The base of a triangle is twelve more than twice its height. If the area of the triangle is 43 square centimeters, find its base and height.

The value of the definite integral [tex]\int\limits^{10}_5 {g(x)} \, dx = 18[/tex]

The question has to do with definite integrals

Definite integrals are integrals obtained within a range of values (or limits) of the independent variable.

Given that

For any integral  [tex]\int\limits^a_c {g(x)} \, dx = \int\limits^a_b {g(x)} \, dx + \int\limits^b_c {g(x)} \, dx[/tex]

So,  [tex]\int\limits^{10}_3 {g(x)} \, dx = \int\limits^5_3 {g(x)} \, dx + \int\limits^{10}_5 {g(x)} \, dx[/tex]

So,   [tex]\int\limits^{10}_5 {g(x)} \, dx = \int\limits^{10}_3 {g(x)} \, dx - \int\limits^5_3 {g(x)} \, dx[/tex]

Since

Substituting the values of the variables into the equation, we have

[tex]\int\limits^{10}_5 {g(x)} \, dx = \int\limits^{10}_3 {g(x)} \, dx - \int\limits^5_3 {g(x)} \, dx[/tex]

[tex]\int\limits^{10}_5 {g(x)} \, dx = 36 - 18 \\\int\limits^{10}_5 {g(x)} \, dx = 18[/tex]

So, the value of the definite integral [tex]\int\limits^{10}_5 {g(x)} \, dx = 18[/tex]

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To get system B, the second equation in system A was replaced by the sum of that equation and the first equation multiplied by -3. The solution of system B will be the same as the solution of system A.

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

System A:

x + 6y = 5 and; 3x - 7y = -35

To get system B, the second equation in system A was replaced by the sum of that equation and the first equation multiplied by -3.

System B:

x + 6y = 5 and; - 25y = -50

The solution of system B will be the same as the solution of system A.

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The value of angle TUS based on the information given about the circle will be 49°.

It should be noted that a circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.

Equivalently, a circle is the curve traced out by a point that moves in a plane so that its distance from a given point is constant.

The radius is the line segment extending from the center of a circle or sphere to the circumference or bounding surface.

Here, the value of TUS will be:

= 1/2 × TRS

= 1/2 × 98°

= 49°

In conclusion, the correct option is 49°.

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Complete question:

Circle R has a radius of 6 inches. Points S, T, and U lie on circle R, clockwise in alphabetical order. If m∠TRS = 98°, what is m∠TUS?

Distribute the summation over the sum.

[tex]\displaystyle \sum_{i=1}^{101} (-5a_i - 12b_i) = -5 \sum_{i=1}^{101} a_i - 12 \sum_{i=1}^{101} b_i[/tex]

Now plug in the known sums and simplify.

[tex]\displaystyle \sum_{i=1}^{101} (-5a_i - 12b_i) = -5(-12) - 12(-19) = \boxed{288}[/tex]

Answer:

17 & 26

Step-by-step explanation:

The equation

[tex]x+(x+9)=43\\2x+9=43[/tex]

[tex]2x=43-9\\2x=34[/tex]

[tex]x=34/2=17[/tex]

One number is 17

The other number is:

[tex]x+9=17+9=26[/tex]

Hope this helps

Using simple interest, it is found that the APR is of 4.472%.

Simple interest is used when there is a single compounding per time period.

The amount of money after t years in is modeled by:

[tex]A(t) = A(0)(1 + rt)[/tex]

In which:

The parameters are given as follows:

A(t) = 6 x 511.18 = 3067.08, A(0) = 3000, t = 0.5.

Hence the APR is found as follows:

[tex]A(t) = A(0)(1 + rt)[/tex]

[tex]3067.08 = 3000(1 + 0.5r)[/tex]

[tex]1 + 0.5r = \frac{3067.08}{3000}[/tex]

1 + 0.5r = 1.02236

r = (1.02236 - 1)/0.5

r = 0.04472.

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Step-by-step explanation:

the equation of a circle centered at the origin is

x² + y² = r²

r being the radius (the distance of the center to every point on the circle's arc).

so, we get a point on the arc : (0, -5).

what is its distance to the origin ?

the origin is (0, 0).

we see, both points have the same x coordinates. they are therefore on the same vertical line going through x=0.

that means there is no distance between them in x direction.

the only distance is in y direction : 0 to -5.

a distance is always positive (no matter in what direction).

so, the distance from 0 to -5 is : 5 units.

that means r = 5.

and our equation is

x² + y² = 5² = 25

Answer:

[tex]\frac{16}{32}[/tex]

Step-by-step explanation:

given

[tex]\frac{1}{2}[/tex] ← multiply numerator and denominator by 16 (2 × 16 = 32 )

= [tex]\frac{16}{32}[/tex]

Answer:

Step-by-step explanation:

x is the number of students

(x+5) is the number of students and chaperons

$2.50·(x+5) is the amount of money the number of students and chaperons will pay for the trip, and that number should be less or equal than $90 because those are all the money they have

2.50(x+5) ≤ 90 which is the same as 90 ≥ 2.50(x+5)

The inequality "90 greater-than 2.50 (x + 5) "

90 > 2.50(x+5) is an error becase it excludes the possibility that the trip can cost exact $90 so we need not just greater than > , yet greater and equal than ≥ sign

90 ≥ 2.50(x+5)

The scaled copy of the polygon is added as an attachment

The complete question is added as an attachment

The coordinates of the polygon are

A = (-7, 6)

B = (-10, 8)

C = (-10, 10)

D = (-6, 10)

The scale factor is 3.

So, the rule of dilation is

(x, y) = (3x, 3y)

Using the above rule, we have:

A' = (-21, 18)

B' = (-30, 24)

C' = (-30, 30)

D' = (-18, 30)

See attachment for the scaled copy of the polygon

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Using proportions, it is found that a force of 22 lb stretches the spring 18 inches.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

The measures are direct proportional, hence the rule of three is:

11 lb - 9 inches

22 lb - n inches

Applying cross multiplication:

11n = 9 x 22

n = 9 x 2

n = 18 inches.

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Answer:

slope is -1

Step-by-step explanation:

Slope of the line is changes in y over changes in x. It can also be referred as rise over run.

We can express mathematically as:

[tex]\displaystyle{m=\dfrac{y_2-y_1}{x_2-x_1}}[/tex]

where m is slope.

Let (-2,5) be [tex]\displaystyle{(x_2,y_2)}[/tex] and (6,-3) be [tex]\displaystyle{(x_1,y_1)}[/tex]. Hence, apply the slope formula:

[tex]\displaystyle{m=\dfrac{5-(-3)}{-2-6}}\\\\\displaystyle{m=\dfrac{5+3}{-8}}\\\\\displaystyle{m=\dfrac{8}{-8}}\\\\\displaystyle{m=-1}[/tex]

Therefore, the slope is -1

Answer:

7 14/45

Step-by-step explanation:

9 1/9 - 1 4/5

82/9 - 9/5

410/45 - 81/45

329/45

7 14/45

Answer:

●7.31

please mark as brainliest

Answer:

a) [tex]f(x) = x + 3[/tex]

b) [tex]f(x) = -x - 5[/tex]

c) [tex]f(x) = 2x + 6[/tex]

Step-by-step explanation:

To determine the equation of a straight line, we need two things:

1. two known points (coordinates) on the line, used to calculate the gradient

2. the y-intercept of the line (the y-coordinate of the point at which the line crosses the y-axis)

Then we can use the equation:

[tex]\boxed {f(x) = ax + q}[/tex]

where a is the gradient and q is the y-intercept, to determine the equation of the line.

a) known points: (0, 3), (-4, -1)

y-intercept: 3

gradient = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]

             ⇒ [tex]\frac{3 - (-1)}{0 - (-4)}[/tex]

             ⇒ [tex]\bf 1[/tex]

∴ a = 1 , q = 3

∴ equation:

[tex]{f(x) = ax + q}[/tex]

[tex]f(x) = 1x + 3[/tex]

⇒ [tex]\bf f(x) = x + 3[/tex]

b) known points: (-7, 2) , (0, -5)

y-intercept = -5

gradient = [tex]\frac{2 - (-5)}{-7 - 0}[/tex]

             ⇒ [tex]\bf -1[/tex]

∴ equation:

[tex]f(x) = -1x + (-5)[/tex]

⇒ [tex]\bf f(x) = -x - 5[/tex]

c) known points: (-3, 0), (0, 6)

y-intercept = 6

gradient = [tex]\frac{6 - 0}{0 - (-3)}[/tex]

             ⇒ [tex]\bf 2[/tex]

∴ equation:

[tex]\bf f(x) = 2x + 6[/tex]

These are the laws of indices. You just have to memorise it, sorry : (

Hope it helps : )

The explicit formula for this  geometric sequence 81, 27, 9, 3, … is aₙ = 81(1/3)ⁿ⁻¹. It has common ratio of 1/3 and first term of 81.

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

A geometric sequence is in the form aₙ = ar⁽ⁿ⁻¹⁾, where a is the first term and r is the common ratio.

The geometric sequence 81, 27, 9, 3, … has common ratio:

r = 27/81 = 1/3

The explicit formula for this  geometric sequence 81, 27, 9, 3, … is aₙ = 81(1/3)ⁿ⁻¹. It has common ratio of 1/3 and first term of 81.

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Answer:

its -14

Step-by-step explanation:

Answer:

[tex]R^{-1}[/tex]={(2,1), (3,2), (9,3), (5,4)}

Step-by-step explanation:

Solution Given:

To find the inverse we need to exchange Domain to Range and vice-versa.

so

[tex]R^{-1}[/tex]={(2,1), (3,2), (9,3), (5,4)}

The experiment is not a binomial experiment.

A binomial experiment is an experiment where there is a fixed number of trials, and the results are usually between two options- a yes or a no.

The conditions for a binomial experiment include:

1. Each trial should be classified either as a success or a failure.

2. There are a fixed number of observations

3. The trials are independent.

4. The number of trials are fixed.

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Using the normal distribution, the probability that x is of at most 40, represented by option B, is given as follows:

[tex]P(X \leq 40) = 0.1587[/tex]

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation of the distribution are given, respectively, by:

[tex]\mu = 51, \sigma = 11[/tex]

The probability that x is of at most 40 is the p-value of Z when X = 40, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{40 - 51}{11}[/tex]

Z = -1

Z = -1 has a p-value of 0.1587.

Hence the probability is:

[tex]P(X \leq 40) = 0.1587[/tex]

Which is the part to the left of X = 40 of the distribution, hence option B is correct.

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Answer:

c

Step-by-step explanation:

because I had a test on these

Answer:

√2² cannot be answer yesah

The given expression is undefined when x = 5 OR x = -5

From the question, we are to determine the value of x for which the given expression is undefined

The given expression is

x-4/3x²-75

An expression is undefined when the denominator equals zero

Thus, the expression is undefined when

3x² - 75 = 0

Now, we will determine the values of x in the equation above

3x² - 75 = 0

3x²  = 75

x² = 75/3

x² = 25

x = ±√25

x = ±5

Hence, the given expression is undefined when x = 5 OR x = -5

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66.90% of the total bankruptcy fillings are not chapter 13 fillings.

What is bankruptcy?

This is a situation where the management of a company declares that it could no longer pay its debt obligations as it does have the cash resources to do so.

In this case, the total number of bankruptcy fillings is 936,795, out of which 310,061 are chapter 13 filings

fillings that were not chapter 13=936,795-310,061

fillings that were not chapter 13=626,734

fillings that were not chapter 13 as % of total fillings=626,734/936,795

fillings that were not chapter 13 as % of total fillings=66.90%

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Answer:

220

Step-by-step explanation :

11 = 5%

100 ÷ 5 = 20

11 × 20 = 220

0.05 × 220 = 11 ✓

0.05 = decimal multiplier of 5%

electronic data interchange

Answer:

it's answer came 20000o