Answer:
x = -4 + 3 i or x = -4 - 3 i
Step-by-step explanation:
Solve for x:
(x + 4)/(x + 5) = (x - 5)/(2 x)
Hint: | Multiply both sides by a polynomial to clear fractions.
Cross multiply:
2 x (x + 4) = (x - 5) (x + 5)
Hint: | Write the quadratic polynomial on the left hand side in standard form.
Expand out terms of the left hand side:
2 x^2 + 8 x = (x - 5) (x + 5)
Hint: | Write the quadratic polynomial on the right hand side in standard form.
Expand out terms of the right hand side:
2 x^2 + 8 x = x^2 - 25
Hint: | Move everything to the left hand side.
Subtract x^2 - 25 from both sides:
x^2 + 8 x + 25 = 0
Hint: | Using the quadratic formula, solve for x.
x = (-8 ± sqrt(8^2 - 4×25))/2 = (-8 ± sqrt(64 - 100))/2 = (-8 ± sqrt(-36))/2:
x = (-8 + sqrt(-36))/2 or x = (-8 - sqrt(-36))/2
Hint: | Express sqrt(-36) in terms of i.
sqrt(-36) = sqrt(-1) sqrt(36) = i sqrt(36):
x = (-8 + i sqrt(36))/2 or x = (-8 - i sqrt(36))/2
Hint: | Simplify radicals.
sqrt(36) = sqrt(4×9) = sqrt(2^2×3^2) = 2×3 = 6:
x = (-8 + i×6)/2 or x = (-8 - i×6)/2
Hint: | Factor the greatest common divisor (gcd) of -8, 6 i and 2 from -8 + 6 i.
Factor 2 from -8 + 6 i giving -8 + 6 i:
x = 1/2-8 + 6 i or x = (-8 - 6 i)/2
Hint: | Cancel common terms in the numerator and denominator.
(-8 + 6 i)/2 = -4 + 3 i:
x = -4 + 3 i or x = (-8 - 6 i)/2
Hint: | Factor the greatest common divisor (gcd) of -8, -6 i and 2 from -8 - 6 i.
Factor 2 from -8 - 6 i giving -8 - 6 i:
x = -4 + 3 i or x = 1/2-8 - 6 i
Hint: | Cancel common terms in the numerator and denominator.
(-8 - 6 i)/2 = -4 - 3 i:
Answer: x = -4 + 3 i or x = -4 - 3 i
Marcus is shopping for pants. The available styles are boot cut (B), skinny (S), and relaxed fit (R). Make an organized list to show all possible outcomes if he buys two new pairs of pants.
Answer:
list in the explanation
Step-by-step explanation:
BOOT x2
SKINNY x2
RELAXED x2
BOOT, SKINNY
BOOT, RELAXED
SKINNY, BOOT
SKINNY, RELAXED
RELAXED, BOOT
RELAXED, SKINNY
The solution set is given by Set A = { BB , SS , RR , BS , BR , SR } , where B , S and R are boot cut (B), skinny (S), and relaxed fit (R) respectively
What is union and intersection of sets?The union of two sets A and B is the set of all those elements which are either in A or in B, i.e. A ∪ B, whereas the intersection of two sets A and B is the set of all elements which are common. The intersection of these two sets is denoted by A ∩ B
The union of two sets is a new set that contains all of the elements that are in at least one of the two sets
The intersection of two sets is a new set that contains all of the elements that are in both sets
Given data ,
Let the set be represented as A
Now , the equation will be
Marcus is shopping for pants and the available pants are boot cut (B), skinny (S), and relaxed fit (R)
He wants to buy 2 pair of pants , and the possible ways of 2 pants are
Set A = { BB , SS , RR , BS , BR , SR }
So , the total number of elements in set A = 6 pairs
Therefore , the value of A is 6 pairs
Hence , the set A is { BB , SS , RR , BS , BR , SR }
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A driver of a car stopped at a gas station to fill up his gas tank. He looked at his watch, and the time read exactly 3:40 p.m. At this time, he started pumping gas into the tank. At exactly 3:44, the tank was full and he noticed that he had pumped 6 gallons.
Answer:
3.625 gpm
Step-by-step explanation:
Given: D is the midpoint of AB; E is the midpoint of AC.
Prove: DE BC
y
Complete the missing parts of the paragraph proof.
Proof:
To prove that DE and BC are parallel, we need to show
that they have the same slope.
slope of DE = 12-11=_C-C
X2 - x1 a + b - b
A(2b, 2c)
D(b, c)
Ela + bc)
slope of BC =
B(0,0)
C(2a, 0)
Therefore, because
DE 1 BC.
Answer:
The lines DE and BC have the same slope, therefore the two lines, DE and BC, are parallel
Step-by-step explanation:
To prove that DE is parallel to BC, we have;
The slope, m of the lines DE and BC are found from the following equation;
[tex]Slope, \, m =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Where;
(x₁, y₁) and (x₂, y₂) = (b, c) and (a + b + c) for DE, we have;
[tex]Slope, \, m =\dfrac{c - c}{a + b-b} = 0[/tex]
Where we have (x₁, y₁) and (x₂, y₂) = (0, 0) and (2a, 0) for BC, we have;
[tex]Slope, \, m =\dfrac{0 - 0}{2a-0} = 0[/tex]
Therefore, because the lines DE and BC have the same slope, the two lines DE and BC are parallel.
Answer:
slope of DE = 0
slope Bc = 0
slopes are =
Step-by-step explanation:
Jack bought a car for $50,000. He spent $5000 on repairs. He sold the car at a profit of $5000. At what price did he sell the car.
Answer:$60,000
Step-by-step explanation:
If he bought it for $50,000 and then spent $5,000 on repairs then he spent a total of $55,000. For a profit of $5,000 he would need to sell it for $60,000 Because
60,000 - 55,000 = 5,000
18. The outside temperature changed - 14 °F over 4 hours. If the temperature changed the same
amount each hour, what was the change in temperature each hour?
The temperature change each hour was
°F.
Answer:
-3.5 °F
Step-by-step explanation:
If the temperature change was the same each hour, we can find the change each hour by dividing -14 by 4.
-14/4= -3.5
= -3.5 °F
I need help asap!!!
5 3/4 - (-3 7/8) = H
What is H ?
Answer:
Step-by-step explanation:
convert mixed fraction into improper fraction
[tex]5\frac{3}{4}=\frac{23}{4}\\\\\\3\frac{7}{8}=\frac{31}{8}\\\\5\frac{3}{4}-[-3\frac{7}{8}]=\frac{23}{4}+\frac{31}{8}\\\\=\frac{23*2}{4*2}+\frac{31}{8}\\\\=\frac{46}{8}+\frac{31}{8}\\\\=\frac{46+31}{8}\\\\\\=\frac{77}{8}\\\\=9\frac{5}{8}[/tex]
Answer:
9 5/8.
Step-by-step explanation:
5 3/4 - (-3 7/8)
= 5 3/4 + 3 7/8
= 5 + 3 + 3/4 + 7/8
= 8 + 3/4 + 7/8
The LCD of 4 and 8 is 8 so we get
8 + 6/8 + 7/8
= 8 + 13/8
= 8 + 1 5/8
= 9 5/8.
Always true, sometimes true, never true?
(x-1)(1+3)>0, x<1
Which of the following is the first step when copying a line segment to construct a new line segment?
a. draw a line segment
b. use a straight edge to connect the point not on the line segment to a point in the arc
c. plot a point not on the original line segment
d. draw an arc
Answer:
The correct option is;
c. Plot a point not on the original line segment
Step-by-step explanation:
The steps to copy a line segment are;
1) Plot a point that will be an endpoint of the new line segment
2) With the compass pin at the beginning of the original line segment, open the compass width to the end of the original line segment
3) With the adjusted compass width from the above step place the compass pin at the plotted point of the new line segment and draw an arc in the region the new line segment is to be located
4) Select a point on the arc where the other end of the new line will be
5) From the selected point from the above step, draw a line to the point plotted as the beginning of the new line segment
6) The length of the line drawn above is the same as the length of the original line segment.
6 times the sum of a number and four is forty- two
Answer:
3
Step-by-step explanation:
6(x+4)=42
x=3
check:
6*(3+4)=42
Yazmin is investigating the growth of plants under different conditions for her science class. Once the little sprouts were 1 inch tall, she found that they were growing at a steady rate of about 1/2 inch per day. Write a function that helps Yazmin to see how many days it takes for the plants to reach a given height. Let h = height of the plant (inches), and let d = number of days (days)
Answer:
0.5+d=h
Step-by-step explanation:
If a plant is growing at a steady rate of 0.5 inches (h) in 1 day (d) then after one day your equation should look like: 0.5+1 which would give you the height of the plant in inches. If this is true, then you would keep the height per day the same (0.5) substitute the 1 for d (one day); then your equation would look like this: 0.5+d which would give you the height of the plant in inches (h).
0.5+d=h
The function that helps Yazmin to see how many days it takes is h = 1 + 0.5d.
What is a function?Functions were originally the idealization of how a varying quantity depends on another quantity.
Now it is given that,
Height of sprout = 1 inch
Growth per day = 1/2 inch
Let h = height of the plant (inches), and let d = number of days (days)
∵ Growth per day = 1/2 inch
So, Growth of plant in d days = d * 1/2 = d/2 = 0.5d
Thus, height of the plant, h = 1 + Growth of plant in d days
⇒ h = 1 + 0.5d
Thus, the function that helps Yazmin to see how many days it takes is h = 1 + 0.5d.
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At what rate per annum will N250 amount to N330 in 4 years.
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{8 \: \% \: }}}}}[/tex]Step-by-step explanation:
Given,
Principal ( P ) = N 250
Time ( T ) = 4 years
Amount ( A ) =N 330
Rate ( R ) = ?
First, finding the Interest :
According to definition of Amount ,
Amount = Principal + Interest
plug the values
⇒[tex] \sf{330 = 250 + I}[/tex]
Move i to left hand side and change it's sign
⇒[tex] \sf{ - I = 250 - 330}[/tex]
Calculate
⇒[tex] \sf{ - I = - 80}[/tex]
Change the signs of the both equation
⇒[tex] \sf{I = 80 }[/tex]
Interest = 80
Finding the rate :
Simple Interest = [tex] \sf{ \frac{PTR}{100} }[/tex]
plug the values
⇒[tex] \sf{80 = \frac{250 \times 4 \times R}{100} }[/tex]
Multiply the numbers
⇒[tex] \sf{80 = \: \frac{1000 \: R}{100} }[/tex]
Apply cross product property
⇒[tex] \sf{1000R = 100 \times 80}[/tex]
Multiply the numbers
⇒[tex] \sf{1000R = 8000}[/tex]
Divide both sides of the equation by 1000
⇒[tex] \sf{ \frac{1000R}{1000} = \frac{8000}{1000} }[/tex]
Calculate
⇒[tex] \sf{R = 8 \: \% \: }[/tex]
Thus, Rate = 8 %
-------------------------------------------------------------------------
Let's learn about Principal , Interest , Time , Rate and Amount :
Principal = The money which is borrowed or deposited is called principal.Interest = The additional amount of money which is paid by borrower to the lender is called interest.Time = The duration of time for which principal us deposited or borrowed is termed as time period.Rate = The condition under which the insterest is charged is called rate.Amount = The sum of principal and Interest is called an amount.Hope I helped!
Best regards!!
Please help! Brainliest answer gets 10 points! what is x^2+x^4?
Answer:
Step-by-step explanation:
You cannot add these because they are not like. IF you have a value for x, then the expression could be evaluated at the x value, but you can't add them.
Determine what type of model best fits the given stituation. Water leaking from a local reservoir at the rate of 500 gallons per hour.
Answer:
Well, in the local reservoir we have an initial amount of water A.
And per hour, the amount of water in the reservoir decreases by 500 gals.
So after t hours, the amount of water in the reservoir is:
W = A - 500gal*t
This is a linear equation, so the model that fits best in the given situation is a linear model.
Where the only thing that you need to take in mind, is that the domain of this model is restricted:
This is because we can not have a negative amount of water in the reservoir, so the maximum value of t accepted is:
W = 0 = A - 500gal*t
t = A/500 hours
So the domain of this linear relation is:
t ∈ {0h, A/500 }
Answer: lin
Step-by-step explanation:
Use sigma notation to represent the sum of the first seven terms of the following sequence -4,-6,-8.....
Answer:Answer:
[tex]\sum\left {{7} \atop {1}} \right -n(3+n)[/tex]
Step-by-step explanation:
Given the sequence -4,-6,-8..., in order to get sigma notation to represent the sum of the first seven terms of the sequence, we need to first calculate the sum of the first seven terms of the sequence as shown;
The sum of an arithmetic series is expressed as [tex]S_n = \frac{n}{2}[2a+(n-1)d][/tex]
n is the number of terms
a is the first term of the sequence
d is the common difference
Given parameters
n = 7, a = -4 and d = -6-(-4) = -8-(-6) = -2
Required
Sum of the first seven terms of the sequence
[tex]S_7 = \frac{7}{2}[2(-4)+(7-1)(-2)]\\\\S_7 = \frac{7}{2}[-8+(6)(-2)]\\\\S_7 = \frac{7}{2}[-8-12]\\\\\\S_7 = \frac{7}{2} * -20\\\\S_7 = -70[/tex]
The sum of the nth term of the sequence will be;
[tex]S_n = \frac{n}{2}[2(-4)+(n-1)(-2)]\\\\S_n = \frac{n}{2}[-8+(-2n+2)]\\\\S_n = \frac{n}{2}[-6-2n]\\\\S_n = \frac{-6n}{2} - \frac{2n^2}{2}\\S_n = -3n-n^2\\\\S_n = -n(3+n)[/tex]
The sigma notation will be expressed as [tex]\sum\left {{7} \atop {1}} \right -n(3+n)[/tex]. The limit ranges from 1 to 7 since we are to find the sum of the first seven terms of the series.
I REALLY NEED HELP ASAP WITH THESE 2 QUESTIONS!!!!!!!!!
Answer:
4. Meena- 3
Jerry- 6
5a. 5
5b. 6
Step-by-step explanation:
We can use the distance formula to solve all of these.
[tex]\sqrt{(x_{2} } -x_{1} )^2+(y_{2} -y_{1} )^2[/tex]
Plug the numbers in and make sure you understand how i got these answers :) Let me know if you see anything wrong about it, and i will try and fix it.
Will give 5 stars, 10 points and maybe brainiest
Answer:
5.25
Step-by-step explanation:
"The median is the middle number in a sorted, ascending or descending, list of numbers and can be more descriptive of that data set than the average"
in that case
1.6, 3.2, 3.6, 4.6 , 4.7 , 5.2 , 5.3, 5.4 , 6.1 , 7.8 , 9.0 , 9.5 ,
1st 2nd 3rd 4th 5th 6th 7th . 8th . 9th 10th 11th 12th
as you can seem 5.2 and 5.3 are both in the middle. that means you take the average of those two numbers. so 5.25
Answer:
The median is 5.25
Step-by-step explanation:
Median is found in the middle of numbers.
First you arrange the number from descending to ascending order:
1.6, 3.2, 3.6, 4.6, 4.7, 5.2, 5.3, 5.4, 6.1, 7.8, 9.0, 9.5
There are 12 numbers.
Then find the number that is in the center. In this case, 5.2 and 5.3 are the numbers in the center. You add them together and divide them by 2:
5.2+5.3 = 10.5/2 = 5.25
The median is 5.25
mrs tay baked some tarts. 25% of the tarts are pineapple tarts and the rest are strawberry tarts. She baked 90 more strawberry tarts than pineapple tarts. How many strawberry tarts did she bake?
Step-by-step explanation:
100 - 25 = 75
75 + 90 = 165
= 165 strawberry .
30 POINTS!! Quadratic function F(x) =2x^2- 4x- 6 is shown below. Which describes the domain of this function.
A. All real numbers greater than or equal to -8
B. All real number less than or equal to -8
C. All real number greater than 10
D. All real numbers
Answer:
D. All real numbers
Step-by-step explanation:
The domain is the set of values that can be used for x. There is no restriction on x, so the domain is all real numbers.
Answer:
all real numbers
Step-by-step explanation:
The domain is the possible input values
Since x can be any value, the domain is all real numbers
If the average of 5, 8, b, 9 and 4 is 7. Find the value of b.
A. 9 B. 8 C. 7 D. 5
So our set of numbers is 5,8,b,9,4 . And we know the average is 7. So first, you have to add all the numbers in the set : 5+8+9+4 which gives you 26. We also know that to get the average of a set of numbers you have to add all the numbers and divide that sum by the how many numbers you have, in thsi case we have 5 numbers including b . So our equation now is : 26+b÷5=7. And if you plug in 9 for b you get 26+9÷5=7 and 26+9÷5 does equal 7 so therefore A is your answer
What is the correct prime factorization of 24
2^3 * 3^1
Go step by step. 24 = 2 x 12. 12 = 2 x 6. 6 = 2 x 3. We can't factor any more.
Therefore, we have 12 = 2 x 6, and since 6 = 2 x 3, we get 12 = 2 x 2 x 3.
Then 24 = 2 x 12, and 12 = 2 x 2 x 3, so 24 = 2 x 2 x 2 x 3.
There are 3 2's and 1 3's, so it's 2^3 * 3^1.
Hope that helped,
-sirswagger21
Answer:
24=2*12=2*6=2*3
Step-by-step explanation:
I could not draw the tree diagram
to do it you take a prime number it is divisible by and a composite number it is divisible by and you prime factorise the composite number and repeat until you get prime numbers
32.
What is the value of x for ∆DEF?
HELP! Answer if you can!!
Step-by-step explanation:
[tex]c^{2} = {a}^{2} + { b}^{2} [/tex]
Pythagoras theorem
x²=12² + 5²
x²=144+25
x²=169
[tex]x = \sqrt{169} [/tex]
x=13
Answer:
x = 13
Step-by-step explanation:
Using the Pythagorean Theorem to find the missing hypotenuse side:
[tex]a^2+b^2=c^2[/tex]
12 and 5 are a and b. 'x' would be c.
[tex]12^2+5^2=c^2\\\\12^2=144\\5^2=25\\\\144+25=c^2\\\\169=c^2\\\\\sqrt{169}=\sqrt{c^2}\\\\\boxed{13=c}[/tex]
'x' should be equal to 13.
Z= -3 - 8i Find the angle θtheta (in degrees) that z makes in the complex plane. Round your answer, if necessary, to the nearest tenth. Express θtheta between -180 180 degrees.
The angle is negative to indicate a clockwise rotation.
======================================================
Explanation:
Z = -3 - 8i is in the form z = a+bi with a = -3 and b = -8
In the complex plane the point (a,b) represents the location of z = a+bi
Define three points with the locations
P = (a,b) = (-3,8)
Q = (0,0)
R = (10,0)
The angle PQR is the angle theta we're looking for. This is the angle formed between the positive x axis and the terminal point (a,b)
Use the arctan function to find theta
theta = arctan(b/a)
theta = arctan( (-8)/(-3) )
theta = 69.4439547804166
theta = 69.4 degrees approximately
Note how this theta value is in quadrant Q1, but (a,b) = (-3, -8) is in Q3
So we need to add 180 degrees to adjust this error.
69.4+180 = 249.4
and we're now in the proper quadrant. We would stop here if your teacher did not put the restriction that theta must be between -180 and 180.
However, this restriction is in place so we need to find the difference of 360 and 249.4 to get 360-249.4 = 110.6
-----------
The angle 249.4 degrees is coterminal to -110.6 degrees. They both point in the same direction.
angle 249.4 degrees is found by starting pointing directly east and rotating 249.4 degrees counterclockwise
angle -110.6 degrees is found by starting directly east and rotating 110.6 degrees clockwise.
Check out the diagram below. I used GeoGebra to make the diagram.
X-5y=-15x−5y=−15x, minus, 5, y, equals, minus, 15 Complete the missing value in the solution to the equation. (-5,(−5,left parenthesis, minus, 5, comma ))
Answer:
The missing value is 2. The coordinate will be (-5, 2)Step-by-step explanation:
The question is not properly written. Find the correct question below.
If x – 5y = -15 . Complete the missing value in the solution to the equation (-5, ____)
Let the coordinate of the variables be (x, y). Comparing the coordinates (x, y) with the given coordinate (-5, __), we will discover that x = -5. To get the y coordinate, we will substitute x = -5 into the given expression as shown;
If x – 5y = -15
-5 - 5y = -15
Adding 5 both sides
-5-5y+5 = -15+5
-5y = -10
Dividing both sides by -5;
-5y/-5 = -10/-5
y = 2
Hence the missing value in the solution of the equation is 2. The coordinate will be (-5, 2)
Answer:
2
Step-by-step explanation:
I did the khan :)
Find the product.
7,352 x 48 =
A. 7,400
B. 88,224
C. 352,886
D. 352,896
Answer:
D
Step-by-step explanation:
7 3 5 2
x 4 8
-----------
352,896
Hey There!!~
Because, First thing to do is mulpity 2 x 8 = 16 so, You bring the 6 and bring up the 1. Then, 5 x 8 = 40 + 1 = 41. So, we bring down the 1 and bring up the 4. Then, 3 x 8 = 24 + 4 = 28. Then, The same thing bring down the 8 and let the 2 stay up there. 7 x 8 = 56 + 2 = 58. So, Right now the answer is 58, 816. So, We just completed the first step, But we're are not done yet... 4 x 2 = 8. Then, 5 x 4 = 20. So, we bring down the 0 and bring up the 2. Then, 4 x 3 = 12 + 2 = 14. So, The 4 stay down and 1 goes up. Then, 7 x 4 = 28 + 1 = 29. So, we just completed the second step. The last step is to add 58, 816 + 29, 408 = 352, 896. Hope This helps!!
QUESTION 2
Solve for X.
3x + 4 + 2 = 15
Answer:
x=3
Step-by-step explanation:
3x+6 =15
x=3
Answer:
3
Step-by-step explanation:
3x + 6 = 15
3x = 15 - 6 = 9
x = 9/3 = 3
An octagonal pyramid ... how many faces are there, how many vertices and how many edges? A triangular prism ... how many faces are there, how many vertices and how many edges? a triangular pyramid ... how many faces are there, how many vertices and how many edges?
1: 8 faces and 9 with the base 9 vertices and 16 edges
2: 3 faces and 5 with the bases 6 vertices and 9 edges
3: 3 faces and 4 with the base 4 vertices and 6 edges
1: 8 faces and 9 with the base 9 vertices and 16 edges
2: 3 faces and 5 with the bases 6 vertices and 9 edges
3: 3 faces and 4 with the base 4 vertices and 6 edges
Please help. Calculate the area of the shaded region in each figure use 3.14 for π and round to the nearest 10th if necessary
The sum of three consecutive multiples of 7 is 777 find these multiples
let the consecutive multiples be 7(n-1) , 7n and 7(n+1)
so 7(n-1)+7n+7(n+1)=777
or 3n=111,
n=37
252,259,266
[tex]7n+7n+7+7n+14=777\\21n=756\\n=36\\\\7n=252\\7n+7=259\\7n+14=266[/tex]
252,259,266
Help!!!! Which number line shows the solution to 6 + (−6)?
Answer: Hi!
The solution to positive 6 and -6 is 0. A negative and a positive of the same absolute value cancel out.
Hope this helps!
Answer:
the answer is zero !
Step-by-step explanation:
when a negative and a positive of the same number go against each other they cancel out
