Answer:
He did not apply the distributive property correctly for 8(1 + 2i).
Step-by-step explanation:
Find two numbers whose sum is 8 and whose product is 17
Answer:
Step-by-step explanation:
x+y = 8
y = 8-x
xy = 17
x(8-x) = 17
8x - x² = 17
x² - 8x + 17 = 0
Quadratic formula
x = [8 ± √(8² – 4·1·17)] / [2·1]
= [8 ± √(-4)] / 2
= [8 ± 2i] /2
= 4±i
x = 4+i
y = 4-i
A quadratic equation is written in the form of ax²+bx+c. The two numbers whose sum is 8 and whose product is 17 are (4+i) and (4-i).
What is a quadratic equation?A quadratic equation is an equation whose leading coefficient is of second degree also the equation has only one unknown while it has 3 unknown numbers. It is written in the form of ax²+bx+c.
Let the first number be 'a' and the second number be 'b'. Therefore, the sum of the two numbers is,
a+b=8
The product of the two numbers is,
ab=17
b=17/a
now, the equation can be written as,
a+b=8
a+(17/a)=8
a² + 17 = 8a
a²-8a+17=0
a = 4±i
Hence, the two numbers whose sum is 8 and whose product is 17 are (4+i) and (4-i).
Learn more about Quadratic Equations:
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3/4 divided by 1/5 PLEASE ANSWER
Answer:
3.75
Step-by-step explanation:
To make it a fraction form answer, you multiply the dividend numerator by the divisor denominator to make a new numerator.
Furthermore, you multiply the dividend denominator by the divisor numerator to make a new denominator:
To make the answer to 3/4 divided by 1/5 in decimal form, you simply divide the numerator by the denominator from the fraction answer above:
15/4 = 3.75
The answer is rounded to the nearest four decimal points if necessary.
15/4 is an improper fraction and should be written as 3 3/4.
Answer:
3.75
Step-by-step explanation:
Working together, two ants named Aran and Beatrice can build an ant hill in 10 hours. Aran and Charlie can build the ant hill in 12 hours. Beatrice and Charlie can build the ant hill in 15 hours. How long, in hours, will it take to build the ant hill if Aran, Beatrice, and Charlie work together?
Answer:
They complete the hill in 8 hours
Step-by-step explanation:
Equations:
Let's call the variables:
Aran can make build the ant hill in A hours
Beatrice can make build the ant hill in B hours
Charlie can make build the ant hill in C hours
In one hour, Aran makes 1/A of the ant hill.
In one hour, Beatrice makes 1/B of the ant hill.
In one hour, Charlie makes 1/C of the ant hill.
Aran and Beatrice build it in 10 hours, thus:
[tex]\displaystyle \frac{1}{A}+\frac{1}{B}=\frac{1}{10}\qquad\qquad[1][/tex]
Similarly:
[tex]\displaystyle \frac{1}{A}+\frac{1}{C}=\frac{1}{12}\qquad\qquad[2][/tex]
[tex]\displaystyle \frac{1}{B}+\frac{1}{C}=\frac{1}{15}\qquad\qquad[3][/tex]
We need to find the time taken for the three ants to build the anthill:
[tex]\displaystyle \frac{1}{A}+\frac{1}{B}+\frac{1}{C}=[/tex]
Adding [1], [2], and [3]:
[tex]\displaystyle \frac{2}{A}+\frac{2}{B}+\frac{2}{C}=\frac{1}{10}+\frac{1}{12}+\frac{1}{15}[/tex]
Adding the fractions (LCM=60):
[tex]\displaystyle \frac{2}{A}+\frac{2}{B}+\frac{2}{C}=\frac{6}{60}+\frac{5}{60}+\frac{4}{60}[/tex]
[tex]\displaystyle \frac{2}{A}+\frac{2}{B}+\frac{2}{C}=\frac{6+5+4}{60}=\frac{15}{60}=\frac{1}{4}[/tex]
Dividing by 2:
[tex]\displaystyle \frac{1}{A}+\frac{1}{B}+\frac{1}{C}=\frac{1}{8}[/tex]
All ants together make 1/8 of the hill, thus they complete the hill in 8 hours
The distance from the ground to where the ladder is touching the wall is 7
feet. The distance from the wall to the base of the ladder is 4 feet. What is
the length of the ladder?
wall
ladder
Answer:
L=8.062 feet
Step-by-step explanation:
wall=7
distance=4
Pythagorean theorem
7^2+4^2=L^2
49+16=L^2
65=L^2
L=8.062 feet
The required length of the ladder is given as 8.06 feet.
What are Pythagorean triplets?In a right-angled triangle, its sides, such as hypotenuse, perpendicular, and base are Pythagorean triplets.
here,
As mentioned in the question,
perpendicular length = 7, base length = 4 feet,
Let the length of the ladder be x,
Following the Pythagoras theorem,
x² = 7 ² + 4²
x ² = 49 + 16
x² = 65
x = √65
x = 8.06
Thus, the required length of the ladder is given as 8.06 feet.
Learn more about Pythagorean triplets here:
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3(2x - 1) + 7 = -44 solve for x
Answer:
I love algebra anyways
The ans is in the picture with the steps how i got it
(hope this helps can i plz have brainlist :D hehe)
Step-by-step explanation:
answer is x =-8
hope that helps^^
descrease £250 by 15%
Answer:
£212.5
Step-by-step explanation:
15% of 250 = 37.5
250 - 37.5 = 212.5
Elena is designing a paint can with thickness ttt millimeters and height hhh centimeters. She calculates that the thickness of the can in milimeters must be at least 0.1, point, 1 times the height of the can in centimeters in order to withstand pressure. Due to cost constraints, the cost of material used, (0.2 + t+ 0.5h)cents, must be at most 12.2, point, 2 cents. Which system of inequalities best models the relationship between height and thickness?
Answer:
[tex]t \ge h[/tex] and [tex]t + 0.5h \le 12.0[/tex]
Step-by-step explanation:
Given
[tex]t= thickness[/tex]
[tex]h =height[/tex]
From the first statement, we have that:
[tex]t\ mm \ge 0.1 * h\ cm[/tex]
Convert mm to cm
[tex]t\ * 0.1*cm \ge 0.1 * h\ cm[/tex]
[tex]t\ *0.1 \ge 0.1 * h[/tex]
Divide both sides by 0.1
[tex]t \ge h[/tex]
From the second statement, we have that:
[tex]Cost \le 12.2[/tex]
Substitute 0.2 + t + 0.5h for Cost
[tex]0.2 + t + 0.5h \le 12.2[/tex]
Collect Like Terms:
[tex]t + 0.5h \le 12.2-0.2[/tex]
[tex]t + 0.5h \le 12.0[/tex]
So, the inequalities are:
[tex]t \ge h[/tex] and [tex]t + 0.5h \le 12.0[/tex]
Answer: it's a, the answer
Step-by-step explanation:
Graphing linear equation using a table [ x = - 1 ]
• • • • • • • • • • • • • • • • • • • • • • • • • • • •
(I only need help in filling the table, aswell as the slope and y-intercept, thanks! ^u^)
0
1
2
3
4
5
take x 1 so 1-1
2-1..........
What is OB'?
1.5 units
3 units
4.5 units
6 units
Answer: it's b on edge
Step-by-step explanation:
Find the difference.
4-(-8)=
Answer:
4
Step-by-step explanation:
subtract negative 4 by negative 8
The lifetimes of a certain brand of light bulbs are known to be normally dsitributed with a mean of 1700 hours and standard deviation of 400 hours. A random sample of 64 of these light bulbs is taken. The probability is 0.20 that the sample mean lifetime is more than how many hours?
A. 1652.
B. 1725.
C. 1752.
D. 1670.
Answer:
1742 hours
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Single light:
Mean of 1700 hours and standard deviation of 400 hours, which means that [tex]\mu = 1700, \sigma = 400[/tex]
Sample of 64:
This means that [tex]n = 64, s = \frac{400}{\sqrt{64}} = 50[/tex]
The probability is 0.20 that the sample mean lifetime is more than how many hours?
This is the 100 - 20 = 80th percentile, which is X when Z has a pvalue of 0.8. So X when Z = 0.84
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]0.84 = \frac{X - 1700}{50}[/tex]
[tex]X - 1700 = 50*0.84[/tex]
[tex]X = 1700 + 50*0.84[/tex]
[tex]X = 1742[/tex]
What is the difference between the greatest and the smallest rational numbers
given below?
7/15,11/20,2/5,12/25
Answer:
The difference between the greatest and smallest rational number [tex]=\frac{3}{20}[/tex]
Step-by-step explanation:
Step(i):-
Given that the rational numbers
[tex]\frac{7}{15} , \frac{11}{20} ,\frac{2}{5} ,\frac{12}{25}[/tex]
we have to find that the difference between the greatest and the smallest rational numbers
solution:-
The greatest rational number = [tex]\frac{11}{20}[/tex]
Convert into decimal = 0.55
The smallest rational number = [tex]\frac{2}{5}[/tex]
Convert into decimal = 0.4
The difference between the greatest and smallest rational number
[tex]= \frac{11}{20} - \frac{2}{5}[/tex]
= [tex]\frac{11-8}{20}[/tex]
[tex]=\frac{3}{20}[/tex]
Final answer:-
The difference between the greatest and smallest rational number [tex]=\frac{3}{20}[/tex]
I need the answers ASAP
Answer:
Image attached
Step-by-step explanation:
Just wandering, no hate, you can post answers on brainly but can't read an analog clock.
BTW I've got one in my house
Name:
1. Dane deposited $5,000 in a savings account. The amount in the account after 1, 2, and 3 years is shown
below.
$5,240, $5,480, $5,720, ...
Which function represents the total amount in her account at the end of t years?
A. M(t) = 5000 + 2400
B. M(t) = 5240 +2400
C. M(t) = 5000t + 240
D. M(t) = 5240t + 240
Answer:
I dont kn0w try g00gle searches
Answer:
B. M(t)= 5240+240t
Step-by-step explanation:
cause
find the logarism of 6395
Answer:
this is clear that answer
Solve the equation x² = 5. (must show equality properties in work so I can earn full credit)
A. x = 5
B. x = 25
C. x = √5
D. x = ±√5
I'm so confused what is the answer plz?
Answer:
option b .
yes, by SAS.
.............
Write the equation of the line in fully simplified slope-intercept form???
Answer:
[tex]y = - \frac{4}{5} x + 3[/tex]
Step-by-step explanation:
[tex]b = 3[/tex]
[tex] - 2 = 4a + 3[/tex]
[tex]a = - \frac{4}{5} [/tex]
Children 4 years old or younger can ride the train for free. Write an inequality that expresses who can ride the train for free.
x<=4
x is less than or equal to four
children less than or equal to four can ride the train for free
Solve the equation.
-6p=48
Answer:
p=-8
Step-by-step explanation:
A negative multiplied by a negative is a positive.
After lunch, you see the bumper cars and want to ride them. Here’s what the sign says:
Bumper Cars:
6 minutes: 8 tickets
8 minutes:12 tickets
Which one gives you more time for your money?
Please help me!!!!!!!!!!
If ABCD is an isosceles trapezoid what is the value of X?
Write the percent as a fraction and as a decimal.
5% tax
Answer:
The answer would be 0.05
Step-by-step explanation:
This is because it is PER Cent so 5% is 0.05 of 1
Answer:
1/20 and 0.05
Step-by-step explanation:
What multiplication equation is represented by this picture? Explain.
Answer:
Step-by-step explanation:
Each circle represents : [tex]\frac{3}{5}[/tex] and 5 circles
5 * [tex]\frac{3}{5}[/tex]
Answer
Step-by-step explanation:
is Each circle represents : 3/2 and 5 circles
if you have 60 G of fluorescent powder and 124 cups of medium base paint, and the ratio is one part powder to five parts paint how many cups of paint can I make with fluorescent powder
Answer:
1.268 cups
Step-by-step explanation:
60 G=0.2536 cups (I found a G to cup converter on the internet)
0.2536x5=1.268 cups of paint it would mix with at a 1 to 5 ratio
please help, I'll give the correct answer brainliest.
find c and d. show your work.
9514 1404 393
Answer:
c = 6√2
d = 12
Step-by-step explanation:
The sides of any isosceles triangle (opposite the congruent angles) are congruent. Hence c = 6√2.
The hypotenuse of an isosceles right triangle is √2 times the side length, so ...
d = c√2 = (6√2)(√2) = 6·2
d = 12
__
If you don't believe that, you can always use the Pythagorean theorem to find d:
d^2 = (6√2)^2 +c^2
d^2 = 72 +72 . . . . . . . . . since c=6√2
d = √144
d = 12
4/5 ÷ 1/5 = ?????????
Answer:
4
Step-by-step explanation:keep change flip 4/5 x 5/1 = 20/5= 4
A homeowner is building a flower bed in the backyard. He plans to put a layer of fertilizer over the entire flower bed.The diagram shows the flower bed and its dimensions in feet.
4w2 + 3w - 1
5w - 2.
Which expression represents the area in square feet that the homeowner will cover with fertilizer?
Answer:
The answer is 4w^2 + 8w - 3
Step-by-step explanation:
Umm I hope it's right
Which value for p makes the expressions 9p - 5 and (3 + p) 5 equivalent?
7
6
4
5
1
10
Answer:
numbers dont do into math please move this to englash
Step-by-step explanation:
it posted Wong