Point B is on line segment \overline{AC}
AC
. Given AB=4x-6,AB=4x−6, AC=2x+10,AC=2x+10, and BC=4,BC=4, determine the numerical length of \overline{AC}.
AC
Answers
Answer:
AC= 22
Step-by-step explanation:
see photo
The numerical length of AC is 22 units.
What is a line segment?In geometry, a line segment is a part of a line that is bounded by two distinct end points,and contains every point on the line that is between its endpoints.
Now it is given that,
Point B is on line segment AC
AB = 4x-6
AC = 2x+10
BC = 4
now since Point B is on line segment AC, therefore
AC = AB + AC
⇒ 2x + 10 = 4x - 6 + 4
⇒ 2x + 10 = 4x - 2
⇒ 2x = 12
⇒ x = 6
Put the value of x in AC, we get
AC = 2(6) + 10
or, AC = 12 + 10
or, AC = 22 units.
Hence, the numerical length of AC is 22 units.
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Related Questions
The daily production cost, C, for x units is modeled by the equation:
C = 200 – 7x + 0.345x2
Answers
Domain is the set of x-values (i.e. units produced) that are feasible. This is all the positive integer values + 0, in case that you only consider that can produce whole units.
Range is the set of possible results for c(x), i.e. possible costs.
You can derive this from the fact that c(x) is a parabole and you can draw it, for which you can find the vertex of the parabola, the roots, the y-intercept, the shape (it open upwards given that the cofficient of x^2 is positive). Also limit the costs to be positive.
You can substitute some values for x to help you, for example:
x y
0 200
1 200 -7 +0.345 = 193.345
2 200 - 14 + .345 (4) = 187.38
3 200 - 21 + .345(9) = 182.105
4 200 - 28 + .345(16) = 177.52
5 200 - 35 + 0.345(25) = 173.625
6 200 - 42 + 0.345(36) = 170.42
10 200 - 70 + 0.345(100) =164.5
11 200 - 77 + 0.345(121) = 164.745
The functions does not have real roots, then the costs never decrease to 0.
The function starts at c(x) = 200, decreases until the vertex, (x =10, c=164.5) and starts to increase.
Then the range goes to 164.5 to infinity, limited to the solutcion for x = positive integers.
Can somebody help?
Answers
Answer:
a its the first one
Step-by-step explanation:
because i did the math and i have dont this question before
Answer:
Angles 1 and 2 are supplementary
Step-by-step explanation:
WILL GIVE BRANLIEST
5(x + 2) over
2x - 14
x = 10
Answers
Answer:
10 .......................
=5(10+2)/2(10)-14
=60/6
=10
mark ice bear Brainliest
he inverse of F(C) = 9 5 C + 32 is C(F) = F −
Answers
Answer:
C(F) = 5/9 F − 160/9
Step-by-step explanation:
[tex]f(c) = \frac{5}{9} (c-32)[/tex] will be the required inverse function of f(c).
The given function is:
[tex]f(c) = \frac{9}{5} c +32[/tex]
What is the inverse of a function?If there is a function f(x), then a function g(x) is called the inverse of the function if f(x) is a bijective function and the domain of f(x) should be equal to the range of g(x) while the range of f(x) should be equal to the domain of g(x).
[tex]f(c) = \frac{9}{5} c +32[/tex],
let us suppose [tex]y= \frac{9}{5} c +32[/tex]
[tex]y-32 = \frac{9}{5} c[/tex]
[tex]c = \frac{5}{9} (y-32)[/tex]
[tex]c = \frac{5}{9} (f(c)-32)[/tex]
In order to get the inverse function, interchange c and f(c),
[tex]f(c) = \frac{5}{9} (c-32)[/tex]
Therefore, [tex]f(c) = \frac{5}{9} (c-32)[/tex] will be the required inverse function of f(c).
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what is the pattern in the sequence 0, 1, 1, 2, 3, 5, 8, 13, 21,
Answers
I need help with #4 please! Thank you!
Answers
Answer:
$54.25
Step-by-step explanation:64-9.75=54.75
Answer:64-9.75=54.25
Step-by-step explanation:
Find g(f(x)) when f(x) = 3x2 + x - 8, and g(x) = 4x + 5.
Answers
Answer: 12x^3 + 19x^2 -27x -40
Step-by-step explanation:
Finding f(x) times g(x) is multiply the two polynomials
(4x+5)(3x^2 + 1x -8) Apply the distributive property twice to solve
4x ( 3x^2 + 1x -8)
12x^3 + 4x^2 - 32x
5(3x^2 + 1x -8)
15x^2 + 5x - 40
12x^3 + 4x^2 - 32x + 15x^2 + 5x -40 now combine like terms
12x^3 + 19x^2 -27x -40
The function g(f(x)) will be written as g(f(x)) = 12x² + 4x - 27.
What is a function?A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.
The functions are given below.
f(x) = 3x² + x - 8 and g(x) = 4x + 5
The function g(f(x)) is written as,
g(f(x)) = 4(3x² + x - 8) + 5
Simplify the function, then we have
g(f(x)) = 4(3x² + x - 8) + 5
g(f(x)) = 12x² + 4x - 32 + 5
g(f(x)) = 12x² + 4x - 27
The capability g(f(x)) will be composed as g(f(x)) = 12x² + 4x - 27.
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What are the x- and y-coordinates of point C, which partitions the directed line segment from A to B into the ratio 5:8? Round to the nearest tenth, if necessary. (–2.2, –6.3) (–2.4, –6.4) (2.7, –0.7) (1.2, –4.7)
Answers
Answer:
(1.2, –4.7)
Step-by-step explanation:
Since in the question it is mentioned that on the plane of coordinate, a line is made from point A (7,-2) to point B(-8,-9)
Also, the ratio of A to B is 5:8
Based on this, the x and y coordinates at point C is
[tex]= [\frac{5\times (-8) + 8\times 7}{5 + 8} , \frac{5\times (-9) + 8\times -2}{5 + 8}]\\\\= [\frac{16}{3}, \frac{-61}{13}][/tex]
= (1.2, –4.7)
Hence, the x and y coordinates of point C is (1.2, –4.7)
Therefore the last option is correct
Answer:
D
Step-by-step explanation:
Could someone help me write and equation and the soultion Will chose brainlest
Answers
Answer:
Step-by-step explanation:
1. Equation: x + 50 = 180 degrees
Solution: x = 180 - 50
x = 130 degrees
2. Equation: x + 45 = 90 degrees
Solution: x = 90 - 45
x = 45 degrees
Answer:
the answer is choose not chose
Step-by-step explanation:
Cassie is baking cookies from scratch. Her recipe calls for 7/8 of a cup of sugar per batch. If she is baking Just 2/3 of abatch of cookies, how much sugar should she use?
Answers
Answer
A
Step-by-step explanation:
Given the Venn diagram below, which statement must be true?
Answers
the Venn diagram below, which statement must be true? If a number is an irrational number, it must also be a rational number. All integers are also whole numbers. All integers are also rational numbers. All natural numbers are irrational numbers.-by-step explanation:
1 Find the shaded area for each of the following shapes.
b
d
6.0m
28 mm
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40 mm
submitted response:
Answers
Answer:
the answer is 40
If 1/3 of a bag of fertilizer will cover 1/9 of a lawn, how many bags of fertilizer are needed for the entire lawn?
Answers
Answer:
3 bags
Step-by-step explanation:
9*(1/3 bag) = 3 bags
This question is confusing. Please help me!This question is confusing. Please help me!
Answers
Answer:
(C) 1/2
Step-by-step explanation:
s + 3s = 4st + 3t = 4tIf 4s is 2 more than 4t, then:
4s = 2+ 4t4s - 4t = 24s/4 - 4t/4 = 2/4s - t = 1/2(C) is the answer
Answer:
C
Step-by-step explanation:
We are given
t + 3t + 2 = s + 3s, that is
4t + 2 = 4s ( subtract 4t from both sides )
2 = 4s - 4t ← factor out 4 from each term
2 = 4(s - t) ← divide both sides by 4 , thus
s - t = [tex]\frac{2}{4}[/tex] = [tex]\frac{1}{2}[/tex] → C
Use the figure to write and solve an equation for x.
Answers
Answer:
x = 33
Step-by-step explanation:
If you have any questions about the way I solved it, don't hesitate to ask :)
In order to win a jar of candy you must guess how many pieces are in a jar within 30. If there are a total of 500 pieces of candy in the jar, what are the maximum and minimum amounts you could guess in order to win?
Answers
Answer:
530, 470.
Step-by-step explanation:
The maximum amount is 500 + 30 = 530.
The minimum amount is 500 - 30 = 470.
There are 4 circles and 20 triangles. What is the simplest ratio of circles to total shapes?
Answers
Answer:
1 :5Step-by-step explanation:
[tex]4\:circles\\20\:triangles\\\\Total\:shapes = 20+4 =24\\\\Circle : Total\:shape\\4 : 20\\\\Cross-cancel\:common\:factor ; 4\\4\div 4 =1\\20\div 4 =5\\\\= 1 :5[/tex]
Answer:
the answer is 1:5 bc if you do your time table connect it all it would be 1 to 5 sorry if you do this and it takes so long but hope this helped :)
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from Edison Elementary, how many were from Lincoln Elementary? Write and
solve an algebraic equation.
Answers
Answer:
s=(73-31)
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s= 42
Step-by-step explanation:
In order to get an exact count of the Lincoln Elementary students you just have to subtract 31 from 73 to get 42 students. Therefore we get s to represent the Lincoln students, so the equation would be 31+s=73.
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Answers
Answer:
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Step-by-step explanation:
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Answers
B) f(g(1))= -8 is your answer
Simplify: (use order of operations)
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*remember to explain your steps!
Answers
Answer:
8
Step-by-step explanation:
Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
1/1 1/4 1/9 what's the pattern
Answers
Answer:
adding a fifth
Step-by-step explanation:
Answer:
adding a fifth
Step-by-step explanation:
duhhhhhhhhhhhh
What is -S to the power of three minus 5st, S= -3 and T= -2.
Answers
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Clint and Jim rode their bicycles to Mill Park at an average of 8 mi/hr. It took then 1 hr longer to return home riding at an average of 7 mi/hr on a route that was 4 mi longer than their route. How long were they riding their bicycles? How man miles did they ride each way?
Answers
Answer:
Total time for which they ride = [tex]\bold{7\ hours}[/tex]
Number of miles they ride each way = 24 mi
Step-by-step explanation:
Average speed = 8 mi/hr
Let the Distance to Mill Park = [tex]D[/tex] mi
Let the time taken = [tex]t[/tex] hours
Formula:
[tex]Distance = Speed \times Time[/tex]
[tex]\Rightarrow D = 8t[/tex] ..... (1)
Now, when average speed = 7 mi/hr
Time taken is 1 hour more, i.e. Time = [tex]t+1[/tex] hours
Distance traveled is 4 mi more, i.e. [tex]D+4[/tex] mi
Using the Formula:
[tex]Distance = Speed \times Time[/tex]
[tex]D+4=7\times (t+1)[/tex]
From equation (1):
[tex]8t+4=7t+7\\\Rightarrow t=3\ hours[/tex]
From equation (1):
[tex]D = 8 \times 3 = 24\ mi[/tex]
Total time for which they ride = [tex]t+t+1 = \bold{7\ hours}[/tex]
Number of miles they ride each way = 24 mi
30 1 5 miles in 2 3 of an hour. What is the average speed, in miles per hour, of the car?
Answers
Answer:
131.086
Step-by-step explanation:
Point G is on line segment FH. Given FG = 4 and FH = 20, determine the
length GH
Answers
Answer:
16
Step-by-step explanation:
20-4=16
Simplify 3/5 • 3/4 .
Answers
Answer:
9/20 as a faction as a decimal 0.45
Step-by-step explanation:
Simplify 3/5 • 3/4
I hope this help
Simplify. 1/3(1−1/4)^2
Answers
Answer:
3
-
16
Step-by-step explanation:
The vertices of a triangle are listed below. E(-1, 2), F(-5, -1), G(-1, -4) What is the area of the triangle? A. 24 square units B. 12 square units C. 16 square units D. 6 square units
Answers
Answer:
B. 12 square units
Step-by-step explanation:
Answer: 12 square units
Step-by-step explanation: 1/2(6)(4)
A sample of gold weighs 100 grams and has a volume of 5.18 cm'. What is the density of gold?