Find the length of the side labeled x. Round intermediate values to the nearest tenth. Use the rounded values to calculate the next value. Round your final answer to the nearest tenth.
Answers
Answer:
x = 42.2 units
Step-by-step explanation:
By applying tangent rule in the right triangle ΔADC,
tan(44)° = [tex]\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]
0.9657 = [tex]\frac{\text{AD}}{\text{DC}}[/tex]
0.9657 = [tex]\frac{AD}{x}[/tex]
AD = 0.9657x
Now we apply cosine rule in ΔADB,
cos(30)° = [tex]\frac{\text{Adjacent side}}{\text{Hyptenuse}}[/tex]
cos(30)° = [tex]\frac{\text{AD}}{\text{AB}}[/tex]
0.866 = [tex]\frac{0.9657x}{47}[/tex]
x = [tex]\frac{47\times 0.866}{0.9657}[/tex]
x = 42.15
x ≈ 42.2 units
Therefore, x = 42.2 units will be the answer.
Related Questions
11- In
how many ways 3 mathematics books, 4 history books ,3
chemisidy books and a biology books can be arranged
on an Shelf so thet all books of the same subjects are
together!
Answers
Answer: 20,736
Step-by-step explanation:
Math and History and Chemistry and Biology and Subjects
3! x 4! x 3! x 1! x 4! = 20,736
Of 1000 randomly selected cases of lung cancer, 823 resulted in death within 10 years.
a. Calculate a 95% two-sided confidence interval on the death rate from lung cancer.
b. Using the point estimate of p obtained from the preliminary sample, what sample size is needed to be 95% confident that the error in estimating the true value of p is less than 0.03?
c. How large must the sample be if you wish to be at least 95% confident that the error in estimating p is less than 0.03, regardless of the true value of p?
Answers
Answer:
a) [tex]0.823 - 1.96\sqrt{\frac{0.823(1-0.823)}{1000}}=0.799[/tex]
[tex]0.823 + 1.96\sqrt{\frac{0.823(1-0.823)}{1000}}=0.847[/tex]
The 95% confidence interval would be given by (0.799;0.847)
b) [tex]n=\frac{0.823(1-0.823)}{(\frac{0.03}{1.96})^2}=621.79[/tex]
And rounded up we have that n=622
c) [tex]n=\frac{0.5(1-0.5)}{(\frac{0.03}{1.96})^2}=1067.11[/tex]
And rounded up we have that n=1068
Step-by-step explanation:
Part a
[tex]\hat p=\frac{823}{1000}=0.823[/tex]
In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by [tex]\alpha=1-0.95=0.05[/tex] and [tex]\alpha/2 =0.025[/tex]. And the critical value would be given by:
[tex]z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96[/tex]
The confidence interval for the mean is given by the following formula:
[tex]\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex]
If we replace the values obtained we got:
[tex]0.823 - 1.96\sqrt{\frac{0.823(1-0.823)}{1000}}=0.799[/tex]
[tex]0.823 + 1.96\sqrt{\frac{0.823(1-0.823)}{1000}}=0.847[/tex]
The 95% confidence interval would be given by (0.799;0.847)
Part b
The margin of error for the proportion interval is given by this formula:
[tex] ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex] (a)
And on this case we have that [tex]ME =\pm 0.03[/tex] and we are interested in order to find the value of n, if we solve n from equation (a) we got:
[tex]n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}[/tex] (b)
And replacing into equation (b) the values from part a we got:
[tex]n=\frac{0.823(1-0.823)}{(\frac{0.03}{1.96})^2}=621.79[/tex]
And rounded up we have that n=622
Part c
[tex]n=\frac{0.5(1-0.5)}{(\frac{0.03}{1.96})^2}=1067.11[/tex]
And rounded up we have that n=1068
The manufacturer of a certain brand of hot dogs claims that the mean fat content per hot dog is 20 grams. Suppose the standard deviation of the population of these hot dogs is 1.9 grams. A sample of these hot dogs is tested, and the mean fat content per hot dog of this sample is found to be 20.5 grams. Find the probability that the sample mean is at least 20.5 when the sample size is 35.
Answers
Answer:
[tex]z=\frac{20.5-20}{\frac{1.9}{\sqrt{35}}}= 1.557[/tex]
And using the normal standard distribution and the complement rule we got:
[tex]P(z>1.557) =1-P(z<1.557) = 1-0.940 = 0.06[/tex]
Step-by-step explanation:
For this case we define our random variable X as "fat content per hot dog" and we know the following parameters:
[tex]\mu = 20, \sigma =1.9[/tex]
We select a sample of n=35 and we want to find the following probability:
[tex] P(\bar X>20.5)[/tex]
For this case since the sample size is >30 we can use the central limit theorem and we use the z score formula given by:
[tex]z=\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
Replacing we got:
[tex]z=\frac{20.5-20}{\frac{1.9}{\sqrt{35}}}= 1.557[/tex]
And using the normal standard distribution and the complement rule we got:
[tex]P(z>1.557) =1-P(z<1.557) = 1-0.940 = 0.06[/tex]
Will give brainliest answer
Answers
Answer:
A=50.26548246units^2
Step-by-step explanation:
Radius is 4 because half the diameter (8) is the radius (4)
A=πr^2
A=π(4)^2
A=50.26548246units^2
Answer:
16 pi unit^2
Step-by-step explanation:
The diameter is 8 so we can find the radius
r = d/2 =8/2 = 4
The area is given by
A = pi r^2
A = pi ( 4)^2
A = pi *16
Brainliest to whoever gets this correct This word problem has too much information. Which fact is not needed to solve the problem? Tanisha tried to sell all her old CDs at a garage sale. She priced them at $2 each. She put 80 CDs in the garage sale, but she sold only 35 of them. How many did she have left? A. All of the information is needed. B. Tanisha sold the CDs for $2 each. C. Tanisha put 80 CDs in the sale. D. Tanisha sold 35 of the CDs.
Answers
Answer:
B. Tanisha sold the CDs for $2 each.
Step-by-step explanation:
Select the expression that is equivalent to (x - 1)2.
O A. x2 - 2x + 2
O B. x2 - x + 2
O C. x2 - x + 1
O D. x2 – 2x + 1
Answers
Answer:
x^2 -2x+1
Step-by-step explanation:
(x - 1)^2
(x-1) * (x-1)
FOIL
first: x^2
outer: -1x
inner: -1x
last: 1
Add together
x^2 -1x-1x+1
Combine like terms
x^2 -2x+1
Answer:
[tex] \boxed{\sf D. \ {x}^{2} - 2x + 1} [/tex]
Step-by-step explanation:
[tex] \sf Expand \: the \: following: \\ \sf \implies {(x - 1)}^{2} \\ \\ \sf \implies (x - 1)(x - 1) \\ \\ \sf \implies x(x - 1) - 1(x - 1) \\ \\ \sf \implies (x)(x) - (1)(x) - (1)(x) - (1)( - 1) \\ \\ \sf \implies {x}^{2} - x - x - ( - 1) \\ \\ \sf \implies {x}^{2} - 2x - ( - 1) \\ \\ \sf \implies {x}^{2} - 2x + 1[/tex]
If we express $2x^2 + 6x + 11$ in the form $a(x - h)^2 + k$, then what is $h$? (ignore the $)
Answers
Answer:
h = - [tex]\frac{3}{2}[/tex]
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
Given
y = 2x² + 6x + 11 ( factor out 2 from the first 2 terms )
= 2(x² + 3x) + 11
Using the method of completing the square
add/subtract ( half the coefficient of the x- term )² to x² + 3x
y = 2(x² + 2([tex]\frac{3}{2}[/tex] )x + [tex]\frac{9}{4}[/tex] - [tex]\frac{9}{4}[/tex] ) + 11
= 2(x + [tex]\frac{3}{2}[/tex] )² - [tex]\frac{9}{2}[/tex] + 11
= 2(x + [tex]\frac{3}{2}[/tex] )² + [tex]\frac{13}{2}[/tex] ← in vertex form
with h = - [tex]\frac{3}{2}[/tex]
In an aquarium, there are 7 large fish and 6 small fish. Half of the small fish are red.
One fish is selected at random. Find the probability that it is a small, red fish.
Write your answer as a fraction in simplest form.
Answers
Answer:
3/13
Step-by-step explanation:
There are a total of 13 fish (6+ 7 = 13). There are 3 small, red fish. (1/2 · 6 = 3). Put the number of small, red fish over the total number of fish because the small, red fish is being selected from the entire tank of fish. 3/13 cannot be simplified any further.
Hurry!! Determine the intervals for which the function shown below is decreasing.
Answers
Answer:
everywhere except between 2 and 5
(between -inf and 2 and between 5 and inf)
Step-by-step explanation:
PLEASE HELP SOLVE THIS!!!!!
Answers
Answer:
20) -43
21) 25
22)-9
Step-by-step explanation:
20) -6 (-6 + 49)/6 = -43
21) 10 - (-10 - (-1 + 6)) = 25
22) 1 - 10/2 - 5 = -9
Step-by-step explanation:
22Let's calculate the expression khowing that m= 1 and n = 5
m-[tex]\frac{m+m}{2}[/tex] -nm- [tex]\frac{2m}{2}[/tex]-n m-m-n0-n0-5-520Let's calculate the expression khowing that n= -7 and p= - 6
[tex]\frac{p(p+n^{2}) }{6}[/tex] [tex]\frac{-6(-6+(-7)^{2}) }{6}[/tex][tex]\frac{-6(-6+49)}{2}[/tex] [tex]\frac{-6*43}{6}[/tex] -1*43-4321Let's calculate the expression khowing that n = -6 and m = -1 and p = -10
mp-(p-(m-n))mp-(p-m+n)mp-p+m-n(-1)*(-10)-(-10)+(-1)-(-6)10+10-1+620-1+619+625Identify the correct HYPOTHESIS used in a hypothesis test of the following claim and sample data: Claim: "The average annual household income in Warren County is $47,500." A random sample of 86 households from this county is obtained, and they have an average annual income of $48,061 with a standard deviation of $2,351. Test the claim at the 0.02 significance level.
Answers
Answer:
We accept H₀
Step-by-step explanation:
Population mean μ₀ = 47500
Population standard deviation unknown
Sample size n = 86 degree of freedom df = 86 - 1 df = 85
Sample mean μ = 48061
Sample standard deviation 2,351
The claim implies a two tail test with t-studend distributon
Null Hypothesis H₀ μ = μ₀
Alternative Hypothesis Hₐ μ ≠ μ₀
Confidence Interval mean α = 0,02 and α/2 = 0,01
With α/2 and df = 85, from t-table we find t(c) critical value
t(c) = 2,3710
We compute t(s) as
t(s) = ( μ - μ₀ ) / s /√n
t(s) = ( 48061 - 47500 )/ 2351/√86
t(s) = 561 * 9,273 / 2351
t(s) = 2,212
Now we compare t(s) and t(c)
t(s) < t(c) 2,212 < 2,371
Then we are in the acceptance region. We accept H₀
Suppose that we don't have a formula for g(x) but we know that g(3) = −1 and g'(x) = x2 + 7 for all x.
(a) Use a linear approximation to estimate g(2.95) and g(3.05).
g(2.95) =
g(3.05) =
(b) Are your estimates in part (a) too large or too small? Explain.
A) The slopes of the tangent lines are positive and the tangents are getting steeper, so the tangent lines lie below the curve. Thus, the estimates are too small.
B) The slopes of the tangent lines are positive but the tangents are becoming less steep, so the tangent lines lie below the curve. Thus, the estimates are too small.
C) The slopes of the tangent lines are positive and the tangents are getting steeper, so the tangent lines lie above the curve. Thus, the estimates are too large.
D) The slopes of the tangent lines are positive but the tangents are becoming less steep, so the tangent lines lie above the curve. Thus, the estimates are too large.
Answers
Answer:
g(2.95) ≈ -1.8; g(3.05) ≈ -0.2A) tangents are increasing in slope, so the tangent is below the curve, and estimates are too small.Step-by-step explanation:
(a) The linear approximation of g(x) at x=b will be ...
g(x) ≈ g'(b)(x -b) +g(b)
Using the given relations, this is ...
g'(3) = 3² +7 = 16
g(x) ≈ 16(x -3) -1
Then the points of interest are ...
g(2.95) ≈ 16(2.95 -3) -1 = -1.8
g(3.05) ≈ 16(3.05 -3) -1 = -0.2
__
(b) At x=3, the slope of the curve is increasing, so the tangent lies below the curve. The estimates are too small. (Matches description A.)
El cuadruple de un número aumentado en 2 es menor igual a 50
Answers
Answer:
[tex]4\cdot x + 2 \leq 50[/tex]. La solución de la inecuación es todo número real menor o igual a 12.
Step-by-step explanation:
El primer paso consiste en traducir la expresión en una expresión algebraica:
1) Un número: [tex]x[/tex]
2) El cuádruplo de un número: [tex]4\cdot x[/tex]
3) El cuádruplo de un número y aumentado en 2: [tex]4\cdot x + 2[/tex]
4) El cuádruplo de un número y aumentado en 2 es menor o igual que 50: [tex]4\cdot x + 2 \leq 50[/tex]
Como siguiente paso, se resuelve la inecuación por métodos algebraicos:
1) [tex]4\cdot x + 2 \leq 50[/tex] Dado
2) [tex]4\cdot x \leq 48[/tex] Compatibilidad con la adición/Existencia del inverso aditivo/Modulatividad en la adición.
3) [tex]x \leq 12[/tex] Compatibilidad con la multiplicación/Existencia del inverso multiplicativo/Modulatividad en la multiplicación/Resultado.
En consecuencia, la solución de la inecuación es todo número real menor o igual a 12.
If the probability that a randomly chosen college student takes statistics is 0.72, then what is the probability that a randomly chosen college student does not take statistics? Give your answer as a decimal.
Answers
Answer:
0.28
Step-by-step explanation:
If the probability that the student does take statistics is 0.72, then it must mean that the rest of the students will not take statistics.
1 - 0.72 = 0.28
0.28 will be the probability that the student does not take statistics.
PLZZZ I NEED HELP I’ll give 20 POINTS
What is the median of the following data set?
(6,3, 9, 1,7)
03
06
08
09
Answers
Answer:
6
Step-by-step explanation:
Arrange the data from smallest to largest
1,3,6,7,9
The median is the middle number
1,3 ,6, 7, 9
The middle number is 6
Tublu buys a cylindrical water tank of height 1.4m and diameter 1.1 to catch rainwater off his roof.he has a full 2 liters tin of paint in his store and decides to paint the tank (not the base) If he uses 25ml to cover 1m^2 will he have enough paint to cover the tank with one layer of paint
Answers
Answer:
yes
Step-by-step explanation:
The lateral area of a cylinder is ...
LA = πdh
Putting in the given numbers, we find the area to be ...
LA = π(1.1 m)(1.4 m) ≈ 4.838 m²
At 25 mL per m², the amount of paint Tublu needs is ...
(4.838 m²)(25 mL/m²) = 120.95 mL
2 liters is 2000 mL, so Tublu easily has enough paint for one layer.
___
The amount he has is enough for more than 16 coats of paint, so he could paint inside and out with the paint he has.
Answer:
he should.
Step-by-step explanation:
7
Find the sum of
and
11
26
13
Answers
Answer:
50
Step-by-step explanation:
If you mean find the sum of 11, 26, and 13, all you have to do is add those three together.
11 + 26 + 13 = 50
Answer:
11+26+13=50
Step-by-step explanation:
PLZ MARK BRAINLIEST
i need this fast plz
Answers
Answer:
180-130 = 50 degrees because its same side angle
m<2 = 50
Step-by-step explanation:
the second one m<1 is 105 for the same reason
What is the radius of a circle what circumference is 44cm
A. 42cm
D. 24cm
B. 48cm
C. 12cm
Answers
Hello!!
Circumference of a circle = 2πr
and
Given, 2πr = 44cm
So,
πr = 44/2 = 22
r = 22 × 7/22
r = 7cm is the answer.
Stay safe and God bless!
- eli <3
Answer:
7 cm
Step-by-step explanation:
Circumference of a circle is 2 π r
2πr = 44
Solve for radius.
r = 44/(2π)
r = 7.002817
A piece of wire 27 m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral triangle.(a) How much wire should be used for the square in order to maximize the total area?(b) How much wire should be used for the square in order to minimize the total area?
Answers
Answer:
a).length of wire for square = 15.25 m
b). length of wire for triangle = 11.75 m
Step-by-step explanation:
Length of a piece of wire = 27 m
This wire was cut into 2 pieces of length 'x' m and (27 - x) m
One was bent into an equilateral triangle and other into a square.
Area of the square shape = Side²
A = [tex](\frac{27-x}{4})^2[/tex]
Similarly, Area of the equilateral triangle = [tex]\frac{\sqrt{3}}{4}(\text{Side})^2[/tex]
A' =[tex]\frac{\sqrt{3}}{4}(\frac{x}{3})^{2}[/tex]
Total area of both the figures = A + A'
F = [tex]\frac{(27-x)^2}{16}+\frac{\sqrt{3}}{4}(\frac{x}{3} )^2[/tex]
Now we find the derivative of 'F' with respect to x and equate it to zero.
F' = [tex]\frac{1}{16}(-1)[2(27-x)]+\frac{\sqrt{3}}{36}(2x)[/tex] = 0
[tex]\frac{\sqrt{3}}{18}(x)=\frac{1}{8}(27-x)[/tex]
x = 15.25 m
a). Length of wire required for a square = 15.25 m
b). Length of wire required for an equilateral triangle = 11.75 m
A) The amount of wire that should be used for the square in order to maximize the area is; 0 m
B) The amount of wire that should be used for the square in order to minimize the area is; 11.74 m
A) We are told that length of wire is 27 m.
Now, let the length cut for the square be x. Thus, length cut for the triangle will be; (27 - x) m.
Since the length for the square is x, then a side of the square is;
Length of side of square = x/4
Length of side of equilateral triangle = (27 - x)/3
Thus;
Area of square; A_s = (x/4)²
Area of equilateral triangle; A_t = ((27 - x)/3)²(¹/₄√3)
Thus, total area is;
A(x) = (x/4)² + ((27 - x)/3)²(¹/₄)√3)
⇒ A(x) = ¹/₁₆x² + ¹/₃₆((27 - x)²√3)
B) Total area is; A(x) = ¹/₁₆x + ¹/₃₆((27 - x)²√3)
To minimize the total area, we will differentiate and equate to zero.
A'(x) = ¹/₈x - ¹/₁₈((27 - x)√3)
At A'(x) = 0, we have;
¹/₈x - ¹/₁₈((27 - x)√3) = 0
¹/₈x = ¹/₁₈((27 - x)√3)
¹/₈x = ³/₂√3 - ˣ/₁₈√3
¹/₈x + ˣ/₁₈√3 = ³/₂√3
x(¹/₈ + ¹/₁₈√3) = ³/₂√3
x = (³/₂√3)/(¹/₈ + ¹/₁₈√3)
x = 11.74 m
Now, A''(x) = ¹/₈ + ¹/₁₈√3
This is greater than zero and so x = 11.74 m is a minimum
Thus, length cut for triangle = 27 - 11.74
length cut for triangle = 15.26 m
Read more at; https://brainly.com/question/16965977
How many meters are in 18,200 milliliter
Answers
Answer:
18.2 :)
Have a great day!!!
The route used by a certain motorist in commuting to work contains two intersections with traffic signals. The probability that he must stop at the first signal is 0.36, the analogous probability for the second signal is 0.51, and the probability that he must stop at least one of the two signals is 0.67.What is theprobability that he must stop.
a) At both signals?
b) At the first signal but not at the second one?
c) At exactly on signal?
Answers
Answer:
a) P(X∩Y) = 0.2
b) [tex]P_1[/tex] = 0.16
c) P = 0.47
Step-by-step explanation:
Let's call X the event that the motorist must stop at the first signal and Y the event that the motorist must stop at the second signal.
So, P(X) = 0.36, P(Y) = 0.51 and P(X∪Y) = 0.67
Then, the probability P(X∩Y) that the motorist must stop at both signal can be calculated as:
P(X∩Y) = P(X) + P(Y) - P(X∪Y)
P(X∩Y) = 0.36 + 0.51 - 0.67
P(X∩Y) = 0.2
On the other hand, the probability [tex]P_1[/tex] that he must stop at the first signal but not at the second one can be calculated as:
[tex]P_1[/tex] = P(X) - P(X∩Y)
[tex]P_1[/tex] = 0.36 - 0.2 = 0.16
At the same way, the probability [tex]P_2[/tex] that he must stop at the second signal but not at the first one can be calculated as:
[tex]P_2[/tex] = P(Y) - P(X∩Y)
[tex]P_2[/tex] = 0.51 - 0.2 = 0.31
So, the probability that he must stop at exactly one signal is:
[tex]P = P_1+P_2\\P=0.16+0.31\\P=0.47[/tex]
22/55 Marks
46%
The table shows the ages of players on a football team.
Age
Frequency
a) Work out the mean age of the team.
Round your answer to 1 decimal place.
19
2
20
3
21
1
22
4
b) A new player joins the team and raises
the mean age to 22.
23
1
Work out the age of this new player.
Answers
Answer:
Step-by-step explanation:
a) So... To work out the average or mean age we must first calculate the total age.
19 x 2 = 38
20 x 3 = 60
21 x 1 = 21
22 x 4 = 88
23 x 1 = 23
Total = 230
Then... Divide the number of players with this figure
Number of players = 2 + 3 + 2 + 4 + 1 = 11
230/11 = 20.9 is the average age of the players
b) We know the average will now be 22 and we know the number of players is now 12.
So... 22 x 12 = 264 (This will be the new total age of all the players)
We know the previous total was 230
So.. 264-230 = 34 (years old)
Hope this helps
Use a proportion to solve the problem. Round to the nearest tenth as needed.
Triangle in a triangle Find the height of the building. Assume that the height of the person is 5 ft.
104 ft
building
13 ft
5 ft
Answers
Answer:
Height of the building is 40 feet
Step-by-step explanation:
From the figure attached,
Height of the person DE = 5 feet
Let height of the building BC = h feet
Since, ΔABC ~ ΔADE,
Their corresponding sides will be proportional,
[tex]\frac{DE}{BC}=\frac{AD}{AB}[/tex]
[tex]\frac{5}{h}=\frac{13}{104}[/tex]
h = [tex]\frac{104\times 5}{13}[/tex]
h = 40 feet
Therefore, height of the building is 40 feet.
Simplfy the following expressions:
Answers
Answer:
1st one = d y^27
2nd one = b 2x^9
Step-by-step explanation:
1st one: since the power is being raised to the power of 3 you multiply the numbers
2nd one: the powers aren't being raised so you add the powers together.
12x^13y^10/6X^4y^10
then dividing for exponents is subtracting them so
2x^9 since y gets canceled out
Use the standard normal table to find P(z ≥ 1.06). Round to the nearest percent.
Answers
Answer:
14%
Step-by-step explanation:
On edge 2020
As an example, 15,000 Men 18-34 watched program X at 7-8 pm on Monday night. 32,000 Men 18-34 had their TV on during the same time period. There are 200,000 Men 18-34 in the television households in the market. What would be the rating for Men 18-34 for program X? Group of answer choices 47 rating points 7.5 rating points 16 rating points 23.5 rating points
Answers
Answer:
7.5 rating points
Step-by-step explanation:
The computation of the rating for Men 18-34 for program X is shown below:
Given that
Number of men 18 -34 watched a program X = 15,000 = X
Number of men 18 - 34 watched in a same time = 32,000
And, the total households in the market = 200,000 = Y
So, the rating for men 18-34 for program x is
[tex]= \frac{X}{Y}[/tex]
[tex]= \frac{15,000}{200,000}[/tex]
= 7.5 rating points
We simply applied the above formula
Use the function below to find f(4).
f(x)=1/3x4^x
A. 8/3
B.256/3
C.64/3
D.16/3
Answers
Answer:
F(4)=1/3*4^4
F(4)=256/3
Step-by-step explanation:
4^4=256
(1/3)*(256)=
256/3
Simply replace X with 4
Answer:
F(4)=1/3*4^4
F(4)=256/3
Step-by-step explanation:
4^4=256
(1/3)*(256)=
256/3
A triangle on a coordinate plane is translated according to the rule T-3,5(x, y). Which is another way to write this rule?
(x, y) - (x - 3, y + 5)
(x, y) - (x-3, y-5)
(x,y) - (x + 3, y-5)
(x, y) = (x + 3, y + 5)
Answers
Explanation:
The notation [tex]T_{-3,5}(x,y)[/tex] or means to move any point (x,y) along the vector <-3,5>. Put another way, it says to shift (x,y) three units to the left and five units up. The x portion deals with left or right shifting, the y portion deals with up or down shifting. Since the x portion is negative, we go in the negative direction on the x axis. Y being positive means we move up rather than down.
This all means we end up with the translation rule [tex](x,y) \to (x-3,y+5)[/tex]
Which of the following points is NOT a solution of the inequality y ≥ Ixl + 3?
A. (-3, 0)
B. (-3, 6)
C. (0, 4)
Answers
Hey there!
To solve this, we need to plug each of our answer options into the inequality and see if it is true. Which ever one doesn't make the inequality true when plugged in is the answer.
OPTION A
(x,y)=(-3,0)
We plug our values into the inequality.
0≥ I-3I+3
You may have noticed the bars surrounding the negative three.. If you didn't know, this is called absolute value. Absolute value is how far the number is from 0 on the number line. -7 is 7 away from 0 on a number line, so the absolute value of -7 is 7. The absolute value of 7 is 7. The absolute value of 0 is 0. Absolute value is signified by these bars. Le'ts finish evaluating.
0≥6
As you can see, zero is not greater than or equal to six. So, option A is false.
Since A is not a solution, we already know that that is the answer, so we don't even need to check B and C. But, we can still evaluate them if you want.
OPTION B
6≥I-3I+3
6≥6
This is true.
OPTION C
4≥I0I+3
4≥3
This is also true.
Therefore, the answer is A. (-3,0)
Have a wonderful day!