Answers
GIven:
[tex]f(x)=-5x+7[/tex]Required:
To find the value of
[tex]\frac{f(x+h)-f(x)}{h},h\ne0[/tex]Explanation:
To find the value of f(x+h) we have to substitute (x+h) in the function f(x) instead of 'x'
The simplify with the given question.
[tex]\begin{gathered} f(x+h)=-5(x+h)+7_{} \\ =-5x-5h+7 \end{gathered}[/tex]Simplifying for the value,
[tex]\begin{gathered} \frac{f(x+h)-f(x)}{h}=\frac{-5x-5h+7-(-5x+7)}{h} \\ =\frac{-5x-5h+7+5x-7}{h} \\ =\frac{-5h}{h} \\ =-5 \end{gathered}[/tex]Final Answer:
[tex]\frac{f(x+h)-f(x)}{h}=-5[/tex]Related Questions
Evaluate the function f(x) = 5 -√x at each specified value and simplify. 1. f(9)
Answers
Answer:
f(9)=2
Explanation:
The function f(x) is defined as follows:
[tex]f(x)=5-\sqrt[]{x}[/tex]To find the value of f(9), we substitute 9 for x in f(x) as follows:
[tex]\begin{gathered} f(9)=5-\sqrt[]{9} \\ =5-3 \\ =2 \end{gathered}[/tex]The size, x, in an automobile tire can affect its performance. Both over-sized and under-sized tires can lead to poor performance and poor mileage. The tire size that yields the best performance for the car Michael wants is given by 0.2(x - 25.5) + 0.3 = - 0.2(x - 16).Find the tire size that will yield the best performance for Michael’s car.
Answers
The tire size that will yield the best performance for Michael’s car is 20.
The equation given is,
0.2(x - 25.5) + 0.3 = - 0.2(x - 16)
From this, we have to solve for x, which will give the size of the tire.
Simplify the equation as follows to find x,
0.2(x - 25.5) + 0.2(x - 16) = - 0.3
0.2x - (0.2 × 25.5) + 0.2x - (0.2 × 16) = - 0.3
0.2x - 5.1 + 0.2x - 3.2 = - 0.3
0.4x - 8.3 = - 0.3
0.4x = - 0.3 + 8.3
0.4x = 8
x = 8/0.4 = 20.
Increasing the wheel diameter also increases the final deceleration which has two consequences. Acceleration potential is reduced but a higher final speed is achieved. In other words, the bigger the car's tires the slower it accelerates but the higher its top speed.
We recommend choosing smaller wheels for more power and as many times as possible for maximum traction. On average, a 15 x 3.75 or larger front wheel gives the best results. For the rear, a 15 x 10 wheelset is ideal.
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21= ______hL how many hL
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We want to convert litres L to Hectolitres hL.
[tex]1L=0.01L[/tex]one litre equals 0.01 hectolitre.
So, to convert 2L to hL, we have;
[tex]\begin{gathered} 1L=0.01L \\ 2L=0.02L \end{gathered}[/tex]Complete the congruence statement.
Answers
Answer:
MCL
Step-by-step explanation:
Answer:
MCL
Step-by-step explanation:
the triangles are flipped in 2 directions so just write the angle like it’s opposite to each other
Hopes this helps please mark brainliest
Solve the inequality - 12 > -16. Then graph the solution.
Answers
Solve the inequality c - 12 > -16.
[tex]\begin{gathered} c-12>-16 \\ c-12+12>-16+12 \\ c>-4 \end{gathered}[/tex]Plot the solution on the number line.
Find the value of angle B, rounding to the nearest tenth of a degree.
Answers
Law of Cosines.
- For a triangle ABC with sides labeled a,b, and c:
[tex]a^2=b^2+c^2-2bc\cos A[/tex][tex]b^2=a^2+c^2-2ac\cos B[/tex][tex]c^2=a^2+b^2-2ab\cos C[/tex]
Since we are asked to look for angle B, we will use
[tex]b^2=a^2+c^2-2ac\cos B[/tex]Given:
a = 12 cm
b = 8 cm
c = 15 cm
Substituting the given values to our equation:
[tex]b^2=a^2+c^2-2ac\cos B[/tex][tex](8)^2=(12)^2+(15)^2-2(12)(15)\cos B[/tex][tex]64=144+225-(360)\cos B[/tex][tex]360\cos B=369-64[/tex][tex]360\cos B=305[/tex][tex]\frac{360\cos B}{360}=\frac{305}{360}[/tex][tex]B=\cos ^{-1}\frac{305}{360}[/tex][tex]B=32.089[/tex]Since we are asked to round the answer to its nearest tenth, the final answer would be 32.1 degrees.
measures of relative position
Answers
Arranging the diameter in the ascending order,
1.31, 1.31, 1.33, 1.36, 1.43, 1.47, 1.48, 1.49, 1.49, 1.53, 1.53, 1.53, 1.58, 1.68, 1.69.
There are 15 data entry in the given data set.
The 78th percentile can be determined as,
[tex]15\times\frac{78}{100}=11.7[/tex]Thus, the 12th data entry in the ascending order has 78th percentile. 1.53 is the required diameter.
which function is equivalent to y = 3(x + 4)² + 5?A) y = 3x² + 21B) y = 3x² + 24x + 63C) y = 3x² + 24x + 53D) y = 3x² + 8x + 21
Answers
Given: The function
[tex]y=3(x+4)^2+5[/tex]To Determine: The equivalent function of the given function
Solution:
Step 1: Expand the parenthesis
[tex]\begin{gathered} y=3(x+4)^2+5 \\ (x+4)^2=(x+4)(x+4) \\ (x+4)^2=x(x+4)+4(x+4) \\ (x+4)^2=x^2+4x+4x+16 \\ (x+4)^2=x^2+8x+16 \end{gathered}[/tex]Step 2: Substitute the expanded into the function
[tex]\begin{gathered} y=3(x+4)^2+5 \\ y=3(x^2+8x+16)+5 \\ y=3x^2+24x+48+5 \\ y=3x^2+24x+53 \end{gathered}[/tex]Hence, the equivalent function to the given is y = 3x²+24x+53, OPTION C
Which statement justifies why ∠ABF measures 130°?Given: angles ABD and DBC are complementary
Answers
SOLUTION:
We are to find the statement that justifies why
Given that
50 degrees +
In conclusion, the justified statement is "a linear pair is two adjacent, supplementary angles.
Answer:
B
Step-by-step explanation:
another person person said it was n had 5stars
42.1069 rounded to the nearest thousandth is
Answers
ANSWER
42.107
EXPLANATION
To round a number to the nearest thousandth we have to look at the next number. If that number is 5 or greater than 5, then we have to add 1 to the thousandths. If it's less than 5, then we leave it like it is and eliminate the other decimals.
In this case, the next number to the thousandth is 9, which is greater than 5. Therefore, we have to turn the 6 into a 7: 42.107
is (18,302) a solution to the equation y=300?
Answers
No
Explanations:Note that:
the solutions to an equation are the values, if substituted into the equation, that will make the equation true.
The given equation is:
y = 300
(18, 302) means that x = 18, y = 302
Since the equation given is y = 300 and not y = 302, the point (18, 302) is not a solution to the equation.
Write an equation in slope-intercept form for the line with slope-2 and y-intercept 3.
Answers
Answer:
wait I will do it
Step-by-step explanation:
i will sent it after sometimes
Can you help me i need the answers
Answers
Given that
The figure is given on the coordinate plane. And we have to find the vertices of the figure after a 90-degree clockwise rotation.
Explanation -
So the figure will be rotated from its position clockwise as
Since the given points are J(-9, -8)
K(-2, -8)
L(-2, -3)
M(-9, -3)
After rotating the points will be
J(
K(-7, -3)
L(-2, -3)
M(-2, 4)
Create a real-world problem involving a cube - Use a perfect cube as its volume - Show using cube roots to find one edge
Answers
PART A
A box of sugar has equal lengths of 6 inches. Calculate the volume of sugar that can fill the box.
The volume of the box can be calculated using the cubic volume formula given to be:
[tex]V=l^3[/tex]Therefore, the volume of the box of sugar is calculated to be:
[tex]\begin{gathered} V=6^3 \\ V=216\text{ cubic inches} \end{gathered}[/tex]PART B
An ice cube is said to contain a volume of 8 cubic inches of water. What will be the length of one side of the cube?
The length of the cube can be calculated using the formula:
[tex]l=\sqrt[3]{V}[/tex]Hence, we can solve to be:
[tex]\begin{gathered} l=\sqrt[3]{8} \\ l=2\text{ inches} \end{gathered}[/tex]The percent markup on the cost price of a dress is the same as the cost price in dollars. If the dress is sold for $24, what was the cost price of the dress ?
Answers
Markup is the difference between a product's selling price and cost as a percentage of the cost.
If we call the cost of the dress as x, the markup is given by the following expression
[tex]markup=\frac{24-x}{x}\times100[/tex]The percent markup on the cost price of a dress is the same as the cost price in dollars, therefore, we can rewrite the previous expression as:
[tex]x=\frac{(24-x)\cdot100}{x}[/tex]Solving for x, we have:
[tex]\begin{gathered} x=\frac{(24-x)\cdot100}{x} \\ x^2=2400-100x \\ x^2+100x-2400=0 \\ \implies x=-120\:or\:x=20 \end{gathered}[/tex]Since we can't have a negative cost price, the markup is 20% and the cost price of the dress is $20.
The fancy restaurant Mackenzie atel at was having asale so her dinner was 80% of the original cost. Theoriginal cost of her dinner was $20.00. What is the saleprice?
Answers
Given data:
The original cost of dinner C=$20.00.
The sale price is 80% of the original cost.
[tex]\begin{gathered} S=\frac{80}{100}(20)_{} \\ =0.8(20) \\ =16 \end{gathered}[/tex]Thus, the final sale price is $16.00.
If f(x) = x, the inverse off, f-1 could be represented by
Answers
Solution
For this case we have the following function given:
y=f(x)= x
And we want to find the inverse so we can do the following steps:
1) replace y with x
x= y
2) solve for y
y = x
Then the folution would be:
A) f-1 (x) =x
What is the value of the expression below when x = 5 and y 5? 6x — бу
Answers
We want to find the value of the given expression;
[tex]6x-6y[/tex]When x=5 and y=5;
Substituting these values in, we have;
[tex]\begin{gathered} 6(5)-6(5) \\ =30-30 \\ =0 \end{gathered}[/tex]Therefore, the answer to this question is zero.
The tables of ordered pairs represent some points on the graphs of Lines F and G.
Line F
x y
2 7
4 10.5
7 15.75
11 22.75
Line G
x y
-3 4
-2 0
1 -12
4 -24
Which system of equations represents Lines F and G?
1. y=1.75x+3.5
y=-4x-8
2. same as 1 but -8 is -2
3. 1.75 and 3.5 are switched
4. 2 and 3 combined
Answers
In linear equation, Equation for line F is y = 1.75x + 3.5 and equation for line G is y = -4x-8.
What is a linear equation example?
Ax+By=C is the typical form for linear equations involving two variables. A linear equation in standard form is, for instance, 2x+3y=5.Finding both intercepts of an equation in this format is rather simple (x and y).y = 1.75x + 3.5 (For line F)
let's take the point (2,7) and put in the equation,
y = 1.75*2 + 3.5
= 3.5 +0.35
= 7
which is true.
Hence, (2,7) satisfies the equation.
y = -4x-8 (For line G)
lets take the point (-3,4) and put in the equation,
y = (-4)*(3) - 8
= 12 - 8
= 4
which is true.
Hence, (-3,4) satisfies the equation.
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Jeremiah wants to send some of his shirts to a dry cleaner. He usually takes his shirts
to Spot-Less Dry Cleaners, where he pays $4.50 per shirt. He sees a sign at No Mess
or Stress Dry Cleaners that says it's $21.00 to have 4 shirts cleaned. Which is the
better deal?
Answers
Answer: Spot-less dry cleaners
Step-by-step explanation:
21/4=$5.25
$4.50<$5.25
16. Which expression shows how to use the Distributive Property to solve 6 x 349? A) (6 x 300) x (6 x 40) x (6 x 9) B) (6 + 300) + (6 + 40) + (6 + 9) C) (6 x 3) + (6 x 4) + (6 x 9) D) (6 x 300) + (6 x 40) + (6 x 9)
Answers
since 349 can be also written as 300+40+9
write the number like so in the multiplication
[tex]6\cdot349=6\cdot(300+40+9)[/tex]apply the distributive property
[tex](6\cdot300)+(6\cdot40)+(6\cdot9)[/tex]Determine if (−2,4) is a solution to the following system of inequalities.-3x > -7y -37x > -5y -4
Answers
Remember that ordered pairs are written in the form (x,y).
Then, to check if (-2,4) is a solution to the system of inequalities, both of the given inequalities should be verified when replacing x=-2 and y=4.
Replace x=-2 and y=4 into the inequalities and check if both of them are satisfied or not.
-3x > -7y - 3
[tex]\begin{gathered} \Rightarrow-3(-2)>-7(4)-3 \\ \Rightarrow6>-28-3 \\ \Rightarrow6>-31 \end{gathered}[/tex]Sice 6 is greater than -31, then this inequality is satisfied by (-2,4).
7x > -5y-4
[tex]\begin{gathered} \Rightarrow7(-2)>-5(4)-4 \\ \Rightarrow-14>-20-4 \\ \Rightarrow-14>-24 \end{gathered}[/tex]Since -14 is greater than -24, then this inequality is satisfied by (-2,4).
Since both inequalities are satisfied by (-2,4) then (-2,4) is a solution to the given system of inequalities.
2) Chang saves up enough money to surprise his momand buy her a new blouse for her birthday. The blousecosts about $70 and he uses a coupon for 20% off. Howmuch does he save by using the coupon?
Answers
2) Chang saves up enough money to surprise his mom and buy her a new blouse for her birthday. The blouse costs about $70 and he uses a coupon for 20% off. How much does he save by using the coupon?
_________________________________
coupon for 20% off
20% = 0.2
The total of 100% of the price minus the discount =
100% - 20% = 80% or 1- 0.2 = 0.8
So then,
$70* 0.8 = $ 56 he pays
70 - 56 = 14 he saves
__________________________
Answer
He saves 14 by using the coupon
____________________
70*0.2= 14
Could I please get some help on my homework for the next question like this please
Answers
we have the equations
x^2+y^2=9
this is the equation of a circle centered at the origin with a radius of 3 units
y=x
this is the equation of a line
therefore
The total points of intersection are 2see the figure below to better understand the problemHi i need help finding the answer? If you could helpMe out?
Answers
Given:
Given a figure.
The side of the square is 8.
The radius of the semicirles is 4.
Required:
To find the perimeter of the given figure.
Explanation:
Here the circumference is
[tex]\begin{gathered} =2\pi r \\ \\ =2\times3.14\times4 \\ \\ =25.12 \end{gathered}[/tex]Now the perimeter is
[tex]\begin{gathered} =25.12\times2 \\ =50.24 \end{gathered}[/tex]Final Answer:
The perimeter of the given figure is 50.24 inches.
The type and number of fish caught in the Charleston Harbor in March was recorded for a month. The results are recorded in the table below. Whatis the probability that the next fish caught is a drum or a flounder? Enter a fraction or round your answer to 4 decimal places, if necessary.Flounder262Number of Fish Caught in MarchBlack DrumBluefish336Red Drum382181Sea Trout190
Answers
1) The first thing we need to do in this question, is to find the sample space, i.e. the total number of outcomes, in this case, fishes.
[tex]262+382+181+336+190=1351[/tex]2) Since no one could pick simultaneously two types of fish, then we can tell that these events are mutually exclusive. So, we can write the following:
[tex]\begin{gathered} P(flounder)=\frac{262}{1351} \\ \\ P(black\:drum)=\frac{181}{1351} \\ \\ P(red\:drum)=\frac{382}{1351} \\ \\ P(drum\:or\:flounder)=\frac{262}{1351}+\frac{181}{1351}+\frac{382}{1351}=\frac{825}{1351}\approx0.6107 \end{gathered}[/tex]Note that by "drum" we are including black and red drum.
That is the answer.
Last year, Milan had $10,000 to invest. He invested some of it in an account that paid 6% simple interests per year, and he invested the rest in an account that paid 9% simple interest per year. After one year, he received a total of $840 in interest. How much did he invest in each account?
Answers
Let's define the next variables
x: amount of money invested in one account
y: amount of money invested in the other account
Milan had $10,000 to invest, then
x + y = 10000 (eq. 1)
The interest Milan gets after one year are: 0.06x and 0.09y. He received a total of $840 in interest, then
0.06x + 0.09y = 840 (eq. 2)
Isolating x from equation 1:
x = 10000 - y
Replacing this result into equation 2,
0.06(10000 - y) + 0.09y = 840
0.06(10000) - 0.06(y) + 0.09y = 840
600 + 0.03y = 840
0.03y = 840 -600
0.03y = 240
y = 240/0.03
y = 8000
Then,
x = 10000 - y
x = 10000 - 8000
x = 2000
He invested $2000 in the account that paid 6% simple interests per year and $8000 in the account that paid 9% simple interests per year
Christina jarred 21 liters of jam after 3 days. How much jam did she jar if she spent 7 days making jam?
Answers
Answer:
49 liters
Explanation:
We know that Christina jarred 21 liters of jam in 3 days, so using this ratio, we can calculate the how much jam she jarred after 7 days as follows
[tex]7\text{ days}\times\frac{21\text{ liters}}{\text{ 3 days}}=49\text{ liters}[/tex]Therefore, the answer is 49 liters.
acellus
Find the point-slope equation for
the line that passes through the
points (9, -9) and (-2, 13). Use the first point in your equation.
Answers
Answer:
y = -2x + 9
Step-by-step explanation:
→ Find the change in x
13 --9 = 22
→ Find the change in y
-2 - 9 = -11
→ Divide to find gradient
22 ÷ -11 = -2
→ Write in standard form
y = -2x + c
→ Substitute in ( 9 , -9 )
-9 = -18 + c
→ Find c
c = 9
→ Write in specified form
y = -2x + 9
HELP! I need this ASAP!!A recursive rule for a sequence is given. Find the first four terms of the sequence. f(1) =5 f(n)= f(n-1) +3, where n is an integer and n ≥ 2
Answers
f(n) = f(n-1) + 3
substitute n= 2 in the above
f(2) = f (2-1) + 3
= f(1) + 3
= 5 + 3
= 8
substitute n = 3 in the formula
f(3) = f(3-1) + 3
= f(2) + 3
= 8 + 3
= 11
substituite n = 4
f(4) = f(4-1) + 3
= f(3) + 3
= 11 + 3
= 14
The first four terms are 5, 8, 11 and 14