Rihanna works in a coffee shop approximately nine miles from her apartment She bikes every day from her apartment to the coffee shop and then back to her apartment in the evening. However, on her way to work, she always stops halfway through to meet her best friend at a park. If the distance from apartment to the park is (5x +2) miles and the trip from the park to the coffee shop is (25x -8) miles long, then what is the value of x?
Answer:
x = 0.5
Step-by-step explanation:
When we add up the distance between the apartment and park with the distance between the park and the coffee shop, the total will equal nine miles.
Our equation will look like this:
(5x + 2) + (25x - 8) = 9
Add up the like terms
5x + 2 + 25x - 8 = 9
30x - 6 = 9
Add 6 to both sides
30x - 6 = 9
+ 6 + 6
30x = 15
Divide both sides by the coefficient, 30, to isolate the variable, x
30x/30 = 15/30
x = 15/30
Reduce
x = 1/2
Which two ratios represent quantities that are proportional? A 25/28 and 5/7 B 22/33 and 14/21 C 16/13 and 13/16 D 48/60 and 35/42
Answer:
Step-by-step explanation:
Derek walks to his best friends house at a rate of 1 block per minute, then turns around and walks home. The graph shows the distance Derek walks in the given amount of time. Write an equation for the graph.
In this question, we have to find an equation for two lines, depending on the input x, which creates the following piecewise function for this graph:
[tex]y = t, 0 \leq t \leq 10, -t + 20, 10 \leq t \leq 20[/tex]
Equation of a line:
The equation of a line is given by:
[tex]y = mt + b[/tex]
In which m is the slope and b is the y-intercept(value of y when x = 0).
This situation:
One line for x between 0 and 10;Another for x between 10 and 20;x between 0 and 10:
From here, we can take two points (t,y). I will take (0,0) and (10,10).
From point (0,0), we get that when [tex]x = 0, y = 0[/tex], which means that the y-intercept is [tex]b = 0[/tex], thus:
[tex]y_1 = mt[/tex]
To find the slope, when we have two points, it is given by change in y divided by change in t, so:
Change in t: 10 - 0 = 10
Change in y: 10 - 0 = 10
Slope: [tex]m = \frac{10}{10} = 1[/tex]
Thus, the first definition is:
[tex]y_1 = t, 0 \leq t < 10[/tex]
x between 10 and 20:
I will take the points (10,10) and (20,0).
First, we find the slope:
Change in t: 20 - 10 = 10
Change in y: 0 - 10 = -10
Slope: [tex]m = \frac{-10}{10} = -1[/tex]
Thus:
[tex]y_2 = -t + b[/tex]
For the intercept, we have point (20,0), which means that when [tex]t = 20, y = 0[/tex]. So
[tex]0 = -20 + b[/tex]
[tex]b = 20[/tex]
Thus, the second definition is:
[tex]y_2 = -t + 20, 10 \leq t \leq 20[/tex]
Write an equation for the graph.
We use the two definitions, that is:
[tex]y = y_1, 0 \leq t \leq 10, y_2, 10 \leq t \leq 20[/tex]
So
[tex]y = t, 0 \leq t \leq 10, -t + 20, 10 \leq t \leq 20[/tex]
A similar question can be found at https://brainly.com/question/16024991
On a separate piece of graph paper, graph y=-Ixl +3 then click on the graph until the correct one appears.
Answer:
That is the graph for y = -|x| + 3
Quadrilateral ABCD is similiar to quadrilateral EFGH. The lengths of the three longest sides in quadrilateral ABCD are 20 feet, 18 feet, and 14 feet long. If the two shortest sides of quadrilateral EFGH are 6 feet long and 5 feet long, how long is the 2nd longest side on quadrilateral EFGH?
A. 9.2 feet
B. 6.4 feet
C. 11.7 feet
D. 7.7 feet
Answer:
7.7 ft
Step-by-step explanation:
The third longest side is also the second shortest side.
The 14 ft side of quadrilateral ABCD corresponds to the 6 ft side of quadrilateral EFGH.
14/6 = 18/x
7/3 = 18/x
7x = 18 * 3
7x = 54
x = 54/7
x = 7.7
Answer: D. 7.7 feet
Answer:
Step-by-step explanation:
7.7
Based only on the information given in the diagram, which congruence
theorems or postulates could be given as reasons why ABC = DEF?
Check all that apply.
A. AAS
B. LA
С. НА
D. HL
E. SAS
F. SSS
Answer:
D, F, E
Step-by-step explanation:
As the legs and hypotenuse are equal, HL can be used. All the sides are equal so SSS can be used. Two pair of sides and 90 degrees are equal so SAS can be used
if you can travel 25 miles in 35 minutes, how long should it take you to travel 12 miles?
Answer:
It's going to take you 17 min to travel 12 miles
assuming you are going with mph
Step-by-step explanation:
I looked at a speed calculator and calculated that to go 25 miles in 35 min, you were going 42 mph. so I changed the imput to 12 miles and I got my answer.
solve it please. Just wanted to check my drawing skill but please solve it
Answer:
Step-by-step explanation:
I'm assuming that strange looking thing is a 9, so begin by multiplying both sides by that denominator to get:
[tex]x-9=\sqrt{x}+3[/tex] then subtract 3 from both sides to get
[tex]x-12=\sqrt{x}[/tex] and then square both sides to get
[tex]x^2-24x+144=x[/tex] and get everything on one side to solve for x by factoring:
[tex]x^2-25x+144=0[/tex] and factor that however it is you have learned to factor second-degree polynomials to get that
x = 16 and x = 9. We have to check for extraneous solutions because anytime you manipulate an equation, as we did by squaring both sides, you run the risk of these solutions that actually don't work when you plug them back into the original equation. Let's try 16 first:
[tex]\frac{16-9}{\sqrt{16}+3 }=1[/tex] If 16 is a solution, then this statement will be mathematically true.
[tex]\frac{7}{4+3}=1[/tex] and [tex]\frac{7}{7}=1[/tex] so 16 works. Let's try 9:
[tex]\frac{9-9}{\sqrt{9}+3 }=1[/tex] We know that one doesn't work, because 9-9 = 0 and 0 over anything = 0, not 1.
x = 16 is the only solution.
Answer:
x = 16
Step-by-step explanation:
[tex]\frac{x-9}{\sqrt{x}+3}=1[/tex]
Cross multiply,
x - 9 = √x + 3
Subtract 3 from both sides
x - 9 - 3 = √x
x - 12 = √x
Square both sides
(x -12)² = (√x)²
x² - 2 * x*12 + 12² = x
x² - 24x + 144 = x
x² - 24x + 144 - x = 0
x² - 25x + 144 = 0
Sum = -25
Product = 144
Factors = -9 , -16 {(-9)+(-16) = -25 & (-)*(-16) = 144}
x² - 25x + 144 = 0
x² - 16x - 9x + (-9)*(-16) = 0
x(x - 16) - 9(x - 16) = 0
(x - 16) (x - 9) = 0
x - 16 = 0 ; x - 9 = 0
x = 16 ; x = 9
x = 9 is an extraneous solution.
When we plug in 9 in the LHS of the equation,
LHS = [tex]\frac{9-9}{\sqrt{9}+3}[/tex]
[tex]= \frac{0}{3+3}[/tex]
= 0 ≠ RHS
So, x = 16 is the only solution
Which inequality is graphed on the coordinate plane shown?
A
y≥2x−6
B
y<2x−6
C
y>2x−6
D
y≤2x−6
Answer:
y ≤ 2x-6
Step-by-step explanation:
First find the equation of the line
The y intercept is -6
The slope is 2
y = 2x-6
The line graphed is solid so we know that there is an equal sign
We are graphing below the line
y ≤ 2x-6
in angle PQR, angleQ=70 angle R=45 then angleP=.....
Answer:
65
Step-by-step explanation:
Because its a triangle,
P + Q + R = 180
So,
P + 70 + 45 = 180
P + 115 = 180
Subtract 115 on both sides
P = 65
can someone help me please.
Answer:
A. 11.18
Step-by-step explanation:
(1, -2) will be x1 and y1.
(-9, 3) will be x2 and y2
The formula is
Distance = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Substitute in all the variables.
[tex]\sqrt{(-9-1)^2+(3-(-2))^2}[/tex]
Solve.
[tex]\sqrt{(-10)^2+5^2}[/tex]
[tex]\sqrt{100+25}[/tex]
[tex]5\sqrt{5}[/tex]
11.18033988.....
I hope this helps!
pls ❤ and mark brainliest pls!
What is the radius of one of the circles?
Answer:
[tex]\sqrt{3}[/tex]
Step-by-step explanation:
[tex]\frac{2\sqrt{3} }{2}=\sqrt{3}[/tex]
I hope this helps!
pls ❤ and give brainliest pls
Believe this is worth 7 pts please help!
Answer:
-12
Step-by-step explanation:
The average rate of change is found by
f(4) - f(2)
---------------
4-2
32 - 56
----------
4-2
-24
------
2
-12
Explain the steps necessary to convert a quadratic function in standard form to vertex form.
Answer:
A quadratic function in standard form is converted to vertex form by completing the square. The first two terms are used to create a perfect square trinomial after a zero pair is added. The zero pair is found by taking half of the x-term coefficient and squaring it. The original constant term and the negative value of the zero pair are then combined.
Step-by-step explanation:
Answer:
A quadratic function in standard form is converted to vertex form by completing the square. The first two terms are used to create a perfect square trinomial after a zero pair is added. The zero pair is found by taking half of the x-term coefficient and squaring it. The original constant term and the negative value of the zero pair are then combined.
Step-by-step explanation:
Sample response
In the last 6 days, Laura has
jogged 39 miles. At what rate did
Laura jog each day?
A: 234 miles per day
B: 33 miles per day
C: 6.5 miles per day
D: 0.15 miles per day
Answer:
6.5 miles per day
Step-by-step explanation:
Take the number of miles and divide by the number of days
39 miles/ 6 days
6.5 miles per day
Answer: 6.5 miles per day is correct
Step-by-step explanation:
You would just need to divide 39 by 6 to find the total miles per day. Therefore C: 6.5 is correct!
A boat goes 24 miles at a constant speed in 4 hours against a river current. It takes the boat 3 hours to go the same distance at the same speed with the current of the river. What is the speed of the boat and what is the current of the river?
Boat speed: Speed of Current:
Answer: 7 miles/h and 1 miles/h
Step-by-step explanation:
With the speed of current = x + 1
Against the speed of current = x - 1
ATQ
4(x-1) = 3(x+1)
4x-4 = 3x+3
4x - 3x = 3+4
x = 7
Speed of boat = 7miles/h
Current of river = 1 miles/h
please click thanks and mark brainliest if you like :)
Answer:
Hello,
Boat speed=7 miles/h
Current speed = 1 mile/h
Step-by-step explanation:
I am going to try to explain.
Let say V the speed of the boot (V like vitesse in french)
Let say v the speed of the current.
distance=24 miles
[tex]\left\{\begin{array}{ccc}V-v&=&\dfrac{24}{4} \\V+v&=&\dfrac{24}{3} \\\end{array}\right.\\\\\left\{\begin{array}{ccc}V-v&=&6 \\V+v&=&8 \\\end{array}\right.\\\\Adding\ the\ 2\ equations\ and\ substracting\ them \\\\\\\left\{\begin{array}{ccc}2V&=&14 \\2v&=&2 \\\end{array}\right.\\\\\\\left\{\begin{array}{ccc}V&=&7 \\v&=&1 \\\end{array}\right.\\\\[/tex]
Boat speed=7 miles/h
Current speed = 1 mile/h
Function: y= x^2 + 5x - 7
Vertex:
Solutions:
( , ) and
( , )
Answer:
Vertex is (-2.5, - 13.25) and x=(-5±sqrt(53))/2
Step-by-step explanation:
x^2+5x-7
x^2+5x+(2.5)^2-(2.5)^2-7
(x+2.5)^2-13.25. Vertex is (-2.5, - 13.25)
Solution of the functions are x=(-5±sqrt(53))/2
help me please !! find the domain and range of the function represented by the graph. determine wether the domain is discrete or continuous.
Answer:
Domain is the whole R and the range is R+. The domain is continuous
The table shows the steps for solving the given inequality 4-3(x-5)>6x-17
Step-by-step explanation:
(=) 1 ( x-5 ) > 6x-17
(=) x-5 > 6x -17
(=) -5x > -12
=> x < 12/5
please help! need the answers in order to move on:) will give brainliest to correct answer!
PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER!!
Answer:
Option C, 832 units²
Step-by-step explanation:
l = 8
w = 7
h = 24
Surface area = 2(wl+hl+hw)
=2×(7×8+24×8+24×7)
=832 units²
Answer: YO ITS ANSWER C)832 UNITS[tex]^{2}[/tex] !!!!
Problem
Write the slope of the line containing each pair of points.
1. (3,4) and (5,7)
Answer:
3/2
Step-by-step explanation:
the slope is the ratio y/x indicating how many units y changes, when x changes a certain amount of units.
so, when we have 2 points, we can look at the difference of the x and y coordinates. y difference / x difference is the slope.
going from (3, 4) to (5, 7) changes x by +2 and y by +3.
so, the slope of the line is 3/2
Prove that angle ADC is congruent to angle CBA
with solution!
Step-by-step explanation:
< i'll use this too represent angle
this is only presuming that this is a parallelogram and i also don't know what those numbers mean
< ACB = < CAD (alt <s of DA II CB) A
< ACD = < CAB (alt <s of DC II AB) A
AB is common S
therefore, ∆ADC is congruent to ∆CBA
if ∆ADC is congruent to ∆CBA
then < ADC = < CBA
Which of the following statements is false?
Answer:
c
Step-by-step explanation:
AB and CD are opposite sides of quadrilateral.
Change 300mm into cm
Answer:
30 centimeters
Step-by-step explanation:
true
Find the inverse of the given function. f(x) = 7x – 4
Hi there!
[tex]\large\boxed{y = \frac{x + 4}{7}}[/tex]
f(x) = 7x - 4
Rewrite f(x) with y:
y = 7x - 4
Swap the x and y variables:
x = 7y - 4
Solve for y:
x + 4 = 7y
y = (x + 4)/7
lilly just paid off a 400$ loan. she had to pay 60 in interest at a simple annual interest rate of 5%. how many years did lily have this loan?
•A.) 2
•B.) 3
•C.) 4.5
•D.) 5
Answer:
B.) 3
Step-by-step explanation:
Interest = prinipical ^ interest rate ^ year
60 = 400 ^ 5% ^ year
year = 60/400^5%
3years
Please help with number 8. And if you can explain how you got the answer please do and I’ll give brainliest
Answer:
X=7.9
Y=7.9
Step-by-step explanation:
We have that x=y
And form Pythagoras theorem we have
[tex]5 \sqrt{5} = \sqrt{x ^{2} + x ^{2} } \\ take \: the \: square \: of \: the \: two \: sides \\ 125 = 2x ^{2} \\ x {}^{2} = 62.5 \\ x = 7.9[/tex]
So x = y = 7.9
What is five ones and eight tenths greater than or less than or equal to fifty eight tenths
Answer:
definetely 2
Step-by-step explanation:
Answer:
Less than
Step-by-step explanation:
Five ones and eight tenths simplifies to 85 and fifty eight tenths simplifies to 580. So, here you can clearly see 85 < 580.
Hope this helps! :)
i need help again.lol
Answer:
[tex]13\ units[/tex]
Step-by-step explanation:
One is asked to find the distance between two points on a coordinate plane. The easiest way to do so is to use the distance formula, this formula is the following:
[tex]D=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2[/tex]
Where ([tex](x_1,y_1)[/tex]) and ([tex](x_2,y_2)[/tex]) are the points which one needs to find the distance between. In this case, these points are as follows:
[tex]k\ (-3,5)[/tex]
[tex]j\ (-8, -7)[/tex]
Substitute these points into the formula and solve for the distance between these points,
[tex]D=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2[/tex]
[tex]D=\sqrt{((-3)-(-8))^2+((5)-(-7))^2[/tex]
Simplify,
[tex]D=\sqrt{((-3)-(-8))^2+((5)-(-7))^2[/tex]
[tex]D=\sqrt{(-3+8)^2+(5+7)^2[/tex]
[tex]D=\sqrt{(5)^2+(12)^2[/tex]
[tex]D=\sqrt{25+144}[/tex]
[tex]D=\sqrt{169}[/tex]
[tex]D=13[/tex]
