A famous painting was purchased for $560,000 in the year 2021. The value has been increasing by $8,000 per year.

By SSS congruency criteria ΔABC ≅ ΔDEF

Two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other.

The given vertices of the triangles are;

ΔABC: A(−4, −3), B(0, 0), C(2, −3)

ΔDEF:  D(3, 1), E(6, -3), F(3, −5)

The lengths of the sides of ΔABC are

AB = √((0+4)² + (0+3)²) = √25 = 5

BC = √((2-0)² + (-3 - 0)²) = √13  

AC = √((2+4)² + (-3 +3)²) = √36 = 6

The lengths of the sides of ΔDEF are;

DE = √25=5

EF = √13

DF = √36 = 6

As,

AB= DE, BC = EF , AC= DF

So, By SSS congruency criteria ΔABC ≅ ΔDEF

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Using the line of best-fit, it is found that:

To find the equation, we need to insert the points (x,y) in the calculator.

In this problem, the points are:

(0,0), (1,2), (2,6).

Hence, using a calculator, the estimate for the battery after x minutes is given as follows:

y = 3x - 0.333.

50% power is obtained when y = 50, hence:

50 = 3x - 0.333

x = 50.333/3

x = 16.8 minutes.

90% power is obtained when y = 90, hence:

90 = 3x - 0.333

x = 90.333/3

x = 30.1 minutes.

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Answer:

C

Step-by-step explanation:

When the run part (the difference between x-coordinates of the two points on the line) is 1, the slope is an integer.

Answer:

The choice D.

Step-by-step explanation:

[tex]f(x) = {( \frac{1}{6} })^{x} \\ \\ f(3) = {( \frac{1}{6} })^{3} = \frac{ ({1})^{3} }{( {6})^{3} } = \frac{1}{216} [/tex]

Answer:

3/8=15/40

Step-by-step explanation:

Multiply both the numerator and the denominator of the first term by 5 and you'll see that it's the same fraction.

Answer: [tex]55^{\circ}[/tex]

Step-by-step explanation:

The measure of the third unknown arc is

[tex]360^{\circ}-70^{\circ}-110^{\circ}=180^{\circ}[/tex].

So, [tex]x=\frac{180^{\circ}-70^{\circ}}{2}=\boxed{55^{\circ}}[/tex]

Answer:

D. g(x) = 5x^2

Step-by-step explanation:

Answer:

D.

Step-by-step explanation:

A point of the function g(x) is known: (1, 5)

The proper function is

[tex]g(x)=5x^{2}[/tex]

Demonstration calculating g(1)

[tex]g(1)=5(1)^{2} =5(1)=5[/tex]

The point (1, 5 ) belongs to this function

Hope this helps

Answer:

_ t&byds

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a) The speed of the boat is 3/5 ft/sec

b) The rate at which the angle changes is 8/125 rad/sec

A right angled triangle is a type of the triangle with one of its angles 90°.

The longest side of the triangle is called the hypotenuse which is the side that faces the right angle. other sides are called the adjacent sides.

Analysis:

The analysis is in the attached file below.

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The equation that results from completing the square in the following equation. x^2−20x+75=0 is (x+2)^2 = 10

The method "completing the squares", as per the name suggests, try to make the quadratic equation of the form such that the x variable is totally covered in single squared term, as the square of a linear expression in x.

GIven;

x^2−20x+75=0

Subtract 75 from each side

x^2−20x+75 - 75 = -75

Take the coefficient of x

20

Divide by 2

10

Square it

100

Add it to each side

x^2 +5x + 100 = -75 + 100

(x+2)^2 = 10

Take the square root of each side

x+2 = 10

x = 8

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The average rate of change within the function f(x)=[tex]x^{2} -x-1[/tex]is -2.

Given The function f(x)=[tex]x^{2} -x-1[/tex]

We have to search out the typical rate of change of function within the interval (-2,1).Interval is largely a variety between numbers lying on the quantity line which may be a line on which different numbers are plotted.

We know that average rate of change =f(b)-f(a)/(b-a)

we have to first know the values of function at different values of x.

f(x)=[tex]x^{2} -x-1[/tex]

f(1)=1-1-1

=-1

f(-2)=4+2-1

=5

b=-2

a=1

put within the formula:

A=-1-5/1+2

=-6/3

=-2

Hence average rate of change of the function within the interval (-2,1) is -2.

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Answer: 7 and 17

Step-by-step explanation:

Since the area of a rectangle is the product of the two sides, the product of these two numbers must be 119.

The factors pairs of 119 are 1 and 119, and 7 and 17.

x+7 and x-3 have a difference of 10. The difference of 7 and 17 is also 10. Hope this helped!

In the future, please take a less blurry photo because I had to guess the part where I think it said x-3.

Answer: The graph of G(x) is the graph of F(x) compressed vertically.

Step-by-step explanation:

See attached image.

The trigonometric form of the complex number 1 + 3i is 3.16[cos(71.57)° + isin(71.57°)]

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

Complex number is in the form z = a + bi, where a, b are real numbers.

Given the complex number z = 1 + 3i

In polar form: r = √(1² + 3²) = 3.16

Ф = tan⁻¹ (3/1) = 71.57⁰

The trigonometric form of the complex number 1 + 3i is 3.16[cos(71.57)° + isin(71.57°)]

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Answer:

10.3. and One solution

Step-by-step explanation:

I had this question, tho it might be different

Inequalities help us to compare two unequal expressions. The solution that will make the value of the function r(x) less than equal to 0 is [3,∞).

Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed.

It is mostly denoted by the symbol <, >, ≤, and ≥.

To find the value of x that will make the function r(x)=x-4x+9 less than or equal to 0 solve the inequality,

x - 4x + 9 ≤ 0

x - 4x ≤ -9

-3x ≤ -9

x ≥ (-9)(-3)

x ≥ 3

Hence, the solution that will make the value of the function r(x) less than equal to 0 is [3,∞).

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f.g and its domain is 24x²-36x-24; all real numbers.

Given, f(x) = 3x - 6; g(x) = 8x +4.

We need to find the value of f.g

The domain of a function; In mathematics, the domain of a function is the set of inputs accepted by the function.

Now, (f.g)(x)=(3x-6)(8x+4)

=24x²-48x+12x-24

=24x²-36x-24

Therefore, f.g and its domain is 24x²-36x-24; all real numbers.

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[tex]\bf{-8x+4\leq 36 }[/tex]

Subtract 4 from both sides.

[tex]\bf{-8x\leq 36-4 }[/tex]

Subtract 4 from 36 to get 32.

[tex]\bf{-8x\leq 32 }[/tex]

Divide both sides by −8. Since −8 is <0, the inequality direction is changed.

[tex]\bf{x\geq \dfrac{32}{-8} }[/tex]

Divide 32 by −8 to get −4.

[tex]\bf{x\geq -4 \ \ \Rightarrow \ \ \ Answer }[/tex]

Question :

Solution :

⇒ -8x + 4 ≤ 36

⇒ -8x ≤ 36 - 4

⇒ -8x ≤ 32

⇒ -x ≤ 32 / 8

⇒ -x ≤ 16 / 4

⇒ -x ≤ 8 / 2

⇒ -x ≤ 4

⇒ x ≥ -4

Answer:

f(5) = 45

Step-by-step explanation:

If f(x) = 2x²-5 , f(5) =

f(5) = 2(5)² - 5

f(5) = 2(25) - 5

f(5) = 50 - 5

f(5) = 45

Pooling can be referred to the process of how an insurance company can pay a large benefit even if it hasn't collected that amount from an individual's or company premium in this type of context.

This is referred to as a type of protection against financial loss or other forms of incidents or risks and there are different types which cater for different purpose or reasons and they include life, vehicle insurance etc. The insurance plan is usually sold by designated insurance companies and are accessible to the public.

Pooling is the process which involves the smaller firms purchasing better interest rates which helps to lessen the cost of coverage. This also ensures that benefits are paid at the right time so as to avoid hassle and other forms of issues which may arise from this important process.

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Answer:

We first need to know the graph of the basic function belonging to the trigonometric family, which is sin x.

Now we need to apply basics of functions to get the graph of y = -sinx from y = sinx

If x is the input in the y = sinx , then sin x will be the output which will be represented on the  y axis. Eg :

If x = pi/2

then output will be y = sin(pi/2) = 1

Hence in the graph of sinx, at x =pi/2 the value of y is 1.

Once we have understood this, we can use the same logic in the case

y = -sinx

If x = pi/2

then output will be y = - sin(pi/2) = -1

Here we can see that the output of y = - sin x will be the exact negative of  of the output of y = sinx

Hence all portions of the graph of  y = sinx in the +y axis will come down to the -y axis for y = -sin x, i.e we will be taking mirror image of the graph along the x axis. Below are the graphs of y=sinx and y= - sinx respectively for your reference:

(image courtesy Microsoft graphic calculator)

The 98% confidence interval of the proportion of all Americans who think that living on their own makes someone feels like an adult is (29.0%, 31.0%)

The given parameters are:

The number of success is then calculated as;

[tex]\bar x = np[/tex]

This gives

[tex]\bar x = 2000 * 28\%[/tex]

Evaluate

[tex]\bar x = 560[/tex]

Hence, 560 successes would be found in the sample of 2000 Americans

The proportion that lives on their own is:

p = 30%

The z-score for 98% confidence interval is

z = 2.326

The confidence interval is calculated as:

[tex]CI = \bar p \pm z * \sqrt{\frac{\bar p(1 - \bar p)}{ n}[/tex]

So, we have:

[tex]CI = 30\% \pm 2.326 * \sqrt{\frac{30\%(1 - 30\%)}{2000}[/tex]

Evaluate

[tex]CI = 30\% \pm 1\%[/tex]

Expand

CI = (30% - 1%, 30% + 1%)

Evaluate

CI = (29%, 31%)

Hence, the 98% confidence interval is (29.0%, 31.0%)

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The domain of the function g(x)=l2xl +2 is all real numbers and the range is from (0,∞).

Given g(x)= l2xl +2

First of all we know that modulas gives two values for x<0 and x>=0.

The function g(x) if opened gives two values.

for x>=0 g(x)=2x+2

for x<0 g(x)=-2x+2

because we have not told about the description about x so we can put any value in the function.

So the domain is all real numbers.

Now when we take g(x)=2x+2 for x>=0

putting x=0 we get 2 and rest are positive values so the value of g(x) keeps increasing as we increase the value of x. So here range is [2,∞).

Now take g(x)=-2x+2 for x<0

putting smallest number starting from zero but not 0 we will get a number near to 0 but not zero and because when a negative number multiplies with -2 it becomes positive and increase the value of g(x) so here the range becomes (0,∞).

When we talk about overall range it will be [2,∞) ∪(0,∞)

it will be (0,∞).

Hence the domain of the function g(x) is all real numbers and range is from 0 to infinity.

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Answer:

1. 1/27 2. 1/16

Step-by-step explanation:

First can be rewritten as (1/9)^(1/2 * 3) and anything to the power of 1/2 is a sqrt. So it is sqrt(1/9)^3. Then (1/3)^3 which is 1/27

Second, the negative bring the number to the bottom, 1/(32)^4/5. Then can be written as [tex]\sqrt[5]{1/32}[/tex]^4. 5th root of 1/32 is 1/2 then 1/2^4 is 1/16

Answer:

260 cm^2

Step-by-step explanation:

The area of a parallelogram is calculated by multiplying its height and base:

The base for this parallelogram is given as 20 and the height is 13

13*20 = 260

The area is stated in square units so the answer is 260 cm^2

Answer:

Step-by-step explanation:

The Compositions of Reflections Over Intersecting Lines Theorem states that if we perform a composition of two reflections over two lines that intersect, the result is equivalent to a single rotation transformation of the original object.

hope it helps! (✿◠‿◠)

The result concluded is equivalent to a single rotation transformation of the original object.

When a graph is reflected along an axis, say x-axis, then that leads the graph to go just on the opposite side of the axis as if we're seeing it in a mirror.

The Compositions of Reflections Over Intersecting Lines states that if we perform a composition of two reflections over two lines that intersect.

The result concluded is equivalent to a single rotation transformation of the original object.

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The system of equations is:

x = 2y

x*$10 + y*8 = $84

Solving it, we see that he worked 3 hours landscaping and 6 hours washing cars.

First, we need to define the variables:

We know that Alexander worked twice as many hours washing cars as he worked hours landscaping, then:

x = 2y

We also know that he earned a total of $84, then:

x*$10 + y*8 = $84

So the system of equations is:

x = 2y

x*$10 + y*8 = $84

To solve it, we just replace the first equation into the second one:

(2y)*$10 + y*8 = $84

y*$28 = $84

y = $84/$28 = 3

So He worked 3 hours landscaping, and:

x = 2*y = 2*3 = 6

6 hours washing cars.

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