[tex](5i)^2\\\\=25\cdot i^2\\\\=25(-1)\\\\=-25[/tex]
(5i)² can be written in integer form as as -25.
What is a Complex number?The numbers which can be expressed in the form of a + ib, where both 'a' and 'b' are real numbers and 'i' an imaginary number is called complex numbers.
So a complex number has a real part and an imaginary part.
The imaginary number 'i' is called iota and value of i is √-1.
We know the value of i.
i = √-1
i² = -1
(5i)² only has an imaginary part.
∴ (5i)² = 5² i²
= 25 × -1
= -25
Hence we can write (5i)² as -25 in the integer form.
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#SPJ2
HELP PLEASE FOR 20 POINTS!!
Toby is x years old. Seth is y years old. Seth is three years less than twice as old as Toby. Which equation correctly relates the ages of Toby and Seth?
!!!!IF YOU GIVE ME A LINK OR NOT THE ANSWER ILL REPORT!!!!!!
Answer:
B) y = 2x - 3
Step-by-step explanation:
Seth's age = y
Twice as old as Toby = 2x
3 years less = -3
Hope this helps!
The population of bulgaria has been decreasing at an annual rate of 0.89%. if the population of bulgaria was about 7,450,349 people in the year 2005, predict its population in the year 2015.
Answer:
i have uploaded an answer i have found from the internet hope this helps :)
Step-by-step explanation:
A group of friends were working on a student film. They spent all their budget on
equipment and props. They spent $369 on equipment, and 55% of the total budget on
props. What was the total budget for their student film?
Answer:
$820
Step-by-step explanation:
Total = Equipment + Props
T = 369 + 0.55T
0.45T = 369
T = 820
I hope this helps!
(WILL MARK BRAINLIST)
Use the function f(x) = x2 – 2x + 8 and the graph of g(x) to determine the difference between the maximum value of g(x) and the minimum value of f(
2.
Answer:
3 or 4, I am confused
Step-by-step explanation:
I'll assume that f(x) = x2 – 2x + 8 is meant to be f(x) = x^2 – 2x + 8
Find the value of f(x) for x = 2:
f(x) = x^2 – 2x + 8
f(2) = (2)^2 – 2*(2) + 8
f(2) = 4 - 4 + 8
f(2) = 8
=============
From the graph, we can find that g(2) = 11
The differece between g(2) and f(2) is thus:
11 - 8 = 3
3 is not an option, so I wonder if the question is asking for the difference between the absolute maximum of g(x) and f(2). If so, the maximum for g(x) is 12, at x = 3.
This would lead to a difference of 12 - 8, or 4. This is still not an option, so I'm confused. Perhaps you can find my error and find the ciorrect answer, or at least one that appears in the options.
I need help, please.
Answer:
2.5
Step-by-step explanation:
you take 15 and divide it by 6 and that gives you 2.5
Answer: is it D). 2.5 hours?
Step-by-step explanation:
Rodrigo is helping make mashed potatoes for Thanksgiving. He plans to add 4 fluid ounces of heavy cream to his potatoes. If he buys a 1-pint carton, how many fluid ounces will he have left?
copy the given expression on your answer sheet
The figure shows a line graph and two shaded triangles that are similar: A line is shown on a coordinate grid. The x axis values are from negative 15 to positive 15 in increments of 3 for each grid line. The y axis values are from negative 5 to positive 5 in increments of 1 for each grid line. The line passes through the ordered pairs negative 12, negative 4, and 0, 0, and 12, 4. A shaded right triangle is formed so that its hypotenuse is from ordered pair 0, 0 labeled O to negative 6, negative 2 labeled A, one leg is from 0, 0 to 0, negative 2, and the second leg is from 0, negative 2 to negative 6, negative 2. Another shaded right triangle is formed with the hypotenuse from negative 6, negative 2 to negative 9, negative 3 labeled B, one leg is from negative 6, negative 2 to negative 6, negative 3, and the second leg is from negative 9, negative 3 to negative 6, negative 3. Which statement about the slope of the line is true? It is 3 throughout the line. It is fraction 1 over 3 throughout the line. The slope from point O to point A is fraction 1 over 3 time the slope of the line from point A to point B. The slope from point O to point A is three times the slope of the line from point A to point B.
hope this helps
The figure below shows a line graph and two shaded triangles that are similar:
A line is shown on a coordinate grid. The x axis values are from negative 20 to positive 20 in increments of 4 for each grid line. The y axis values are from negative 5 to positive 5 in increments of 1 for each grid line. The line passes through the ordered pairs negative 16, 4, and 0, 0, and 16, negative 4. A shaded right triangle is formed so that its hypotenuse is from ordered pair 0, 0 labeled as O to negative 8, 2 labeled as A, one leg is from 0, 0 to negative 8, 0, and the second leg is from negative 8, 0 to negative 8, 2. Another shaded right triangle is formed with the hypotenuse from negative 8, 2 to negative 12, 3 labeled as B, one leg is from negative 8, 2 to negative 12, 2, and the second leg is from negative 12, 2 to negative 12, 3.
Which statement about the slope of the line is true?
The slope from point O to point A is fraction 1 over 4 times the slope of the line from point A to point B.
The slope from point O to point A is 4 times the slope of the line from point A to point B.
It is fraction negative 1 over 4 throughout the line.
It is −4 throughout the line
Step-by-step explanation:
not my answer found it on a different page but it should help.
It takes 102 pounds of seed to completely plant a 12 -acre field. How many acres can be planted per pound of seed?
Answer:
8.5 acres
Step-by-step explanation:
12 pound = 102
1 pound= 102/12= 8.5
So we can plant 8.5 acre field with 1 pound of seed.
Please give me brainliest . :-)
What is the product? startfraction 2 y over y minus 3 endfraction divided by startfraction 4 y minus 12 over 2 y 6 endfraction two-thirds ten-ninths startfraction 4 y over y minus 3 endfraction startfraction 4 y over y 3 endfraction
The product of the expression [tex]\rm \dfrac{\dfrac{2y}{y-3} }{\dfrac{4y-12}{2y+6}}\\\\\\[/tex] is [tex]\rm \dfrac{(y^2+3y)}{(y^2-6y+9)}\\[/tex].
What is the product?In mathematics, the term 'product' refers to the answer to a multiplication problem.
The product of the given expression is determined in the following steps given below.
[tex]\rm =\dfrac{\dfrac{2y}{y-3} }{\dfrac{4y-12}{2y+6}}\\\\\\=\dfrac{2y}{y-3}\times \dfrac{2y+6}{4y-12}\\\\= \dfrac{2y \times 2y + 2y \times 6}{y(4y-12)-3(4y-12)}\\\\=\dfrac{4y^2+12y}{4y^2-12y-12y+36}\\\\=\dfrac{4y^2+12y}{4y^2-24y+36}\\\\=\dfrac{4(y^2+3y)}{4(y^2-6y+9)}\\\\ =\dfrac{(y^2+3y)}{(y^2-6y+9)}\\[/tex]
Hence, the product of the expression [tex]\rm \dfrac{\dfrac{2y}{y-3} }{\dfrac{4y-12}{2y+6}}\\\\\\[/tex] is [tex]\rm \dfrac{(y^2+3y)}{(y^2-6y+9)}\\[/tex].
To know more about the product click the link given below.
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Answer:
3
Step-by-step explanation:
D on edge 2022
The box plots display the same data for the number of crackers in each snack bag, but one includes the outlier in the data and the other excludes it. 4, 14, 15, 15, 16, 16, 18, 19, 20, 20, 21 number of crackers in each bag, with outlier a number line goes from 0 to 26. the whiskers range from 4 to 21, and the box ranges from 15 to 20. a line divides the box at 16. number of crackers in each bag, without outlier a number line goes from 0 to 26. the whiskers range from 14 to 21, and the box ranges from 15 to 20. a line divides the box at 17. which statement comparing the box plots is true? both the median and the range changed. both the range and the lower quartile changed. both the median and the interquartile range changed. both the interquartile range and the lower quartile changed.
Both the median and the range changed, the correct option is A.
What is the median?Median, in statistics, is the middle value of the given list of data, when arranged in an order.
The data set that contains the outlier is given as:
4, 14, 15, 15, 16, 16, 18, 19, 20, 20, 21
The minimum value of the data is: 4
The median or middle quartile i.e. [tex]\rm Q_2[/tex] is the central tendency of the data and exists in the middle of the data.
The median is: 16
Also, the lower set of data is:
4,14,15,15,16
The lower quartile i.e. [tex]\rm Q_1[/tex] is the median of the lower set of data.
The lower quartile i.e. [tex]\rm Q_1[/tex] = 15
Similarly, the upper set of data is:
18, 19, 20, 20, 21
the upper quartile i.e. [tex]\rm Q_3[/tex] is the median of the upper set of data.
upper quartile i.e. [tex]\rm Q_3[/tex] = 20
Also, the interquartile range is:
[tex]\rm Q_3-Q_1=20-15=5[/tex]
The maximum value of the set is 21.
Range = Maximum value-Minimum value =21 - 4 = 17
As we know that 4 is the outlier of the data as it is the smallest as compared to all the data points.
After removing the outlier the data set is:
14, 15, 15, 16, 16, 18, 19, 20, 20, 21
The minimum value of the set =14
The maximum value of set =21
Range = Maximum value-Minimum value =21-14 = 7
Hence, Both the median and the range changed.
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What is the length of the cylinder's height? Please help
Answer:
Height = 9 cm which means Option C is the answerStep-by-step explanation:
In the question we are given ,
Volume of cylinder = 225π cm³Radius of cylinder = 5 cmAnd , we have to find the height of cylinder .
We know that ,
[tex]
\longrightarrow \pink{ \boxed{Volume \: of \: Cylinder = \pi r {}^{2}h }} \longleftarrow[/tex]
Our solution starts from here :
[tex] \longmapsto \: \pi \: r {}^{2} h = 225\pi[/tex]
Step 1 : Cancelling π with π :
[tex] \longmapsto \: \cancel{\pi} \: r {}^{2} h = 225 \cancel{\pi}[/tex]
Step 2 : Substituting value of radius which is 5 cm in the formula :
[tex] \longmapsto \: (5) {}^{2} \times h = 225[/tex]
[tex] \longmapsto \: 25h = 225[/tex]
Step 3 : Transposing 25 to right hand side :
[tex] \longmapsto \: h = \frac{225}{25} [/tex]
Step 4 : Cancelling 225 by 25 :
[tex] \longmapsto \: \red{\boxed{h = 9 \: cm}}[/tex]
Henceforth , height of cylinder is 9 cm#Keep LearningWhat is formula for Standard Deviation (σ)
In Individual series
☙[tex] \huge \mathfrak{\pink{ \fbox{ \green{S.D}}}}[/tex]
Answer:
[tex]sd = \sqrt{ \frac{ fx {}^{2} }{f} - ( \frac{fx}{f}) {}^{2} } [/tex]
a_n=
a
n
=
\,\,-5+10(n+1)
−5+10(n+1)
Answer:
that makes no sense
Step-by-step explanation:
In a recent survey, 2\3 of the students
said they rode the bus to school.
There were 24 students who took
the survey. How many said that they
rode the bus to school?
Answer:
16
Step-by-step explanation:
2/3 of 24 students
2/3 * 24 = 16
cos^2-sin^2=1/3
so what is cos^4-sin^4
Step-by-step explanation:
[tex]cos ^{2} x - \sin ^{2} x = \frac{1}{3} [/tex]
[tex] \frac{(cos ^{2}x - \sin ^{2} x)(cos ^{2}x + \sin ^{2} x)}{(cos ^{2}x + \sin ^{2} x)} = \frac{1}{3} [/tex]
[tex] \frac{(cos ^{4}x - \sin ^{4} x)}{1} = \frac{1}{3} [/tex]
as cos²x+sin²x=1
Hence
cos⁴x-sin⁴x=1/3
Find the missing angle using the diagram below. The figure is a parallelogram.
(5x + 5)°
135
28
180
90
145
Answer:
145°
Step-by-step explanation:
35+(5x+5)° = 180° (opposite angles sum up to 180°)
35+5x+5 = 180
40+5x = 180
5x= 180- 40
5x = 140
x = 28
therefore, the missing angle = (5x+5)°
= (5×28+5)= 140+5= 145°
Find the length x.
3.5
2.5
0
5
X
Answer:
x
=
3.5
=
2.5
=
0
=
5
X
=
Step-by-step explanation:
Indicate the equation of the given line in standard form. Write the answer in the equation box below.
The line containing the hypotenuse of right triangle ABC where A (–5, 5), B (1, 1), and C (3, 4) are the vertices.
Answer:
x + 8y - 35 = 0.
Step-by-step explanation:
The hypotenuse is the line joining A and C.
Slope = (4-5) / (3 + 5)
= -1/8.
Equation is:
y - 4 = -1/8(x - 3)
y - 4 = -1/8x + 3/8
1/8x + y - 35/8 = 0
x + 8y - 35 = 0
EASY! PLEASE HELP, I AM STUCK
Answer:
A. 16 seconds.
Step-by-step explanation:
Well, it would take him 4 seconds to get 4/16 of the way, or 1/4. So just multply that by 4 and boom, 16 seconds. (yes ik my technique is weird)
Emily practices piano for 2/3 of an hour on Monday and 1/2 hour on Wednesdays. How many hours does Emily spend practicing piano in one week?
Answer:
50 minutes
Step-by-step explanation:
Given:
[tex]\bullet \ \ \text{Monday:} \ \dfrac{2}{3} \times \text{Hour}\\\\\bullet \ \text{Wednesday:} \ \dfrac{1}{2} \times \text{Hour}[/tex]
Since Emily only practiced on Monday and Wednesday, the sum of time on both days is the time Emily practiced on the piano for a week.
[tex]\implies \text{Monday + Wednesday = Total time practiced on piano for a week}[/tex]
Substitute the times in the equation
[tex]\implies (\dfrac{2}{3} \times \text{Hour}) + (\dfrac{1}{2} \times \text{Hour}) = \text{Total time practiced on piano for a week}[/tex]
Simplify the equation
[tex]\implies (\dfrac{2}{3} \times 60 \ \text{minutes}) + (\dfrac{1}{2} \times 60 \ \text{minutes}) = \text{Total time practiced on piano for a week}[/tex]
[tex]\implies (20 \ \text{minutes}) + (30 \ \text{minutes}) = \text{Total time practiced on piano for a week}[/tex]
[tex]\implies \boxed{50 \ \text{minutes} = \text{Total time practiced on piano for a week}}[/tex]
Mary put $2225.50 into an investment at 1.2% for eight years. What will the balance be at the end of eight years? ( what is the total amount of the investment plus interest after 8 years?) round to the nearest hundreth.
interest: $_____
+$2,225.50
=$____(total)
Answer: $2400
Step-by-step explanation:
$2225.50 x 1.2% = $26.71 + $2225.50 = $2252.21 - Year 1
$2252.21 x 1.2% = $27.03 + $2252.21 = $2279.23 - Year 2
$2279.23 x 1.2% = $27.35 + $2279.23 = $2306.58 - Year 3
$2306.58 x 1.2% = $27.68 + $2334.26 = $2334.26 - Year 4
$2334.26 x 1.2% = $28.01 + $2362.27 = $2362.27 - Year 5
$2362.27 x 1.2% = $28.35 + $2362.27 = $2390.62 - Year 6
$2390.62 x 1.2% = $28.69 + $2390.62 = $2419.31 - Year 7
$2419.31 x 1.2% = $29.03 + $2419.31 = $2448.34 - Year 8
Rounded to the nearest 100th = $2400
The data set represents the length, in inches, of some crayons.
4342
3222
2434
Click above the number line to create a dot plot for the data set
Answer:The data set represents the length, in inches, of some crayons.
4342
3222
2434
Step-by-step explanation:
please help me !!!!!!!!!!
[tex]y = - x - 1[/tex]
[tex]y = - 5x - 13[/tex]
Multiply the lower equation by -1:[tex]y = - x - 1[/tex]
[tex] - y = 5x + 13[/tex]
Add the systems:[tex]0 = 4x + 12[/tex]
[tex]4x = - 12[/tex]
[tex]x = \frac{ - 12}{4} = - 3[/tex]
Substitute x=3 in any equation:
[tex]y = - x - 1[/tex]
[tex]y = - ( - 3) - 1[/tex]
[tex]y = 3 - 1 = 2[/tex]
SoLuTiOn PaiR:( -3 , 2 )Ian's house and land have a market price of $225,000 and an assessed value of 55% of that amount. his state has a property tax rate of 0.088. how much does ian pay in property tax every year? a. $19,800 b. $18,900 c. $10,890 d. $8,910
Ian pay $10,890 in property tax every year if the assessed value of 55% of that amount and his state has a property tax rate of 0.088 option (c) is correct.
What is property tax?It is defined as the amount paid by the owner of the property such as land, buildings etc.
We have:
Lan's house and land have a market = $225,000
Assessed value = 55% ⇒ 0.55
Property tax rate = 0.088
We know the formula for property tax is given by:
Property tax = tax rate×assessed value×market value
Put the values in the above formula, we get:
Property tax = 0.088×0.55×225000
= $10,890
Thus, Ian pay $10,890 in property tax every year if the assessed value of 55% of that amount and his state has a property tax rate of 0.088.
Learn more about the property tax here:
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the radius of a circle is 10.8ft the length of a chord is 12ft what is the approximate distance of the chord from the center of the circle
Answer:
9.0 ft (nearest tenth)
Step-by-step explanation:
The chord is the base of an isosceles triangle with sides of the radius.
To calculate the approximate distance of the chord from the center of the circle, we need to find the height of this triangle.
[tex]\sf height=\sqrt{s^2-(\frac{b}{2})^2}[/tex]
(where s is the side length and b is the base length of an isosceles triangle)
Given:
s = radius = 10.8 ftb = chord = 12 ft[tex]\begin{aligned}\implies \sf height & =\sqrt{10.8^2-\left(\frac{12}{2}\right)^2}\\ & = \sqrt{116.64-36}\\ & = \sqrt{80.64}\\ & = 8.979977728...\\ & = 9.0\: \sf ft\:(nearest\:tenth) \end{aligned}[/tex]
Perpendicular=P=?
Apply Pythagorean theorem
P²=H²-B²P²=10.8²-6²P²=80.64P=8.97P≈9ftWhat is the sum of 4x and 7?
A. 4x+7
B. 3x
C. 11x
D. 3
Answer:
A. 4x+7
Step-by-step explanation:
What is the sum of 4x and 7?
Add 4x + 7
A. 4x+7B. 3x
C. 11x
D. 3
Answer:
A. 4x+7
Step-by-step explanation:
4x has x-term as a variable while 7 only remains as a constant. Therefore, you cannot combine both terms as 11x since 4x and 7 are not like term.
Like terms are terms that have same variables and degrees. Some examples are:
2x and x are like term.3x and 8x are like term.Non-like terms are terms that have different variables and degree. Some examples are:
x and y are not like term.x² and x are not like term.Like terms operation:
2x + x = 3x4x + 5x = 9x9z + 2z = 11zNon-like terms operation:
2x + 3y remains as itself.sum of 4 and 7x is 4 + 7x.Let me know if you have any questions.
Can anyone help me with this one to
What type of quadrilateral is this? Select all that apply.
options:
parallelogram
rhombus
rectangle
square
Answer:rhombus
Step-by-step explanation: Its a square but one of the corners is holding it up and all sides are equal it might not seem at first but its an rhombus for sure!
Hope i helped
The anwser is down below
Answer:
B) 2/9
Step-by-step explanation:
2 + 3 + 5 = 10 marbles altogether
One blue is taken out, so it's now 2 and 9 (10-1).
The population standard deviation for the price of the Big Mac is six cents. If
we want to be 82% confident that the sample mean price is within three cents
of the true population mean price, how many randomly selected stores must
be analyzed?
Round your answer up to the whole number, i. E. , 4. 02 stores will be rounded
to 5 stores.
Using the z-distribution, as we have the standard deviation for the population, it is found that 8 stores must be analyzed.
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 population.The margin of error is given by:
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In this problem, we have an 82% confidence level, hence[tex]\alpha = 0.82[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.82}{2} = 0.91[/tex], so the critical value is z = 1.34.
The standard deviation for the population is of [tex]\sigma = 0.06[/tex], and we want a margin of error of M = 0.03, hence we solve for n to find the sample size needed.
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]0.03 = 1.34\frac{0.06}{\sqrt{n}}[/tex]
[tex]0.03\sqrt{n} = 1.34 \times 0.06[/tex]
Simplifying by 0.03:
[tex]\sqrt{n} = 1.34 \times 2[/tex]
[tex](\sqrt{n})^2 = (1.34 \times 2)^2[/tex]
[tex]n = 7.2[/tex]
Rounding up, 8 stores must be analyzed.
More can be learned about the z-distribution at https://brainly.com/question/25890103