The simplified form of the expression √-25 - 4 is 5i - 4.
What is the simplified form of the expression?Given the expression in the question.
√-25 - 4
To simplify, rewrite -25 as -1(25)
√-1(25) - 4
Rewrite √-1(25) as √-1 × √25
√-1 × √25 - 4
Rewrite √-1 as i
i × √25 - 4
Rewrite 25 as 5²
i × √5² - 4
Now, pull terms out from under the radical, assuming positive real numbers.
i × 5 - 4
Multiply i and 5
5i - 4
Therefore, the simplified form is 5i - 4.
Option C) 5i - 4 is the correct answer.
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which of the following is the product of the rational expression shown below? make sure your answer is in reduced form x+1/x-4 * 5/x+1
Answer:
C
Step-by-step explanation:
[tex]\frac{x+1}{x-4}[/tex] × [tex]\frac{5x}{x+1}[/tex] ← cancel x + 1 on numerator and denominator
= [tex]\frac{1}{x-4}[/tex] × [tex]\frac{5x}{1}[/tex]
= [tex]\frac{5x}{x-4}[/tex]
Answer:
5x/(x-4)
Step-by-step explanation:
To multiply fractions, all we have to do is multiply the numerators together and the denominators together. If we do that, we get the following:
[tex]\frac{x+1}{x-4}*\frac{5x}{x+1}=\frac{(x+1)(5x)}{(x-4)(x+1)}[/tex]
We notice that both the numerator and the denominator have an (x+1) term. Whenever you have something divided by itself, you get 1. In other words, they cancel out. As such, we can remove them from our answer to simplify it:
[tex]\frac{5x}{x-4}[/tex]
If we do that, we get the expression above. 5x/(x-4) is the reduced product of the rational expression given.
x + x/3 = 4/9
solve for x!!
Answer:
x=1/3
Step-by-step explanation:
A can of popcorn is to be packed in a box for shipping as shown. The can is 18
inches tall and has a radius of 7 inches. The box is 19 inches tall and has a square
base with sides of length 15 inches. All empty space around the can is to be filled
with packing material. How many cubic inches of packing material will be needed?
The amount of packing material is 1506 cubic inches
How to determine the amount of packing material?The given parameters are:
Can
Radius, r = 7 inches
Height, h = 18 inches
Box
Base dimension, l = 15 inches
Height, h = 19 inches
The volume of the can is:
[tex]V = \pi r^2h[/tex]
So, we have:
[tex]V_1 = 3.14 * 7^2 * 18[/tex]
[tex]V_1 = 2769[/tex]
The volume of the box is
[tex]V =l^2h[/tex]
So, we have:
[tex]V_2 =15^2 * 19[/tex]
[tex]V_2 =4275[/tex]
The amount of packing material is;
Amount = V2 - V1
This gives
Amount = 4275 - 2769
Evaluate
Amount = 1506
Hence, the amount of packing material is 1506 cubic inches
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The graph of f(x)= |x| is transformed to g(x) = x + 11-7. On which interval is the function decreasing?
O (-∞, -7)
O (-00,-1)
O (-00, 1)
O (-∞0,7)
Answer:
The interval of the decreasing function is (-∞ , -1) ⇒ g(x)
The interval of the decreasing function is (-∞ , 0) ⇒ f(x)
Step-by-step explanation:
* Lets explain how to solve it
- Decreasing function means a function with a graph that moves
downward as it is followed from left to right.
- For example, any line with a negative slope is decreasing function
- Lets look to the attached graph to understand the meaning of the
decreasing function
∵ f(x) = IxI ⇒ green graph
∵ g(x) = Ix + 1I - 7 ⇒ purple graph
- From the graph f(x) translated 1 unit to the left and 7 units down to
form g(x)
- The domains of f(x) and g(x) are all real numbers {x : x ∈ R}
- The range of f(x) is {y : y ≥ 0}
- The range of g(x) is {y : y ≥ -7}
# For f(x)
- The slope of the green line from (-∞ , 0) is negative
- The slope of the green line from (0 , ∞) is positive
# For g(x)
- The slope of the purple line from (-∞ , -1) is negative
- The slope of the purple line from (-1 , ∞) is positive
∵ The line with negative slope represent decreasing function
∴ The interval of the decreasing function is (-∞ , -1) ⇒ g(x)
∴ The interval of the decreasing function is (-∞ , 0) ⇒ f(x)
pls pls pls helppp
------------------
Answer:
y = 4x^2 + 8x - 12
4(x^2 + 2x - 3) = 0
4(x - 1)(x + 3) = 0
x = 1, -3
Answer:
[tex]\fbox {x-intercepts : (1, 0) and (-3, 0)}[/tex]
[tex]\fbox {Roots : x = 1, x = -3}[/tex]
Step-by-step explanation:
Given :
y = 4x² + 8x - 124 cancels throughout.
y = x² + 2x - 4Solving by quadratic formula :
x = -8 ± √(8)² - 4(4)(-12) / 8x = -8 ± √64 + 192 / 8x = -8 ± √256 / 8x = -8 ± 16 / 8x = -1 ± 2x = 1 and x = -3∴ Hence, the x-intercepts are (1, 0) and (-3, 0). The roots of the equation are 1 and -3.
The set $\{2, 4, 6, \dots, n\}$ contains the positive consecutive even integers from 2 through $n$. When one of the integers from the set is removed, the average of the remaining integers in the set is 28. What is the least possible value of $n$
The least possible value of n is 27.
According to the statement
We have given that the set which is {2,4,6,8.....n} and and one set is removed from them the average of remaining integers is 28.
Then
Firstly set contain n numbers
But after that set contain n-1 numbers after removal of 1 digit from them.
and average value of remaining digit is 28 then 28th term become after removal is
28th term =28*2
28th term = 56.
then
we use the formula to calculate n
n-1 =28
then the value of n become 27.
the least possible value of n is 27.
So, The least possible value of n is 27.
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On a monday a friend says he will meet you again in 34 days. What day of the week will that be?
Answer:
On a Sunday?
Step-by-step explanation:
Please help with the bonus! Thank you:)
a. The function that models the situation is F(t) = 48(1.08)ˣ
b. The price of the stock 6 years from now is $76.17
c. Find the graph in the attachment
d. I receive a dividend of $0.026.
a. Write a function f(t) that models the situation.Since the stock price increases at a rate of 8% every year, and is initially $48, it follows exponential growth.
So, the current price [tex]F(t) = A(1 + r)^{t}[/tex] where
A = price at current moment = $48, r = rate of growth = 8% = 0.08 and t = number of yearsSo, [tex]F(t) = A(1 + r)^{t}[/tex]
[tex]F(t) = 48(1 + 0.08)^{t} \\= 48(1.08)^{t}[/tex]
So, the function that models the situation is F(t) = 48(1.08)ˣ
b. Determine the price of the stock 6 years from now?The price of the stock 6 years from now is gotten when t = 6.
So,
[tex]F(t) = 48(1.08)^{t} \\= 48(1.08)^{6} \\= 48(1.5869)\\= 76.17[/tex]
So, the price of the stock 6 years from now is $76.17
c. Sketch a graph of the price of the function vs time in yearsFind the graph in the attachment
d. BonusSince every quarter, the company pays a dividend of 1.5 %, the rate per year would be r = 1.5 % ÷ 1/4 year = 1.5 % × 4 = 6 % per year.
Since they pay at a rate, r = 6 % = 0.06 of the stock price, F(t) as dividend.
After n years, the dividend is D = (r)ⁿF(t)
= (0.06)ⁿF(t)
So, [tex]D = (0.06)^{t}F(t) \\= (0.06)^{t}[4.8(1.08)^{t}][/tex]
So, after 3 years when t = 3,
[tex]D = (0.06)^{t}[4.8(1.08)^{t}]\\D = (0.06)^{3}[4.8(1.08)^{3}]\\D = 0.000216 \times 48 \times 1.2597\\D = 0.013[/tex]
Since there are 3 shares, the total dividend would be D' = 3D
= 3 × 0.013
= 0.026
So, i receive a dividend of $0.026
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Suppose that the height (in centimeters) of a candle is a linear function of the amount of time (in hours) it has been burning. After 10 hours of burning, a candle has a height of 25 centimeters. After 26 hours of burning, its height is 17 centimeters. What is the height of the candle after 21 hours
If the height of candle after 10 and 26 hours are 25 cm and 17 cm then the height of candle after 21 hours is 19.5 cm.
Given height of candle after 10 hours is 25 cm , height of candle after 26 hours is 17 cm.
We have to find the height of candle after 21 hours.
We have been given two points of linear function (10,25),(26,17).
We have to first form an equation which shows the height of candle after x hours.
let the hours be x and the height be y.
Equation from two points will be as under:
[tex](y-y_{1} )=(y_{2} -y_{1} )/(x_{2} -x_{1} )*(x- x_{1} )[/tex]
(y-25)=(17-25)/(26-10)* (x-10)
y-25=-8/16 *(x-10)
16(y-25)=-8(x-10)
16y-400=-8x+80
8x+16y=480
Now we have to put x=21 to find the height of candle after 21 years.
8*21+16y=480
168+16y=480
16y=480-168
16y=312
y=312/16
y=19.5
Hence the height of candle after 21 hours is 19.5 cm.
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A triangular face of the roof of the garage has two sides
that are √93 feet in length each and a base of length
186 feet. Is the roof a right triangle? Explain the steps
to take to determine whether the roof forms a right
triangle.
Answer:
The roof does form a right triangle.
Step-by-step explanation:
If it is a right triangle then it will obey the Pythagoras Theorem.
Now (√186)^2 = (√93)^2 + (√93)^2
186 = 93 + 93 = 186
So it obeys the theorem and is therefore a right triangle.
Which pair of complex numbers has a real-number product? (1 2i)(8i) (1 2i)(2 – 5i) (1 2i)(1 – 2i) (1 2i)(4i)
The third pair [(1+2i)(1-2i)] have a real number product and other pairs have complex number.
According to the statement
we have given Following are the pairs of the complex number:
(1+2i)(8i),
(1 + 2i)(2 – 5i)
(1+2i)(1-2i) and (1+2i)(4i)
We have to check which pair out of these is a real number product, which means which pair do not contain terms consisting of "i".
So, For this purpose
we have to multiply these pairs with each other.
So,
(1+2i)(8i) = 8i +16(i)^2
And
(1 + 2i)(2 – 5i) = 2 +4i - 5i +10(i)^2
And
(1+2i)(1-2i) = 1 -4(i)^2 -2i +2i = 1+4 = 5
And
(1+2i)(4i) = 4i + 6(i)^2
From these multiplication we found that the third pair have a real number product.
So, The third pair [(1+2i)(1-2i)] have a real number product and other pairs have complex number.
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Select the correct answer.
The variable b varies directly as the square root of c. If b= 100 when c=4, which equation can be used to find other combinations of b and c?
A b= 25c
B.
b = 50√e
OC. b = 200c
OD. b√e 50
-
Reset
Next
The equation in which b varies directly as the square root of c is b = 50 · √c. (Correct choice: B)
What is the equation of the direct variation between two variables?
In this problem we have a case of direct variation between two variables, which is mathematically described by a direct proportionality model, whose form and characteristics are shown below:
b ∝ √c
b = k · √c (1)
Where k is the proportionality constant.
First, we determine the value of the constant of proportionality by substituting on b and c and clearing the variable: (b = 100, c = 4)
k = b / √c
k = 100 / √4
k = 100 / 2
k = 50
Then, the equation in which b varies directly as the square root of c is b = 50 · √c. (Correct choice: B)
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While traveling to Europe, Phelan exchanged 250 US dollars for euros. He spent 150 euros on his trip. After returning to the United States he converts his money back to US dollars. How much of the original 250 US dollars does Phelan now have? Round to the nearest cent.
The computation shows that the amount will be 44.70 Dollars.
How to illustrate the information?The options are missing: Here are the missing options:
A. 44.70 US dollars
B. 73.06 US dollars
C. 136.87 US dollars
D. 140.41 US dollars
For solving this question first we will convert the USD to euros.
The conversion rate we have is:
1 euro = 1.3687 USD
250/1.3687 = 182.655 euros
Now we will subtract it from what he has spent:
= 182.655 - 150
= 32.655 euros
Now we will again convert it back to USD. This will be:
32.655 euros * 1.3687 = 44,695 us dollars
Therefore, the answer is 44.70.
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Two fishing boats leave the same dock at the same time. One boat heads northeast and is travelling at a speed of 15 km/h while the other is travelling northwest at 18 km/h. After 45 minutes, the boats are 14.0 km apart. Assuming that both boats are travelling in straight paths, what is the angle between their paths to the nearest degree?
The angle between their paths to the nearest degree is 68⁰.
Displacement of each boats after 45 minutes
first displacement, a = 15 km/h x (45/60)
first displacement, a = 11.25 km
second displacement, b = 18 km/h x (45/60)
b = 13.5 km
Angle between their paths to the nearest degreec² = a² + b² - 2ab(cosθ)
2ab(cosθ) = a² + b² - c²
cosθ = (a² + b² - c²)/(2ab)
cosθ = (11.25² + 13.5² - 14²) / (2 x 11.25 x 13.5)
cosθ = 0.371
θ = arc cos(0.371)
θ = 68.22 ⁰
Thus, the angle between their paths to the nearest degree is 68⁰.
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what is the temperature in Celsius? (LOOK AT PIC)
Answer:
21
Step-by-step explanation:
(69.8-32)×(5/9)=21
David has kept track of his family’s grocery bills for the past 10 weeks, as shown in the table.
Week 1 2 3 4 5 6 7 8 9 10
Bill ($) 92 106 129 115 100 84 110 156 98 87
Would you choose to use a histogram, a circle graph, or a line graph to display the data? Explain your choice. Then make a display.
The best option that would be used to show the data would be the line graph.
Why the line graph is the bestThe reason I chose the line graph is that it would show us the trend in the data. This is in a way that we would see the periods there was a high bills.
Also the line graph is very simple to understand. The relationship and the changes in the data is easily seen.
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calculate the volume of the composite shape
please please help giving brainliest!!
[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
There are two hemispheres in there with radius 3 cm, so we can consider it as a whole one. and the other shape in between is Cylinder with radius 3 cm and height 4 cm.
Volume of whole ahape = volume of Cylinder + volume of sphere ~
Volume of sphere :
[tex]\qquad \sf \dashrightarrow \: \cfrac{4}{3} \pi {r}^{3} [/tex]
[tex]\qquad \sf \dashrightarrow \: \cfrac{4}{3} \sdot3.14 \sdot {(3)}^{3} [/tex]
[tex]\qquad \sf \dashrightarrow \: (4 )\sdot(3.14) \sdot(9)[/tex]
[tex]\qquad \sf \dashrightarrow \: 113.04 \: \: cm {}^{3} [/tex]
Volume of Cylinder :
[tex]\qquad \sf \dashrightarrow \: \pi {r}^{2} h[/tex]
[tex]\qquad \sf \dashrightarrow \: 3.14 \cdot(3) {}^{2} \sdot4[/tex]
[tex]\qquad \sf \dashrightarrow \: 3.14 \sdot(9) \sdot(4)[/tex]
[tex]\qquad \sf \dashrightarrow \: 113.04 \: \: cm {}^{3} [/tex]
Volume of whole shape :
[tex]\qquad \sf \dashrightarrow \: 113.04 + 113.04 = 226.08 \: \: cm {}^{3} [/tex]
[tex]\qquad \sf \dashrightarrow \: 226.08 \: \: cm {}^{3}[/tex]
Which of the following functions has a vertical asymptote at x=2, a horizontal asymptote at f(x)=1, and a root at x=−1?
A. f(x)=3x+2+1
B. f(x)=−3x−2+1
C. f(x)=3x+2−1
D. f(x)=3x−2+1
There are 3 pieces of glass that are cracked. if a rock is thrown by a lawn mower hits the window, what is the probability, that the rock hits a piece of glass that is cracked?
The chance or chance that the lawn mower will hit a chunk of glass that is already cracked is calculated with the aid of dividing the variety of glasses that are cracked by way of the full quantity of glasses. on this item, the unknown may be calculated through . The solution is, therefore, 0.20.
Opportunity is a measure of the chance of an event to arise. Many occasions cannot be predicted with overall reality. We are able to are expecting only the danger of an event to arise i.e. how likely they're to manifest, using it.
The possibility is the branch of arithmetic regarding numerical descriptions of how in all likelihood an occasion is to arise, or how possibly it's miles that a proposition is actual. The possibility of an occasion various between 0 and 1, where, roughly talking, 0 indicates the impossibility of the event and 1 shows reality.
The probability of an event can be calculated by possibility components via surely dividing the favorable range of effects through the full range of possible outcomes.
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To find the 95% confidence interval for the population standard deviation using the bootstrap method. You repeatedly sample with replacement from the sample, tens of thousands of times. For each sample, you compute the sample standard deviation. What is the next step?.
The next line after computing the sample standard deviation is to; determine the 2.5th and 97.5th percentiles of the values.
How can the 95% confidence interval be determined?It follows from the task content that the 95% confidence interval for the population standard deviation using the bootstrap method in which case, after numerous sampling, the 2.5th and 97.5th percentiles of the standard deviations are determined.
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TRUE OR FALSE: No matter the population distribution from which a sample of size n is taken, we can use the normal distribution to approximate the distribution of the sample mean as long as n is large enough.
Answer:
true
Step-by-step explanation:
mean we show up the distribution
What percentage of rolls were a 6?
Step-by-step explanation:
1 ----> 22 times
2 ----> 16 times
3 ----> 26 times
4 ----> 29 times
5 ----> 1 times
6 ----> 6 times
so , total ----> 100 times
so , percentage of rolls 6 is :-
(6/100 ) × 100%
= 6%
Can someone help me?
Answer:
discriminant = b^2 - 4ac
Step-by-step explanation:
discriminant = b^2 - 4ac
2^2 - 4x 3x2 = 4-24 = 20
Two fishing boats leave the same dock at the same time. One boat heads northeast and is travelling at a speed of 15 km/h while the other is travelling northwest at 18 km/h. After 45 minutes, the boats are 14.0 km apart. Assuming that both boats are travelling in straight paths, what is the angle between their paths to the nearest degree?
The boat speeds of 15 km/h and 18 km/h, directions, and the time of travel of 45 minutes gives the angle between their paths as approximately 68°.
How can the angle between the paths of the boats be found?The given parameters are;
Direction of the first boat = Northeast
Speed of the first boat = 15 km/h
Direction of the second boat = Northwest
Speed of the second boat = 18 km/h
Distance between the boats after 45 minutes = 14.0 km.
45 minutes = 0.75 × 1 hour
Distance traveled by the first boat in 45 minutes, d1, is therefore;
d1 = 15 km/h × 0.75 hr = 11.25 km
For the second boat, we have;
d2 = 18 km/h × 0.75 hr = 13.5 km
Using cosine rule, we have;
14² = 11.25² + 13.5² - 2 × 11.25 × 13.5 × cos(A)
Where A is the angle between the paths of the two boats.
Which gives;
[tex]cos(A) = \frac{361}{972} [/tex]
[tex] A= \mathbf{ arccos\left(\frac{361}{972} \right) }\approx 68^\circ [/tex]
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A coffee shop gives the customer a free cup of coffee after the purchase of 5 cups: a.) industrial marketing program b.) loyalty marketing program c.) product sampling program d.) cooperative marketing program
I cant figure this out
Answer:
x = 2 or x = -1/4
Step-by-step explanation:
Let's solve your equation step-by-step.
4x2−7x−2=0
For this equation: a=4, b=-7, c=-2
4x^2+−7x+−2=0
Step 1: Use quadratic formula with a=4, b=-7, c=-2.
[tex]x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]
[tex]x=\frac{-(-7)\pm\sqrt{(-7)^2-4(4)(-2)} }{2(4)}[/tex]
[tex]x=\frac{7\pm\sqrt{81} }{8}[/tex]
x = 2 or x = -1/4
Answer:
x = 2 or x = -1/4
the height of a can of coke is in 11 cm and the radius is 6 cm calculate the total surface area of the can in cm^3 assuming that the can is a closed cylinder
The total surface area of the can of coke is 641.143 cm².
What is the total surface area of the can?A can of coke has the shape of a cylinder. A cylinder is a three-dimensional object that is made up of a prism and two circular bases. The total surface area of a closed cylinder can be determined by adding the area of all its faces.
Total surface area of the closed cylinder = 2πr(r + h)
Where:
r = radius = 6cm h = height = 11 cm r = pi = 22 / 7Total surface area of the closed cylinder = (2 x 22/7 x 6) x (6 + 11)
(264 / 7) x (17)
37.714 x 17 = 641.143 cm²
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I WILL MARK BRAINLIEST FOR CORRECT ANSWERS WITH AN EXPLANATION!
Solve for x
If you need more information than what’s been provided, please let me know in the comments!
The value of x in the triangle is 9.3
How to find the side x of a triangle?The side x of a triangle can be found as follows:
The triangle ABC is similar to triangle ADE.
Therefore, corresponding sides of similar triangles are in the same ratios.
Hence,
7 / 13 = x / x + 8
cross multiply
7(x + 8) = 13x
7x + 56 = 13x
subtract 7x from both sides of the equation
7x - 7x + 56 = 13x - 7x
56 = 6x
divide both sides by 6
x = 56 / 6
x = 9.33333333333
x = 9.3
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Given: Quadrilateral PAST, TX = AX; TP || AS
Prove: Quadrilateral PAST is a parallelogram.
1) Quadrilateral PAST, TX=AX, [tex]\overline{TP} \parallel\overline{AS}[/tex] (given)
2) [tex]\angle XPT \cong \angle XSA[/tex] and [tex]\angle XTP \cong \angle XAS[/tex] (alternate interior angles theorem)
3) [tex]\triangle TXP \cong \triangle AXS[/tex] (AAS)
4) [tex]\overline{TP} \cong \overline{AS}[/tex] (CPCTC)
5) PAST is a parallelogram (a quadrilateral with two pairs of opposite congruent sides is a parallelogram)
(Adding to the other person's answer)
For the 5th step reason, put this: A quadrilateral is a parallelogram if a pair of opposite sides are parallel and congruent.
It won't work to just say something like the def. of parallelograms.
The perimeter of square JKLM is 48 units.
Square J K L M is shown. The length of J K is x + 3.
What is the value of x?
6
9
12
15
Answer:
9
(Correct On Edgen)