ƒ(x) = 4x² + 5x – 3
g(x) = 4x³ - 3x² +5
Find (ƒ + g)(x)

When the converted costs are compared, the earlier edition of the history book is more expensive.

The consumer price index measures the changes in price of a basket of good. It is used to measure inflation.

Converted price of the earlier edition = (CPI in 1992 / CPI in 1999) x later edition of the book

(140.3 / 166.3) x $43 = $36.28

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The true statements about the triangles RST and DEF are: (a), (d) and (e)

The statement ΔRST ≅ ΔDEF means that the triangles RST and DEF are congruent.

This above implies that:

The above means that the possible true statements are: (a), (d) and (e)

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Graph is in attached image.

[tex]|2x+1|=10\\2x+1=10 \vee 2x+1=-10\\2x=9 \vee 2x=-11\\x=4.5 \vee x=-5.5[/tex]

Answer:

[tex]x= \dfrac 92~~\textbf{or}~~x = -\dfrac{11}2\\\\[/tex]

Step-by-step explanation:

[tex]\underline {\textbf{Absolute value rule: }}\\\\\textbf{If}~ |a| = b~ \textbf{then} ~a =b~ \textbf{or}~ a =-b \\\\\underline{\textbf{Solution;}}\\\\\textbf{Given that,}\\\\~~~~~~~|2x+1| = 10\\\\\implies 2x +1 = 10~~~~~~\textbf{or} ~~~~~~~~~~~2x+1 = -10\\\\\implies 2x = 10-1~~~~~~\textbf{or}~~~~~~~~~~~2x = -10-1\\\\\implies 2x = 9~~~~~~~~~~~~~\textbf{or}~~~~~~~~~~~2x = -11\\\\\implies x= \dfrac 92~~~~~~~~~~~~~~\textbf{or}~~~~~~~~~~~x = -\dfrac{11}2\\\\[/tex]

The two points are (-4, -2) and (4, 5) and the equation of the line is 8y = 7x + 12 passing through the two points.

It is defined as the change in coordinates and the shape of the geometrical body. It is also referred to as a two-dimensional transformation. In the geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.

We have a quadrilateral ABCD which is reflected over a line and formed a mirror image A'B'C'D' of the quadrilateral.

From the graph:

The two points are (-4, -2) and (4, 5)

The line equation passing through two points:

[y - 5] = (5+2)/(4+4)[x - 4]

y - 5 = 7/8[x - 4]

8y - 40 = 7x - 28

8y = 7x + 12

Thus, the two points are (-4, -2) and (4, 5) and the equation of the line is 8y = 7x + 12 passing through the two points.

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Answer:

Simplifying

-9 + 4 = 40

Combine like terms: -9 + 4 = -5

-5 = 40

Solving

-5 = 40

Couldn't find a variable to solve for.

This equation is a the left and right sides are not equal, therefore there is no solution.

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Answer:

56/64 simplified is 0.875 or 7/8 as a fraction

Answer:

whats nine + 10

Step-by-step explanation:

21

pencil is .10

pen is .90

Step-by-step explanation:

x = pencil y = pen

3x + y = 1.20

7x + 2y = 2.50

try make x or y cancelable

-2 times (3x + y = 1.20) = -6x - 2y = - 2.40

7x + 2y = 2.50

-6x - 2y = - 2.40

x = .10

plug .10 back into one of the equations

3(.10) + y = 1.20

.30 + y = 1.20

y = .90

Squares are the results of multiplying a value by itself.  The value of 2.4494897… is equivalent to √6.

Squares are the results of multiplying a value by itself. Whereas the square root of a number is a value that when multiplied by itself yields the original value. As a result, both are vice versa approaches. For example, the square of 2 is 4 and the square root of 4 is 2.

The value of 2.4494897… is equivalent to √6.

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Step-by-step explanation:

so, this sounds like the blimp is located between the stadium and the planetarium.

we have a triangle :

the ground distance between the stadium and the planetarium is the baseline.

and the 2 lines of sight from the blimp on one side to the stadium and on the other side to the planetarium are the 2 legs.

we know the height of this triangle is 600 ft.

the angle of depression down to the stadium is 37°. which makes the inner triangle angle at the ground point at the stadium also 37°.

and the angle of depression down to the planetarium is 29°. which makes the inner triangle angle at the ground point at the planetarium also 29°.

and because the sum of all angles in a triangle is always 180°, we know the angle at the blimp is

180 - 37 - 29 = 114°

in order to solve this triangle, we need to split it into 2 right-angled triangles by using the height of the main triangle as delimiter.

we get a stadium side and a planetarium side triangle.

the baselines (Hypotenuses) of the 2 triangles are the corresponding lines of sight from the blimp.

the height of the large triangle is also a height and a leg in each small triangle.

and the stadium side part of the large baseline (between ground point and intersection with the height) is the second leg for the stadium side triangle.

and correspondingly, the planetarium side part of the large baseline (between ground point and intersection with the height) is the second leg for the planetarium side triangle.

the inner blimp angle of the stadium side triangle is

180 - 37 - 90 = 53°

and the inner blimp angle of the planetarium side triangle is

180 - 29 - 90 = 61°

now we can use the law of sine to get the lengths of the 2 parts of the baseline of the large triangle.

and when we add these 2 numbers we get the distance between stadium and planetarium.

law of sine is

a/sin(A) = b/sin(B) = c/sin(C)

with the sides being opposite of the associated angles.

for the stadium side triangle we get

part1/sin(53) = 600/sin(37)

part1 = 600×sin(53)/sin(37) = 796.226893... ft

for the planetarium side triangle we get

part2/sin(61) = 600/sin(29)

part2 = 600×sin(61)/sin(29) = 1,082.428653... ft

the distance between the stadium and the planetarium is

part1 + part2 = 1,878.655546... ft

Answer:

[tex]x=\dfrac{2}{3},-\dfrac{3}{2}[/tex]

Step-by-step explanation:

Given equation:

[tex]6x^2+5x-6=0[/tex]

First, factor the left side of the given equation.

To factor a quadratic in the form [tex]ax^2+bx+c[/tex] find two numbers that multiply to [tex]ac[/tex] and sum to [tex]b[/tex]:

[tex]\implies ac=6\cdot-6=-36[/tex]

[tex]\implies b=5[/tex]

So the two numbers are: 9 and -4

Rewrite [tex]b[/tex] as the sum of these two numbers:

[tex]\implies 6x^2+9x-4x-6=0[/tex]

Factorize the first two terms and the last two terms separately:

[tex]\implies 3x(2x+3)-2(2x+3)=0[/tex]

Factor out the common term [tex](2x+3)[/tex]:

[tex]\implies (3x-2)(2x+3)=0[/tex]

To solve for x:

[tex]\begin{aligned}\implies (3x-2) & =0 & \implies (2x+3) & = 0\\3x & = 2 & 2x & = -3\\x & = \dfrac{2}{3} & x & = -\dfrac{3}{2}\end{aligned}[/tex]

Therefore:

[tex]x=\dfrac{2}{3},-\dfrac{3}{2}[/tex]

Answer:

4 and 11

Step-by-step explanation:

See attached image

[tex]|a+bi|=\sqrt{a^2+b^2}[/tex]

[tex]|6-8i|=\sqrt{6^2+(-8)^2}=\sqrt{36+64}=\sqrt{100}=10[/tex]

Answer:

i am not sure about your question but if it is 3 divided by y-3 =12 divide by y+3 you can use this

Step-by-step explanation:

3÷y-3=12÷y+3

cross multiply

12(y-3)=3(y+3)............brackets off

12y-36=3y+9..............group the same

12y-3y=9+36

9y=45.......duved by 9 both sides

y=5

Answer: x = 4

Step-by-step explanation:

(√x + 2)(√x - 2) = 0

√x*√x - 2√x + 2√x -4 = 0

x - 0 - 4 = 0

x = 4

Answer:

[tex]x=4[/tex]

Step-by-step explanation:

(√x + 2)(√x - 2) = 0

√x × √x - √x · 2 + 2 · √x - 2 · 2 = 0

√xx - 2 × √x + 2 · √x - 4 = 0

√x^1+1 - 2 · √x + 2 × √x - 4= 0

√x² - 2 · √x + 2· √x - 4 = 0

x^2/2 - 2 × √x + 2 · √x - 4 = 0

x - 2· √x + 2 · √x - 4 = 0

x - 4 = 0

(x - 4) + 4 =  0

x - 4 + 4 = 0

x = 4

Answer:

x=5

Step-by-step explanation:

The two lines are the same length

2x+7 = 5x-8

15 = 3x

x = 5

=================================================================

Explanation:

Imagine rotating the figure so that the triangular face is flat on the ground. This makes the triangular faces to be the floor and ceiling of this room.

The floor is a triangle with base 24 meters and height 7 meters. The floor area is base*height/2 = 24*7/2 = 84 square meters.

Multiply this floor area with the height of the room (22 m) to get the volume of the room.

volume = (floor area)*(height) = 84*22 = 1848 cubic meters

Answer:

130 degrees

Step-by-step explanation:

3:40, it has traveled 6 * 40 = 240 degrees  which is 110 degrees from vertical The difference is 240 - 110 = 130 degrees, which is the final answer.

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[tex]\begin{cases} v=5i-7j\\\\ w=3i+2j \end{cases}\qquad \begin{cases} < \stackrel{a}{5}~~,~~\stackrel{b}{-7} > \\\\ < \stackrel{a}{3}~~,~~\stackrel{b}{2} > \end{cases}\qquad \qquad \stackrel{magnitude}{\sqrt{a^2 + b^2}} \\\\[-0.35em] ~\dotfill\\\\ ||v||~~ - ~~||w||\implies \sqrt{5^2+(-7)^2}~~ - ~~\sqrt{3^2 + 2^2}\implies \sqrt{74}-\sqrt{13} ~~ \approx ~~ 5[/tex]

Answer:

1) Ans; C .

2) Ans; D.

3) Ans; A.

4) Ans; C.

[tex]\displaystyle\\|\Omega|=\binom{72}{4}=\dfrac{72!}{4!68!}=\dfrac{69\cdot70\cdot71\cdot72}{2\cdot3\cdot4}=1028790\\|A|=\binom{46}{4}=\dfrac{46!}{4!42!}=\dfrac{43\cdot44\cdot45\cdot46}{2\cdot3\cdot4}=163185\\\\P(A)=\dfrac{163185}{1028790}=\dfrac{473}{2982}\approx0.1586[/tex]

Answer:

about 127.28 feet

Step-by-step explanation:

The length of the hypotenuse of a right triangle with a base and a height of 90 feet each.

root (90)^2 + (90)^2

Answer:

A) x = 113°

Explanation:

Given three sides: 6.4 cm, 5.8 cm, 10.2 cm

Use the cosine rule:

c² = a² + b² - 2ab cos(C)

Insert/put variables:

[tex]\rightarrow \sf 10.2^2 = 5.8^2 + 6.4^2 - 2(5.8)(6.4) cos(x)[/tex]

[tex]\rightarrow \sf -74.24 cos(x) = 10.2^2 - 5.8^2 - 6.4^2[/tex]

[tex]\sf \rightarrow -74.24 cos(x) = 29.44[/tex]

[tex]\rightarrow \sf cos(x) = \dfrac{29.44}{-74.24}[/tex]

[tex]\rightarrow \sf x = cos^{-1}(-\dfrac{23}{58})[/tex]   = 113.36°  ≈ 113°  (rounded to nearest degree)

Reason:

Refer to the diagram below. The tiny square angle markers tell us we have a 90 degree angle, meaning those lines are perpendicular.

You can think of the parallel lines being the metal part of train tracks, while the perpendicular line connecting the metal rails is the wooden part of the train tracks.

Answer:

[tex]31.8\%[/tex]

Step-by-step explanation:

The area of the circle is [tex]A=\pi r^2=\pi(4)^2=16\pi[/tex]

The area of the triangle is [tex]A=\frac{bh}{2}=\frac{8*4}{2}=\frac{32}{2}=16[/tex]

Hence, the probability of a randomly selected point within the circle falls in the red shaded area is [tex]\frac{16}{16\pi}=\frac{1}{\pi}\approx0.318\approx31.8\%[/tex]

Answer:

12345678910

Step-by-step explanation:

TANQR

The standard notation of 7,250,000 is [tex]7.25 \times 10^6[/tex]

The standard notation of 0.000045 is [tex]4.5 \times 10^{-5}[/tex]

It is the way of writing a large number between 1 to 10 with a power of 10.

We have,

7,250,000

To write this number in standard notation, we can use powers of 10.

We start by counting the number of digits to the left of the decimal point.

In this case, there are 7 digits to the left of the decimal point.

We can then express this number in scientific notation as:

[tex]7.25 \times 10^6[/tex]

This means that we have 7.25 times 10 raised to the power of 6.

Now,

0.000045

To write this number in standard notation, we can again use powers of 10. We start by counting the number of digits to the right of the decimal point. In this case, there are 5 digits to the right of the decimal point.

We can then express this number in scientific notation as:

[tex]4.5 \times 10^{-5}[/tex]

This means that we have 4.5 times 10 raised to the power of -5.

Thus,

The standard notation of 7,250,000 is [tex]7.25 \times 10^6[/tex]

The standard notation of 0.000045 is [tex]4.5 \times 10^{-5}[/tex]

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The complete question.

Write this number in standard notation.

7,250,000

0.000045