(4x+3)(6x-3) = 0
What is the positive solution to the problem?

Answer:

Θ = 50°

Step-by-step explanation:

Using the cofunction identity

tan(90 - x)° = cotx°

Given

cot40°, then

tan Θ = tan(90 - 40)° = tan50°

Thus Θ = 50°

The function g(x) is a linear function, and the rate of change over the interval  -2 ≤ x ≤ 4 is 6

The function f is given as:

f(x) =6x - 4

When translated down by 6 units, the rule of translation is:

g(x) = f(x) - 4

So, we have:

g(x) = 6x - 4 - 4

Evaluate

g(x) = 6x - 8

The rate of change over -2 ≤ x ≤ 4 is then calculated using:

g'(x) = [g(b) - g(a)]/[b - a]

So, we have:

g'(x) = [g(4) - g(-2)]/[4 + 2]

Evaluate

g'(x) = [g(4) - g(-2)]/[6]

Calculate g(4) and g(-2)

g(4) = 6 * 4 - 8 = 16

g(-2) = 6 * -2 - 8 = -20

So, we have:

g'(x) = (16 + 20)/6

Evaluate

g'(x) = 6

Hence, the rate of change over the interval  -2 ≤ x ≤ 4 is 6

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Answer:

72 times 0.45 is equal to 33.75

Step-by-step explanation:

You can use a calculator to find this out.

Answer:

32.4

Step-by-step explanation:

After repeatedly adding 0.45 a total of 72 times. You end up getting 32.5

To check the answer you divide 32.5 by 72 and receive 0.45. Checking the answer

Answer:

28

Step-by-step explanation:

28 is the number that appears first for both.

For first sequence:

7 × 4 = 28 × 4 = 112 × 4 = 448

For second sequence:

8 + 5 = 13 + 5 = 18 + 5 = 23 + 5 = 28

The experimental probability that a coin toss results in two heads showing is 3/14

The sample space of two coins is:

S = {HH, HT, TH, TT}

In the above sample space, we have:

The theoretical probability of two heads is calculated as:

P = n(HH)/Total

This gives

P = 1/4

Hence, the theoretical probability of two heads is 1/4

To do this, we make use of the table in the question

The table is given as:

Result                                  Frequency

Two heads (HH)                     30

Two tails  (TT)                        40

One head, one tail (HT)        70

Total                                     140

The experimental probability of two heads is calculated as:

P = n(HH)/Total

This gives

P = 30/140

Simplify

P = 3/14

Hence, the experimental probability of two heads is 3/14

Using the sample space in (a), we have:

The theoretical probability of two tails is calculated as:

P = n(TT)/Total

This gives

P = 1/4

Hence, the theoretical probability of two tails is 1/4

From the table in the question, we have:

Two tails  (TT)  =40

Total = 140

The experimental probability of two tails is calculated as:

P = n(TT)/Total

This gives

P = 40/140

Simplify

P = 2/7

Hence, the experimental probability of two tails is 2/7

Using the sample space in (a), we have:

The theoretical probability of one head and one tail is calculated as:

P = n(HT)/Total

This gives

P = 2/4

Simplify

P = 1/2

Hence, the theoretical probability of one head and one tail is 1/2

From the table in the question, we have:

One head one tail  (HT)  = 70

Total = 140

The experimental probability of one head one tail is calculated as:

P = n(HT)/Total

This gives

P = 70/140

Simplify

P = 1/2

Hence, the experimental probability of one head one tail is 1/2

The reason for the difference between the probability types is because one is as a result of an actual experiment, while the other is an estimate of the experiment.

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Answer:

6^7

Step-by-step explanation:

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 6 from 13 to get 7.

​

Answer:

6^7

Step-by-step explanation:

6^13/6^6 = 6^7

Step-by-step explanation:

when you are on that level of math that you get this type of question - this is totally easy.

we get the extreme point(s) of a function by finding the zeros of the first derivative of the function.

f'(x) = 4x - 8

so,

0 = 4x - 8

8 = 4x

x = 2

to determine whether it is a minimum or a maximum, we have 2 choices :

the quick way for a quadratic (parabola) equation by looking at the factor of x² : is it >0, then the parabola opens up upwards, and the extreme point is therefore a minimum. if it is <0, then it opens downward, and the extreme point is a maximum.

in our case : 2 is larger than 0, therefore minimum.

or the formal way for any type of function : create the second derivative and see, if it is >0 (minimum) or <0 (maximum) for the extreme x.

in our case

f''(x) = 4

this is larger than 0 for all x, so the extreme point is a minimum.

According to a survey report in 2018, the percentage of Bolivians that are Catholics is about: A. 77%

The Bolivians are people from the country, Bolivia. The country Bolivia is described a predominantly Catholic country as a result of its relations between the Church and the state.

Based on a survey report in 2018, about 77% of Bolivians were said to be Catholics.

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Answer:

1. b- El trópico

2. A- 77%

Step-by-step explanation:

got a 100 and i jus took the test

Answer:

the answer is 76.8

Step-by-step explanation:

multiple of the number

[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]

Let's evaluate ~

[tex]\qquad \sf  \dashrightarrow \:f(x) =- 8x + 14 + 15 {x}^{2} [/tex]

we have to find value of f(-3), so plug the value of x as -3 in the equation ~

[tex]\qquad \sf  \dashrightarrow \:f( - 3) =- 8( - 3) + 14 + 15 {( - 3)}^{2} [/tex]

[tex]\qquad \sf  \dashrightarrow \:f( - 3) = 24 + 14 + 15 {(9)}^{} [/tex]

[tex]\qquad \sf  \dashrightarrow \:f( - 3) = 38+ 135 [/tex]

[tex]\qquad \sf  \dashrightarrow \:f( - 3) = 173 [/tex]

I hope it's easy to understand now ~

f(-3):

[tex]\\ \rm\Rrightarrow 15x²-8x+14[/tex]

[tex]\\ \rm\Rrightarrow 15(-3)²-8(-3)+14[/tex]

[tex]\\ \rm\Rrightarrow 15(9)+24+14[/tex]

[tex]\\ \rm\Rrightarrow 135+38[/tex]

[tex]\\ \rm\Rrightarrow 173[/tex]

Answer:

[tex] \frac{2}{9} \: is \: less \: than \: \frac{1}{3} [/tex]

and

[tex] \frac{1}{3} + \frac{1}{6} \: must \: be \: more \: than \: \frac{1}{3} [/tex]

Answer:

slope = - 4

Step-by-step explanation:

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (4, - 9 ) and (x₂, y₂ ) = 1, 3 )

m = [tex]\frac{3-(-9)}{1-4}[/tex] = [tex]\frac{3+9}{-3}[/tex] = [tex]\frac{12}{-3}[/tex] = - 4

Answer:

[tex]m=-4[/tex]; the slope is -4

Step-by-step explanation:

[tex]slope=\frac{rise}{run} =\frac{y^2-y^1}{x^2-x^1}[/tex]

coordinates: (4,-9) (1,3)

[tex]\frac{3-(-9)}{1-4}=\frac{-12}{-3} =-4[/tex]

= -4 is your answer

hope this helped

~rere

Answer:

$1525

Step-by-step explanation:

The sum or difference modeled by the algebraic tiles is (-x²+2x+3) + (-x²-2x-1) = -2x²+2

From the complete question, we have the following expressions:

(-x²+2x+3) and (-x²-2x-1)

Add both expressions

(-x²+2x+3) + (-x²-2x-1)

Expand

-x²+2x+3 -x²-2x-1

Collect the like terms

-x² -x² + 2x - 2x + 3 -1

Evaluate the like terms

-2x²+2

Hence, the sum or difference modeled by the algebraic tiles is (-x²+2x+3) + (-x²-2x-1) = -2x²+2

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Answer:

[tex]\frac{1}{2}[/tex]

Step-by-step explanation:

P(odd number)= [tex]\frac{3}{6}[/tex]

                        =[tex]\frac{1}{2}[/tex]

Answer:

the answer is B.

Step-by-step explanation:

the formula for circumference of a circle is [tex]\pi[/tex]×diameter=C

[tex]\pi[/tex]·8=25.13

[tex]\pi[/tex]·4=12.56

12.56·2=25.13

Answer:

b = 49 cm

Step-by-step explanation:

Volume of a rectangular prism = width × length × height

Given:

Substituting the given values into the formula and solving for b:

⇒ 48608 = 16 × b × 62

⇒ 48608 = 992 b

⇒ b = 48608 ÷ 992

⇒ b = 49

Answer:

b = 49 cm

Step-by-step explanation:

Volume of a rectangular prism: length × width × height

V = L×W×H

Substitute the values above and solve for b:

48,608 = b × 16 × 62

48,608 = 992b

48,608/992 = 992b/992

49 = b

Final answer: 49 cm

Hope this helps!

Answer:

[tex]f(x)=2(x+4)^2-27[/tex]

Step-by-step explanation:

Complete the square

[tex]f(x)=2x^2+8x+5\\f(x)=2(x^2+8x+\frac{5}{2})\\f(x)+2(\frac{27}{2})=2(x^2+8x+\frac{5}{2}+\frac{27}{2})\\f(x)+27=2(x^2+8x+16)\\f(x)+27=2(x+4)^2\\f(x)=2(x+4)^2-27[/tex]

This tells us that the vertex of the parabola is [tex](-4,-27)[/tex].

Answer:

4 litres.

Step-by-step explanation:

By proportion that would be:

1.5 * 8/3

= 12/3

= 4 litres.

The standard deviation statistic should use to measure the spread of the two sets of data.

It is defined as the measure of data disbursement, It gives an idea about how much is the data spread out.

As we know, the shape of a normal curve is dictated by its mean and standard deviation, hence standard deviations are important.

Thus, the standard deviation statistic should use to measure the spread of the two sets of data of snowfall which is collected by the scientist.

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The vertex of the function is a maximum and on the interval (-1,0), the function approaches negative infinity as x approaches positive infinity

The function is given as:

f(x)= -2|x+1| + 2

The above function is an absolute value function

An absolute value function is represented as:

y = a|x - h| + k

Where the vertex is:

Vertex = (h, k)

When a is less than 0, then the vertex is at maximum

By comparison, we have:

a = -2

(h,k) = (-1, 2)

-2 is less than 0

Hence, the vertex of the function is a maximum and on the interval (-1,0), the function approaches negative infinity as x approaches positive infinity

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The median is always at the center of the box, we can say the median of our question is also at the middle of the box.

A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.

The description of the measures given has been done below and also what they indicate about the shape of the box and whisker plot have been given.

From the given data we see that;

Mean = 39,500

Median = 20000

Mode = 23000

Minimum = 15,000

Maximum = 255000

A general view of a box and whisker plot has been attached.

From the attached file, we can see the following;

- whiskers to the left and right of the box.

- The box starts from the lower quartile and stops at the upper quartile.

- The median is at the middle of the box

- The minimum is at the end of the left whisker

- The maximum is at the end of the right whisker.

1) Now, since median is always at the center of the box, we can say the median of our question is also at the middle of the box.

2) The median is 20000 but the minimum which is the end of the left whisker is 15000 while the maximum which is the end of the right whisker is 255000. This means the minimum is very close to the median and as such the left whisker would be very short. In contrast, the right whisker will be very long since the maximum is far larger than the median.

3) Since the right whisker is far larger than the left whisker, then we can say the shape of the box and whisker plot is heavily skewed to the right.

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Answer:

a) 28.34 m

Step-by-step explanation:

Finding ∠RQS :

Length of arc RS :

Answer:

See below

Step-by-step explanation:

Use this tool to plot
https://quickmath.com/webMathematica3/quickmath/graphs/inequalities/basic.jsp#form?v2=graph

The results are shown in the accompanying screenshots

The equation of a line that is passing through the points (0, 4) and (1, 6) will be y = 2x + 4.

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

A coordinate plane. The x-axis and y-axis are each scaled by one.

A graph of a line goes through the points (0, 4) and (1, 6) will be

The equation of a line that is passing through the points (0, 4) and (1, 6) will be

y - 4 = [6 - 4 / 1 - 0] (x - 0)

y - 4 = 2x

    y = 2x + 4

The graph is given below.

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Answer:y=x-5

Step-by-step explanation:

khan academy