Suppose f(x)=2 x-5 and g(x)=|-3 x-1| Find the value. g(2)-f(0)
g(2)- f(0) = 12
Given:
f(x)=2 x- 5
g(x)=|-3 x-1|
To find g(2), substitute x=2 in g(x).
g(x)=|-3 x-1|
g(2)=|-3 (2)-1|
=|-6-1|
=|-7|
g(2) = 7
To find f(0), substitute x=0 in f(x).
f(x)=2 x- 5
f(0)=2(0)- 5
f(0) = -5
Now, g(2)-f(0) =7-(-5)
=7+5
=12
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Solve each equation using the Quadratic Formula. x(x-5)=-4 .
Answer:
x
2
−4x−5=0
All equations of the form ax
2
+bx+c=0 can be solved using the quadratic formula:
2a
−b±
b
2
−4ac
. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.
x
2
−4x−5=0
This equation is in standard form: ax
2
+bx+c=0. Substitute 1 for a, −4 for b, and −5 for c in the quadratic formula,
2a
−b±
b
2
−4ac
.
x=
2
−(−4)±
(−4)
2
−4(−5)
Square −4.
x=
2
−(−4)±
16−4(−5)
Multiply −4 times −5.
x=
2
−(−4)±
16+20
Add 16 to 20.
x=
2
−(−4)±
36
Take the square root of 36.
x=
2
−(−4)±6
The opposite of −4 is 4.
x=
2
4±6
Now solve the equation x=
2
4±6
when ± is plus. Add 4 to 6.
x=
2
10
Divide 10 by 2.
x=5
Now solve the equation x=
2
4±6
when ± is minus. Subtract 6 from 4.
x=
2
−2
Divide −2 by 2.
x=−1
The equation is now solved.
x=5
x=−1
c. Will bought a tennis racket on sale for $24.60. If the sale was 20% off,
how much was the tennis racket originally?
Answer:
$30.75
Step-by-step explanation:
Since the sale was 20% off, the tennis racket is 80% of its original price.
[tex].8p = 24.60[/tex]
[tex]p = 30.75[/tex]
7x+ 6y=2
- 28x- 24y = -8
Answer:
x=2/7 - 6y/7
Step-by- explanation:
Evaluate A² for A = -3.
-6
9
6
-9
Answer:
b) 9
Step-by-step explanation:
Given that,
→ A = -3
Then the value of A² will be,
→ (-3)² = 9
Hence, option (b) is correct.
Add. 7/6 + 1/3
i've been asking a lot of fraction questions lol :D
Answer:
Hope this helps :)
All of these are the answers, the final answer is the simplified one, and the explanation is below.
9/6 (improper fraction)
1 3/6 (mixed number)
1 1/2 (simplified)
Step-by-step explanation:
1. Common denominators which is 6.
7/6 + 1/3
1/3 × 2/2 = 2/6
2. Add the numerators since they already have common denominators.
7/6 + 2/6 = 9/6
3. Change into mixed number and simplify if needed.
9/6 = 1 3/6 = 1 1/2
WHAT are the angle relationships formed when a third line
intersects two parallel lines?
the angles are the same as their pair
the pairs are
1 and 5
2 and 6
4 and 8
3 and 7
What is the slope of the line that passes through the points (- 2, 6) and (4, - 2) ?
Answer:
-4/3
Step-by-step explanation:
[tex] \frac{6 - ( - 2)}{ - 2 - 4} = - \frac{8}{6} = - \frac{4}{3} [/tex]
54 yards to mm bridge method
Solve each system by elimination.
x + y = 12 , x - y = 2
By elimination, the solution of the system of equations, x + y = 12 and x - y = 2, is (7 , 5).
A system of equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy all the equations.
There are three methods that can be used to solve system of equations.
1. Elimination
2. Substitution
3. Graphing
Using the elimination method, given two equations in x and y, a variable should be eliminated by adding/subtracting the two equations.
Adding the two equations will eliminate the variable y.
x + y = 12 (equation 1)
x - y = 2 (equation 2)
2x + 0y = 14
x = 7
Substitute the value of x to any of the two equation and solve for y.
x + y = 12 (equation 1)
7 + y = 12
y = 12 - 7
y = 5
Hence, the solution of the system of equations is (7 , 5).
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Evaluate each expression for x=5 .
(5/3) (3x-6)-(6-4 x)
The value of the given expression (5/3)(3x - 6) - (6 - 4x) at x = 5 is 29.
According to the given question.
We have an expression (5/3)(3x - 6) - (6 - 4x).
So, the value of the given expression (5/3)(3x - 6) - (6 - 4x) at x = 5 is given by
(5/3)(3x - 6) - (6 - 4x)
= 5x - 10 - (6 - 4x) (by distributive rule)
= 5x - 10 - 6 + 4x
= 9x - 16
= 9(5) - 16 (at x = 5)
= 29
Hence, the value of the given expression (5/3)(3x - 6) - (6 - 4x) at x = 5 is 29.
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A television programme begins at 6:10pm the programme ends at 7:05 how long will the television last
Answer:
55 minutes
Step-by-step explanation:
→ Work out long it will take to get to 7:00
7:00 - 6:10 = 50 minutes
→ Work out how much extra time after 7:00
7:05 - 7:00 = 5 minutes
→ Add the 2 answers together
50 + 5 = 55 minutes
Can someone please solve these? Identify the segment bisect of XY. Then find XY
The length of the line segment XY which was bisected at point M is;
1) 32
2) 6
How to solve division of line segments?
1) From the given line segments, it is clear that XM is congruent to YM since M bisects XY. Thus;
XM = YM and XM + YM = XY
We are given that;
XM = 3x + 1
YM = 8x - 24
Thus;
3x + 1 = 8x - 24
8x - 3x = 1 + 24
5x = 25
x = 25/5
x = 5
Thus;
XM = 3(5) + 1 = 16
YM = 8(5) - 24 = 16
XY = 16 + 16 = 32
2) From the given line segments, it is clear that XM is congruent to YM since M bisects XY. Thus;
XM = YM and XM + YM = XY
We are given that;
XM = 5x + 8
YM = 9x + 12
Thus;
5x + 8 = 9x + 12
9x - 5x = 8 - 12
4x = -4
x = -1
XM = 5(-1) + 8 = 3
YM = 9(-1) + 12 = 3
XY = 6
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express the function f(x)=1+|2x-5| in piecewise form without using absolute values
The function f(x)=1+|2x-5| in piecewise form without using absolute values will be f₁ = 4, f₂ = 2 and a = 5/2.
Given that,
f(x) = 1 + |2x - 5|
And,
f(x) = {f₁ x < a
{f₂ x ≥ a
Now,
We have,
f(x) = 1 + |2x - 5|
And,
By definition of absolute value,
|x| = {x x ≥ 0
{-x x < 0
And,
Given the absolute value,
|2x - 5|
Solve for x,
i.e.
2x - 5 = 0
We get,
x = 5/2 = 2.5
i.e.
a = 5/2
i.e.
For all values greater than x = 5/2, 2x - 5 is positive,
And,
For all values less than x = 5/2, 2x - 5 is negative.
So,
|x| = {x x ≥ 5/2
{-x x < 5/2
i.e.
|2x - 5| = {2x - 5 x ≥ 5/2
{-(2x - 5) x < 5/2
Now,
f(1) = 1 + |2(1) - 5|
We get,
f₁ = 4
And,
f(2) = 1 + |2(2) - 5|
We get,
f₂ = 2
Hence we can say that the function f(x)=1+|2x-5| in piecewise form without using absolute values will be f₁ = 4, f₂ = 2 and a = 5/2.
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Simplify. *
-2√- 45 - 3√125
A.-13i√5
B.-17i√5
C. -17√5
D.-21i√5
According to the question, the given expression can be simplified with the help of factors.
Given expression = [tex]-2\sqrt{-45}-3\sqrt{125}[/tex]
Do the factors of 45 as well as 125 and take the common things out from the square root:
Required expression = [tex]-2(3)\sqrt{-5}-3(5)\sqrt{-5}= -21i\sqrt{5}[/tex]
In the theory of complex number, [tex]i^{2} = -1[/tex] is already defined.
Hence, the answer for the given expression is [tex]-21i\sqrt{5}[/tex].
What is simplification?
Simplification is the process to make the expression as simple for the calculation. That means, to calculate the solution of a complex expression.
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Find the quotient of the quantity 32 times ten raised to the negative twenty second power end quantity divided by the quantity 8 times ten raised to the negative twenty second power end quantity.. write the final answer in scientific notation. 4 x 10−44 4 x 1044 4 x 1022 4 x 100
The final answer in scientific notation is 4 × 10⁰.
Firstly writing both dividend and divisor in scientific notation.
Dividend = 32 × 10⁻²²
Divisor = 8 × 10⁻²²
Now performing division to find the quotient.
Quotient = Dividend ÷ Divisor
Quotient = 32 × 10⁻²² ÷ 8 × 10⁻²²
As per the known rule of exponents, aˣ ÷ aⁿ = aˣ⁻ⁿ
Quotient = (32 ÷ 8) × 10⁻²² ⁻ ⁽⁻²²⁾
Dividing the base numbers
Quotient = 4 × 10⁻²²⁺²²
Performing subtraction on exponents
Quotient = 4 × 10⁰
Also, as per the known fact, a⁰ = 1. So, the final answer is 4 and in scientific notation the final answer is 4 × 10⁰.
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Solve each inequality. Check your solution. (x/3) + 5 ≥ 1/6
The inequality given by (x/3) + 5 ≥ 1/6 has the solution x ≥ -29/2 or [-29/2 , +∞).
Inequality refers to the relationship between two non-equal expressions. It can be denoted by > for greater than, < for less than, >/= for greater than and equal to, and </= for less than and equal to.
To solve an inequality is to find the values of x such that when we substitute that number for x we have a true statement.
Given the inequality (x/3) + 5 ≥ 1/6, subtract 5 from both sides.
(x/3) + 5 - 5 ≥ 1/6 - 5
x/3 ≥ -29/6
Multiply both sides by 3.
3(x/3) ≥ 3(-29/6)
x ≥ -29/2
To check, let x = -29/2
x = -29/2 ≥ -29/2
Substitute this value to the inequality.
(x/3) + 5 ≥ 1/6
(-29/2)/3 + 5 ≥ 1/6
1/6 ≥ 1/6
let x = -14,
x = -14 ≥ -29/2
Substitute this value to the inequality.
(x/3) + 5 ≥ 1/6
-14/3 + 5 ≥ 1/6
1/3 ≥ 1/6
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Find the distance between the points (1, 6) and (9, 0).
Answer:
You have to use the distance formula
d=√(x2-x1)^2 + (y2-y1)^2
replace the points and get 10
Engineers evaluate the efficiency of the memory and speed of a computer. What does evaluate mean in mathematics?
To evaluate anything is to determine its monetary value. Finding all of the values of a variable or collection of variables necessary to make a statement true is what it means to solve something.
What does evaluate mean in mathematics?It is to figure out or compute a formula, function, or relation's value.Middle school math involves evaluating solely arithmetic expressions.It is like to evaluate the equation with a specific value of x or y or any variable.As opposed to solution, which essentially involves going backwards and undoing all of the changes made to the input.Evaluating the value of an algebraic expression when a specified integer is used to replace a variable is known as evaluating the expression. We use the given number to replace the expression's variable before applying the order of operations to simplify the expression.To evaluate anything is to determine its monetary value. Finding all of the values of a variable or collection of variables necessary to make a statement true is what it means to solve something.To learn more about evaluate, refer to:
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Step up an inequality for this situation below. Define your variable, but do not solve.
Mr. Bass charges his music students $25 per lesson plus a recital fee of $50. How many lessons can a student take if they pay no more than $175?
The inequality that models the situation is:
$50 + $25*x < $175
Where x is the number of lessons that the student can take.
How to write the inequality?
We know that Mr. Bass charges $25 per class plus a fixed fee of $50.
Then if a student takes x classes, the cost is given by the expression:
$50 + $25*x
And we know that this needs to be smaller than $175, then we can write the inequality:
$50 + $25*x < $175
Now we can solve this for x:
$25*x < $175 - $50
$25*x < $125
x < $125/$25
x < 5
So the student needs to take less than 5 classes.
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Which floating-point literal correctly represents the scientific notation value: 2.3 x 10^7?
The floating-point literal that correctly represents the scientific notation value: 2.3 x 10^7 will be A. 2.3e^7.
What is scientific notation?It should be noted that scientific notation simply means. way that's used to express numbers that are either too large or too small to be written in decimal form.
Therefore, it should be noted that the floating-point literal that correctly represents the scientific notation value: 2.3 x 10^7 will be:
= 2.3 × 20^7
= 2.3 × e^7
= 2.3e7
The correct option is A.
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Which floating-point literal correctly represents the scientific notation value: 2.3 x 10^7?
a. 2.3e^7
b. 2.3 × 10e^7
c. 2.3e × 10^7
d. 2.3 × e^7
PLEASE HELP ME
The frequency distribution shows the widths, in inches, of available cell phones at a technology store.
What is the mean of the frequency distribution? Round answers to tenths place, if answer is a whole number
than put a zero in the tenths place so it will be counted correct.
For given data set, The value of mean is 6.02.
What is mean?The sum of a set of numbers divided by the total number of numbers in the set is known as the arithmetic mean or arithmetic average in mathematics and statistics.
The formula to calculate mean is = sum of all observations / total number of observations
x = 4 5 6 7 8
f = 12 1 8 18 4 ∑f = 43
fx = 48 5 48 126 32 ∑fx = 259
The formula of mean = ∑fx / ∑f
= 6.02
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m/KLM = 135º.
Find the value of y and m/MLN
L
M
K
47°
(16y)⁰
N
Stuart’s bank account had a balance of $-51.41 last month. This month he won a cash prize of $77.63 for winning a competition. How much money does Stuart have at the end of this month , if there are no other transactions?
Answer:
$26.22
Step-by-step explanation:
Stuart's bank account balance (before) : $ - 51.41
Profit/Loss : + $ 77.63
Therefore:
- $ 5 1 . 4 1
+
$ 7 7 . 6 3
_____________
$ 2 6 . 2 2
Therefore, Stuart has $26.22 in his bank account at the end of the month assuming there are no other other transactions.
Please mark me as brainliest!!!
-BALL
Help me
In solving this question
Answer:
She could have planted 250 seeds on Wednesday
State whether the sentence is true or false. If false, replace the underlined word or number to make a true sentence.
Line t is called the transversal for lines p and q .
The statement "Line t is called the transversal for lines p and q" is true
Given,
The statement "Line t is called the transversal for lines p and q"
In the figure we can see that line t cut two parallel line p and q
So the line t is transversal for lines p and q
So the given statement "Line t is called the transversal for lines p and q" is true
Hence, the The statement "Line t is called the transversal for lines p and q" is true
The complete question is:
State whether the sentence is true or false. If false, replace the underlined word or number to make a true sentence.
Line t is called the transversal for lines p and q .
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Jai's family took a road trip to Mount Rushmore. Jai fell asleep after they had
travelled 259 miles. If the total length of the trip was 740 miles, what
percentage of the total trip had they travelled when Jai fell asleep?
The total percentage they travelled when Jai fell asleep is 35%.
In mathematics, a percentage is a ratio or value that is expressed as a fraction of 100. The Latin term "per centum," which means "by a hundred," is the source of the English word "percent." The sign "%" stands for percentage. We apply the percentage method to determine the portion of a whole expressed in terms of 100. Use the percentage formula to convert a number to a fraction of 100.
The total length of trip was 740 miles.
Jai travelled before they fell asleep = 259 miles
Therefore the percentage of total trip travelled before Jai fell asleep =
= [tex]\frac{259}{740}\times100[/tex]
= 35 %
So by 35% of the total trip, they travelled when Jai fell asleep.
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Point b is on line segment \overline{ac} ac . given ab=2x+10,ab=2x+10, bc=x,bc=x, and ac=5x,ac=5x, determine the numerical length of \overline{ac}. ac
The numerical length of line segment AC is 25.
A line segment refers to a straight line connecting two points.
If point B is on line segment AC, then point B divides the line segment into segments AB and BC.
AB + BC = AC
Given that AB =2x + 10, BC = x, and AC = 5x, substitute these expressions in the equation AB + BC = AC.
AB + BC = AC
2x + 10 + x = 5x
3x + 10 = 5x
5x - 3x = 10
2x = 10
x = 5
To determine the numerical length of line segment AC, substitute the value of x in the equation AC = 5x.
AC = 5x
AC = 5(5)
AC = 25
Hence, the numerical length of line segment AC is 25.
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Find two numbers with a sum of 65. Twice the lesser number is 10 more than greater number.
Answer:
a=25
b=40
Step-by-step explanation:
We can get two equations from these statements
1.a+b=65
2.a<b
therefore 2a=10+b
and 2a-10=b
substitute into original equation
a+(2a-10)=65
3a=75
a=25
b=65-25
=40
HELP HELP HELP HELP HELP 4/9×4/5=
Answer: 16/45
Step-by-step explanation:
[tex]\displaystyle\\\frac{4}{9}*\frac{4}{5}= \\\\\frac{4*4}{9*5}=\\\\\frac{16}{45}[/tex]
Find the value of x to the nearest tenth. tan x° = 90 89.9 89.6 89.4
Answer:
89.4
Step-by-step explanation:
89.9,89.6 are more than five so we'll be using the lowest number as the nearest thenth
