In right triangle ABC, point D is on side BC, as shown. If BC= 5 x BD and the area of Triangle ABD is 8 in2, what is the area of Triangle ABC?

Answer:

51/3

Step-by-step explanation:

Angles opposite congruent sides of a triangle are congruent.

[tex]x+17=4x-34 \\ \\ 17=3x-34 \\ \\ 51=3x \\ \\ x=51/3[/tex]

The linear function that gives a(t), the dollar amount in the account t months after she starts withdrawing money is [tex]a(t)=785000-3875t[/tex]

The money in the account 80 months after she starts withdrawing money is [tex]a(80) & =\$ 475000\end{aligned}$$[/tex]

The amount of money she withdraw in 40 months

[tex]& \Rightarrow \$(785000-630000) \\& =\$ 155000\end{aligned}$$[/tex]

She withdraw money per month at constant rate

[tex]=\frac{155000}{40}$$[/tex]

The amount of money a(t) in t months.

[tex]a(t)=785000-\frac{155000 t}{40}$$[/tex]

[tex]a(t)=785000-3875t[/tex]

Therefore the linear function that gives a(t), the dollar amount in the account t months after she starts withdrawing money is [tex]a(t)=785000-3875t[/tex]

(b) The money in the account after 80 months.

[tex]$$\begin{aligned}a(80) & =785000-3875(80) \\& =785000-310000 \\a(80) & =\$ 475000\end{aligned}$$[/tex]

Therefore the money in the account 80 months after she starts withdrawing money is [tex]a(80) & =\$ 475000\end{aligned}$$[/tex]

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Answer:

2

Step-by-step explanation:

This question is asking about the multiplication rule of exponents. When you multiply two exponents of the same base, the exponents add. With the parameters x=4, y=6, and z=8, the first one is true because 2+4=6. The third one is true because 6+6=12. The second one isn't true because 6+8=14, not 4.

The explicit formula for the given arithmetic sequence is aₙ = 23 + (n - 1)11. Here the first term is a1 = 23 and the common difference is d = 11.

The explicit formula for an arithmetic sequence gives the nth term of the sequence. I.e.,

aₙ = a1 + (n - 1)d

Here a1 is the first term; d is a common difference, it is calculated by

d = aₙ₊₁ - aₙ = aₙ₋₁ - aₙ

The given sequence is 23, 34, 45, 56,...

Here the first term a1 = 23

So, the common difference between the terms in the sequence is

d = 34 - 23 = 11

Then, the explicit formula for the given sequence is

aₙ = a1 + (n - 1)d

⇒ aₙ = 23 + (n - 1)11

Therefore, the nth term of the explicit formula for the given arithmetic sequence is aₙ = 23 + (n - 1)11.

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Answer:

yes seems like you understand

Answer:

yes

Step-by-step explanation:

yes

The equation written in slope-intercept form is y = -(3/4)x +2.

The slope-intercept form of a line is y = mx +c where m is the slope of the line and c is the y-intercept.

The given inequality is y < -3/4x + 2

Rewrite the inequality as an equation in slope-intercept form:

y < (-3/4)x + 2

y = (-3/4)x + 2

Where m = -3/4 and b = 2

Hence, the equation written in slope-intercept form is y = -(3/4)x +2.

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If the initial population of a town is 100,231 and it grows with a doubling time of 98 years, the population after 31 years is  124803

The initial population of the town = 100231 people

The doubling time = 98 years

We have to find the population in 31 year

The exponential function will be

f(t) = fo(2)^(t/98)

f(t) is the population of the town in t years

fo is the population of the town in t = 0 years

t is the number of years

2 because it doubling time

The value of t = 31 years

Substitute the values in the function

f(31) = 100231×(2)^(31/98)

Do the arithmetic operations

f(31) = 100231 × 1.245

f(31) = 124803.23

f(31) ≈ 124803

Therefore, the population after 31 years is 124803

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Answer:

Step-by-step explanation:

m% = m/100

what = a variable ... "x". for example.

"is" means "="

"of" means multiply

n = (m/100)•x

Answer:

attached is the graph and other data

Step-by-step explanation:

Answer:

Federal Reserve banks

Step-by-step explanation:

Hope it helps!

Answer:

x=826

Step-by-step explanation:

If one quarter of the Texas Guff coast is national seashore or state park  at the given figures, the length of the Texas shoreline is 0.8835km

The length is the measure of how long the shoreline is.

The given parameters sare

mileage of the seashore = 372 miles

Advancement of 0.0095 miles per year.

1/4 taken as gulf coast

Applying these parameters we have

372*0.0095*1/4*12

⇒ 96.102 miles

= 96.102/1000 = 0.96102 km

1000 miles = 1km

Therefore divide the value by 1000 to get

Therefore the length is 0.96102km

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Answer:

24i√3

Step-by-step explanation:

simplify the radical by breaking the radicand up into a product of known factors, assuming positive real numbers.

I tried.

The account statement for Account B is incorrect.

What is simple rate of interest?

Simple rate of interest is a type of interest calculation where interest is calculated only on the principal amount of a loan. Simple interest is calculated periodically, usually monthly or annually, as a fixed percentage of the principal. It is different from compound interest, which applies interest to both the principal and the accumulated interest. It is simpler to calculate than compound interest, and is generally used for short-term loans.

Given: Account A: $100, 3.4% and Account B: $300, 1.8%

We know, Simple Interest = Principal × Rate × Time

Interest for Account B = $300 × 1.8%

                                     = $5.40

The bank statement after one year should be $5.40 instead of $540.00.

Hence, Account B's statement is incorrect.

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Answer:

m =  7cm

Step-by-step explanation:

Perimeter of a triangle is all the sides added up, so a+ b + c.

Given that a= 6 and b= 6, that's 12cm together. So just subtract the perimeter 19cm by 12cm to get your answer of 7cm.

Answer:

Step-by-step explanation:

7 1+1

8 2+2

9 4+4

10 1+1+2+2+4+4=69

The basic unit of length in the metric system is the meter. All units of length in the metric system are derived from the meter.

Length of the car is 12 inches equal to 192 feet.

Given ,

3 inches : 4 feet

3 inches : 4*12

3 inches :48

1 inches : 16 feet

Length of the car is 12 inches = 12 * 16

Length of the car is 12 inches = 192 feet

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Answer:

option a is correct i.e 6.25 = 25/4

Step-by-step explanation:

= 6.25

= 625 / 100

both being divisible by 5

we get

= 25/4

we know ,

the probability=no of repeated value/total number

factorial of 3 and 2

and factorial of total number

=3ḷ×2ḷ/7ḷ

=3×2×1×2×1/7×6×5×4×3×2×1

=1/7×5×4×3

=1/420

=0.23809

or

=0.238

what is Probability?

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means.

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Since, Both the numbers used for the difference calculation are whole numbers, The answer is B) The difference is a whole number.

Both rational and irrational numbers are considered to be real numbers. Real numbers include all rational and irrational numbers, including integers (-2, 0, 1) and fractions (1/2, 2.5).

Whole numbers are natural numbers including zero with it.

56 is a whole number

34 is a whole number

the difference, 56-34 = 22 is also a whole number.

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Answer:

The area of the circle is 30.25π cm^2.

Step-by-step explanation:

The circumference of a circle is equal to the diameter of the circle times π. Therefore, if the circumference of the circle is 11π cm, the diameter must be 11 cm.

The formula for the area of a circle is A = πr^2, where r is the radius of the circle. The radius of the circle is half the diameter, so the radius is (1/2) * 11 cm = 5.5 cm.

Substituting this value for r into the formula for the area of a circle, we get:

A = π * (5.5 cm)^2

= π * 30.25 cm^2

= 30.25π cm^2

Therefore, the area of the circle is 30.25π cm^2.

Step-by-step explanation:

you do understand that the diameter of a circle is simply 2 times the radius, yes ?

imagine a circle and you draw a radius line (from the center of the circle to the circle arc).

and now imagine to draw another radius line, just in the opposite direction.

when you look at the result, you have 1 straight line going from the circle arc to the circle arc and passing through the center of the circle. that is what a diameter is.

how long is it ? well, we drew 2 radius lines to create this line. so, it is 2×radius long.

so, the diameter of the seal is

2×2 = 4 yards

Assuming timmy completes all chores, the number of dollars timmy will have 7 weeks after his birthday is 85 dollars.

In mathematics, an equation is a claim that two expressions are equivalent. It is a mathematical expression that employs the equals symbol, "=", to indicate that two quantities have values that are equal. Problems in algebra, geometry, calculus, and other branches of mathematics are frequently solved using equations. In algebra, equations are frequently used to depict the connection between variables and constants, as well as to discover the value of an unknown variable. For example, the equation x + 2 = 5 may be utilised to get the value of x, which is 3. Equations can be linear, quadratic, or higher-degree, and they can involve multiple variables.

How to solve?

Let x be the number of weeks after Timmy's birthday.

The total number of dollars Timmy will have after x weeks is 50 + 5x.

Therefore, Timmy will have 50 + 5(7) =85 dollars after 7 weeks

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The  718.85 < x  inequality says that : He must print 719 photos or more.

Given,

In the question:

Rick bought a photo printer and supplies for $186. 90, which will allow him to print photos for $0. 29 each.

and, A photo store charges $0. 55 to print each photo.

To find the how many photos must Rick print before his total cost is less than getting prints made at the photo store?

Now, According to the question:

Let the photos be x

Rick bought a photo printer be $186.90

A photo store charges $0. 55 to print each photo.

The question is based on inequality:

Photo Printer <  photo store

1.86.90 + 0.29x <  0.55x

            - 0.29x     - 0.29x

______________________

 1.86.90    < 0.26x

Divide by 0.26x on both sides

= 718.85 < x

Hence, The  718.85 < x  inequality says that : He must print 719 photos or more.

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If Lillian has a rectangular garden with an area of 10x² +33x – 7 square feet.The expressions that would represent the length and width of the garden will be (5x-1)(2x+7)

It is defined as the combination of constants and variables with mathematical operators.

It is given that, Lillian has a rectangular garden with an area of 10x² +33x – 7 square feet.

We have to find the expression representing the length and width of the garden.

[tex]=10x^2+33x-7 \\\\ =\left(10x^2-2x\right)+\left(35x-7\right) \\\\ =2x\left(5x-1\right)+7\left(5x-1\right)\\\\ =\left(5x-1\right)\left(2x+7\right)[/tex]

The area of the rectangular garden is,

A = L × B

Comparing the expression with the obtained expression we get the expressions that would represent the length and width of the garden as,

A= (5x-1)(2x+7)

Thus, if Lillian has a rectangular garden with an area of 10x² +33x – 7 square feet. The expressions that would represent the length and width of the garden will be (5x-1)(2x+7)

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Answer:

  60°

Step-by-step explanation:

You want the measure of angle 1 in the given diagram.

Transversal TR creates corresponding angles 1 and 5, so those are congruent.

It is given that angles 4 and 5 are congruent.

Transversal SE creates alternate interior angles 2 and 4, so those are congruent.

Angle bisector SE creates angles 2 and 3 congruent.

Now we have ∠1≅∠5≅∠4≅∠2≅∠3.

Hence all of the angles are congruent to each other, and angle 1 is 1/3 of 180°.

  m∠1 = 60°

Answer:

D

Step-by-step explanation:

the numerator of the exponent is the exponent of x

the denominator is the the index of the root

The value of x=10 is y=4 if y=8 if x=20.

Mathematical expressions can be used to depict situations or issues, and algebra is the field of mathematics that does this. For a mathematical expression to have meaning, it needs to include variables like x, y, and z as well as mathematical operations like addition, subtraction, multiplication, and division. Mathematics has several different subfields, including algebra. Algebra is the study of mathematical symbols and the rules for using them in formulas; it is a common thread that runs through practically all of mathematics. It is also used to name specific types of algebraic structures, such as an algebra over a field, which is frequently referred to as an algebra. The word algebra is used to name both a mathematical field and some of its subfields.

When x=20, y=8

The value of y is 0.4 times of x.

y=0.4×20

y=8

So, when x=10

y=0.4×10

y=4

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Answer:

Yes

Step-by-step explanation:

Every input has only one output.