The function is f(x) = x² +3,then f (x + h) = [tex]x^2+2xh +h^2+3[/tex].
Given,
In the question:
The function is given as:
f(x) = x² +3
To find the f (x + h) = ?
Now, According to the question:
Substitute x = x + h into f(x) = x² +3
f(x + h) = (x+ h)² +3
Expand the expression using:
[tex](a +b)^2 = a^2 +2ab+b^2[/tex]
f(x + h) = [tex]x^2+2xh +h^2+3[/tex]
Hence, The function is f(x) = x² +3,then f (x + h) = [tex]x^2+2xh +h^2+3[/tex].
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The graph of a linear function is shown on the grid.Y(-3, 3.6(5,2)XYo -2What is the rate of change of y with respect to x for this function?Choose the grid that is labeled and bubbled with the correct answer.
(x, y) = (-3, 3.6); (5, 2)
Slope (m) = (y2 - y1) / (x2 - x1)
m = (2 - 3.6) / (5 - - 3) = - 1.6/8
m = -0.2
Expand this problem.
The result of the expression (x / m^2 - 2x / m)(3x^2y / m) is (3x^3y / m^3) - (6x^3y / m^2)
The given expression is
(x / m^2 - 2x / m)(3x^2y / m)
Here we have to apply distributive property
The distributive property states that multiplying the sum of two or more variable by a number gives the same result as when each variable is multiplied individually by the number and the products are added together.
The distributive property of subtraction is
A(B-C) = AB - AC
Apply the distributive property
(x / m^2 - 2x / m)(3x^2y / m)
= (x / m^2)(3x^2y / m) - (2x / m)(3x^2y / m)
Multiply the terms
= (3x^3y / m^3) - (6x^3y / m^2)
Hence, the result of the expression (x / m^2 - 2x / m)(3x^2y / m) is (3x^3y / m^3) - (6x^3y / m^2)
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Find the unknown length.
Answer:
I believe is x 25
when f(x) = -3 what is x?
The function f(x) = -3; the value of x is not defined as the function is independent of 'x'.
What is defined as the independent function?The independent variables are function inputs, while the dependent variables are function outputs.
The value of the a dependent variable is determined by the input. The independent variable, on the other hand, is unrelated to anything; it is simply whatever you want to put in! The connection between the dependent as well as independent variables can be investigated.We can openly manipulate independent variables by trying to plug in any input value. In most math problems, we consider x to be the independent variable because it is the one we generally change.On a graph, we generally plot the independent variable just on horizontal axis (which we also call the x-axis).For the given question;
The given function is;
f(x) = -3
To find the value of x, which is to be substituted in the function to find f(x).
But as there is no x value present for the function, the function f(x) is said to be independent function.
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The height of an iceberg above the
water is 23 meters. The bottom of the
iceberg is 15 meters below sea level.
What is the total height and depth of
the iceberg.
The total height of the iceberg is 38 meters and the total depth of the iceberg is 15 meters.
What is meant by height and depth?Height is a mathematical term that refers to the vertical distance between an object's top and base. Sometimes, it has the designation altitude. The measurement of an item along the y-axis in coordinate geometry is referred to as height in geometry.
The depth of an object is the separation between its closest and farthest ends. Jane, for instance, measures a box. Jane estimates the depth of the box by calculating the distance between the end of the box that is closest to her and the end that is farthest away.
Given, the height of an iceberg above the water is 23 meters.
And also given that the bottom of the iceberg is 15 meters below sea level.
Total height = above the water + below the water
Total height=23+15=38 meters
Depth= total height - iceberg above the water
Depth=38-23=15 meters
The total height of the iceberg is 38 meters.
The total depth of the iceberg is 15 meters.
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can you help with this
In the given parallelogram ABCD:
CD=5x-18
BC=3x-6
AB=2x+12
From the properties of parallelogram: The opposite sides of parallelogram are equal
Pair of opposite sides are:
AB & CD
BC & DA
Opposite sides are equal:
[tex]\begin{gathered} AB=CD \\ 2x+12=5x-18 \\ 5x-2x=12+18 \\ 3x=30 \\ x=\frac{30}{3} \\ x=10 \end{gathered}[/tex]x = 10
Substitute the value of x = 10 in the expression of BC
BC = 3x - 6
BC = 3(10) - 6
BC = 30 - 6
BC = 24
Opposite sides are equal: BC = DA
BC = 24 = DA
DA = 24
Answer: DA = 24
The number of men and women receiving bachelor's degrees each year has been steadily increasing. For the years 1970 through the projection of 2014, the number of men receiving degrees (in thousands) is given by the equation y= 3.6x + 444 and for women, the equation is y= 14.2x + 315 where x is the number of years after 1970.
The solution to the system of equations is x = 12
Equal number of men and women have received bachelor's degrees up till 1982Women have a higher rate of receiving bachelor's degrees each year than menThe solution to the system of equationsThe system of equations is given as
y = 3.6x + 444
y = 14.2x + 315
Substitute y = 14.2x + 315 in y = 3.6x + 444
14.2x + 315 = 3.6x + 444
Evaluate the like terms
10.6x = 129
Divide both sides by 10.6
x = 12
Interpret the result in (a)In (a), we have
x = 12
Where
x is the number of years after 1970.
This means that
Year = 1970 + 12
Evaluate
Year = 1982
So, it means that the total number of men and women that have received bachelor's degrees up till 1982 are equal
The trend for men and womenSee attachment for the graph
On the graph, we can interpret the trends to be:
More women receive bachelor's degrees each year than men
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Missing part in the question
A. Use the substitution method to solve this system of equations. (Round your final results to the nearest whole numbers.)
B. Explain the meaning of your answer to part (a).
C. Sketch a graph of the system of equations. Write a sentence describing the trends for men and women receiving bachelor degrees.
there are 85 pints of juice in 5 containers.Find the unit rate
Answer:
17 pints per container
Step-by-step explanation:
We take 85 : 5. Divide by 5, 17 : 1. 17 pints per container.
Lynn and Trey each stood at a different location on a field and threw a ball. Lynn threw to the 24-yard line and Trey threw to the 19-yard line. Who threw farther, and how do you know?
Lynn threw a ball farther because 24 yard line > 19 yard line
In this question we have been given Lynn and Trey each stood at a different location on a field and threw a ball.
Lynn threw to the 24-yard line and Trey threw to the 19-yard line.
We need to determine who threw a ball farther.
As we know 24 yards > 19 yards
So, Lynn threw a ball farther
Therefore, Lynn threw a ball farther because 24 yard line > 19 yard line
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Please help asap now please Ik this easy for u not for me I’m not good whit shapes
The shape has some right angles .
The correct option is (D).
Given,
In the question:
Complete the sentences :
The shape has ____
Now, According to the question:
From the figure,
There are four option:
Select the one option according to the figure.
To see that :
The figure says that :
Correct Answer is some right angles because the sides are not exactly the same .
Hence, The shape has some right angles .
The correct option is (D).
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An elf drew a picture of a reindeer using the scale 3 inches = 2 feet. If the reindeer in the picture was 6 %. Inches tall, how tall is the actual reindeer?
He drew a picture of reindeer . He used a scale 3 inches = 2 feet. The reindeer in the picture is 6 % inches tall . The height of the actual reindeer can be calculated below
[tex]\begin{gathered} 6\text{ \% of an inch tall = }0.06\text{ inches} \\ 3\text{ inches = 2 f}eet \\ 0.06\text{ inches =?} \\ \text{actual height of the reind}eer=\frac{0.06\times2}{3}=\frac{0.12}{3}=\text{ }0.04\text{ fe}et \end{gathered}[/tex]The coordinate plane shows rectangle PQRS . The length of side QR is 4 units. What is the area of PQRS?
QR = 4 unit
Let us find RS, which is the length of the rectangle . Therefore
[tex]\begin{gathered} RS=\sqrt[]{(1-5)^2+(-4-6)^2} \\ RS=\sqrt[]{16+100} \\ RS=\sqrt[]{116} \end{gathered}[/tex][tex]\begin{gathered} \text{area}=lw \\ \text{area}=\sqrt[]{116}\times4 \\ \text{area}=4\sqrt[]{116\text{ }}unit^2 \end{gathered}[/tex]angles
FIND THE VALUE OF THE GIVEN ALPHABET.
Answer:
y=75
Step-by-step explanation:
2y=150y=150/2y=72Use the following function rule to find f(9).
f(x) = x + 6
f(9) = [
What does f(9) =
Answer:
f(9) = 15Step-by-step explanation:
In order to find f(9) we substitute the value of x that's 9 into f(X) that's where there's x we substitute it with 9 and calculate.
We have
[tex]f(x) = x + 6[/tex]
[tex]f(9) = 9 + 6 \\ = 15[/tex]
We have the final answer as
f(9) = 15Hope this helps you
The area of a rectangular picture frame is 4 3/8 square inches. The length of the frame is 1 2/5 inches. Find the width of the frame
The width of the rectangular frame is 3 1/8 inches.
What is the width?It should be noted that the area of a rectangular picture frame is 4 3/8 square inches and the length of the frame is 1 2/5 inches.
The area of a rectangle is:
= Length * Width
Therefore, the width will be:
= Area / Length
= 4 3/8 ÷ 1 2/5.
= 4.375 / 1.4
= 3.125 or 3 1/8.
The width is 3 1/8 feet.
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Qsn 1.4.1 have never done a problem of this kind before so will need background explanation for every step in the answer.
Answer
Maximum area = 4900 m²
Step-by-step explanation
1.4.1 The perimeter of a rectangle is calculated as follows:
[tex]P=2(l+w)[/tex]where l is the length and w is the width of the rectangle.
Substituting P = 280 m, l = 2x meters, and w = y meters, and solving for y:
[tex]\begin{gathered} 280=2(2x+y) \\ \frac{280}{2}=\frac{2(2x+y)}{2} \\ 140=2x+y \\ 140-2x=2x+y-2x \\ 140-2x=y \end{gathered}[/tex]The area of a rectangle is calculated as follows:
[tex]A=l\cdot w[/tex]Substituting l = 2x and w = y = 140 - 2x:
[tex]\begin{gathered} A=2x(140-2x) \\ A=2x(140)-2x(2x) \\ A=280x-4x^2 \end{gathered}[/tex]1.4.2 Given that Area's formula is a quadratic function, its maximum is placed at its vertex. The x-coordinate of the vertex is found as follows:
[tex]x_V=\frac{-b}{2a}[/tex]where a is the leading coefficient and b is the x-coefficient of the function. In this case, the coefficients are a = -4 and b = 280, then:
[tex]\begin{gathered} x_V=\frac{-280}{2(-4)} \\ x_V=\frac{-280}{-8} \\ x_V=35 \end{gathered}[/tex]Evaluating the Area at x = 35, the maximum Area is:
[tex]\begin{gathered} A=280(35)-4(35)^2 \\ A=4900\text{ m}^2 \end{gathered}[/tex]The table below represents the number of paintings, y, that Jordan completed in x years. Jordan's Paintings Year (x) Paintings (y) 1 4 2 7 3 10 4 13 Which equation describes the relmionship between the number of paintings and the year? A. y = x+3 B. y = 3x + 1 D.y = 4x + 3 C. y = 3x + 4
Method 1
Concept
Pick two points and find the equation of a line.
Point ( 1. 4 ) and ( 2, 7 )
Step 2: Represent each point
[tex]\begin{gathered} x_1\text{ = 1} \\ y_1\text{ = 4} \\ x_2\text{ = 2} \\ y_2\text{ = 7} \end{gathered}[/tex]Step 3: Substitute the values in the two points equation of a line formula
[tex]\frac{y-y_1}{x-x_1}\text{ = }\frac{y_2-y_1}{x_2-x_1}[/tex][tex]\begin{gathered} \frac{y\text{ - 4}}{x\text{ - 1}}\text{ = }\frac{7\text{ - 4}}{2\text{ - 1}} \\ \frac{y\text{ - 4}}{x\text{ - 1}}\text{ = }\frac{3}{1} \\ \frac{y\text{ - 4}}{x\text{ - 1}}\text{ = 3} \\ \text{Cross multiply} \\ y\text{ - 4 = 3(x - 1)} \\ y\text{ - 4 = 3x - 3} \\ y\text{ = 3x - 3 + 4} \\ y\text{ = 3x + 1} \end{gathered}[/tex]Step 4: Final answer
y = 3x + 1 Option B
Multiple Representations of a Story Juan is ordering a flower arrangement online for Valentine's Day. Each rose costs $5 and the vase sells for $10. enter the equation of the line
Let:
r be the number of roses
c be the cost of a flower arrangement
Let's consider that a flower arrangement has 1 vase and "r" roses.
Then, the cost of a flower arrangement is:
c = cost of vase + cost of roses
c = 10 + 5r
Which is the same as
c = 5r + 10
Answer:
c = 5r + 10
ContactExtras30To add or subtract fractions with different denominators, change the fractions toequivalent fractions with the same denominator. The new denominator is the leastcommon denominator (LCD).Question 22What is18+ 1 / 2? Give your answer as a mixed fraction.3 1/2© ©4 418476I don't knowOne attemptYou answered 1 out of 1 correctly. Asking up to 9.
answer: 18 1/2
Isabella's baby weighed 8.5 lbs
when it was first born. 20 days
later, it weighed 10.8 lbs. what is the rate of change of the baby's weight per day?
0.115 lbs/day is the rate of change of baby's weight.
What is rate of change ?When anything changes over time, it does so at a certain rate, or ROC. Therefore, rather than the size of each change individually, it is the pace of change—or, more specifically, its acceleration or deceleration. Rate of change in the financial world is utilized to comprehend price returns and spot trend momentum.
Calculationrate of change in baby's weight will be = (10.8 - 8.5)/ 20
= 2.3 / 20
= 0.115 lbs/day
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Is it a
linear function ?
I NEED HELP
-7/3 divided by 1/3 plus one
how to do y intercept form??????????
Answer:
-1,1 + 2,4 it think
Please help! I need explanation on why the answer is what it is.
I can’t understand slope :(
The correct equation that represents the slope equation using the given information will be (B) y = -5x + 2.
What exactly are slopes?The slope of a line can be used to gauge how steep it is.Divide the change in y by the change in x, or "rise over run," to find the slope in mathematics.Locate two locations along the chosen line and find their coordinates.Find the y-coordinate difference between these two places (rise).Find the difference between the x-coordinates of these two points (run).Subtract the difference in y-coordinates from the difference in x-coordinates (rise/run or slope).So, the slope equation will be:
Slope form: y = MX + bM is -5 and points are (-1, 2).Now, the correct question will be:
y = MX + by = -5x + 2Therefore, the correct equation that represents the slope equation using the given information will be (B) y = -5x + 2.
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Correct questions:
Get the correct equation of the slope -5 and points (-1, 2).
(A) y = 5x + 2
(B) y = -5x + 2
(C) y = -5x - 2
(D) y = 5x - 2
Simplify and determine the coefficient of (-x)(5y)(-2x).
Answer:
10x^2y
Step-by-step explanation:
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shelbyblanchard15, this is the solution:
e. (7 * 10^6) * (8 * 10^5) = 5.6 * 10 ^12
f. 10,000,000 * 0.000 005
10,000,000 = 10 ^7
0.000 005 = 5 * 10 ^ -6
5 * 10^1 = 5 * 10
g. 30,000/0.0004
30,000 = 3 * 10^4
0.0004 = 4 * 10^-4
3 * 10^4/4 * 10^-4 = 7.5 * 10^7
Agnes pays state income tax equal to 3.75% of her federal taxable income. She pays federal income tax equal to 28.4% of her federal taxable income. This year she paid $15,449.60 in federal income tax. How much did Agnes pay in state income tax?
The amount that Agnes paid in state income tax is; SI = $2,040
How to calculate state income tax?To find the state income tax in this situation, we would use this equation:
t = px
Where;
t = Total paid
p = percentage
x = federal income tax
In this case, we would need to find what x is.
We are given;
Total paid = $15,449.60
Percentage of federal tax = 28.4% = 0.284
The equation is;
15,449.60 = 0.284x
dividing both sides by 0.284 gives;
x = $54,400.
Now, we can calculate Agnes' state income tax from the formula:
SI = x × p
SI = 54400 × 0.0375
SI = $2,040
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What figure can be made using the net shown?
a hexagonal prism
an octagonal prism
a hexagonal pyramid
an octagonal pyramid
Answer:
Step-by-step explanation:
an hexagonal pyramid
(-x) + (-3) = x + 3
x =
Answer:
x = -3
Step-by-step explanation:
-x +- 3 = x + 3
-x - 3 = x + 3 (+- is equal to -)
- 3 = 2x + 3 (add x to both sides, to remove the x on the left side)
- 6 = 2x (subtract 3 on both sides)
x = -3 (divide by 2)
Write an equation of the line that passes through (-5,0) and is parallel to the line y=-2/3x-1
The equation of the line that passes through (-5,0) and is parallel to the line y = -2/3x - 1 is y = - 2 / 3 x - 10 / 3
How to find the equation of a line?The equation of a line can be represented in different form such as point slope form, slope intercept form, standard form and general form.
The equation of a line in slope intercept form is as follow:
y = mx + b
where
m = slopeb = y-interceptTherefore, the equation of the line passes through (-5,0) and is parallel to the line y = -2/3x - 1.
Parallel line has the same slope.
Therefore, the slope of the line is - 2 / 3.
Hence, let's find the y-intercept using (-5, 0)
0 = - 2 / 3(-5) + b
b = - 10 / 3
Therefore, the equation is y = - 2 / 3 x - 10 / 3
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