Answer: 28 and 7
7 x 4 = 28
28 + 7= 35
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.
Answer:
Step-by-step explanation:
Let ABC be an isosceles triangle with lateral sides AB and AC, a base of BC, and medians of AC and AB, respectively, at BD and CE.
In △ACE and △ABD ,
AB≅AC lateral sides of isosceles triangle
∠A≅∠A common angle
AE≅AD half segments of equal lateral sides
As a result, ACE ≅ABD according to the side angle side theorem. as a result, median BD is consistent with median CE.
If any two figures can be positioned exactly over one another, the congruence between them can be seen. The relationship between two figures is referred to as their congruence, and is expressed using the word "congruence".
In other terms, two geometric figures are said to be congruent if they can be superimposed on one another.
All figures, including triangles, quadrilaterals, and other shapes, have this feature. Along with figures, line segments and angles that have the same measure are also said to be congruent. To comprehend what congruent figures represent, look at the following figure.
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$6,000 at 5% compounded daily for 3 years
6000 dollars at 5% compounded daily for 3 years will amount to $6,970.93.
How to solve compound interest?Compound interest is the interest you earn on interest. In other words, compound interest is the interest calculated on the principal and the interest accumulated over the previous period.
Compound interest formula can be use to find the amount of the money after 3 years.
Using the compound interest formula,
[tex]A = p(1 + \frac{r}{n} )^{nt}[/tex]
where
p =principalr = raten = number of timest = time in yearsA = amountTherefore,
p = 6000 dollars
rate = 5% = 0.05
n = 365
t = 3
Hence,
[tex]A = 6000(1+\frac{0.05}{365} )^{(365)(3)}[/tex]
A = 6,000.00(1 + 0.00013698630136986)¹⁰⁹⁵
Therefore,
A = $6,970.93
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Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Select two options. x2 + (y – 3)2 = 36 x2 + (y – 5)2 = 6 (x – 4)² + y² = 36 (x + 6)² + y² = 144 x2 + (y + 8)2 = 36
The equation that represents circles that have a diameter of 12 units and a center that lies on the y-axis is x²+ (y-3)² = 36
The standard form for finding the equation of a circle is expressed as;
[tex](x-a)^{2} + (y-b)^{2} = b = r^{2}[/tex]
where;
(a, b) is the center of the circle
r is the radius of the circle
Given the following
diameter = 12 units
radius = 12/2 = 6 units
If the centre lies on the y-axis, the center will be at (0, 3).
Substituting into the formula, we will have[tex](x-0)^{2} + (y-3)^{2} = (6)^{2}[/tex]equivalent to x²+ (y-3)² = 36
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Simplify [tex]\sqrt[3]{125z}[/tex] - [tex]\sqrt[3]{64z}[/tex]
Answer:
[tex] \sqrt[3]{z} [/tex]
Step-by-step explanation:
[tex] \sqrt[3]{125z} = \sqrt[3]{ {5}^{3} z} = 5 \sqrt[3]{z} [/tex][tex] \sqrt[3]{64z} = \sqrt[3]{ {4}^{3}z } = 4 \sqrt[3]{z} [/tex][tex]5 \sqrt[3]{z} - 4 \sqrt[3]{z} = \sqrt[3]{z} [/tex]On a scale drawing of a horse, the scale is 1 in: 10 ft. If the real horse is 25 ft tall, how tall is the horse on the scale drawing?
Answer: 2.5 inch
Step-by-step explanation:
Pleaseee help! I don’t really get math
Answer:
GE is congruent to GE
Step-by-step explanation:
This is true because both triangles use this same line, so it is referred to as the reflexive property.
Classify the given angle.
right angle
obtuse angle
acute angle
straight angle
Answer: Acute Angle
Step-by-step explanation: It is less than 90 degrees (right angle) so it is an acute angle
Answer:
Step-by-step explanation:
Acute Angle 100% Correct!!
(25 points)
Which inequality is represented by this number line?
Answer:
C
Step-by-step explanation:
Pick point 7 and sub into the equations
eq 1 not equal to 10
eq 2 not equal to 12
eq 3 is equal to 15
eq 4 not equal to 18
Now sub in the value of -3 into equation 3 Yes equal to 15
so answer is eq 3
numbers greater than 7 and less than -3 are also true ....
Determine whether the following statement is true or false. In a normal distribution, the z-score for the mean is 0. Choose the correct answer below. * OA. The statement is true because a z-score describes how many standard deviations a data item in a normal distribution lies above or below the mean. B. The statement is false. The z-score for the standard deviation is 0. OC. The statement is false. The z-score for the mean is always 1. D. The statement is false. The z-score for the mean depends on the data item.
The statement "In a normal distribution, the z-score for the mean is 0" is true. A z-score describes how many standard deviations a data item in a normal distribution lies above or below the mean. Since the mean of a normal distribution is defined as the value at which the distribution is centered, a data item with a value equal to the mean will have a z-score of 0.
Therefore, the correct answer is option A: "The statement is true because a z-score describes how many standard deviations a data item in a normal distribution lies above or below the mean." Option B, C, and D are all false because they do not accurately describe the relationship between z-scores and the mean in a normal distribution.
What is the relationship between a 90% confidence interval around a mean and a 95% confidence interval around a mean?.
Answer: With a 95 percent confidence interval, you have a 5 percent chance of being wrong. With a 90 percent confidence interval, you have a 10 percent chance of being wrong. A 99 percent confidence interval would be wider than a 95 percent confidence interval (for example, plus or minus 4.5 percent instead of 3.5 percent)
Step-by-step explanation:
Will mark as brainiest. Please help more points!
The total area of the two shaded faces of the cuboid below is = 112[tex]cm^{2}[/tex]
Since the two shaded faces of the cuboid shown are adjutant to each other and are of the same dimensions so according to the calculations -
Let us consider only one side of the shaded portion-
The length of the shaded part = 8cm
The width of the shaded portion = 7cm
So it appears that due to the uneven measure of length and breath this is a rectangle, so the area of a rectangle
= [ length (l) x width(w) ]
= 8cm x 7cm
= 56[tex]cm^{2}[/tex]
Since the question asks the total area of both sides so because both the shaded sides are equal then total area = 56 x 2 = 112 [tex]cm^{2}[/tex]
Therefore, the total area of the shaded faces of the cuboid = 112[tex]cm^{2}[/tex]
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The cubic polynomial | f(x) = 6x ^ 3 - 7x ^ 2 - 11x + d has a 2 factor (x-1)
(a)Find the value of d
( b )Find the remainder when the polynomial is divided by (x + 2)
Answer:
d=12 and the remainder is -42
Step-by-step explanation:
a.
put x=1 into f(x)
6(1)³-7(1)²-11(1)+d=0
6-7-11+d=0
-12+d=0
d=12
b.
Put x=-2 into the polynomial
6(-2)³-7(-2)²-11(-2)+12
6(-8)-7(4)+22+12
-48-28+22+12
-42
Please Answer Correctly.
Answer:
10 should be the correct answer
Step-by-step explanation:
im sooooo sorry if its wrong :|
what do you think the true slope is? you do not need an exact number. hint: can you provide an interval that you think the true slope falls in?
A line's equation can be written as y = mx + b, y = ax + b, or y = a + bx. As may be seen, the equation for the regression line is similar as true slope.
Explain the term true slope?Understanding the distinction between negative, positive, zero, and undefinable slopes is crucial.
In summary, the function operates "uphill" if the slope equals positive and y rises as x rises (going left to right). If a slope is negative, the function is downward-sloping because y falls off as x rises. If the slope is zero, y remains constant—a horizontal line—and does not vary. Problematic vertical lines are those in which x remains constant. Because it is divided by zero, our formula is therefore undefinable. Some people will refer to this situation as having an infinite slope, but we are unable to determine whether it is negative or positive infinity!As a result, the rather perplexing term "no slope" is also frequently used in this context.
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Clayton place towel I pell the word time and a bowl. He draw one tile from the ball and then without replacing it draw another child. What i the ample pace of doe it repreent in the letter picked him to
On solving the question, The possible combinations when choosing two letters randomly are: T-I, T-M, T-E, I-T, I-M, I-E, E-T, E-M, E-I, M-I, M-T, M-E.
What is combination ?When the order of selection is irrelevant, the mathematical operation of combining counts the number of possible configurations for a set of elements.
[tex]Letters are given as - T I M E[/tex]
Given that there is no alternative for the choice, we have the following number of possibilities:
[tex]= > n = 4^2\\[/tex]
here -
4 =the number of letters
2 =the number of selection
so, n= 16
The choices are then shown as follows:
TI, TM, TE
IT, IM, IE
MT, MI, ME
ET, EI, ET
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help: find the measure of each angle indicated
Answer: 27
Step-by-step explanation:
You know that the whole shape equals 180. So you add 133+20=153 then subtract that from 180 and that should give you 27.
Hope that helps!
Given the system below,
9x+3y=-18
y=x+7
What is the ordered pair for the intersection
)?
Answer:
(-3.25,3.75)
Step-by-step explanation:
Thuis can be answered with either of two approaches: Graphing and Matematical. We'll do both:
Graphing
Graph both equations. It is helpful to use a free online graphing utility: DESMOS.
The attached graph reveals the intersection of the lines at point (-3.25, 3.75).
Matematical
Solve the equations be using substitution. Rearrange either equation to isolate one of the two variables (x or y).
Lets use the second, since y is already isolated, making the task simple and fast. But the other equation could also be used, if desired.
y=x+7
Now use this expression of y in the other equation:
9x+3y=-18
9x+3(x+7)=-18
9x +3x +21 = -18
12x = -39
x = -(39/12)
x = -3 - (3/12)
x = -3.25
Now use x= -3.25 in either equation tand solve for y:
y=x+7
y=(-3.25)+7
y = 3.75
The solution to this series of equations is (-3.25,3.75)
ABC has vertices at a(11,6), B(5,6), and (5,17).
The correct statements regarding the congruent triangles are given as follows:
Triangle ABC and triangle MNO are congruent by a sequence of rotations and translations.Triangle JKL and triangle ABC are congruent by a single rotation.What are congruent triangles?Congruent triangles are triangles in which the outer side lengths have the same measure.
Then the triangles ABC and triangle MNO are congruent by a sequence of rotations and translations, as both are right triangles.
Triangle JKL and triangle ABC are congruent by a single rotation, as the distances between the vertices of each triangle are equal.
Missing InformationThe problem is given by the image shown at the end of the answer.
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Select the statement that correctly describes the
solution to this system of equations,
18x-2y=-4
4x-y=-2
There is exactly one solution at (2.0),
There is no solution,
There is exactly one solution at (0-2).
There are infinitely many solutions.
HELP ASAP
The solution of the equations 18x - 2y = -4 and 4x - y = -2 is (0,-2). Hence option c is the correct option.
What is an equation?
A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.
Given pair of equations is
18x - 2y = -4 ....(i)
4x - y = -2 .....(ii)
To solve the equation apply elimination method.
Multiply equation (ii) by 2 and subtract it from (i):
18x - 2y = -4
8x - 2y = -4
(-) (+) (+)
_________
10x = 0
x = 0
Putting x = 0 equation (ii)
0 - y = -2
y = 2
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17
Select the correct answer from each drop-down menu.
Rita is planting saplings along her garden fence. When she started, she had x packages of saplings with 5 saplings per package. She planted 15
saplings and has at most 20 left. How many packages of saplings did she start with? What would the solution look like on a number line graph?
When Rita started, she had
with an arrow to the
packages of saplings. The solution can be represented as
Reset
Next
Note that:
When Rita started, she had 7 packages;The solution can be represented on a number line graph, it will begin at 4 (the number of packages Rita still has) and progress to the right to 7, the number of packages when Rita began planting if we plot x (the number of sapling packages).What is the rationale for the above answer?Recall that we are given the following:
To determine the number of packages Rita started with, we must resolve:
(Number of saplings planted by Rita + Number of saplings left)/Number of saplings per package
that is:
x = (15 + 20)/5
x = 35/5
x = 7
Thus, when she started, she actually had 7 packages. By the time she was done, she had 4.
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Find the correct answer & explaining why
The line segment will be needed to create step 4 is 30. Hence option D is the correct option.
What is line segment?
Line segment is line whose distance fixed. There are two fixed end points. The difference between a line and a line segment is that a line has no endpoints and can go on forever in either direction.
The number of line segment in step 1 is 2.
The number of line segment in step 2 is 6.
The number of line segment in step 3 is 14.
Now finding the pattern:
Step 2: 6 = 2 × 2 + 2
Step 3: 14 = 6 × 2 + 2
The number of line segment is equal to 2 more than 2 times the number of line segment of previous step.
According to this pattern,
step 4: 14 × 2 + 2 = 30
The number of line segment is 30.
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A translation stretches or compresses the graph of a function.
True false question.
True
False
Answer:
False, a transformation is the one that stretches or compresses the graph. A translation just shifts the graph up, down, left, or right.
Answer: False
Step-by-step explanation:
A translation is just moving the graph up, down, left, and right! It doesn't make a graph bigger or smaller, so this is a False
A cyclist rides her bike at a speed of 18 miles per hour. What is this speed in kilometers per hour? How many kilometers will the cyclist travel in 5 hours? In your
computations, assume that 1 mile is equal to 1.6 kilometers. Do not round your answers.
Speed: Distance traveled in 5 hours:
The speed in kilometres per hour is 28.8 km/hr.
The distance in kilometres the cyclist will travel in 5 hours is 144 km.
How to find speed and distance?A cyclist rides her bike at a speed of 18 miles per hour. The speed in kilometres per hour an be calculated as follows;
1 miles = 1.6 km
18 miles = ?
cross multiply
distance in km = 18 × 1.6
distance in km = 28.8 km
Therefore, the speed in kilometres per hour is 28.8.
The kilometres the cyclist will travel in 5 hours can be calculated as follows;
speed = distance / time
28.8 = d / 5
cross multiply
distance travelled in km = 28.8 × 5
Therefore,
distance travelled in km = 144 km
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All hats are on sale for 22.5% off the original price.
Abrien is buying a hat that is originally priced at h.
Sales tax is 8.875%.
Part A: Which expression would calculate the final price
of a hat?
Part B: If the original price of a hat is $42, what is the
final price of buying four hats after the discount and
sales tax? (round your answer to the nearest dollar) Untitled Title
A. Part A: h(0.225)(0.08875)
Part B: 41
B. Part A: 4h(0.775)(1.08875)
Part B: $142
C. Part A: h(0.775)(1.08875)
Part B: $142
D. Part A: h(0.775)(0.08875)
Part B: $156
The expression for the final price of a hat would be h(0.775)(0.08875) and the final price of buying four hats after the discount and sales tax would be $142.
Option (C) is correct.
What is a discount?
A discount is a reduction in the price of a product or service. It can be offered for a variety of reasons, such as to encourage customers to make a purchase or to clear inventory. Discounts can be expressed as a percentage off the original price, or as a fixed dollar amount.
Part A: The expression that would calculate the final price of a hat is h(0.775)(1.08875). This takes into account the 22.5% discount by multiplying the original price by 0.775, and then adds the 8.875% sales tax by multiplying the discounted price by 1.08875.
Part B: If the original price of a hat is $42, then the final price of buying four hats after the discount and sales tax would be $42 x 4 x 0.775 x 1.08875 = $142.
Hence, the expression for the final price of a hat would be h(0.775)(0.08875) and the final price of buying four hats after the discount and sales tax would be $142.
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Convince me that...
the √(25) is 5.
Step-by-step explanation:
The square root of 25 is 5. It is the positive solution of the equation x2 = 25. The number 25 is a perfect square.
Answer:
Yeah, √(25) is 5.
Step-by-step explanation:
Given problem,
→ √(25) = 5
Checking the equation,
→ √(25) = 5
→ 25 = (5)²
→ 25 = 25
→ LHS = RHS
Thus, equation is proved.
Hello, can someone help me out with these two questions please!?!?!?
Answer: No solution
Step-by-step explanation:
3(2x + 3) - 3x = 9 + 3x
6x + 3 - 3x = 9 + 3x - 3x
6x + 3 - 6x = 9
3 = 9
No solution
A 140 ft diameter helicopter pad covers an area of about how many square feet? What value did you use for pi and why did you choose it?
15,386 ft² an area of helicopter pad covers .
What does a circle's area mean?
The area a circle occupies in a two-dimensional plane is known as the area of the circle. It can be simply calculated using the formula A = r2, (Pi r-squared), where r is the circle's radius.
Area is measured in square units, such as m2, cm2, etc. Where = 22/7 or 3.14, the area of a circle is equal to r2 or d2/4, in square units.
D = 140
r = 140/2 = 70
area of helicopter = πr²
= 3.14 ×70 × 70
= 15,386 ft²
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is x^4+2x^3-x^2+7x+11 a quintic binomial
On solving the provide question, we got that - [tex]x^4+2x^3-x^2+7x+11[/tex] is not a quintic binomial
What is quintic polynomial?A mathematical word raised to the fifth power of the independent variable. B. Or 5th order polynomial in the form of 5th order or 5th order for 5th order (not equivalent).
What is an example of a quintic polynomial?A polynomial of degree 5. Examples: x5 – x3 + x, y5 + y4 + y3 + y2 + y + 1, and 42a3b2.
[tex]x^4+2x^3-x^2+7x+11[/tex] is not a quintic binomial
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If g(x)=x^2+6 and f(x)=2x-4, find g(f(x))
The value of the function g(f(x)) is 2x² - 8x + 11.
What is function?
In the composition of functions, we completely swap out one function for another. The function f with g has the notation (fg)(x)=f(g(x)) and is read as f of g of x. It signifies that the function g(x) is substituted for every instance of an x in the function f.The combination of two functions is frequently referred to as a "function of a function," and g*f is sometimes represented as g.f.g(x) = x² + 6
f(x) = 2x - 4
g(f(x)) = (2x-4)² + 6
= 4x² - 16x + 16 + 6
= 4x² - 16x + 22
= 2x² - 8x + 11
Hence, the value of the function g(f(x)) is 2x² - 8x + 11.
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A bank features a savings account that has an annual percentage rate of r=3.5% with interest compounded quarterly. Althea deposits $3,500 into the account.
What values should be used P, r, and n?
How much money will Althea have in the account in 8 years? Round to the nearest penny.
Althea will have a $4625.32 compound amount in the account in 8 years.
What is compound interest?
The interest earned on savings that are computed using both the original principal and the interest accrued over time is known as compound interest. Compound interest is computed as interest on the initial principal plus any accrued interest from prior periods.
Given,
Principal (P) = $3,500
rate of interest (r) =3.5% = 0.035
for compounded quarterly (n) = 4
time (t) = 8 years
The compound amount is given by
[tex]A = P(1+\frac{r}{n})^{nt}\\A = 3500(1+\frac{0.035}{4})^{4*8}[/tex]
A = 4625.32
Hence, Althea will have $4625.32 in the account in 8 years.
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