Unit 3 Lesson 8 Cumulative Practice Problems
1. This is an invalid proof that all isosceles triangles are similar. Explain which step is
invalid and why.
1. Draw 2 isosceles triangles ABC and DEF where AC = BC and DF = EF.
2. Dilate triangle ABC to a new triangle A'B'C using center C and scale factor de so
that A'C = B'C = DF = EF.
3. Translate by directed line segment CF to take A'B'C to a new triangle A"B" F.
Since translation preserves distance, A" F = A'C= DF and B" F = BC = EF.
4. Since A" F = DF, we can rotate using center F to take A" to D.
5. Since B" F = EF, we can rotate using center F to take B" to E.
6. We have now established a sequence of dilations, translations, and rotations that
takes A to D, B to E, and C to F, so the triangles are similar. ​

The answer to this Question based on Compound Interest is 1690.2$

What is Compound Interest?

Compound interest is a type of interest that is calculated not only on the initial principal but also on the accumulated interest of previous periods. It is the result of reinvesting interest, rather than paying it out, so that interest in the next period is then earned on the principal plus previously accumulated interest. It is the concept of earning interest on interest, which causes the total balance to grow at a faster rate than simple interest. Compound interest is often referred to as the eighth wonder of the world, as it is a powerful financial concept that can yield impressive results over a long period.

Initial money deposited = 900$
1$ turns into 1.878$ after 12 years of Compound Interest
hence by basic manipulation we can do like
900$ turns  into 900 multiplied by 1.878 which comes out to b 1690$
Hence after 12 years final amount will be 1690$

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The measures of the angles are v = 80°, y = 100°, w = 45°, and x = 55°.

An inscribed four-sided polygon in a circle is known as a cyclic quadrilateral. With the specified side lengths, it has the largest area feasible.

Given the quadrilateral inside a circle.

The angle v is given by:

45° +v + 55°=180°

v + 100° = 180°

v = 180° - 100°

v = 80°

Since the quadrilateral is cyclic, the sum of its opposite angle is 180°.

Therefore,

y + v = 180°

y + 80° = 180°

y = 100°

Using the property of cyclic quadrilateral, it follows:

w = 45° and x = 55°

Hence, the measures of the angles are v = 80°, y = 100°, w = 45°, and x = 55°.

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The no: of textbooks Guillermo bought is 7

Issue with the internal transfer concept Sum questions involve subtracting from one unknown and adding to another, leaving the original total amount unaffected. It's also referred to as the Constant Total idea.

Follow The Problem-Solving Process Step by Step.

Review Old Issues; Write Down What Doesn't Work; "3 Before Me"

Ask open-ended questions, promote grappling, place an emphasis on process over product, and use the techniques yourself!

Let the no: of notebooks be 2

The no: of textbooks are : 3+ (2*2)

=7

Hence, the total no: of books are 7

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Answer:

z = 56

Step-by-step explanation:

I'll assume 1.25/0.06 = z−6 /2.4 is actuallY:  1.25/0.06 = (z−6)/2.4  (and not 1.25/0.06 = z−(6 /2.4)).

1.25/0.06 = (z−6)/2.4

1.25*(2.4) = (z−6)*(0.06)  [Multiply both sides by 0.06 and then 2.4]

  3 =  0.06z - 0.36

3.36 =  0.06z

z = (3.36/0.06)

z = 56

Answer: 196

Step-by-step explanation:

[tex]f(7)=(-7-7)^2 =196[/tex]

The definition of the domain of the function f: {4, 6, 8} ⇒{2, 3} over  {(4, 2), (6, 2), (8, 2)} is given as {4,6,8}, while the range is given as 2.

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Four main categories can be used to classify different sorts of functions. One to one function, many to one function, onto function, one to one and into function—all based on the element. A relation between a domain and range is called a function when each value in the domain only has one value in the range.

Here,

function f : {4, 6, 8} → {2, 3} is defined as {(4, 2), (6, 2), (8, 2)},

domain={4,6,8}

range={2}

The domain of function f : {4, 6, 8} → {2, 3} is defined as {(4, 2), (6, 2), (8, 2)} will be {4,6,8} and range will be {2}.

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Answer:y=-6x-10

Step-by-step explanation:

The slope intercept form is y=mx+b

m=slope

b=y intercept

we can find the slope using the slope formula y2-y1/x2-x1

8-(-4)/-3-(-1)

12/-2

m=-6

substitute in the slope, and one of the points so solve for b

y=-6x+b

-4=-6(-1)+b

-4=6+b

b=-10

y=-6x-10

Answer:

y = -6x - 10

Step-by-step explanation:

(-1, -4), (-3, 8)

(x₁, y₁)  (x₂, y₂)

        y₂ - y₁         8 - (-4)          8 + 4         12

m = ------------ = -------------- = ------------ = ------- = -6

        x₂ - x₁          -3 - (-1)         -3 + 1        -2

y - y₁ = m(x - x₁)

y - (-4) = -6(x - (-1))

y + 4 = -6(x + 1)

y + 4 = -6x - 6

   -4            -4

------------------------

y = -6x - 10

I hope this helps!

Answer:

D

Step-by-step explanation:

It passes through -1 and has a negative gradient

Using the formula of the combination and for the values of 'p' and 'q'. The statement is false.

Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant. You can choose the components of combos in any order.

The formula is:

[tex]C(p,q) = \frac{p!}{q!(p-q)!}[/tex]

p=4 and put q=0 to 4

C(4,2) > C(4,0),C(4,1),C(4,3),C(4,4)

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Answer: The ratio of red marbles to blue marbles is 3:6. This can be written as a fraction as 3/6, which simplifies to 1/2.

Step-by-step explanation:

To find the ratio of two quantities, you can divide the number of one type of item by the number of another type of item. In this case, the ratio of red marbles to blue marbles is 3 marbles / 6 marbles, which simplifies to 1/2.

It's important to note that a ratio is not the same thing as a percentage or a fraction. A ratio is a comparison of two quantities, while a percentage is a measure of a quantity relative to the total amount and a fraction is a division of one number by another.

Answer: 35

Step-by-step explanation:

Using the trapezoid midsegment theorem,

[tex]\frac{13+q}{2}=24\\\\13+q=48\\\\q=35[/tex]

The evaluation of the given expression 9/g + 2h + 5 when g = 3 and h = 6 gives the result 20

9/g + 2h + 5

When,

g = 3

h = 6

Substitute the value of g and h into the expression

9/g + 2h + 5

= 9/3 + 2(6) + 5

= 3 + 12 + 5

= 20

Therefore, the expression 9/g + 2h + 5 when evaluated gives the result 20

Complete question:

Evaluate 9/g + 2h + 5 when g = 3 and h = 6

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The percentage markdown only affects the price of the baseball bat, not the price of the baseball. Therefore, the price of a baseball will remain the same at $12.

One technique to express a number as a fraction of 100 is through the use of percentage. It is typically used to denote a percentage or share of a larger whole, and it is frequently written with the sign "%." For instance, a student who obtains an 80 is referred to as having gotten a "80%" or "80%".

Percentages can be used to compare distinct numbers, to assess change over time, or to establish the proportion of a group or population that fits into a specific category. For example, a survey may state that 60% of respondents said "yes" to a certain question, or that the price of a product has grown by 10% in the last year.

How to solve.

If the price of a baseball is marked down by the same percentage as a baseball bat, then the price of a baseball will not change.

The percentage markdown only affects the price of the baseball bat, not the price of the baseball. Therefore, the price of a baseball will remain the same at $12.

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The vertices of the dilated triangle are (-2, 2), (3, 4), and (1, 1).

Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered. There is no effect of dilation on the angle.

The coordinates of the triangle are (-4, 4), (6, 8), and (2, 2).

The scale factor of the triangle is 1/2 centered at the origin. Then the coordinate of the triangle will be given as,

⇒ (-4/2, 4/2), (6/2, 8/2), (2/2, 2/2)

⇒ (-2, 2), (3, 4), (1, 1)

The vertices of the dilated triangle are (-2, 2), (3, 4), and (1, 1).

The image of the triangle and dilated triangle is given below.

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Answer: The other answer is incorrect, the graph below shows the correct answer.

Coordinates of each point

A: (3,4)

B: (-2,2)

C: (1,1)

I know this is late, but I wanted to help those in the future who needed help with the question. Good Luck <3

Answer:

4t + 109.99 = 347.95

Step-by-step explanation:

They bought 4 tickets so that is how we got 4t

they spent altogether $109.99 to make the total

347.95

Bonus : 1 ticket is 59.49

Step-by-step explanation:

just a question should I help you with all of them?

The statement describes values of x and y such that x/y could be an irrational number is B. The value of x is the square root of an integer, and the value of y is an integer greater than zero.

The square root of an integer for x and a positive integer greater than zero for y are described in the statement as values of x and y that could be irrational numbers.

We have provided x and y values that could be irrational numbers. Any real number that cannot be expressed as the quotient of two integers is considered an irrational number. Positive whole numbers are not considered negative integers, nor are negative integers, or numbers below zero.

Consequently, we can say that A, C, or D do not demonstrate the irrational numbers since they are all expressed as integers.

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Answer:

Step-by-step explanation:

Start at origin 0,0 make a point

go up 1 and over 2 make a point

connect with straight line  

The first set represents a function but the second case does not represent a function.

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

The value of 'y' for each value of 'x' must be distinct. Then the relation is a function. Otherwise, it will not be a function.

A)  {(1, 0), (-2, 0)}

In the above relation, for each value of 'x' the value of 'y' is the same. Then the relation is function.

B)  {(-2, 3), (1, 4), (3, 5), (-2, 6), (5, 7)}

In the above relation, at x = -2, the number of values of 'y' is 2. then the relation is not a function

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The normal distribution have an importance in statistics of whether or not out appears in nature, because it fits several natural phenomena.

For exa. measurement error, heights, IQ scores, and physical activity measures all follow the normal distribution.

In this question we need to describe why does the normal distribution have an importance in statistics of whether or not out appears in nature.

We know that if we plot the probability distribution and it forms a bell-shaped curve. If the mean, mode, and median of the sample are equal then the variable has normal distribution.

A normal distribution is dependent on two parameters of the data set: mean and the standard deviation of the sample.

This characteristic of the normal distribution makes it extremely simple.

Also, the normal distribution is important because of the Central limit theorem.

It makes math easy - like calculating moments, correlations between variables, and other calculations that are domain specific.

So, the normal distribution have an importance in statistics of whether or not out appears in nature.

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Answer:

Part A: A

Part B: 1 is the y-intercept and is 0 the horizontal asymptote

Step-by-step explanation:

The balance sheet that correctly represents the daycare's income, expenses, and balance is given as follows:

A) Income

Amount

Weekly Income $21,000.00

Total Monthly Income $84,000.00

Expenses

Percent Amount

Employee Wages 42% $35,280.00

Building Rent 10% $8,400.00

Supplies 15% $12,600.00

Equipment 5% $4,200.00

Educational Licensing 2% $1,680.00

Food 10% $8,400.00

Utilities 10% $8,400.00

Maintenance 3% $2,500.00

Emergency/Repair 3% $2,500.00

$84,000.00

Balance

Income $84,000.00

Expenses $84,000.00

Balance $0

A balance sheet is a financial statement that lists the assets and liabilities of a corporation at a certain point in time. It is one of the three primary financial statements—the other two being the income statement and cash flow statement—that are used to assess a company's performance.

The weekly income is of $21,000, while a month is composed by four weeks, hence the monthly income is of:

=4 x $21,000

= $84,000.

Then the percentages of each expenses are applied to find the values, for example, 42% of that is for employee wages, hence:

= 0.42 x 84,000

= $ 35, 280

From the details we get Employee Wages 42% of $35,280.00

Hence, the balance will be of zero and option A is correct.

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Answer: The line that divides the plane into an area that is triangular and an area that is rectangular.

The magnitude of length BC in the triangle ABC is equivalent to 8.49 units.

Pythagoras theorem states that -

"In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“.

Mathematically, we can write-

[tex]a^2 + b^2 = c^2[/tex]

Given is that ABC is a right triangle, with right angle at B. Side AC has a length of 13 units. Side AB has a length of 5 units.

Using the Pythagoras theorem in the triangle ABC, we get -

AC² = BC² + AB²

BC² = AC² - AB²

BC² = (AC + AB)(AC - AB)

BC² = (13 + 5)(13 - 9)

BC² = 18 x 4

BC² = 72

BC = √(72)

BC = 8.49 units

Therefore, the length of the side BC is equivalent to 8.49 units.

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Answer:

Step-by-step explanation:

To make F the subject of the formula, you need to solve for F in the equation C = 5(F-32)/9.

You can do this by first multiplying both sides of the equation by 9 to get rid of the fraction:

C * 9 = 5(F-32)

Then, you can distribute the 5 on the right side of the equation:

C * 9 = 5F - 160

Then, you can add 160 to both sides of the equation to isolate the F term:

C * 9 + 160 = 5F

Finally, you can divide both sides of the equation by 5 to solve for F:

F = (C * 9 + 160)/5

This gives you the final form of the equation:

F = (9C + 160)/5

In this form, F is the subject of the formula. a = 9, b = 160, and c = 5 are all positive integers.

Answer:

[tex]F=\dfrac{9C+160}{5}[/tex]

Step-by-step explanation:

Given equation:

[tex]C=\dfrac{5(F-32)}{9}[/tex]

Multiply both sides by 9:

[tex]\implies 9C=5(F-32)[/tex]

Divide both sides by 5:

[tex]\implies \dfrac{9C}{5}=F-32[/tex]

Add 32 to both sides:

[tex]\implies \dfrac{9C}{5}+32=F[/tex]

[tex]\implies F=\dfrac{9C}{5}+32[/tex]

Rewrite 32 as a fraction with denominator 5:

[tex]\implies F=\dfrac{9C}{5}+\dfrac{32 \cdot 5}{5}[/tex]

[tex]\implies F=\dfrac{9C}{5}+\dfrac{160}{5}[/tex]

[tex]\textsf{Apply the fraction rule} \quad \dfrac{a}{c}+\dfrac{b}{c}=\dfrac{a+b}{c}:[/tex]

[tex]\implies F=\dfrac{9C+160}{5}[/tex]

B) 3 is the ratio of his speed and his car's fuel economy.

Velocity is the pace and direction of an object's movement, whereas speed is the time rate at which an object is traveling along a path. In other words, velocity is a vector, whereas speed is a scalar value.

[tex]\frac{speed}{fuel economy} =\frac{\frac{60 miles}{hour} }{\frac{20 miles}{gallon} } \\\frac{speed}{fuel economy}={\frac{60 miles}{hour} .{\frac{gallon}{20 miles} }\\[/tex]

[tex]\frac{speed}{fuel economy}=\frac{3 gallons}{hour}[/tex]

Inserting this 3 in the given equation 15 = 3t and including each term, we see the units cancel out:

[tex]15 gallons = \frac{3 gallons}{hour}.t(hours)[/tex]

3 is the ratio of his speed and his car's fuel economy.

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Answer:

4:1

Step-by-step explanation:

find the gcf: 4

divide by the gcf: 16/4 and 4/4

-2/3,  is the slope of the line that passes.

A line's steepness and direction are measured by the line's slope.

Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.

Any two different points on a line can be used to calculate the slope of any line.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively.

Two locations located on a straight line can be used to determine a line's slope. We can use the slope of line formula if we know the two spots' coordinates. These two points' coordinates should be-

P1 = (x1, y1) and P2 = (x2, y2)

According to our question-

The slope equation is [y2-y1/x2-x1]. For substitution and solution, use the provided points.

12-8/4-10

4/-6

-2/3

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