Let ABCD be a parallelogram such that AB = 10 , BC = 14, and Angle A = 45. Find the area of the parallelogram. Please do not answer in decimal form. Answer using a square root
Answers
Answer:
70√2 units²
Step-by-step explanation:
(see attached for reference notes on parallelograms)
we are given ABCD is a parallelogram where
Short Length, AB = 10 units
Long Length, BC = 14 units
Angle A = 45°
The area of the parallelogram is hence,
= AB x BC sin 45°
= 10 x 14 x sin 45
= 140 sin 45° (recall from special angles, that sin 45° = 1/√2)
= 140/√2 (remove radical from denominator by multiplying by √2/√2)
= (140/√2) x (√2/√2)
=70√2 units²
Related Questions
Math problem: If Alexander the Great had lived 9 years more his reign would have lasted 1/2 his life, while if he had lived 9 years less his reign would have lasted 1/8 of his life. How old was Alexander when he died? And how long did he reign?
Answers
Answer: lived 48 years
reigned for 15 years
Step-by-step explanation:
Let x represent the number of years he reigned.
Let y represent Alexander's age.
Use the given information to create a system of equations:
Equation 1: x + 9 = (1/2)y
Equation 2: x - 9 = (1/8)y
Multiply the second equation by -1 and add the equations to eliminate x:
[tex].\quad x+9=\dfrac{1}{2}y\\\\\underline{-x+9}=\underline{-\dfrac{1}{8}}y\\\\.\qquad 18=\dfrac{3}{8}y\\\\.\qquad 48=y[/tex]
Input y = 48 into either equation to solve for x:
[tex].\quad x+9=\dfrac{1}{2}(48)\\\\.\quad x+9 = 24\\\\.\qquad x = 15[/tex]
I AM GONNA CRY PLEASE PLEASE HELP ME
You invest $5,000 dollars in an account at 1.6% interest and interest is compounded
annually (once a year).
a) Write an equation that shows the amount of money you have after x years.
b) How much money would you have after 15 years?
Answers
Part (a)
Answer: y = 5000(1.016)^x------------------
Explanation:
You use the compound interest formula
A = P(1 + r/n)^(n*t)
where
A = final amount after t yearsP = amount deposited (principal) = 5000r = decimal form of interest rate = 0.016n = number of times we compound per year = 1t = number of years = x, some unknown numberAfter plugging those values in, you would go from A = P(1 + r/n)^(n*t) to
A = P(1 + r/n)^(n*t)
A = 5000(1 + 0.016/1)^(1*x)
A = 5000(1.016)^x
Since you're using x for the input, it's possible your teacher wants you to use y for the output. So replace A with y to get y = 5000(1.016)^x
==============================================
Part (b)
Answer: 6344.18 dollars--------------------------
Explanation:
Plug x = 15 into the equation we found back in part (a). Use your calculator to simplify. Round to the nearest hundredth which is rounding to the nearest penny.
y = 5000(1.016)^x
y = 5000(1.016)^15
y = 6344.1818561953
y = 6344.18
Answer:
girlie u gotta chill
Step-by-step explanation:
What is the value of x in the equation 2(5x + 4) = 17? (5 points) a start fraction five over two end fraction b start fraction two over five end fraction c start fraction nine over 10 end fraction d start fraction 17 over 18 end fraction
Answers
pls help!!
will give the brainliest!
Need explanation
Urgent!!!
Answers
Answer:
h=4 and k=-4....
Step-by-step explanation:
hopevit helps you
Step-by-step explanation:
[tex]A^2= \begin{bmatrix} 4 & 0 \\ 4 & 4 \end{bmatrix}[/tex]
Equate this to $hA + kI$
Thus,
[tex] A^2= h \begin{bmatrix} 2 & 0 \\ 1 & 2 \end{bmatrix} + k \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}[/tex]
Hence we have the following equations (by equating corresponding terms on both sides):
$2h+k=4$
$h=4$
Solve these to get $h=4$ and $k=-4$
A student took a survey of the class. There are 42 students in the class. The student surveyed favorite foods. 10 said hamburgers, 22 said pizza, 8 said french fries, and 2 said salad. Which percentage of the class chose pizza?
Answers
Answer:
52.38%
Step-by-step explanation:
Given that,
Total number of students in the class is 42
Out of 42, 10 like hamburgers, 22 like pizza, 8 like french fries, and 2 like salad.
We need to find the percentage of the class chose pizza. There are 22 student who like to have pizza. Required percentage is given by :
[tex]P=\dfrac{22}{42}\times 100\\\\P=52.38\%[/tex]
So, 52.38% of students chose pizza.
Use the Binomial Theorem to expand (x - 4y)³.
Answers
Answer:
x^3-64y^3
Step-by-step explanation:
(x-4y)^3
(x)^3-(4y)^3
x^3-64y^3
Hope this helps ;) ❤❤❤
what is your average speed if you drive 100km south and then 130km east and it takes 3.25 hours give your answers in km/hr and ft/sec
Answers
Answer:
Answer:
speed = 43.974 miles per hour
= 43.974 mi/h
Step-by-step explanation: speed calculator
Solve for all values of x in simplest form
Answers
Answer:
x = -16/5 or
x = 6/5
Step-by-step explanation:
[tex]-\left|5+5x\right|-9=-20\\\\\mathrm{Add\:}9\mathrm{\:to\:both\:sides}\\-\left|5+5x\right|-9+9=-20+9\\\\Simplify\\-\left|5+5x\right|=-11\\\\\mathrm{Divide\:both\:sides\:by\:}-1\\\\\frac{-\left|5+5x\right|}{-1}=\frac{-11}{-1}\\\\\left|5+5x\right|=11\\\\\mathrm{Apply\:absolute\:rule}:\\\\\mathrm{If}\:|u|\:=\:a,\:a>0\:\mathrm{then}\:u\:=\:a\:\quad \mathrm{or}\quad \:u\:=\:-a\\5+5x=-11\quad \mathrm{or}\quad \:5+5x=11\\\\5+5x=-11\quad :\quad x=-\frac{16}{5}\\\\5+5x=11\quad :\quad x=\frac{6}{5}\\[/tex]
[tex]x=-\frac{16}{5}\quad \mathrm{or}\quad \:x=\frac{6}{5}\\[/tex]
The value of x after solving the expression -|5 + 5x| - 9 = -20 is equal to x = -16/5 or x = 6/5.
What do you mean by algebraic expressions ?
Algebraic expression is an equation which consists of variables and the arithmetic operations such as division , multiplication , etc.
The algebraic expression given is -|5 + 5x| - 9 = -20
We know that a modulus sign is a representation of ran absolute value which has two values either a positive or negative value.\
After solving the expression we get :
-|5 + 5x| - 9 = -20
So , after removing the modulus sign we will get two expressions :
-(-(5 + 5x) - 9 = -20
5 + 5x = -11
or
-(5 + 5x) - 9 = -20
-(5 + 5x) = -11
Solving the two expressions we get the value of x as :
x = -16/5
or
x = 6/5
Therefore , the value of x after solving the expression -|5 + 5x| - 9 = -20 is equal to x = -16/5 or x = 6/5.
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which one is greater 24*36 or 18 twenty-fourths doblulded
Answers
Answer:
SO 18²⁴ IS GREATER
Step-by-step explanation:
24×36=864
18²⁴=1.3382588×10³⁰
HOPE IT WILL HELP ^_^
Answer:
24*26
Step-by-step explanation:
18/24ths doubled will result in a fraction while 24*26 is going to be an integer (864) much larger than 3/2= (18/24)*2
In Point-Slope Form, what is the equation of the line perpendicular to y = -8x - 5 that passes through (2,-4)
Answers
Answer:
line: y = (1/8)x - 17/4
Step-by-step explanation:
To find perpendicular of line (negative reciprocal the given slope)
y = -8x-5
Perpendicular slope = (1/8)x
-4 = (1/8)(2) + b
-4 = 1/4 +b
Multiply everything by 4 to make it eaiser
-16 = 1 -+4b
-17 = 4b
b = -17/4
Select all of the following statements that are true. All real numbers are natural numbers. All whole numbers are integers. All integers are whole numbers. All natural numbers are rational numbers. All irrational numbers are dense.
Answers
Answer:
All whole numbers are integers. AND All natural numbers are rational numbers.
Step-by-step explanation:
Answer:
The answer is D and E
Step-by-step explanation:
0.4r = 1.6 pls answer ASAP and pls show how to correct
Answers
Answer:
r = 4.
Step-by-step explanation:
0.4r = 1.6
4r = 16
2r = 8
r = 4.
0.4(4) = 1.6
1.6 = 1.6
Hope this helps!
Please Help, i will give brainiest. Please solve the problem about Sara kicking football.
Answers
Answer:
20 m
Step-by-step explanation:
The maximum height is given by the vertex form of the equation, that is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
Given
h(t) = - 5t² + 20t ← factor out - 5 from each term
= - 5(t² - 4t)
Using the method of completing the square
add/subtract ( half the coefficient of the t- term)² to t² - 4t
h(t) = - 5(t² + 2(- 2)t + 4 - 4 )
= - 5(t - 2)² + 20 ← in vertex form
with vertex = (2, 20 )
The maximum height is at the value of k = 20
That is the maximum height is 20 m
Please help!! What is 6(4 - y) = 5 + 3?
Answers
Answer:
[tex] \boxed{ \boxed{ \bold{ \sf{2.6}}}}[/tex]Step-by-step explanation:
[tex] \sf{6(4 - y) = 5 + 3}[/tex]
Distribute 6 through the parentheses
[tex] \sf{24 - 6y = 5 + 3}[/tex]
Add the numbers
[tex] \sf{24 - 6y = 8}[/tex]
Move constant to right hand side and change it's sign
[tex] \sf{ - 6y = 8 - 24}[/tex]
Calculate
[tex] \sf{ - 6y = - 16}[/tex]
Divide both sides of the equation by -6
[tex] \sf{ \frac{ - 6y}{ - 6} = \frac{ - 16}{ - 6} }[/tex]
Calculate
[tex] \sf{y = 2.6}[/tex]
Hope I helped!
Best regards!!
Answer: Hi!
First, we need to distribute 6 to the terms inside of the parentheses, 4 and -y.
6 * 4 = 24
6 * (-y) = -6y
Our equation now looks like this:
24 - 6y = 5 + 3
We can now combine like terms.
24 - 6y = 5 + 3
5 + 3 = 8
Our equation now looks like this:
24 - 6y = 8
We can now use inverse operations to get rid of 24. Remember, our goal is to isolate the x. The inverse operation for addition (24 is positive) is subtraction, so we subtract 24 on both sides:
24 - 6y = 8
- 24 - 24
Our equation now looks like this:
-6y = -16
Last step! We now use inverse operations to get rid of -6. The inverse operation for multiplication is division (-6 is being multiplied by y); so we divide -6 on both sides.
-6y/-6 = y
-16/-6 = 8/3 = 2 2/3
Our equation now looks like this:
y = 2 2/3
Therefore, your solution is 2 2/3.
Hope this helps!
What is the conjugate of 7-8i?
Answers
Answer:
7 + 8i
Step-by-step explanation:
Conjugate of 7 - 8i is 7 + 8i
Answer:
Step-by-step explanation:
7+8i
Select the inequality that represents the relationship described below.
The sum of three times a number and seven is greater than four times the number.
Answers
Answer:
(C) [tex]3x + 7 > 4x[/tex]
Step-by-step explanation:
Let [tex]x[/tex] represent the number that is unknown.
Using the words, we can write out each equation.
"The sum of three times a number and seven" will be adding 7 to 3x. So [tex]3x + 7[/tex].
"is greater than four times the number." will include a greater than sign and then 4 times the number, x. So:
[tex]> 4x[/tex]
Combining these, we get [tex]3x + 7 > 4x[/tex].
Hope this helped!
===============================================
Work Shown:
x = a number (something unknown)
3x = 3 times a number
3x+7 = the sum of 3 times a number and 7
4x = 4 times a number
3x+7 > 4x is the inequality that forms because the "the sum of 3 times a number and 7" portion is greater than the "4 times a number" portion
How many solutions are there to the equation below 14x+2=12x
Answers
the 3rd and the 4th terms of an arithmetic progression are 6and30 respectively determine the common term,first term and the 10th term
Answers
Answer:
first term= -42
common difference= 24
10th term= 174
36m2 - 25 = 0 please show work :)! Factoring problem
Answers
a^2-b^2=(a+b)(a-b)
Therefore,
36m^2-25=(6m-5)(6m+5)
Rayne sold 3 desks at the local trade show. He paid $4.00 to rent the booth. He gave half of his revenue to the carpenter and was left with $185.50. At what price did Rayne sell each desk?
Answers
Rayne sell each desk at the price of $125.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
Given the following information;
The Number of desks sold = 3
The Amount of rent paid = $4
The Amount paid to carpenter = 1/2 of revenue
The Amount left = $185.50
If Rayee gave half of his revenue to the carpenter and then had $185.50 left.
The his revenue before paying the carpenter will be twice what he has left will be;
($185.50 * 2) = $371
Hence, the total revenue from the sale of 3 desk = ($371 + rent)
= (371 + 4)
= $375
Then each desk cost :
$375 / 3 = 125
Hence, Rayne sell each desk at the price of $125.
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The addition is one of the four fundamental mathematical operations. The selling price of each desk is $122.33.
What is Addition?The addition is one of the four fundamental mathematical operations, the others being subtraction, multiplication, and division. When two whole numbers are added together, the total quantity or sum of those values is obtained.
Revenue generated = Revenue left with Rayne + Revenue with carpenter
Since Rayne gave half of his revenue to the carpenter, therefore, both of them will have the same revenue will them
Revenue generated = Revenue left with Rayne + Revenue left with Rayne
Revenue generated = 2(Revenue left with Rayne)
Revenue generated = 2($185.50)
Revenue generated = $371
Also, Rayne paid a booth rent of $4. Therefore, the total revenue generated will be,
Total revenue generated = Revenue generated + $4
= $371 + $4
= $367
Since Rayne sell 3 desks, therefore, the selling price of each desk will be,
Selling price = $367 / 3
= $122.33
Hence, the selling price of each desk is $122.33.
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solve 36x^2+23=60x using quadratic formula
Answers
Answer:
x₁ = 0.6
x₂ = 1.07
Step-by-step explanation:
36x² + 23 = 60x
36x² - 60x + 23 = 0
x = {-(-60)±√((-60²)-(4*36*23))} / (2*36)
x = {60±√(3600-3312)} / 72
x = {60±√288) / 72
x = {60±16.97) / 72
x₁ = {60-16.97} / 72 = 43.03/72 = 0.6 aprox.
x₂ = {60+16.97} / 72 = 76.97/72 = 1.07 aprox.
verify:
x₁
36*0.6² + 23 = 60*0.6
36*0.36 + 23 = 36
13 + 23 = 36
x₂
36*1.07² + 23 = 60*1.07
36*1.145 + 23 = 64.2
41.2 + 23 = 64.2
Here is a number line with some points labeled. Type the answers into the boxes below. a. Write the number
A as a fraction.
B as a decimal
C as a decimial and a fraction
Answers
Answer:
A = 2/4
B = 1.25
C = 11/4 , 2.75
Step-by-step explanation:
convert the repeating decimals to fractions
1:) repeating 7
?
Answers
16/9
Step-by-step explanation:1,7777777777777 =
= 1,(7)
= (17 - 1)/9
= 16/9
The sum of the measures of the angles of a triangle is 180 degrees the second angle of a triangle is twice the measure of the first angle the third is 20 more than 5 times the first what are the measures of the three angles
Answers
Greetings from Brasil...
As said:
1° angle: X
2° angle: 2X
3° angle: 20 + 5X
"...The sum of the measures of the angles of a triangle is 180 degrees..."
(1° angle) + (2° angle) + (3° angle) = 180
X + 2X + (20 + 5X) = 180
X + 2X + 5X = 180 - 20
8X = 160
X = 160/8
X = 20
But the problem asks for the value of each angle. Thus
1° angle: X
as X = 20, so
1° angle: X = 20
2° angle: 2X
as X = 20, so
2° angle: 2.20 = 40
3° angle: 20 + 5X
as X = 20, so
3° angle: 20 + 5.20 = 20 + 100 = 120
The values of the first, second, and third angles are 20°, 40° and 120° respectively.
Let the first angle = x
Let the second angle = 2 × x = 2x
Let the third angle = 20 + (5 × x) = 20+5x
Total angles in the triangle = 180°
Based on the information above, the angles will be calculated thus:
x + 2x + 5x + 20 = 180
Collect like terms
8x = 180 - 20
8x = 160
x = 160/8
x = 20
First angle = 20°
Second angle = 2x = 2 × 20° = 40°
Third angle = 5x + 20 = (5 × 20°) + 20° = 120°
The angles are 20°, 40°, and 120°
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Solve the equation for x (if possible please show work)
Answers
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{x = - 4}}}}}[/tex]
Step-by-step explanation:
[tex] \sf{3x - 5 = 2x - 9}[/tex]
Move 2x to left hand side and change it's sign
⇒[tex] \sf{3x - 2x - 5 = - 9}[/tex]
Move 5 to right hand side and change it's sign
⇒[tex] \sf{3x - 2x = - 9 + 5}[/tex]
Collect like terms
⇒[tex] \sf{x = - 9 + 5}[/tex]
Calculate
⇒[tex] \sf{x = - 4}[/tex]
Hope I helped!
Best regards!!
Which of the following equations is quadratic? (a) x1x² + 1) = 0
(b) 5(4x + 2) = 3
(c) (x+3)(x + 4) = 5
Answers
Answer:
(c) (x+3)(x+4)=5
Step-by-step explanation:
It's in factored form, and you would use the method of finding the perfect square to get the equation set to zero and find the solutions.
The children from a football club are put into rows in the sports hall. When put in rows of 6 children, there are 3 children left over. When put in rows of 8, there are 3 children left over. What is the least number of children in this football club
Answers
Answe:
27
Step-by-step explanation:
Let total children =x
when x divide by 6 we got 3
and when divide by 8 we also got 3
since x divided by both 6 and 8 got 3, we can use LCM to find the number to children in the club exclude the 3 player. you will get 24 and by adding 3 the total players that you will get is 27
Write a justification for each step given that EG=FH
Answers
Answer:
Option (C)
Step-by-step explanation:
Statements Reasons
1). EG = FH 1). Given information
2). EG = EF + FG 2). Segment addition postulate
3). FH = FG + GH 3). Segment addition postulate
4). EF + FG = FG + GH 4). Definition of congruent segments
5). EF = GH 5). Subtraction property of equality
Therefore, reasons given in Option (C) will be the answer.
what is the missing length? help plssss
Answers
========================================
Work Shown:
LK = 65
LR = 52
RK = LK - LR = 65 - 52 = 13
The triangles are similar, so the corresponding sides form equal ratios
LK corresponds to RK as they are both on the same side
LK/RK is one ratio and it is equal to MK/SK
----------------
LK/RK = MK/SK
65/13 = 60/x
65x = 13*60 ... cross multiply
65x = 780
x = 780/65 ... divide both sides by 65
x = 12
SK = 12
Answer:
12
Step-by-step explanation:
RK = 65- 52= 13
similar triangle (∆RKS and ∆LKM)
[tex] \frac{13}{65} = \frac{x}{60} [/tex]
[tex]x = \frac{60 \times 13}{65} [/tex]
[tex]x = 12[/tex]
Tyrone ran 7 laps on he quarter mile track during practice. Which subset of real numbers would include the distance Tyrone ran at practice?
Answers
Answer:
Step-by-step explanation:
7 quarter mile laps totals 7/4 miles, or 1 3/4 miles.
1 3/4 miles is between 1 and 2, a subset of real numbers.