For this case we can raise a rule of three:
[tex]\frac {3} {4}[/tex]cup of water ---------> [tex]\frac {1} {8}[/tex] pound of flour
x --------------------------------- > 1 pound of flour
Where:
x: Represents the amount of water that Tamie must use with 1 pound of flour.
[tex]x = \frac {1 * \frac {3} {4}} {\frac {1} {8}}\\x = \frac {\frac {3} {4}} {\frac {1} {8}}\\x = \frac {3 * 8} {4 * 1}\\x = \frac {24} {4}\\x = 6[/tex]
So, Tamie should use 6 cups of water
Answer:
6 cups of water
The parent function of the function g(x) = (x – h)2 + k is f(x) = x2. The vertex of the function g(x) is located at (9, –8). What are the values of h and k? g(x) = (x - ??)^2 + ? Will mark as the Brainliest.
Answer:
h = 9 and k = -8
Step-by-step explanation:
The skateboard that Jose wants costs $90. Jose has a coupon for 1 5 off the retail price. If Jose saves $18 a week, how long will it take to save enough to buy the skateboard?
What is the quotient? 7x^2-3x-9 divided by x-1
ANSWER[tex]q(x) = 7x + 4[/tex]
EXPLANATION
We want to find the quotient when [tex]7{x}^{2}-3x-9[/tex] is divided by x-1
We can quickly perform a synthetic division.
We write out the coefficients of the polynomial
[tex]7{x}^{2}-3x-9[/tex]
7 -3 -9
1| 7 4
7 4 -5
To obtain the top row.When we equate the divisor to zero, we get;[tex]x - 1 = 0[/tex][tex]\implies\:x=1[/tex]
This gives the 1 in the far left.The first two numbers in the last row are the coefficients of the quotient. The last number in the last row is the remainder.Therefore the quotient is [tex]7x + 4[/tex] and the remainder is -5
Remember this polynomial can be written as:
Dividend= Divisor * Quotient + Remainder
[tex]7x^2-3x-9=(x-1)(7x+4)-5[/tex]
Therefore Quotient=7x+4
HELP PLEASE!!!!!!!!!!!
Answer:
Part 1) [tex]y=-x^{2}[/tex] ---> Translated up by 1 units
Part 2) [tex]y=x^{2}+1[/tex] ---> Reflected across the x-axis
Part 3) [tex]y=-(x+1)^{2}-1[/tex] ---> Translated left by 1 unit
Part 4) [tex]y=-(x-1)^{2}-1[/tex] ----> Translated right by 1 unit
Part 5) [tex]y=-x^{2}-1[/tex] ----> Reflected across the y-axis
Part 6) [tex]y=-x^{2}-2[/tex] ----> Translated down by 1 unit
Step-by-step explanation:
we know that
The parent function is
[tex]y=-x^{2}-1[/tex] ----> this is a vertical parabola open downward with vertex at (0,-1)
Calculate each case
Part 1) Translated up by 1 unit
The rule of the translation is
(x,y) -----> (x,y+1)
so
(0,-1) ----> (0,-1+1)
(0,1) ----> (0,0) ----> the new vertex
The new function is equal to
[tex]y=-x^{2}[/tex]
Part 2) Reflected across the x-axis
The rule of the reflection is
(x,y) -----> (x,-y)
so
(0,-1) ----> (0,1) ----> the new vertex
The new function is equal to
[tex]y=x^{2}+1[/tex]
Part 3) Translated left by 1 unit
The rule of the translation is
(x,y) -----> (x-1,y)
so
(0,-1) ----> (0-1,-1)
(0,1) ----> (-1,-1) ----> the new vertex
The new function is equal to
[tex]y=-(x+1)^{2}-1[/tex]
Part 4) Translated right by 1 unit
The rule of the translation is
(x,y) -----> (x+1,y)
so
(0,-1) ----> (0+1,-1)
(0,1) ----> (1,-1) ----> the new vertex
The new function is equal to
[tex]y=-(x-1)^{2}-1[/tex]
Part 5) Reflected across the y-axis
The rule of the reflection is
(x,y) -----> (-x,y)
so
(0,-1) ----> (0,-1) ----> the new vertex
The new function is equal to
[tex]y=-x^{2}-1[/tex]
Part 6) Translated down by 1 unit
The rule of the translation is
(x,y) -----> (x,y-1)
so
(0,-1) ----> (0,-1-1)
(0,1) ----> (0,-2) ----> the new vertex
The new function is equal to
[tex]y=-x^{2}-2[/tex]
Which expression models the phrase “Wally mowed two more lawns than he mowed last week”?
n+2
n-2
2-n
2n
For this case we have to:
n: It's the variable that represents the number of lawns that mowed Wally last week.
If you tell us as a fact that this week Wally mowed two more lawns, then we have the following expression:
[tex]n + 2[/tex]
Finally, the expression is:
[tex]n + 2[/tex]
Answer:
[tex]n + 2[/tex]
Option A
Solve for x: √x-13=2 The solution is
Answer:
x=225
Step-by-step explanation:
\sqrt{x} + (-13 + 13) = 2 + 13
\sqrt{x} = 15
√x-13=2
x=225
If you meant to write...
[tex]\sqrt{x - 13} = 2[/tex]
Then the following is the answer:
To solve this you must get rid of the square root. The opposite of square root is square. You must square both sides since what you do to one side you must do to the other...
([tex]\sqrt{x-13} )^{2}[/tex] = [tex]2^{2}[/tex]
x - 13 = 4
Finish completely isolating x. To do this first add 13 to both sides (what you do on one side you must do to the other). Since 13 is being subtracted, addition (the opposite of subtraction) will cancel it out (make it zero) from the left side and bring it over to the right side.
x + (-13 + 13) = 4 + 13
x + 0 = 17
x = 17
If you meant to write...
[tex]\sqrt{x}[/tex] - 13 = 2
Then the following is the answer:
To isolate [tex]\sqrt{x}[/tex]. To do this first add 13 to both sides (what you do on one side you must do to the other). Since 13 is being subtracted, addition (the opposite of subtraction) will cancel it out (make it zero) from the left side and bring it over to the right side.
[tex]\sqrt{x}[/tex] + (-13 + 13) = 2 + 13
[tex]\sqrt{x}[/tex] = 15
To completely isolate x you must get rid of the square root. The opposite of square root is square. You must square both sides since what you do to one side you must do to the other...
[tex](\sqrt{x})^{2} = 15^{2}[/tex]
x = 225
Hope this helped!
~Just a girl in love with Shawn Mendes
what is the product of 6 1/2 x 3?
Answer:
19 1/2 or 19.5
Step-by-step explanation:
you could either:
break it up
6*3=18
1/2*3=1 1/2 = 1.5
18+1.5=
and get 19.5
or
just multiply it as decimal
6 1/2 = 6.5
6.5
x 3
1 5
+1 8 0
1 9 5
add decimal points = 19.5 (because 6.5 has 1 number to the right of the decimal pointor
multiply it as a improper fraction
6 1/2= 13/2
3= 3/1
13 x 3 = 39 =?
2 x 1 = 2 =?
?=19.5=39/2
*sorry if format or placement is not placed right because I did this in computer*
Can someone please help me with this???
The green square is 15 ft wide by 15 ft tall.
The area of one green square is 15 x 15 = 225 square feet.
There are 4 sides plus the base : 225 x 5 = 1125 square feet for the green part.
One triangle has a base 15 feet wide and a height of 9 feet.
The area for one triangle is 1/2 x 15 x 9 = 67.5 square feet.
There are 4 triangles: 67.5 x 4 = 270 square feet.
Total: 1125 + 270 = 1,395 square feet.
An electrician charges a service call fee of $60 plus $55 per hour. Another electrician charges a service call fee of $20 plus $65 per hour. Set up and solve an equation to determine the number of hours, h, for which the cost would be the same for hiring both electricians.
Final answer:
By setting up an equation where the total costs for both electricians are equal and solving for h, we find that the number of hours for which the costs are the same is 4 hours.
Explanation:
To determine the number of hours, h, for which the cost would be the same for hiring both electricians, we set up an equation where both cost expressions are equal. The equation, which expresses the total cost for each electrician's services, is:
First electrician: Cost = $60 + $55h
Second electrician: Cost = $20 + $65h
We now equate the two expressions and solve for h:
$60 + $55h = $20 + $65h
$55h - $65h = $20 - $60
-$10h = -$40
Divide each side by -10: h = 4
Thus, the number of hours for which the costs are the same is 4 hours.
Final answer:
The number of hours for which both electricians would charge the same is 4 hours. We find this by setting up an equation based on their fees and hourly rates, solving this equation yields the result of 4 hours.
Explanation:
To determine the number of hours, h, for which the cost would be the same for hiring both electricians, we can set up an equation based on their charges. The first electrician charges a service call fee of $60 and $55 per hour. Therefore, the cost for the first electrician, C1, can be expressed as:
C1 = 60 + 55h
The second electrician charges a service call fee of $20 plus $65 per hour, which means the cost for the second electrician, C2, is:
C2 = 20 + 65h
To find when the costs are the same (C1 = C2), we set the two expressions equal to each other:
60 + 55h = 20 + 65h
Now we solve for h:
60 + 55h = 20 + 65h
55h - 65h = 20 - 60
-10h = -40
h = 4
The costs are the same when the electricians work for 4 hours.
Which graph shows the solution to the equation log2 (3x – 1) = 2?
Answer:
Option 2
Step-by-step explanation:
Given : Equation [tex]\log_2(3x-1)=2[/tex]
To find : Which graph shows the solution to the equation?
Solution :
First we distribute the equation into two equation.
Let Equation 1 be [tex]y=\log_2(3x-1)[/tex]
and Equation 2 be [tex]y=2[/tex]
Plot these two equation,
The equation 1 with purple line and equation 2 with orange line.
As these equation are equal there intersection point is given by,
Intersection point (1.667,2)
From the given graph only option 2 gives the correxct intersection point.
So, option 2 is correct.
Refer the attached figures below.
Answer:
graph 2
Step-by-step explanation:
edg '23
Need help with a math question
Answer:
Equation = x²+(y+3)²=5²
Step-by-step explanation:
The question is on equation of a circle in a center-radius form
The general equation is
(x-h)² + (y-k)² = r² where the center is at (h,k) and the radius is r
Given
point P=(3,1) and point Q= (-3,-7)
Find the diameter PQ
[tex]d=\sqrt{(X2-X1)^2 + (Y2-Y1)^2\\[/tex]
[tex]d= \sqrt{(-7-1)^2 + (-3-3)^2}[/tex]
[tex]d=\sqrt{-8^2 + -6^2}[/tex]
[tex]d= \sqrt{64+36} = 10[/tex]
d= 10 units hence radius is 10/2 =5 units
Find the center of the circle
center =[ (x₁+x₂)/2, (y₁+y₂)/2]
center=[ (3+-3)/2 , (1+-7)/2]
center= [ 0/2 ,-6/2]
center= [0,-3]
Equation = x²+(y+3)²=5²
Answer:
5^2
Step-by-step explanation:
BRAINLIEST!!!! writ the following equation in standard form.state wether the graph of the equation is a parabola,circle,ellipse or hyperbola.
x^2+4y^2+2x-24y+33=0
Answer:
x² + 4y²+ 2x - 24y + 33 = 0
= (x+1)² + 4(y-3)² - 1 - 36 + 33 = 0
= (x+1)² + 4(y-3)² = 4
= (x + 1)²/2² + (y - 3)²/1² = 1
This is an Ellipse: C(-1,3)
The Standard Form of an Equation of an Ellipse is : (x - h)²/a²/ (y - k)²/b² = 1
where Pt(h,k) is the center. (a variable positioned to correspond with major axis)
a and b are the respective vertices distances from center
and√a² - b²are the foci distances from center: a > b
Your friend gives you a simple regression fit for predicting house prices from square feet. the estimated intercept is –44850 and the estimated slope is 280.76. you believe that your housing market behaves very similarly, but houses are measured in square meters. to make predictions for inputs in square meters, what slope must you use? (there are 0.092903 square meters in 1 square foot).
Answer:
3022.08 . . . dollars per square meter
Step-by-step explanation:
The slope is multiplied by the factor that changes units:
(280.76 dollars/ft²)×(1 ft²)/(.092303 m²) ≈ 3022.08 dollars/m²
To make predictions for house prices in square meters, you would have to multiply the given slope of 280.76 by the conversion factor of 1/0.092903, which will give an estimated slope of approximately 3017.9
Explanation:The problem here is related to the conversion of units from square feet to square meters. Your friend gives you a simple regression fit for predicting house prices from square feet with an estimated intercept of -44850 and the estimated slope is 280.76.
Given that there are 0.092903 square meters in 1 square foot, a square foot equals to 1/0.092903 square meters. When you are making a prediction based on square meters rather than square feet, you need to consider this factor. This means the new slope would be calculated by multiplying the old slope with this conversion factor as:
Slope for prediction in square meters = Old slope * (1/0.092903) = 280.76 / 0.092903 = 3017.9 approximately.
Learn more about Units Conversion here:https://brainly.com/question/32030244
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Three friends share a pizza Sam ate 0.25 of the pizza mark ate 0.3 of the pizza and Jill ate 0.35 of the pizza can you write the amount each child ate as a fraction? What fraction of the pizza is left?
Step-by-step explanation :
Sam : 0.25 = [tex]\frac{25}{100}[/tex] = [tex]\frac{1}{4}[/tex] (Answer)
Mark : 0.30 = [tex]\frac{30}{100}[/tex] = [tex]\frac{3}{10}[/tex] (Answer)
Jill : 0.35 = [tex]\frac{35}{100}[/tex] = [tex]\frac{7}{20}[/tex] (Answer)
Total amount of pizza eaten = 0.25 + 0.30 + 0.35 = 0.9
Amount of pizza left = 1.0 - 0.9 = 0.1 = [tex]\frac{10}{100}[/tex] = [tex]\frac{1}{10}[/tex] (Answer)
What is the approximate volume of a can that is 5 inches tall and has a 2.5 inch diameter?
Answer:
24.5 cubic inches
Step-by-step explanation:
The formula for the volume of a cylinder is ...
V = πr²h
A can with a diameter of 2.5 inches has a radius of 1.25 inches. Filling in the given values, the volume is ...
V = π(1.25²)(5) = 7.8125π ≈ 24.54 . . . . cubic inches
The approximate volume is 24.5 cubic inches.
The volume of a cylinder is 24.54 inches³
What is Volume of cylinder?The volume of a cylinder is equal to the product of the area of the circular base and the height of the cylinder. The volume of a cylinder is measured in cubic units.
We know that the volume of cylinder is
V = πr²h
Given that:
diameter = 2.5 inches
radius = 1.25 inches.
Height= 5 inches
V = π(1.25²)(5)
= 7.8125π
≈ 24.54 inches³
Hence, the volume of cylinder is 24.54 inches³
Learn more about Volume of cylinder here:
https://brainly.com/question/16134180
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a
10ft tree casts a 14 ft shadow .if a building cast a 280ft tall shadow how tall is the building
Suppose that G(X) = F(x+ 9). Which statement best compares the graph of
G(x) with the graph of f(x)?
Answer: Option D
Step-by-step explanation:
By definition if we have a function F (x) and perform a transformation of the form
[tex]G (x) = F (x + c)[/tex]
Then it is true that:
If c is negative the graph of G(x) will be equal to the graph of F(x) displaced horizontally c units to the right
If c is positive, the graph of G(x) will be equal to the graph of F(x) displaced horizontally c units to the left.
Note that in this case the transformation is:
[tex]G (x) = F (x + 9)[/tex]
Then [tex]c = 9[/tex] and [tex]c> 0[/tex]
Therefore the graph of G(x) will be equal to the graph of F(x) displaced horizontally 9 units to the left
The answer is the option D.
ANSWER
D. The graph of G(x) is the graph of F(x) shifted 9 units to the left.
EXPLANATION
The given functions are F(x) and G(x).
The function, G(x) is obtain by translating or shifting the graph of F(x).
This translation is of the form.
[tex]G(x) = F(x+ 9)[/tex]
The '+9' within the parenthesis tells us that the shift is 9 units to the left.
Remember that for horizontal shift:
+ means a shift to the left.
The correct answer is D.
Need some help, please. What do I plot? I attempted to figure the questions out many times, but I've come to no clear conclusion, whoops.
Answer:
vertex is (4,-4) and another point is (6,0) or you could use (2,0) or many other options :)
Step-by-step explanation:
The cool thing about this question your quadratic is in factored form so your x-intercepts are easy to figure out, they are 2 and 6.
So you can plot (6,0) and (2,0).
The vertex will lie half between x=2 and x=6... so it lays at (6+2)/2=4
We just have to find the y-coordinate for when x=4.
Plug in 4 gives you (4-2)(4-6)=(2)(-2)=-4.
So the vertex is at (4,-4).
RST is circumscribed about circle A
Answer:
ST, RS, and RT
Step-by-step explanation:
A line is tangent to a circle if it intersects it at only one point.
ST, RS, and RT are all tangent to circle A.
AP intersects the circle at two points when extended.
XT intersects the circle at two points as well.
Answer:
A. [tex]\overline{ST}[/tex]
B. [tex]\overline{RS}[/tex]
D. [tex]\overline{RT}[/tex]
Step-by-step explanation:
We have been given that triangle RST is circumscribed about circle A. We are asked to choose that tangent of our given circle fro the provided choices.
We know that tangent of circle is a straight line that touches the circle exactly at one point. This point is known as point of tangency.
Upon looking at our given diagram, we can see that line segment RX touches circle A exactly at one point that is X. Line segment SX touches circle A exactly at one point that is X, therefore, line segment RS is tangent to our given circle.
Similarly, line segments SQ and TQ touch circle A exactly at one point that is Q, therefore, line segment ST is tangent to our given circle.
We can see that line segments RP and TP touch circle A exactly at one point that is P, therefore, line segment ST is tangent to our given circle.
AP is radius of circle, therefore, AP is not a tangent for our given circle.
If we draw a line joining points XT, it will intersect circle at two points, therefore, XT is not a tangent for our given circle.
[30 points] provide an explanation/show your work! Positive integer a has two different prime factors p and q (p<q) such that a = p*q. positive integer b is greater than a and the quotient a^2/b is an integer. How many possible values of b are there?
Circle the correct answer:
a) 2
b) 3
c) 4
d) 5
e) more than 5.
Thank you! I will give Brainliest to the best answer. :)
[tex]\dfrac{a^2}{b}[/tex] is an integer, where [tex]a,b\in\mathbb{Z_+}[/tex], therefore [tex]b|a^2[/tex] and [tex]b\leq a^2[/tex]
[tex]a=pq[/tex] therefore [tex]a^2=p^2q^2[/tex]
[tex]b>a\wedge b\leq a^2[/tex], therefore [tex]pq<b\leq p^2q^2[/tex]
So,
[tex]b\in\{p^2q,pq^2,p^2q^2\} \\|\{p^2q,pq^2,p^2q^2\}|=3 \implies \text{B}[/tex]
What is the value of x?
Answer:
B
Step-by-step explanation:the other corner is 75 so that leaves the other corner to be 50. 75+55+50=180
Hello There!
Other corner to be 50. 75+55+50=180
need help fasttt
GIve p(6,6) and q=(-5,-3) find the magnitude of 2p+3q
A.2 sqr3
B. 3 sqr2
its not C
D.14
Answer:a or b
Step-by-step explanation:
Answer:
B. 3 sqrt 2
Step-by-step explanation:
got oit right on edge
Simplify cosθ + cosθtan2θ.
1
cscθ
secθ
sin2θ
Answer:
csc0
Step-by-step explanation:
Answer:
it is c
Step-by-step explanation:
1. Maryann is tracking the change in her vertical jump over 6 months. Use the table to write a linear function that models her jump distance.
Month Vertical Jump in inches
0 16
2 17
4 18
6 19
A.f of x equals one half times x plus 16
B.f of x equals one half times x plus 19
C.f(x) = 2x + 16
D.f(x) = 2x + 19
2. What is the equation of a line that contains the points (5, 0) and (5, −2)?
A.x = 5
B.x = 0
C.y = 0
D.y = 5
3. Choose the equation that represents a line that passes through points (−1, 2) and (3, 1).
A.4x − y = −6
B.x + 4y = 7
C.x − 4y = −9
D.4x + y = 2
4Jewels has $6.75 to ride the ferry around Connecticut. It will cost her $0.45 every time she rides. Identify the dependent variable and independent variable in this scenario.
A. The number of rides is the independent variable, and the total cost is the dependent variable.
B. The total cost is the independent variable, and the number of rides is the dependent variable.
C. The number of rides and the total cost are both independent variables.
D. The number of rides and the total cost are both dependent variables.
Answer:
Part 1) Option A. f of x equals one half times x plus 16
Part 2) Option A. x = 5
Part 3) Option C. x − 4y = −9
Part 4) Option A. The number of rides is the independent variable, and the total cost is the dependent variable.
Step-by-step explanation:
Part 1)
Let
x -----> the number of months
y ----> vertical jump in inches
step 1
Find the slope
we have the points
(0,16) and (2,17)
[tex]m=(17-16)/(2-0)=\frac{1}{2}[/tex]
The equation of the line in slope intercept form is
[tex]y=mx+b[/tex]
we have
[tex]m=\frac{1}{2}[/tex]
[tex]b=16[/tex] -----> the point (0,16) is the y-intercept
substitute
[tex]y=\frac{1}{2}x+16[/tex]
convert to function notation
f(x)=y
[tex]f(x)=\frac{1}{2}x+16[/tex]
Part 2) What is the equation of a line that contains the points (5, 0) and (5, −2)?
step 1
Find the slope
we have the points
(5, 0) and (5, −2)
[tex]m=(-2-0)/(5-5)=\frac{-2}{0}[/tex]
the slope is undefined
This is a vertical line (parallel to the y-axis)
therefore
The equation is
x=5
Part 3) Choose the equation that represents a line that passes through points (−1, 2) and (3, 1)
step 1
Find the slope
we have the points
(−1, 2) and (3, 1)
[tex]m=(1-2)/(3+1)=-\frac{1}{4}[/tex]
step 2
Find the equation of the line into point slope form
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=-\frac{1}{4}[/tex]
[tex]point\ (3, 1)[/tex]
substitute
[tex]y-1=-\frac{1}{4}(x-5)[/tex]
Convert to standard form
Multiply by 4 both sides to remove the fraction
[tex]4y-4=-(x-5)[/tex]
[tex]4y-4=-x+5[/tex]
[tex]x-4y=-4-5[/tex]
[tex]x-4y=-9[/tex]
Part 4) Jewels has $6.75 to ride the ferry around Connecticut. It will cost her $0.45 every time she rides. Identify the dependent variable and independent variable in this scenario
we know that
The independent variable is the variable whose change isn’t affected by any other variable (An example the age and time)
The dependent variable it’s what changes as a result of the changes to the independent variable (An example of a dependent variable is how tall you are at different ages. The dependent variable (height) depends on the independent variable (age))
Let
x ----> the number of rides
y ----> the total cost in dollars
In this problem
The independent variable or input is the number of rides
The dependent variable or output is the total cost
The correct linear function for Maryann's vertical jump is f(x) = ½x + 16. The equation of the line containing points (5, 0) and (5, −2) is x = 5. For the line through points (−1, 2) and (3, 1), the correct equation is 4x − y = −6, and in Jewels' scenario, the number of ferry rides is the independent variable, and the total cost is the dependent variable.
To write a linear function that models Maryann's vertical jump over 6 months, we need to determine the slope (rate of change) and the y-intercept (starting value). Given the increments of 1 inch over every 2 months, we can calculate the slope as 1 inch per 2 months or 0.5 (one half) inches per month. The starting value when the time (month) is 0 is 16 inches. Hence, the linear function is f(x) = ½x + 16, which corresponds to option A.The equation of a line that contains the points (5, 0) and (5, −2) is vertical because both points have the same x-coordinate. A vertical line's equation is x = some constant value, which in this case is x = 5, corresponding to option A.To find the equation that represents a line passing through points (−1, 2) and (3, 1), we can use the two-point formula or slope-intercept form, but by checking the given options, we see that option A fits the points: 4x − y = −6.In the scenario of Jewels riding the ferry, the independent variable is the number of rides she takes, and the dependent variable is the total cost, which depends on the number of rides taken. This corresponds to option A.Dorothy has a mysterious $?$ button on her calculator. When she types in an integer and hits the $?$ button, if the input is odd, the calculator outputs $1$ less than triple the input. if the input is even but not divisible by $4$, the calculator outputs $1$ more than half the number. if the input is divisible by $4$, the calculator outputs one-fourth of the input. Dorothy typed in an integer, hit the $?$ button, and saw an output of $13$. What are all possible integers Dorothy may have input?
Answer:
{52}
Step-by-step explanation:
The calculator function appears to be ...
f(x) = {3x -1, x odd; x/2 +1, x not divisible by 4; x/4, x divisible by 4}
The inverse of the first function is ...
x = 3y -1
(x+1)/3 = y . . . . (y must be odd)
For x = 13, this is 14/3, which is not an integer.
__
The inverse of the second function is ...
x = y/2+1
2(x-1) = y . . . . (y must not be divisible by 4)
For x = 13, this is 2·12 = 24, which is divisible by 4, so 24 is not the input value.
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The inverse of the third function is ...
x = y/4
4x = y . . . . (y must be, and is, divisible by 4)
For x = 13, this is 4·13 = 52.
The only possible input value for an output of 13 is 52.
consider the line y=7x-3 fine the equation that pass through -5,6 of a perpendicular
Answer:
[tex]y=-\frac{1}{7}x+\frac{37}{7}[/tex]
Step-by-step explanation:
Your equation is in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept. Your line has a slope of 7. In order to find the line perpendicular to this line, we have to take the opposite reciprocal of the slope. The perpendicular slope to m = 7 is m = -1/7. Now we go through x = -5 and y = 6 to find the new equation.
6 = -1/7(-5) + b gives us
6 = 5/7 + b and
b = 37/7
Therefore, the equation of the line perpendicular to your original line is
[tex]y = -\frac{1}{7}x + \frac{37}{7}[/tex]
Select the correct answer. Ryan opens a bank account with $50. Each month he deposits an amount that doubles his savings. Ryan gets $2 from the bank each month as an incentive for maintaining this savings pattern. Which recursive function represents the amount in Ryan's account in any month?
Answer:
next = 2 x now + 2, starting at 50
Step-by-step explanation:
A national study found that a car's value decreases by 15 percent annually. If the car was purchased for 66,000. How much will the car be worth in 10 years?
Answer:
$12,993.71
Step-by-step explanation:
The formula we want for this is exponential decay which is
[tex]A(t)=a(1-r)^t[/tex]
where A(t) is the value of the car after the depreciation, a is the initial value of the car, r is the interest rate at which it depreciates in decimal form, and t is the time in years. We have everything we need to fill in to solve for A(t):
[tex]A(t)=66,000(1-.15)^{10}[/tex]
We will do some simplifying first:
[tex]A(t)=66,000(.85)^{10}[/tex]
First raise .85 to the 10th power to get
A(t) = 66,000(.1968744043)
and then multiply to get
A(t) = $12,993.71
Answer:
$12,993.71
Step-by-step explanation:
First raise .85 to the 10th power to get
A(t) = 66,000(.1968744043)
and then multiply to get
A(t) = $12,993.71
Identify the reflection of the figure with vertices H(17,34), I(−5,10), and J(28,−14) across the line y=x.
Answer:
B
Step-by-step explanation:
Under a reflection in y = x
a point (x, y) → (y, x)
Given
H(17, 34 ) → H'(34, 17)
I(- 5, 10) → I'(10, - 5)
J(28, - 14) → J'(- 14, 28)
B represents the image coordinates of H, I, J
For the given figure with vertices H(17,34), I(-5,10), and J(28,-14) across the line y=x, the reflection will appear at H(34,17), I(10,-5), J(28,-14). This is because at y=x the reflection will have the coordinates with interchanged values.
Reflection at y=x:Across y=x, the reflection will have interchanged coordinates.
that is (x, y) → (y, x)
For the given vertices across the line y=x,
H(17,34) → H'(34,17)
I(-5,10) → I'(10,-5)
J(28,-14) → J'(-14,28)
So, option (2) is correct that is H(34,17), I(10,-5), J(-14,28) which undergoes reflection across y=x.
Learn more about reflection here:
https://brainly.com/question/26642069
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3x - 8y = 29
3x + y = -2
Question 4 options:
(0.5, -3.5)
(0, -2)
(0.75, -2.25)
(0, -3.75)
Answer:
The best estimate for the solution is the point (0.5,-3.5)
Step-by-step explanation:
we have
-----> equation A
-----> equation B
we know that
The solution of the system of equations is the intersection point both graphs
Using a graphing tool
The intersection point is
see the attached figure
therefore
The solution of the system of equations is the point
The best estimate for the solution is the point