Answer:
a) The inverse is g(x) = (1/70)*x - 50/70
b) The slope intercept form is y = -6*x - 47
Step-by-step explanation:
a) When we have a function f(x), the inverse of this function (let's call it g(x)) is such that:
g(f(x)) = x
f(g(x)) = x
for every x.
In this case, we have:
f(x) = 70*x + 50
This is a linear function, and the inverse will be also a linear function.
Then the inverse will be something like:
g(x) = a*x + b
then:
g( f(x)) = x = a*( 70*x + 50) + b
then we can just solve the equation:
x = a*( 70*x + 50) + b
x = a*70*x + a*50 + b
If we separate terms by the powers of x in each side of the equation, we have:
1*x + 0*x^0 = (a*70)*x + (a*50 + b)*x^0
(where x^0 = 1)
then:
1 = (a*70)
a = 1/70
and:
0 = (a*50 + b)
0 = 50/70 + b
-50/70 = b
Then the inverse of f(x) is:
g(x) = (1/70)*x - 50/70.
b) The slop-intercept form of a linear equation is:
y = a*x + b
where a is the slope, and b is the y-intercept.
We want to write in this form the equation:
y + 5 = -6*(x + 7)
The first step is to isolate the "y" in one side of the equation:
y = -6*(x + 7) - 5
Now let's simplify the right side:
y = -6*x - 6*7 - 5
y = -6*x - 42 - 5
y = -6*x - 47
This is the slope-intercept form, where the slope is -6, and the y-intercept is -42.
Find x and y so the quadrilateral is a parallelogram.
Answer:
We conclude that:
The value of x = 7The value of y = 4Step-by-step explanation:
Given
The parallelogram PQRSWe know that the diagonals of a parallelogram bisect each other.
so
[tex]RT = TP[/tex]
Given
RT = xTP = 5x-28so substituting RT = x, and TP = 5x-28
[tex]RT = TP[/tex]
[tex]x = 5x-28[/tex]
[tex]5x = x+28[/tex]
[tex]5x-x = 28[/tex]
[tex]4x = 28[/tex]
divide both sides by 4
[tex]4x/4 = 28/4[/tex]
[tex]x = 7[/tex]
Therefore, the value of x:
x = 7Similarly,
[tex]QT = TS[/tex]
Given
QT = 5yTS = 2y+12so substituting QT = 5y, and TS = 2y+12
[tex]QT = TS[/tex]
[tex]5y = 2y+12[/tex]
[tex]5y-2y = 12[/tex]
[tex]3y = 12[/tex]
divide both sides by 3
[tex]3y/3 = 12/3[/tex]
[tex]y = 4[/tex]
Therefore, the value of y:
y = 4
Therefore, we conclude that:
The value of x = 7The value of y = 4Q
A rectangular field is 16m broad
and the ratio of the length and
find the length of the field
breadth is 3:2.
Find the length of the field
james is in charge of the decorations. he hs a total budget of $50 to spend for all of the decorations. james spends $20 on one banner and would like to buy balloons that cost $2 each with the rest of the money. Write an equation to represent the situation.
How many balloons can james buy?
WEEEEEEEEEEEEEEEEEEEEEEE
Answer:
1/6y^4
Step-by-step explanation:
sorry if I'm wrong
pls answer asap pls pls
Answer:
A
Hindi po ako sigurado po ahhhh
Yo can someone help me?
Answer:
angle v equals 75.8 degrees
Step-by-step explanation:
since the lines parallel, then angle u and angle v would be the same as they are alternate interior angles. you can also subtract 180 with angle w to find angle v as well (180 - 104.2 = 75.8)
Answer the question please
Answer:
C
There's clusters of data around the indicated points.
Find the area of each geometric figure or product of the polynomial.
(-6r + 3) (-3r - 3)
A) 18r2 + 9r - 9
B) -30r2 - 38r + 16
C) 40r2 + 20r - 20
D) 40r2 + 60r + 20
Answer:
Step-by-step explanation:
Nose
can somone answer this please
Answer:
4
7
6
9
Step-by-step explanation:
plz brainliestt
8a-9÷3 if a=7/8
its algebra i need help
Answer:
4
Step-by-step explanation:
Plug 7/8 into a.
8(7/8)-9/3 Multiply.
7-9/3 Divide.
7-3 Subtract.
4
Hope this helps!! Have a great day! (｡･∀･)ﾉﾞ
100 points! Will mark brainliest! Only answer if u know it. Random answers will be reported
Step-by-step explanation:
Hey there!
According to the question, you need to find out the distance from your friend's house to school.
Firstly figure out the coordinate of your school and school. Then use formula of distance.
So, we find the coordinates as (7,7) and (5,0).
So, x 1 = 7 y1= 7
x 2 = 5 y2 = 0
~ Use distance formula.
[tex]d = \sqrt{( {x2 - x1)}^{2} + ( {y2 - y1)}^{2} } [/tex]
~ Put all values.
[tex]d = \sqrt{ {(5 - 7)}^{2} + ( {0 - 7)}^{2} } [/tex]
~ Simplify it.
[tex]d = \sqrt{ {( - 2)}^{2} + {( - 7)}^{2} } [/tex]
[tex]d = \sqrt{4 + 49} [/tex]
[tex]d = \sqrt{53} [/tex]
D= 7.280
Therefore, the distance between your friend's house and your school is 7.3 units.
Hope it helps....
you need to find out the distance from your friend's house to school.
Firstly figure out the coordinate of your school and school. Then use formula of distance.
So, we find the coordinates as (7,7) and (5,0).
So, x 1 = 7 y1= 7
x 2 = 5 y2 = 0
~ Use distance formula.
~ Put all values.
~ Simplify it.
D= 7.280
Therefore, the distance between your friend's house and your school is 7.3 units
Maria makes a fruit salad.
The table shows the amounts of different kinds of fruit that she uses.
Kind of Fruit Amount
Grapes 323 cups
Melon 214 cups
Pineapple 234 cups
Strawberries ?
The amount of strawberries that Maria uses is 38 times the amount of the other fruits combined.
How many cups of strawberries does Maria use?
Answer:
If my calculations are correct it would be 6,168 cups of strawberries
Step-by-step explanation:
If it’s 8 times the amount of them combined then you add all of the other fruit together and then multiply by 8 giving you:
323+214+234=771
771*8=6,168 cups of strawberries.
Only in math would someone need that much fruit
Suppose that you bought a new car at a price of $27,600.
According to research on this make and model, similar cars
have straight line depreciated to O value after 12 years. How
much will your car be worth after 9 years?
b. What is the slope of the line?
A. 2300
B.27600
C. 2300
D.12
Answer:
x intercept=12,0
y intercept= 0,2700
Step-by-step explanation:
At basketball camp, Kylie made 18% of her free throws. Based on this information, which is the best prediction of the number of free throws she will make out of 50 attempts?
Answer:
whn you do 18% of 50, you get 9 freethrows
A breakfast menu liste 3 eggs with 2 sausage for $4.15 or 4 eggs with 1 sausage for $4.30 . What is the cost of 1 egg, and what is the cost for 1 sausage?
Answer:
Cost of 1 egg = x = $0.89
Cost of 1 sausage = y = $0.74
Step-by-step explanation:
Let the:
Cost of 1 egg = x
Cost of 1 sausage = y
A breakfast menu lists:
3 eggs with 2 sausage for $4.15
3x + 2y = 4.15......Equation 1
4 eggs with 1 sausage for $4.30 .
4x + y = 4.30...... Equation 2
y = 4.30 - 4x
We substitute 4.30 - 4x for y in Equation 1
3x + 2(4.30 - 4x) = 4.15
3x + 8.6 - 8x = 4.15
3x - 8x = 4.15 - 8.6
-5x = -4.45
x = -4.45/-5
x = $0.89
Solving for y
y = 4.30 - 4x
y = 4.30 - 4(0.89)
y = 4.30 - 3.56
y = $0.74
Therefore,
Cost of 1 egg = x = $0.89
Cost of 1 sausage = y = $0.74
ZX and zy or supplementary angles. zy measures 49 degrees what is the measure of ZX
Answer:
131˙
Step-by-step explanation:
Supplementary angles are angles that add up to 180˙. If you subtract 49 from 180, you get 131.
Brainliest? Maybe?
what is the maximum value of f(x)=−4x2+4x−2?
Answer: -1
Step-by-step explanation: A typical quadratic equation is [tex]ax^{2} +bx+c[/tex] and the maximum value formula is -b/2a, so let plug it in -4/2(-4) which equals 1/2. Then let plug 1/2 into the equation,
-4(1/2)^2+4(1/2)-2=
-1+2-2=
-1
If the simple interest on $2000 for 10 years is $,1000 then what is the interest rate?
[tex] \bf \underline{Given :}[/tex]
[tex] \sf{• \: Principal \: (P) = \$ \: 2000}
[/tex]
[tex] \sf{• \: Simple \: Interest \: (I) = \$ \: 1000}
[/tex]
[tex] \sf{• \: Time \: (T) = 10 \: years}[/tex]
[tex] \sf{• \: Interest \: Rate \: (R) = \: ?}[/tex]
[tex] \bf \underline{Solution:-}[/tex]
[tex] \sf {We \: know \: that, }[/tex]
[tex]\bf \red{\bigstar{ \: I = PRT}}[/tex]
[tex] \sf{⟹1000 = 2000 \times \frac{R}{100} \times 10 }[/tex]
[tex] \sf{⟹1000 = \frac{R}{100} \times 20000}[/tex]
[tex] \sf{⟹ \frac{R}{100} = \frac{1000}{20000} }[/tex]
[tex] \sf{⟹R = \frac{1}{20} \times 100 }[/tex]
[tex] \sf⟹ R = 5[/tex]
[tex] \pink{\bf{Hence, \: the \: interest \: rate \: is \: 5 \: \%. }}[/tex]
3x² ×2x³
help please
Hope you have a good day!〜
Also please tell me if I'm wrong or not...
Also also if I'm right can I please have Brainliest?
.
From 24 to 30 teachers
Posted this question 1000times. Plz some answer plz plz i beg. Plz show all working, thank you sir
Answer:
[tex]\approx 26.16\:\mathrm{m}[/tex]
Step-by-step explanation:
Let [tex]h[/tex] be the height of the tree. In reference to the tree and bird, a right triangle is formed. We can write the following trig function for that right triangle:
[tex]\tan28^{\circ}=\frac{h}{15},\\h=15\tan28^{\circ},\\h\approx 7.98\:\mathrm{m}[/tex].
Now we can use this to find the hypotenuse of this triangle (the distance between the cat and the bird):
Let the distance between the cat and bird be [tex]k[/tex]. Then,
[tex]7.98^2+15^2=k^2,\\k\approx 16.99\:\mathrm{m}[/tex]. This is one side of the triangle that is formed by the cat, bird, and mouse.
The right triangle formed by the tree, cat, and mouse shares the height [tex]h[/tex] with the other right triangle, as we found earlier. Let [tex]l[/tex] represent the hypotenuse of this triangle or the distance between the cat and mouse. We then have the following trig function:
[tex]\sin 40^{\circ}=\frac{7.98}{l},\\l=\frac{7.98}{\sin40^{\circ}}\approx 12.41\:\mathrm{m}[/tex]. This is another side of the triangle that is formed by the cat, bird, and mouse.
The triangle that is formed by the cat, bird, and mouse has shares an angle of [tex]125^{\circ}[/tex] with the base of the auxiliary pyramid. The other angles, however, are not shared.
Since we have two sides and the angle between these two sides, we can use the Law of Cosines to find the other side (the distance between the mouse and bird). The Law of Cosines is given by:
[tex]m^2=k^2+l^2-2kl\cos M[/tex], where [tex]m[/tex] is the distance between the bird and the mouse and the other variables are defined above.
Plugging in values, we get:
[tex]m^2=16.99^2+12.41^2-2\cdot16.99\cdot12.41\cdot\cos 125^{\circ}[/tex]
Solving, we get:
[tex]m\approx \fbox{$26.16\:\mathrm{m}$}[/tex].
Plzzzzzz help
Graph y-2= 2/3(x+4)
Answer: y= 2/3x + 14/3
Step-by-step explanation:
Ella buys 5 packs of muffins. She uses a coupon and saves $3 off the total. Which expression represents her total cost?
A. 5m -3
B. 5 -3m
C.5+3
D. 5m + 3
Answer:
The answer is A. 5m - 3
Step-by-step explanation:
Ella bought 5 packs of muffins but since we don't know how many muffins are in each pack, we put a variable in place so it's 5m. Since she saved $3 off the total, that means you would subtract 3 from the total, so the problem would be 5m - 3
Need help pleaseee help
5.7 inches is the correct answer
Evaluate the expression when a= 1/4 and b = 6.
16a2 – 4b=
Step-by-step explanation:
HERE,
a=[tex]\bold{\dfrac{1}{4} }[/tex]
b=6
so,
According to the question,
[tex]\bold{16a^2-4b }[/tex]
[tex]\bold{16\times(\dfrac{1}{4})^2-4\times 6 }[/tex]
[tex]\bold{ 16\times \dfrac{1}{16}-24 }[/tex]
[tex]\bold{\cancel{16}\times \dfrac{1}{\cancel{16}}-24 }[/tex]
[tex]\bold{1-24 }[/tex]
[tex]\bold{ -23 }[/tex]
The table shows a proportional relationship between the milliliters (\text{mL})(mL)left parenthesis, start text, m, L, end text, right parenthesis of red paint and milliliters of yellow paint to make a certain shade of orange. Paint mixtures Red (\text{mL})(mL)left parenthesis, start text, m, L, end text, right parenthesis Yellow (\text{mL})(mL)left parenthesis, start text, m, L, end text, right parenthesis 10.510.510, point, 5 282828 7.57.57, point, 5 202020 999 242424 ? ? A row of values is missing in the table. Which of the following mixtures of paint could be used as the missing values in the table? Choose 2 answers: Choose 2 answers: (Choice A) A 1.25\,\text{mL}1.25mL1, point, 25, start text, m, L, end text red and 5\,\text{mL}5mL5, start text, m, L, end text yellow (Choice B) B 1.5\,\text{mL}1.5mL1, point, 5, start text, m, L, end text red and 4\,\text{mL}4mL4, start text, m, L, end text yellow (Choice C) C 8\,\text{mL}8mL8, start text, m, L, end text red and 3\,\text{mL}3mL3, start text, m, L, end text yellow (Choice D) D 7\,\text{mL}7mL7, start text, m, L, end text red and 16\,\text{mL}16mL16, start text, m, L, end text yellow (Choice E) E 4.5\,\text{mL}4.5mL4, point, 5, start text, m, L, end text red and 12\,\text{mL}12mL12, start text, m, L, end text yellow
this is for khan academy
Answer:
it is B and E
Step-by-step explanation:
The table shows a proportional relationship between the milliliters (\text{mL})(mL)left parenthesis, start text, m, L, end text, right parenthesis of red paint and milliliters of yellow paint to make a certain shade of orange.
Paint mixtures
Red (\text{mL})(mL)left parenthesis, start text, m, L, end text, right parenthesis Yellow (\text{mL})(mL)left parenthesis, start text, m, L, end text, right parenthesis
10.510.510, point, 5 282828
7.57.57, point, 5 202020
999 242424
? ?
A row of values is missing in the table.
Which of the following mixtures of paint could be used as the missing values in the table?
Choose 2 answers:
Choose 2 answers:
(Choice A)
A
1.25\,\text{mL}1.25mL1, point, 25, start text, m, L, end text red and 5\,\text{mL}5mL5, start text, m, L, end text yellow
(Choice B)
B
1.5\,\text{mL}1.5mL1, point, 5, start text, m, L, end text red and 4\,\text{mL}4mL4, start text, m, L, end text yellow
(Choice C)
C
8\,\text{mL}8mL8, start text, m, L, end text red and 3\,\text{mL}3mL3, start text, m, L, end text yellow
(Choice D)
D
7\,\text{mL}7mL7, start text, m, L, end text red and 16\,\text{mL}16mL16, start text, m, L, end text yellow
(Choice E)
E
4.5\,\text{mL}4.5mL4, point, 5, start text, m, L, end text red and 12\,\text{mL}12mL12, start text, m, L, end text yellow
PLEASE help, i’ll give brainliest
Step-by-step explanation: I think it is 18 tell me if I am wrong
Paulo sells 249 medium pumpkins for $8 each and 84 large pumpkins for $14 each. How much money does Paulo collect selling the medium and the large pumpkins
Answer: $3,168
Step-by-step explanation:
Paulo sells 249 medium pumpkins for $8 each. The money Paulo makes from this is:
= 249 * 8
= $1,992
Paulo also sells 84 large pumpkins for $14. The money made is:
= $1,176
Total from selling both is:
= 1,992 + 1,176
= $3,168
Which graph has a y-intercept of -1/2?
Answer:
C.
Step-by-step explanation:
Y-intercept basically means where on the graph does the line "cut" through the y-axis (the vertical line). In the graphs, there is only one line which cuts through the y-axis at -1/2, which is C. .
Question 6 Multiple Choice Worth 5 points)
(04.07A LC)
Which equation does the graph below represent?
20
16
12
8
4
1
2
3
5
-5 -4 -3 -2 -1 0
4
-8
-12
-16
-20
y = a + x
y = 1 X
y = 4 + x
y = 4x
Answer:
The equation of the graph is;
y = 4·x
Step-by-step explanation:
The coordinates of two points, (x₁, y₁), and (x₂, y₂) respectively on the straight line graph are;
(-3, 12), and (2, 8)
The slope, m, of the straight line graph is given as follows;
[tex]Slope, \, m =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Therefore, by substitution of the values, we have;
[tex]Slope, \, m =\dfrac{8-(-12)}{2-(-3)} = \dfrac{8 + 12}{2 + 3} =\dfrac{20}{5} = 4[/tex]
The equation of the graph in point slope form is therefore;
(y - 8) = 4×(x - 2)
y = 4·x - 8 + 8 = 4·x
y = 4·x.