Find the area of a polygon with vertices at (1, 3), (7, 3), (7, 7), and (4, 7). a. 24 units2 b. 10 units2 c. 12 units2 d. 18 units2
Answers
Answer:
Option D
Step-by-step explanation:
Vertices of the polygon are A(1, 3), B(7, 3), C(7, 7), D(4, 7)
Measure of AB = 7 - 1 = 6 units
Measure of BC = 7 - 3 = 4 units
Measure of CD = 7 - 4 = 3 units
From the figure attached,
Area of the trapezoid = [tex]\frac{1}{2}(AB+CD)(BC)[/tex] [Here, AB and CD are the parallel bases and BC is the height of the trapezoid]
= [tex]\frac{1}{2}(6+3)(4)[/tex]
= 18 square units
Therefore, Option D will be the correct option.
Related Questions
4/5 divided by 3/4
I need help please!! :)
Answers
Answer:
1 1/5 in fraction form :))
Type the missing number that makes these fractions equal: 4/?=8/14
Answers
Answer:
4/7 = 8/14
Step-by-step explanation:
Answer:
7
Step-by-step explanation:
[tex]\frac{4}{x} =\frac{8}{14} \\[/tex]
cross multiply
8x = 14 x 4
8x = 56
x = 7
Which equation is correct?
a) cos G = 15/17
b) cos G = 8/15
c) sin G = 15/17
d) sin G = 8/15
Answers
PLEASE HELP WILL AWARD BRAINLIEST:)
Answers
Answer:
x = 4 units
Step-by-step explanation:
By geometric mean theorem:
Length of perpendicular
[tex] =\sqrt{2\times 6}[/tex]
[tex] =\sqrt{12}[/tex]
Next, by Pythagoras theorem:
[tex] x^2 = 2^2 + (\sqrt {12})^2 [/tex]
[tex] \therefore x^2 = 4 + 12 [/tex]
[tex] \therefore x^2 = 16 [/tex]
[tex] \therefore x =\sqrt{ 16 }[/tex]
[tex] \therefore x =4\: units[/tex]
The curve
[tex]y = \sqrt{x - 3} [/tex]
has a tangent with gradient
[tex] \frac{1}{2} [/tex]
at point N.
Find the coordinates of N.
Answers
Answer:
Point N(4, 1)
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityAlgebra I
Coordinates (x, y)FunctionsFunction NotationTerms/CoefficientsAnything to the 0th power is 1Exponential Rule [Rewrite]: [tex]\displaystyle b^{-m} = \frac{1}{b^m}[/tex] Exponential Rule [Root Rewrite]: [tex]\displaystyle \sqrt[n]{x} = x^{\frac{1}{n}}[/tex]Calculus
Derivatives
Derivative Notation
Derivative of a constant is 0
Basic Power Rule:
f(x) = cxⁿ f’(x) = c·nxⁿ⁻¹Derivative Rule [Chain Rule]: [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]
Step-by-step explanation:
Step 1: Define
[tex]\displaystyle y = \sqrt{x - 3}[/tex]
[tex]\displaystyle y' = \frac{1}{2}[/tex]
Step 2: Differentiate
[Function] Rewrite [Exponential Rule - Root Rewrite]: [tex]\displaystyle y = (x - 3)^{\frac{1}{2}}[/tex]Chain Rule: [tex]\displaystyle y' = \frac{d}{dx}[(x - 3)^{\frac{1}{2}}] \cdot \frac{d}{dx}[x - 3][/tex]Basic Power Rule: [tex]\displaystyle y' = \frac{1}{2}(x - 3)^{\frac{1}{2} - 1} \cdot (1 \cdot x^{1 - 1} - 0)[/tex]Simplify: [tex]\displaystyle y' = \frac{1}{2}(x - 3)^{-\frac{1}{2}} \cdot 1[/tex]Multiply: [tex]\displaystyle y' = \frac{1}{2}(x - 3)^{-\frac{1}{2}}[/tex][Derivative] Rewrite [Exponential Rule - Rewrite]: [tex]\displaystyle y' = \frac{1}{2(x - 3)^{\frac{1}{2}}}[/tex][Derivative] Rewrite [Exponential Rule - Root Rewrite]: [tex]\displaystyle y' = \frac{1}{2\sqrt{x - 3}}[/tex]Step 3: Solve
Find coordinates
x-coordinate
Substitute in y' [Derivative]: [tex]\displaystyle \frac{1}{2} = \frac{1}{2\sqrt{x - 3}}[/tex][Multiplication Property of Equality] Multiply 2 on both sides: [tex]\displaystyle 1 = \frac{1}{\sqrt{x - 3}}[/tex][Multiplication Property of Equality] Multiply √(x - 3) on both sides: [tex]\displaystyle \sqrt{x - 3} = 1[/tex][Equality Property] Square both sides: [tex]\displaystyle x - 3 = 1[/tex][Addition Property of Equality] Add 3 on both sides: [tex]\displaystyle x = 4[/tex]y-coordinate
Substitute in x [Function]: [tex]\displaystyle y = \sqrt{4 - 3}[/tex][√Radical] Subtract: [tex]\displaystyle y = \sqrt{1}[/tex][√Radical] Evaluate: [tex]\displaystyle y = 1[/tex]∴ Coordinates of Point N is (4, 1).
Topic: AP Calculus AB/BC (Calculus I/II)
Unit: Derivatives
Book: College Calculus 10e
Which is the equation of a line that has a slope of 3 and passes through point
(-3,-1)2
A. y=-3x+1
B. y--3x+3
C. y = 2 x -
D. y-22 8x-3
Answers
Answer:
y = -2/3x - 3
Step-by-step explanation:
y = -2/3x + b
-1 = -2/3(-3) + b
-1 = 2 + b
-3 = b
y = -2/3x - 3
The Barnes family has a coupon for 10% off their dinner. If their bill comes to $82.50 and they wish to tip 15%, what will they pay in total?
Answers
Answer:
Total cost= $86.25
Step-by-step explanation:
Giving the following information:
Discount= 10%
Nill= $82.5
Tip= 15%
First, we need to calculate the discounted price:
Discount price= 82.5 / 1.1= $75
Now, the tip:
Tip= 75*0.15= $11.25
Finally, the total cost:
Total cost= 75 + 11.25
Total cost= $86.25
Plz help I will give BRAINLY
Answers
Answer:
I believe it is C
Step-by-step explanation:
Sorry if I got it wrong but hopefully you got it right
Samantha has chocolate bars and lollipops in the the ratio 4:5. If she has 12 chocolate bars,how many lollipops does she have?
Answers
5 • 3 = 15
she has 15 lollipops
Pls help me also show your work bc I need to understand
Answers
9514 1404 393
Answer:
x = ±√13x = ±3√6x = ±√66x = 0 or 8Step-by-step explanation:
As in any "solve for" situation, you "undo" what is done to the variable.
Here, (for 3 of the 4 problems) the variable is ...
squaredmultiplied by a constantadded to a constantWe undo these operations in reverse order. First, we add the opposite of the added constant. Then we divide by the coefficient of x². Finally, we take the square root to "undo" the squaring operation.
1. 4x² -30 = 22 . . . . . . given
4x² = 52 . . . . . . . . . add 30 to both sides
x² = 13 . . . . . . . . . . . divide both sides by 4
x = ±√13 . . . . . . . . . take the square root. Both signs are solutions.
__
2. 3x² +4 = 166 . . . . . given
3x² = 162 . . . . . . . . add -4 to both sides
x² = 54 . . . . . . . . . . divide both sides by 3
x = ±√54 . . . . . . . . take the square root. 54 = 3²·6 has a square factor
x = ±3√6 . . . . . . . simplified result
__
3. (1/3)x² +14 = 36 . . . . given
(1/3)x² = 22 . . . . . . . . add -14 to both sides
x² = 66 . . . . . . . . . . . multiply both sides by 3
x = ±√66 . . . . . . . . take the square root
__
4. The same "undo" idea applies. Here, we can start with the square root.
(x -4)² = 16 . . . . . given
x -4 = ±4 . . . . . . . square root
x = 4 ± 4 . . . . . . add 4 to both sides
This means x = 4-4 = 0, or x = 4+4 = 8.
The solutions are x = 0, x = 8.
list some things I could spend a million dollars on.. doing a math worksheet and I can’t think of things.. help!
Answers
Answer:
A car, college, and house, bills. and Airplane? would those work?
Step-by-step explanation:
Find the measure of angle 1
HELP
Answers
Answer:
75°
Step-by-step explanation:
The chord- chord angle is half the sum of of the arcs intercepted by the angle and its vertical angle, then
∠ 1 = [tex]\frac{1}{2}[/tex] (110 + 40)° = 0.5 × 150° = 75°
Ms. Benton drew a right angle and split it into 2 angles. one of the labels inside was labeled 5x and the other angle was labeled 4x. what does x equal?
Answer choices:
5°
10°
15°
20°
please help
Answers
Answer:
B-10⁰
Step-by-step explanation:
5 x 10 is 50, 4 x 10 is 40, add those and you get 90⁰
if r 1 and 0 = 7pi/6 what is the approximate arc length
Answers
= (1)(7pi/6)
= 3.7 unit
How would you solve problems like this
Answers
Kim sold christmas pies for 5.00$ each. She earned 156 how many pies she sold also let x repersent the number of pies, x, kim sold
Answers
Answer: 31.2 pies
Step-by-step explanation:
Kim sold pies for $5.00 each and earned $156 from doing so.
The number of pies she sold to get to this was x pies.
The formula for doing so is therefore:
5 * x pies = 156
5x = 156
x = 156 / 5
= 31.2 pies
Write the recursive formula for the sequence
37, 67, 97, 127, 157
Answers
Answer:
The recursive formula for this arithmetic sequence would be [tex]a_{1} = 37[/tex], [tex]a_{i} = a_{i-1} + 30[/tex].
Step-by-step explanation:
A recursive formula is a formula that defines each term of a sequence using the preceding term(s). Recursive formulas must always state the initial term, or terms, of the sequence, as well as an equation defining [tex]a_{i}[/tex] in terms of preceding terms. Since the first term of this sequence is 37, that means [tex]a_{1} = 37[/tex]. The pattern in this arithmetic sequence between each term in ascending order would be 30 more than the previous term, so you can create the function [tex]a_{i} = a_{i-1} + 30[/tex]. So the recursive formula for this arithmetic sequence would be [tex]a_{1} = 37[/tex] and [tex]a_{i} = a_{i-1} + 30[/tex].
Someone help me please with this ? Like right now please
Answers
Answer: 6472
Step-by-step explanation:
You have to multiply and add
The square root 24 is between which two numbers on the number line
A)
1 and 2
B)
2 and 3
C)
3 and 4
D)
4 and 5
Answers
Answer:
Step-by-step explanation:
4²=16
5²=25
so √24 is between 4 and 5.
yes
Which would it be please?Help if you can.
Answers
Answer:
B
Step-by-step explanation:
Area = length times width, in this case, both length and width is x.
While 5 and 2 are the lengths and widths for the unshaded part.
x^2 = whole square
x^2 - (5)(2) = area of shaded region
PLEASE HELP ME URGENT what is the correct answer to my question.
Answers
I'm fully sure but maybe you add 12+40
Show all the steps that you used to solve this problem.
Write an inequality for the graph.
Answers
Answer:
h(x) ≥ |x - 5| +1
Step-by-step explanation:
Given graph represents an absolute function (parent function)
f(x) = |x|
Since, graph of the function 'f' has been shifted 5 units to the right new function will be,
g(x) = f(x - 5)
g(x) = |x - 5|
Again function 'g' is shifted 1 unit upwards along the y-axis then the new function will be,
h(x) = g(x) + 1
h(x) = |x - 5| + 1
There is a shaded region representing the solution area lying above the intersecting dark lines,
Therefore, solution region will be re[presented by the inequality,
h(x) ≥ |x - 5| + 1
Which of the following is NOT one of the benefits of owning your own home?
a.
Pride of ownership, privacy, and quality of life
b.
Predictable payments and added stability
c.
Tax deductions for interest costs
d.
Lower maintenance or repair costs compared to renting your home
e.
Homeownership usually serves as protection against inflation
Answers
Answer:
c Tax deductions for interest costs
Step-by-step explanation:
This is because it is the only one that wouldn't make a home owner happy. Most people hate doing taxes therefore it would be a disadvantage not a benefit
Find the median and mean of the data set below:
36,4,27,46,46
Answers
Answer:
The mean is
31.8
The median is 36
600 raffle tickets were sold for $5 each. There is one $500 first prize and three $200 second prizes. The remainder of the tickets do not win anything. What is the expected value of this raffle?
Answers
Answer:
its -$3.17
Step-by-step explanation:
500-5=495
200-5=195
the remainder of the tickets is -$5
the expected value is $495 x 1/600 + $ 19583/600 + (-$5) 596/600= -$3.17
if anyone could help answer this question that would be great.
Answers
First break it off into 2 rectangles on is 4 width and 10 length other is 8 length and 10 width. Then multiple to find area 10•4=40 8•3=24 then add 40+24= 64
the difference between two numbers is 14. if 1/3 of the larger number is subtracted from the smaller number ,the result equals 1/10 of their sum. find both numbers
Step by step please
Answers
Answer:
Step-by-step explanation:
x-y=14
x-1/3y=1/10
-y=14-x
y=-14+x
take out the factors
x-10/30y=3/30
30x-10y=3
substitute
30x-10(-14+x)=3
30x+140-10x=3-140
20x/20=-137/20
x=-6.85
y=-14+(-6.85)
y=-20.85
The two numbers are 143/20 and 423/20.
What is a linear system of equations?A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.
Given that, the difference between two numbers is 14.
Let the smaller number be x and the larger number be y.
Here, y-x=14 ------------(i)
If 1/3 of the larger number is subtracted from the smaller number ,the result equals 1/10.
1/3 of larger number is 1/3 y
x-y/3 =1/10 ------------(ii)
From equation (i), substitute y=14+x in equation (ii), we get
x-(14+x)/3 =1/10
10(3x-14-x)=3
30x-140-10=3
20x-140=3
20x=143
x=143/20
Substitute x=143/20 in equation (i), we get
y-143/20=14
y=14+143/20
y=(280+143)/20
y=423/20
Therefore, the two numbers are 143/20 and 423/20.
To learn more about the linear system of an equations visit:
https://brainly.com/question/27664510.
#SPJ3
What is the value of 1,608 divided by 10 cubed
Answers
Answer:
16 2/25
Step-by-step explanation:
1608 / 10^2
1608/100
16 8/100
16 4/50
16 2/25
Answer:
1.608
Step-by-step explanation:
1608 ÷ 1000 = 1.608
Please can someone help been struggle with this problem
Answers
Step-by-step explanation:
domain = { x/ x € Real}
range = { y/ y > -3 , y € Real }
No one wants to help me ! :(((( need help on algebra: modeling dot plots Box plots and histograms.!