Answer:
(3 + i)(4 + 2i) = 10 + 10iStep-by-step explanation:
Use FOIL: (a + b)(c + d) = ac + ad + bc + bd
and i² = -1
[tex](3+i)(4+2i)\\\\=(3)(4)+(3)(2i)+(i)(4)+(i)(2i)\\\\=12+6i+4i+2i^2\qquad\text{combine like terms}\\\\=(12-2)+(6i+4i)\\\\=10+10i[/tex]
Answer:
11 + 10i
Step-by-step explanation:
Note that we're multiplying two binomials here, and thus may use the FOIL method. This requires four multiplications, as follows:
3*4 + 3*2i + 4i - 1 (The last term is 1 because i(i) = i^2 = -1.)
Simplifying, we get:
12 + 6i + 4i -1, or:
11 + 10i
I need to find the volume of a nose cone.
The cylinder has a height of 6ft and a diameter of 8ft. the formula for volume is πrrh
The cone has the same dimensions. the formula is πrrh÷2.
well then, the volume of the nose cone will just be the sum of the volume of the cylinder below and the cone above.
since the diameter for both is 8, then their radius is half that, or 4.
[tex]\bf \stackrel{\textit{volume of a cone}}{V=\cfrac{\pi r^2 h}{3}}~~ \begin{cases} r=radius\\ h=height\\ \cline{1-1} r=4\\ h=6 \end{cases}\implies V=\cfrac{\pi (4)^2(6)}{3}\implies V=32\pi \\\\\\ \stackrel{\textit{volume of a cylinder}}{V=\pi r^2 h}~~ \begin{cases} r=radius\\ h=height\\ \cline{1-1} r=4\\ h=6 \end{cases}\implies V=\pi (4)^2(6)\implies V=96\pi \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{volume of the nose cone}}{32\pi +96\pi \implies 128\pi }\qquad \approx \qquad 402.12[/tex]
Find the area of the parallelogram. Please need help very badly.
Answer:
A = bh
A = 15(8)
A = 120 square centimeters
What is the length of the hypotenuse of the triangle ?
Answer: The answer is d 10 times 2 squared-the last choise.
BECAUSE:a squared + b squared = c squared
10 squared + 10 squared = c squared
100+100=c squared
the square root of 200 = c squared
PUT ME AS BRAINLIESTTTTTTTTTTT!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
10√2 units
Step-by-step explanation:
Given : A right angles triangle QRS
QS= SR = 10 units
To Find : Hypotenuse
Solution:
Perpendicular = 10 units
Base = 10 units
Hypotenuse = QR
Now we will use Pythagoras theorem
[tex]Hypotenuse^2=Perpendicular^2+Base^2[/tex]
[tex]QR^2=QS^2+SR^2[/tex]
[tex]QR^2=10^2+10^2[/tex]
[tex]QR^2=100+100[/tex]
[tex]QR^2=200[/tex]
[tex]QR=\sqrt{200}[/tex]
[tex]QR=10\sqrt{2}[/tex]
Hence the length of the hypotenuse of the triangle is 10√2 units
So, Option D is correct.
Find the slope of the line whose equation is 2x - 3y + 6 = 0.
2/3
-2/3
-2
The slope would be the first one, 2/3. Hope this helps! Please mark brainliest! :) Thanks v much! :)
Answer:
2/3
Step-by-step explanation:
My paychecks gross pay came to 663.87 for the week. If 20% is taken out for taxes how much is my net pay
Answer:
Final Price: 531.10
Discount: 132.77
Step-by-step explanation:
663.87 is 100%
? is 20%
?=20•663.87/100~$132.77 taxes
Net pay= 663.87-132.77=$531.1
X represents the # of trees. Y represents the height. How many 150
Answers
105
50
30
80
Answer: 30
Step-by-step explanation:
(Very easy) Find the surface area of this figure
The surface area of the two triangles is 12 cm^2.
3*4=12
The surface area of the bottom rectangle is 8 cm^2.
4*2=8
The surface area of the rectangle that is on the left side of the figure is 6 cm^2.
3*2=6
The surface area of the rectangle that is on the top side of the figure is 10 cm^2.
To find the third side of the triangle, use the Pythagorean theorem.
3^2+4^2=h^2
9+16=25
The third side of the triangle is 5 cm.
The surface area of the whole figure is 36 cm^2.
12+8+6+10=36
help me with this i suck at mathematical reasoing
Answer:
6Step-by-step explanation:
The formula of an area of a rectangle:
[tex]A_r=lw[/tex]
l - length
w - width
We have l = 12 in and w = 8 in.
Substitute:
[tex]A_r=(12)(8)=96\ in^2[/tex]
The formula of an area of a triangle:
[tex]A_t=\dfrac{bh}{2}[/tex]
b - base
h - altitutde
We have b = 32 in and A - 96 in².
Substitute:
[tex]\dfrac{32h}{2}=96[/tex]
[tex]16h=96[/tex] divide both sides by 16
[tex]h=6\ in[/tex]
How do you Graph 0.5x+0.8y=240
Answer:
y= 300 - 5/9x
Step-by-step explanation:
0.8y = 240 - 0.5x
divide both sides by 0.8,
y= 300 - 5/9x
-5/9 is your gradient
300 is your y-intercept
To graph 0.5x + 0.8y = 240, first arrange the equation into y = mx + b form, where m is the slope and b is the y-intercept. Finally, plot this equation on a graph using the slope and y-intercept.
Explanation:To graph the equation 0.5x + 0.8y = 240, you need to first arrange it in the form of y = mx + b (slope-intercept form), where m is the slope and b is the y-intercept.
Solving for y, we get:
0.8y = -0.5x + 240
y = -0.625x + 300
Then you can plot this equation in the format y = mx + b on a graph. Place the y-intercept at 300 on the y-axis. From there, use the slope (-0.625) to find the second point: down 0.625 units and to the right 1 unit. Repeat this step to plot a few points and then draw a line passing through them.
Learn more about Graphing Linear Equations here:https://brainly.com/question/14240165
#SPJ3
Which function is increasing?
A. f(x) =(1/4) ^x
B. f(x) =(1/4) ^x
C. f(x) = 4^x
D. f(x) = (0.4)^x
Answer:
f(x) = 4^x
Step-by-step explanation:
In f(x) = (1/4)^x, 1/4 is equal to 0.25, which is less than 1, so its decreasing
In f(x) = 4^x, 4 is greater than 1, so its increasing
In f(x) = (0.4)^x, 0.4 is less than 1, so its decreasing
This is why f(x) = 4^x is the correct answer
I hope this helps!
2. Find the area and circumference of the circle to the right.
16.6 m
Answer:
AREA:
[tex]A=216.42m^2[/tex]
CIRCUMFERENCE:
[tex]C=52.15m[/tex]
Step-by-step explanation:
The formula that is used to calculate the area of a circle is:
[tex]A=\pi r^2[/tex]
Where "r" is the radius of the circle.
The formula for calculate the circumference of a circle is:
[tex]C=2\pi r[/tex]
Where "r" is the radius of the circle.
Then, you need to find the radius. This is:
[tex]r=\frac{16.6m}{2}=8.3m[/tex]
Substituting the radius, you get that the area and the circumference are:
AREA:
[tex]A=\pi (8.3m)^2=216.42m^2[/tex]
CIRCUMFERENCE:
[tex]C=2\pi (8.3m)=52.15m[/tex]
Answer with step-by-step explanation:
We are given a circle which is divided into two halves and has a diameter of 16.6 meter. We are to find the area and circumference of the circle to the right.
It means that our radius will be the half of the given diameter.
Radius = 16.6/2 = 8.3 m
Area = [tex]\pi r^2[/tex] = [tex]\frac{\pi \times (8.3)^2}{2}[/tex] = 216.4 m^2
Circumference = [tex]2 \pi r[/tex] = [tex]2 \times \pi \times 8.3[/tex] = 52.2 m
The definition of a circle uses what undefined term
Answer:
The definition of a circle uses the undefined term is plane then the undefined term can contain parallel lines is plane and. The definition of an angle uses the undefined term is point likewise there are 3 possible geometry will fall.
Hope I helped
Step-by-step explanation:
find the x and y intercepts of the following function.
g(x)=x^2-5x-84
Answer:
see explanation
Step-by-step explanation:
To find the y- intercept let x = 0 in the function
g(0) = 0 - 0 - 84 = - 84 ← y- intercept
To find the x- intercepts let y = 0, that is
x² - 5x - 84 = 0
To factor the quadratic
Consider the factors of the constant term (- 84) which sum to give the coefficient of the x- term
The factors are - 12 and + 7, since
- 12 × 7 = - 84 and - 12 + 7 = - 5, thus
(x - 12)(x + 7) = 0
Equate each factor to zero and solve for x
x - 12 = 0 ⇒ x = 12
x + 7 = 0 ⇒ x = - 7
x- intercepts are x = - 7 and x = 12
A jacket was $50 and is now on sale for $35. What is the percent change in the cost?
from 50 to 35 is 15, so it went down by $15.
if we take 50 to be the 100%, what is 15 off of it in percentage?
[tex]\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} 50&100\\ 15&x \end{array}\implies \cfrac{50}{15}=\cfrac{100}{x}\implies \cfrac{10}{3}=\cfrac{100}{x}\implies 10x=300 \\\\\\ x=\cfrac{300}{10}\implies x=30[/tex]
Answer:
-30%
Step-by-step explanation:
The decrease in price was $15.
Divide $15 by $50, obtaining 0.30, which in turn is mult. by 100%.
The percentage change, from $50 to $35, was -30%.
What are the solutions for x when y is equal to 0 in the following quadratic
function?
y = x² + 10x – 24
OA) X= -4 or x = -6
OB) x = -6 or x = 4
OC) x = -2 or x = 12
OD) x = -12 or x = 2
O E) no real solutions
Answer:
D) x = -12 or x = 2
Step-by-step explanation:
The given quadratic equation is:
[tex]y=x^2+10x-24[/tex]
When y=0, we obtain:
[tex]x^2+10x-24=0[/tex]
We split the middle term with -2, 12 because their product is is -24 and their sum is 10.
[tex]x^2-2x+12x-24=0[/tex]
We factor by grouping to obtain:
[tex]x(x-2)+12(x-2)=0[/tex]
[tex](x-2)(x+12)=0[/tex]
Either [tex](x-2)=0[/tex] or [tex](x+12)=0[/tex]
Either [tex]x=2[/tex] or [tex]x=-12[/tex]
the vector u is graphed. which of the vectors below would be orthogonal to vector u?
ANSWER
[tex]< \frac{1}{5} , - \frac{1}{3} \: >[/tex]
EXPLANATION
The given vector , u has the following components,
[tex]u = < \: - 5 , - 3 \: > [/tex]
If two vectors are orthogonal, then their dot product is zero.
[tex]< \: - 5 , - 3 \: > \bullet < \: \frac{1}{5} , - \frac{1}{3} \: > = - 5 \times \frac{1}{5} \times - 3 \times - \frac{1}{3} = - 1 + 1 = 0[/tex]
Hence,the vector
[tex] < \frac{1}{5} , - \frac{1}{3} \: >[/tex]
is orthogonal to vector u.
WILL MARK BRAINLIEST!
If the circle graph represents the responses from 500 people, how many more people prefer burgers than cheeseburgers?
subs-10%
Tacos-10%
Chicken-10%
Pizza-30%
burger-25%
Cheeseburgers-15%
125
75
50
25
Answer:
50
Step-by-step explanation:
[tex]500 \div 100 \times 25 = 125[/tex]
[tex]500 \div 100 \times 15 = 75[/tex]
[tex]125 - 75 = 50[/tex]
50. From 500 people, 25% that prefer burger represent 125 people and 15% that prefer cheeseburger represent 75. This mean there are 50 more people that prefer burgers than cheeseburgers.
The key to solve this problem is by direct rule of three, we will place the 3 values (which we will call “a”, “b”, and “c”) and the unknown value that we want to figure out (“x”) to apply the formula:
a -----------> b
c -----------> x
[tex]x=\frac{b.c}{a}[/tex]
The circle graph represents the responses from 500 people in percentage.
To calculate the amount of people that prefer burgers:
If 100% ----------------> 500 people
25% ----------------> x
[tex]x=\frac{(500)(25)}{100}= 125[/tex] which means 125 people prefer burgers
To calculate the amount of people that prefer cheeseburgers:
If 100% ----------------> 500 people
15% ----------------> x
[tex]x=\frac{(500)(15)}{100}= 75[/tex] which means 75 people prefer cheeseburgers.
In order to know how many more people prefer burgers than cheeseburgers, let's apply the difference between people who prefer burgers and people who prefer cheeseburgers:
125 - 75 = 50 which mean 50 more people prefer burgers than cheeseburgers.
3.5d + 6.25 = 1 + 5.25d
The solution is d =
Answer:
d = 3
Step-by-step explanation:
3.5d + 6.25 = 1 + 5.25d
5.25d - 3.5d = 6.25 - 1
1.75d = 5.25
d = 5.25 ÷ 1.75 = 3
Which set of the side lenths form a right triangle?
Answer:
15m, 20m, 25mStep-by-step explanation:
If for x ≤ y < z
x² + y² = z²
then x, y and z form a right triangle.
1 .
15m, 20m, 25m
15² + 20² = 225 + 400 = 625
25² = 625
CORRECT :)
2.
3ft, 6ft, 5ft
3² + 5² = 9 + 25 = 34
6² = 36
34 ≠ 36
3.
10in, 41in, 40in
10² + 40² = 100 + 1600 = 1700
41² = 1681
1700 ≠ 1681
4.
7cm, 8cm, 10cm
7² + 8² = 49 + 64 = 113
10² = 100
113 ≠ 100
Bradley dropped a ball from a roof 16feet high. Each time the ball hits the ground it bounces 3/5 the previous height. Find the height ball will bounce after hitting the ground the fourth time
Answer: 2.0736 ft
Step-by-step explanation:
Bounce 1: 16*3/5=9.6
Bounce 2: 9.6*3/5=5.76
Bounce 3: 5.76*3/5=3.456
Bounce 4: 3.456*3/5=2.0736
Answer:
The ball will bounce to 2.07 feet after 4th drop.
Step-by-step explanation:
Bradley dropped a ball from a roof 16 feet high. So, its the initial height.
Each time the ball hits the ground it bounces 3/5 the previous height.
Means after 1st drop, the ball will again rise to [tex]\frac{3}{5}\times16= 9.6[/tex] feet.
Similarly after 2nd drop, it will bounce to [tex]\frac{3}{5}\times9.6=5.76[/tex]
After 3rd drop, it will bounce to [tex]\frac{3}{5}\times5.76=3.456[/tex] feet
After 4th drop, it will bounce to [tex]\frac{3}{5}\times3.456=2.0736[/tex] feet
Hence, the ball will bounce to 2.07 feet after 4th drop.
A pair of sneakers cost $75. This is $15 less than the cost of a pair of jeans. Write an equation that someone could use to find the amount of money that the jeans cost.
15+75=J.
So the jeans should be $90
Answer-
add 15 from 75 then that is it
75+15=90
answer fffffgggggggggggggggggg
Answer:
50 is the change per week. And the starting total is 650.
Step-by-step explanation:
It is in the question.
How many degrees has ABC been rotated about the origin?
The answers is A: 90 Degrees
Answer: The correct option is (A) 90°.
Step-by-step explanation: We are given to find the number of degrees by which the triangle ABC has been rotated counterclockwise about the origin.
From the graph, we note that
the co-ordinates of the vertices of triangle ABC are A(-8, 6), B(-5, 9) and C(-2, 6).
And, the co-ordinates of the vertices of the rotated triangle A'B'C' are (-6, -8), B(-9, -5) and C(-6, -2).
That is, the transformation is as follows :
(x, y) ⇒ (-y, x).
Since this is the transformation rule for 90 degrees counterclockwise, so the required number of degrees is 90 degrees.
Option (A) is CORRECT.
PLEASE HELP & SHOW WORK , ITS URGENT
it’s appreciated <3 !!
see if u understand the answer
Answer:
C
Step-by-step explanation:
The circumference (C) of a circle is calculated using
C= 2πr ← r is the radius and has to be found
Given C = 20π , then
2πr = 20π ( divide both sides by 2π )
r = [tex]\frac{20\pi }{2\pi }[/tex] = 10
The area (A) of a circle is calculated using the formula
A = πr² = π × 10² = 100π m² → C
Given FGE, find m=HFE if m=G - 65°
A. 25°
B. 50°
C. 60°
D. 65°
Answer:
The correct answer is option A. 25°
Step-by-step explanation:
From the figure we can see an isosceles triangle. FGE
<G = 65° (given)
m<G = m<E = 65°
To find the value of m<HFE
Consider the triangle FHE in the figure we get,
m<E + m<HFE + m<FHE = 180
m<HFE = 180 - (m<E + m<FHE)
= 180 - (65 + 90) = 25°
Therefore m<HFE = 25°
The correct answer is option A. 25°
The correct answer is option A. 25°
PLEASE HELP!!
If the circle graph below represents the responses from 350 people, how many people chose silver as their favorite car color?
Black-25%
White-10%
Silver-10%
Yellow-5%
Red-50%
350
10
35
100
For this you have to make two proportions that are [tex]\frac{part}{whole}[/tex] and set them equal to each other.
The first proportion represents the percent of people who like silver as their favorite car color
Since this is a circle graph the whole will always be 100 because percents are always taken out of 100
The part would be 10 because only 10% out of the 100% like silver
The second proportion is the people that represent the response.
350 would be the whole because that is the total amount of people surveyed
The part is unknown and what you are solving for.
Here is how the proportion should look like:
[tex]\frac{10}{100} = \frac{x}{350}[/tex]
Cross multiply (If you don't know what this is look at the image below to see my work)
The cross multiplication will give you:
3500 = 100x
Isolate x by dividing 100 to both sides
3500/100 = 100x/100
35 = x
This means that 35 people out of the 350 surveyed like silver cars
Hope this helped!
Answer:
If the circle graph below represents the responses from 350 people, how many people chose silver as their favorite car color?
100
35
10
350
Step-by-step explanation:
D. is right plz put me Brainliest plz
graph the line y=-3x
Answer:
Step-by-step explanation:
Graph y = -3x. Start at the origin (0, 0). Place a dark dot there. Now, starting with your pencil point on that dot, move 1 space to the right and from this new point move 3 spaces down. Place a dark dot at this new point.
Now draw a straight line through both dark dots. This is the desired graph.
Step-by-step explanation: Let's graph the equation y = -3x using its slope and y-intercept. The problem here is that our equation doesn't match up quite so well with the formula y = mx + b
Our slope or m which is represented by the coefficient of the x-term is clearly -3. However, you might be asking what is our y-intercept or b. Well, y = -3x can be thought of as y = -3x + 0. So you can now see that our b or y-intercept equals 0.
To graph the line, we start with the y-intercept. So our first point is a 0 on the y-axis and we call that point A. When the slope is a integer, you can change it to a fraction by putting it over 1. So our slope of -3 can be thought of as -3/1.
From point A, we would go down 3 units and over 1 unit to plot point B. Now we can connect points A and B like I did in the picture and we have our line.
List the positive factors of 30.
Answer:
1, 2, 3, 5, 6, 10, 15, 30.
Answer:
Positive factors of 30 are: 1, 2, 3, 5, 6, 10, 15, 30
Step-by-step explanation:
We are asked to list the positive factors of the number 30.
Factors are the whole numbers which when multiplied together produce another number. So positive factors only include the whole numbers that are greater than 0.
Positive factors of 30 include the following whole numbers:
[tex]1, 2, 3, 5, 6, 10, 15, 30[/tex]
The tree diagram below shows the possible combinations of juice and snack that can be offered at the school fair.
How many different combinations are modeled by the diagram?
Answer:
B) 8
Step-by-step explanation:
To count the number of possibilities on a tree diagram, all you need to do is count the total number of "branches" at the end of the "tree". Here, that is 8. Also, if the tree gets too big, you can multiply the number of combinations in the first sector, then the second, and so on. So, that will be 4 * 2 = 8.
Answer:
B). 8
Step-by-step explanation:
i go this right on my quiz if u want proof scroll down
I really hope this helps someone! have a great day!!
write 8.54 x 10 to the 3rd power in standard notation
Answer:
= 8.54 × 101
(scientific notation)
= 8.54e1
(scientific e notation)
= 85.4 × 100
(engineering notation)
(one)
= 85.4
(real number)