Answer:
The scale factor that transforms quadrilateral ABCD to quadrilateral A'B'C'D' is 3
Step-by-step explanation:
Quadrilateral ABCD has the following coordinates
A(1, 5), B(2, 6), C(3, 3) and D(1, 3)
The image A'B'C'D' has the following coordinates;
A'(-3, 1), B'(0, 4), C'(3, -5), D'(-3, -5)
The length of segment [tex]\overline {AB}[/tex] = √((2 - 1)² + (6 - 5)²) = √2
The length of segment [tex]\overline {BC}[/tex] = √((3 - 6)² + (3 - 2)²) = √10
The length of segment [tex]\overline {CD}[/tex] = √((1 - 3)² + (3 - 3)²) = 2
The length of segment [tex]\overline {DA}[/tex] = √((1 - 1)² + (3 - 5)²) = 2
For quadrilateral, we have;
A'(-3, 1), B'(0, 4), C'(3, -5), D'(-3, -5)
The length of segment [tex]\overline {A'B'}[/tex] = √(0 - (-3))² + (4 - 1)²) = 3·√2
The length of segment [tex]\overline {B'C'}[/tex] = √((3 - 0)² + (-5 - 4)²) = 3·√10
The length of segment [tex]\overline {C'D'}[/tex] = √((-3) - 3)² + (-5 - (-5))²) = 6
The length of segment [tex]\overline {D'A'}[/tex] = √((-3) - (-3))² + ((-5) - 1)²) = 6
The scale factor that transforms quadrilateral ABCD to A'B'C'D' is given as follows;
[tex]The \, scale \, factor \, of \, transformation = \dfrac{\overline {A'B'}}{\overline {AB}} = \dfrac{\overline {B'C'}}{\overline {BC}} = \dfrac{\overline {C'D'}}{\overline {CD}} = \dfrac{\overline {D'A'}}{\overline {DA}} = 3[/tex]
Therefore, the scale factor that transforms quadrilateral ABCD to A'B'C'D' = 3
a plywood plank measures 1cmx 8cm x 90cm and it weighs 396g.What is the density
answer
Answer:
the answer is 0.55
density=mass/volume
density=396/720(8*1*90)
Need help ASAP!!!plz
Answer:
The answer is D
Step-by-step explanation:
Jim invests $1240 at a 3.6 interest rate in an account that is compounded quarterly. What is the value of the account after 6 years
Answer:
$1507.84
Step-by-step explanation:
First, converting R percent to r a decimal
r = R/100 = 3.6%/100 = 0.036 per year,
then, solving our equation
I = 1240 × 0.036 × 6 = 267.84
I = $ 267.84
The simple interest accumulated
on a principal of $ 1,240.00
at a rate of 3.6% per year
for 6 years is $ 267.84.
Select all the expressions that are equivalent to 24x + 12.
2(12x + 6)
–6(–4x – 2)
–3(8x – 4)
12(1 + 2x)
–4(–6 – 3x)
Answer:
2(12x + 6)
-6(-4x - 2)
12(1 + 2x)
The expressions that are equivalent to 24x + 12 are:
2(12x + 6)
-6(-4x - 2)
12(1 + 2x)
Let's go through each expression and simplify them to determine if they are equivalent to 24x + 12.
2(12x + 6):
We can use the distributive property to simplify this expression:
2 * 12x + 2 * 6 = 24x + 12
This expression is equivalent to 24x + 12.
–6(–4x – 2):
Again, using the distributive property, we simplify:
–6 * –4x + –6 * –2 = 24x + 12
This expression is equivalent to 24x + 12.
–3(8x – 4):
Once again, applying the distributive property:
–3 * 8x + –3 * –4 = –24x + 12
This expression is not equivalent to 24x + 12.
12(1 + 2x):
Using the distributive property:
12 * 1 + 12 * 2x = 12 + 24x = 24x + 12
This expression is equivalent to 24x + 12.
–4(–6 – 3x):
Applying the distributive property:
–4 * –6 + –4 * –3x = 24 + 12x = 12x + 24
This expression is not equivalent to 24x + 12.
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Please help I needed it badly
Answer:
The answer is C trust me I did this
Will give random brainliest if 10 users comment or answer and put #brainliest
Answer:
#brainliest
Step-by-step explanation:
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Answer:
HEY
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Step-by-step explanation:
What equation of a line would be parrallel to y=4/1X+-3
Answer:
y=4/1x+7
Step-by-step explanation:
it has the same gradient
the number being c (y=mx+c) can be anything
3pts 7.) Clare is cycling at a speed of 12 miles per hour. If she starts at a position chosen as zero, what will her position be after 45 minutes?
9514 1404 393
Answer:
9 miles
Step-by-step explanation:
Of course, 45 min = 45/60 hours = 3/4 hours.
__
The relationship between time, speed, and distance is ...
distance = speed · time
distance = (12 mi/h) · (3/4 h) = 9 mi
Her position will be 9 miles from 0 after 3/4 hour.
how would you factor 12b^4+3b^2
Answer:
3b²(4b²+1)
Step-by-step explanation:
You can factor out a 3b²
3b²(4b²+1)
Answer:
Hey friend, need some help if you factor 3b^2 out of 12b^4+3b^2, in other words, 3b^2 (4b^2 + 1)
Show your work:
3b^2 (3b^2 / 12b^4) + (3b^2 / 3b^2)
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Answer:
-0.6, -1/4, 0.3, 1/2
Step-by-step explanation:
Give me brainliest.
Answer:
-0.6, -1/4, 0.3, 1/2
Step-by-step explanation:
Solve for x.
(x + 10)°
(4x - 35)°
Answer:
x = 15
Step-by-step explanation:
x+10=4x−35
x+10−4x=4x−35−4x
−3x+10−10=−35−10
−3x=−45
x = 15
Use the limit definition of the derivative to find the slope of the tangent line to the curve
f(x)= 7x^2 + 7x + 3 at x= 4
Answer:
[tex]\displaystyle f'(4) = 63[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightDistributive Property
Algebra I
Expand by FOIL (First Outside Inside Last)FactoringFunction NotationTerms/CoefficientsCalculus
Derivatives
The definition of a derivative is the slope of the tangent line.
Limit Definition of a Derivative: [tex]\displaystyle f'(x)= \lim_{h \to 0} \frac{f(x+h)-f(x)}{h}[/tex]
Step-by-step explanation:
Step 1: Define
f(x) = 7x² + 7x + 3
Slope of tangent line at x = 4
Step 2: Differentiate
Substitute in function [Limit Definition of a Derivative]: [tex]\displaystyle f'(x)= \lim_{h \to 0} \frac{[7(x + h)^2 + 7(x + h) + 3]-(7x^2 + 7x + 3)}{h}[/tex][Limit - Fraction] Expand [FOIL]: [tex]\displaystyle f'(x)= \lim_{h \to 0} \frac{[7(x^2 + 2xh + h^2) + 7(x + h) + 3]-(7x^2 + 7x + 3)}{h}[/tex][Limit - Fraction] Distribute: [tex]\displaystyle f'(x)= \lim_{h \to 0} \frac{[7x^2 + 14xh + 7h^2 + 7x + 7h + 3] - 7x^2 - 7x - 3}{h}[/tex][Limit - Fraction] Combine like terms (x²): [tex]\displaystyle f'(x)= \lim_{h \to 0} \frac{14xh + 7h^2 + 7x + 7h + 3 - 7x - 3}{h}[/tex][Limit - Fraction] Combine like terms (x): [tex]\displaystyle f'(x)= \lim_{h \to 0} \frac{14xh + 7h^2 + 7h + 3 - 3}{h}[/tex][Limit - Fraction] Combine like terms: [tex]\displaystyle f'(x)= \lim_{h \to 0} \frac{14xh + 7h^2 + 7h}{h}[/tex][Limit - Fraction] Factor: [tex]\displaystyle f'(x)= \lim_{h \to 0} \frac{h(14x + 7h + 7)}{h}[/tex][Limit - Fraction] Simplify: [tex]\displaystyle f'(x)= \lim_{h \to 0} 14x + 7h + 7[/tex][Limit] Evaluate: [tex]\displaystyle f'(x) = 14x + 7[/tex]Step 3: Find Slope
Substitute in x: [tex]\displaystyle f'(4) = 14(4) + 7[/tex]Multiply: [tex]\displaystyle f'(4) = 56 + 7[/tex]Add: [tex]\displaystyle f'(4) = 63[/tex]This means that the slope of the tangent line at x = 4 is equal to 63.
Hope this helps!
Topic: Calculus AB/1
Unit: Chapter 2 - Definition of a Derivative
(College Calculus 10e)
One box of nails weighs 3.4 pounds and another box weighs 5.2 pounds. How much more does the heavier box weigh?
Answer:
1.8 pounds
Step-by-step explanation:
Write the quadratic equation in standard form:
x^2- 1 = -7x
Answer:
standard form: ax² + bx + c = 0
x² - 1 = -7x
x² + 7x - 1 = 0
Students from Oak Middle School and Lake Middle School are holding a car wash to raise money for charity. The expression 70 +60 represents the amount Oak Middle School raises. The
expression By + 30 represents the amount Lake Middle School raises. Which expression shows the total amount the two schools raise?
15x90
Soxy90
O 7x+By90
15190
The expression that shows the total amount the two schools raise is 7x + 8y + 90.
What is an expression?It should be noted that an expression is simply used to show the relationship between the variables that are used.
From the information, the expression 7x +60 represents the amount Oak Middle School raises and the expression 8y + 30 represents the amount Lake Middle School raises.
Therefore, the total amount will be:
= 7x + 60 + 8y + 30
= 7x + 8y + 90
The total amount is 7x + 8y + 90.
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Please can someone helpppp
18. Complete the table below.
PLZ HELP ME A
Answer:
6/10 | 60% | 0.60
¾ | 75% | .75
23/100 | 23% | .23
⅛ | 12.5% | .125
9/50 | 18% | .18
⅔ | 67% | .67
Please help! image is below
Explanation = brainliest
Answer:
x=67.5ft
Step-by-step explanation:
similarity and congruence
the length of one side of the bigger triangle divided by the length of the similar side of the smaller triangle
equate the unknown ratio with a known ratio
71.5/49.5=97.5/x
x=(97.5 x 49.5)/71.5
x=67.5 ft
How many buses do you need for 600 people if each bus holds 65 people?
Answer:
You would need 10 buses
Step-by-step explanation:
To find the amount of buses needed, you just divide the total amount of people, and the capacity of each bus.
600/65
This would get you 9.23076923077, but obviously you can't have .23076923077 of a bus and you can't leave people behind. This means you would have to round the number up to 10
Answer:
10
Step-by-step explanation:
What will be the perimeter and the area of the rectangle below if it is enlarged using a scale factor of 6.5? (5 points)
A rectangle is shown. The length of the rectangle is labeled as 8 cm, and the width is labeled as 6 cm.
Perimeter = 54 cm, area = 181.25 cm2
Perimeter = 54 cm, area = 2,028 cm2
Perimeter = 182 cm, area = 2,028 cm2
Perimeter = 182 cm, area = 181.25 cm2
Answer:
Perimeter = 182 cm, area = 2,028 cm2
Step-by-step explanation:
original perimeter=2*(8+6)+28 cm
original area=8*6= 48 cm²
You would have to do the old length and width times the scale factor
Multiply both of the width's
8 * 6.5 = 52 cm
scale factor: 6 * 6.5 = 39 cm
To get perimeter = 2(length + width)
2(52+39)=182 cm.
So you would have to do length(52 cm) * width(39 cm)
To get 2028 cm^2
the third one
Step-by-step explanation:
Because I’m right
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Hey! I really need help figuring this problem out. I have a test in a few hours and I don't know how to find the answer to questions like these, I would really appreciate it if you show your work so I can figure out how to solve these myself. Thank you!
Answer:
(2, -1)Step-by-step explanation:
Given system:
-3x - 2y = -49x + 3y = 15Solving by elimination
Multiply the first equation by 3 and add up equations, then solve for y:
3(-3x) - 3(2y) + 9x + 3y = 3(-4) + 15-9x - 6y + 9x + 3y = -12 + 15-3y = 3y = 3/(-3)y = -1Find the value of x:
-3x - 2(-1) = -4-3x + 2 = -4-3x = - 4 - 2-3x = -6x = -6/(-3)x = 2The answer is: (2, -1)
An airplane ticket to new york is priced at $1232.10 inclusive of 11% sales tax what amount would the airline ticket cost exclusive of sales tax
Answer:
net is before tax
gross is after tax
Factor the trinomial below.Thanks
Answer:
A. (3x+2)(3x+2)
Step-by-step explanation:
(3x+2)(3x+2)= 9x^2+12x+4
FINDING SLOPE given GRAPHS, TABLES, POINTS and EQUATIONS!! Thank youu
The formula for slope is vertical change ÷ horizontal change, which means choose two points, (x1,y1) and (x2,y2), then do (y2-y1) ÷ (x2-x1).
For the graph, just pick two random points that you like. For the table, pick two sets of numbers (for example -10,-47 and 4,9). For the equation, create two sets of coordinates. For example, if you have f(x) = x + 3, then if x = 1, y = 4 and if x = 2, y = 5.
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Answer:
125
Step-by-step explanation:
hope this helps :) have a nice day !!
How can you get 24 by using 1, 1/2, 3 and 6 (one each) with simple mathematical operations?
Answer:
(3+1)X 6
Step-by-step explanation:
that means 4x6
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16 ÷ 2 + 6(8 - 2^2 )
Answer:
The answer is 32.
Step-by-step explanation:
Answer:
32
Step-by-step explanation:
PEMDAS:
16 ÷ 2 + 6(8 - 2^2 )
2^2 = 4
(8-4) = 4
16 ÷ 2 + 6(4)
16 ÷ 2 + 24
8 + 24
32
Which pair of angles are alternate exterior angles ?
8 and 1 are alternate exterior angles.
Answer:
<8 and <1
Step-by-step explanation:
<8 and <1 are both outside of the parallel so they are exterior and opposite to each other which is alternative exterior.
Hope this helps, thank you !!
PLEASE HELPPPP EASY 10 POINTS
Answer:
y=x+5
Step-by-step explanation:
Answer:
Step-by-step explanation:
10.
A plane that carries mail makes a round trip each day from Chicago to New York. It makes 1 intermediate stop on the way to New York and 1 intermediate stop on the way back to Chicago. Suppose you make a graph of the altitude of the plane for one day, with time on the horizontal axis and altitude on the vertical axis. How many times will the graph touch the horizontal axis?
A. 5
B. 4
C. 7
D. 2
Answer:
C. 7
Step-by-step explanation:
The graph that is drawn here shows the altitude as a function of time. When the plane takes off from Chicago, the graph will start from the horizontal axis.
Next, when the plane takes 3 intermediate stops, altitude will touch the horizontal axis 3 times.
Next, when the plane lands in New York the altitude will touch the horizontal axis.
Next, when plane takes off from New York and takes an intermediate stop, altitude will touch horizontal axis.
Lastly the altitude will touch the axis when plane lands back in Chicago.
So, cumulatively the altitude will touch the horizontal axis seven times.