Answers
Answer:
(5,-6)
Step-by-step explanation:
ONE WAY:
If [tex]f(x)=x^2-6x+3[/tex], then [tex]f(x-2)=(x-2)^2-6(x-2)+3[/tex].
Let's simplify that.
Distribute with [tex]-6(x-2)[/tex]:
[tex]f(x-2)=(x-2)^2-6x+12+3[/tex]
Combine the end like terms [tex]12+3[/tex]:
[tex]f(x-2)=(x-2)^2-6x+15[/tex]
Use [tex](x-b)^2=x^2-2bx+b^2[/tex] identity for [tex](x-2)^2[/tex]:
[tex]f(x-2)=x^2-4x+4-6x+15[/tex]
Combine like terms [tex]-4x-6x[/tex] and [tex]4+15[/tex]:
[tex]f(x-2)=x^2-10x+19[/tex]
We are given [tex]g(x)=f(x-2)[/tex].
So we have that [tex]g(x)=x^2-10x+19[/tex].
The vertex happens at [tex]x=\frac{-b}{2a}[/tex].
Compare [tex]x^2-10x+19[/tex] to [tex]ax^2+bx+c[/tex] to determine [tex]a,b,\text{ and } c[/tex].
[tex]a=1[/tex]
[tex]b=-10[/tex]
[tex]c=19[/tex]
Let's plug it in.
[tex]\frac{-b}{2a}[/tex]
[tex]\frac{-(-10)}{2(1)}[/tex]
[tex]\frac{10}{2}[/tex]
[tex]5[/tex]
So the [tex]x-[/tex] coordinate is 5.
Let's find the corresponding [tex]y-[/tex] coordinate by evaluating our expression named [tex]g[/tex] at [tex]x=5[/tex]:
[tex]5^2-10(5)+19[/tex]
[tex]25-50+19[/tex]
[tex]-25+19[/tex]
[tex]-6[/tex]
So the ordered pair of the vertex is (5,-6).
ANOTHER WAY:
The vertex form of a quadratic is [tex]a(x-h)^2+k[/tex] where the vertex is [tex](h,k)[/tex].
Let's put [tex]f[/tex] into this form.
We are given [tex]f(x)=x^2-6x+3[/tex].
We will need to complete the square.
I like to use the identity [tex]x^2+kx+(\frac{k}{2})^2=(x+\frac{k}{2})^2[/tex].
So If you add something in, you will have to take it out (and vice versa).
[tex]x^2-6x+3[/tex]
[tex]x^2-6x+(\frac{6}{2})^2+3-(\frac{6}{2})^2[/tex]
[tex](x+\frac{-6}{2})^2+3-3^2[/tex]
[tex](x+-3)^2+3-9[/tex]
[tex](x-3)^2+-6[/tex]
So we have in vertex form [tex]f[/tex] is:
[tex]f(x)=(x-3)^2+-6[/tex].
The vertex is (3,-6).
So if we are dealing with the function [tex]g(x)=f(x-2)[/tex].
This means we are going to move the vertex of [tex]f[/tex] right 2 units to figure out the vertex of [tex]g[/tex] which puts us at (3+2,-6)=(5,-6).
The [tex]y-[/tex] coordinate was not effected here because we were only moving horizontally not up/down.
Related Questions
Rewrite the equation of the circle (x + 2)^2 + (y + 5)^2 = 9 in general form.
Answers
Answer:
x² + 4x + y² + 10y + 20 = 0
Step-by-step explanation:
Step 1: Expand (x + 2)²
x² + 2x + 2x + 4 + (y + 5)² = 9
Step 2: Combine like terms
x² + 4x + 4 + (y + 5)² = 9
Step 3: Expand (y + 5)²
x² + 4x + 4 + y² + 5y + 5y + 25 = 9
Step 4: Combine like terms
x² + 4x + 4 + y² + 10y + 25 = 9
Step 5: Move 9 over
x² + 4x + 4 + y² + 10y + 25 - 9 = 0
Step 6: Combine like terms
x² + 4x + y² + 10y + 20 = 0
Answer:
x^2+y^2+4x+10y+20=0
Step-by-step explanation:
(x+2)^2+(y+5)^2=9
x^2+4x+4+y^2+10y+25-9=0
general form: x^2+y^2+4x+10y+20=0
MATH HELP ME ASAP!!!!
Answers
Answer: Zak - Resp after 24 months = $4,344.00
Zak - Technology Fund after 24 months = $1,102.98
Zak's Technology Fund has enough money to buy a laptop.
Zak's Savings (Resp) will last less than 6 months
Step-by-step explanation for Zak:
January - June 2019
$15/hr x 20 hr x 4 wks x 6 months = $7200 Gross Income
Resp (15%): $7200(0.15) = $1080CPP(5%): $7200(0.05) = $360EI(2%): $7200(0.02) = $144Taxable Income is $7200 - $1080 = $6120 (Annual Income $12,240)
Income Tax (0% for 0-9,000 Annual): $4500(0) = $0Income Tax (8% for 9-25,000 Annual): ($6,120-$4,500)(0.08) = $129.60→ $7,200 - ($1080 + $360 + $144 + $0 + $129.60) = $5,486.40 Net Income
Tech Fund (5%): $5486.40(0.05) = $274.32
Food Expense (30%): $5486.40(0.3) = $1,645.92
Clothing Expense (30%): $5486.40(0.3) = $1,645.92
Entertainment Expense (25%): $5486.40(0.25) = $1,371.60
Miscellaneous Expense (10%): $5486.40(0.1) = $548.64
Other Expenses: $5,212.08
July - December 2019 (excluding August)
$16/hr x 20 hr x 4 wks x 5 months = $6400 Gross Income
Resp (15%): $6400(0.15) = $960CPP(5%): $6400(0.05) = $320EI(2%): $6400(0.02) = $128Taxable Income is $6400 - $960 = $5440 (Annual Income $11,560)
Income Tax (0% for 0-9,000 Annual): $4500(0) = $0Income Tax (8% for 9-25,000 Annual): ($5,440-$4,500)(0.08) = $75.20→ $6,400 - ($960 + $320 + $128 + $0 + $75.20) = $4,916.80 Net Income
Tech Fund (5%): $4916.80(0.05) = $245.84
Food Expense (30%): $4916.80(0.3) = $1,475.04
Clothing Expense (30%): $4916.80(0.3) = $1,475.04
Entertainment Expense (25%): $4916.80(0.25) = $1,229.20
Miscellaneous Expense (10%): $4916.80(0.1) = $491.68
Other Expenses: $4,670.96
January - June 2020
$17/hr x 20 hr x 4 wks x 6 months = $8160 Gross Income
Resp (15%): $8160(0.15) = $1224CPP(5%): $8160(0.05) = $408EI(2%): $8160(0.02) = $163.20Taxable Income is $8160 - $1224 = $6936 (Annual Income $13,872)
Income Tax (0% for 0-9,000 Annual): $4500(0) = $0Income Tax (8% for 9-25,000 Annual): ($6,936-$4,500)(0.08) = $194.88→ $8,160 - ($1224 + $408 + $163.20 + $0 + $194.88) = $6,169.92 Net Income
Tech Fund (5%): $6169.92(0.05) = $308.50
Food Expense (30%): $6169.92(0.3) = $1,850.98
Clothing Expense (30%): $6169.92(0.3) = $1,850.98
Entertainment Expense (25%): $6169.92(0.25) = $1,542.48
Miscellaneous Expense (10%): $6169.92(0.1) = $616.98
Other Expenses: $5,861.42
July - December 2020 (excluding August)
$18/hr x 20 hr x 4 wks x 5 months = $7200 Gross Income
Resp (15%): $7200(0.15) = $1080CPP(5%): $7200(0.05) = $360EI(2%): $7200(0.02) = $144Taxable Income is $7200 - $1080 = $6120 (Annual Income $13,056)
Income Tax (0% for 0-9,000 Annual): $4500(0) = $0Income Tax (8% for 9-25,000 Annual): ($6,120-$4,500)(0.08) = $129.60→ $7,200 - ($1080 + $360 + $144 + $0 + $129.60) = $5,486.40 Net Income
Tech Fund (5%): $4916.80(0.05) = $274.32
Food Expense (30%): $5486.40(0.3) = $1,645.92
Clothing Expense (30%): $5486.40(0.3) = $1,645.92
Entertainment Expense (25%): $5486.40(0.25) = $1,371.60
Miscellaneous Expense (10%): $5486.40(0.1) = $548.64
Other Expenses: $5,212.08
[tex]\boxed{\begin{array}{l|r|r|r|r||r}\underline{ZAK}&\underline{Jan-Jun'19}&\underline{Jul-Dec'19}&\underline{Jan-Jun'20}&\underline{Jul-Dec'20}&\underline{Totals\quad }\\Gross&\$7200.00&\$6400.00&\$8160.00&\$7200.00&\$28960.00\\Resp&\$1080.00&\$960.00&\$1224.00&\$1080.00&\$4344.00\\Net&\$5486.40&\$4916.80&\$6169.92&\$5486.40&\$22059.52\\Other&\$5212.08&\$4670.96&\$5861.42&\$5212.08&\$20956.54\\Tech&\$274.32&\$245.84&\$308.50&\$274.32&\$1102.98\end{array}}[/tex]
Select all the correct answers. Which statements are correct interpretations of the logarithmic function f(x) = 7 log2 x, with respect to the context? The password is weakest if it uses a single symbol for all 7 characters. The strength of the password increases with a decrease in the number of symbols. The password is stronger with an increase in the number of symbols. The password is strongest if a single symbol is used for all 7 characters. There are 2 possible symbol options per character to produce a password of strength of 7 bits. There are 7 possible symbol options per character to produce a password of strength of 7 bits.
Answers
Answer:
The password is weakest if it uses a single symbol for all 7 characters.
The strength of password increases with an increase in the number of symbols.
There are 7 possible symbol options per character to produce a password of strength of 7 bits.
Step-by-step explanation:
The password strength is determined by the usage of symbols and upper case and lower case letters along with a numeric character. The strength of password increases when different symbols are used. It is considered as weak password if only single symbol is used for all the 7 characters. The strong passwords are not easy to break and decode.
Answer:
The three correct options are:
The password is weakest if it uses a single symbol for all 7 characters.
The password is stronger with an increase in the number of symbols.
There are 2 possible symbol options per character to produce a password of strength of 7 bits.
A county real estate appraiser wants to develop a statistical model to predict the appraised value of houses in a section of the county called East Meadow. One of the many variables thought to be an important predictor of appraised value is the number of rooms in the house. Consequently, the appraiser decided to fit the simple linear regression model, y=Po+B1x, where y appraised value of the house (in $thousands) and x number of rooms. Using data collected for a sample of n 74 houses in East Meadow, the accompanying results were obtained. Give a practical interpretation of the estimate of the slope of the least squares line. i Click the icon to view the results.
A. For each additional dollar of appraised value, the number of rooms in the house is estimated to increase by 22.71 rooms.
B. For a house with 0 rooms, the appraised value is estimated to be $74,800.
C. For each additional room in the house, the appraised value is estimated to increase $22,710
D. For each additional room in the house, the appraised value is estimated to increase $74,800.
Answers
Answer:
D. For each additional room in the house, the appraised value is estimated to increase $74,800
Step-by-step explanation:
The statistical model is used to predict the appraised value of houses in East Meadows. The value of a house is determined by using variables. The regression model helps to analyse the value of a house. It is predictive modelling technique which determines a relationship between dependent and independent variable.
Which of the following are solutions to the quadratic equation? Check all that apply.
x2 + x-12 = 0
A. -1
B. 28
C. 2
D. 4
E. 3
F. -4
Answers
Answer:
x= -4 x= 3
Step-by-step explanation:
x2 + x-12 = 0
Factor
What 2 numbers multiply to -12 and add to 1
4 * -3 = -12
4+3 = 1
( x+4) ( x-3) =0
Using the zero product property
x= -4 x= 3
Answer:
E, F
Step-by-step explanation:
x² + x - 12 = 0
Let’s factor left side.
Find 2 numbers that multiply to get -12 and add to get 1
4 × -3 = -12
4 + 3 = 1
x² - 3x + 4x - 12 = 0
x(x - 3) + 4(x - 3) = 0
(x + 4)(x - 3) = 0
Set factors equal to 0.
x + 4 = 0
x = -4
x - 3 = 0
x = 3
(Mathematics Question)
House Insurance 50 per $100
Contents Insurance 25 per $100
The above shows the rates charged by an insurance company. How much will a person pay for his insurance, if his house is valued at $50,000, and the content at $10,000?
(A) $225
(B) $275
(C) $450
(D) $500
Answers
Answer: B.) $275
Step-by-step explanation:
Rates charged by insurance company :
House Insurance 50 per $100
Contents Insurance 25 per $100
Value of House = $50,000
Insurance Fee:
$50,000 / $100 = 500
500, 50 cent payment,
50 cent × 500 = 25000 cent
Value of content = $10,000
Insurance Fee:
$10,000 / $100 = 100
100, 25 cent payment
25 cent × 100 = 2500 cent
Total insurance fee:
(25000 + 2500) cent
= 27500 cent
27,500 cent / 100
= $275
What is the length of AC?
Please help me ASAP!!!
Answers
Answer:
a
Step-by-step explanation:
Find the perimeter of the shaded figure. Please help,thanks!
Answers
Answer:
I believe its 40
Step-by-step explanation:
Answer:
Hey there!
The perimeter can be expressed as 10+7+2+2+6+2+2+7, or 38.
Hope this helps :)
Help please.... what is the solution of sqrt -4x=100? A- x=-2500 B-x=-50 C-x=-2.5 D-no solutions
Answers
Answer:
A. x = -2,500.
Step-by-step explanation:
sqrt(-4x) = 100
(sqrt(-4x)^2 = (100)^2
-4x = 10,000
4x = -10,000
x = -2,500
Check your work...
sqrt(-4(-2,500))
= sqrt(4 * 2,500)
= sqrt(10,000)
= plus or minus 100
A. x = -2,500 is your answer.
Hope this helps!
Answer:
The answer would be A, x=-2500
Explanation:
To remove the radical on the left side of the equation, square both sides of the equation.
√ − 4 x^ 2 = 100^ 2
Simplify each side of the equation.
− 4 x = 10000
Divide each term by
−4
and simplify.
x = -2500
Determine whether the study is an observational study or an experiment.
Research is conducted to determine if there is a relation between hearing loss and exposure to mumps. Does the description correspond to an observational study or an experiment?
Answers
Researchers are observing those with mumps to see how it affects hearing loss at all. There may be strong correlation, weak correlation, or no correlation at all.
With an experiment, researchers would break the participants into two groups: control group and treatment group. Those in the control group get the placebo (fake treatment) while the treatment group gets the treatment applied to them. If we were dealing with an experiment for this context, then the treatment group would get exposed to mumps on purpose. Of course, this is unethical and dangerous so an experiment for this type of project is not a good idea. It's better to go with an observational study.
Find the area of the shaded region
Answers
Answer:
[tex] \mathsf{ {5x}^{2} + 28x + 21}[/tex]
Option A is the right option.
Step-by-step explanation:
Let's find the area of large rectangle:
[tex] \mathsf{(3x + 6)(2x + 4)}[/tex]
Multiply each term in the first parentheses by each term in the second parentheses
[tex] \mathsf{ = 3x(2x + 4) + 6(2x + 4)}[/tex]
Calculate the product
[tex] \mathsf{ = 6 {x}^{2} + 12x + 12x + 6 \times 4}[/tex]
Multiply the numbers
[tex] \mathsf{ = 6 {x}^{2} + 12x + 12x + 24}[/tex]
Collect like terms
[tex] \mathsf{ = {6x}^{2} + 24x + 24}[/tex]
Let's find the area of small rectangle
[tex] \mathsf{(x - 3)(x - 1)}[/tex]
Multiply each term in the first parentheses by each term in the second parentheses
[tex] \mathsf{ = x( x - 1) - 3(x - 1)}[/tex]
Calculate the product
[tex] \mathsf{ = {x}^{2} - x - 3x - 3 \times ( - 1)}[/tex]
Multiply the numbers
[tex] \mathsf{ = {x}^{2} - x - 3x + 3}[/tex]
Collect like terms
[tex] \mathsf{ = {x}^{2} - 4x + 3}[/tex]
Now, let's find the area of shaded region:
Area of large rectangle - Area of smaller rectangle
[tex] \mathsf{6 {x}^{2} + 24x + 24 - ( {x}^{2} - 4x + 3)}[/tex]
When there is a ( - ) in front of an expression in parentheses, change the sign of each term in the expression
[tex] \mathsf{ = {6x}^{2} + 24x + 24 - {x}^{2} + 4x - 3}[/tex]
Collect like terms
[tex] \mathsf{ = {5x}^{2} + 28x + 21}[/tex]
Hope I helped!
Best regards!
You make a scale drawing of a garden plot using the scale 2 in. = 17
ft. If the length of a row of vegetables on the drawing is 3 in., how
long is the actual row?
42.5 ft
25.5 ft
17 ft
34 ft
Answers
Answer 158Step-by-step explanation: you have to multiply the fraction by the numerator and divided by itsself and the subtract everything thren get myy642565780
what is
5/14 mulitypled by 4 in simplest form
Answers
Answer:1 3/7
Step-by-step explanation:When you multiply the nominator and 4you get 20.So it would 20/14 but if you find the simplest form of fraction you would get 1 3/7
Una máquina llena 4 baldes de helado en 30 minutos, funcionando siempre a la misma velocidad Si ante un corte de luz, solo funcionó durante 45 minutos, ¿cuántos baldes habrá llenado?
Answers
Answer:
La máquina llenó:
6 baldes
Step-by-step explanation:
Por regla de tres:
4 baldes son a 30 minutos
M baldes son a 45 minutos
M = 45*4/30
M = 180/30
M = 6
A circular track is 1000 yards in circumference. Cyclists A, B, and C start at the same place and time, and race around the track at the following rates per minute: A at 700 yards, B at 800 yards, and C at 900 yards. What is the least number of minutes it mus take for all three to be together again?
Answers
Answer:
B gains 100 yards every minute. So, after 10 minutes, B has lapped A once.
C gains 100 yards on B every minute, so after 10 minutes C has lapped B.
Thus, after 10 minutes, A has gone 7 laps, B has gone 8 laps, C has gone 9 laps, and all are even again.
The function h(x) is defined as shown. h(x) = StartLayout Enlarged left-brace 1st row 1st column x + 2, 2nd column x less-than 3 2nd row 1st column negative x + 8, 2nd column x greater-than-or-equal-to 3 EndLayout What is the range of h(x)? –∞ < h(x) < ∞ h(x) ≤ 5 h(x) ≥ 5 h(x) ≥ 3
Answers
Answer: B
Step-by-step explanation:
Answer:
b
Step-by-step explanation:
PLEASE HELP!! A car manufacturer does performance tests on its cars. During one test, a car starts from rest, and accelerates at a constant rate for 20 seconds. another car starts from rest three seconds later, and accelerates at a faster constant rate. The equation that models the distance (d) in metres the first cars equation is d=1.16t^2, where t is time, in seconds, after the car starts. The equation for the second car is: d=1.74(t-3)^2. a) in context, what is a suitable domain for the graph of the system? b) at what time will both cars have driven the same distance? c) how far will they have driven at this time?
Answers
Answer:
0 ≤ t ≤ 2516.348 seconds310.0 metersStep-by-step explanation:
a) Since these are production vehicles, we don't expect their top speed to be more than about 70 m/s, so the distance functions probably lose their validity after t = 25. Of course, t < 0 has no meaning in this case, so the suitable domain is about ...
0 ≤ t ≤ 25
Note that the domain for the second car would be 3 ≤ t ≤ 25.
__
b) The graph of this system shows the cars will both have driven the same distance after 16.348 seconds.
__
c) At that time, the cars will have driven 310.0 meters.
_____
Non-graphical solution
If you like, you can solve the equation for t:
d1 = d2
1.16t^2 = 1.74(t -3)^2
0 = 0.58t^2 -10.44t +15.66
t = (10.44 +√(10.44^2 -4(0.58)(15.66)))/(2(0.58)) = (10.44+8.524)/1.16
t = 16.348 . . . . time in seconds the cars are at the same distance
That distance is found using either equation for distance:
1.16t^2 = 1.16(16.348^2) = 310.036 . . . meters
Use the cubic model y = 10x3 − 12x to find the value of y when x = 9.
Answers
Answer:
7182
Step-by-step explanation:
All you shoud do is to replace x by 9
● y = 10 * 9^3 -12*9
● y = 7182
help me Please!!!!!!!
Answers
Answer:
[tex]\boxed{Option \ C}[/tex]
Step-by-step explanation:
[tex]Sin \ Y = \frac{Opposite }{Hypotenuse } = \frac{XZ}{XY}[/tex]
[tex]Cos \ Y = \frac{Adjacent}{Hypotenuse} = \frac{YZ}{XY}[/tex]
[tex]Tan Y = \frac{opposite}{adjacent} = \frac{XZ}{ZY}[/tex]
Answer:
[tex]\boxed{\mathrm{C}}[/tex]
Step-by-step explanation:
sin [tex]\theta[/tex] = Opposite/Hypotenuse
sin (Y) = [tex]\frac{XZ}{XY}[/tex]
cos [tex]\theta[/tex] = Adjacent/Hypotenuse
cos (Y) = [tex]\frac{YZ}{XY}[/tex]
tan [tex]\theta[/tex] = Opposite/Adjacent
tan (Y) = [tex]\frac{XZ}{YZ}[/tex]
What type of linear system is shown below?
A inconsistent
B. consistent and independent
C. consistent and dependent
D. inconsistent and dependent
Graph is attached , please help
Answers
Answer:
The linear system shown on the graph is consistent and independent
Step-by-step explanation:
The linear system shown on the graph is consistent because it has at least one solution which satisfy both linear graphs. The solution is at the point of interception of the two line graphs.
The linear system shown on the graph is independent because the two line graphs are distinct and not parallel or dependent on one another.
Therefore, The linear system shown on the graph is consistent and independent
What is the approximate circumference of the circle shown below?
Answers
Answer:
[tex]\boxed{\sf 43.35 \ cm}[/tex]
Step-by-step explanation:
Apply formula for the circumference of a circle.
[tex]\sf C=\pi d[/tex]
The diameter [tex]\sf d[/tex] is 13.8 cm.
[tex]\sf C=\pi (13.8)[/tex]
[tex]\sf C= 43.3539786195...[/tex]
[tex]\sf{C} \approx \sf{43.35}[/tex]
Answer:
43.4 cm
Step-by-step explanation:
Circumference of the circle = 2πr
r = radius, π = [tex]\frac{22}{7}[/tex]
f = diameter÷2
=13.8 ÷ 2
= 6.9
circumference = [tex]2 * \frac{22}{7} * 6.9\\[/tex]
= [tex]\frac{303.6}{7}[/tex]
= 43.37 cm or 43.4 cm
Find m∠ABC. (2x+14) (x+7)
Answers
Answer:
A= 2
B=28
C=0
Step-by-step explanation:
ax2 + bx + c=0
(Help now ) please help that will be much appreciated
Answers
Answer:
[tex](2x+3)(2x+3)[/tex]
Step-by-step explanation:
The given expression is
[tex]4x^2+12x+9[/tex]
Here, a=4, b=12, c=9.
Step 1: Multiply [tex]a\cdot c=4\cdot 9=36[/tex]
Step 2: Find the factors of ac that add to b.[tex]6\cdot 6=36[/tex] and [tex]6+6=12=b[/tex] So, two factors of ac are 6 and 6.
Step 3:[tex]4x^2+6x+6x+9[/tex]
Step 4:[tex](4x^2+6x)+(6x+9)[/tex]
Step 5:[tex]2x(2x+3)+3(2x+3)[/tex]
Step 6:[tex](2x+3)(2x+3)[/tex]
Therefore, the required factor form is [tex](2x+3)(2x+3)[/tex]. It can also written as [tex](2x+3)^2[/tex].
Complete the statements about the system of linear
equations represented by the tables.
The equation representing the left table is
y = 1.5x - 6.
The equation representing the right table is
y=-4x + 6.1
The solution to the system of equations is?
Answers
Answer:
(2.2, -2.7)Step-by-step explanation:
y = y1.5x - 6 = -4x + 6.1+4x+6 +4x+6
5.5x = 12.1÷5.5 ÷5.5
x = 2.2y = -4×2.2 + 6.1 = - 8.8 + 6.1 = - 2.7Answer:
Left table: y= 1.5x - 6
Right table : y= -4x + 6.1
Solution : (2.2 , -2.7)
Step-by-step explanation:
:)
Help it’s urgent please
Answers
Answer:
[tex] \frac{5 {x}^{2} + 20xy + 20 {y}^{2} }{x ^{2} - xy - {6y}^{2} } [/tex]
To simplify first factorize both the numerator and the denominator
For the numerator
5x² + 20xy + 20y²
Factor 5 out
5 ( x² + 4xy + 4y²)
Using a² + 2ab + b² = ( a + b)²
The numerator is
5( x + 2y)²
For the denominator
x² - xy - 6y²
Rewrite -xy as a difference
x² + 2xy - 3xy - 6y²
Factorize
We have the denominator as
( x + 2y)( x - 3y)
So we now have
[tex] \frac{5(x + 2y)(x + 2y)}{(x + 2y)(x - 3y)} [/tex]Simplify
[tex] \frac{5(x + 2y)}{x - 3y} [/tex]We have the final answer as
[tex] \frac{5x + 10y}{x - 3y} [/tex]Hope this helps you
a girl spent 2/3 of her pocket money and was left with $1800.00 . How much was her pocket money
Answers
Answer: She had $5400
Step-by-step explanation:
We will let x represent the total amount of money in her pocket .
So we know that 1/3 of x has to equal 1800 because 2/3 of the money is already been spent so 1/3 will of the money will be left.
1/3 * x = 1800 solve for x by divide both sides by 2/3
x=5400
Check.
1/3 * 5400 =1800
Which system of inequalities has this graph as it’s solution
Answers
Answer:
Option (B)
Step-by-step explanation:
In the graph attached,
Two lines graphed have the equations as,
y = 2x - 3 [A line having y-intercept as (-3)]
[tex]y=\frac{1}{3}x+4[/tex] [Line having y-intercept as (4)]
Since both the lines have been represented by the dotted lines therefore, these lines will represent the inequalities [having the signs less than (<) or greater than (>)].
Now shaded region will decide the signs of the inequalities.
Since, shaded region of y = 2x - 3 is on the left side, inequality showing this region will be,
y > 2x - 3
Since, shaded region of [tex]y=\frac{1}{3}x+4[/tex] is above the line, inequality showing this region will be,
[tex]y>\frac{1}{3}x+4[/tex]
Therefore, Option (B) will be the answer.
Answer:
B
Step-by-step explanation:
Just is cuh
Which linear function has the steepest slope? On a coordinate plane, a line goes through points (0, 1) and (1, negative 2). A 2-column table with 4 rows. Column 1 is labeled x with entries 3, 6, 9, 12. Column 2 is labeled y with entries 10, 13, 16, 19. On a coordinate plane, a line goes through points (0, negative 2) and (1, 0). A 2-column table with 4 rows. Column 1 is labeled x with entries 2, 4, 6, 8. Column 2 is labeled y with entries negative 4, negative 12, negative 20, negative 28.
Answers
Answer:
D
Step-by-step explanation:
Answer:d
Step-by-step explanation:
D
pls help me do this (atleast one) using quadratic formula
Answers
Drag the tiles to the correct boxes to complete the pairs.
This table gives Information about vehicles sold at a dealership in a month.
Gasoline Diesel
18
5
Hatchback
Sedan
15
12
SUV
3
7
Analyze this data, and match each percentage to the description It represents. Round your answers to the nearest whole number.
30%
44%
21%
8%
42%
78%
the percentage of hatchbacks that run on gasoline
the percentage of diesel vehicles that are hatchbacks
tum. All rights reserved.
Answers
Answer:
The percentage of hatchbacks that run on gasoline: 78%
The percentage of diesel vehicles that are hatchbacks: 21 %
Step-by-step explanation:
The given table represents the following:
Hatchbacks that run on Gasoline = 18
Hatchbacks that run on Diesel = 5
Total number of hatchbacks = 23
Sedan that run on Gasoline = 15
Sedans that run on Diesel = 12
Total number of sedans = 27
SUVs that run on Gasoline = 3
SUVs that run on Diesel = 7
Total number of SUVs = 23
Total number of gasoline vehicles = 36
Total number of Diesel vehicles = 24
To find:
the percentage of hatchbacks that run on gasoline
the percentage of diesel vehicles that are hatchbacks
Solution:
[tex]\text{Percentage of hatchbacks that run on gasoline = } \dfrac{\text{Number of hatchbacks on gasoline}}{\text{Total number of hatchbacks}}\times 100\\\Rightarrow \text{Percentage of hatchbacks that run on gasoline = } \dfrac{18}{23}\times 100 \approx 78\%[/tex]
[tex]\text{Percentage of diesel vehicles that are hatchbacks = } \dfrac{\text{Number of hatchbacks that run on diesel}}{\text{Total number of diesel vehicles}}\times 100\\\Rightarrow \text{Percentage of diesel vehicles that are hatchbacks = } \dfrac{5}{24}\times 100 \approx 21\%[/tex]
So, the answer is:
The percentage of hatchbacks that run on gasoline: 78%
The percentage of diesel vehicles that are hatchbacks: 21%
Answer:
I used a calculator and this is what can up with
Step-by-step explanation:
