19. The function f(x) = 27x – 67.5 has an
* -intercept at (a,0). The function g(x) is
defined in the table below and has an
x-intercept at (b,0). How much greater is the
value of b than the value of a?
Answer:
First we have the function f(x) = 27*x - 67.5
It has an x-intercept at (a, 0)
This means that:
f(a) = 0 = 27*a - 67.5
Solving the above equation we can find the value of a.
0 = 27*a - 67.5
67.5 = 27*a
67.5/27 = a = 2.5
Now let's look at equation g(x).
It is a linear equation, remember that a linear equation can be written as:
g(x) = y = A*x + B
Where:
A is the slope, and B is the y-intercept.
If the line passes through the points (x₁, y₁) and (x₂. y₂), the slope can be written as:
A = (y₂ - y₁)/(x₂ - x₁)
In this case we can select any two points from the table, for example, I will use the second and third points:
(1, 39) and (2, 32.5)
Then the slope is:
A = (32.5 - 39)/(2 - 1) = -6.5/1 = -6.5
Then the equation is something like:
g(x) = y = -6.5*x + B
B is the y-intercept, to find this value, we can use one of the two points we used before.
For example, (1, 39) means that g(1) = 39
Then:
g(1) = -6.5*1 + B = 39
= B = 39 + 6.5 = 45.5
Then the equation for g(x) is:
g(x) = -6.5*x + 45.5
Now, we know that g(x) has an x-intercept at (b, 0)
this means that:
g(b) = 0 = -6.5*b + 45.5
6.5*b = 45.5
b = 45.5/6.5 = 7
Then the difference between b and a is:
b - a = 7 - 2.5 = 4.5
b is equal to a plus 4.5
And the ratio is:
b/a = 7/2.5 = 2.8
b is 2,8 times larger than a.
What is the value of y in the solution to the system of equations?
3x + 4y = 30
3x + 5y = 33
Answer:
y = 3
Step-by-step explanation:
3x + 5y = 33 ---------------(I)
3x + 4y = 30 ----------------(II) {subtract equation (II) from (I)}
- - = -
1y = 3
y = 3
Jackson earns $17 per hour tutoring students in math. Which equation and solution shows how many hours he has to work to earn $476?
Answer:
476 ÷ 17 = 28
Step-by-step explanation:
$17 an hour is multiplication. so, just do the opposite.
476 ÷ 17.
~R3V0
plsss help lollll :)))
Answer:
Step-by-step explanation:
V = (4/3)πr3 so put it on a calculator (4/3)3.14 (or Pi) times radius which is r to the 3rd power so your answer would be 33.51 but make sure
can someone help me?
Answer: She has 6 nickles and 9 dimes.
Step-by-step explanation:
Let n be the # of nickles. Let d be the # of dimes.
n+d=15
0.05n + 0.1d =1.2
5n+10d=120
5(15-d)+10d=120
75-5d+10d=120
5d=45
d=9
n=15-d
n=15-9
n=6
Write an equivalent expression using Distributive property.
28 + 42
( How did you solve)
Answer:
the answer is 7(4 +6)
Step-by-step explanation:
24 + 42
7(4 + 6)
You deposit $100 in your bank account. The account earns 2% simple interest in 5 years. How much interest did you earn?
A spinner with two equal sectors is spun 5 times.
What is the number of possible outcomes?
Answer: 32
Explanation: 2^5
Answer:
There are 32 outcomes that are possible
Step-by-step explanation:
PLEASE HELP MEEEEEEE!!!!
The median is the middle number in a sorted, ascending or descending.
I believe that the answer is A.
I hope this helps!
Thank you to anyone who answers .
Answer:
B: 33 3/4
Step-by-step explanation:
Whoever gives an answer first gets Brainliest
Answer:
answer to what?
Step-by-step explanation:
Answer:
Thanks mate n.n
Have a good one !
what is the mean of the data? 24,31,12,38,12,15
Answer:
Hello Love! Answer: 22
Step-by-step explanation:
The mean is just an average of all the numbers added up then divided by how many numbers there are so I add up those numbers and I get 132 now I will just divide that by 6 sense there are 6 numbers and I get 22!
The dimensions of a rectangular piece of paper are 10.5 inches and 10 inches Ben Folds a piece of paper along its diagonal find the length of the diagonal in inches
Answer:
14.5
Step-by-step explanation:
Isla wants to solve the equation 2.5x – 1.75 = 5(7 – 0.5x).
She uses a graphing program to graph the equations y = 2.5x – 1.75 and y = 5(7 – 0.5x).
Use the graph to find the solution of 2.5x – 1.75 = 5(7 – 0.5x).
Answer:
7.35
Step-by-step explanation:
If you solve the equation
2.5– 1.75 = 5(7 – 0.5)
Then...
x=7.35
Answer:
7.35
Step-by-step explanation:
Girrls and boys plsss i need help like frl:)
D- Most babysit because it pays more per-hour.
The reason this is the correct answer is because the question said which is NOT a valid response. This one is not because it didnt tell you how much they get paid per-hour so its incorrect.
Hope this helps!
Have a great day!
- Hailey
The building on Daughtery road are even numbered from 12-136. How many buildings have an address with at least one 4?
Answer:
Total 22 buildings have at least one 4 in their address
Step-by-step explanation:
Number between 12 to 136 are as given below -
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
Total numbers having at least 1 four are
14
24
34
40
41
42
43
44
45
46
47
48
49
54
64
74
84
94
104
114
124
134
Total 22 buildings have at least one 4 in their address
X - 2y = -3
2x + y = -1
Answer:
y = 1
x = -1
Step-by-step explanation:
x - 2y = -3, then x = 2y - 3
2x + y = -1
substitute for x:
2(2y - 3) + y = -1
4y - 6 + y = -1
5y = 5
y = 1
x = 2 - 3 = -1
Answer:
it can only be simp[lified
so it will be
(x+2x)+(y+2y)=-3-1
3x+3y=-4
cannot be solved further
Step-by-step explanation:
There is a line that includes the point (4, 1) and has a slope of 1/4. what is its equation in
slope-intercept form?
Answer:
y=1/4x
Step-by-step explanation:
y=mx+b
m=1/4
so, y=1/4x+b
Now, look at our line's equation so far: . b is what we want, the 1/4 is already set and x and y are just two "free variables" sitting there. We can plug anything we want in for x and y here, but we want the equation for the line that specfically passes through the the point (4,1).
So, why not plug in for x the number 4 and for y the number 1? This will allow us to solve for b for the particular line that passes through the point you gave!.
(4,1). y=mx+b or 1=1/4 × 4+b, or solving for b: b=1-(1/4)(4). b=0.
y=1/4x+0
below are two parallel lines with a third line intersecting them.
Answer:
x = 136
Step-by-step explanation:
x and 44 are supplementary angles which mean they add up to 180:
x + 44 = 180
x = 180 - 44
x = 136
The diameter of a circle is 14 ft.
What is the area of the circle in terms of π?
Answer:
49π ft²
Step-by-step explanation:
[tex]A=\pi r^2[/tex] where r is the radius of the circle
To find the radius, divide the diameter by 2:
14 ft ÷ 2 = 7 ft
Plug the radius 7 ft into the equation
[tex]A=\pi (7)^2\\A=49\pi[/tex]
Therefore, the area of the circle in terms of pi is 49π ft².
I hope this helps!
Answer:
49π
Step-by-step explanation:
Diameter=14
Radius=14/2=7
Area=πr squared
Area=7 squared π
Area=49π
please help! will give brainliest. review the graph of function h(x). what is lim x-2 h(x), if it exists
Answer:
the answer is 0 or a
Help me with this, will give brainlist to best explained asnwer
Answer:
I'd say the mode, 21, is the best response. It appears the most frequently and it's also the median.
Explanation:
Mean: 115 / 5 = 23
Median: 19, 21, 21, 26, 28
Mode: 19, 21, 21, 26, 28
Claim shape a is a rectangle please help
Answer:
ummkmmmm
Step-by-step explanation:
Answer:
No, the shape is not a rectangle.
Step-by-step explanation:
A rectangle is a 2-dimensional shape with two sets of parallel sides and four right angles. Shape a has both sets of parallel sides, but the corners of the figure are not right angles. It is a rhombus. So, the answer is no, the shape is not a rectangle.
Good luck ^^
what is the correct form of the partial fraction decomposition for: start fraction 35-27x over 4xsquared+28x endfraction
Answer: The answer is A
Step-by-step explanation:
A/4x+B/x+7
The correct form of the partial fraction decomposition for the given expression is Option A
What is Partial Fraction Decomposition ?Partial Fraction Decomposition is the method of simplifying rational expressions.
The expression given is
[tex]\rm \dfrac{ 35-27x} { 4x^2+28x}[/tex]
Applying Partial Decomposition
[tex]\rm \rm \dfrac{ 35-27x} { 4x(x+7)}\\\\\\\dfrac{35}{4x(x+7)} - \dfrac{27x}{4x(x+7)}\\\\\\Taking \;A = 35/ x+7\\\\Taking \; B = -27/4\\\\[/tex]
It can be written as
[tex]\rm \dfrac{A}{4x} + \dfrac{B}{x+7}[/tex]
Therefore Option A is the answer.
To know more about Partial Factor Decomposition
https://brainly.com/question/2516522
#SPJ2
do the step by step process thank u soooooo much
Answer:
Surface area: 199.27 cm
Volume: 129.8 cm³
Step-by-step explanation:
Find the surface area of the rectangular prism.
5 in.
7 in
4 in.
Answer:
A=166
that's all can calculate
The new Vigo the Vampire Hunter novel is 520 pages. Skyler has read 145 pages in 5 hours. Ramon has read 124 pages in 4 hours.
About how long will it take Ramon to read the entire novel if he continues to read at his current rate? ROUND TO THE NEAREST WHOLE NUMBER.
Answer:
17 hours
Step-by-step explanation:
so first since there are 520 pages we divide it by 124 pages we get 4.19
4.19x4 = 16.77
Rounded is 17
Plz help me giving branliest. I need help with both
Answer:
The first one is 30
The second one is 20
Step-by-step explanation:
a record impact books at a rate of 48 books every 2 minutes how many minutes do the worker need to unpack 168 books?
Answer:
7minutes
Step-by-step explanation:
so if 48 books are sorted in 120 seconds what about 168 books if you cross multiply you will get 420 seconds which converted to minutes is 7
the greatest common factor of 9w2 and 10w4.
Answer:
9 and 2: 1
10 and 4: 2
Step-by-step explanation:
9: 1, 3, 9
2: 1, 2
Answer: 1
10: 1, 2, 5, 10
4: 1, 2, 4
Answer: 2