The expression f(x) = 3 · x² - 2 · x + 4 evaluated at x = a + h is equal to the expression f(x) = 3 · a² + 6 · a · h + 3 · h² - 2 · a - 2 · h + 4.
How to evaluate and simplify a quadratic equation
In this question we find a quadratic equation, which has to be evaluated at x = a + h and simplified afterwards. Then, the complete procedure is shown below:
f(x) = 3 · (a + h)² - 2 · (a + h) + 4
f(x) = 3 · (a² + 2 · a · h + h²) - 2 · a - 2 · h + 4
f(x) = 3 · a² + 6 · a · h + 3 · h² - 2 · a - 2 · h + 4
The expression f(x) = 3 · x² - 2 · x + 4 evaluated at x = a + h is equal to the expression f(x) = 3 · a² + 6 · a · h + 3 · h² - 2 · a - 2 · h + 4.
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Find a solution to the linear equation 13x +y =26 by filling in the bows with a valid value of x and y.
The solution to the linear equation are x = 2 - y/13 and y = 26 - 13x.
It is required to find the solution to the linear equation.
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. Equation, statement of equality between two expressions consisting of variables and/or numbers.
Given:
The equation is
13x + y = 26
We have to find the value of x and y .
According to given question we have
13x + y = 26
Subtract 13x from both sides we get,
y = 26 - 13x
Subtract y from both sides
13x = 26 - y
Divide through by 13
x = 2 - y/13
Therefore, the solution to the linear equation are x = 2 - y/13 and y = 26 - 13x.
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Is this true
4. When you subtract two numbers, if you reduce the first number in the subtraction by one, the result is one less. For example, 12 – 4 is 8 and 11 – 4 is 7
Answer:
The answer is True
Step-by-step explanation:
In the substraction, if you reduce or increase the substrahend by a number, the result is the same number less or more
XZ is the perpendicular bisector of segment WY. Solve for m. Enter a NUMBER only.
2(6m+12)=180
12m+24=180
12m=156
m=13
can someone help me with this domain and function question :)
Answer: (-∞, ∞)
Step-by-step explanation:
|2x+5|+3 can't equal 0. The denominator can't equal 0.
|2x+5|+3[tex]\neq[/tex]0
|2x+5|[tex]\neq[/tex]-3 ==> Absolute value functions can't be negative, so the denominator will never equal 0.
Hence, domain is x equals all real numbers: (-∞, ∞)
Can you explain this to me?
1. Rewrite Divide
2. Rewrite Simplify
3. Rewrite Simplify Expressions
4. Simplify Fractions
5. and Solve
What fractions is in simplest form? 4/10, 15/18, 17/51, 9/21
Step-by-step explanation:
2/5
5/6
1/3
3/7
...........
A ball was thrown off a bridge. The table relates to the height of the ball above the ground in feet to the time in seconds after it was thrown. Use the data to enter a quadratic model in vertex form and convert it to standard form. Use the model to find the height of the ball at 1.5 seconds.
The peak height reached at 144 feet, and the graph passing through points (0, 120), (1, 144), (2, 120), gives;
1. The vertex form of a quadratic equation is f(x) = a•(x - h)² + k
Where;
a = The leading coefficient
(h, k) = The coordinates of the vertex.
Let t represent the time of travel of the ball and let h represent the height.
From the given table, we have;
f(t) = a•(t - h)² + k
f(0) = 120 = a•(0 - h)² + k = a•h² + k
120 = a•h² + k
f(1) = 144 = a•(1 - h)² + k = a•(h² - 2•h + 1) + k
f(1) = a•(h² - 2•h + 1) + k
f(1) - f(0) = 144 - 120 = 24 = -((2•h - 1)•a
24 = -((2•h - 1)•a
f(2) = 120 = a•(2 - h)² + k
f(2) - f(1) = -24 = -((2•h - 3)•a
(f(1) - f(0)) - (f(2) - f(1)) = 48 = -2•a
Therefore;
a = -24
24 = -((2•h - 1)•a
24 = -((2•h - 1)×(-24)
-1 = -((2•h - 1)
2•h - 1 = 1
h = 2/2 = 1
h = 1
120 = a•(2 - h)² + k
120 = (-24)•(2 - 1)² + k
k = 120 + 24 = 144
k = 144Which gives;
The vertex form is y = -24•(x-1)² + 144
From the vertex form, we have;
y = -24•(x-1)² + 144 = -24•(x²-2•t+1) + 144
y = -24•(x²-2•tlx+1)+ 144 = -24•x²+48•x - 24 + 144
y = -24•x²+48•x + 120
y = -24•x² + 48•x - 24 + 144 = -24•x²+ 48•x + 120
y = -24•x² + 48•x + 120
The height of the ball after 1.5 seconds is
y = -24×1.5² + 48×1.5 + 120 = 138
The height of the ball at t = 1.5 seconds is 138 feetLearn more about quadratic equations here:
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Nigel is going from London, UK, to Moscow, Russia, by train. He goes 296 miles on a train from London to Paris, France. He takes another train 500 miles to Munich, Germany, and switches trains in Munich to ride 256 miles on a train to Vienna, Austria. His last train ride carries him 1,298 miles from Vienna to Moscow. Find his total distance by first rounding each distance to the nearest hundred miles before adding.
Answer: 2400 miles
Step-by-step explanation:
Round;
256 to 300
500 to 500
296 to 300
1,298 to 1,300
Add; 300 + 300 + 500 + 1,300 to get your 2,400 miles.
whats the simplest form of b⁴ b²?
Answer:
Step-by-step explanation:
Simplify ((b^4)^4) / ((b^2)^3).First lets simplify the numerator. ((b^4)^4). The notation is b to the fourth power, to the fourth power, which is multiplying sixteen b’s. That explains why we multiple the exponents, to get b^(16) for the numerator.Similarly we simplify the denominator by multiplying the exponents for ((b^2)^3) = b^6.Putting the simplified numerator and denominator together is (b^(16))/(b^6).The six b’s in the denominator cancel six b’s in the numerator for (b^(16))/(b^6) = b^(10). Final answer b^(10).Note, another way to view (b^(16))/(b^6) = (b^(16)) * (b^(-6)) then add the exponents to have the same answer (b^(10))
Pablo received a gift card of $100 for a pizza restaurant .The restaurant charges $15 per pizza. Teresa received a gift card of $70 for a different pizza restaurant .the restaurant charges $10 per pizza .let X be the number of pizzas purchase. for each card write an expression for the amount of money left on the card after purchasing X pizzas.
a)Amount of money left on Pablo's card in dollars = $100 - $15x
= $(90 - 15x)
b) Amount of money left on Teresa's card in dollars= $70 - $10x
= $(70 - 10x)
c) Write an equation to show that the two cards have the same amount of money left on them [don't know how to do this part.
$100 - 15x = $70 - 10x
Let x be the number of pizzas purchased. For each card, write an expression for the amount of money left on the card after purchasing x pizzas.
For Pablo
Keith received a gift card of $100 for a pizza restaurant. The restaurant charges $15 per pizza.
x numbers of pizza costs = $15x
Hence, the amount of money left on Pablo's card after purchasing x pizzas = $100 - $15x
For Teresa,
Mary received a gift card of $70 for a different pizza restaurant. The restaurant charges $10 per pizza.
Hence, x number of pizzas cost =$10 × x
= $10x
Therefore, the amount of money left on Mary's card after she buys x pizzas =
$70 - $10x
Amount of money left on Pablo's card in dollars = __________
Amount of money left on Teresa's card in dollars=____________
Write an equation to show that the two cards have the same amount of money left on them.
To find the equation that shows that the two cards have the same amount of money =
Equation 1 = Equation 2
$100 - 15x = $70 - 10x
Collect like terms
-15x + 10x = $70 - $100
-5x = -30
x = 30/5
x = 6
Hence, anytime Pablo and Teresa buys ,6 pizzas their gift card will have the same amount of money left on them.
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Which of the following must be a factor of the function
Answer:
(A) (x -2)
Step-by-step explanation:
You want to know a factor of the function whose values given in the table include (x, y) = (2, 0).
Polynomial zerosA polynomial function y = p(x) will have a factor of (x-a) if and only if p(a) = 0.
The table shows y=0 for x=2, so this polynomial function will have a factor of (x -2).
__
Additional comment
The function shown in the table is ...
y = (x -2)²
so it actually has two factors that are (x -2).
You can tell this is a polynomial function of degree 2 because the 2nd differences are constant.
First differences between successive y-values: -7, -5, -3, -1, 1, 3
Second differences between successive first differences: 2, 2, 2, 2, 2.
Carlos find the absolute value of -5.3 and then if I the opposite of an answer. Jason find the opposite of -5.3 and then find the absolute value of his answer. Who’s final value is greater? Explain.
The person who has a greater number will be Carlos since 5.3 is more than -5.3.
How to illustrate the information?It should be noted that Carlos find the absolute value of -5.3. This will be - (-5.3) = 5.3.
On the other hand, Jason find the opposite of -5.3 and then find the absolute value of his answer. This will still be -5.4
Therefore, the person who has a greater number will be Carlos.
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How many degrees must figure A be rotated counterclockwise around the origin in order to line up with Figure B?
Answer:
270
Step-by-step explanation:
One turn would put you in quadrant 2 and would be 90. A second turn would put you in quadrant 3 and that would be 180. A third turn would put you in quadrant 4 and that would be 270. I know that it is hard to see what I mean by a turn. It would be if you had a piece of tracing paper with the figure drawn on it and you turn the paper at the origin so that the lines at the corners would like up, each turn would be 90 more degrees.
what does a sqiggley equal sign mean.
Answer:
Approximately ≈
Step-by-step explanation:
Answer:
approximately equal to
or
Approximate equality
Use the fact that 1 kilometer = 0.62 miles to convert 3,070 meters to miles.
Round to the nearest hundredth
Answer: 1.90 miles
Step-by-step explanation:
The conversion rate for meters to kilometers is 1 meter for 0.001 kilometers. Using this rate you can do, [tex]3070m*\frac{0.001km}{1m}[/tex]. The m units cancel and you're left with 3.07km. Since we are given the conversion rate of 1 kilometer = 0.62 miles, we can do, [tex]3.07km*\frac{0.62mi}{1km}[/tex]. again the km units cancel and you're left with 1.9034 mi. Rounded to the nearest hundredth to get 1.90.
Between what two integers does square root of -19 lies
Answer:
4 and 5
Step-by-step explanation:
4^2=4xx4=16,
5^2=5xx5=25, and 19 is between those two squares
a bouquet has 10 flowers.among them,3 are red. at the same ratio, how many red flowers are needed to prepare two bouquets
Answer:
in one bouquet there are 3 red so in two bouquets there must be 6
2,720 divided by 20 what’s the answer
Answer:
136
Step-by-step explanation:
2720 / 20 = 136
Simplify the complex fraction below.
Answer: 6
:)
___________________________________
Answer:
[tex] \sf \large \: \frac{2}{27} [/tex]
Step-by-step explanation:
Let's solve this equation step by step
2/3/1/9
= 2/3/9/1
= 2/27
A binomial experiment has the given number of trials and the given success probability n=2 p=0.2
The mean of binomial experiment has the given number of trials and the given success probability n=2 p=0.2 is 0.2
Bernoulli distribution may be a distinct likelihood distribution wherever the Bernoulli variate will have solely zero or one because the outcome.p is that the likelihood of success and one - p is that the likelihood of failure.The mean of a distribution is E[X] = p and also the variance, Var[X] = p(1-p).Bernoulli distribution may be a special case of statistical distribution once just one trial is conducted.It is given that probability of success is 0.2.
According to Bernoulli distribution
Mean = probability of success
= 0.2
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The complete question is given below :
A binomial experiment has the given number of trials and the given success probability n=2 p=0.2 then find mean
Wharton, Inc., pays income taxes on capital gains (including gains on marketable securities) at a rate of 30 percent. At December 31, year 1, the company owns marketable securities that cost $180,000 but have a current market value of $220,000. b. As of December 31, year 1, what income taxes has Wharton paid on the increase in value of these investments? c. Prepare a journal entry at January 4, year 2, to record the cash sale of these investments at $220,000. d. What effect will the sale recorded in part c have on Wharton’s tax obligation for year 2?
The sale of investments at a price above cost is 102,000 units.
What are Marketable Securities?Any unrestricted financial instrument that can be bought or sold on a public stock exchange or a public bond exchange is defined as marketable security. As a result, marketable securities are either marketable equity securities or marketable debt securities. Marketable securities include stocks, bonds, preferred shares, and exchange-traded funds (ETFs). Marketable securities can also include money market instruments, futures, options, and hedge fund investments. The most important feature of marketable securities is their liquidity.To record the sale:
(Refer to the table shown below)
To document the sale of the security:
850k market price - 180k cost = 340k profit on the sale(Refer to the table shown below)
Record the income tax payable for the security gain:
Gain of 340,000 × 30% tax rate = 102,000Therefore, the sale of investments at a price above cost is 102,000 units.
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The correct question is given below:
Wharton, Inc. pays income taxes on capital gains at a rate of 30 percent. On December 31, 2015, the company owns marketable securities that cost $180,000 but have a current market value of $520,000. Record the sale of investments at a price above cost.
what is the direction of vector v if it ends at (-3,-10)
The direction of the vector v in standard position is approximately 253.301°.
What is the direction of a given vector?
Vectors in rectangular form present the change of each of the two variables parallel to orthogonal axes. Each point is described by the following definition:
v = (Δx, Δy) (1)
And the direction of a vector is equal to this inverse trigonometric function:
θ = tan⁻¹ (Δy / Δx) (2)
If we know that Δx = - 3 and Δy = - 10, then the direction of the vector is:
θ = tan⁻¹ (- 10 / - 3)
θ = tan⁻¹ (10 / 3)
θ ≈ 253.301°
The direction of the vector v in standard position is approximately 253.301°.
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Use the formula for the area of a trapezoid A = h (bi+b²), 2 where A is area, b₁ and b₂ are the length of the bases, and h is the height, to answer the question. How many square feet of grass are there on a trapezoidal field with a height of 75 ft and bases of 125 ft and 81 ft?
Answer:
7725 ft³===================
Use the given numbers and formula to calculate the area:
[tex]A = h(b_1+b_2)/2[/tex][tex]A = 75(125+81)/2=75(206)/2=75(103)=7725[/tex]11. -7.5 -2.75 help me and make sure you simpfily
Answer:
-10.25
Step-by-step explanation:
I'm not sure if this is what you want, but -7.5-2.75= -10.25
Eighty meters of fencing is available to enclose the rectangular garden of Mang
Gustin. Give a function A that can represent the area that can be enclosed in
terms of x.
A function that can represent the area that can be enclosed in terms of x is 40x-x².
Given that Eighty meters of fencing is available to enclose the rectangular garden of Mang Gustin.
Area is defined as the amount of space that can be used within a flat surface or the surface of a solid. Perimeter is defined as a continuous line that forms a boundary to define a two-dimensional shape.
Let the length of garden, l=x
and the given perimeter, p=80
As we know, perimeter of rectangle is P=2(l+b).
Now, we will substitute the values and find the value of b, we get
80=2(x+b)
Now, we will divide both sides by 2, we get
80/2=2(x+b)/2
40=x+b
Further, subtract x from both sides, we get
40-x=x+b-x
40-x=b
Now, we will find the area of rectangle by using the formula A=lb.
Substitute the values in above formula, we get
A=x(40-x)
A=40x-x²
Hence, the area that can be enclosed in terms of x is 40x-x².
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A rectangular room is 15 ft long and 10 ft wide. A scale drawing of the room had a width of 5 inches.What is the length of the room in the drawing?
Answer:
7.5 inches
Step-by-step explanation:
15 ft long and 10 ft wide becomes 3/2 when converted into a ratio
we now have 3/2 and five inches
3 is 1.5*2
5*1.5 is 7.5
Answer:
7.5in
Step-by-step explanation:
If the original room's dimensions are (15ft x 10ft). Then the new scaled-down version is (?ft x 5in) we can set up a ratio of 10/5 = 2 to find that the scale from the room to the drawing is being shrunk by a factor of 2. So if you take 15/2 you will get your final answer of the new length of 7.5in!
What is the smallest prime number that divides evenly into 45?
Answer: It's 3, because 3 is a prime number and divides evenly into 45.
Step-by-step explanation:
45 / 3 = 15
Can I have brainliest? It would help me out, if not thanks anyways! Hope this helped and have a nice day!
what integer would be added to 4 to result in a sum of zero
Answer:
-4
Step-by-step explanation:
4+(-4) =
4-4 =
0
the equation sin(40)=b/20can be used to determine the length of segment ac . what is the length of ac? round to the nearest tenth
If the equation [tex]sin(40)=\frac{b}{20}[/tex] can be used to determine the length of segment AC, then the length of AC is 12.85 units
Given,
The equation,
sin 40 = [tex]\frac{b}{20}[/tex]
We know,
According to trigonometric equation
sin θ= Opposite side / Hypotenuse.
Length of the segment AC = b
Then,
sin 40 = [tex]\frac{b}{20}[/tex]
b= sin 40 × 20
b= 12.85 units
Hence, if the equation [tex]sin(40)=\frac{b}{20}[/tex] can be used to determine the length of segment AC, then the length of AC is 12.85 units
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ASAP, yk the pain too, help me out!!! begging
2x+p/q=2x+q/p, p DOESNt equal to 0, q doesn’t equal to 0
Answer: If p=q, ______. If p doesn’t equal q, _______.
The equation, [tex] \frac{2 \cdot x + p}{q} = \frac{2 \cdot x + q}{p} [/tex], gives;
When p = q, the number of solutions is infinite.
When p ≠ q, the equation has no solution
How can the given equation be evaluated?The given equation is presented as follows;
[tex] \frac{2 \cdot x + p}{q} = \frac{2 \cdot x + q}{p} [/tex]
If p = q, we have;
[tex] \frac{2 \cdot x + q}{q} = \frac{2 \cdot x + q}{q} [/tex]
[tex] \frac{2 \cdot x + p}{p} = \frac{2 \cdot x + p}{p} [/tex]
Therefore, the equation has an infinite number of solutions when p = Q
If p ≠ q, and x = 3, we have;
[tex] \frac{2 \cdot x + p}{q} = \frac{2 \times 3 + p}{q} = \frac{6 + p}{q} [/tex]
[tex] \frac{2 \cdot x + q}{p} = \frac{6 + q}{p} [/tex]
[tex] \frac{6 + p}{q} [/tex] = \frac{6 + q}{p} [/tex]
6•p + p² = 6•q + q²
However;
p ≠ q
Therefore;
6•p ≠ 6•q
p² ≠ q²
6•p + p² ≠ 6•q + q²
Which gives;
[tex] \frac{6 + p}{q} \neq \frac{6 + q}{p} [/tex]
The equation is not defined when p ≠ q
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