Answer:
(4x -3yi) (4x+3yi)
Step-by-step explanation:
We have a^2 + b^2
Over the complex number, this is equal to
(a-bi) (a+bi)
(4x -3yi) (4x+3yi)
Answer:
(4x -3yi) (4x+3yi)
Step-by-step explanation:
The expression 16x^2 + 9y^2 is a sum of squares, and it can be factored over the complex numbers using the difference of squares formula:
a^2 + b^2 = (a + bi)(a - bi)
In your expression:
a = 4x
b = 3y
So, applying the difference of squares formula:
16x^2 + 9y^2 = (4x + 3yi)(4x - 3yi)
This is the factored form of the expression 16x^2 + 9y^2 over the complex numbers.
Can u help cause the complication is getting real ?
Hello There!
The answer would be "B"
We have to move the decimal place over for each one depending on what the power of the number is.
Answer:
your answer would be B. :)
Step-by-step explanation:
Use the converse of the side-splitter theorem to determine if . Which statement is true?
Line segment TU is parallel to line segment RS because .
Line segment TU is not parallel to line segment RS because .
Line segment TU is parallel to line segment RS because .
Line segment TU is not parallel to line segment RS because .
Answer:
The answer to this question is the first option:
Line segment TU is parallel to line segment RS because 32/36=40/45
Answer:
The correct option is 1.
Step-by-step explanation:
From the given figure it is clear that QT=32, TR=36, QU=40 and US=45.
The converse of side splitter theorem states that if a line divides two sides proportionally, then that line is parallel to the third side.
The ratio in which TU divides the two sides is
[tex]\frac{QT}{TR}=\frac{32}{36}=\frac{8}{9}[/tex]
[tex]\frac{QU}{US}=\frac{40}{45}=\frac{8}{9}[/tex]
[tex]\frac{QT}{TR}=\frac{QU}{US}=\frac{8}{9}[/tex]
It means the line TU divides two sides proportionally.
Using converse of side splitter theorem, Line segment TU is parallel to line segment RS because
[tex]\frac{32}{36}=\frac{40}{45}[/tex]
Therefore the correct option is 1.
The sides of a parallelogram are 24cm and 16cm. The distance between the 24cm sides is 8 cm. Find the distance between the 16cm sides
Answer:
12 cm.
Step-by-step explanation:
The distance between the opposite sides is a perpendicular line so we can form a right angled triangle by drawing a perpendicular line from one corner of the parallelogram to the opposite 24 cm side.
So one angle of the parallelogram will have a sine of 8/16 = 1/2 so this angle = 30 degrees.
In a similar way to the above we form a right angled triangle from the same corner by drawing a perpendicular line to the opposite 16 cm side.
This has an angle of 30 degrees ( opposite angles in a parallelogram are congruent).
So sine 30 = x / 24
1/2 = x /24
x = 12 feet.
Another way to do this is by noting that the 2 triangles are similar (because 2 corresponding angles are equal).
So 8/ 16 = x/24
16x = 192
x = 12 feet.
Final answer:
The distance between the 16 cm sides of the parallelogram is 12 cm, determined by calculating the area of the parallelogram and then using it to find the missing dimension.
Explanation:
The student in the question is dealing with a geometrical problem involving the calculation of the distance between sides of a parallelogram. To solve the problem, we must understand that the opposite sides of a parallelogram are equal in length, and the area can be calculated as the product of the base and the height (the distance between the parallel sides). The question is analogous to finding the height of a parallelogram when the area and the base are known and can be approached in a similar way to finding dimensions of scaled geometric figures.
Given that the parallelogram's sides are 24 cm and 16 cm and the distance between the 24 cm sides is 8 cm, we can calculate the area of the parallelogram as:Area = base × height = 24 cm × 8 cm = 192 cm²Now to find the distance between the 16 cm sides (let's call this distance d), we can use the area formula again with the other pair of sides:Area = base × height = 16 cm × d = 192 cm²Hence, we can solve for d:192 cm² ÷ 16 cm = d = 12 cmTherefore, the distance between the 16 cm sides of the parallelogram is 12 cm.
Find the value of y.
A. 4
B. 6
C. 10
D. 12
Answer:
D. 12
Step-by-step explanation:
We have been given a diagram of a triangle. We are asked to find the value of y for our given triangle.
First of all, we will find 3rd side of larger triangle using Pythagoras theorem.
[tex]\text{3rd side}^2=16^2-8^2[/tex]
[tex]\text{3rd side}^2=256-64[/tex]
[tex]\text{3rd side}^2=192[/tex]
[tex]\text{3rd side}^2=192[/tex]
We will use geometric mean (leg) theorem to solve our given problem.
[tex]\text{3rd side}^2=y\times 16[/tex]
[tex]192=y\times 16[/tex]
[tex]\frac{192}{16}=\frac{y\times 16}{16}[/tex]
[tex]y=12[/tex]
Therefore, the value of y is 12 and option D is the correct choice.
find the value -2/3÷ 4/6.
A -1
B 4/9
C -9/4
D 1
Factor.
x2−5x+6
Enter your answer in the boxes.
x2−5x-6= ( ) ( )
Answer:
[tex](x-6)(x+1)[/tex]
Step-by-step explanation:
Factoring is usually just a bit of guess and check. [tex]x^2-5x-6[/tex] is written in the form [tex]a^2+b+c[/tex], where [tex]a=1[/tex], [tex]b=-5[/tex], and [tex]c=-6[/tex].
You need to find the two numbers that multiply together to equal [tex]-6[/tex] and can be added together to get [tex]-5[/tex]. These are [tex]-6[/tex] and [tex]1[/tex] in this case.
Now, put them together in the form [tex](x-6)(x+1)[/tex]. We will now check this answer using the FOIL method.
First term in each parentheses: [tex]x * x = x^2[/tex]
Outside terms: [tex]x * 1 = x[/tex]
Inside terms: [tex]-6 * x = -6x[/tex]
Last term in each parentheses: [tex]-6 * 1 = -6[/tex]
Now, add these together: [tex]x^2 + x - 6x - 6 = x^2 - 5x - 6[/tex]
Since we get the original expression, this is correct.
The graph of which of the following will be parallel to the graph of 4x – 3y = –12? A.y= 4/3x -3/2 B.6x-4y=-8 C. y=3/4x+1 D.4x- 2y=-12
Answer:
A. [tex]y = \frac{4}{3} x - \frac{3}{2}[/tex]
Step-by-step explanation:
First, we have to turn 4x - 3y = -12 into slope-intercept form (y = mx + b). To do this, we first have to isolate 3y.
4x - 3y = -12
+3y +12 Add 3y to both sides and add 12 to both sides
4x + 12 = 3y
3y = 4x + 12
Isolate y by dividing 3 from both sides.
y = [tex]\frac{4}{3}[/tex]x + 4
The graph that is parallel will have the same slope as this equation, which is [tex]\frac{4}{3}[/tex].
Therefore, A. [tex]y = \frac{4}{3} x - \frac{3}{2}[/tex] would be the correct answer.
Answer:
A
Step-by-step explanation:
Solve for y.
4x – 3y = -12
4x + 12 = 3y
y = 4/3 x + 4
The slope of the line is 4/3. So you need another line with the same slope. So the answer is A.
What is the value of x a.20 b.35 c.60 d.70
Answer:
20°
Step-by-step explanation:
They are Vertically Opposite angles and hence are equal.
So, x + 40 = 3x.
Answer:
a. 20
Step-by-step explanation:
You are solving vertical angles. Put the measurements equal to each other:
x + 40 = 3x
Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Subtract x from both sides.
x (-x) + 40 = 3x (-x)
40 = 3x - x
40 = 2x
Isolate the variable x. Divide 2 from both sides:
(2x)/2 = (40)/2
x = 40/2
x = 20
a. 20 is your answer.
~
examples of exponents product rule
Hello There!
I attached an image below which explains everything and gives some examples.
Final answer:
The product rule for exponents allows you to add the exponents when multiplying two terms with the same base, simplifying the calculation. Examples include multiplying powers of the same number, or dealing with terms in scientific notation.
Explanation:
Understanding the Product Rule for Exponents
The product rule for exponents states that when you multiply two expressions with the same base, you can simply add the exponents. This rule simplifies the multiplication of exponentiated quantities.
Examples of Using the Product Rule
For instance, if you have 53 multiplied by 54, the product rule allows you to add the exponents: 53+4 = 57. Another example involves numbers in scientific notation. When you multiply 3.2 x 103 by 2 x 102, the result is 6.4 x 103+2 = 6.4 x 105.
If both terms have exponents, multiply the digit terms as usual and then add the exponents of the exponential terms. This concept also applies to logarithms, where the logarithm of a product of two numbers equals the sum of their individual logarithms.
Order the simplification steps of the expression below using the properties of rational exponents.
Answer:
Step-by-step explanation:
Uploaded a pic of the answer. It’s correct
Given: We have the expression [tex]\sqrt[3]{875x^{5}y^{9}}[/tex]
Step-1: [tex]\sqrt[3]{875x^{5}y^{9}}[/tex]
Step-2: [tex]\left ( 875\times x^{5} \times y^{}\right )^{1/3}[/tex] [break the cuberoot as power [tex]1/3[/tex]]
Step-3: [tex]\left ( 125.7 \right )^{1/3}\times x^{5/3}\times y^{9/3}[/tex] [break [tex]875=125\times 7[/tex]]
Step-4: [tex]\left ( 5^{3} \right )^{1/3}\times 7^{1/3}\times x^{\left ( 1+2/3 \right )}\times y^{9/3}[/tex] [ [tex]125=5^{3} \\\frac{5}{3} =1+\frac{2}{3}[/tex]]
Step-5: [tex]5^{1}\times 7^{1/3}\times x^{1}\times x^{2/3}\times y^{3}[/tex] [break the power of [tex]x[/tex]]
Step-6: [tex]5\times x\times y^{3}\left ( 7^{1/3}\times x^{2/3} \right )[/tex]
Step-7: [tex]5xy^{3}\left ( 7x^{2} \right )^{1/3}[/tex]
Step-8: [tex]5xy^{3}\sqrt[3]{7x^{2}}[/tex]
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What is the range of the discrete finite function?
Answer:
The answer is A. (3,5,8)
Write a linear function f with the values f(0)=−5 and f(1)=−3?
Answer:
f(x) = ax + b;
f(0) = -5;
a·0 + b = -5;
b = -5;
f(1) = -3;
a·1 + (-5) = -3;
a - 5 = -3;
a = 5 - 3;
a = 2;
f(x) = 2x - 5;
Step-by-step explanation:
The linear function with the values f(0)=−5 and f(1)=−3 is f(x) = 2x - 5
The linear function can be represented as follows:
y = mx + b
where
m = slope
b = y-intercept
The y-intercept is the value of y when x = 0
Since,
f(0) = -5
Therefore,
b = -5
The equation will be as follows
f(x) = mx - 5
lets find the slope(m) using the f(1)=−3
-3 = m - 5
m = -3 + 5
m = 2
Therefore,
f(x) = 2x - 5
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What is 15 to the third power
Answer:
your answer should be 45
Step-by-step explanation:
Answer:
15 to the third power would be 3375
Step-by-step explanation:
You start by multiplying
15 X 15 X 15
First you would get
225 X 15
Then you do the final multiplication
3375
In a triangle, the measure of the first angle is twice the measure of the second angle. The measure of third angle os 88 degrees more then the measure of the second angle. Use the fact that the sum of the measures of the three angles of a triangle is 180 to find the measures of each angle.
Answer:
Answers: 46, 23, and 111
Step-by-step explanation:
To answer, we need to know the angles. Therefore, give each angle a name. Angle 1 will be x, 2 will be y, 3 will be z. So, using this system of equations:
x=2y
z=y+88
x+y+z=180
Substituting, z = 1/2(x)+88, now plug z into the third equation:
x+1/2(x)+1/2(x)+88=180
this simplifies to 2x+88=180
subtracting 88 from both sides leaves 2x=92
x=46
plug this in to the first equation: 46 = 2y, so y = 23
plug this into the third one leaves z = 111
Hope this helps!
1. Given the graph to the right, what is the coordinate of point A?
2.Given the graph to the right, in which quadrant is point E?
(will pick brainiest)
Answer:
1. A(-2, 3)2. Quadrant IIIStep-by-step explanation:
Look at the picture.
Coordinates of a point (x, y)
x - from x-axis
y - from y-axis
Adam put $100 in a savings account. After 10 years, he had $1649 in the
account. What rate of interest did he earn? Use the formula A = Per, where A
is the ending amount, Pis the principal (initial amount), r is the interest rate,
and t is time.
Adam earned approximately 12.48% interest on his savings account over 10 years.
To find the rate of interest (r) earned by Adam, we can use the formula for compound interest:
A = P * (1 + r[tex])^{t}[/tex]
where:
A = ending amount ($1649 in this case)
P = principal (initial amount) ($100 in this case)
r = interest rate (what we want to find)
t = time (in years) (10 years in this case)
We know the values of A, P, and t, so we can plug them into the formula and solve for r:
1649 = 100 * (1 + r)¹⁰
Divide both sides of the equation by 100:
16.49 = (1 + r)¹⁰
Now, let's isolate (1 + r) by taking the 10th root of both sides:
(1 + r) = √(16.49)
(1 + r) ≈ 1.12479
Now, subtract 1 from both sides to find the value of r:
r ≈ 1.12479 - 1
r ≈ 0.12479
Finally, convert the decimal to a percentage to get the interest rate:
r ≈ 0.12479 * 100
r ≈ 12.48%
So, Adam earned approximately 12.48% interest on his savings account over 10 years.
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If (a, –5) is a solution to the equation 3a = –2b – 7, what is a?
Question 8 options:
a)
4
b)
0
c)
-1
d)
1
Answer:
d) 1
Step-by-step explanation:
3a = –2b – 7
We have the point (a, -5) so b = -5
Substituting in
3a = -2(-5) -7
3a = 10-7
3a = 3
Divide each side by 3
3a/3 = 3/3
a =1
To find the value of a in the equation 3a = -2b - 7, substitute the coordinates of the given point and solve for a. The value of a is -5.
Explanation:In this given equation 3a = -2b - 7, o find the value of a, we can substitute the coordinates of the given point into the equation and solve for a. Let's substitute the value of a as -5:
3(-5) = -2b - 7
Simplifying the equation:
-15 = -2b - 7
Adding 7 to both sides:
-8 = -2b
Dividing both sides by -2:
b = 4
So, the value of a is -5.
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A student find the slope of the line between (8,17) and (1,4)
She writes 17-4/ 1-8. What mistake did she make
[tex]\bf (\stackrel{x_1}{8}~,~\stackrel{y_1}{17})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{4}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{4-17}{1-8}\implies \cfrac{-13}{-7}\implies \cfrac{13}{7} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \cfrac{17-4}{1-8}\stackrel{\leftarrow \textit{atop she used }y_1-y_2}{\frac{}{}}~\hfill[/tex]
For this case we have that by definition, the slope of a line is given by:
[tex]m = \frac {y_ {2} -y_ {1}} {x_{2} -x_ {1}}[/tex]
According to the data we have the following points:
[tex](x_ {1}, y_ {1}) :( 1,4)\\(x_ {2}, y_ {2}) :( 8,17)[/tex]
Substituting we have:
[tex]m = \frac {17-4} {8-1}\\m = \frac {13} {7}[/tex]
So, the slope is [tex]\frac {13} {7}[/tex]
ANswer:
The student's mistake was to erroneously subtract the "x" coordinates from the points
Which of the following equations represents a line that is parallel to y=-4x-1
and passes through the point, (2, 2)?
A. y = -4x- 6
B. y = -x+2
C. y=-4x +10
D. y = -4x+4
Answer:
Option C : y = -4x+10
Step-by-step explanation:
Given equation of line is:
[tex]y = -4x-1[/tex]
Comparing it with standard form
y=mx+b
m = -4
As the slopes of parallel lines are equal, the slop of other line will also be -4.
Now, to find the value of b
[tex]2 = -4(2) + b\\2 = -8 + b\\2+8=b\\b=10[/tex]
Putting the values of b and m in standard form
[tex]y=mx+b\\y = (-4)x+10\\y= -4x+10[/tex]
Hence,
Option C is the correct answer ..
For this case we have that the equation of a line of the slope-intersection form is given by:
[tex]y = mx + b[/tex]
Where:
m: It's the slope
b: It is the cut point with the y axis.
By definition, if two straight lines are parallel then their slopes are equal.
So, if we have:
[tex]y = -4x-1[/tex]
A parallel line has slope [tex]m = -4[/tex]
y = -4x + b
We substitute the point (2,2) to find "b":
[tex]2 = -4 (2) + b\\2 = -8 + b\\b = 2 + 8\\b = 10[/tex]
Finally we have:
[tex]y = -4x + 10[/tex]
Answer:
Option C
Eugene had $24 to spend on three pencils.
After buying them he had $18. How
much did each pencil cost?
Answer:
$2
Step-by-step explanation:
Step 1: Subtract the amount he had left from the amount he had to spend. 24 - 18 is 6. That's the amount spent on pencils.
Step 2: Divide the amount spent on pencils by 3. 6/3 is 2. That's the total cost of each pencil.
what measure is represented by 17 feet in this figure below
Answer:
The answer is B. the diameter of the base
Step-by-step explanation:
Just got it right on edg! Have a great day!
During a sale, 20-cent candy bars were sold at 3 for 50 cents. How much is saved on 9 bars?
Make a Selection:
A. $0.36
B. $0.30
C. $0.25
D. $0.94
Answer:
B. $0.30
Step-by-step explanation:
1 bar of candy = $0.20
3 bars of candy = $0.50
To solve, multiply for both:
If you pay for each candy bar individually, they each cost $0.20. Multiply 9 with 0.20:
9 x 0.20 = $1.80
If you pay for the candy bars by 3's, they cost $0.50 each pack. Divide 9 with 3, then multiply by 0.50:
9/3 = 3
3 x 0.50 = $1.50
Subtract the total cost of the individual from the pack:
$1.80 - $1.50 = $0.30
B. $0.30 is your answer.
~
consecutive angles in a parallelogram are_?
Answer:
supplementary
Step-by-step explanation:
Consecutive angles in a parallelogram sum to 180°
That is they are supplementary.
PLEASE HURRY!!!!!!
10 points !!!!!!!!!!! What is the value of x??
Answer:
x = 98°
Step-by-step explanation:
The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.
x is an exterior angle and 53° and 45° are the opposite interior angles, hence
x = 53° + 45° = 98°
If the sum of the interior angle measures of a polygon with n sides is 2280 degrees, find n.
Please Help Me!!
Final answer:
Using the sum of the interior angles formula for a polygon, S = (n - 2) x 180 degrees, and substituting the provided sum of 2280 degrees, it is calculated that the polygon has 14 sides.
Explanation:
To solve for the number of sides n in a polygon given the sum of the interior angles, we use the formula:
S = (n - 2) × 180°
where S is the sum of the interior angles in degrees. Given that the sum of the interior angles S is 2280 degrees, we can set up the equation:
2280 = (n - 2) × 180
Divide both sides of the equation by 180:
2280 ÷ 180 = n - 2
12 = n - 2
Now, add 2 to both sides of the equation to find n:
n = 12 + 2
n = 14
So, the polygon has 14 sides.
How many combinations of four books can be made from eight different books?
Answer:
70
Step-by-step explanation:
70 combinations of four books can be made from eight different books.
solve the equation, ab + 10c = 9 , for the variable, a
Answer:
[tex]a=(9-10c)/b[/tex]
Step-by-step explanation:
we have
[tex]ab+10c=9[/tex]
Solve for the variable a
That means----> isolate the variable a
Subtract 10c both sides
[tex]ab+10c-10c=9-10c[/tex]
[tex]ab=9-10c[/tex]
Divide by b both sides
[tex]ab/b=(9-10c)/b[/tex]
[tex]a=(9-10c)/b[/tex]
convert 15 in binary system
Answer:
The Answer is 1111
Step-by-step explanation:
15 = 2(7)+1
7=2(3)+1
3=2(1)+1
1=2(0)+1
look the remainder of division by 2 : 1111 in binary system
verify : 15 = 1(2^0)+ 1(2^1)+ 1(2^2)+ 1(2^3 = 1+2+4+8=15 .....right
The cost of a sweatshirt was on sale for $18. Find the
percent of decrease if the sweatshirt was originally
$25.
The percentage decrease(loss) of selling sweatshirts is 28%.
How to find percentage change?To find the percentage change of any value we need to divide by that change to the original value and then multiply by 100.
Percentage change = (change in value × 100)÷(riginal value).
Given that the selling cost of sweatshirts is $18.
The cost of the sweatshirt was $25.
Change of value
$25 - $18 = $7
By the formula
Percentage decrease = ($7)×100÷ ($25) %
Percentage decrease = 28% Hence,the percentage decreases is 28$.
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8.
(g.g)(x)
(4x-1)(3x-6)
Answer:
12x+6
Step-by-step explanation:
Multiply the like terms.
4x • 3x=12x
-1 • -6= 6
put it back into equation form
12x + 6