Solve the inequality: -16< 4(2x + 8) <40

Given:

A figure of a circle. A secant SU and a tangent SR is drawn to the circle from the external point S.

To find:

The measure of the line segment TU.

Solution:

According to the secant tangent segment theorem, the square of tangent is equal to the product of secant and external segment of the secant.

Using secant tangent segment theorem, we get

[tex]SR^2=SU\times ST[/tex]

[tex](40)^2=(32+2x-2)\times (32)[/tex]

[tex]1600=(30+2x)(32)[/tex]

[tex]1600=960+64x[/tex]

Subtract both sides by 960.

[tex]1600-960=64x[/tex]

[tex]640=64x[/tex]

Divide both sides by 64.

[tex]\dfrac{640}{64}=x[/tex]

[tex]10=x[/tex]

Now, the measure of the line segment TU is:

[tex]TU=2x-2[/tex]

[tex]TU=2(10)-2[/tex]

[tex]TU=20-2[/tex]

[tex]TU=18[/tex]

Therefore, the correct option is C.

Answer:

if it is 46-2004 then the answer is  -1958

Step-by-step explanation:

Answer:

b = 5

Step-by-step explanation:

The given equation is :

[tex]0.3x^2+5x-7=0[/tex] .......(1)

It is in the form of quadratic equation. The general form of a quadratic equation is as follows :

[tex]ax^2+bx+c=0[/tex] .....(2)

Comparing equations (1) and (2), we get :

a = 0.3, b = 5 and c = -7

Hence, the value of b is equal to 5.

Answer:

$0.90

Step-by-step explanation:

[tex]\frac{4}{10}=0.4[/tex]

3 dozen = 36

[tex]\frac{36}{0.4} =\frac{y}{0.1}[/tex]

0.4 × y = 36 × 0.1

0.4y = 3.6

0.4y ÷ 0.4 = 3.6 ÷ 0.4

y = 9

Answer:

The answer is D

Step-by-step explanation:

took the test

The polar expression of a complex number in its rectangular form 4(cos120° + i sin120°) = -2 + 2√3 i.

Let Z = a + ib be a complex number in the cartesian form represented by point P(a, b) in the complex plane then Z = r cos∅ + i r sin∅ =r is called the polar form of a complex number.

We have.

z = 4(cos120° + i sin120°)

z = 4(cos(90 + 30)° + i sin(90 + 30)°)

Using trigonometry

cos (90 + ∅) = -sin ∅ and sin (90 + ∅) = -cos ∅

So, 4( -sin (30)° + i cos (30)°)

= 4 ( -1/2 + i √3/2)

= -4(-1/2) + i 4(√3/2)

= -2 + 2√3 i

Thus, the rectangular form is 4(cos120° + i sin120°) = -2 + 2√3 i.

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Answer:

109.18

Step-by-step explanation:

Subtract 13.4-7.2 then solve the triangle (base x height) getting 32.86. Next solve the rectangle getting 76.32. Then add all of it concluding in 109.18.

The value of x is 18.

An equation is an expression that shows the relationship between two or more numbers and variables.

First, both angles shown are equal to each other.

5x + 5 = 95

Next, the opposite side of the equation to isolate x value (5x).

5x + 5 (-5) = 95 (-5)

5x = 90

Finally, we need to divide both sides of the equation by 5.

5x / 5 = 90 / 5

x = 18

The final answer: x = 18

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Answer:

b.) x= 6, m∠XOY= 18

Step-by-step explanation:

comment if u need explanation :))

Answer:

The mechanic spent 12 hours on the repair.

Step-by-step explanation:

The mechanic spent 12 hours on the repair.

The expression can be written as [tex]90,000(3.71)^{\frac{t}{5} }[/tex]

A function whose value is a constant raised to the power of the argument, especially the function where the constant is e.

Given that, we have to express the function [tex]f(t) = 90,000(1.3)^t[/tex] in the form of [tex]f(t) = ab^{\frac{t}{5} }[/tex]

Comparing both the functions,

[tex]b^\frac{t}{5} = (1.3)^t[/tex]

We can write, [tex](1.3)^t[/tex] as

[tex](1.3)^t = (1.3^5)^\frac{t}{5}[/tex]

[tex]= 3.71^\frac{t}{5}[/tex]

Therefore, the equation ca be written as,  [tex]90,000(3.71)^{\frac{t}{5} }[/tex]

Hence, the expression can be written as [tex]90,000(3.71)^{\frac{t}{5} }[/tex]

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Answer:

F. 4 ÷ 5

Step-by-step explanation:

Answer:

30 goats, and 40 animals

Step-by-step explanation:

so since the problem says 10 goats are in the garden, and the ratio of sheep to goats is 3:1 you do 3*10. it's basically saying for every 1 goat you have 3 sheep. so if you take away the 0 from 30 and 10 you get 3:1. : )

Answer:

A.

What were the sixth grade student scores of the final exam?

Answer:

178.48

Step-by-step explanation:

We are asked what is 46 percent out of 388.

To solve this, we need to follow the formula when finding the percentage of a number.

P being the percentage

X being the number

Y being the answer, the forumla is

Y = P * X

Substitute :

Y = 46% * 388

Convert the percentage into a decimal,

46%/100

0.46

Y = 0.46 * 388

Multiply :

178.48 = 0.46 * 388

178.48

your welcome btw

Step-by-step explanation:

The space comprising all possible outcomes (sample space) is represented by the 6×66×6 matrix formed by the possible pairs representing the outcome of dice:

From the above sample space, there are six events wherein the first die is 44 (all elements of the fourth row in the matrix). That is, n(F)=6n(F)=6. Moreover, there are six events wherein doubles are rolled (all diagonal elements in the matrix). That is, n(D)=6n(D)=6. The result (4,4)(4,4) is the intersection of both events. That is, n(D∩F)=1n(D∩F)=1.

Therefore, the possibility/probability that the first die is 4 or that doubles are rolled is computed as follows:

P(D∪F)=P(D)+P(F)−P(D∩F)=n(D)n(S)+n(F)n(S)−n(D∩F)n(S)=636+636−136=1136P(D∪F)=P(D)+P(F)−P(D∩F)=n(D)n(S)+n(F)n(S)−n(D∩F)n(S)=636+636−136=1136

Answer:

If you have two points, (x1, y1) and (x2, y2), you can define the exponential function that passes through these points by substituting them in the equation y = abx and solving for a and b. In general, you have to solve this pair of equations: y1 = abx1 and y2 = abx2, .

Step-by-step explanation:

Answer:b

Step-by-step explanation:

i took that test

Answer:

tanga bono ulaga kase tatamadtamad

Answer:

280 inches

Step-by-step explanation:

8 x 8 = 64

9 × 24 = 216

64 + 216 = 280

The rectangle that has side lengths of 7 units and 8 units is (a) a rectangle that has an area of 56 square units

From the question, we have the following parameters that can be used in our computation:

Side lengths of 7 units and 8 units

These parameters can be represented as

Length = 7 units

Width = 8 units

Using the options in the question as a guide, we have the following computations

We start by calculating the area of the rectangle

The area of the rectangle can be calculated using the following area formula

Area = length * width

Substitute the known values in the above equation, so, we have the following representation

Area = 7 * 8

Evaluate

Area = 56

Hence, the rectangle is (a)

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Complete question

Which rectangle has side lengths of 7 units and 8 units?

(a) a rectangle that has an area of 56 square units

(b) a rectangle that has a perimeter of 56 square units

(c) a rectangle that has an area of 65 square units

(b) a rectangle that has a perimeter of 6 units

The value of the exponential graph y = ( 1/2 )ˣ is graphed

When you raise a quotient to a power you raise both the numerator and the denominator to the power. When you raise a number to a zero power you'll always get 1. Negative exponents are the reciprocals of the positive exponents.

The different Laws of exponents are:

mᵃ×mᵇ = mᵃ⁺ᵇ

mᵃ / mᵇ = mᵃ⁻ᵇ

( mᵃ )ᵇ = mᵃᵇ

mᵃ / nᵃ = ( m / n )ᵃ

m⁰ = 1

m⁻ᵃ = ( 1 / mᵃ )

Given data ,

Let the exponential equation be represented as A

Now , the value of A is

y =  ( 1/2 )ˣ   be equation (1)

On simplifying the equation , we get

y = 1 / (2ˣ)

Now , the graph of the function y =  ( 1/2 )ˣ  will be a slanting line which will not touch the x axis and passes through the point y = 1

The graph of the function y =  ( 1/2 )ˣ is given below

Hence , the function is solved and the graph is plotted

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Answer:

( d ) grease

Step-by-step explanation:

Grease could be effectively used to reduce friction.

Answer:

-4±2√3

Step-by-step explanation:

quadratic formula: (-b±√(b²-4ac))/(2a)

a = 1

b = 8

c = 4

(-8±√(8²-4*1*4))/(2*1)

(-8±√(64-16))/(2)

(-8±√48)/(2)

(-8±4√3)/(2)

-4±2√3

Answer:

Since the calculated value of  z= 1.6279 does not fall in the critical region Z ≥ ±1.96 we conclude that there is no difference between the population variance and the sample variance.

Step-by-step explanation:

The data given is

Population mean μ= $ 7.18

Population variance= σ²= 3.81

Population Standard Deviation = √σ²= √3.81= 1.952

Sample Mean= x`= $ 8.02

Sample Standard Deviation =s = $ 2.08

Sample Size = 15

Significance Level = ∝= 0.05

The null and alternate hypotheses are

H0: σ1=σ2 against the claim that Ha: σ1≠ σ2

where  σ1 is the population variance and

σ2 is the sample variance

The rejection region is Z ≥ ±1.96 for two tailed test  at ∝= 0.05

The test statistic z is used

z= x`-  μ/ σ/√n

Putting the values

Z= 8.02-7.18/1.952/√15

z= 0.84/0.51599

z= 1.6279

Since the calculated value of  z= 1.6279 does not fall in the critical region Z ≥ ±1.96 we conclude that there is no difference between the population variance and the sample variance.

Answer:

4 x 8.5 x 12.5 =425 (multiple hight x width x length)

The volume of the box is [tex]425in^{3}[/tex]

Answer:

425 in³

Step-by-step explanation:

V = whl

12 1/2 · 8 1/2 · 4 = 425

The exponential function  can be written as y = 700e^-0.094t.

We know that the term function would have to do with a mathematical rule that we can use to be able to obtain specific values. Now we have to know that there was a sample of 700 milligrams of a radioactive substance to start a study. Since then, the sample has decayed by 9.4% each year.

We can use;

N = Noe^-rt

N = amount at time t

No = Amount at the beginning

r = decay rate

t = time taken

Thus we have; y = 700e^-0.094t

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Answer:

Read step by step explanation

Step-by-step explanation:

The owner already knows that the limit for the average time delivered pizzas is 38 minutes. So we conclude

1.-The resulting mean from sample data ( x ) ( 27 customers) need to be smaller than 38 minutes, any value of sample above 38 minutes means more time for the delivery action and will indicate a failure for the future project

2.-As sample size is smaller than 30 the test has to be  t-student one tail test to the left

Test hypothesis

Null hypothesis                       H₀                  x  = 38

Alternative hypothesis           Hₐ                  x  <  38

We should test at a significance level α  = 0,05       (α = 5%)

If the result of the test is to accept  H₀  delivery project won´t be implemented, if on the other hand, H₀ is rejected then in the condition of the alternative hypothesis we accept Hₐ the sample indicates that we have a smaller average time than 38 minutes.

Therefore ,the value of a given fraction is equal to 10/12, which equals 5/6, after resolving the given problem.

To represent a whole, divide it into any number of comparable parts, or fractions. How many units of a particular size there are is expression using fractions in standard English. 8, 3/4. Parts of a whole are included. Numbers in mathematics are stated as a ratio of the excess to the denominator. These are each simple fractions that represent an integer. A fraction is contained in the fraction or reduction of a complex fraction. When a fraction is true, its numerators are less than its denominators. An amount that makes up a fraction of a whole is called a fraction. You can assess the whole by dissecting it into smaller pieces.

Here,

Given : 5/8 X 4/3

=> 5/8 X 4/3 = 20/24

on condensing,

10/12 = 5/6

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