TWO EASY QUESTIONS 8TH GRADE MATH
9. Complete the missing steps in the paragraph proof of Theorem 3-8.
11. Solve for the value of x in the triangle shown below. Show your work! (1 point for equation, 1 point for answer)
Answers
<2 and <6 are right angles by the definition of perpendicular lines.
Since corresponding angles are congruent, m || n.
11.
In a triangle, the measures of the three angles add to 180 degrees.
If one angle is a right angle, then that angle measures 90 degrees. The other two angle measures plus 90 degrees add to 180 degrees, so the other two angle measures add to 90 degrees. In a right triangle there is a right angle and two other angles that are complementary.
Now look at your problem.
One angle is a right angle.
The other two angles are complementary, so their measures add to 90 deg.
8x + 2 + 9x + 3 = 90
17x + 5 = 90
17x = 85
x = 5
Related Questions
The length of a rectangle is 10 m less than three times the width, and the area of the rectangle is 77 m2 . find the dimensions of the rectangle
Answers
Area of a rectangle is length times width: x(3x-10)=77 => 3x^2-10x-77=0
Factor this quadratic equation: (x-7)(3x+11)=0 =.x=7 or x=-11/3
width cannot be negative, so the only answer is x=7
width is 7m, length is 11m
The length and width of the rectangle are 11 m and 7 m respectively.
What is rectangle?A rectangle is a part of a quadrilateral, whose sides are parallel to each other and equal.
Given that,
Length of the rectangle is 10 m less than three times the width,
And area of rectangle = 77 m²
Let the width of rectangle is x m,
Then length of rectangle = 3x -10 m.
The area of rectangle = 77
length × width = 77
x × (3x - 10) = 77
The value of x = 7 satisfy the equation,
Therefore, the width of rectangle is x = 7 m
And length of the rectangle is 3x - 10 = 21 - 10 = 11 m
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Solve each problem and write your answer in scientific notation. (6.0x10^5)x(3.0x10^4)
Answers
The simplified form of the given expression is [tex]1.8\times10^{10}[/tex].
The given expression is [tex](6.0\times10^5)\times(3.0\times10^4)[/tex].
We need to solve the given expression and write the answer in scientific notation.
What is a scientific notation?The scientific notation helps us to represent the numbers that are very huge or very tiny in a form of multiplication of single-digit numbers and 10 raised to the power of the respective exponent. The exponent is positive if the number is very large and it is negative if the number is very small.
Now, [tex](6.0\times10^5)\times(3.0\times10^4)=18\times10^5\times10^4[/tex]
[tex]=18\times10^{5+4}[/tex]
[tex]=18\times10^9[/tex]
[tex]=1.8\times10^{10}[/tex]
Therefore, the simplified form of the given expression is [tex]1.8\times10^{10}[/tex].
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find the greatest common factor.
4x^3a^2+4x^2a^3
Answers
Each week, Stephanie is paid a $180 base salary and a 3% commission on her total sales generated for the week. Which expression represents her weekly income when Stephanie generates w dollars in total sales? A180+0.03 w
B 180+0.03+w
C 180(0.03)w
D 180(0.03)+w
Answers
Each week, Stephanie is paid a $180 base salary and a 3% commission on her total sales generated for the week. Which expression represents her weekly income when Stephanie generates w dollars in total sales?
Result
A. 180 + 0.03w
Solution
You are adding 3% of her total sales on top of her base salary. To calculate commission, you must multiply the percent and the number or variable. Knowing this, the answer would be as it is above.
The expression represents her weekly income when Stephanie generates w dollars in total sales will be 180 + 0.03w. Then the correct option is A.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
Each week, Stephanie is paid a $180 base salary and a 3% commission on her total sales generated for the week.
Let 'w' be the total sales in dollars weekly. Then the expression is given as,
⇒ 180 + 0.03w
The expression represents her weekly income when Stephanie generates w dollars in total sales will be 180 + 0.03w. Then the correct option is A.
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Find the z-score such that the area under the standard normal curve to the right is 0.370.37. loading... click the icon to view a table of areas under the normal curve. the approximate z-score that corresponds to a right tail area of 0.370.37
Answers
Using the standard normal table, it is found that the z-score is z = 0.33.
-------------------------
In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the standard normal table and find the p-value associated with this z-score, which is the percentile of X. This p-value is the left-tailed area.The right-tailed area is 1 subtracted by the p-value.In this problem:
Right-tailed area of 0.37, thus the p-value is of 1 - 0.37 = 0.63.Looking at the standard normal table, the z-score is z = 0.33.A similar problem is given at https://brainly.com/question/7001627
The perimeter of a pool table is 30 ft. The table is twice as long as it is wide. What is the length of the pool table
Answers
l=2w
2(2w)+2w=30
4w+2w=30
6w=30
w=5
l=2(w)
l=2(5)
length=10 ft
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Triangle MNP is the image of triangle JKL after a 120 degrees counterclockwise rotation about point Q. If the measure of angle L is 47 degrees and the measure of angle N is 57 degrees, determine the measure of angle M. Explain how you arrived at your answer.
Answers
The measure of angle M in triangle MNP is 76 degrees. This is determined by utilizing the sum of interior angles property of triangles and understanding the correspondence of angles in rotated or transformed figures.
Explanation:The problem given is associated with the geometry of triangles. From the problem statement, we know that triangle MNP is the image of triangle JKL after 120 degrees counterclockwise rotation. This indicates that the angles of both triangles are the same. Hence, angle M will correspond to angle J of the original triangle.
However, since we are not given the measure of angle J, we need to calculate it using the property of triangles. In triangles, the sum of the interior angles amounts to 180 degrees. Therefore, the measure of angle J can be found by subtracting the measures of the other two angles (angle K and angle L) from 180 degrees.
Given the measure of angle L is 47 degrees and the measure of angle N (which corresponds to angle K in triangle JKL) is 57 degrees, we use the equation:
Angle J = 180 - (angle K + angle L) = 180 - (57+47) = 76 degrees.
Thus, the measure of angle M in triangle MNP, which is corresponding to angle J in triangle JKL, is 76 degrees.
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Constance invested $4500 for 3 years in a savings account paying simple interest with a yearly interest rate of 3.5%. How much simple interest did she earn?
Answers
Answer:
$420
Step-by-step explanation:
what is the x intercept of the line 6x-3y=24
Answers
6x - 3(0) = 24
6x = 24
x = 4 Answer
How to solve this P-1=5p+3p-8
Answers
P=8p-7
7p=7
P=1
Check it
1-1=5(1)+3(1)-8
0=0
We're essentially just trying to get "p" isolated, or by itself.
So, we must subtract 5p from both sides.
p - 1 - 5p = 3p - 8
Then, you subtract 3p from both sides.
p - 1 - 5p - 3p = -8
You then add 1 to both sides.
p - 5p - 3p = -8 + 1
Simplify.
-4p - 3p = -7
Simplify.
-7p = -7
Divide both sides b -7.
p = 1
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What is the area of a rectangle with vertices at (−6, 3) , (−3, 6) , (1, 2) , and (−2, −1) ? Enter your answer in the box. Do not round any side lengths.
Answers
I drew out each point and arrive at the conclusion that the longest side is equal to 4 and the shorter side to 3
so that means the answer is 12
Answer:
Area of the rectangle is 24
Step-by-step explanation:
Given the vertices of the rectangle to be (−6, 3) , (−3, 6) , (1, 2) , and (−2, −1)
Let the the vertices be at point ABCD respectively
so that A(-6, 3) B(-3,6) C(1,2) D(-2 -1)
To find the area, we need to first find the length and height of the rectangle
We let AB to be the length of the rectangle and BC be the height of the triangle. so first, we will find the distance between the two points AB
A(-6, 3) B(-3,6)
Using the distance formula
|AB| = √([tex]x_{2}[/tex] - [tex]x_{1}[/tex])² + ([tex]y_{2}[/tex] - [tex]y_{1}[/tex])²
=√(-3+6)² + (6-3)²
=√(3)² + (3)²
= √(9+9)
=√18
=√(9 ×2)
=√9 × √2
=3√2
|AB| = 3√2
The length of the rectangle is 3√2
We will now proceed to find the height of the rectangle which is the distance between point the two point BC
B(-3,6) C(1,2)
Using the distance formula;
|BC |= √([tex]x_{2}[/tex] - [tex]x_{1}[/tex])² + ([tex]y_{2}[/tex] - [tex]y_{1}[/tex])²
=√(1+3)² + (2-4)²
=√4² + 4²
= √(16 + 16)
=√32
=√(16 × 2)
=√16 × √2
=4√2
|BC| = 4√2
Therefore, the height of the triangle is 4√2
Area of rectangle = l × h
= |AB| . |BC|
= 3√2 × 4√2
=12 (2)
=24
Therefore area of the rectangle is 24
The volume of a rectangular prism can be computed using the formula v = lwh. what is the length of a prism that has a volume of 1344 cubic centimeters, a width of 8 centimeters, and a height of 12 centimeters?
a. 111 cm
b. 18 cm
c. 896 cm
d. 14 cm
Answers
We are given the formula:
V = l w h
and the following values:
l = ?
V = 1344 cm^3
w = 8 cm
h = 12 cm
SO rewriting the formula in terms of l:
l = V / w h
l = 1344 cm^3 / (8 cm * 12 cm)
l = 14 cm
Answer:
d
The answer would be 14
if 1 factor of 3x3+7x2-7x-3 is (x+3) what are the other two factors
Answers
= (x + 3)(x - 1)(3x + 1)
answer
other two factors (3x + 1) and (x - 1)
To find the remaining factors of the polynomial 3x^3+7x^2-7x-3 after knowing that (x+3) is a factor, divide the polynomial by x+3 and then factor the resulting quadratic polynomial.
If x+3 is a factor of the polynomial 3x3+7x2-7x-3, the other two factors can be found by performing polynomial long division or synthetic division to divide the polynomial by x+3. Once the polynomial is divided, the quotient will be a quadratic equation, which we can then factor or use the quadratic formula to find the remaining factors.
Steps for Polynomial Division:
Divide the polynomial 3x3+7x2-7x-3 by x+3.Obtain the quotient, which should be a quadratic polynomial.Factor the quadratic polynomial or use the quadratic formula to find the other two factors of the original polynomial.HURRY ASAP NO JOKE 2 MINUTES PLZ HURRY ASAP PLZZZZZ HELP
Answers
This isosceles triangle has two sides of equal length , a, that are longer than the length of the base , b. The perimeter of the triangle is 15.7 cm. The equation 2a + b = 15.7 models this information. If one of the longer sides is 6.3 cm, which equation can be used to find the length of the base ?
Answers
2a + b = 15.7
where b represents the base.
Now, if we want to calculate the length of the base, all we have to do is isolate the b in one side of the equation as follows:
b = 15.7 - 2a
We know that a = 6.3 cm, therefore, the length of the base can be calculated as follows:
b = 15.7 - 2(6.3) = 3.1 cm
Eddie is reading a novel for English class he has read 173 out of 480 pages about what percent of the book has he read
Answers
Answer: The percent of the book has he read is 36.04 %.
Step-by-step explanation:
Given: The number of pages read by Eddie= 173
The total number of pages = 480
The percent of the book has he read is given by:_
[tex]P=\frac{\text{number of pages read}}{\text{total pages}}\times100\\\\\Rightarrow\ P=\frac{173}{480}\\\\\Rightarrow\ P=0.36041\times100\\\\\Rightarrow\ P=36.04\%[/tex]
Hence, the percent of the book has he read is 36.04 %.
The expression −50x+100 represents the balance, in dollars, of a bank account after x months.
What is the rate of change, in dollars per month, of the bank account balance?
i got -50
Answers
how do I solve
-9+8k=7+4k
Answers
subtract 4k from both sides
-9+4k=7
add 9 to both sides
4k=16
divide both sides by 4
k=4
What is the value of the discriminate of the quadratic equation -1=5x^2-2x
Answers
Help me please thanks
Answers
56.34 + 0.49x
hope it helps
Joan has a credit card that uses the previous balance method. The opening balance of one of her 30-day billing cycles was $6390, but that was her balance for only the first 3 days of the billing cycle, because she then paid off her entire balance and didn't make any new purchases. If her credit card's APR is 17%, which of these expressions could be used to calculate the amount Joan was charged in interest for the billing cycle?
Answers
Answer:
Step-by-step explanation:
(0.17/365 x30)(6390)
The expression that represents the amount Joan was charged in interest for the billing cycle is $26.84.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.com
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
To calculate the amount Joan was charged in interest for the billing cycle using the previous balance method, we need to find the average daily balance for the billing cycle, which is calculated as the sum of the daily balances divided by the number of days in the billing cycle.
The daily balance is the balance at the end of each day, and it is calculated by adding new purchases and subtracting payments and credits from the previous day's balance.
In this case,
Joan had a balance of $6390 for the first 3 days of the billing cycle, so her average daily balance for the billing cycle can be calculated as:
((3 x 6390) + (27 x 0)) / 30
= 1917
This means that her average daily balance for the billing cycle was $1917.
To calculate the amount of interest Joan was charged for the billing cycle, we can use the following expression:
Interest = Average Daily Balance x Daily Interest Rate x Number of Days in Billing Cycle
The daily interest rate is calculated as the APR divided by 365 since there are 365 days in a year. In this case, the daily interest rate is:
0.17 / 365
= 0.000465753
So, the expression that can be used to calculate the amount of interest Joan was charged for the billing cycle is:
Interest = 1917 x 0.000465753 x 30
= $26.84 (rounded to the nearest cent)
Therefore,
The expression that represents the amount Joan was charged in interest for the billing cycle is $26.84.
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The coordinates of the vertices of a polygon are (−5, 1) , (−1, 3) , (2, 3) , (2, −2) , and (−3, −1) .
What is the perimeter of the polygon?
Enter your answer as a decimal, rounded to the nearest tenth of a unit, in the box.
Answers
Which is the property that justifies the action?
Answers
Have a look:
(x/4)x4=16x4
x=64
As you can see, the value of x can be found by multiplying 4 on both sides.
Hope I helped :)
Then, Since we are multiplying it would be the multiplication property of equality, no tricks there.
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What is the square root of the fraction 25/100?
Answers
3469131824 what would be the next number
Answers
Hope this helps!
What happens to a line when the y-intercept is changed ?
Answers
notice the original blue line with a y-intercept of y = 1, it goes up 2 units, then goes down 3 units, notice what happens to the line.
so, the y-intercept acts like a seesaw, if you change it, the line goes over the seesaw.
Find the greatest common factor of 75, 8, and 21
Answers
8=2×2×2
21=3×7
there's is no common factor between them aside 1
except u typed the wrong question
What is the equation of the axis of symmetry for the function shown below? y-2=-(x+5)^2?
Answers
Answer:
-5
Step-by-step explanation:
The volume of a rectangular prism can be computed using the formula V = lwh. What is the height of a prism that has a volume of 2376 cubic centimeters, a length of 18 centimeters, and a width of 11 centimeters?
A. 24 cm
B. 726 cm
C. 16 cm
D. 12 cm
Answers
Answer:
The Correct Answer is D
Step-by-step explanation:
it cost $526.30 to repaire Carol's car. rounded to the nearest ten dollars, how much did carol pay?
A. $500
B. $520
C. $530
D. $550
Answers
It is neither A nor B because she wouldn’t round down. This would mean she would not have payed the full amount. It would not be D either because that is rounding to far up.
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