Answer:
option D is correct.
y=9x represents a proportional situation
Step-by-step explanation:
If two quantities are said to have a proportional relationship if they vary in such a way that one of the quantities is a constant multiple of the other i.e,
y = |k|x ; where |k| is constant proportionality.
By definition :
y =9x where k =9 is constant , represents a proportional relationship.
Answer:
The correct answer option is y = 9x.
Step-by-step explanation:
From the given equations as the possible answer options, y = 9x is the correct answer which represents a proportional situation.
Two values (variables in this case) are said to be proportional if they change in a way such that there is a constant multiple multiplied to one of the values.
Here, in the equation y = 9x, y and x are the two variable and 9 is the constant multiple.
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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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
Plz help
Which expression is equal to 228−−√−563−−√ ?
−377√
−7√
7√
−117√
Answer:
the correct answer is -11v7
Step-by-step explanation:
The correct expression that is equal to (2√28 - 5√63) is;
Option D; -11√7
The correct question is;
Which expression is equal to 2√28 - 5√63
The correct options are in the link at the end of this answer.
The given expression is in surd form. To solve it, we first have to break down the numbers inside the square roots into a product of two numbers with one of the numbers being a perfect square.
We know that;
28 can be expressed as 7 × 4 = 28
Also; 63 can be expressed as 7 × 9 = 63
Thus;
2√28 - 5√63 will be written as; 2√(7 × 4) - 5√(9 × 7)
From product law of surds, we know that;
√(a × b) = √a × √b
Thus, our expression is;
2(√4 × √7) - 5(√9 × √7)
⇒ 2(2√7) - 5(3√7)
⇒ 4√7 - 15√7
Factorize √7 out to get;
(4 - 15)√7
⇒ -11√7
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(15 points)
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.
Find the leg of each isosceles right triangle when the hypotenuse is of the given measure.
Given = 5√6
Answer:
Each of the legs of isosceles right triangle is 5[tex]\sqrt{3}[/tex]
Step-by-step explanation:
Watch the attached figure for the isosceles right angled triangle
Looking at the figure we see that AB=5√6 and BC=CA
According to the Pythagorean theorem the square of the hypotenuse is equal to the sum of the squares of the other two sides of a right triangle.
1) Applying the Pythagorean theorem to the isosceles right triangle, we have
[tex]BC^{2} + CA^{2} = AB^{2}[/tex]
2) Let BC=a and CA=a as they both are equal
So,
[tex]a^{2} + a^{2} = (5\sqrt{6} )^{2}[/tex]
=> [tex]2a^{2} = (5\sqrt{6} )(5\sqrt{6} )[/tex]
=> [tex]2a^{2} = 5*5*\sqrt{6}*\sqrt{6}[/tex]
=> [tex]2a^{2} = 25*6[/tex] (since √6*√6 = (√6)²= 6)
=> [tex]2a^{2} = 150[/tex]
3) Dividing both sides by 2, we get
[tex]\frac{2a^{2} }{2} =\frac{150}{2}[/tex]
4) Cancelling out the 2's on the left, we get
[tex]a^{2}[/tex] = 75
5) Taking the square root on both sides, we have
[tex]\sqrt{a^{2}} = \sqrt{75}[/tex]
=> a = 5[tex]\sqrt{3}[/tex]
So,
Each of the legs of isosceles right triangle is 5[tex]\sqrt{3}[/tex]
Answer:
Hi :) if you're coming from heritage and/or your answer needs a 2 in it, it would be 6 sqrt 2
Step-by-step explanation:
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:
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.
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
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:
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]
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.
For which function will both ordered pairs (2, 8) and (6, 12) be solutions?
y = 4x
y = 6 + x
y = 2x
y = 18 - x
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:
Trever and Marisa together have 28 t shirts to sell if marissa has 4 fewer t shirts than trevor find how many t shirt Trevor has
Answer:
Trevor has 16 number of shirts
Step-by-step explanation:
We have been given that Trevor and Marisa together have 28 t shirts to sell if Marissa has 4 fewer t shirts than Trevor
let the number of shirts Trevor have be x
And since, Marissa has 4 fewer than Trevor so number of shirts Marissa will have be x-4
Hence, according to question equation becomes:
x+x-4=28
We will solve for x to find the number of t shirts Trevor has
2x -4 =28
2x = 32
x =16
Hence, Trevor has 16 number of shirts
A recipe that will make 3 pies calls for 7cups of flour. How many pies can you make with 28 cups of flour?
A problem states: "There are 2 more horses than cows in a field. There are 16 animals in the field in all. How many horses are there in the field?"
Let h represent the number of horses.
Which equation represents the situation?
2h + 2 = 16
h + 2 = 16
2(h+2)=16
2h−2=16
Answer:
Correct choice is D
Step-by-step explanation:
Let h represent the number of horses. If there are 2 more horses than cows in a field, then (h-2) represent the number of cows. In total there are h+(h-2) animals. It is known that there are 16 animals in the field in all, then
h+h-2=16,
2h-2=16.
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]
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
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
WILL MARK BRAINLIEST!!! PLEASE HELP!!!! Triangle RDW below is a right triangle. Line RW is 26 units, Line WD is 24 units, and Line DR is 10 units. The measure of angle W is 50°. Find the sine W.
A. 5/10
B. 5/13
C. 13/5
D. 12/13
Answer:
5/13
Step-by-step explanation:
sine W = sine 50 degrees = opposite /hypotenuse
= 10/26
= 5/13
Final answer:
The sine of angle W in the right triangle is the ratio of the side opposite to angle W (24 units) to the hypotenuse (26 units). Therefore, the sine of angle W is 12/13(option D).
Explanation:
The problem describes a right triangle with sides of length 26 units, 24 units, and 10 units, and it asks for the sine of angle W, which is known to be 50 degrees. In a right triangle, the sine of an angle is the ratio of the length of the opposite side to the angle over the length of the hypotenuse. Thus, to find the sine of angle W, we need the opposite side to angle W, which is WD measuring 24 units, and the hypotenuse RW, measuring 26 units.
The sine of angle W is calculated by the formula
sine of angle W = WD\RW
24\26
12\13
What is the greatest possible integer value of x for whichsquare root of x-5 is an imaginary number?
Answer: 4
Step-by-step explanation:
√x imaginary if and only if x < 0
√(x-5) imaginary ifi x-5 < 0
x<5
4 is the largest integer < 5.
Answer: It is 4
Step-by-step explanation: I got it correct on mines.
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
You earn $1,166 gross taxable income every week, and have claimed no exemptions. Assuming that you have no other sources of income, what is the amount of income tax withheld each week? a. $323 b. $337 c. $340 d. $344Please select the best answer from the choices provided
Answer:
C
Step-by-step explanation:
Gross taxable Income = $ 1,166
Rate of Income tax = 30%
Amount of income tax = 30 % of 1,166
= [tex]\frac{30*1166}{100}[/tex]
=$339.6
≅$340
Answer:
$340
Step-by-step explanation:
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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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
PLEASE HELP The Brick Corporation pays its cumulative preferred stockholders $1.95 per share. There are 40,000 shares of preferred stock and 80,000 shares of common stock. In 2001, 2002, and 2003, Brick Corporation did not declare a dividend. In 2004, the Board of Directors declared a $600,000.00 dividend. What is the amount that the common shareholder will receive per share?
Answer:
$5.00
Step-by-step explanation:
Dividend Per Share = Total Dividends Paid / Shares Outstanding
How many shares outstanding?
Preferred stock + common stock
80,000+40000=120000
Dividend Per Share = $600,000.00 /120000
=$5.00
The preferred shareholder gets 1.95 per share plus dividends.
The common shareholder only gets dividends.
Answer:
$3.60
Step-by-step explanation:
The beginning balance of Zerina's savings account for the month of July was $1800 and it remained this way for the first 12 days of the month. On July 13, Zerina made a withdrawal of $400, so her balance changed, and it remained the same for a total of 8 days. On July 21, Zerina made a deposit of $1200, so her balance changed again, and it remained the same for 11 days to finish out the month. If Zerina's savings account has an APR of 7.3%, calculates interest daily, and pays interest at the end of the month, how much did Zernia earn in interest in the month of July?
Answer:
Interest income in the month = $12.28
Final balance = 2612.28
Step-by-step explanation:
The initial amount of $1800 remains in the account for the first 12 days of July. Then:
Interest earned = [tex]\frac{1800 * 0.073 * 12}{365} = 4.32[/tex]
Withdrawal = 400
New balance = 1800 - 400 = 1400
The amount 1400 remains in the account for 8 days. Then:
Interest Earned = [tex]\frac{1400 * 0.073 * 8}{365} = 2.24[/tex]
Deposit = 1200
New balance = 1400 + 1200 = 2600
The amount 2600 remains in the account for 11 days. Then:
Interest Earned = [tex]\frac{2600 * 0.073 * 11}{365} = 5.72[/tex]
Balance = 2600 + 4.32 + 2.24 + 5.72 = 2612.28
Interest income in the month = 4.32 + 2.24 + 5.72 = $12.28
What must the length of segment AD be for the quadrilateral to be a parallelogram? 8 units 16 units 31 units 62 units
Answer:
the answer is C. 31 units
I just did the assignment
The length of segment AD be for the quadrilateral to be a parallelogram is 8 units. Therefore, option A is the correct answer.
What is parallelogram?A parallelogram is a special kind of quadrilateral that is formed by parallel lines. The angle between the adjacent sides of a parallelogram may vary but the opposite sides need to be parallel for it to be a parallelogram. A quadrilateral will be a parallelogram if its opposite sides are parallel and congruent.
In quadrilateral ABCD, AD║BC.
Here, AD=BC
3x+7=5x-9
2x=16
x=8
Therefore, option A is the correct answer.
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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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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
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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