Answer:
X=1 Y=8
Step-by-step explanation:
[tex] - 3x + 11 = 7x + 1 \\ 10 = 10x \\ x = 1 \\ y = 7 \times1 + 1 \\ y = 8[/tex]
A boat can travel 20 miles on 10 gallons of gasoline. How much gasoline will it need to go 34 miles?
Answer:
20 divided by 10 is 2 so for every 2 miles it travels it uses 1 gallon of gasoline. 20 + 14 is 34 so you divide 14 by 2 to get 7. then you add 10+7 to get 17. it will take 17 gallons of gasoline to go 34 miles
Step-by-step explanation:
Suppose g(x) = f(x) + k. Identify a value of k that transforms f into g.
Answer:
[tex]k = 5[/tex]
Step-by-step explanation:
Given
[tex]g(x) = f(x) + k[/tex]
Required
Determine the value of k
First, we need to determine the equation of g(x)
Start by calculating the slope (m)
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Where x and y are two corresponding values:
[tex](x_1,y_1) = (1,1)[/tex]
[tex](x_2,y_2) = (0,-3)[/tex]
The slope (m) is:
[tex]m = \frac{-3- 1}{0 - 1}[/tex]
[tex]m = \frac{-4}{- 1}[/tex]
[tex]m = 4[/tex]
The equation is calculated using:
[tex]y - y_1 = m(x - x_1)[/tex]
Where
[tex]m = 4[/tex] and [tex](x_1,y_1) = (1,1)[/tex]
[tex]y - 1 = 4(x - 1)[/tex]
[tex]y - 1 = 4x - 4[/tex]
Make y the subject of formula
[tex]y = 4x - 4 + 1[/tex]
[tex]y = 4x - 3[/tex]
So:
[tex]f(x) = 4x - 3[/tex]
Next, we determine the equation of f(x)
Start by calculating the slope (m)
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Where x and y are two corresponding values:
[tex](x_1,y_1) = (-1,-2)[/tex]
[tex](x_2,y_2) = (0,2)[/tex]
The slope (m) is:
[tex]m = \frac{2- (-2)}{0 - (-1)}[/tex]
[tex]m = \frac{2+2}{0+1}[/tex]
[tex]m = \frac{4}{1}[/tex]
[tex]m = 4[/tex]
The equation is calculated using:
[tex]y - y_1 = m(x - x_1)[/tex]
Where
[tex]m = 4[/tex] and [tex](x_1,y_1) = (-1,-2)[/tex]
[tex]y - (-2) = 4(x - (-1))[/tex]
[tex]y + 2 = 4(x +1)[/tex]
[tex]y + 2 = 4x +4[/tex]
Make y the subject of formula
[tex]y = 4x + 4 - 2[/tex]
[tex]y = 4x + 2[/tex]
So:
[tex]g(x) = 4x + 2[/tex]
Recall that
[tex]g(x) = f(x) + k[/tex]
Make k the subject
[tex]k = g(x) - f(x)[/tex]
Substitute values for g(x) and f(x)
[tex]k = 4x + 2 - (4x - 3)[/tex]
[tex]k = 4x + 2 - 4x + 3[/tex]
[tex]k = 4x - 4x+ 2 + 3[/tex]
[tex]k = 5[/tex]
The transformation that maps f into g is a translation transformation,
involving the addition of k to the value of f(x).
The value of k that transforms f into g is; k = -5Reasons:
Points on the graph of g(x) are; (0, -3) and (0, 1)
[tex]\mathrm{The \ slope \ of \ the \ graph \ of \ g(x)} =\dfrac{-3 - 1}{0 - 1} = 4[/tex]
The equation of g(x) is; y - (-3) = 4·x, which gives;
y = 4·x - 3
The y-intercept = -3
Points on the graph of f(x) are; (-1 -2) and (0, 2)
[tex]\mathrm{The \ slope \ of \ the \ graph \ of \ f(x)} =\dfrac{-2 - 2}{-1 - 0} = 4[/tex]
The equation of f(x) is; y - (-2) = 4·(x - (-1)), which gives;
y = 4·x + 4 - 2 = 4·x + 2
The y-intercept = 2
The slopes of the graphs of f(x) and g(x) are equal, therefore, f(x) ║ g(x)
The difference or the transformation that takes the y-intercept of f(x) to the
y-intercept of g(x) is; k = y-intercept(g(x)) - y-intercept(f(x)) = -3 - 2 = -5
Therefore, k = -5
Which gives;
g(x) = f(x) - 5
The value of k that transforms f into g is; k = -5
Learn more here:
https://brainly.com/question/23570234
https://brainly.com/question/10049947
Solve: 1,241 ÷ 32
Show the remainder as a fraction.
Answer: 38 25/32
Step-by-step explanation:
Answer: (1241/32) ÷ 2 = 19.390625
Step-by-step explanation:
a) x2 when x = 5
b) y2 when y = -2
c) z2 when z = 0.5
Answer:
A) 25
B) 4
C) 0.25
Thank you and please rate me as brainliest as it will help me to level up
Can you complete the pattern? pls do. 101, 94, 87, 80, __, __, __ *
Answer:
73, 66, 59
Step-by-step explanation:
Each number has a value of 7 difference
Answer:
73, 66, 59
Step-by-step explanation:
Enter a response to each question.
1. Dear Math Helper,
I am in need of your help! I have a job where I design games. I am designing a game that involves a playing area
with 12 equal sections. Players randomly end up in one of the sections.
1 labeled one section, "Gain 40 points," four sections, "Gain 10 points," and the rest, "Try Again." Also, each
player automatically gives up 10 points with each move,
After trying out the game on some volunteers, I noticed that players tend to lose points in the long run. Without
changing the sizes of the sections, what adjustments can I make so that players are likely to earn at least one
Point in the long run?
Answer: Let them start off with a certain amount of money. So before they make a move they would have some points ahead of time.
Step-by-step explanation: Hope this helped!! :)
Well, you can actually increase the number of points for those sections and spread them across the sections so that as the players get in the long run, some points will be available for them.
What is video game?Video game refers to a device which is electronically controlled and played and involves the controlling of images displayed on the screen. Video games has really improved as technology keep advancing.
Thus, from the question above, if players will not lose points at the long run, then it's necessary points need to increase at the long run.
Learn more about video game on https://brainly.com/question/908343
#SPJ2
Let them start off with a certain amount of money. So before they make a move they would have some points ahead of time.
(2/3x + 2) - (1/3x - 4 )
help me! :( will appreciate any type of help
Answer:32
Step-by-step explanation: (2+3x)= 98 then solve
What is the product? 2x+8 x2 + 3x-4 x(x-4)(x-1) 20x+4) 2 (x+4)(x-4) 2x(x-1) 2x(x+4)
=−640x10+1280x9+19904x8−40728x7−144488x6+323904x5−162304x4+1024x3+2048x2
step by step
(2x+8x2+3x−4x(x−4)(x−1)(20)x+4)(2)(x+4)(x−4)(2)x(x−1)(2)x(x+4)
=((2x+8x2+3x−4x(x−4)(x−1)(20)x+4)(2)(x+4)(x−4)(2)x(x−1)(2)x)(x+4)
=((2x+8x2+3x−4x(x−4)(x−1)(20)x+4)(2)(x+4)(x−4)(2)x(x−1)(2)x)(x)+((2x+8x2+3x−4x(x−4)(x−1)(20)x+4)(2)(x+4)(x−4)(2)x(x−1)(2)x)(4)
=−640x10+3840x9+4544x8−58904x7+91128x6−40608x5+128x4+512x3−2560x9+15360x8+18176x7−235616x6+364512x5−162432x4+512x3+2048x2
=−640x10+1280x9+19904x8−40728x7−144488x6+323904x5−162304x4+1024x3+2048x2
Ellie has a 352-ounce bag of dog food. Her dog eats 24 ounces each day. How many full days will Ellie feed her dog before she needs another bag of dog food?
Answer: 14 days
Step-by-step explanation:
352/24= 14.66666667
So it can feed her dog for 14 full days
A recipe needs 3/4 cups of sugar to make 24 cookies.How much will be needed to make 36 cookies?
Answer:
Step-by-step explanation:
36 cookies = 1.5 times 24 cookies. therefore 1.5 times ¾ c of sugar will be required. Total sugar needed for 36 cookies is 9/8 c or 1.125 c.
This recipe makes four portions of soup.
Navina follows this recipe but only wants to make enough for one portion of soup.
How much of each ingredient does she need?
Recipe: Serves 4.
180 g onions
100 g carrots
3 tablespoons of oil
600 g tomatoes
1.2 / vegetable stock
g onions
g carrots
tbsps oil
g tomatoes
Answer:
i need help
Step-by-step explanation:
In the Alt J song, In Cold
Blood, the singer sings a
number, 01110011. If this
number is in base 2, what
would it be in base 10?
01110011
two
Answer:
kjjhgyufg
Step-by-step explanation:
Lin rode a bike 20 miles in 150 minutes at a constant
speed.
Answer:
7.5 miles per minute
Step-by-step explanation:
The value of 8 dimes and 5 pennies is what percentage of a dollar
Answer: 85% because 1 dime = 10 cent. 10x8=80
80+5=85
85% of 100
Step-by-step explanation:
The price of a pair of shoes increases from $62 to $81. What is the percent increase to the nearest percent?
Answer:
Step-by-step explanation:
$19 increase is about 31%
62*31%= 19.22
30% increase is $18.60 increase
At a school, 40% of the sixth-grade students said that hip-hop is their favorite kind of music. If there are 275 sixth-grade students at the school, how many sixth-grade students prefer hip hop music?
Answer:
Around 80 students
Step by step explaining:
My big brain
-5/2a+5=25 what does a equal
Answer:
-8
Step-by-step explanation:
The claim is that the standard deviation of the speeds of drivers in Bradford is 8 mph. An experienced driver feels that this is very low. If a random speed check is conducted for 50 drivers, the standard deviation is 10.5 mph. Can we reject the null at
Answer:
Null hypothesis is rejected. Standard deviation is > 8 miles per hour
Step-by-step explanation:
σ [Population standard deviation] = 8 , s [sample standard deviation] = s
n [no of items] = 8
H0 [Null] : σ = 8 ; H1 [Alternate - Right Tail] : σ > 8
χ2 = (n - 1) . s^2 / σ^2
= 49 x (10.5)^2 / 82 = 5402.25 / 64
χ2 = 84.410
df [degree of freedom] = n -1 = 50 - 1 = 49
P value (χ^2 49 > 84.410) = 0.00125
p = 0.0013
p < α ie 0.05
So, H0 is rejected
Hence we state that standard deviation is > 8 miles per hpur
In the diagram below, segments RS and RT intersect line m at points T and S, respectively.
Which of these statements is true?
Triangle RST is an isosceles triangle.
Triangle RST is a scalene triangle.
Triangle RST is a right triangle.
Triangle RST is an equilateral triangle.
Answer:
RST is an isosceles triangle
Step-by-step explanation:.
Required
Determine what type of triangle, is RST.
First, we need to determine the angles in RST
Angle on a straight line is 180°.
So, if <mTS = 130°
Then,
<STR = 180° - 130°
<STR = 50°
Similarly,
<TSR = 180° - 130°
<TSR = 50°
The sum of angles in a triangle is 180°.
So:
<TSR + <STR + <TRS = 180°
50 + 50 + <TSR = 180°
100 + <TSR = 180°
<TSR = 180° - 100°
<TSR = 80°
Hence, the three angles of the triangle are: 50°, 50° and 80°
When just two angles of a triangle are equal; such triangle is referred to as an isosceles triangle
Hence, option A answers the question.
Options
-0
- negative
- undefined
- positive
Answer:
Positive
Step-by-step explanation:
the line isn’t in the negative side (going towards the right) so it’s positive
Which expression are equal to the value of 3 in the number 14,397
Answer:
300
Step-by-step explanation:
This is a place value problem.
The given figure is;
14, 397:
Pronounced as;
Fourteen thousand, three hundred and ninety seven:
14, 397;
10 000 ten thousand
4000 four thousand
300 three hundred
90 ninety
7 seven
The place value of 3 is hundreds.
Item 8
Calculator
Quadrilaterals LMNO and STUV are similar.
What is the value of x in inches?
6.6 in.
8.2 in.
22.9 in.
27.1 in.
Answer: 6.6
Step-by-step explanation:
Ayo!!
First you use the formula SF=N/O. The new is the big triangle. The Old is the small triangle. Next you tick the sides of each triangle. So lets say 4.1 will be 1 tick and 2.2 will be 2 ticks. Now the old triangle is done now to the new triangle. 12.3 is the 1 tick and x is the 2 ticks.
Lets set up the formula. N-/N--= O-/O--= 12.3/x and 4.1/2.2. Now u cross multiply. 4.1x=12.3*2.2=4.1x=27.06. Then you divide 4.1x by 4.1 and 27.06 by 4 aswell. 4.1x divided by 4.1 cancel each other out so you are left with 27.06 divided by 4.1 and that equals 6.6. So the answer is 6.6.
PS: If i did the new and old triangles wrong just reverse them and just do it like I explained it.
Hope this helped! :)
Answer:
6.6
Step-by-step explanation:
i took the test
Current Attempt in Progress Present value. On the first day of your college career you decide that you want to make one deposit into a mutual fund so that exactly four years later you have enough to purchase a car costing $30000. Given that the account will generate a yield of 4.7% interest compounded monthly, what should your initial deposit be in order to have that big pot of money at graduation? Round the answer to two decimal places. Check your answer by plugging into initial equation to be sure you would not be short of $30000. _____________ $
Answer:
You will need to invest $24,867.52 at the beginning to reach the future value of $30,000.00.
Step-by-step explanation:
a) Data and Calculations:
Future value for the purchase of a car = $30,000
Interest rate = 4.7%
Monthly interest = 0.39167% (4.7%/12)
Period of interest = 48 months (12 * 4)
FV (Future Value) $30,000
PV (Present Value) $24,867.52
N (Number of Periods) 48.000
I/Y (Interest Rate) 0.392%
PMT (Periodic Payment) $0.00
Starting Investment $24,867.52
Total Principal $24,867.52
Total Interest $5,132.48
What is the sum of the exterior angles of a 54-gon?
Answer: The sum of the exterior angles of a 54-gon should be 360°.
Step-by-step explanation:
A polygon is a closed figure made up of straight lines like triangle (3-gon) , quadrilateral (4-gon) , square(4-gon), pentagon (5-gon) , octagon(8-gon) etc.
The sum of exterior angles of any polygon with n sides ( or n-gon ) is always 360 degrees.
A 54-gon is a polygon with 54 sides.
Therefore , the sum of the exterior angles of a 54-gon should be 360°.
Final answers must be in standard form
(Y+8)(y-1)
Answer:
y^2 + 7y - 8
Step-by-step explanation:
(y + 8)(y - 1)
y^2 -1y + 8y - 8
y^2 +7y - 8
Answer:
y²+7y-8
Explanation:
y times y equals y²
y times -1 equals -1y
8 times y equals 8y
8 times -1 equals -8
-1y combines with 8y to make 7y
Put all values in decreasing order
A) x=5
B) x= 4
C) x= -1.5
D) x= -2
Answer:
x=-1.5
Step-by-step explanation:
Answer:
B) X=4
Step-by-step explanation:
Since opposite sides of a rectangle are equal that means line AD and line BC are equal to eachother
8x-12=20
+12 +12
8x=32
/8 /8
x=4
What is the answer for
(3/4)(3/5)=
Answer:
9/20 or 0.45
Step-by-step explanation:
we multiply them
3×3/4×5
9/20
or 0.45
See image below for problem, thank you :))
Given: ∠XAM = ∠YBM = 90° and AM = BM
To prove: BX ≅ AY
Proof:
In the triangle XAM and BYM:
∠3 = ∠4 [vertically opposite angles]AM = BM [Given]∠XAM = ∠YBM [Both are 90°]From the ASA rule of congruency, we can say that: ΔXAM ≅ ΔYBM
Since ΔXAM ≅ ΔYBM: We can say that XM ≅ MY [CPCT - Common Part of Congruent triangles]
In the Triangle AMY and XMB:
∠1 = ∠2 [vertically opposite angles]AM = BM [Given]XM = MY [Proved above]From the SAS rule of congruency, we can say that: ΔAMY ≅ ΔXMB
Since ΔAMY ≅ ΔXMB: We can finally say that BX ≅ AY [CPCT]
Hence Proved!
2
Find the slope and y-intercept from the following graph of a linear equation.
4
-5
-4
-3
- 2
N
2
3
4
5
-1
X
-2
-3
-
-5
Answer:
is 5
Step-by-step explanation:m
..