Answer:
Stefan spend originally $110 and the money stefan make by selling the bicycle and helmet to jin is $22 .
Step-by-step explanation:
As given
Stefan sells jin a bicycle for $114 and a helmet for $18.
Total cost of the bicycle and helmet = $114 + $18
= $132
The total cost for jin is 120% of what stefan spent originally to buy the bike and helmet.
120% is written in the decimal form.
[tex]= \frac{120}{100}[/tex]
= 1.20
Let us assume that the Stefan spend originally for bike and helmets be x.
Than the equation becomes
1.20 × x = 132
1.20x = 132
[tex]x = \frac{132}{1.20}[/tex]
x = $110
Therefore stefan spend originally be $110 .
Now find out how much money did he make by selling the bicycle and helmet to jin .
Money make by Stefan = Total selling cost of helmet and bicycle - Total amount of stefan spends for purchasing.
Money make by Stefan = 132 - 110
Money make by Stefan = $22
Therefore the money stefan make by selling the bicycle and helmet to jin is $22 .
Stefan's original expenditure for the bicycle and helmet was $110. He made a profit of $22 by selling these items to Jin.
Explanation:Stefan sold the bicycle and helmet to Jin for a total of $132 ($114 + $18). We know that this amount represents 120% of what Stefan originally spent. To determine Stefan's original expenditure, we'll therefore divide the total amount he earned by 120 and then multiply by 100 (as the cost is 100% for him). So, Stefan's original expenditure would be (132/120)*100 = $110.
Now, to determine Stefan's profit, we subtract his original expenditure from the amount for which he sold the items to Jin. That is, $132 - $110 = $22. So, Stefan made a $22 profit from selling the bicycle and helmet.
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In a recent survey 55% of pet owners have more than one pet if there was 620 pet owners survey which proportion could be used to find the number who owned more than one pet
Answer:
341..
Step-by-step explanation:
i would personally say 341 because 620 multiplied by 55% or .55, as written on a calculator, would be 341.
Answer: if you are looking to put it in a proportional relationship you get the same answer but I can show you how to do it.
Step-by-step explanation:
55/ 100 ✖️ n/620=
34100/100 equals 100n ➗ 100 equals 341= n
The coordinates of the vertices of parallelogram RMBS are R(–4, 5), M(1, 4), B(2, –1), and S(–3, 0). Using the diagonals, prove that RMBS is a rhombus. Show all your work and state appropriate formulas and theorems used.
To prove a rhombus you need to show that the sides are congruent and the diagonals are perpendicular.
Sides:
[tex]d_{RM}=\sqrt{(-4-1)^2+(5-4)^2}[/tex]
[tex]=\sqrt{(-5)^2+(1)^2}[/tex]
[tex]=\sqrt{25+1}[/tex]
[tex]=\sqrt{26}[/tex]
[tex]d_{MB}=\sqrt{(1-2)^2+(4+1)^2}[/tex]
[tex]=\sqrt{(-1)^2+(15)^2}[/tex]
[tex]=\sqrt{1+25}[/tex]
[tex]=\sqrt{26}[/tex]
[tex]d_{BS}=\sqrt{(2+3)^2+(-1-0)^2}[/tex]
[tex]=\sqrt{(5)^2+(-1)^2}[/tex]
[tex]=\sqrt{25+1}[/tex]
[tex]=\sqrt{26}[/tex]
[tex]d_{SR}=\sqrt{(-3+4)^2+(0-5)^2}[/tex]
[tex]=\sqrt{(1)^2+(-5)^2}[/tex]
[tex]=\sqrt{1+25}[/tex]
[tex]=\sqrt{26}[/tex]
[tex]\overline{RM}[/tex] ≅ [tex]\overline{MB}[/tex] ≅ [tex]\overline{BS}[/tex] ≅ [tex]\overline{SR}[/tex]
Diagonals:
Use the slope formula: [tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m_{RB}=\dfrac{5+1}{-4-2}[/tex]
[tex]=\dfrac{6}{-6}[/tex]
= -1
[tex]m_{MS}=\dfrac{4-0}{1+3}[/tex]
[tex]=\dfrac{4}{4}[/tex]
= 1
Slopes are opposite reciprocals so they are perpendicular.
***************************************************************************
All of the sides are congruent and the diagonals are perpendicular so RMBS is a rhombus.
He orders 5 veggie pizzas he orders enough for everybody to 5/6 of a pizzas.How many people can he feed
Answer: 25 people
Step-by-step explanation: 6 x 5 = 30 30-5 = 25
Quadrilateral ABCD is located at A(−2, 2), B(−2, 4), C(2, 4), and D(2, 2). The quadrilateral is then transformed using the rule (x + 2, y − 3) to form the image A'B'C'D'. What are the new coordinates of A', B', C', and D'? Describe what characteristics you would find if the corresponding vertices were connected with line segments.
Answer:
A' (0, -1)
B' (0, 1)
C' (4, 1)
D' (4, -1)
Step-by-step explanation:
We have the following points of a quadrilateral ABCD:
A(−2, 2), B(−2, 4), C(2, 4), and D(2, 2)
and the rule of the translation is given by:
(x, y) ---> (x + 2, y − 3)
which means that each point will move means 3 units to the left and 4 units upwards.
So the points after transformation will be:
A(−2, 2) ---> (-2+2, 2-3) ---> A' (0, -1)
B(−2, 4) ---> (-2+2, 4-3) ---> B' (0, 1)
C(2, 4) ---> (2+2, 4-3) ---> C' (4, 1)
D(2, 2) ---> (2+2, 2-3) ---> D' (4, -1)
If we plot these points on a graph and join the corresponding vertices with line segments, then we will see that all the the lines will be parallel to each other since they followed the same rule of transformation.
The new coordinates of the transformed vertices A', B', C', and D' are:
A' (0, -1)
B' (0, 1)
C' (4, 1)
D' (4, -1)
To find the new coordinates of the transformed vertices A', B', C', and D', you need to apply the transformation rule (x + 2, y - 3) to the original coordinates of A, B, C, and D.
A' = (x + 2, y - 3)
A' = (-2 + 2, 2 - 3)
A' = (0, -1)
B' = (x + 2, y - 3)
B' = (-2 + 2, 4 - 3)
B' = (0, 1)
C' = (x + 2, y - 3)
C' = (2 + 2, 4 - 3)
C' = (4, 1)
D' = (x + 2, y - 3)
D' = (2 + 2, 2 - 3)
D' = (4, -1)
So, the new coordinates of the transformed vertices A', B', C', and D' are:
A' (0, -1)
B' (0, 1)
C' (4, 1)
D' (4, -1)
Now, let's describe the characteristics of the quadrilateral ABCD and its image A'B'C'D' when the corresponding vertices are connected with line segments:
Quadrilateral ABCD:
A(−2, 2), B(−2, 4), C(2, 4), and D(2, 2)
ABCD is a trapezoid with two parallel sides (AB and CD) and two non-parallel sides (BC and AD).
The trapezoid is located in the first quadrant.
Image A'B'C'D':
A'(0, -1), B'(0, 1), C'(4, 1), and D'(4, -1)
A'B'C'D' is also a trapezoid with two parallel sides (A'B' and C'D') and two non-parallel sides (B'C' and A'D').
A'B'C'D' is located in a different position due to the transformation. It has been shifted 2 units to the right and 3 units down.
The transformation (x + 2, y - 3) has effectively shifted the entire quadrilateral 2 units to the right and 3 units down in the coordinate plane. The basic shape and characteristics of the trapezoid are preserved, but its position in the plane has changed.
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1)Meesha has a pocket full of change consisting of dimes and quarters. The total value is $3.15. There are 7 more quarters than dimes. How many of each coin are there?
2)How much pure bleach must be combined with a solution that is 4% bleach to make 12oz of a 12% bleach solution?
Please help me
Answer:
1) 11 quaters and 4 dimes
Step-by-step explanation:
1) 11 quaters = 2.75
4 dimes = .40
$2.75 + .40 = 3.15
Final answer:
Meesha has 4 dimes and 11 quarters. To make a 12oz 12% bleach solution, 1 ounce of pure bleach must be combined with a 4% solution.
Explanation:
Solving Coin and Bleach Solution Problems
Problem 1: Coin Combination
Meesha has dimes and quarters adding up to $3.15, with 7 more quarters than dimes. To solve this, let's denote the number of dimes as d and the number of quarters as q. We have two equations based on the problem statement:
0.10d + 0.25q = 3.15 (The total value in dollars.)
q = d + 7 (There are 7 more quarters than dimes.)
Substituting the second equation into the first gives:
0.10d + 0.25(d + 7) = 3.15
This simplifies to:
0.10d + 0.25d + 1.75 = 3.15
Combining like terms:
0.35d = 3.15 - 1.75
0.35d = 1.40
Dividing both sides by 0.35 gives:
d = 1.40 / 0.35 = 4
Therefore, there are 4 dimes and substituting back:
q = 4 + 7 = 11 quarters.
Problem 2: Mixing Bleach Solutions
To make a 12oz 12% bleach solution from a 4% solution, let's denote the amount of pure bleach needed as b ounces. The amount of 4% solution would then be 12 - b ounces. The equation representing the mixture is:
(12 - b) * 0.04 + b = 12 * 0.12
This simplifies to:
0.48 - 0.04b + b = 1.44
0.96b = 0.96
b = 0.96 / 0.96 = 1 ounce of pure bleach is needed.
how many roots does the polynomial function y=(x-2)(x+3)^2 have
Answer:
3
Step-by-step explanation:
There is one root for each binomial factor.
... y = (x -2)(x +3)(x +3) . . . has 3 binomial factors
_____
The roots are the values of x that make the factors be zero.
... (x -2) = 0 when x = 2
... (x +3) = 0 when x = -3
... (x +3) = 0 when x = -3
The root at x = -3 is said to have multiplicity 2.
_____
Sometimes, we're concerned with the number of distinct roots. Since the three roots only have two different values, there are 2 distinct roots.
Step-by-step explanation:
1) Graph the function (if you don't know how you can use the website Desmos, it's an online graphing calculator.
2) Count the roots (roots are the number of times the line touches the x-axis)
Confirmed answer on ∧pe×
^just check that the equation is the exact same
Use the substitution method to solve the system of equations
Answer:
(12,14)
Step-by-step explanation:
9x-3(3x-4)=14
9x-9x+12=14
12=14
Is the triangle with side lengths of 18cm, 24cm and 30 cm a right triangle ?
If a, b and c are the lengths of a right triangle and c is the longest side, then:
[tex]a^2+b^2=c^2[/tex]
We have a = 18cm, b = 24cm and c = 30cm. Substitute and check:
[tex]L_s=18^2+24^2=324+576=900\\\\R_s=30^2=900\\\\L_s=R_s[/tex]
Answer: It's the right triangle.The triangle with side lengths of 18cm, 24cm, and 30cm is a right triangle and this can be determined by using the Pythagorean theorem.
Given :
The triangle with side lengths of 18cm, 24cm, and 30 cm.
The following steps can be used to determine the given triangle is a right triangle or not:
Step 1 - The Pythagorean theorem can be used to determine whether the given triangle is a right triangle or not.
Step 2 - According to the Pythagorean theorem, the sum of the square of the two shorter sides of the triangle is equal to the square of the larger side of the triangle that is:
[tex]\rm H^2 = P^2+B^2[/tex]
where H is the hypotenuse, P is the perpendicular, and B is the base of the right angle triangle.
Step 3 - To determine the given triangle is a right angle triangle, the Pythagorean theorem must be satisfied.
[tex]24^2 + 18^2 = 30^2[/tex]
LHS = [tex]24^2+18^2[/tex]
= 576 + 324
= 900
RHS = [tex]30^2[/tex]
= 900
So, LHS is equal to RHS. Therefore, the given triangle is a right angle triangle.
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write an equation in slope- intercept form y=mx=b of the line through point p(6,7) with slope -2
Answer:
The equation would be y = -2x + 19
Step-by-step explanation:
To find this, we can use the point and the slope in point-slope form. The we solve for y.
y - y1 = m(x - x1)
y - 7 = -2(x - 6)
y - 7 = -2x + 12
y = -2x + 19
To write an equation in slope-intercept form, use the formula y = mx + b. In this case, substitute the given point and slope into the equation.
Explanation:To write an equation in slope-intercept form, we need to use the formula y = mx + b, where m is the slope and b is the y-intercept. In this case, we are given a point P(6,7) and a slope of -2. We can substitute these values into the equation to find the y-intercept.
Using the point-slope form of the equation: y - y1 = m(x - x1), we substitute x1 = 6, y1 = 7, and m = -2. This gives us the equation: y - 7 = -2(x - 6).
Distributing the -2 on the right side of the equation, we get: y - 7 = -2x + 12. Finally, we can rearrange the equation to slope-intercept form by isolating y on one side: y = -2x + 12 + 7, which simplifies to y = -2x + 19.
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Alaina is selling wreaths and poinsettias for her chorus fundraiser. Wreaths cost $27 each poinsettia cost $20 each. If she sold 15 poinsettias and made $543, how many wreaths did she sell?
Answer:
The number of wreaths Alaina sells is 9 .
Step-by-step explanation:
As given
Alaina is selling wreaths and poinsettias for her chorus fundraiser.
Wreaths cost $27 each poinsettia cost $20 each.
If she sold 15 poinsettias and made $543.
Let us assume that the number of wreaths Alaina sells = x
As the number of poinsettias Alaina sells = 15
Than the equation becomes
27x + 15 × 20 = 543
27x + 300 = 543
27x = 543 - 300
27x = 243
[tex]x = \frac{243}{27}[/tex]
x = 9
Therefore the number of wreaths Alaina sells is 9 .
Alaina sold 9 wreaths. After calculating the revenue from poinsettias ($300), the remaining amount ($243) was divided by the cost of one wreath ($27) to find the number of wreaths sold.
To determine how many wreaths Alaina sold, we first need to calculate the total revenue from selling 15 poinsettias. Since each poinsettia costs $20, we multiply 15 by $20:
15 poinsettias x $20/poinsettia = $300Now, subtract the total revenue from poinsettias from the total amount made:
$543 total made - $300 from poinsettias = $243 remainingThis remaining amount must be from the sale of wreaths. Since each wreath costs $27, we divide $243 by the cost of one wreath:
$243 / $27 per wreath = 9 wreaths soldTherefore, Alaina sold 9 wreaths.
b&b inc. has ordered machine parts and receives a charge of $15 for shipping and handling plus $20 per part. write an equation that represents the cost c of ordering p parts.
Answer:
C = 15 + 20*p
Step-by-step explanation:
Cost for ordering = shipping and handling plus cost per part * number of parts
C = 15 + 20*p
The linear equation representing the cost of ordering machine parts from B&B Inc. is c = 15 + 20p. This accounts for a fixed shipping cost of $15 and a variable cost of $20 per part.
Explanation:The subject of this question is linear equations in Mathematics. B&B Inc. is ordering machine parts and incurs a fixed shipping and handling cost of $15, plus a variable cost of $20 per part. The equation representing this situation can be developed with 'c' representing the total cost and 'p' representing the number of parts ordered. Considering the fixed and variable costs, the equation would be c = 15 + 20p where $15 is the fixed shipping and handling cost, and $20p represents the variable cost which depends on the number of parts ordered.
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Given the literal equation for the area formula of a trapezoid: equation is in the photo attached. Only do the first one. PLEASE SHOW WORK :)
Answer:
2A/h - b1 = b2
Step-by-step explanation:
A = 1/2 h ( b1+b2)
We want to solve for b2
Multiply each side by 2
2A = 2* 1/2 h ( b1+b2)
2A = h ( b1+b2)
Divide each side by h
2A / h = h/h ( b1+b2)
2A / h = b1+b2
Subtract b1 from each side
2A/h - b1 = b1 + b2 -b1
2A/h - b1 = b2
Find the value of x in the figure below:
20
60
180
40
Answer:
40
Step-by-step explanation:
x + 2x + x + 20 = 180
4x + 20 = 180
4x = 160
x = 40
Answer:
Step-by-step explanation:
x=40
For which function will both ordered pairs (2, 8) and (6, 12) be solutions?
y = 4x
y = 6 + x
y = 2x
y = 18 - x
Kate wants to buy a new bicycle from a sporting goods store. The bicycle she wants normally sells for $270. The store has a sale where all bicycles cost 4 9 of the regular price. What is the sale price of the bicycle?
Answer:
The sale price of the bicycle is $120.
Step-by-step explanation:
To find the amount, simply multiply the cost by the fraction of the cost that you are paying.
$270 * 4/9 = $120
This would be the cost of the bike.
A square measures 8 inches on each side. What is its area rounded off to the nearest square centimeter? (Note: 1 inch ≈ 2.54 cm) a) 413 sq cm b) 512 in.² c) 64 cm² d) 32 in.²
Answer:
C.) 413 cm^2
Step-by-step explanation:
To figure out the area of a square, much like a rectangle we multiply length × width. In this case because the length and width are the same (definition of a square) then it's simply [tex]s^2[/tex] and 8 inches is 20.32 cm (8x2.54):
[tex]s^2=20.32^2=412.90 \approx 413[/tex]
a.) 413 cm^2
Answer:
41 sq cm is the answer
Step-by-step explanation:
Given that [tex]2^x[/tex] = 7, find the value of [tex]4^x^-^1[/tex].
Answer:
[tex] \dfrac{49}{4} = 12.25 [/tex]
Step-by-step explanation:
[tex] 4^{x-1} = [/tex]
[tex] = (2^2)^{x - 1} [/tex]
[tex] = 2^{2(x - 1)} [/tex]
[tex] = 2^{2x - 2} [/tex]
[tex] = 2^{x + x - 2} [/tex]
[tex] = 2^x \times 2^x \times 2^{-2} [/tex]
[tex] = 7 \times 7 \times \dfrac{1}{2^2} [/tex]
[tex] = \dfrac{49}{4} = 12.25 [/tex]
Kendyl is memorizing a piece of saxophone music to perform at a local festival. She currently has the first eight bars memorized and plans to memorize two more bars everyday until she has the whole piece memorized. Write a recursive formula to model Kendyl's progress.
Answer:
The recursive formula to model Kendyl's progress is:
Fourth option: an=an-1 + 2, a1=8
Step-by-step explanation:
She currently has the first eight bars memorized: The first value is 8:
a1=8
She plans to memorize two more bars everyday until she has the whole piece memorized:
The number of bars memorized is two more than the last day:
an=an-1 + 2
Then, the recursive formula is:
an=an-1 + 2, a1=8
Answer:
D an=an-1 + 2, a1=8 hope that helps
I am redecorating my home. I am adding tile to the kitchen which is 18' long and 16' wide. I am also tiling the master bathroom. It is 12' wide and 15' long. I need to buy enough tile to cover both spaces. How many square feet of tile do I need for the kitchen? How many square feet of tile will I need for the bathroom? If the tile costs $2.50 per sq ft, how much money will I spend on tile?
Blank # 1
Blank # 2
Blank # 3
Answer:
The kitchen requires 288 sq. ft. of tile
The master bathroom requires 180 sq. ft. of tile
In total, we will spend $1170
Step-by-step explanation:
The area of the kitchen is length * width:
Area of Kitchen = [tex]18*16=288[/tex] sq. ft.
The area of the master bathroom is length * width:
Area of Master Bathroom = [tex]12*15=180[/tex] sq. ft.
The kitchen requires 288 sq. ft. of tile
Question 2: " How many square feet of tile will I need for the bathroom?"The master bathroom requires 180 sq. ft. of tile
Question 3: "If the tile costs $2.50 per sq ft, how much money will I spend on tile?"In total, we require [tex]288+180=468[/tex] sq. ft. of tiles. If $2.50 is charged per square feet, in total we will spend:
[tex]468*2.5=1170[/tex] dollars
You'll need 288 square feet of tile for the kitchen, 180 square feet for the bathroom, and the total cost for the tile will be $1170.
To calculate the amount of tile needed for the kitchen and the master bathroom, you first need to determine the area of each room. Area is calculated by multiplying the length by the width of the room.
For the kitchen:
Length = 18 feet
Width = 16 feet
Area = Length x Width = 18 ft x 16 ft = 288 square feet
For the master bathroom:
Length = 15 feet
Width = 12 feet
Area = Length x Width = 15 ft x 12 ft = 180 square feet
To calculate the total cost of the tile:
Cost per square foot = $2.50
Total area = Area of kitchen + Area of bathroom = 288 sq ft + 180 sq ft = 468 square feet
Total cost = Total area x Cost per square foot = 468 sq ft x $2.50 = $1170
A 24000 gallon of pool is being filled at the rate of 40 gallons per minute at this rate how many minutes will it take to fill up this pool A.450 B.560 C.600 D.150
Answer:
Option no C 600 minutes
Step-by-step explanation:
Given:
gallons of pool = 24000 gallon
Rate at which it is filled = 40 gallons per minute
To find :
Time taken to fill the pool=?
Solution:
We know that rate is the time in which a thing is being done at per minute or per hour or per second. In our question it is given that the rate is 40 gallons per minute which means that 40 gallons are filled in one minute
Now
In one minute = 40 gallons filled
Total pool size = 24000 gallons
Total time taken = [tex]\frac{Total pool size}{gallon filled in one minute}[/tex]
Putting in the values
Total time taken = [tex]\frac{24000}{40}[/tex]
Total time taken = 600 minutes
So the answer is option c which is 600 minutes
1. Which of the following is not equivalent to the formula for angular velocity, v = wr?
vw = r
v/w = r
v/wr = 1
v/r= w
2. Lucy's goal for her cycling class at the gym is to burn 450 calories in one hour. The number of calories (c) she actually burns in one hour varies no more than 45 calories. Which inequality below represents this scenario?
|c − 450| ≤ 45
|c + 450| ≥ 45
|c − 45| ≤ 450
|c − 45| ≥ 450
Answer:
vw = r This is not correct
abs ( c - 450) <= 45
Step-by-step explanation:
1. v = wr
Divide by w Divide by wr Divide by r
v/w = wr/w =r v/wr = wr/wr =1 v/r = wr/r =w
vw = r This is not correct
v/w = r This one is good
v/wr = 1 This one is good
v/r= w This one is good
2. When working with absolute values, the amount that can vary is on the other side from the absolute value.
abs( value - target) inequality amount that it varies by
the target is 450
no more than is less than or equal to
the amount we can vary by is 45
abs ( c - 450) <= 45
1. The first offered choice is equivalent to ...
... v = r/w . . . . . divide both sides by w
which is not the same as v = wr.
___
2. The wording "no more than 45" means ≤ 45. There's only one formula with such a relationship—the first one.
Comment on "this scenario"
The problem statement describes several relationships, and never tells us whether Lucy's goal is met. The precise "scenario" that is intended to be modeled is not clear. The first inequality has a solution that is the range of calories Lucy might have burned had she reached her goal.
The other inequalities describe other "scenarios," some of which are harder to describe.
The letters in the word MISSISSIPPI are put into a bag. What is the probability of randomly selecting the letter S from the bag?
Strep throat is caused by Streptococcus bacteria. The amount of bacteria multiplies at a rate of 10^13 per 10^2 hours. Part B What is the total amount of bacteria present after 10^3 hours? Show your work.
Answer:
10^14
Step-by-step explanation:
Number of bacteria For 10^2 hours = 10^13
Number of bacteria for 1 hour = 10^13/10^2 = 10^11
Number of bacteria for 10^3 hours = 10^11 x 10^3 = 10^ (11+3) = 10^14
1. What is the smallest whole number greater than √30 + √50 + √110?
2. For how many single-digit positive integers d are there an integer n for which the units digit of [tex]d^{n}[/tex] is 6?
3. A rectangular prism with whole number dimensions has faces with areas 54, 72, and 108 square inches. How many cubic inches are there in its volume?
60 points! Partial answers accepted as well.
For the members of a neighborhood meeting group, the probability of randomly selecting a member who likes to cook is 42%, the probability of randomly selecting a member who likes to sew is 23%, and the probability of randomly selecting a member who likes to both cook and sew is 7%.
What is the probability of randomly selecting a member who likes to cook or likes to sew?
Answer: Probability of randomly selecting a member who likes to cook or likes to sew = 58%
Step-by-step explanation:
Since we have given that
Probability of a randomly selecting a member who likes to cook=P(C) = 42%
Probability of a randomly selecting a member who likes to sew =P(S)= 23%
Probability of a randomly selecting a member who likes to both cook and sew
[tex]P(C\cap S)=7\%[/tex]
As we know the "Probability rules " :
[tex]P(C\cup S)=P(C)+P(S)-P(S\cap C)\\\\P(C\cup S)=42+23-7\\\\P(C\cup S)=58[/tex]
So, Probability of randomly selecting a member who likes to cook or likes to sew = 58%
Answer:
58%
Step-by-step explanation:
Which property is illustrated by the following statement statement
Answer:
C) Symmetric
Step-by-step explanation:
The symmetric property is the idea that if A = B, then B = A. Flipping the equation around doesn't matter.
It's like saying 2+3 = 5 is the same as 5 = 2+3. We can extend the symmetric property to not only deal with equations, but include congruence statements as well.
Answer:symmetric
Step-by-step explanation: a p e x
M∠A = 75 + 5x
m∠B = 111 − 6x
m∠C = 87 + 3x
m∠D = 39 + 6x
Quadrilateral ABCD is a parallelogram if both pairs of opposite angles are congruent. Prove that quadrilateral ABCD is a parallelogram by finding the measures of the opposite angle pairs?
A) 95°, 85°
B) 105°, 75°
C) 115°, 65°
D) 125°, 55°
Answer:
See below
Step-by-step explanation:
For a parallelogram m < A = m < C so:-
75 + 5x = 87 + 3x
2x = 12
x = 6
and m< A = 75 + 30 = 105
and m < C = 87 + 18 = 105
Now if the other 2 angles are = 75 degrees( that is the same side angles add up to 180 degrees) we have proved that it is a parallelogram.
m < B = m < D
111 - 6x = 39 + 6x
-12x = -72
x = 6
m < B = 111 - 36 = 75 and m < D = 39 + 36 = 75
So this has been proved.
To prove that quadrilateral ABCD is a parallelogram, solve for x to find the values that make the opposite angles congruent. Plug in the values of x to find the measures of the opposite angle pairs. None of the given answer choices are correct.
Explanation:To prove that quadrilateral ABCD is a parallelogram, we need to show that both pairs of opposite angles are congruent. We are given the measures of the angles using variable expressions. We can set the expressions for opposite angles equal to each other and solve for x to find the values of x that make the opposite angles congruent. Finally, we plug in the values of x to find the measures of the opposite angle pairs.
Step 1: Set the expressions for opposite angles equal to each other: 75 + 5x = 39 + 6x and 111 - 6x = 87 + 3xStep 2: Solve the equations for x. For the first equation, subtract 5x and 39 from both sides to get -64 = x. For the second equation, subtract 87 and 3x from both sides to get 24 = 9x. Divide both sides by 9 to get x = 8/3.Step 3: Plug in the values of x into the expressions for the opposite angles to find their measures. For angle A, substitute x = -64 into 75 + 5x to get 75 + 5(-64) = -205. For angle D, substitute x = -64 into 39 + 6x to get 39 + 6(-64) = -375. For angle B, substitute x = 8/3 into 111 - 6x to get 111 - 6(8/3) = 89. For angle C, substitute x = 8/3 into 87 + 3x to get 87 + 3(8/3) = 95.Step 4: Check if the opposite angles are congruent. Angle A and angle C have measures of -205 and 95, respectively, which are not congruent. Angle B and angle D have measures of 89 and -375, respectively, which are also not congruent.Since the opposite angles are not congruent, we cannot conclude that quadrilateral ABCD is a parallelogram. Therefore, none of the given answer choices (A) 95°, 85°, (B) 105°, 75°, (C) 115°, 65°, or (D) 125°, 55°, are correct.
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Suppose that you invest $6000 into a high yield savings account that earns 2% annual interest and is compounded monthly. If you do not deposit or withdraw any money from the account, how much money will be in the account after 20 years?
i will only be adding the answer due to the fact that I have to leave soon and i have been helping people with this all day.
8916 AFTER 20 YEARS
Find the coordinates of point P along the directed line segment AB so that AP to PB is the given ratio. A(−8, 0) , B(−3, 5) ; 2 to 3
Answer:
Step-by-step explanation:
[tex]\bf ~~~~~~~~~~~~\textit{internal division of a line segment} \\\\\\ A(-8,0)\qquad B(-3,5)\qquad \qquad \stackrel{\textit{ratio from 2 to 3}}{2:3} \\\\\\ \cfrac{A\underline{P}}{\underline{P} B} = \cfrac{2}{3}\implies \cfrac{A}{B} = \cfrac{2}{3}\implies 3A=2B\implies 3(-8,0)=2(-3,5)\\\\[-0.35em] ~\dotfill\\\\ P=\left(\frac{\textit{sum of "x" values}}{\textit{sum of ratios}}\quad ,\quad \frac{\textit{sum of "y" values}}{\textit{sum of ratios}}\right)\\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf P=\left(\cfrac{(3\cdot -8)+(2\cdot -3)}{2+3}\quad ,\quad \cfrac{(3\cdot 0)+(2\cdot 5)}{2+3}\right) \\\\\\ P=\left(\cfrac{-24-6}{5}~,~\cfrac{0+10}{5} \right)\implies P=(-6~,~2)[/tex]
The height of a triangle is 2 less than 5 times its base. If the base of the triangle is x feet, and the area of the triangle is 12 square feet, which equation models this situation?
A. 5x2 − 2x − 24 = 0
B. 5x2 − 2x − 6 = 0
C. 5x2 − 2x − 12 = 0
D. 25x2 − 10x − 24 = 0
Answer:
A. 5x^2 − 2x − 24 = 0
Step-by-step explanation:
height = 5b-2
b =x
We can rewrite the height as
h = 5x-2
We know the formula for area of a triangle
A = 1/2 bh
A =1/2 x * (5x-2)
Distributing the x
A= 1/2 (5x^2 - 2x)
We know A =12
12 = 1/2 (5x^2 - 2x)
Multiply each side by 2
12*2 = 2*1/2 (5x^2 - 2x)
24 = 5x^2 - 2x
Subtract 24 from each side
24-24 = 5x^2 - 2x-24
0 = 5x^2 - 2x-24
Answer:
C. 5x^2 − 2x − 24 = 0
Step-by-step explanation: