Answer:
5 - 3i.
Step-by-step explanation:
2 + 4i + 3 - 7i Bring like terms together:
= 2 + 3 + 4i - 71
= 5 - 3i.
Answer:
5 - 3i
Step-by-step explanation:
Real numbers are a subset of the complex numbers. Therefore it would only make sense that the complex numbers follow the same rule of additivity and multiplication as real numbers do:
[tex](2+4i)+(3-7i)=2+3+4i-7i=5-3i[/tex]
If the chance of getting a disease is 20 out of 100, this would be the same as having a ______ % chance
Answer:
20
Step-by-step explanation:
To calculate percent from a fraction, you can multiply the value of the fraction by 100. 20/100*100 is 20, so there is a 20% chance.
The required blank space could be filled with 20% as, If the chance of getting a disease is 20 out of 100, this would be the same as having a 20% chance.
Given that,
If the chance of getting a disease is 20 out of 100, this would be the same as having a ______ % chance, to determine what value can be put.
The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.
Here,
According to the question,
percentage of get affected by disease = 20 / 100 = 0.20 or 20%
Thus, the required blank space could be filled with 20% as, If the chance of getting a disease is 20 out of 100, this would be the same as having a 20% chance.
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The mother gave the two sons the same amount of money. When the older son spent $ 275 and the younger $ 250, the younger had 3 times more money than the older. How much money did the mother give to each son? solution: 292
Answer:
Each son received from their mother $287.50
Step-by-step explanation:
3(x - 275) = x - 250
2x = 825 - 250
x = 287.50
$287.50 - $275 = $12.50
Check the answer:
After spending the older son has $12.50
$287.50 - $250 = $37.50
After spending the younger son has $37.50
$37.50 ÷ $12.50 = 3 times
WHAT IS THE FORMULA FOR SEMICIRCLE AREA
Answer:
The formula for semicircle area is [tex]\frac{1}{2} \pi r^2[/tex]
Very similar to the formula for finding area of a circle, but since a semicircle is half of a circle, the formula will be revolving around halves.
Pls Help i'm stuck Solve for m∠C
m∠C =
Answer:
92 Degrees.
Step-by-step explanation:
As this is a Quadliateral inscribed in a circle, you can use a trick that is always true for these types of problems. Opposite angles will always be the same, since 92Degrees is A and is opposite to C, this means C is also 92Degrees, these type of shapes are also known as cyclic quadrilaterals
Use the digits 1-9 at lost one time each to make the equation true and give the solution
Answer:
[tex]2-3x=6x-7\\x=1[/tex]
(There are a lot more combinations tho. Read more!)
Step-by-step explanation:
The first thing to notice is that the answer has to be a whole number and that there are only 5 spaces.
Another thing to notice is that one of the x's is negative.
So the easiest thing is to set [tex]x=1[/tex].
The we can work backwards. There are multiple solutions that we can use. But any combination that adds to the same number will work.
Such as:
[tex]2-3x=6x-7\\x=1[/tex]
or
[tex]2-5x=3x-6\\x=1[/tex]
And so on.
Graph this parabola
Show all steps please!!!
In this case, the equation is in vertex form. To graph the parabola, we need to determine the y-intercept, x-intercept(s), and the vertex.
Vertex of Parabola:Vertex form: y = a(x + h)² - k
⇒ [y = 3(x + 2)² - 1] and [y = a(x - h)² - k] ⇒ Vertex: (h, k) ⇒ (-2, -1)X-intercept(s) of Parabola:Assume "y" as 0.
[tex]\implies 0 = 3(x + 2)^{2} - 1[/tex]
[tex]\implies 1 = 3(x + 2)^{2}[/tex]
Take square root both sides and simplify:
[tex]\implies\sqrt{1} = \sqrt{3(x + 2)^{2}}[/tex]
[tex]\implies1 = \sqrt{3 \times (x + 2) \times (x + 2)}[/tex]
[tex]\implies1 = (x + 2) \times \sqrt{3[/tex]
Divide √3 both sides:
[tex]\implies \±\huge\text{(}\dfrac{1 }{\sqrt{3}} \huge\text{)} = (x + 2)[/tex]
[tex]\implies \±\huge\text{(}\dfrac{\sqrt{1} }{\sqrt{3}} \huge\text{)} = (x + 2)[/tex]
Multiply √3 to the numerator and the denominator:
[tex]\implies \±\huge\text{(}\dfrac{\sqrt{1} \times \sqrt{3} }{\sqrt{3\times \sqrt{3}}} \huge\text{)} = (x + 2)[/tex]
[tex]\implies \±\huge\text{(}\dfrac{\sqrt{3} }{3}} \huge\text{)} = (x + 2)[/tex]
[tex]\implies \±\huge\text{(}\dfrac{\sqrt{3} }{3}} \huge\text{)} - 2 =x[/tex]
[tex]\implies x = \underline{-2.6...} \ \text{and} \ \underline{-1.4...} \ \ \ \ (\text{Nearest tenth})[/tex]
Y-intercept of Parabola:Assume "x" as 0.
⇒ y = 3(0 + 2)² - 1⇒ y = 3(2)² - 1⇒ y = 3(4) - 1⇒ y = 12 - 1⇒ y = 11y-intercept = 11 ⇒ (0, 11)
Determining the direction of the parabola:Since the first cooeficient is positive (+3), the direction of the parabola will be upwards.
Determining the axis of symmetry line:Axis of symmetry line: x-coordinate of vertex
Axis of symmetry line: x = -2
Plot the following on the graph:
y-intercept ---> 11 -----> (0, 11)x-intercept(s) -----> -1.4 and -2.6 -------> (-1.4, 0) and (-2.6, 0)Vertex -------> (-2, -1)Axis of symmetry ----> x = -2Refer to graph attached.
Answer:
VertexVertex form of a quadratic equation:
[tex]y=a(x-h)^2+k\quad \textsf{where }(h,k)\:\textsf{is the vertex}[/tex]
Given equation: [tex]y=3(x+2)^2-1[/tex]
Therefore, the vertex is (-2, -1)
x-intercepts (zeros)The x-intercepts are when [tex]y=0[/tex]:
[tex]\implies 3(x+2)^2-1=0[/tex]
[tex]\implies 3(x+2)^2=1[/tex]
[tex]\implies (x+2)^2=\dfrac13[/tex]
[tex]\implies x+2=\pm\sqrt{\dfrac13}[/tex]
[tex]\implies x+2=\pm\dfrac{\sqrt{3}}{3}[/tex]
[tex]\implies x=-2\pm\dfrac{\sqrt{3}}{3}[/tex]
[tex]\implies x=\dfrac{-6\pm\sqrt{3}}{3}[/tex]
Therefore, the x-intercepts are at -2.6 and -1.4 (nearest tenth)
y-interceptThe y-intercept is when [tex]x=0[/tex]:
[tex]\implies 3(0+2)^2-1=11[/tex]
So the y-intercept is at (0, 11)
Plot the graphAs the leading coefficient is positive, the parabola will open upwards.Plot the vertex at (-2, -1)Plot the x-intercepts (-2.6, 0) and (-1.4, 0)Plot the y-intercept (0, 11)The axis of symmetry is the x-value of the vertex. Therefore, the parabola is symmetrical about x = -2
**You don't need to plot the axis of symmetry - I have added it so that it is easier to draw the curve**
Polynomial? If so, is the
polynomial a monomial, binomial, or trinomial?
5/3m^2n^2p
Answer:
yes it is a polynomial. it is a monomial
Which of the following triangles have three sides of different length?
What steps are used to find the mean of a data set? Use the following data set as an example: 5, 4, 2, 6, 4, 3
Answer:
The mean would be 4
Step-by-step explanation:
Steps to find the mean.
1. Least to greatest.
2,3,4,4,5,6
2. Add all the numbers.
2+3+4+5+5,6
=24
3. Divided by how many numbers you have.
24÷6
=4
Hope this helps! Mark me brainlest if you want, have a great day!! :))
Answer: It would be 4
Step-by-step explanation: Hope that helps!
Which is part of the process in the formation of hail pellets? They are tossed up and down in clouds. They lose layers of ice and grow smaller. They grow to less than 5 mm in diameter. They form ice crystals directly from water vapor.
Answer:
A. They are tossed up and down in clouds
Step-by-step explanation:
The solution is, D. They grow heavy and fall to the ground., is part of the process in the formation of hail pellets.
What is hail pellets?Graupel is also called snow pellets or soft hail, as the graupel particles are particularly fragile and generally disintegrate when handled. Sleet are small ice particles that form from the freezing of liquid water drops, such as raindrops.
here we have,
Hail is a form of precipitation when droplets of water freeze together in the cold upper reaches of the thunderstorms.
Thee chunks of that range from 5 to 15 cm can be round and jagged. Hail fall on the ground in a solid form they are often associated with tornadoes and certain parts of the world receive more hail than other parts do.
These frozen droplets of water when fall from the clouds get uplifted by wind and that adds another layer to them. The freezing occurs below the zero degrees at an altitude of 11,000 feet.
Mostly found in North America Nebraska, colorado and Wyoming states. and African regions in winter and South America in summer.
Varies in diameter from peas shape to size of a softball.
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solve the triangle.round to the nearest degree.
Answer:
30°, 60°
Step-by-step explanation: AB:BC:CA=√3:1:2
A container of oatmeal is cylindrical. It is 9 inches tall and the base has a radius of 2 inches. There is 6 inches of oatmeal remaining in the container. What is the volume of the remaining oatmeal? Use 3.14 for TT. Round your answer to the nearest tenth.
Answer:
a cylindrical carton of oatmeal with radius 3.5 in. is 9 in. tall. all cardboard, how much cardboard is used to make the oatmeal carton?
Step-by-step explanation:
Abel ran more than 8 miles this week. which set of steps shows how to write an inequality that represents the number of miles abel ran? identify the variable as the number of miles. identify the inequality symbol as less than. identify the constant as 8 miles. write the inequality as m less-than 8. identify the variable as the number of miles. identify the inequality symbol as less than. identify the constant as negative 8 miles. write the inequality as m less-than negative 8. identify the variable as the number of miles. identify the inequality symbol as greater than. identify the constant as negative 8 miles. write the inequality as m greater-than negative 8. identify the variable as the number of miles, m. identify the inequality symbol as greater than. identify the constant as 8 miles. write the inequality as m greater-than 8.
The inequality that represents the scenario is x > 8
How to determine the inequality?From the question, we understand that:
Abel ran more than 8 miles this week
Let the number of miles be x.
The text "more than" means that we make use of the greater than inequality symbol
So, the inequality that determines the steps is:
x > 8
Read more about inequality at:
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Answer:
m
Step-by-step explanation:
The side lengths of four triangles are listed below.
Determine whether each triangle is a right triangle.
Select all options that do create a right triangle.
a. Sides 4,5,6
b. Sides 10,15,20
c. Sides 5,12,13
d. Sides 8,15,17
Answer:
C and D
Step-by-step explanation:
Use Pythagorean theorem to test
a^2 + b^2 = c^2 ? a and b are the shorter two sides c = longest side
Doing this for each data set shows C and D ARE rt triangles
What is the equation of the line that passes through the point (-2, 1) and has a
slope of 5/2?
Answer:
is it (3,3)
Step-by-step explanation:
(x,y)=(-2+5,1+2)
(x,y)=(3,3)
Find the area of the parallelogram below, after the
purple triangle-sized hole was removed.
Answer:
142.5
Step-by-step explanation:
Area of a triangle = 1/2*a*h
1/2*9*3 = 13.5
Area of a parallelogram = a*h
12*13 = 156
156-13.5 = 142.5
Choose all the common denominators for 1/9 and 1/2
Answer:
Common denominators of 9 and 2 are 18,36
Step-by-step explanation:
How many ways can Caroline choose 2 courses of each type?
Answer:
Step-by-step explanation:
I need more explanation to answer
i need this answerd ASAP ill give brainliest to whoever solves it first along with 3
40 points
Answer:
Below.
Step-by-step explanation:
Mean = (61+59+60+50+54+56+61+63)/8
= 464/8
= 58 degrees
Deviations:
61 - 58 = 3
59-58 = 1
60-58 = 2
50-58 = -8 = 8 (absolute value)
54-58= -4 = 4
56-58 = -2 = 2
61-58 = 3
63-58 = 6
MAD = (3+1+2+8+4+2+3+6) / 8
= 3.625
= 3.6 to the nearest tenth.
Find the surface area of the cone in terms of pi. 15cm 3cm
Answer:
SA = 54π cm^2
A
Step-by-step explanation:
[tex]{\pi}rs + {\pi} {r}^{2} [/tex]
radius = 3cm
slant height = 15 cm
follow the formula
3
If tan 0 =
4
what does sin O = ?
Answer:
B) 3/5
----------------------------------------------------------------------------------------------------------
SolveSo, we know that tantheta is 0.75, or 3 quarters, but we have to find the value of sintheta. If there are 4 angles on a triangle, we can label them as BC and AB.[tex]because~of~the~angles\\BC = 3k\\AB = 4k[/tex]
Now, we must find the value of AC using the pythagoras theorem.⇒ (AB)² + (BC)² = (AC)²
in which because of AB and BC's values, goes into...
⇒ (4k)² + (3k)² = (AC)²
because of that ↑ you get the values of what is below.
⇒ (AC)² = 16 k² + 9 k²
add 16k and 9k for the result below.
⇒ (AC)² = 25 k²
⇒ AC = ±5k
Hmm. An angle cannot be negative, so turn 5k to positive 5k. Last but- not least, we have to find the sintheta.the sin is the side opposite to the angle, so find the hypotenuse and opposite angle.
[tex]Side~opposite~to~angletheta\\= BC(3k)\\\\Hypotenuse\\= AC(5k)[/tex]
That said → [tex]sintheta = \frac{BC}{AC} = \frac{3k}{5k} = \frac{3}{5}[/tex]
________________________________________________________
Questions?Ask in comments.
The graph of linear function g passes through the points (-7, -4) and (7, 6)
Answer:
C. The slope is 5/7, and the y-intercept is 1.Step-by-step explanation:
You must solve the slope-intercept form with the graph of the linear function g passing through the points.
Use the slope-intercept form.
[tex]\underline{\text{SLOPE-INTERCEPT FORM:}}[/tex]
[tex]\Longrightarrow: \sf{y=mx+b}[/tex]
M= slopeB= y-intercept.Use the slope formula.
[tex]\underline{\text{SLOPE:}}[/tex]
[tex]\Longrightarrow \sf{\dfrac{y_2-y_1}{x_2-x_1} }[/tex]
(-7,-4) and (7,6)
y2=6y1=(-4)x2=7x1=(-7)[tex]\sf{\dfrac{6-\left(-4\right)}{7-\left(-7\right)}}[/tex]
Solve.
[tex]\sf{\dfrac{6-\left(-4\right)}{7-\left(-7\right)}=\sf{\dfrac{10}{14}=\dfrac{10\div2}{14\div2}=\dfrac{5}{7} }}[/tex]
Therefore, the slope is 5/7 and y-intercept is 1.The correct answer is C. "The slope is 5/7, and the y-intercept is 1."I hope this helps. Let me know if you have any questions.
4. The distance light travels in one year is approximately 5,870,000,000,000 miles. The distance light travels in 100 years is: (a) 587 × 10^8 miles,
(b) 587 × 10^10 miles,
(c) 587 × 10^-10 miles,
(d) 587 × 10^12 miles,
(e) 587 × 10^-12 miles
5,870,000,000,000 miles.
to find:The distance light travels in 100 years.
solution:The distance of the light travels in 100 years is:
5,870,000,000,000 × 100 miles.
= 587,000,000,000,000 miles
= 587 × 10^12 miles.
answer= option d
[tex]1 \: year = 5870000000000 \: miles[/tex]
To find:The distance which light can travel in 100 years.
Solution:to find the distance which light can travel in 100 years, multiply the distance which light can travel in 1 year (5,870,000,000,000 miles) by 100.
[tex] = 5870000000000 \times 100[/tex]
[tex] = 587000000000000 \: miles[/tex]
[tex] = 587 \times {10}^{12} [/tex]
Hence, the correct answer is option D
The following figures show the first two steps of a proof of the pythagorean theorem. which of the following statements about this proof is false?
Answer: C
Step-by-step explanation:
The area of the larger square is a^2 and the area of the smaller square is b^2, so the area is a^2 + b^2, not (a+b)^2.
Please help! 23, 24, and 25
Answer:
please let's remove all the scamers on brainly, help me by not clicking on such scam links
How do you solve this???[tex]\frac{3}{2}r = -1[/tex]
Answer:
[tex]\boxed{\sf{r=-\dfrac{2}{3} }}[/tex]Step-by-step explanation:
Isolate the term of r, from one side of the equation.
3/2r=-1First, multiply by 2 from both sides.
2*3/2r=2(-1)
Solve.
3r=-2
Then, you divide by 3 from both sides.
3r/3=-2/3
Solve.
Divide the numbers from left to right.
r=-2/3
-2/3=-0.66
[tex]\Longrightarrow: \boxed{\sf{r=-\dfrac{2}{3}}}[/tex]
Therefore, the correct answer is r=-2/3.I hope this helps! Let me know if you have any questions.
Answer:
[tex]{ \qquad{ {{ \tt{ - \frac{2}{3} }}}}} \\ \\[/tex]
Given equation,
[tex] \\ { \longrightarrow \qquad{ {{ \tt{ \frac{3}{2} \: r = -1 }}}}} \\ \\[/tex]
Multiplying both sides by [tex] \sf \dfrac{1}{3}[/tex] we get :
[tex] \\ { \longrightarrow \qquad{ {{ \tt{ \frac{1}{3} \times \frac{3}{2}r = \frac{1}{3} \times -1 }}}}} \\ \\[/tex]
[tex] { \longrightarrow \qquad{ {{ \tt{ \frac{1}{ \cancel3} \times \frac{ \cancel3}{2}r = - \frac{ 1}{ 3} }}}}} \\ \\[/tex]
[tex] { \longrightarrow \qquad{ {{ \tt{ \frac{1}{2}r = - \frac{1}{3} }}}}} \\ \\[/tex]
Now, Multiplying both sides by 2 we get :
[tex] \\ { \longrightarrow \qquad{ {{ \tt{ 2 \times \frac{1}{2}r = 2 \times - \frac{1}{3} }}}}} \\ \\[/tex]
[tex]{ \longrightarrow \qquad{ {{ \tt{ \cancel2 \times \frac{1}{ \cancel2}r = - \frac{2}{3} }}}}} \\ \\[/tex]
[tex]{ \longrightarrow \qquad{ {{ \tt{ {1}r = - \frac{2}{3} }}}}} \\ \\[/tex]
[tex]{ \longrightarrow \qquad{ \frak {{ \pmb{ r = - \frac{2}{3} }}}}} \\ \\[/tex]
Simplify Each Radical Expression. Leave in radical form. (Do not use decimals.)
√(196) + √(441)
[tex]\sqrt{196} + \sqrt{441}\\\\=\sqrt{14^2} + \sqrt{21^2}\\\\=14+21\\\\=35[/tex]
(I need help ASAP please
Answer:
C) 24
Step-by-step explanation:
Alternate interior angles are equal
so angle 1 equals angle 6
3x+10=x+58
subtract 10 from both sides
3x=x+48
then subtract x from both sides
2x=48
dived each side by two
x=24
A triangle has two sides of length 6 and 19. What is the largest possible whole-number length for the third side?
Answer: 18
Step-by-step explanation:
If 19 Is hypotenuse and 6 is one of the sides
Mr. Richardson is driving to a town 85 miles away. He drives 35 miles per hour for 2 hours before stopping for lunch. He drives 6 more miles and stops for gas. Which expression shows how many miles Mr. Richardson has left to drive?
85 - (35 x 2) - 6
85 - 35 - 2 - 6
(85 - 35) x 2 - 6
85 - 35 + 2 - 6
Answer:
(a) 85 - (35 x 2) - 6
Step-by-step explanation:
The miles Mr. Richardson has left to drive will be the difference between the distance to his goal and the miles he has alread driven. The relation between distance, speed, and time can be used to find the miles he drove before lunch.
__
before lunchdistance = speed × time
miles before lunch = (35 mi/h) × (2 h) = (35 × 2) mi
total drivenThe total miles driven before stopping for gas will be ...
miles before stopping for gas = (miles before lunch) + (6 more miles)
= 35 ×2 +6 . . . miles
miles remainingThen the remaining miles are ...
remaining = trip miles - miles driven
= 85 -(35 ×2 +6)
= 85 - (35 ×2) -6 . . . . . miles left to drive