[tex]~~~~x^4+4x^3 +4x^2 +4x +3=0\\\\\implies x^4 +x^3 +3x^3 + 3x^2 +x^2+x+3x+3=0\\\\\implies x^3(x+1) +3x^2(x+1) + x(x+1) +3(x+1)=0\\\\\implies (x+1) (x^3+3x^2 +x +3)=0\\\\\implies (x+1) \textbf{[} x^2(x+3)+(x+3)\textbf{]}=0\\\\\implies (x+1)(x+3)(x^2+1)=0\\\\\implies x = -1 ,~~ x = -3,~~ x = \pm i[/tex]
A cylinder has a radius 3 inches and height 5 inches. A cone has the same radius and height. What is the volume of the cylinder
✰ Given Information :-
⠀
A cylinder with following dimensions :
Radius = 3 inchesHeight = 5 inches⠀
✰ To Find :-
⠀
The volume of the cylinder⠀
✰ Formula Used :-
⠀
[tex] \qquad \star \: \underline{ \boxed{ \purple{\sf Volume_{Cylinder} = \pi {r}^{2} h}}} \: \star[/tex]
⠀
Where,
r = radius h = height⠀
✰ Solution :-
⠀
Putting the values in the formula, we get,
⠀
[tex] \sf \longrightarrow Volume=3.14 \times {(3)}^{2} \times 5 \\ \\ \\ \sf \longrightarrow Volume=3.14 \times 45 \: cm \: \: \: \: \: \\ \\ \\ \sf \longrightarrow \underline{ \boxed{ \green{ \frak{Volume= {141 .3 \: cm}^{3} }}}} \: \star \: \: \: \: \: \\ [/tex]
⠀
Thus, the volume of the cylinder is 141.3 cm³.
⠀
[tex] \underline{ \rule{230pt}{2pt}} \\ \\ [/tex]
Step-by-step explanation:
As it is given that, a cylinder has radius 3 inches and height 5 inches and we are to find the volume of the cylinder, also a extra information is given that is a cone has the same radius and height.
[tex] \: [/tex]
We know,
[tex]{ \longrightarrow\qquad{\frak {\pmb{Volume_{(cylinder) } = \pi {r}^{2}h }}}} \\ \\[/tex]
Where,
r is the radius of the cylinder.h is the height of the cylinder.Here, we will take the value of π as 3.14 approximately .[tex] \: [/tex]
Now, we will substitute the given values in the formula :
[tex] \: [/tex]
[tex]{ \longrightarrow\qquad{\sf {\pmb{Volume_{(cylinder) } = 3.14 \times ( {3})^{2} \times 5 }}}} \\ \\[/tex]
[tex]{ \longrightarrow\qquad{\sf {\pmb{Volume_{(cylinder) } = 3.14 \times 9 \times 5 }}}} \\ \\[/tex]
[tex]{ \longrightarrow\qquad{\sf {\pmb{Volume_{(cylinder) } = 3.14 \times 45 }}}} \\ \\[/tex]
[tex]{ \longrightarrow\qquad{\frak {\pmb{Volume_{(cylinder) } = 141.3 }}}} \\ \\[/tex]
Note :
Answer might be different if we take the value of π as 22/7 .You would use a back-to-back stem-and-leaf plot when you want to analyze the heights of the boys on the basketball team.
False
True
Answer:
true because there are going to be many heights already
Step-by-step explanation:
i it's true
this is because already there will be
so many heights
The whole number m is a term in an arithmetic sequence with common difference 2. Show that the sum of the term m and the next two terms is a multiple of 3, no matter what the value of m.
Answer:
S
ThenSn=n(a1+an)2Sn=n(a1 + an)2 , where nn is the number of terms, a1a1 is the first term and anan is the last term. The sum of the first nn terms of an arithmetic sequence is called an arithmetic series .
Step-by-step explanation:
a=[4 -7 3 -2] find the determinant
Answer:
13
Step-by-step explanation:
[tex]\text{determinant of A} =\begin{vmatrix}4&-7\\ 3&-2\end{vmatrix}[/tex]
[tex]\text{determinant of A} =\left( 4\times \left( -2\right) \right) -\left( 3\times \left( -7\right) \right)[/tex]
[tex]\text{determinant of A} =-8+21=13[/tex]
pls help me uwuwuwuuwuwuww
Answer:
128
6
12
48
Step-by-step explanation:
Calculate the magnitude of :
1.1.
[tex] \alpha [/tex]
Answer:
135°
have a nice day
hope it helps
17,18,22,31,47, ... what's next
Answer:
Step-by-step explanation:
First establish the pattern. Notice the sequence of numbers below. These are the ones making up the pattern. You can go as far as 47 - 31 which gives 16 which is 4^2.
18 -17 = 1 = 1^2
22 - 18 = 4 = 2^2
31 - 22 = 9 = 3^2
47 - 31 = 16 = 4^2
=================
Call the number comming x. 47 taken from x must give 5^2 which is 25
x - 47 = 5^2
x - 47 = 25 Add 47 to both sides
x -47 + 47 = 25 + 47
x = 72
=================
72 -47 = 25 which is 5^2.
Answer: The next number is 72
Solve the equation.
If necessary:
Combine Terms
5
3-4x=3 = -9x32
Axt/
6
Apply properties:
Add
Subtract
Multiply Divide
To start over:
Reset
I need to know how the answer
Answer:
A=1/2(b*h)
A=(3x2*4xy)
A=1/2(12x3y)
A=6x3y
so the answer is option (d)
What is the value of the expression below when x=4 and y=3?
The question is 5x to the 3rd power plus 4y to the 3rd power
[tex]x = 4\\y = 3[/tex]
Question is [tex]5x^3 + 4y^3[/tex]
We know what [tex]x[/tex] and [tex]y[/tex] are.
[tex]5x^3 + 4y^3 = 5 \times 4^3 + 4 \times 3^3\\= 5 \times 64 + 4 \times 27\\= 320 + 108\\= 428[/tex]
A factory produces 72 pairs of
legging 6 minutes. At the same rate,how many pairs of leggings will the factory produce in 8 minutes?
Answer:
96 pairs
Step-by-step explanation:
72 pairs / 6 minutes will simplify to 12 pairs per minute.
Then (12 pairs / minute)(8 minutes) =
96 pairs
15<96–q
what is the value of q
Answer: q < 81
Step-by-step explanation:
isolate q
15 < 96 - q
-81 < -q
divide by negative 1 but flip inequality because you are dividing by a negative
81 > q so
q < 81
Help asap for brainliest
Answer:
282 ft
Step-by-step explanation:
Area of 2 triangles = 6+6
= 12 ft
Area of 3 rectangles = 90+90+90
= 270 ft
therefore
the surface area = 12 + 270
= 282 ft
I think that I am right
Which statement(s) are true?
No event can be impossible.
No event can be certain.
The more unlikely an event, the closer it is to impossible.
The more likely an event, the closer it is to certain.
Answer:
no event can be impossible
Answer: no event can be impossible
Step-by-step explanation:
Slope:
Y-intercept=
Equation Y=
Answer:
Slope = -3
Y-intercept = (0,-4)
Equation = -3x-4
Step-by-step explanation:
Slope is [tex]\frac{rise}{run}[/tex] or [tex]\frac{Y2-Y1}{X2-X1}[/tex]. Apply this from the data in the table, for example:
[tex]\frac{5-8}{-3-(-4)} = \frac{rise}{run}\\ \frac{-3}{1} = \frac{rise}{run}\\\\-3= \frac{rise}{run}[/tex]
Y-intercept is located where x=0. If we look at the table, we will find that when x=0, y=-4. If we turn it into a (x,y) point format, we will get (0,4).
The function can be found using the Y-intercept and the slope. Since at x=0, y=-4, we know that the function must have a -4 in it, therefore: [tex]y = x-4[/tex]. Our function decreases by 3 for every positive x and increases by 3 for every negative x, therefore [tex]y = -3x-4[/tex].
Which of the
following graphs
satisfies these
inequalities?
x- y< 2.
x + 2y > 8
y<4
A
B
2
f
B
is the answer. Good luck!!
the day before yesterday is 2 days after Sunday what day is today
Thursday
Explanation:
Two days after Sunday is Tuesday
Tuesday would be the day before yesterday (Wednesday)
So today is Thursday
Answer:
The Day before the day before yesterday was two days after the day before my birthday. Today is Thursday. The following steps can be used in order to determine the day on birthday: Step 1 - Remember today is Thursday according to the given data. Step 2 - Now, the Day before the day before yesterday is Monday. Step 3 - The two days before Monday is Saturday. Step 4 - And the day of the birthday is after Saturday that is Sunday
Step-by-step explanation:
A chemist has three different acid solutions.
The first solution contains 15 % acid, the second contains 30 % acid, and the third contains 50 %
acid,
She created 78 liters of a 35 % acid mixture, using all three solutions. The number of liters of 50 %
solution used is 3 times the number of liters of 30 % solution used.
How many liters of each solution was used?
Answer:
Its 50 and it can reach 60
june uses 12eggs to make cupcakes she uses 4eggs for each batch of cupcake
Answer:
12/4=3
Step-by-step explanation:
12/4
Answer:
3 batches
Step-by-step explanation:
Assuming that you are asking for how many batches she can make, we can divide 12 by 4 to find the number of batches.
which equation is equivalent to 3(2x - 5) = 4 (x + 3) ?
Step-by-step explanation:
3(2x - 5) = 4(x+3)
Distribute. Multiply 3 by 2x so the product keeps the variable, multiply 3 by 5 and keep the subtraction symbol. Multiply 4 by x so it would be 4x, multiply 4 by 3
(6x-5=4x+12) Answer
57771298
How would the mode change if the number 5 were added to the set?
Answer:
The mode of this list of numbers would still be [tex]7[/tex] (the mode did not change) after "[tex]5[/tex]" was added to the list.
Step-by-step explanation:
The mode of a list of elements is the member that appears the most frequently.
The original list of numbers in this question [tex][5,\, 7,\, 7,\, 7,\, 1,\, 2,\, 9,\, 8][/tex] included the following members:
[tex]\begin{array}{c|c} \text{Member} & \text{Number of appearances} \\ \hline\hline 1 & 1 \\\hline 2 & 1 \\\hline 5 & 1\\\hline 7 & 3 \\\hline 8 & 1 \\\hline 9 & 1 \\\end{array}[/tex]
[tex]\begin{array}{c|c} \text{Member} & \text{Number of appearances} \\ \cline{1-2}\\[-1em]\cline{1-2} 1 & 1 \\\cline{1-2} 2 & 1 \\\cline{1-2} 5 & 1\\\cline{1-2} 7 & 3 \\\cline{1-2} 8 & 1 \\\cline{1-2} 9 & 1 \\\end{array}[/tex].
The member "[tex]7[/tex]" appeared more often than any other member of this list. Thus, the mode of the original list was "[tex]7\![/tex]".
Adding "[tex]5[/tex]" to the original list would give the list [tex][5,\, 7,\, 7,\, 7,\, 1,\, 2,\, 9,\, 8,\, 5][/tex]. Members of this list are:
[tex]\begin{array}{c|c} \text{Member} & \text{Number of appearances} \\ \hline\hline 1 & 1 \\\hline 2 & 1 \\\hline 5 & 2\\\hline 7 & 3 \\\hline 8 & 1 \\\hline 9 & 1 \\\end{array}[/tex]
[tex]\begin{array}{c|c} \text{Member} & \text{Number of appearances} \\ \cline{1-2}\\[-1em]\cline{1-2} 1 & 1 \\\cline{1-2} 2 & 1 \\\cline{1-2} 5 & 2\\\cline{1-2} 7 & 3 \\\cline{1-2} 8 & 1 \\\cline{1-2} 9 & 1 \\\end{array}[/tex].
The member "[tex]7[/tex]" still appeared more often than any other member of this list. Thus, the mode of the new list would also be "[tex]7\![/tex]".
Question 3
Compute the probability of Susan turning 44 years old (event A), given that Carl has reached the age of 44 (event B).
Answer:
Events A and B are independent of each other, so P(B∣A)=P(B)=0.95726.
Explanation -
I got this answer from Plato.
Data from a sample of 576 people in a city was used to estimate the mean monthly bill
paid by city residents for internet service to be $45 with a standard deviation of $0.48.
Enter a number in the box to complete the sentence below.
S
Use the formula M=1.96 x to calculate the margin of error for a 95% confidence
VN
interval, to the nearest hundredth, $
dollars.
Using the z-distribution, it is found that the margin of error for a 95% confidence interval is of $0.04.
What is a z-distribution confidence interval?The confidence interval is:
[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.z is the critical value.n is the sample size.[tex]\sigma[/tex] is the standard deviation for the sample.The margin of error is given by:
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In this problem, the values of the parameters are:
[tex]z = 1.96, \sigma = 0.48, n = 576[/tex].
Hence, the margin of error, in dollars, is given by:
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]M = 1.96\frac{0.48}{\sqrt{576}}[/tex]
M = 0.04.
More can be learned about the z-distribution at https://brainly.com/question/25890103
It is estimated that 60% of U.S. households subscribe to cable TV. You would like to verify this statement for your class in mass communications. If you want your estimate to be within 5 percentage points, with a 95% level of confidence, how many households should you sample
Using the z-distribution, as we are working with a proportion, it is found that you should sample 577 households.
What is a confidence interval of proportions?A confidence interval of proportions is given by:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which:
[tex]\pi[/tex] is the sample proportion.z is the critical value.n is the sample size.The margin of error is given by:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In this problem, we have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
In this problem, the estimate is of [tex]\pi = 0.6[/tex], and we want a margin of error of M = 0.05, hence we solve for n to find the sample size.
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.05 = 1.96\sqrt{\frac{0.6(0.4)}{n}}[/tex]
[tex]0.05\sqrt{n} = 1.96\sqrt{0.6(0.4)}[/tex]
[tex]\sqrt{n} = \frac{1.96\sqrt{0.6(0.4)}}{0.05}[/tex]
[tex](\sqrt{n})^2 = \left(\frac{1.96\sqrt{0.6(0.4)}}{0.05}\right)^2[/tex]
[tex]n = 576.24[/tex]
Rounding up, you should sample 577 households.
More can be learned about the z-distribution at https://brainly.com/question/25890103
What is the surface area of a sphere with a radius of 15 cm?
Answer:
2827.43 cm^2
Step-by-step explanation:
Hope this helped! <3 Have a great day :) Brainliest please?
how many real numbers solutions does the equation have
Answer:
this would be 2
Step-by-step explanation:
[tex]1. ) \: \frac{4}{5} + \frac{2}{3} = [/tex]
[tex]2. )4 \: \frac{8}{12} + 3 \frac{1}{6} =[/tex]
[tex]3. \frac{13}{17} + \frac{3}{4} = [/tex]
[tex]4. 23 \frac{1}{5} - 7 \frac{1}{4} =[/tex]
[tex] \\ [/tex]
With Solution!!
Answer:
1. 4/5+2/3=?
The fractions have unlike denominators. First, find the Least Common Denominator and rewrite the fractions with the common denominator.
LCD(4/5, 2/3) = 15
Multiply both the numerator and denominator of each fraction by the number that makes its denominator equal the LCD. This is basically multiplying each fraction by 1.
(45×33)+(23×55)=?
Complete the multiplication and the equation becomes
12/15+10/15=?
The two fractions now have like denominators so you can add the numerators.
Then: 12+10/15=22/15
This fraction cannot be reduced. The fraction
22/15 is the same as 22÷15
Convert to a mixed number using long division for 22 ÷ 15 = 1R7, so
22/15=17/15
Therefore: 4/5+2/3=17/15
Solution by Formulas Apply the fractions formula for addition, to 4/5+2/3 and solve
(4×3)+(2×5)/5×3
=12+10/15
=22/15 Convert to a mixed number using long division for 22 ÷ 15 = 1R7, so 22/15=17/15 Therefore:4/5+2/3=1 7/15
Step-by-step explanation:
Answer:
See below.
Step-by-step explanation:
1.
4/5 + 2/312/15 + 10/1522/15 or 1 7/152.
4 8/12 + 3 1/64 2/3 + 3 1/614/3 + 19/628/6 + 19/647/6 or 7 5/63.
13/17 + 3/452/68 + 51/68103/68 or 1 35/684.
23 1/5 - 7 1/4116/5 - 29/423.2 - 7.2515.95319/20 or 15 19/20I need extra help. Someone
Answer:
C. tanS = 5/12, tanT = 12/5
Step-by-step explanation:
Tangent has NOTHING to do with hypotenuse, do we can easily eliminate answer choices involving 13, the hypotenuse. For angle S, the opposite side measures 5 and the adjacent side measures 12. For angle T, the opposite side measures 12 and the adjacent side measures 5. See this below algebraically
tanθ = opp/adj
tanS = 5/12
tanT = 12/5
I hope this helps!
5 chocolate bars cost $5.75
2 chocolate bars and 3 packets of sweets cost $7.85 work out the cost of one packet of sweets
Answer:
The answer is $1.85
Step-by-step explanation:
Given;The cost of 5 chocolate bars = $5.75The cost of 2 chocolate bars and 3 packets of sweets = $7.85To Find;The cost of one packet of sweets.Now, we know that the cost of 5 chocolate bars are $5.75.
For 1 chocolate bar
5.75 ÷ 5 = $1.15
Here, we get the price of 1 chocolate bar
So, the cost of 2 chocolate bars and 3 packets of sweets are $7.85.
2 × chocolate bar = 2 × (1.15) = $2.3
Now, we want to find only the cost of one packet of sweets.
So,
7.85 – 2.3 = $5.55
3 packets of sweets cost $5.55
For 1 packets of sweets
5.55 ÷ 3 = $1.85
Thus, The cost of one packet of sweets = $1.85
Use the given information about angles ABC and DBC to solve for x and the measures of each of the angles. ABC andDBC are supplementary angles. mABC = 3x + 19 and mDBC = 7x - 9. Solve for x and the measures ofABC andDBC. Complete your work in the space provided. Include your calculations and the steps necessary to solve for the measures ofABC andDBC.
Answer:
Below in bold.
Step-by-step explanation:
Supplementary angles add up to 180 dgrees, so we have the equation:
3x + 19 + 7x - 9 = 180
10x + 10 = 180
10x = 180 - 10
10x = 170
x = 17.
So m <ABC = 3(17) + 19 = 70 degrees
and m < DBC = 7(17) - 9 = 110 degrees.
Answer:
3x + 19+7x-9=180
10x+10=180
10x=180-10
10x=170
x =17