Answer:
The answer is
[tex] {16}^{2} [/tex]
Which expression is equal to
to (-10 – 2i) + (3 + i)?
0 -7 ti
o – 13 –
07-
-7-
Answer:
- 7 - i
Step-by-step explanation:
Given
(- 10 - 2i) + (3 + i) ← remove parenthesis
= - 10 - 2i + 3 + i ← collect like terms
= - 7 - i
If the Discriminant is 73 how many roots are there
The solution is 2 roots
The number of roots the equation will have if the value of the discriminant is 73 will be 2 roots
What is Quadratic Equation?
A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the quadratic equation be A
where A = ax² + bx + c=0
Let the discriminant of the equation be D
Now , the value of D = 73
To calculate the number of roots a quadratic equation A
We need to compute the discriminant (b² - 4ac).
If the discriminant is less than 0, then the quadratic has no real roots.
If the discriminant is equal to zero then the quadratic has equal roots.
If the discriminant is more than zero then it has 2 distinct roots.
So , the value of D > 0
Therefore , the equation has 2 roots
Hence , the number of roots of the quadratic equation is 2 roots
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John went on a bike ride to the store 4 miles away. If it took John 3 1/0 of an hour to get there and 12 of an hour to get back, what was his average rate of speed (miles per hour) for the entire trip?
Answer:
His average rate of speed for the entire trip is 10 miles/hour.
Step-by-step explanation:
We are given that John went on a bike ride to the store 4 miles away. If it took John 3/10 of an hour to get there and 1/2 of an hour to get back.
And we have to find his average rate of speed (miles per hour) for the entire trip.
As we know that the Distance-Speed-Time formula is given by;
[tex]\text{Speed}=\dfrac{\text{Distance}}{\text{Time}}[/tex]
Here, the distance for the entire trip = 8 miles (4 miles for reaching store and 4 miles for returning back)
The time taken for the entire trip = [tex](\frac{3}{10} )[/tex] of an hour to reach the store and [tex](\frac{1}{2})[/tex] an hour to get back.
So, the average rate of speed for the entire trip = [tex]\frac{\text{Total Distance}}{\text{Total Time}}[/tex]
= [tex]\frac{8}{\frac{3}{10}+\frac{1}{2} }[/tex]
= [tex]\frac{8}{\frac{8}{10} }[/tex] = 10 miles per hour
Hence, his average rate of speed for the entire trip is 10 miles/hour.
the ratio of the weights of two men is 1/2:1/3 if weight of the first person is 22 1/2kg then find the weight of the second person
Answer:
15 kg
Step-by-step explanation:
We can multiply the given ratio units by 6 to make them be integers:
(1/2) : (1/3) = 3 : 2
Then we can see that the second man has 2/3 the weight of the first man.
(2/3)(22.5 kg) = 15 kg
The second person weighs 15 kg.
What is the simplest form of (4x3 + 6x – 7) + (3x3 – 5x2 – 5x + 9)
Answer:
The simplest form of the given expression is 7x³ + 5x² + x + 2
Step-by-step explanation:
(4x³ + 6x - 7) + (3x³ - 5x² - 5x + 9)
Group like terms together.
(4x³ + 3x³) + 5x² + (6x - 5x) + (-7 + 9)
Combine like terms.
7x³ + 5x² + x + 2
So, this will be your simplest form of the given equation.
Answer:
7x³ + 5x² + x + 2
Step-by-step explanation:
A cruise ship charges $125 per night for a room there are 250 rooms on the ship if every room on the ship is booked how much money does the cruise ship make in a single night
Answer:
125
×
250
_____
000
6250
25000
answer 31250
125
⋅
250
is
31250
Answer:$31250
Step-by-step explanation: 125x250=000+6250+25000=$31250
complete the table for the given rule.
Answer:
x y
10 → 6
4 → 0
8 → 4
Step-by-step explanation:
Using the given rule, plug in any known values:
[tex]y=x-4\\\\6=x-4[/tex]
Solve for x. Add 4 to both sides of the equation to isolate the variable:
[tex]6+4=x-4+4\\\\x=10[/tex]
Repeat:
[tex]y=x-4\\\\0=x-4\\\\0+4=x-4+4\\\\x=4[/tex]
[tex]y=x-4\\\\4=x-4\\\\4+4=x-4+4\\\\x=8[/tex]
:Done
A rectangular carpet has a perimeter of 234 inches. The length of the carpet is 83 inches more than the width. What are the dimensions of the carpet?
Answer:
Perimeter = 2 x length + 2 x width
Width = x
Length = x + 71
234 = 2*(x + 71) + 2*(x)
234 = 2x + 142 + 2x
234 = 4x + 142
4x = 234 - 142
4x = 92
x = 23
Width = 23 inches
Length = 94 inches
Step-by-step explanation:
The dimensions of the rectangular carpet are 100 and 17 inches.
Let the length of the rectangle be L. Let the width of the rectangle be W.Given the following data:
Perimeter = 234 inchesTranslating the word problem into an algebraic equation, we have;
[tex]L = W + 83[/tex]
To find the dimensions of the rectangular carpet;
Mathematically, the perimeter of a rectangle is given by the formula;
[tex]Perimeter = 2(L+W)[/tex]
Substituting the values into the formula, we have;
[tex]234 = 2(W + 83 + W)[/tex]
[tex]234 = 2(2W + 83)\\\\234 = 4W + 166\\\\4W = 234 - 166\\\\4W = 68\\\\W = \frac{68}{4}[/tex]
Width, W = 17 inches
Next, we would find the value of L;
[tex]L = W + 83[/tex]
Substituting the value of W, we have;
[tex]L = 17 + 83[/tex]
L = 100 inches.
Therefore, the dimensions of the rectangular carpet are 100 and 17 inches.
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Jeff wants to go to a university where the tuition is $9,000 per year he has a scholarship that pays for 70% of his tuition yesterday his $3,000 toward the first Year's tuition does he have enough to pay for the first year tuition?
Scholarship will pay=
After the scholarship, Jeff will pay=
Answer:
Step-by-step explanation:
Amount of Jeff tuition per year = $9,000
If Jeff has a scholarship that pays 70% of his tuition, the amount the scholarship will pat Jeff = 70% of his yearly tuition fee.
Scholarship amount = 70/100 * $9,000
Scholarship amount = 70*90
Scholarship amount = $6,300
Hence the scholarship will pay Jeff $6,300
If the amount saved by Jeff is $3,000
Total amount that Jeff has = Scholarship amount + Amount saved
Total amount that Jeff has = $6,300 + $3000 = $9300
Since the total amount that Jeff has is more than the yearly tuition fee, this shows that he has enough to pay for the first year's tuition
Given: <2 and <4 are vertical angles.
Prove: <2 ~= <4
Statements Reasons
Assemble the proof by dragging tiles to
the Statements and Reasons columns
Statement 1: [tex]\angle 2[/tex] and [tex]\angle 4[/tex] are vertical angles
Reason 1: Given
We basically just restate the given information word for word. This is true of any two column proof.
-------------------------------------
Statement 2: [tex]m \angle 2 + m \angle 3 = 180[/tex]
Reason 2: [tex]\angle 2[/tex] and [tex]\angle 3[/tex] are a linear pair
The term "linear pair" means the angles are adjacent and supplementary (they form a straight line), so this is why the two angles add to 180.
--------------------------------------
Statement 3: [tex]m \angle 3 + m \angle 4 = 180[/tex]
Reason 3: [tex]\angle 3[/tex] and [tex]\angle 4[/tex] are a linear pair
--------------------------------------
Statement 4: [tex]m \angle 2 + m \angle 3 = m \angle 3 + m \angle 4[/tex]
Reason 4: Substitution
Each of the equations formed in statements 2 and 3 above have 180 on the right side, so the left hand sides must be the same
--------------------------------------
Statement 5: [tex]m \angle 2 = m \angle 4[/tex]
Reason 5: Subtraction property of equality
We subtracted the quantity [tex]m \angle 3[/tex] from both sides (they go away)
--------------------------------------
Statement 6: [tex]\angle 2 \cong \angle 4[/tex]
Reason 6: Definition of congruence
If two items are congruent, then they have the same measure. In other words, they are the same.
The proof of [tex]\angle 2 \ and \ \angle4[/tex] are vertical angles is explained below.
Given, [tex]\angle 2 \ and \ \angle4[/tex] are vertical angles as shown in fig.
We know that, Vertical angles are formed when two straight lines intersect at a point.Vertical angles are two angles which are vertically opposite and have the same measure. So, the two angles are to be congruent.
We have to prove that angle 2 and angle 4 congruent.
Given [tex]\angle 2 \ and\ \angle 3[/tex] makes linear pair so,
[tex]\angle 2+\angle 3= 180[/tex]
[tex]\angle 3 =180-\angle 2[/tex]..........(1)
Again [tex]\angle 3 \ and \ \angle 4[/tex] makes linear pair so,
[tex]\angle 3+\angle 4= 180[/tex]
[tex]\angle 3 =180-\angle 4[/tex].......(2)
From (1) and (2) we get,
[tex]180-\angle 2=180-\angle 4[/tex]
Subtracting 180 from both the sides we get,
[tex]-\angle 2=-\angle 4[/tex]
Or, [tex]\angle 2=\angle 4[/tex]
Hence angle 2 and angle 4 are congruent.
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the length of a rectangle is 4 units more then its breadth.its perimeter is 28 units. what is the length
Hi there! :)
Answer:
[tex]\huge\boxed{L = 9 \text { units}}[/tex]
Given:
Perimeter = 28
Let the breadth = x. The length is 4 units greater, so we can represent this as (x + 4).
Set up an expression. Remember that the formula for the perimeter of a rectangle is:
P = 2(l) + 2(w)
Substitute:
28 = 2(x) + 2(x+ 4)
Distribute:
28 = 2x + 2x + 8
Combine like terms and simplify:
28 = 4x + 8
20 = 4x
x = 5.
The length of the breadth is 5 units. Substitute in 5 to solve for the length:
(5) + 4 = 9 units.
The length of the rectangle is 9 units.
Solve 3x+2y−z=2 2y+z=7 −2x−4z=−2 Enter your answer, in the form (x,y,z), in the boxes in simplest terms. x= y= z=
Answer:
(-1, 3, 1)
x=-1, y=3, z=1.
Step-by-step explanation:
So we have the three equations:
[tex]3x+2y-z=2\\2y+z=7\\-2x-4z=-2[/tex]
And we want to find the value of each variable.
To do so, look at the equations and try to think about what we can do to isolate one of the variables by itself.
We can see that both the second and equation has a variable and then the variable z.
In other words, we can solve for y in the second equation and x in the third equation and then substitute them in the first equation to isolate the variable z and then solve for z. With that, we can then easily arrive at our solution.
Therefore, solve for y in the second equation:
[tex]2y+z=7[/tex]
Subtract z from both sides. The zs on the left side cancels:
[tex](2y+z)-z=(7)-z\\2y=7-z[/tex]
Now, divide both sides by 2. The 2s on the left cancel and we've isolated the y variable:
[tex]\frac{(2y)}{2} = \frac{(7-z)}{2}\\y=\frac{(7-z)}{2}[/tex]
Now, do the same for the third equation. Isolate the x variable:
[tex]-2x-4z=-2[/tex]
First, divide everything by -2 to make things simpler:
[tex]\frac{(-2x-4z)}{-2}=\frac{(-2)}{-2}\\ x+2z=1[/tex]
Now, subtract 2z from both sides to isolate the x variable:
[tex](x+2z)-2z=1-2z\\x=1-2z[/tex]
We have isolated the x and y variables. They are:
[tex]y=\frac{(7-z)}{2}\\x=1-2z[/tex]
Now, we can substitute them back into the first equation. Therefore:
[tex]3x+2y-z=2\\3(1-2z)+2(\frac{7-z}{2})-z=2[/tex]
Distribute the first and second terms. The second term cancels out:
[tex]3(1)-3(2z)+(7-z)-z=2\\3-6z+7-z-z=2[/tex]
Combine like terms:
[tex]-6z-z-z+3+7=2\\-8z+10=2\\[/tex]
Subtract 10 from both sides:
[tex](-8z+10)-10=2-10\\-8z=-8[/tex]
Divide both sides by -8:
[tex]z=1[/tex]
Now that we've determined that z=1, plug it back into the isolated second and third equations:
Second equation:
[tex]y=\frac{(7-z)}{2}\\y=(7-1)/2\\y=(6)/2=3[/tex]
Third equation:
[tex]x=1-2z\\x=1-2(1)\\x=1-2=-1[/tex]
Therefore, our answer is (-1, 3, 1)
Answer:
(x, y, z) = (-1, 3, 1)
Step-by-step explanation:
Any of a number of web sites will solve systems of equations for you. Your graphing calculator will, too.
The solution is the right-most column in reduced row echelon form. Top to bottom, the variables are in order x, y, z.
(x, y, z) = (-1, 3, 1)
_____
If you like, you can use substitution to do this by hand.
z = 3x +2y -2 . . . . from the first equation
2y +(3x +2y -2) = 7 . . . . substituting into the second equation
3x +4y = 9 . . . . . in standard form
-2x -4(3x +2y -2) = -2 . . . . substituting for z into the third equation
14x +8y = 10 . . . . . in standard form
Subtract half the second equation from the first:
(3x +4y) -(7x +4y) = (9) -(5)
-4x = 4 . . . simplify
x = -1 . . . . . divide by 4
y = (9 -3x)/4 = (9 -3(-1))/4 = 12/4 = 3
z = 3(-1) +2(3) -2 = 1
The solution is (x, y, z) = (-1, 3, 1).
please answer the question 6 please asap
Answer:
we
Step-by-step explanation:
ee
−4 − 6 + 2 + 5 + 8 − 3 (8 − 6 − 3) − (−6 − 2 − 5) (9 − 4)(−6 − 3) pls help me
Answer:
-577
Step-by-step explanation:
−4 − 6 + 2 + 5 + 8 − 3 (8 − 6 − 3) − (−6 − 2 − 5) (9 − 4)(−6 − 3)
Factor each of the following polynomial
lows.
1. 2x2 - 8x
Answer:
2x (x - 4)
Step-by-step explanation:
The graph of a line passes through the two points (-2, 1) and (2, 1). What is the equation of the line written in general form? y - 1 = 0 x - y + 1 = 0 x + y - 1= 0 Please explain your answer! Thanks!
Answer:
Step-by-step explanation:
Slope = 0
The line is parallel to x-axis
Equation: y = 1
y -1 = 0
Answer:
y - 1 = 0
Step-by-step explanation:
As we move from the first point to the second, x increases by 4 (this is the 'run') but y does not change (that is, the 'rise' is zero). Thus, the slope of the line is 0, and the equation of the line is y = 1, or (equivalently) y - 1 = 0.
Please solve this
Wrong answer I’ll report
Answer:
z = 27
Step-by-step explanation:
Given that z² is proportional to x³ then the equation relating them is
z² = kx³ ← k is the constant of proportion
To find k use the condition z = 8 when x = 4, thus
8² = k × 4³
64 = 64k ( divide both sides by 64 )
k = 1
z² = x³ ← equation of proportion
When x = 9, then
z² = 9³ = 729 ( take the square root of both sides )
z = [tex]\sqrt{729}[/tex] = 27
solve the system by adding or subtracting
-3x-3y=9
3x+8y=6
Answer:
x = -6 y = 3
Step-by-step explanation:
Adding the two equations and you get, -3x-3y + 3x+8y= 6+9
=> 5y = 15
=> y = 3
Plug y in each equation
-3x -3(3) = 9
-3x -9 = 9
-3x = 18
x = -6
3x + 8(3) = 6
3x +24 = 6
3x = -18
x = -6
If x= 4y + 3 and y = -2x - 3, what is the value of xy?
Given that :-
x = 4y +3 y = -2x -3To Find :-
Value of x.ySolution :-
→ x = 4y + 3 equation 1st
→ y = -2x -3 equation 2nd .
Now putting the value of x from first equation to second equation.
→ y = -2(4y +3 ) -3
→ y = -8y - 6 - 3
→ y + 8y = -9
→ 9y = -9
→ y = -1
Now putting the value of y in equation first .
→ x = 4(-1) + 3
→ x = -4 + 3
→ x = -1
Now multiply and X and y.
→ x.y = -1(-1)
→ x.y = 1 .
[tex]\huge {\bold {\star {\fcolorbox {black} {yellow} {Answer}}}} [/tex]
Given, x = 4y + 3 ⠀⠀⠀⠀⠀⠀ iy = -2x - 3⠀⠀⠀⠀⠀⠀⠀⠀iiTo find;The value of xy [tex]{\boxed{\red{\underline{\sf{Solution:}}}}}[/tex]Putting the value of x in ii, we get ;
➝ y = - 2(4y+3) - 3
➝ y = - 8y - 6 - 3
➝ y = - 8y - 9
➝ y + 8y = - 9
➝ 9y = - 9
∴ y = - 1
Putting the value of y in i, we get ;
➝ x = 4y + 3
➝ x = 4(-1) + 3
➝ x = - 4 + 3
∴ x = - 1
Now,➛ xy = (- 1)(-1)
⛬ xy = 1
A ladder is placed with its foot 5m from the bottom of a wall 12m high. The top of the ladder just
reaches the top of the wall. Find the length of the ladder 5
(3 Points)
14m
13m
169m
15m
Answer:
13 m
Step-by-step explanation:
The ladder forms a right triangle with the wall that has legs of 5 and 12. We need to solve for the length of the ladder, which in this case, is the hypotenuse of the right triangle. You could use the Pythagorean Theorem but there's an easier way to do this. We can use the 5 - 12 - 13 Pythagorean triple so we know that the length of the ladder is 13 m.
8x - 2 = -9 + 7x what does x equal
Answer:
x = - 7
Step-by-step explanation:
8x - 2 = -9 + 7x (add 2 to both sides)
8x - 2 + 2 = -9 + 7x + 2
8x = 7x - 7 (subtract 7x from both sides)
8x - 7x = 7x - 7 - 7x
x = - 7
Answer:x=-7
Step-by-step explanation:
Regroup terms.
8x-2=7x-98x−2=7x−9
2 Subtract 7x7x from both sides.
8x-2-7x=-98x−2−7x=−9
3 Simplify 8x-2-7x8x−2−7x to x-2x−2.
x-2=-9x−2=−9
4 Add 22 to both sides.
x=-9+2x=−9+2
5 Simplify -9+2−9+2 to -7−7.
x=-7x=−7
2x - 2y = 2(x - y)
Name the property that justifies the given statement.
Answer:
Distributive property (Reversed)
Step-by-step explanation:
With the distributive property, it is possible to simplify expressions that consist of an expression term such as (a + b) being multiplied by one singular term such as c given as follows
c ×(a + b) = c·a + c·b
Factoring, which is the reverse use of the distributive property enables the difference or the sum of two products, each having a common factor to be the presented as the difference or the sum of two numbers multiplied by the common factor as follows;
2·x - 2·y = 2·(x - y).
For the given congruence, list the six poirs of congruent parts.
Answer:
ummm
Step-by-step explanation:
look it up
I'm helping you look it up right now
il comment when I find ... ok?
84 POINTS!!!!!!!! The hands on a clock represents rays. At 6:00, they forn opposite rays. What undefined term do the hands of the clock represents at 6:00?
A. Point
B.Line
C. Plane
D. Space
Answer:
B
Step-by-step explanation:
The clock at six o clock form a line:
12
|
9 | 3
|
6
What is the VERTEX of the quadratic y = 2
(x + 4)² + 1
A(4,1)
B(-4,1)
Please explain if you know
Answer:
The vertex is ( -4,1)
Step-by-step explanation:
The equation for a parabola can be written as
y = a( x-h)^2 +k where ( h,k) is the vertex
y = 2 (x + 4)² + 1
Rewriting
y = 2 (x - -4)² + 1
The vertex is ( -4,1)
Answer:
the vertex is located at (-4, 1)
Step-by-step explanation:
The vertex equation of a vertical parabola is
y = a(x - h)^2 + k
where (h, k) is the vertex.
Comparing this to the given
y = 2(x + 4)² + 1, we see that the vertex is located at (-4, 1) and that the graph is stretched vertically by a factor of 2.
Write two inequalities to compare 25 and 23
Answer:
[tex]\huge \boxed{25>23} \\ \\ \huge \boxed{25 \geq 23}[/tex]
Step-by-step explanation:
25 is greater than 23.
greater than ⇒ [tex]>[/tex]
25 is greater than or equal to 23.
greater than or equal to ⇒ [tex]\geq[/tex]
Answer:
1) [tex]25 > 23[/tex]
2) [tex]25 \geq 23[/tex]
Step-by-step explanation:
25 is greater than 23
=> [tex]25 > 23[/tex]
25 is also almost equal to 23
=> [tex]25 \geq 23[/tex]
What is the relationship between the slope of the line and the side lengths of the triangles?
For the smaller triangle, the rise is 2 since this is the length of the vertical component. The horizontal component is 3, meaning the run is 3
Slope = rise/run
Slope = 2/3
---------------
The larger triangle leads to the same slope because
slope = rise/run
slope = 4/6
slope = (2*2)/(2*3)
slope = 2/3
Because we get the same slope value, this confirms that both triangles have their hypotenuse on the same straight line.
The two triangles are similar. The larger triangle's sides are twice as long as its smaller counterpart.
The linear function is represented by the equation y = Negative three-fifthsx – 2. What can be determined of this equation written in slope-intercept form? Check all that apply.
The y-intercept is Negative three-fifths
The y-intercept is 2.
The y-intercept is –2.
The slope is Negative three-fifths
The slope is 2.
The slope is –2.
Answer:
The y-intercept is –2.
The slope is Negative three-fifths
Step-by-step explanation:
A linear function is a function whose graph is a straight line. A linear function can be represented as:
f(x) = y = a + bx
where y is the dependent variable and x is the independent variable. The equation of a linear function in slope intercept form is given as:
y = mx + c
Where m is the slope and c is the y intercept.
Given that:
[tex]y=-\frac{3}{5}x-2[/tex], and comparing with y = mx + c:
The slope (m) = [tex]-\frac{3}{5}[/tex]
The y intercept (c) = -2
Answer:
The y-intercept is –2.
The slope is Negative three-fifths
Step-by-step explanation:
The midpoint M and one endpoint of JK are given. Find the coordinates of the other endpoint. J(7,2) and M(1,-2)
Step-by-step explanation:
Xj + Xk/2 = Xm
7 + Xk/2 = 1
to get rid of the bracket, multiply all two sides by the denominator.
2(7 + Xk/2) = 1(2)
7 + Xk = 2
Xk = 2 - 7
Xk = -5
Yj + Yk/2 = Ym
2 + Yk/2 = -2
to get rid of the bracket, multiply all two sides by the denominator.
2(2 + Yk/2) = -2(2)
2 + Yk = -4
Yk = -4 - 2
Yk = -6
Therefore the coordinates of point K is (-5,-6)
5/6 divided by -5/6. Please don’t say -1 put the answer as a fraction
Answer:
1/-30
Step-by-step explanation:
5/6/-5/6
= 5/6 x 6/-5
= 5/30 x 6/-30
= 30/-900
= 1/-30