Which of the following options correctly represents the complete factored
form of the polynomial F(x) = x^4 +5x2 +4
Answer:
(x-5)(x+2)(x+4)
Step-by-step explanation:
I just did It
hi a little confused, please help 15 points
Answer:
#3
20tan(53) + 5 feet OR 31.54 feet (rounded to nearest hundredth)
#4
6tan(32) feet OR 3.75 km (rounded to nearest hundredth)
Step-by-step explanation:
#3
The horizontal line is at Chloe's eye level, which is 5 feet.
She looks up at an angle of 53 degrees, and is 20 feet away from the statue. This creates a right triangle that you can use basic trigonometry to solve.
Let's call the shorter leg (upper half of statue) as x and the longer leg (distance between Chloe and statue) is 20 feet. We are given the opposite and adjacent sides (from the given angle) so we can use tan.
tan = opp/adj, so tan(53)=x/20
If you plug 20 tan 53 into your calculator to find x, you get 26.54089643
But you have to add 5 feet to your answer because that is her eye level.
#4
The horizontal distance from airplane to raft is 6km, the angle of depression is 32 degrees from the airplane, and we are asked to find the altitude of the plane (x).
We are given an adjacent side and are tasked to find the opposite side, so we will use tan.
tan 32=x/6
Plug this into your calculator and you get x=3.749216111 km.
unit 1 lesson 11 practice problems answers
Answer:
? more information needed
Step-by-step explanation:
Find the graph of the inequality ys-=x+ 1.
Answer:
C
Step-by-step explanation
The y-intercept is 1, the slope is -1/3, and the shaded area is under the graph because y is LESS than -x/3 + 1.
A square based prism and a cylinder both have the same height of 4cm and the same base area. If the volume of the square based prism is 452cm cubed based on the concepts of Cavalieri's principle, what is the approximate circumference of the base of the cylinder?
The approximate circumference of the base of the cylinder is 37.7 cm
How to find circumference of a cylinder?The square based prism and a cylinder both have the same height of 4cm and the same base area.
volume = BH
where
B = base areaH = heightTherefore,
volume of squared base prism = 452
452 = 4B
B = 452 / 4
B = 113
Therefore,
base area of the cylinder = 113 = πr²
Hence,
113 / π = r²
r = √113 / π
circumference of the base of the cylinder = 2πr
circumference of the base of the cylinder = 2 × π × √113 / π
circumference of the base of the cylinder = 2 × 3.14 × 5.99891656885
circumference of the base of the cylinder = 37.6731960524
circumference of the base of the cylinder = 37.7 cm
learn more on circumference here: brainly.com/question/12073337
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Tyna simplified the expression StartFraction 3 x cubed Over 12 x Superscript negative 2 Baseline EndFraction to StartFraction x Over 4 EndFraction. What was Tyna's mistake? She divided the coefficients incorrectly. She added the exponents instead of subtracting them. She divided the coefficients instead of subtracting them. She subtracted the exponents instead of dividing them.
Answer:
She divided the coefficients incorrectly
Step-by-step explanation:
A. She divided the coefficients incorrectly.
B. She added the exponents instead of subtracting them.
C. She divided the coefficients instead of subtracting them.
D. She subtracted the exponents instead of dividing them.
Correct calculation:
3x³/12x^-2
= 3x³ ÷ 12x^-2
= 3x³ ÷ 1/12x²
= 3x³ × 12x²/1
= 36x^5
Tyna's calculation:
3x³/12x^-2 = x/4
Answer:the answer is A
Step-by-step explanation:
got 100 on the test
if a person invests $220 at 7% annual interest, find the approximate value of the investment at the end of 10 years
Answer:
Amount of investment after 10 year = $432.76 (Approx.)
Step-by-step explanation:
Given;
Amount of investment = $220
Annual rate = 7% = 0.07
Number of year = 10 years
Find:
Amount of investment after 10 year
Computation:
A = P[1+r]ⁿ
Amount of investment after 10 year = 220[1+0.07]¹⁰
Amount of investment after 10 year = 220[1.07]¹⁰
Amount of investment after 10 year = 220[1.9671]
Amount of investment after 10 year = 432.762
Amount of investment after 10 year = $432.76 (Approx.)
Which equation relates the population (P) in millions to the time that has passed (T) if the growth rate is 4% per year and the starting
population is 10 million people?
(1) P = 10(0.96)^T
(2) P = 10(1.04)^T
(3) P = 10 + 10(0.04)^T
(4) P = 10(1.4)^T
Answer:
Step-by-step explanation:
The model for exponential growth/decay is
[tex]P(t)=a(b)^t[/tex] where a is the initial population and b is the growth/decay rate. Filling in the info you were given:
[tex]P(t)=10(1.04)^t[/tex]
Because this is a growth rate, we have 100% of the population and that population is growing by 4%, which is .04 in decimal form. If the population is not declining, we are adding to the 100% of the population we already have. That's why the growth rate is 1.04.
.96 means that the population is declining at 4% each year; and 1.4 means that the population is growing at 140% instead of the 104% that it is.
A juice machine is set to dispense 16 ounces of juice. The amount of juice
dispensed is normally distributed, with a mean of 16.15 ounces and a
standard deviation of 0.25 ounces. In which range will the amount of juice
dispensed be found 68% of the time?
Answer: A): 15.90 ounces to 16.4 ounces.
Step-by-step explanation:
Considering the standard deviation is 0.25 ounces. The mean of the juice is 16.15 ounces. Additionally, 68% is one standard deviation away from the mean.
With that being said, you would do the following calculations:
[tex]16.15-0.25=15.90\\\\16.15+0.25=16.40[/tex]
This question relates to The Empirical Rule and understanding how it works. A brief summary is that within one standard deviation of the mean, that is where 68% of the data lies. Two standards deviations is 95%. And three standard deviations is 99.5%.
The formula: [tex]u\frac{+}{-} o[/tex]
the mean PLUS OR MINUS the standard deviation.
Answer:
A
Step-by-step explanation:
3. A straight line passes through two points with
coordinates (6,8) and (0,5).
Work out the equation of the line.
Answer:
Step-by-step explanation:
Find the slope of the line
(x₁ , y₁) = (6 , 8) & (x₂ , y₂) = (0 , 5)
[tex]Slope = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\=\frac{5-8}{0-6}\\\\=\frac{-3}{-6}\\\\=\frac{1}{2}[/tex]
m = 1/2 ;(x₁ , y₁) = (6 , 8)
y - y₁ = m(x - x₁)
[tex]y - 8 = \frac{1}{2}(x - 6)\\\\y - 8 =\frac{1}{2}x -\frac{1}{2}*6\\\\y - 8 =\frac{1}{2}x- 3\\\\y = \frac{1}{2}x - 3 + 8\\\\y = \frac{1}{2}x + 5[/tex]
mutual sold an item for sh.3250 after allowing his customers a 12% discount on the marked price.if he had sold the article without giving a discount,he would have made a profit of 25%.calculate the percentage profit he made by selling the article at a discount?
Answer:
lol Step-by-step explanation:
"A parabola has the equation = ^ + − . What are the coordinates of the vertex? (You must solve by factoring)!!!!!" I NEED THE ANSWER TO THIS FAST WITH STEPS I'm a grade 10 academic student by the way
Answer:
1
Step-by-step explanation:
1
Determine whether 7^2m · 6^2m is equivalent to each of the following expressions:
42^6m
42^m
42^9m
Answer:
Not equivalent to any of the options
Step-by-step explanation:
Given:
7^2m * 6^2m
Since, they both have different bases, multiply the bases and add the powers
7^2m * 6^2m
= (7 * 6)^(2m + 2m)
= 42^4m
Therefore,
7^2m * 6^2m is equivalent to 42^4m
A. 42^6m
Not equivalent
B. 42^m
Not equivalent
C. 42^9m
Not equivalent
→
If u vector= a vector-b vector and v vector= a vector+b vector and magnitude of a = b = 2, then magnitude of u vector multiply v vector =???
Answer:
zero
Step-by-step explanation:
[tex]\overrightarrow{u} = \overrightarrow{a} - \overrightarrow{b}\\\\\overrightarrow{v}= \overrightarrow{a} + \overrightarrow{b}\\\\\overrightarrow{u} . \overrightarrow{v} = a^2 - b^2 \\\\\overrightarrow{u} . \overrightarrow{v} = 2^2 - 2^2 = 0[/tex]
So, vector u and vector v are perpendicular to each other.
Lucy drove 200 miles using 9 gallons of gas. At this rate, how many gallons of gas would she need to drive 420 miles
Answer:
18.9
Step-by-step explanation:
if 200miles = 9gallons
then 420miles = ?
note:if more less divide and if less more divide.
so it is 420/200×9=18.9
SEE QUESTION IN IMAGE
Find the mean of the distribution above (a) ½ (b) 1 (c) 3 (d) 2
Answer:
d) 2Step-by-step explanation:
Total number of oranges:
0*5 + 1*8 + 2*6 + 3*6 + 4*3 + 5*2 = 60Number of baskets:
5 + 8 + 6 + 6 + 3 + 2 = 30Mean of the distribution of oranges:
60/30 = 2Correct choice is d
Please help explanation if possible
Answer:
I don't know ask to your teacher
find the measure of the missing angles in the kite
Answer:
x = y = 104°
Step-by-step explanation:
The sum of the interior angles = 360°
The opposite angles x and y are congruent , that is y = x , then
92 + 60 + x + x = 360
152 + 2x = 360 ( subtract 152 from both sides )
2x = 208 ( divide both sides by 2 )
x = 104
Then
x = y = 104°
13. A recent survey by the cancer society has shown that the probability that someone is a smoker is P(S) = 0.31. They have also determined that the probability that someone has lung
cancer, given that they are a smoker is P(LCS) = 0.226. What is the probability (rounded to the nearest hundredth) that a random person is a smoker and has lung cancer
P(SnLC)?
-0.08
-0.73
-0.25
-0.07
=======================================================
Work Shown:
S = person is a smokerLC = person has lung cancerP(S) = 0.31 = probability someone is a smokerP(LC given S) = probability someone has lung cancer, given they are a smokerP(LC given S) = 0.226Use that given info to say the following:
P(LC given S) = P(LC and S)/P(S)
P(LC and S) = P(LC given S)*P(S)
P(LC and S) = 0.31*0.226
P(LC and S) = 0.07006
P(LC and S) = 0.07
This problem is an example of using conditional probability.
I used "and" in place of the intersection symbol [tex]\cap[/tex]
Saying P(LC and S) is the same as P(S and LC). The order doesn't matter.
The factored form of the expression -25t - 175 is
Answer:
-25(t +7)
Step-by-step explanation:
-25t - 175
Factor out -25
-25 *t +-25* 7
-25(t +7)
Find the value of b. Round
the nearest tenth.
Answer:
b= sin(43°) * 8 / sin(55°) ≈ 6.7
Step-by-step explanation:
Regarding the law of sines, each angle corresponds to the side opposite of it. Here, that means that the 82 degree angle is opposite of side c (so they correspond) and that the 55 degree angle corresponds to the side with 8cm. However, we are trying to find the length of side b. Therefore, assuming that the side with 8cm is side A, if we know that
sin A / a = sinB/b = sin C / C
= sin(55°)/8 = sinB/b = sin(82°) / c, we can take c out of the equation to get
sin(55°)/8 = sinB/b
If we know sinB, we can multiply both sides by 8 to remove a denominator to get
sin(55°) * b / 8 = sinB
multiply both sides by 8 to remove the other denominator to get
sin(55°) * b = sinB * 8
divide both sides by sin(55°) to isolate the b
b = sinB * 8/sin(55°).
Therefore, if we know sinB, we can figure out the length of b.
Because the angles of a triangle add up to 180 degrees, we can say that
180 = 82 + 55 + angle B
180 = 137 + B
subtract both sides by 137 to isolate B
43 = B
b= sin(43°) * 8 / sin(55°) ≈ 6.7
Plz help similarity theorems
Answer:
b is the answer bro and try first then ask questions
Design the image of UAE Mars mission-rocket in the following graph sheet and write
down any six coordinate points of its outline.
i hope these 3 images helps
what is the difference between a theorem and an axion ?
Answer:
An axiom is often a statement assumed to be true for the sake of expressing a logical sequence. ... These statements, which are derived from axioms, are called theorems. A theorem, by definition, is a statement proven based on axioms, other theorems, and some set of logical connectives.
hope it helps
PLEASE MARK BRAINLIEST
Answer:
A theorem, by definition, is a statement proven based on axioms, other theorems, and some set of logical connectives. ... An axiom is a statement that is assumed to be true without any proof, while a theory is subject to be proven before it is considered to be true or false.
[/tex][tex]\sf\purple{\dfrac{tanθ}{secθ - 1} = \dfrac{tanθ + secθ + 1}{tanθ + secθ - 1{cm}^{2}}[/tex][/tex]
[tex]\\[/tex]
[tex]\sf\purple{\dfrac{tanθ}{secθ - 1} = \dfrac{tanθ + secθ + 1}{tanθ + secθ - 1}{cm}^{2}}[/tex]
[tex]\:[/tex]
[tex]\sf{\red{\dfrac{\tan\theta}{\sec\theta - 1}=\dfrac{\tan\theta + \sec\theta + 1}{\tan\theta + \sec\theta - 1}\:cm^{2}}}[/tex]
In 2010, 1 Canadian dollar cost .56 British pounds and in 2012 it cost .63 British pounds. How much would 1 British pound purchase in Canadian dollars in 2010 and 2012? 2010: 1.78 dollars, 2012: 1.57 dollars 2010: 1.79 dollars, 2012: 1.59 dollars 2010: 1.87 dollars, 2012: 1.65 dollars 2010: 1.97 dollars, 2012: 1.75 dollars
Answer:
2010: 1.79 dollars, 2012: 1.59 dollars
Step-by-step explanation:
In 2010,
1 Canadian dollar = .56 British pounds.
We want to find how many pounds go into a dollar, so we somehow have to make the equation equal to 1 pound. To do this, we can multiply the amount of pounds by its reciprocal to equal 1. To find the reciprocal of a number, we simply divide 1 by it. For .56, this is (1/.56). Therefore, we can multiply both sides by (1/.56) to get
1.79 Canadian dollars = 1 British pound
Similarly, for 2012, we have 1 dollar = .63 pounds. Multiplying both sides by 1/.63, we get
1.59 Canadian dollars = 1 British pound
What are the domain and range of f(x) = |x + 6|? Domain: (negative infinity, infinity); range: f(x) > 0 domain: x < -6; range: (negative infinity, infinity) domain: x > -6; range: (negative infinity, infinity) domain: (negative infinity, infinity) ; range: f(x) < 0
Answer:
Domain: [tex](-\infty,\infty)[/tex]
Range: [tex]f(x) \ge 0[/tex]
Step-by-step explanation:
Given
[tex]f(x) = |x + 6|[/tex]
Required
The domain and the range
First, we calculate the domain
[tex]f(x) = |x + 6|[/tex]
The above function does not have roots or fraction, where x is the denominator. This means that the domain is all real numbers, i.e. [tex](-\infty,\infty)[/tex]
The range
The function is an absolute function; So, the minimum value is 0.
Hence, the range is:
[tex]f(x) \ge 0[/tex]
Answer:
A
Step-by-step explanation:
on edge
Which of the following is a point-slope equation of a line that passes through
the points (-1,4) and (8, -2)?
O A. y-1--3(x-1)
O B. y 4 = {(x+1)
O C. y-4--(x+1)
O D. y-4--2(x+1)
Answer:
y - 4 = -2/3 (x + 1)
Step-by-step explanation:
y2 - y1 / x2 - x1 -2 - 4 / 8 - (-1) -6/9 = -2/3
y - 4 = -2/3 (x + 1)
Here is the histogram of a data distribution.
What is the shape of this distribution?
Answer:
Unimodal-Skewed
Step-by-step explanation:
A distribution is called unimodal if it has only one hump in the histogram.
A symmetric distribution is equally divided on both sides of the highest hump.
The given histogram has only one hump at 4 and as it is not symmetrically distributed, it is skewed.
So the correct answer is:
Unimodal-Skewed ..
Make x the subject of the formula (help again)
I'm really bad at these
xk-w=y
Answer:
x = (y+w)/k
Step-by-step explanation:
xk-w=y
Add w to each side
xk-w+w=y+w
xk = y+w
Divide each side by k
xk/k = (y+w)/k
x = (y+w)/k
Answer:
x=[tex]\frac{y+w}{k}[/tex]
Step-by-step explanation:
Have a nice day
I need help to Find the value of x. Round to
the nearest tenth.
Answer:
4.5
Step-by-step explanation:
We are given opposite and adjacent, so use tangent
tan(37)=x/6
6tan(37)=4.521324301
