If f(x)=3x-1+4 and g(x)=4x-7 what is (f-g)(x)
Answer: [tex](f-g)(x)=-x+10[/tex]
Step-by-step explanation:
Given the function f(x):
[tex]f(x)=3x-1+4[/tex]
And given the function g(x):
[tex]g(x)=4x-7[/tex]
You must subtract both functions is order to find [tex](f-g)(x)[/tex].
You need to remember the multiplication of signs:
[tex](+)(+)=+\\(-)(-)=+\\(+)(-)=-[/tex]
Then:
[tex](f-g)(x)=3x-1+4-(4x-7)[/tex]
Now, you must distribute the negative sign:
[tex](f-g)(x)=3x-1+4-4x+7[/tex]
And finally, add the like terms. Then you get that [tex](f-g)(x)[/tex] is:
[tex](f-g)(x)=-x+10[/tex]
What is the positive square root of 0.81
Enter your answer in the box.
[tex] \sqrt{0.81} = (0.9)[/tex]
Answer:
the correct answer is .9
.9 times .9 is .81
blackpink dun dunna dun dun dun dunna
What is the midpoint of the segment shown below A. 10,-4 B 5,-4 C.5,-2 D.10-2
Answer:
C. (5, -2)
Step-by-step explanation:
Midpoint:
x = (x1+x2)/2 = (16-6)/2 = 10/2 = 5
y = (y1+y2)/2 = (5 - 9)/2 = -4/2 = -2
Answer
Midpoint (5, -2)
The midpoint of the graphed line segment is (5, -2)
The correct option is C) (5, -2).
What is the midpoint of the line segment?The midpoint formula is expressed as;
Midpoint = ( ( x₁+x₂ )/2, ( y₁+y₂ )/2 )
From the graph:
Point 1 (16, 5)
x₁ = 16
y₁ = 5
Point 2 (-6,-9)
x₂ = -6
y₂ = -9
Plug the coordinates into the above formula and solve for the midpoint:
Midpoint = ( ( x₁+x₂ )/2, ( y₁+y₂ )/2 )
Midpoint = ( ( 16+(-6) )/2, ( 5+(-9) )/2 )
Midpoint = ( ( 16 - 6 )/2, ( 5 - 9 )/2 )
Midpoint = ( 10/2, -4/2 )
Midpoint = ( 5, -2 )
Therefore, the midpoint is (5, -2).
Option C) (5, -2) is the correct answer.
Learn more about the midpoint formula here: https://brainly.com/question/28577846
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F(x)=x^2+3x+2 is shifted 2 units right the reuslt is g(x) what is g(x)
Answer:
[tex]g(x)=x^2-x[/tex]
Step-by-step explanation:
Given function is [tex]F\left(x\right)=x^2+3x+2[/tex].
Function [tex]F\left(x\right)=x^2+3x+2[/tex] is shifted 2 units right and gives result to a new function g(x).
Now we need to find about what is the equation of g(x).
We know that f(x-h) indicates right shift by "h" units.
So to get 2 units shift, replace x by (x-2) into given function
[tex]g(x)=F\left(x-2\right)[/tex]
[tex]g(x)=(x-2)^2+3(x-2)+2[/tex]
[tex]g(x)=x^2-4x+4+3x-6+2[/tex]
[tex]g(x)=x^2-x[/tex]
Hence final answer is [tex]g(x)=x^2-x[/tex].
How many choices are possible with 1 topping
The answer is 45, I believe so
Evaluate: −4 + 12 ÷(−3)/10 + 3(−2)
Answer:
Step-by-step explanation:
First we calculate (-3)÷10 = -0.3
Then 12÷(-0.3) = -40
After that -4 + (-40) = -44
3(-2) = -6
Finally -44 + (-6) = -50
For this case we have that the order of algebraic operations is determined by PEMDAS:
P: Perform any calculation inside the parentheses, making the most internal ones first.
E: Simplify any exponential expressions.
MD: Do all the multiplications and divisions, from left to right, as they appear.
AS: Do all the addition and subtraction, from left to right, as they appear.
Then, we have the following expression:
-4 + 12 ÷ (-3) ÷ 10 + 3 (-2) =
-4-4 ÷ 10 + 3 (-2) =
-4-0.4 + 3 (-2) =
-4-0.4-6 =
-4.4-6 =
-10.4
Answer:
-10.4
Which stamens is true about f(x)=-6|x+5|-2?
A.) The graph of f(x) is horizontally compressed.
B.) The graph of f(x) is horizontally stretched.
C.) The graph of f(x) opens upward.
D.) The graph of f(x) opens to the right.
ANSWER
A.) The graph of f(x) is horizontally compressed.
EXPLANATION
The given absolute value function is
[tex]f(x) = - 6 |x + 5| - 2[/tex]
The parent function is
[tex]y = |x| [/tex]
Since the factor -6 has an absolute value greater than 1, the graph of the given function will be narrower than the graph of the base function.
Hence the graph is horizontally stretched by a factor of 6.
The graph opens downwards because of the negative sign.
It has vertex at (-5,-2)
Suppose f varies directly as g, and f varies inversely as h. Find g when f = 12 and h = 10, if g = 198 when h = –11 and f = –6. Round your answer to the nearest hundredth, if necessary.
Question 5 options:
–360
–40
40
360
Answer:
360
Step-by-step explanation:
f varies directly as g
f = kg where k is the constant of variation
f varies inversely as h
f = kg/h
We know g = 198 when h = –11 and f = –6. Substituting in
-6 = k*198/(-11)
-6 =k*(-18)
Dividing each side by -18
-6/-18 = k*-18/-18
1/3 =k
Our equation is
f = 1/3 g/h
Letting f = 12 and h = 10
12 = 1/3 g/10
Multiply each side by 10
12*10 =1/3 g/10*10
120 = 1/3 g
Multiply each side by 3
120*3 =1/3 g *3
360 =g
Find the product , select the simplest form
Answer:
the answer is 3
Step-by-step explanation:
21/8 simplify is 3
Yeah, The answer is 3
Find the range. 4.7 6.3 5.4 3.2 4.9 3.1 –3.1 9.5 –9.5
Answer:
The range is 19
Step-by-step explanation:
First, you have to order the numbers from least to greatest:
-9.5, -3.1, 3.1, 3.2, 4.7, 4.9, 5.4, 6.3, 9.5
Then, you have to find the difference between the largest number and and smallest number. You do this by subtracting them:
9.5 - (-9.5)= 19
So, the range is 19
A student reads 65 pages per hour.
3 hours equals 195.
5 hours equals 325
9 hours equals 585
10 hours equals 650
To find this I multiplied the hours by 65 pages.
Hope this helps :)
the sum of two numbers is 52 and the difference is 14. What are the numbers?
14+38=52
52-38= 14
Answer: 38 and 14.
I think this is the answer.
33 and 19
33+19=52
33-19=14
Determine the slope of a line parallel to a line whose slope is -5
Answer:
-5
Step-by-step explanation:
A line that is parallel to another line must have the same slope.
Answer:
-5
Step-by-step explanation:
Parallel lines all have the same slope (as each other). Both of the parallel lines you are describing have a slope of -5.
Daniel is choosing between two cellphone plans. "Plan A" charges $80 per month, which includes unlimited text messaging. "Plan B" costs $20 per month plus $0.15 per text message.
What is the system of equation that represents the fees of both "Plan A" and "Plan B"? Identify what your variables represent.
Answer:
Plan A:
C = $80
C = cost
Plan B:
C = 0.15t + 20
C = cost; t = amount of text messages
Step-by-step explanation:
Let C = cost.
Let t = amount of text messages.
Plan A:
C = $80
Plan B:
C = 0.15t + 20
If the next question asks for you to solve when Plan B will be equal to Plan A, set the two equations equal to each other.
80 = 0.15t + 20
Isolate the variable, t. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.
First, subtract 20 from both sides.
80 (-20) = 0.15t + 20 (-20)
80 - 20 = 0.15t
60 = 0.15t
Divide 0.15 from both sides.
(60)/0.15 = (0.15t)/0.15
60/0.15 = t
t = 400
Those who use Plan B must send at least 400 text message to have the same price as Plan A.
~
Which is the graph of y = cos(x) + 3? HURRYY!!
Answer:
See attachment
Step-by-step explanation:
The given function is [tex]y=\cos x +3[/tex]
The base function is [tex]y=\cos x[/tex]
The single transformation applied to this function is a vertical upward shift by 3 units.
Therefore the graph of [tex]y=\cos x +3[/tex] is graph of [tex]y=\cos x [/tex] shifted up 3 units.
See attachment
Answer: B
Step-by-step explanation:
Just did the test on edge
What is the equation of the line that passes through the point (3, 0) and is perpendicular to the line 2x – y = 5?
Answer:
[tex]\large\boxed{y=-\dfrac{1}{2}x+\dfrac{3}{2}}[/tex]
Step-by-step explanation:
[tex]\text{Let}\ k:y=_1x+b_1\ \text{and}\ l:y=m_2x+b_2.\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\============================\\\\\text{We have}\ 2x-y=5.\\\\\text{Convert to the slope-intercept form y = mx + b:}\\\\2x-y=5\qquad\text{subtract 2x from both sides}\\\\-y=-2x+5\qquad\text{change the signs}\\\\y=2x-5\to m_1=2\\\\\text{Therefore}\ m_2=-\dfrac{1}{2}.[/tex]
[tex]\text{The equation of the searched line:}\ y=-\dfrac{1}{2}x+b.\\\\\text{The line passes through }(3,\ 0).\\\\\text{Put the coordinates of the point to the equation.}\ x=3,\ y=0:\\\\0=-\dfrac{1}{2}(3)+b\\\\0=-\dfrac{3}{2}+b\qquad\text{add}\ \dfrac{3}{2} \text{to both sides}\\\\b=\dfrac{3}{2}[/tex]
Please Help Quickly!!!
If lim x--> 4 f(x) = 5
Answer:
D
Step-by-step explanation:
Value of the function [tex]\lim_{x \to 4} \dfrac {g}{h}(x)[/tex] is zero.
Correct option is b.
What is limit?Limits are defined as values to which the function approximates the output for given input values. The limit is the unique real numbers. Given a real-valued function "f" and a real number "c", the limit is usually defined as [tex]\lim_{x \to c} f(x) = L[/tex]. We read that "the limit of f of x is equal to L as x approaches c". "lim" represents the limit, and the right arrow indicates that the function f(x) approaches the limit L as x approaches c.
Given functions,
[tex]\lim_{x \to 4} f(x) = 5 , \lim_{x \to 4} g(x) = 0, \lim_{x \to 4} h(x) = -2[/tex]
[tex]=\lim_{x \to 4} \dfrac {g}{h}(x)[/tex]
[tex]=\lim_{x \to 4} \dfrac {g(x)}{h(x)}[/tex]
[tex]=\dfrac{\lim_{x \to 4} g(x)} {\lim_{x \to 4} h(x)}[/tex]
= 0/-2
= 0
Hence, 0 is the value of function [tex]\lim_{x \to 4} \dfrac {g}{h}(x)[/tex] .
Learn more about limit here:
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If the ratio of a circle’s sector to its total area is 1/3, what is the measure of its sector’s arc?
1/3 = 33%
33% * 390 = 118.8
Your answer 118.8 degrees
Answer: 120 degrees
Step-by-step explanation:
Just did it.
If the endpoints of have the coordinates A(9, 8) and B(-1, -2), what is the midpoint of ?
A.
(5, 3)
B.
(4, 5)
C.
(5, 5)
D.
(4, 3)
Your answer is D. (4,3)
ANSWER
D(4,3)
EXPLANATION
The endpoints of AB have the coordinates A(9, 8) and B(-1, -2).
To calculate the coordinates of the midpoint of AB, we use the midpoint formula,
[tex]( \frac{x_1+x_2}{2},\frac{y_1+y_2}{2} )[/tex]
We substitute the coordinates of the endpoints into the formula to get,
[tex]( \frac{9+ - 1}{2},\frac{8+ - 2}{2} )[/tex]
[tex]( \frac{8}{2},\frac{6}{2} )[/tex]
We simplify further to obtain,
[tex]( 4,3)[/tex]
the hypotenuse of a right triangle is 20 centimeters. one of the legs is 4 cm longer than the other leg. find the area of the triangle.
Answer:
hypotenuse = 20
leg = x + 4
other leg = x
From the Pythagorean Theorem we know that
20^2 = (x + 4)^2 + x^2
400 = x^2 + 8x + 16 + x^2
2 x^2 + 8x -384 = 0
Solving the quadratic equation we get
x = 12 and x = -16
x = 12 and so the lengths of the 2 legs are:
12 and 16
Right Triangle Area = (leg1 * leg2) / 2
Right Triangle Area = (12 * 16) / 2
Area = 192 / 2
Area = 96 square centimeters
Step-by-step explanation:
To find the area of the triangle, we used the Pythagorean theorem to solve for the legs, obtaining lengths of 16 cm and 12 cm. The area is then calculated using the formula for the area of a right triangle (1/2 * base * height), resulting in an area of 96 cm².
We are given a right triangle with a hypotenuse of 20 cm and two legs where one leg (let's call it a) is 4 cm longer than the other leg (let's call it b). Using the Pythagorean theorem, we can express the relationship between the legs and the hypotenuse: a² + b² = 20². We know that a = b + 4, so if we substitute a into the equation, we get:
(b + 4)² + b² = 400
b² + 8b + 16 + b2 = 400
2b² + 8b - 384 = 0
Dividing everything by 2, we get:
b² + 4b - 192 = 0
Using the quadratic formula or factoring, we find that b = 12 (b can't be negative). Consequently, a = 16. The area of the triangle is given by 1/2 * base * height, which is:
Area = 1/2 * a * b
Area = 1/2 * 16 * 12
Area = 1/2 * 192
Area = 96 cm²
How do you write 900.5 and expanded form and word form?
(9 x 100) + (5 x 0.1)
OR
900 + .5
Nine hundred and five tenths
Hope this helped!
Hello!
-EXPANDED FORM- To make the number 900.5 in expanded form, We use 900 and then add 0.5 which is also 1/2.
-WORD FORM- To make the number 900.5 in word form, the answer would be nine hundred and five tenths
please help i am timed
Answer:
Step-by-step explanation:
2x-10 is your answer
Answer:
D. 2x+5
Step-by-step explanation
All you have to do is put them all together and there you have it your answer of D 2x+5
x y
0 3
1 1
2 -1
Which set of values in the RANGE corresponds to the set {0,2} in the DOMAIN?
2, -1. I think, possibly.
Answer:
3, -1
Step-by-step explanation:
convert 0.5 to a percent value
0.5 as a percent is 50%
0.5 to a percent value is 50%
f(x)=x^2+x-30
complete the square
f(x)= x[tex]x^2+x-30[/tex
= [tex](x)^2+2*x*\frac{1}{2} +(\frac{1}{2} )^2-(\frac{1}{2} )^2-30[/tex]
= [tex](x+\frac{1}{2} )^2-\frac{1}{4} -30[/tex]
= [tex](x+\frac{1}{2} )^2-\frac{121}{4}[/tex]
=[tex](x+\frac{1}{2} )^2-30\frac{1}{4}[/tex] (Answer)
Solve |x| > 3
{-3, 3}
{x|x < -3 ∪ x > 3}
{x|x < -3 ∩ x > 3}
Answer: Second Option
{x| x< -3 ∪ x > 3}
Step-by-step explanation:
To solve the inequality
[tex]| x | >3[/tex] there are two cases:
Case 1. [tex]x>0[/tex]
[tex]x > 3[/tex]
Case2. [tex]x<0[/tex]
[tex]-x > 3[/tex]
[tex]x < -3[/tex]
The final solution is the union of the solution of each case
This is:
[tex]x < -3[/tex] or [tex]x > 3[/tex]
{x| x< -3 ∪ x > 3}
Write a second inequality with the same meaning. −18 ≤ b
ANSWER
[tex]b \geqslant - 18[/tex]
EXPLANATION
The given inequality is:
[tex] - 18 \leqslant b[/tex]
We can rewrite this as:
[tex]b \geqslant - 18[/tex]
The above two inequalities have the same meaning.
Reading from right to left, the first inequality says, "b is greater than or equal to negative 18."
Reading from left to right, the second inequality says, "b is greater than or equal to negative 18."
Therefore the two inequalities have the same meaning.
Step-by-step Answer:
Many inequalities are possible, for example:
Keeping the less than or equal to sign, we could write
-18-b<=0
or, switching sides,
b>= -18 (just by switching sides)
b+18>=0 (by transposing -18 to the left)
Then again, we can multiply both sides by -1, but we need to change the direction of the inequality:
18>=-b
or equivalently, by transposing 18 to the other side
0>=-b-18
and similarly
b+18>=0 (we already had this above)
Guess time to stop!
Identify the following equation as that of a line, a circle, an ellipse, a parabola, or a hyperbola.
y = x 2 + 1
Answer:
The equation [tex]y=x^2+1[/tex] will be a parabola when it is graphed
Answer:
It's a parabola
Step-by-step explanation:
The equation seems to a parabolic function. The parabola is defined as:
[tex]y=Ax^2+b[/tex]
where b is a displacement, we can notice that in our case A=1 and b=1
so it is a parabola with a vertical displacement of one unit.
A bag contains 10 marbles. Four of the marbles are purple. What is the probability you will choose a purple marble from the bag
1/2
3/10
2/5
1/5
Answer:
2/5
Step-by-step explanation:
There are 10 marbles and 4 of them are purple. That would give you the fraction 4/10. 4/10 can be simplified to 2/5. So, you have a 2/5ths chance of choosing a purple marble.
The probability of selecting a purple marble from a bag containing 10 marbles, 4 of which are purple, is 2/5.
The question asks: "A bag contains 10 marbles. Four of the marbles are purple. What is the probability you will choose a purple marble from the bag?" To find the probability, you divide the number of favorable outcomes (choosing a purple marble) by the total number of outcomes (all the marbles in the bag). Here, there are 4 purple marbles and 10 marbles in total.
The probability is therefore 4/10, which can be simplified to 2/5. So, the probability of choosing a purple marble from the bag is 2/5.
A tank with a volume of 61.25 cubic meters is filled with pull. The oil has a density of 865 kilograms per cubic meter that is the mass in kilometers of the oil?
Answer:
Step-by-step explanation:
Density is mass divided by volume:
ρ = M / V
So mass is density times volume:
M = ρV
If the density is 865 kg/m³ and the volume is 61.25 m³:
M = (865 kg/m³) (61.25 m³)
M = 52981.25 kg
Final answer:
To find the mass of oil in a tank, multiply the tank's volume (61.25 cubic meters) by the oil's density (865 kg/m³), resulting in 52,981.25 kilograms. The mass is not measured in kilometers, which suggests a typo in the original question.
Explanation:
The question concerns the calculation of the mass of oil if its density and the volume of the tank it fills are known. To find the mass, you would multiply the volume of the oil by its density:
Step-by-Step Calculation:
Determine the volume of the oil. In this case, the volume is already given as 61.25 cubic meters.
Identify the density of the oil. According to the question, it is 865 kilograms per cubic meter.
Multiply the volume by the density to get the mass. That is:
61.25 m³ × 865 kg/m³ = 52,981.25 kilograms.
In terms of mass in kilometers, there appears to be a typo, as mass is not measured in distances like kilometers. The correct unit should likely be kilograms.