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A) Check the graph below, please. B) Horizontal translation to the left in 2 units. C) Vertical shift 4 units
1) Given that we have the function h(x) = |x+2| and g(x)= |x| + 4
A) Let's set a pair of tables, and pick 3 arbitrary values for x and then plug into each one
h(x) = |x+2|
x | y = |x+2|
-1 | 1 y =|-1 +2| = |1| = 1
0 | 2 y =|0+2| = |2| = 2
1 | 3 y =|1+2| = |1| = 1
g(x) =|x| + 4
x | y
-1 | 5
0 | 4
1 | 5
Let's plot those absolute value functions:
B) Considering the parent function f(x) =|x| we can notice that h(x) is a translation to the left, in two units. This we can see better this way:
Note that f(x) is in red, and h(x) in pink or light red.
C) Considering that f(x) = |x| we can see that g(x) = is a vertical shift 4 units up.
Related Questions
PLS HELP ME WITH THIS
you need to use the y=mx+b
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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
Danielle earns $36.80 for 4 hours of yardwork. How much does Danielle earn for 10 hours of yardwork?
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Log z 2 + log 2x
pahelp po
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Which of the following expressions is equivalent to 3x(2+5y)
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Answer:
[tex]15xy+6x[/tex]
Please help!!!!!!!!!!!
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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
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
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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 linesHi, 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]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 waysQuestlon 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
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Answer:
C - 3/4
Step-by-step explanation:
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)
You put together allowance money and head toward a distant planet forsome routine experiments on alien life forms. You abduct 12 aliens from thestrange planet, and you capture the internal body temperature of each(harmlessly of course). That data is presented above. Does this species ofaliens have an average internal body temperature less than that of the humanaverage of 98.6°F?
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Solution
The mean of the internal body temperature of the 12 abducted aliens is given by;
[tex]\frac{96.8+98.3+97.6+98.5+97.5+97.5+98.5+65.6+95.4+98+97.4}{12}=87.14<98.6[/tex]Describe a series of transformations Matt can perform to device if the two windows are congruent
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Answer:
the transformation matt can from A
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 :)
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°
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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 D4x - 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]Given the Frequency Distribution: (SHOW WORK)
Find the:
(A) Range
(B) Mean
(C) Mode
(D) Median
(E) Variance
(F) Standard Deviation of This Sample
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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
Read more about Frequency distribution at; https://brainly.com/question/27820465
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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 company prices its tornado insurance using the following assumptions:
• In any calendar year, there can be at most one tornado.
• In any calendar year, the probability of a tornado is 0.09.
• The number of tornadoes in any calendar year is independent of the number of tornados in any other calendar year.
Using the company's assumptions, calculate the probability that there are fewer than 2 tornadoes in a 14-year period.Round your answer to 4 decimals.
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The probability that there are fewer than 3 tornadoes in a 14-year period is 0.992333
Let x = number of tornados
n = 14
p = 0.03
There are just two outcomes that can occur in these independent, fixed trials, and the success probability is 0.03
Consequently, we may determine the probability using the binomial distribution.
Here we want to find P( X < 3) = P( X < = 3-1) = P(X <=2)
Using Excel:
P( X <=2) = "=BINOMDIST(2,14,0.03,1)" = 0.992333
Be aware that the default Excel command to find binomial probabilities that are less than or equal is "=BINOMDIST(x, n, p, 1)"
Therefore, 0.9923333 percent of the time there won't be more than 3 tornadoes in a 14-year period.
To know more about Probability, refer to this link:
https://brainly.com/question/12629667
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A 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
Find the area of a square with a diagonal that measures 4 square root of 2
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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.
Divide and simplify 7/8 ÷ -13/7
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I only need the answer
THANK YOU!!
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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]
=================================================
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.
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?
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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
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]What value is equivalent to (8+2)2 + (6 − 4) × 3?
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Answer:
26
Step-by-step explanation:
PEMDAS
8 + 2 = 10
6 - 4 = 2
10 x 2 = 20
2 x 3 = 6
20 + 6 = 26
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.
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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.
Mary's dog weighs 25 pounds. How many ounces does the dog weigh? Remember, there are 16 ounces in a pound.
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Answer:
400
Step-by-step explanation:
4 x 10^, 20^2
Answer:
25 pounds 16 ounces = 6400
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
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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: