(1 + t²)

1/SQ = 1/{(a/t²)(1 + t²)} = t²/{a(1 + t²)} →→→Eqn(2)

Therefore, (1/SP) + (1/SQ)

= 1/{a(t² + 1)} + t²/{a(1 + t²)}

= (1 + t²)/a(1 + t²)

= 1/a

1/a is independent of 't'.

Answer:

n=1

Step-by-step explanation:

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