What are the domain and range of the function f(x)=3x-1 /2

Given:

QR=20, TS=4x-3, RS=16.

To find:

The value of x and TS.

Solution:

In the figure QR is tangent and RT is secant to the given circle.

According to the secant-tangent theorem, the square of the length of the tangent segment is equal to the product of the lengths of the secant and its external segment, if the tangent and secant are drawn to a  from the an external point.

Using secant-tangent theorem, we get

\(QR^2=RS\times RT\)

\(QR^2=RS\times (TS+RS)\)

\(20^2=16\times (4x-3+16)\)

\(400=16\times (4x+13)\)

Divide both sides by 16.

\(25=4x+13\)

Subtracting both sides by 13.

\(25-13=4x\)

\(12=4x\)

Divide both sides by 4.

\(3=x\)

Now,

\(TS=4x-3\)

\(TS=4(3)-3\)

\(TS=12-3\)

\(TS=9\)

Therefore, the value of x is 3 and the measure of TS is 9 units.

Answer:

Step-by-step explanation:

1) f(-4) --> if x < or equal to 3

2) 1/(-4)-4

3) The answer is - 1/8

The inequalities representing the graph are y ≥ - 3x + 2 and y ≥ (2/3)x - 1.

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

First, we have to determine the two lines.

Line₁.

(0, 2) and (1, - 1).

m = (- 1 - 2)/(1 - 0).

m = - 3.

- 1 = - 3(1) + b.

b = 2.

y = - 3x + 2.

Line₂.

(0, - 2) and (3, 0).

m = (0 + 2)/(3 - 0).

m = 2/3.

0 = (2/3)(3) + b.

b = - 1.

y = (2/3)x - 1.

So, The two inequalities are y ≥ - 3x + 2 and y ≥ (2/3)x - 1.

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The total area from the graph is 2.737.

Area is the amount of space occupied by a two-dimensional figure. In other words, it is the quantity that measures the number of unit squares that cover the surface of a closed figure. The standard unit of area is square units which is generally represented as square inches, square feet, etc.

First of all, lets calculate the points of intersection (P, Q, R)

x²+3=(x+2) +5

x²-2=√(x+2)

x⁴+4-4x²=x+2

x⁴-4x²-x+2=0

(x-2)(x³+2x²-1)=0

(x-2)(x+1)(x²+x-1)=0

x=2, -1, -1±√(1+4)/2

Clearly, the x-coordinate of Q is -1, P is -1-√5/2, R is -1+√5/2, S is 2

So the limit of integration will be

P( (-1-√5)/2, (-1-√5/2)² +3)=P((-1-√5)/2, (3+√5/2))

Q(-1, (-1)²+3)=Q(-1, 4)

Area A:

\(\int\limits^\frac{3+\sqrt{5} }{2} _4 {-\sqrt{-y-3}-((y-5)^2 -2)} \, dx\)

= \([\frac{-(y-3)^\frac{3}{2} }{\frac{3}{2} }-\frac{(y-5)^3}{3}+3y]^{\frac{3+\sqrt{5} }{2} }_4\)

= 2.07

Area B:

\(\int\limits^\frac{-1+\sqrt{5} }{2} _4 {-\sqrt{x+2}+5-(x^2+3)} \, dx\)

= \([\frac{-(x+2)^\frac{3}{2} }{\frac{3}{2} }+5x-\frac{x^3}{3}-3x]^{\frac{-1+\sqrt{5} }{2} }_{-1}\)

= 0.667

Total area = 2.07+0.667

= 2.737

Therefore, the total area from the graph is 2.737.

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Answer:

this very easy to factorize this because (-+)is- (+-)-

(++)+ (--)+ but the sign which is bigger we have to keep that

Answer: Angle 3 and Angle 2

Step-by-step explanation:

The angles form a linear pair, which means they are supplementary.

Answer:

\(\displaystyle \frac{\pi(5e^4+8e^2-1)}{2e^4}\approx9.526\)

Step-by-step explanation:

This can be solved with either the washer (easier) or the shell method (harder). For the disk/washer method, the slice is perpendicular to the axis of revolution, whereas, for the shell method, the slice is parallel to the axis of revolution.  I'll show how to do it with both:

Shell Method (Horizontal Axis)

\(\displaystyle V=2\pi\int^d_cr(y)h(y)\,dy\)

Radius: \(r(y)=2-y\) (distance from y=2 to x-axis)

Height: \(h(y)=2-(-\ln y)=2+\ln y\) (\(y=e^{-x}\) is the same as \(x=-\ln y\))

Bounds: \([c,d]=[e^{-2},1]\) (plugging x-bounds in gets you this)

Plugging in our integral, we get:

\(\displaystyle V=2\pi\int^1_{e^{-2}}(2-y)(2+\ln y)\,dy=\frac{\pi(5e^4+8e^2-1)}{2e^4}\approx9.526\)

Washer Method (Parallel to x-axis)

\(\displaystyle V=\pi\int^b_a\biggr(R(x)^2-r(x)^2\biggr)\,dx\)

Outer Radius: \(R(x)=2-e^{-x}\) (distance between \(y=2\) and \(y=e^{-x}\))

Inner Radius: \(r(x)=2-1=1\) (distance between \(y=2\) and \(y=1\))

Bounds: \([a,b]=[0,2]\)

Plugging in our integral, we get:

\(\displaystyle V=\pi\int^2_0\biggr((2-e^{-x})^2-1^2\biggr)\,dx\\\\V=\pi\int^2_0\biggr((4-4e^{-x}+e^{-2x})-1\biggr)\,dx\\\\V=\pi\int^2_0(3-4e^{-x}+e^{-2x})\,dx\\\\V=\pi\biggr(3x+4e^{-x}-\frac{1}{2}e^{-2x}\biggr)\biggr|^2_0\\\\V=\pi\biggr[\biggr(3(2)+4e^{-2}-\frac{1}{2}e^{-2(2)}\biggr)-\biggr(3(0)+4e^{-0}-\frac{1}{2}e^{-2(0)}\biggr)\biggr]\\\\V=\pi\biggr[\biggr(6+4e^{-2}-\frac{1}{2}e^{-4}\biggr)-\biggr(4-\frac{1}{2}\biggr)\biggr]\)

\(\displaystyle V=\pi\biggr[\biggr(6+4e^{-2}-\frac{1}{2}e^{-4}\biggr)-\frac{7}{2}\biggr]\\\\V=\pi\biggr(\frac{5}{2}+4e^{-2}-\frac{1}{2}e^{-4}\biggr)\\\\V=\pi\biggr(\frac{5}{2}+\frac{4}{e^2}-\frac{1}{2e^4}\biggr)\\\\V=\pi\biggr(\frac{5e^4}{2e^4}+\frac{8e^2}{2e^4}-\frac{1}{2e^4}\biggr)\\\\V=\pi\biggr(\frac{5e^4+8e^2-1}{2e^4}\biggr)\\\\V=\frac{\pi(5e^4+8e^2-1)}{2e^4}\approx9.526\)

Use your best judgment when deciding on what method you use when visualizing the solid, but I hope this helped!

Answer:

B.

Step-by-step explanation:

A figure rotated 90° CW about the origin will be the same size and shape as the original. Any figure rotated by any angle will be the same size and shape as the original.

Answer:

60x^2 + 40x - 48xy - 32y

Step-by-step explanation:

Let's solve this using the FOIL (first, inner, outer, last) method.

(10x-8y) (6x+4)

= 10x × 6x + 10x × 4 - 8y × 6x - 8y × 4

= 60x^2 + 40x - 48xy - 32y

Answer: 60x^2 + 40x - 48xy - 32y

Soory for the wrong answer i re solved it :)

The sets of side measurements that can form a triangle are: c. 8, 3, 11

d. 5, 11, 8

To determine which set of side measurements could be used to form a triangle, we need to apply the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Let's evaluate each set of side measurements:

a. 12, 23, 7

In this case, the sum of the lengths of the two shorter sides (12 and 7) is 19, which is less than the length of the longest side (23). Therefore, this set of side measurements cannot form a triangle.

b. 10, 7, 2

Here, the sum of the two shorter sides (10 and 2) is 12, which is greater than the length of the longest side (7). This set of side measurements also fails to satisfy the triangle inequality theorem and cannot form a triangle.

c. 8, 3, 11

The sum of the two shorter sides (8 and 3) is 11, which is greater than the length of the longest side (11). Therefore, this set of side measurements can form a triangle.

d. 5, 11, 8

In this case, the sum of the lengths of the two shorter sides (5 and 8) is 13, which is greater than the length of the longest side (11). Hence, this set of side measurements can also form a triangle.

In summary, the sets of side measurements that can form a triangle are:

c. 8, 3, 11

d. 5, 11, 8

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Answer:

I will answer them from top to bottom

1. 2A

2. 2A-B

3. 2A+3A

4. 2(A-B)

Step-by-step explanation:

You don't need an explanation. I am just putting this here so my answer does not get taken down.

Answer:

z = 99

Step-by-step explanation:

\(\frac{z}{9}\) + 4 = 15 ( subtract 4 from both sides )

\(\frac{z}{9}\) = 11 ( multiply both sides by 9 to clear the fraction )

z = 99

The graph of the function \(f(x) = (9/4)x^2\) is a symmetric upward-opening parabola.

Overall, the graph represents a quadratic function with a positive leading coefficient, resulting in an upward-opening parabolic curve. The graph has been attached.

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The two angles are related in that they are supplementary angles

Supplementary angles would add tuo to 180 degrees according to the angle Theorem.

Adding the two given angles :

These angles are supplementary

The angles aren't vertical in that , vertical angles should have the same vertex. Complementary angles on the other hand add to 90 degrees. While the angles doesn't share the same side, hence, they aren't adjacent.

Hence, the angles are related as they are supplementary angles .

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Answer:

x=132

Step-by-step explanation:

Hey There!

The angle that is equal to 48 and angle x are supplementary angles meaning that they will add up to equal 180

so to find x we subtract 48 from 180

180-48=132

therefore x=132

The value of x will be;

⇒ x = 132°

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

The triangle is shown in figure.

The interior angles are;

⇒ 60°, 72° and 48°

Now,

We know that;

The sum of two opposite interior angle of the a triangle is equal to the exterior angle of the triangle.

So, We get;

⇒ x = 60° + 72°

⇒ x = 132°

Thus, The value of x = 132°

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Answer:

$1.62

Step-by-step explanation:

If you divide $2.43 by 3 it's 0.81 and that's the cost of one loaf of bread so multiply that by 2 and you get the cost of two loaves of bread which is $1.62

Answer:

The correct option is c which is if this test was one-tailed instead of two-tailed, you would reject the null.

Step-by-step explanation:

a: This statement cannot be true as the p-value for a 1 tailed test is dependent on the level of significance and other features.

b: This statement cannot be true as there is no valid mathematical correlation between the p-value of the one-tailed test and the current p-value.

c: This statement is true because due to the enhanced level of significance, the null hypothesis will not be rejected.

d: This statement is inverse of statement c which cannot be true.

e: The statement cannot be true as there is no correlation between the current p-value and the p-value of 1 tailed test. The correlation exists between the values of one-tailed and two-tailed p-values.

Step-by-step explanation:

use the pythagorean theorem to find the length of the leg in the triangle below

Answer:

Angle X = 73 degrees, Angle Z = 34 degrees, and Angle Y = 146 degrees

Answer:

draw a rectangle

Step-by-step explanation:

a rectangle has 2 long sides and 2 short ones it has 2 sets of simailer and has 2 perpundicular

Answer: 20+7b

Step-by-step explanation:

Given

 (6+7b)+14

Take off parentheses

=6+7b+14

Move like terms together (Commutative property)

=6+14+7b

Combine like terms

=20+7b

Hope this helps!! :)

Please let me know if you have any question

Answer:

\(\huge\boxed{ answer}\)

\(\blue\star\)6 + 7b + 14 = 0

\(\blue\star\)7b + 20 = 0

\(\blue\star\)7b = - 20

\(\blue\star\)b = -20\7

\(\star\)simplified form

\(\blue\star\)(6 + 7b) +14

firstly remove the brackets.

\(\blue\star\)6 + 7b +14

seprate terms and variables

\(\blue\star\) 7b +20

\(\huge\boxed{7b + 20}\)

Hope it helps..

Step-by-step explanation:

12

Answer:

11

Step-by-step explanation:

11+12+13 =36

So  Kate would be 11. Bradley would be 12. And Cameron would be 13

Answer:

100

Step-by-step explanation:

Reason: The two line segments CF and AH point in the same direction, and they never intersect. Therefore, we consider them parallel.

Skew lines are ones that point in different directions. An example of a pair of skew lines would be AB and DE. Skew lines never intersect, but we don't consider them parallel.

Answer:

yes and there a r godd film?

Step-by-step explanation:

Answer:

d) 189.3 in²

Step-by-step explanation:

Area of rectangle is,

→ w × l

→ 10 × 15

→ 150 in²

Area of semi circle is,

→ (1/2)πr²

→ (1/2) × 3.14 × (5)²

→ 1.57 × 25

→ 39.3 in²

Now the total area will be,

→ 150 + 39

→ 189.3 in²

Thus, total area is 189.3 in².

The art teacher can make a maximum of 24 identical kits using all the crayons and drawing paper for proper distribution.

To determine the largest number of identical kits the art teacher can make using all the crayons and drawing paper, we need to find the greatest common divisor (GCD) of the quantities.

The GCD represents the largest number that can divide all the quantities without leaving a remainder.

The GCD of the quantities of crayons can be found by considering the prime factorization:

72 = 2³ × 3²

48 = 2⁴ × 3

48 = 2⁴ × 3

48 = 2⁴ × 3

The GCD of the crayons is 2³ × 3 , which is 24.

Now, we need to find the GCD of the quantity of drawing paper:

120 = 2³ × 3 × 5

The GCD of the drawing paper is also 2³ × 3 , which is 24.

Since the GCD of both the crayons and drawing paper is 24, the art teacher can make a maximum of 24 identical kits using all the crayons and drawing paper.

Each kit would contain an equal distribution of crayons and drawing paper.

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Answer:

On average, Tonya makes $312 more than Emily on a typical day.

Step-by-step explanation:

I was just studying that question a few hours ago

The present value of the annuity is approximately `7032.08. The correct answer is option (d) None of these.

To find the present value of an annuity, we can use the formula:

PV = PMT * (1 - (1 + r)^(-n)) / r

Where PV is the present value, PMT is the periodic payment, r is the interest rate per period, and n is the number of periods.

In this case, the periodic payment is `200, the interest rate is 5% (or 0.05) converted quarterly, and the number of periods is 10 years, which equals 40 quarters.

Plugging in these values into the formula, we get:

PV = 200 * (1 - (1 + 0.05)^(-40)) / 0.05

Simplifying the equation, we find:

PV ≈ 200 * (1 - 0.12198) / 0.05

PV ≈ 200 * 0.87802 / 0.05

PV ≈ 35160.4 / 0.05

PV ≈ 7032.08

Therefore, the present value of the annuity is approximately `7032.08.

None of the provided answer options (a), (b), or (c) match this result. The correct answer is (d) None of these.

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Answer:

The approximate user base of the social media site 10 months from now would be approximately 52,374.

Step-by-step explanation:

To calculate the approximate user base of the social media site 10 months from now, considering a 4% increase per month, we can use the following steps:

1. Calculate the monthly growth factor: 1 + (4% / 100) = 1 + 0.04 = 1.04

2. Apply the growth factor to the current user base for each month:

  Month 1: 35,930 * 1.04 = 37,387.2 (approx.)

  Month 2: 37,387.2 * 1.04 = 38,868.49 (approx.)

  ...

  Month 10: Previous Month * 1.04

By repeating this calculation for each month, we can determine the approximate user base 10 months from now.

Month 1: 37,387.2

Month 2: 38,868.49

Month 3: 40,391.33

Month 4: 41,957.61

Month 5: 43,569.34

Month 6: 45,228.24

Month 7: 46,936.32

Month 8: 48,695.44

Month 9: 50,507.45

Month 10: 52,374.40 (approx.)

Therefore, the approximate user base of the social media site 10 months from now would be approximately 52,374.