f(x) = 4x² + 5x - 3
g(x) = 4x³
3x² + 5
Find (f+g)(x).

Applying the circle theorems, we have:

4. y = 120°

x = 45°

5. x = 90°

y = 32°

6. x = 40°

y = 20°

7. x = 116°

y = 98°

8. x = 100°

y = 60°

9. x = 54°

y = 75°

The angle formed outside a circle by the intersection of two secants equals half the positive difference of the measures of the intercepted arcs, based on the angle of intersecting secants theorem.

The angle formed when two chords of a circle intersect, equals the half the sum of the measures of the intercepted arcs, based on the angle of intersecting chords theorem.

4. y = 360 - 95 - 30 - 115 = 120°

x = 1/2(120 - 30) [angle of intersecting secants theorem]

x = 45°

5. x = 90° [based on the tangent theorem]

y = 180 - 90 - 58 [triangle sum theorem]

y = 32°

6. x = 360 - 160 - 160 [central angle theorem]

x = 40°

y = 1/2(40) [inscribed angle theorem]

y = 20°

7. x = 180 - 2(32)

x = 116°

y = 1/2[132 + 2(32)] [angle of intersecting chords theorem]

y = 98°

8. x = 180 - 80 [opposite angles of an inscribed quadrilateral are supplementary]

x = 100°

y = 1/2[(2(80) - 90) + 50] [inscribed angle theorem]

y = 1/2[70 + 50]

y = 60°

9. 40 = 1/2(134 - x) [angle of intersecting secants theorem]

2(40) = 134 - x

80 = 134 - x

80 - 134 = - x

-54 = -x

x = 54°

y = 360 - 134 - 54 - 97

y = 75°

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Answer:

a=15.7mm2,31.4

b=18.84in2,37.68

Answer:

-3/2

Step-by-step explanation:

See attached image

Answer:

[tex]m=\frac{-3}{2}[/tex]

Step-by-step explanation:

m = slope
[tex]m=\frac{-4-5}{4--2}[/tex]  
[tex]m=\frac{-9}{6}[/tex]
[tex]m=\frac{-3}{2}[/tex]

Answer:

Equation 75 X .45 = P

P = 33.75

Answer:

Step-by-step explanation:

2x+6 ≤ 10  or  2x + 8 > 20

⇔ 2x ≤ 4  or  2x > 12

⇔ x ≤ 2  or  x > 6

Answer:

Step-by-step explanation:

400: 100 you find 1% you multiply it by 20 and you have 20%

400 : 100 * 20 =

4 * 20 =                                    

The evaluation is (2sin2∅-cos2∅)sec2∅.

Trigonometric functions are functions used to relate the sides of a triangle with its angles.

Analysis:

2tan2∅ -(1- tan2∅)

2tan2∅ - 1 + tan2∅

3tan2∅ - 1

3([tex]\frac{sin2\alpha }{cos2\alpha }[/tex]) - 1

(3sin2∅/cos2∅) - 1

(3sin2∅ - cos2∅)/cos2∅

but 1/cos2∅ = sec2∅

(3sin2∅ - cos2∅)/sec2∅

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Answer:232 inch^2

Step-by-step explanation:to solve, add the surface area of each side. Remember, there are 3 pairs of sides and the pairs have equal area. Area =length x length. So we have 2x(8x2)+2x(2x10)+2x(10x8) in square inches.

Answer:

D. 105

Step-by-step explanation:

500-270, there's 230 total 2 head.

270-100 of one head, is 170 purple one head. 170+125 purple equals 295.

296 subtract from 500 total is 205 for total green.

205-100, 105 2 head.

Answer:

A

Step-by-step explanation:

height (y-axis) = constant × width (x-axis)

let's look at the point coordinates.

remember, an ordered pair of point coordinates consists of an x value and an associated (typically calculated by a function) y value.

we see that all y values are half of the x values (3 and 1.5, 2 and 1, 7 and 3.5, 8 and 4).

so, the constant in our equation is responsible for returning half of the x value back as the y value.

what constant factor turns a number in half ?

x × c = x/2

c = 1/2

and so, A is the right answer.

Celina says true that each of the following expressions is actually a binomial expression.

The binomial is a polynomial of two-term only. For example, x + 5 where x and 5 are the two separate terms.

Celina says that each of the following expressions is actually a binomial in disguise:

a.  5abc - 2a² + 6abc = 11abc - 2a²

The is a binomial expression.

b.  5x³∙2x² - 10x⁴ + 3x⁵ + 3x∙(-2) x⁴ = 7x⁵ - 10x⁴

The is a binomial expression.

c.  (t+2)² - 4t = t² + 4

The is a binomial expression.

d.  5(a - 1) - 10(a - 1) + 100(a - 1) = 95a - 95

The is a binomial expression.

e.  (2πr - πr² )r - (2πr - πr²)∙2r = -2πr² + πr³

The is a binomial expression.

Celina says true that each of the following expressions is actually a binomial expression.

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Work Shown:

tan(angle) = opposite/adjacent

tan(61) = x/9

x = 9*tan(61)

x = 16.2364298 approximately

Your calculator needs to be in degree mode. One quick way to check is to type in something like tan(45) and the result should be 1.

Using the permutation formula, it is found that the people can be chosen for the roles in 6840 ways.

The order in which the people are chosen is important, as there are different roles, hence the permutation formula is used.

The number of possible permutations of x elements from a set of n elements is given by:

[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]

In this problem, 3 people will be chosen from a set of 20 people, hence the number of ways is given by:

[tex]P_{20,3} = \frac{20!}{17!} = 6840[/tex]

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Answer:

hello how are you nice to meet you

Answer: A

It has a negative gradient.

Hope this helps :))

P.s. Can you  mark me as the brainliest? <3

Answer:

Step-by-step explanation:

Remark

You can read the y intercept right off the graph. Follow the y axis upwards until the line intercepts the y axis. I think you will find it is at 0,5

So far what you know is

y = mx + 5

Finding m is a little harder. I would use 6,0 and 0,5 as the two points that will define m.

Givens

x1 = 6

x2 = 0

y1 = 0

y2 = 5

Equation

m = (y2 - y1) / (x2 - x1)           Put the givens into this equation.

Solution

m = (5 - 0) / (0 - 6)

m = 5/-6

m = - 5/6

Answer

The line is

y = -5/6 x + 5

Based on the properties of a kite, the statement that is true is: D. KPE = TPE.

A kite is a quadrilateral in which its diagonals intersect at right angles.

Also, the non-vertex angles of a kite are congruent, that is they have equal measure.

Angle KPE and angle TPE in the given kite are right angles formed at the point of intersection of the two diagonals of the kite. They both equal 90 degrees.

Therefore, the true statement is:

D. KPE = TPE

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Answer:

3

Step-by-step explanation:

A function cannot have two y values for any value of x

answer three has two y values for x =1

Answer:

x ≈ 0.5

Step-by-step explanation:

using the tangent ratio in the right triangle

tan63° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{IJ}{JK}[/tex] = [tex]\frac{1}{x}[/tex] ( multiply both sides by x )

x × tan63° = 1 ( divide both sides by tan63° )

x = [tex]\frac{1}{tan63}[/tex] ≈ 0.5 ( to the nearest tenth )

Answer:

x = 0.5

Step-by-step explanation:

We can use tan Θ to find the value of x.

tan Θ = Opposite ÷ Adjacent

Let us solve it now

tan 63 = 1 ÷ x

1.9626 = 1 ÷ x

x = 1 ÷ 1.9626

x = 0.5095

x ≈ 0.5  ( nearest 10th )

Answer:

x = 61°

Step-by-step explanation:

since the triangle has 2 congruent sides then it is isosceles with the 2 base angle being congruent, both x°

the sum of the 3 angles in the triangle = 180° , then

x + x + 58° = 180°

2x + 58° = 180° ( subtract 58° from both sides )

2x = 122° ( divide both sides by 2 )

x = 61°

Considering that 12 is a root of the function, the value of coefficient Q is of 12.

It means that f(x) = 0.

In this problem, the function is given by:

f(x) = x² - 13x + q.

Since 12 is a root, we have that f(12) = 0, hence:

12² - 13 x 12 + q = 0

q - 12 = 0.

q = 12.

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Answer:

If I am not mistaken the number is 54,810.

Hope I helped.

We will get the areas of each one of the given triangles:

7) A = 12.69 mm²

8) A = 19.21 in²

9) A = 16.81 yd²

7) First, we have an equilateral triangle, where all the sides measure 5.4mm

For an equilateral triangle of side length S, the area is:

[tex]A = \frac{\sqrt{3} }{4}S^2[/tex]

In this case, S = 5.4 mm, replacing we get:

[tex]A = \frac{\sqrt{3} }{4}(5.4mm)^2 = 12.62 mm^2[/tex]

8) Now we have two equal sides and one different. The general area of a triangle of base B and height H is:

A = B*H/2.

In this case, the base measures 3.4 in.

To get the height, let's divide the triangle into two right triangles, such that one cathetus is 3.4in/2 = 1.7 in.

The hypotenuse measures 5.9 in

And the other cathetus is the height of the triangle.

Then, by using the Pythagorean theorem, we see that the height is:

[tex]H = \sqrt{(5.9 in)^2 - (1.7in)^2} = 5.65 in[/tex]

Then the area of this triangle is:

[tex]A = (3.4 in)*(5.65 in)/2 = 19.21 in^2[/tex]

9) Here the base measures 8.2 yds, and the height 4.1 yds, so the area is just:

[tex]A = (4.1 yd)*(8.2 yd)/2 = 16.81 yd^2[/tex]

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Step-by-step explanation:

See above graph.......

Answer:

[tex]\frac{100}{a}[/tex]

Step-by-step explanation:

Hello!

a% is the same as [tex]\frac a{100}[/tex].

a% of a can be found by multiplying them both, giving us [tex]\frac {a^2}{100}[/tex]

The value of the expression is [tex]\frac{100}{a}[/tex]

Answer:

34/48

Step-by-step explanation:

So to answer this problem, we need to know two things:
1) The number of people who made a purchase
2) The number of people who came into the store

The problem gives us 1), which is 34.
The answer for 2) is 34+14, since that's the total number of people who came into the store. This means that the ratio is 34/48.

The students who has the method that is most representative of the school’s population is Amir.

Population refers to the group of people being studied in an experiment or the group from which a sample is drawn.

Amir has the method that is most representative of the school’s population because the method includes all students in the school studying different subjects but picked at random (every tenth students)

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