Answers
When we have a function and want to evalueate it for some "x", we just substitute every "x" with the value in parenthesis. So, to evaluate f(a + 2), we have x = a + 2, so we need to substitute every "x" in the function with a + 2:
[tex]f(a+2)=(a+2)^2-2(a+2)+1[/tex]Now, to simplify, we first need to use the distributive property on the second parenthesis and evaluate the binomial in the first:
[tex]f(a+2)=a^2+4a+4-2a-4+1[/tex]Now, we group the like-terms and add them:
[tex]\begin{gathered} f(a+2)=a^2+4a-2a+4+4+1 \\ f(a+2)=a^2+2a+1 \end{gathered}[/tex]For yhe other one, Let's do each term and then make the substraction:
[tex]\begin{gathered} f(a+h)=(a+h)^2-2(a+h)+1 \\ f(a+h)=a^2+2ah+h^2-2a-2h+1 \\ f(a+h)=a^2+h^2+2ah-2a-2h+1 \end{gathered}[/tex][tex]f(a)=a^2-2a+1[/tex]So:
[tex]\begin{gathered} f(a+h)-f(a)=a^2+h^2+2ah-2a-2h+1-(a^2-2a+1) \\ f(a+h)-f(a)=a^2-a^2+h^2+2ah-2a+2a-2h+1-1 \\ f(a+h)-f(a)=h^2+2ah-2h \end{gathered}[/tex]Related Questions
You pick a card at random, put it back, and then pick another card at random.
4 5 6 7
What is the probability of picking a 7 and then picking an odd number?
Simplify your answer and write it as a fraction or whole number.
Answers
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Explanation:
A = probability of picking a 7
A = 1/4 since one card is labeled "7" out of four cards total
B = probability of picking an odd number
B = 2/4 = 1/2 because there are 2 cards that are odd (5 and 7) out of 4 cards total.
C = A*B = probability events A and B happen
C = (1/4)*(1/2)
C = 1/8
This only works when we put the first card back, which means each event is independent.
In the expression 7^4 = 2,401, the value of the____ is 7.A. BaseB. PowerC. exponent
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The value of the base is 7 (option A)
Explanation:Given:
[tex]7^4\text{ = 2401}[/tex]To find:
To complefe the sentence by ill ingthe blanks
In powers and exponents:
[tex]For\text{ }a^b:\text{ a = base, b = exponent}[/tex][tex]\begin{gathered} Applying\text{ same principle:} \\ 7^4:\text{ Base = 7, exponent = 4} \end{gathered}[/tex]The value of the base is 7 (option A)
Questlon 14 of 25 What is the slope of the line containing (-3, 1) and (1, -2)? O A. A - 3 O B. 4 O c. - 3 4 O D. SUBMIT
Answers
Answer:
C - 3/4
Step-by-step explanation:
Simplify (z9z−3)−2.
1 over z raised to the twelfth power
1 over z raised to the sixth power
−z^12
−z^6
Answers
Answer:
A. 1 over z raised to the twelfth power
Step-by-step explanation:
Hope this helps! :))
Please tell me if this is incorrect
Answer:
1 over z raised to the twelfth power
Step-by-step explanation:
Given the Frequency Distribution: (SHOW WORK)
Find the:
(A) Range
(B) Mean
(C) Mode
(D) Median
(E) Variance
(F) Standard Deviation of This Sample
Answers
The measures of the frequency distribution is;
(A) Range = 7
(B) Mean = 29
(C) Mode = 12
(D) Median = 29
(E) Variance = 7.612
(F) Standard Deviation = 2.759
How to solve frequency distribution?
A) The range of a frequency distribution is;
Range = Highest Value - Lowest Value
Thus;
Range = 32 - 25
Range = 7
B) Mean is expressed as;
x' = ∑fx/∑f
x' = [(25 * 4) + (26 * 6) + (28 * 6) + (30 * 4) + (32 * 12)]
x' = 928/32
x' = 29
C) Mode is the value with the highest frequency and so in this case;
Mode = 12
D) Median is the middle term when arranged from lowest to highest. In this case, it is the 16.5th term. Thus; Median = (28 + 30)/2 = 29
E) Variance = 7.612
F) The standard deviation is;
σ = √Variance
σ = 2.759
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If P = 3+5+7+9+...+99 and Q = 7+9+11+13+...+101 are sums of arithmetic sequences, determine which is
greater, P or Q, and by how much.
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Answer:
Q is greater than P by 291
Step-by-step explanation:
The terms of these Arithmetic Sequences are odd natural numbers, because their common difference is 2
And, sum of 'n' odd natural numbers starting from 1 = n²
P = 99² - (1) = 9800
Q = 101² - (1 + 3 + 5) = 10192
Q - P = 291
Precalc please help Answers:A. 5 sin 60°/sin 70°B. 5/sin 50° sin 70°C. 5/sin 50°D. 5 sin 50°/sin 70°
Answers
step 1
Find out the measure of angle P
Remember that the sum of the interior angles in any triangle must be equal to 180 degrees
so
P+Q+R=180 degrees
substitute given values
P+70+60=180
P=180-130
P=50 degrees
step 2
Applying the law of sines
QR/sin P=PR/sin 70
substitute given values
QR/ sin 50=5/sin 70
QR=(5/sin 70)*sin 50
the answer is option DMary's dog weighs 25 pounds. How many ounces does the dog weigh? Remember, there are 16 ounces in a pound.
Answers
Answer:
400
Step-by-step explanation:
4 x 10^, 20^2
Answer:
25 pounds 16 ounces = 6400
Step-by-step explanation:
Find the area of a square with a diagonal that measures 4 square root of 2
Answers
Let's draw the figure to better understand the scenario:
Let,
s = the measure of the sides of the square
For us to be able to determine the area, let's first find out the measure of its side.
We will be using the Pythagorean Theorem:
[tex]\text{ a}^2+b^2=c^2[/tex][tex]\text{ s}^2+\text{ s}^2=(4\sqrt[]{2})^2[/tex][tex]\text{ 2s}^2=32[/tex][tex]\text{ }\frac{\text{2s}^2}{2}=\frac{32}{2}[/tex][tex]\text{ }\sqrt{\text{s}^2}=\sqrt{16}[/tex][tex]\text{ s = 16}[/tex]Let's now determine the area of the square:
[tex]\text{ Area = s}^2[/tex][tex]\text{ = 4}^2[/tex][tex]\text{Area = 16}[/tex]Therefore, the area of the square is 16.
how many ways can nine trophies be arranged on a shelf
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we know that
There are: 9 ways to put the first trophy.
8 ways to put the second trophy after putting the first one.
7 ways to put the third trophy after putting the second one.
6 ways .............the third one
5 ways --------> the fourth
4 ways------> 5
3 ways -----> 6
2 ways ----> 7
1 ways-----> 8
therefore
n!
where n=9
9!=9*8*7*6*5*4*4*2*1
9!=362,880
the answer is
362,880 waysI only need the answer
THANK YOU!!
Answers
Answers:
[tex]\cos(\theta) = \frac{-3\sqrt{5}}{7}\\\\\tan(\theta) = -\frac{2}{3\sqrt{5}} = -\frac{2\sqrt{5}}{15}\\\\\csc(\theta) = \frac{7}{2}\\\\\sec(\theta) = -\frac{7}{3\sqrt{5}} = -\frac{7\sqrt{5}}{15}\\\\\cot(\theta) = \frac{-3\sqrt{5}}{2}\\\\[/tex]
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Explanation:
We're given that [tex]\sin(\theta) = \frac{2}{7}\\\\[/tex]
Plug that into the pythagorean trig identity [tex]\sin^2(\theta)+\cos^2(\theta) = 1\\\\[/tex] and solve for cosine to find that [tex]\cos(\theta) = \frac{-3\sqrt{5}}{7}\\\\[/tex]
I skipped steps in solving so let me know if you need to see them.
Keep in mind that cosine is negative in quadrant 2
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Once you've determined cosine, divide sine over cosine to get tangent
[tex]\tan(\theta) = \sin(\theta) \div \cos(\theta)\\\\\tan(\theta) = \frac{2}{7} \div \frac{-3\sqrt{5}}{7}\\\\\tan(\theta) = \frac{2}{7} \times -\frac{7}{3\sqrt{5}}\\\\\tan(\theta) = -\frac{2*7}{7*3\sqrt{5}}\\\\\tan(\theta) = -\frac{2}{3\sqrt{5}}\\\\\tan(\theta) = -\frac{2\sqrt{5}}{3\sqrt{5}*\sqrt{5}}\\\\\tan(\theta) = -\frac{2\sqrt{5}}{3*5}\\\\\tan(\theta) = -\frac{2\sqrt{5}}{15}\\\\[/tex]
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To determine cosecant, we apply the reciprocal to sine.
[tex]\sin(\theta) = \frac{2}{7} \to \csc(\theta) = \frac{1}{\sin(\theta)} = \frac{7}{2}\\\\[/tex]
Similarly, secant is the reciprocal of cosine
[tex]\cos(\theta) = \frac{-3\sqrt{5}}{7} \to \sec(\theta) = \frac{1}{\cos(\theta)} = -\frac{7}{3\sqrt{5}} = -\frac{7\sqrt{5}}{15}\\\\[/tex]
Depending on your teacher, rationalizing the denominator may be optional.
Lastly, cotangent is the reciprocal of tangent
[tex]\tan(\theta) = -\frac{2}{3\sqrt{5}}\to \cot(\theta) = \frac{1}{\tan(\theta)} = \frac{-3\sqrt{5}}{2}[/tex]
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Side notes:
Sine and cosecant are the only things positive in Q2
Everything else (cosine, tangent, secant, cotangent) are negative in Q2.
Which of the following expressions is equivalent to 3x(2+5y)
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Answer:
[tex]15xy+6x[/tex]
Log z 2 + log 2x
pahelp po
Answers
Divide and simplify 7/8 ÷ -13/7
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PLS HELP ME WITH THIS
you need to use the y=mx+b
Answers
Hello!
What is a slope-intercept line:
[tex]y = mx + b[/tex]
m: slope[tex]slope = \dfrac{y_2-y_1}{x_2-x_1} =\frac{-4--2}{3-0} =-\dfrac{2}{3}[/tex]
y-intercept or point whose x-coordinate is '0'==> value of y-intercept is '-2'
Thus the equation is [tex]y=-\dfrac{2}{3}x-2[/tex]
Hope that helps!
Answer: y=-2/3x-2
Step-by-step explanation:
1) Draw a triangle from one point to the next point.
For this example, I will use (-3,0) and (0,-2).
You can see that the number goes down 2 and right 3. From this, you can conclude that the rate is -2/3 using the equation rise/run.
2) Find the y-intercept
Looking at the graph, you can find that the y-intercept is (0,-2).
3) Fill in the y=mx+b
y=-2/3x-2
Describe a series of transformations Matt can perform to device if the two windows are congruent
Answers
Answer:
the transformation matt can from A
The graph shows the mass of the bucket containing liquid depends on the volume of liquid in the bucket. Use the graph to find the range of the function.
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The range of the graph is 0 <= M <= 5.5
How to find the range of the function?The range of a function is the set of output values of the graph.
This in other words mean the range of a function is the set of y values of the graph.
How to determine the domain and the range?The domain
On the graph of the function, we can see that:
The x values start from 0 and it ends at 7.5
This means that the domain is 0 <= x <= 7.5
The range
On the graph of the function, we can see that:
The x values start from 0 and it ends at 5.5
This means that the range is 0 <= M <= 5.5
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Answer:
0 <= M <= 5.5
Step-by-step explanation:
Danielle earns $36.80 for 4 hours of yardwork. How much does Danielle earn for 10 hours of yardwork?
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Victoria's speedboat can travel 105 miles upstream against a 4-mph current in the same amount of time it travels 125 miles downstream with a 4-mph current. Find the speed of Victoria's boat.
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Recall that:
[tex]\text{ time }=\frac{\text{ distance}}{\text{ speed}}[/tex]Let Victoria's speed be v.
Therefore, Victoria's resultant speed upstream is v - 4 and her resultant speed downstream is v + 4.
Hence the time of journey upstream is given by:
[tex]\frac{105}{v-4}[/tex]And the time of journey downstream is given by:
[tex]\frac{125}{v+4}[/tex]Since the time of journey upstream is the same as the time of journey downstream, it follows that:
[tex]\begin{gathered} \frac{105}{v-4}=\frac{125}{v+4} \\ \text{ Divide both sides by }5: \\ \frac{21}{v-4}=\frac{25}{v+4} \\ \text{ Cross-multiplying, we have:} \\ 21(v+4)=25(v-4) \\ \text{ Expanding the expressions, we have:} \\ 21v+84=25v-100 \\ 25v-21v=100+84 \\ 4v=184 \\ v=\frac{184}{4}=46 \end{gathered}[/tex]Therefore, Victoria's speed is 46 mph
Simplify the expression.Can you help me with this one. I'm stuck at 12^x4 - 15x^2
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Simplify the given expression as shown below
[tex]\begin{gathered} 3x(4x^4-5x)=3x*4x^4+3x(-5x)=12x^5+(-15x^2) \\ =12x^5-15x^2 \end{gathered}[/tex]Therefore, the answer is 12x^5-15x^2A cone has a radious of 5inches and a height of 10.125inches.What is the volume of the cone in inch rounded to the nearest tenth?
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Answer:
264.9 in³
Explanation:
The volume of a cone can be calculated using the following equation:
[tex]V=\frac{\pi\cdot r^2\cdot h}{3}[/tex]Where π is approximately 3.14, r is the radius of the cone and h is the height.
So, replacing r by 5 in and h by 10.125 in, we get:
[tex]\begin{gathered} V=\frac{3.14\cdot(5)^2\cdot(10.125)}{3} \\ V=\frac{3.14\cdot25\cdot10.125}{3} \\ V=\frac{794.8}{3} \\ V=264.9 \end{gathered}[/tex]Therefore, the volume of the cone is 264.9 in³
What value is equivalent to (8+2)2 + (6 − 4) × 3?
Answers
Answer:
26
Step-by-step explanation:
PEMDAS
8 + 2 = 10
6 - 4 = 2
10 x 2 = 20
2 x 3 = 6
20 + 6 = 26
12–23. Tony Ring wants to attend Northeast College. He will need $60,000 4 years from today. Assume Tony’s bank pays 12% interest compounded semiannually. What must Tony deposit today so he will have $60,000 in4 years?
Answers
Answer:
See below
Step-by-step explanation:
Period = 1/2 year total 4years = 8 periods
i = interest per period in decimal form = .12/2 = .06
initial deposit = ?
Final value = 60 000
60 000 = ? ( 1 + .06)^8
? = 37644.74
Hi, I need help differentiating using the product rule, thanks
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Differentiate using the product rule:
g. We take out the constant:
[tex]4\frac{dy}{dx}\left(x\left(3x-2\right)^5\right)[/tex]So:
[tex]=4\left(\frac{d}{dx}\left(x\right)\left(3x-2\right)^5+\frac{d}{dx}\left(\left(3x-2\right)^5\right)x\right)[/tex]Now
[tex]\begin{gathered} \frac{d}{dx}\left(x\right)=1 \\ \frac{d}{dx}\left(\left(3x-2\right)^5\right)=5(3x-2)^4\cdot\frac{d}{dx}\left(\left(3x-2\right)^5\right)=5\left(3x-2\right)^4\cdot\:3=15\left(3x-2\right)^4 \end{gathered}[/tex]Substituting the derivatives found:
[tex]=4\left(1\cdot\left(3x-2\right)^5+15\left(3x-2\right)^4x\right)[/tex]Simplify:
[tex]=4\left(\left(3x-2\right)^5+15x\left(3x-2\right)^4\right)[/tex]Answer:
[tex]=4\left(\left(3x-2\right)^5+15x\left(3x-2\right)^4\right)[/tex]4x - 2y = 8Solve for yy = 4x + 8y = -2x + 4y = 2x - 4y = -x
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This question has to do with the change in the subject of the formula.
So we will proceed thus:
[tex]\begin{gathered} 4x-2y=8 \\ \text{Making y the subject of formula will give:} \\ \end{gathered}[/tex][tex]\begin{gathered} 4x-8=2y \\ \text{Divide both sides by 2} \\ \frac{4x-8}{2}=\frac{2y}{2} \\ 2x-4=y \end{gathered}[/tex]The correct answer, therefore, is the third option:
[tex]y=2x-4[/tex]What is the quotient in simplest form? State any restrictions on the variable.see image
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we have the expression
[tex]\frac{z^2-4}{z-3}\div\frac{z+2}{z^2+z-12}[/tex]Multiply in cross
[tex]\frac{(z^2-4)(z^2+z-12)}{(z-3)(z+2)}[/tex]Simplify
z^2-4=(z+2)(z-2) -----> difference of squares
z^2+z-12=(z+4)(z-3)
substitute in the above expression
[tex]\frac{\mleft(z+2\mright)\mleft(z-2\mright)\mleft(z+4\mright)\mleft(z-3\mright)}{(z-3)(z+2)}[/tex]Simplify
[tex](z-2)(z+4)[/tex]PLEASE HURRY IM SO CONFUSED
What is the product of (−4)(23)(−7)?
Answers
Answer:
644
Step-by-step explanation:
-4x23=-92
-92x-7=644
i hope this helped :)
Select the GCF for each pair of numbers. 9,15 12,18 15,27 30,54
Answers
The Greatest common factors for each pair of numbers are;
1, ( 9 , 15 ) = 3
2. ( 12 , 18 ) = 6
3. ( 15 , 27 ) = 3
4. (30, 54) = 6
What is Greatest common factors?
The highest number that divides exactly into two more numbers, is called Greatest common factors.
Given that;
The pairs of numbers are;
1, ( 9 , 15 )
2. ( 12 , 18 )
3. ( 15 , 27 )
4. (30, 54)
Now,
Find the Greatest common factors of the pairs of the numbers as;
1, ( 9 , 15 )
LCM of 9 = 3 x 3
LCM of 15 = 3 x 5
So, GCF of 9 and 15 = 3
2. ( 12 , 18 )
LCM of 12 = 2 x 3 x 2
LCM of 18 = 3 x 3 x 2
So, GCF of 12 and 18 = 3 x 2 = 6
3. ( 15 , 27 )
LCM of 15 = 3 x 5
LCM of 27 = 3 x 3 x 3
So, GCF of 15 and 27 = 3
4. (30, 54)
LCM of 30 = 2 x 3 x 5
LCM of 18 = 3 x 3 x 2
So, GCF of 30 and 54 = 3 x 2 = 6
Thus, The Greatest common factors for each pair of numbers are;
1, ( 9 , 15 ) = 3
2. ( 12 , 18 ) = 6
3. ( 15 , 27 ) = 3
4. (30, 54) = 6
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Please help!!!!!!!!!!!
Answers
Which equation represents a line which is parallel to the line y=8x-4?A x+8y=-16B x-8y=-40C y-8x=-1D 8x+y=3
Answers
Two parallel lines has the same slope.
The given line:
[tex]y=8x-4[/tex]Is written in the form y=mx+b where m is the slope.
The slope is 8
To find the parallel line you need to write the given options in the form y=mx+b by solving y, as follow:
[tex]\begin{gathered} A \\ x+8y=-16 \\ 8y=-x-16 \\ y=-\frac{1}{8}x-\frac{16}{8} \\ \\ y=-\frac{1}{8}x-2 \end{gathered}[/tex]Slope is -1/8 (it is not parallel to given line)
_______________
[tex]\begin{gathered} B \\ x-8y=-40 \\ -8y=-x-40 \\ y=\frac{-x}{-8}-\frac{40}{-8} \\ \\ y=\frac{1}{8}x+5 \end{gathered}[/tex]Slope is 1/8 (it is not parallel to given line)
________________
[tex]\begin{gathered} C \\ y-8x=-1 \\ y=8x-1 \end{gathered}[/tex]Slope is 8 (It is parallel to given line)___________[tex]\begin{gathered} D \\ 8x+y=3 \\ y=-8x+3 \end{gathered}[/tex]Slope is -8 (it is not parallel to given line)
Then, as given line and line in option C have the same slope (8) they are parallel lines