Answer:
[tex]\sqrt{274}[/tex]
Step-by-step explanation:
Given [tex]z_1=-8+3i,\ z_2=7-4i.[/tex]
1. Find the difference [tex]z_1-z_2:[/tex]
[tex]z=z_1-z_2=-8+3i-(7-4i)=-8+3i-7+4i=(-8-7)+(3i+4i)=-15+7i.[/tex]
This complex number has real part [tex]Rez=-15[/tex] and imaginary part [tex]Imz=7.[/tex]
2. The modulus of complex number z is
[tex]|z|=\sqrt{Re^2z+Im^2z}=\sqrt{(-15)^2+7^2}=\sqrt{225+49}=\sqrt{274}.[/tex]
The distance between [tex]z_1\ \text{and}\ z_2[/tex] is:
16.5529 units
Step-by-step explanation:We know that the difference between two complex numbers:
[tex]z_1=a_1+ib_1\ \text{and}\ z_2=a_2+ib_2[/tex] is given by:
[tex]|z_1-z_2|=|(a_1+ib_1)-(a_2+ib_2)|\\\\i.e.\\\\|z_1-z_2|=|(a_1-a_2)+i(b_1-b_2)|\\\\|z_1-z_2|=\sqrt{(a_1-a_2)^2+(b_1-b_2)^2}[/tex]
Here we have:
[tex]z_1=-8+3i\ \text{and}\ z_2=7-4i[/tex]
i.e.
[tex]a_1=-8\ ,\ b_1=3,\ a_2=7\ \text{and}\ b_2=-4[/tex]
i.e. we have:
[tex]|z_1-z_2|=\sqrt{(-8-7)^2+(3-(-4))^2}\\\\|z_1-z_2|=\sqrt{15^2+7^2}\\\\|z_1-z_2|=\sqrt{225+49}\\\\|z_1-z_2|=\sqrt{274}\\\\|z_1-z_2|=16.5529[/tex]
What’s 1.28 round to the nearest tenth
Answer:
I.3 is the answer
Answer:
It would be 1.30
Step-by-step explanation: It would be 1.3 because to round up it has to be over 5 and to round down it has to be under 5. So in this case it is 28 and 8 is over 5, so you would round to the nearest tenth which would be 1.30.
if the bases of an isosceles trapezoid have lengths of 13 and 26 what is the length of the median
Answer: the answer is C . 19.5 units - APEX :D
Answer:
Answer is 19.5 units
Step-by-step explanation:
Given that there is a trapezoid.
Its bases are 13 and 26 respectively.
Non parallel sides are congruent
To find the median that is the length of line connecting the midpoints of the non parallel sides
If we draw any one diagonal we see that median is the line connecting the mid point of two triangles with the parallel sides as bases
Hence length of median= 1/2 (base 1+base 2)
(By triangle mid point theorem)
= 1/2 (13+26)
=19.5 units
Identify this conic section.
9x 2 + 4y 2 = 36
Answer:
The correct answer on Odyssey is Ellipse
Step-by-step explanation:
I got it correct on Odyssey
Find the correct answer and solve?
|y-9|=6
The solutions to the absolute value equation |y-9|=6 are y= 15 and y= 3. These values make the original equation true.
Explanation:The mathematical question asked is: |y-9|=6. This represents an absolute value equation. In an absolute value equation, the quantity inside the absolute value brackets can either equal the positive or negative value on the other side of the equation. Therefore, you can create two separate equations out of this original equation: y-9 = 6 and y-9 = -6. Solving for y in these equations will give you the answers: y = 15 and y = 3.
So, the solutions to the absolute value equation are y = 15 and y = 3. These results mean that if y equals either 15 or 3, the original equation will hold true.
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The absolute value equation |y-9|=6 has two solutions: y= 15 and y= 3. The original equation is true with these values.
The |y-9|=6 is the mathematical question. This is an absolute value equation. The quantity inside the absolute value brackets in an absolute value equation can either equal the positive or negative value on the other side of the equation. As a result, you can deduce two independent equations from this original one: y-9 = 6 and y-9 = -6. Solving for y in these equations yields the following results: y = 15 and y = 3.
As a result, the absolute value equation answers are y = 15 and y = 3. These findings imply that the original equation will be true whether y equals either 15 or 3.
Below are two different function f(x) and g(x) what can be determined about their slopes? Need this answer ASAP plzzzz!!!
D) The function g(x) has a larger slope
The change between any two y-coordinates in g(x) is greater than any change in the y-coordinates in f(x)
-2|3-2r|<-34 how do you solve this?
[tex]|a|<b\iff a< b\ and\ a > -b\\\\|a|>b\iff a>b\ or\ a<-b[/tex]
[tex]-2|3-2r|<-34\qquad\text{change the signs}\\\\2|3-2r|>34\qquad\text{divide both sides by 2}\\\\|3-2r|>17\iff3-2r>17\ or\ 3-2r<-17\qquad\text{subtract 3 from both sides}\\\\-2r>14\ or\ -2r<-20\qquad\text{change the signs}\\\\2r<-14\ or\ 2r>20\qquad\text{divide both sides by 2}\\\\\boxeD{r<-7\ or\ r>10}[/tex]
I need help! I need to know how to do the work and what the answer is plzzz
Answer:
36 ft
Step-by-step explanation:
So the proportion of the big triangle is 48:4 or 12:1. So if the small triangle’s height is 3 feet, then 3*12 is 36 feet.
Answer: 36 ft
Step-by-step explanation:
Similar triangles means there is a constant proportion between the left legs, the base legs, and the hypotenuses.
[tex]\frac{LeftLeg(large)}{LeftLeg(small)}= \frac{BaseLeg(large)}{BaseLeg(small)}[/tex]
[tex]\frac{x}{3}= \frac{48}{4}[/tex]
Cross multiply: x(4) = 3(48)
solve for x: ÷4 ÷4
x = 3(12)
= 36
What is the equation of a line with a slope of 3 and a point (3, 1) on the line?
Express the equation in the form of y=mx+b where m is the slope and b is the y-intercept.
Enter your answer in the box.
Answer:
The equation of the line would be y = 3x - 8
Step-by-step explanation:
To find any equation when you have the slope and a point, start with point-slope form and then solve for y.
y - y1 = m(x - x1)
y - 1 = 3(x - 3)
y - 1 = 3x - 9
y = 3x - 8
Daisy wants to buy a car battery that has a full price of $85 plus a 6% sales tax, which is the better offer, a 20%-off sale or a $15 coupon?
Answer: 20% off sale because Daisey will have to pay a total of 72
Step-by-step explanation:
Please help with this question
Answer:
The answer is y=1.4x
Step-by-step explanation:
You have to find the change of y over the change of x. So you have to find how much each value is changing by.
Y-side
5.6-2.8= 2.8
8.4-5.6=2.8
11.2-8.4=2.8
X-side
4-2=2
6-4=2
8-6=2
If you divide 2.8 by 2 you get 1.4
So the slope is 1.4
what is 2fifth times 6seventh
Answer:
12/35
Step-by-step explanation:
"2fifth" = 2/5
"6seventh" = 6/7
"times" = *
Multiply across:
(2/5) * (6/7) = 12/35
12/35 is your answer
~
Answer:
12/35
Step-by-step explanation:
2/5 times 6/7
First multiply the numerators.
2 x 6 = 12
Then multiply the denominators.
5 x 7 = 35
Your answer is 12/35
Becky created a graph to represent her distance away from home one afternoon . She left home and ran to the park , met some friends and stayed at the park , and then walked back home using the same route . Which graph could Becky have created ?
Answer:
A discrete graph
Step-by-step explanation:
It would make sense because you can track the distances on the coordinate plane
Answer:
The first graph or A.
Step-by-step explanation:
I need help please. Must be correct. 10 points. Thanks
We have the supplementary angles.
The sum of the measures of the two Supplementary Angles is 180°.
Therefore we have the equation:
13x - 2 + 39 = 180
13x + 37 = 180 subtract 37 from both sides
13x = 143 divide both sides by 13
x = 11
Answer: 11The recipe for mint chocolate ice cream requires 2 1/4 cups of cream for 5 people. You need ice cream for 15 people. How much cream will you need?
Answer:
Step-by-step explanation:
i know it'
convert 2 1/4 into improper fraction or do it as same as it is
So, this is ratio and proportion. so, multiply 2 1/4 or 2.25 to 8 and divide it to 5. so, the answer is 3.6 or 3 3/5.
The following is an incomplete paragraph proving that the opposite sides of parallelogram ABCD are congruent:
Parallelogram ABCD is shown where segment AB is parallel to segment DC and segment BC is parallel to segment AD.
According to the given information, segment AB is parallel to segment DC and segment BC is parallel to segment AD.. Construct diagonal A C with a straightedge. It is congruent to itself by the Reflexive Property of Equality. Angles BAC and DCA are congruent by the Alternate Interior Angles Theorem. Angles BCA and DAC are congruent by the same theorem. __________. By CPCTC, opposite sides AB and CD, as well as sides BC and DA, are congruent.
Which sentence accurately completes the proof?
Triangles BCA and DAC are congruent according to the Angle-Angle-Side (AAS) Theorem.
Triangles BCA and DAC are congruent according to the Angle-Side-Angle (ASA) Theorem.
Angles ABC and CDA are congruent according to a property of parallelograms (opposite angles congruent).
Angles BAD and ADC, as well as angles DCB and CBA, are supplementary by the Same-Side Interior Angles Theorem.
Answer: Triangles BCA and DAC are congruent according to the Angle-Side-Angle (ASA) Theorem.
Step-by-step explanation:
Given : ABCD is a parallelogram.
That is, AB ║ CD and AD ║BC
We have to prove that: AB≅CD and AD≅BC
Proof:
Construct diagonal AC in the parallelogram ABCD.
Since, AC ≅ AC ( reflexive)
∠ BAC ≅ ∠ DCA ( By the alternative interior angle theorem)
∠ BCA ≅ ∠ DAC ( By the alternative interior angle theorem)
⇒ Δ BCA ≅ Δ DAC ( By ASA congruence postulate )
⇒ AB≅CD as well as AD≅BC ( BY CPCTC )
Thus, the opposite side of the parallelogram are congruent.
Diagonal AC is congruent to itself by the Reflexive Property of Equality.
Translate the sentence into an equation. Five more than the quotient of a number and 7 is equal to 8 . Use the variable c for the unknown number .
Answer:
c ÷ 7 + 5 = 8
Step-by-step explanation:
The Translate the sentence into an equation is c/7 +5 =8.
What is Algebraic expression ?
Algebraic expressions are the idea of expressing numbers using letters or alphabets without specifying their actual values. The basics of algebra taught us how to express an unknown value using letters such as x, y, z, etc. These letters are called here as variables. An algebraic expression can be a combination of both variables and constants. Any value that is placed before and multiplied by a variable is a coefficient.
given variable is given as c therefore, the translation of the given equation Five more than the quotient of a number and 7 is equal to 8 will be :
c/7 +5 =8
Therefore, the Translate the sentence into an equation is c/7 +5 =8.
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Integration of (3X(X^2+3)^4) dx
[tex] [/tex]
Answer:
Step-by-step explanation:
[tex]\int 3x(x^2+3)^4 \ dx[/tex].
It is apparently obvious we could expand the bracket and integrate term-by-term. This method would work but is very time consuming (and you could easily make a mistake) so we use a different method: integration by substitution.
Integration by substitution involves swapping the variable [tex]x[/tex] for another variable which depends on x: [tex]u(x)[/tex]. (We are going to choose [tex]u[/tex] for this question).
The very first step is to choose a suitable substitution. That is, an equation [tex]u=f(x)[/tex] which is going to make the integration easier. There is a trick for spotting this however: if an integral contains both a term and it's derivative then use the substitution [tex]u=\text{The Term}[/tex].
Your integral contains the term [tex]x^2 + 3[/tex]. The derivative is [tex]2x[/tex] and (ignoring the constants) we see [tex]x[/tex] is also in the integral and so the substitution [tex]u=x^2+3[/tex] will unravel this integral!
Step 2: We must now swap the variable of integration from x to u. That means interchanging all the x's in the integrand (the term being integrated) for u's and also swapping (dx" to "du").
[tex]u=x^2+3 \Rightarrow \frac{du}{dx}=2x \Rightarrow dx = \frac{1}{2x} du[/tex]
Then,
[tex]\int 3x(x^2+3)^4 \ dx = \int 3x \cdot u^4 \cdot \frac{1}{2x} du = \int \frac{3}{2}u^4\ du[/tex].
The substitution has made this integral is easy to solve!
[tex]\int \frac{3}{2}u^4\ du= \frac{3}{10}u^5 + C[/tex]
Finally we can substitute back to get the answer in terms of x:
[tex]\int 3x(x^2+3)^4 \ dx = \frac{3}{10}(x^2+3)^5+C[/tex]
Write an expression to represent: Four minus the product of one and a number x.
Answer:
4 - x
Step-by-step explanation:
product means multiply
the product of 1 and x = 1 × x = x
This is then subtracted ( minus ) from 4 giving
4 - x ← expression representing the situation
Answer:
2*4-6
Step-by-step explanation:
PLEASE HELP ME: if the equation of the regression line for the data set (3,6),(6,2),(9,10) is y=2/3x+2, what is the SSE for the data set?
The SSE for the data set is: 24
Step-by-step explanation:The data points are given by:
(3,6),(6,2),(9,10)
The data points are as follows:
when x=3 y=6
when x=6 y=2
and when x=9 y=10
Also, the line of best fit is as follows:
[tex]y=\dfrac{2}{3}x+2[/tex]
The SSE( sum of square for error ) is calculated as follows:
Firstly we find the y-values from the line of best fit corresponding to x-values as in the data points.Now we find the residual corresponding to each x.( i.e. difference between the actual y-value and y-value on the line of best fit)Square this difference quantities and add them up to get SSE of the data set.The y-values from the line of best fitwhen x=3
from the line of best fit we have: y=4
when x=6
then y=6
when x=9
then y=8
Hence, the residual value is:when x=3 6-4= -2
when x=6 2-6= -4
and when x=9 10-8=2
Hence, the square of these difference quantity is:
(-2)²=4
(-4)²=16
and (2)²=4
Hence, the sum of these square quantity is: 4+16+4=24
Hence, the SSE of data is: 24
Assessment items Veena ate lunch at a deli. She ordered a turkey sandwich for $9.25 and a salad for $4.35. The tax was 7.5%. What is the amount of tax for Veena's meal?
I can't remember how to add tax! Please help me! First correct answer gets Brainleist!
Answer:
$1.02
Step-by-step explanation:
9.25+4.35=13.60
13.60X0.075=1.02
Tax= 1.02
Answer:
$1.02
Step-by-step explanation:
$9.25+$4.35=$13.60
7.5----0.075
$13.60 times 0.075
$1.02
To add tax you take the decimal and move it to the left 2 times,
example: 6%---- .06
you then would multiply .06 by the price to get the price of the tax.
76-42+65/2. ONLY ANSWER IF YOU KNOW IT FOR SURE.
Answer:
49.5
Step-by-step explanation:
76-42+65 is 99, the you divide by 2, and that is 49.5
Which of the functions below could have created this graph?
Answer:
The answer is C
Step-by-step explanation:
The correct option is A. (F(x)=-x^{7}+4x^{3}-2x^{2}). This function matches all the key properties observed in the graph.
Sure, I've analyzed the image you sent and I can help you determine the correct option.
Based on the graph, we can see that it has the following properties:
It has three turning points, one minimum point and two maximum points.
The end behavior as x approaches positive or negative infinity is that the function increases without bound.
It intersects the x-axis three times.
Let's analyze the answer choices based on these observations:
Option A: (F(x)=-x^{7}+4x^{3}-2x^{2})This function has an odd leading term, which aligns with the increasing end behavior.
It has three factors, matching the number of x-intercepts.
By graphing this function, we can see that it matches the shape of the given graph with a minimum point followed by two maximum points.
Option B: (F(x)=x^{8}+4x^{4}+20x^{2})This function has an even leading term, which does not align with the increasing end behavior.
Even though it has four factors, it intersects the x-axis only twice.
Option C: (F(x)=x^{9}+12x^{8}+x^{7})This function has an odd leading term, which aligns with the increasing end behavior.
However, it only has two factors, not matching the three x-intercepts of the graph.
Option D: (F(x)=-x^{6}+x^{3}-x^{2})This function has an even leading term, which does not align with the increasing end behavior.
It also only has two factors, not matching the three x-intercepts of the graph.
Points M, N, and P are respectively the midpoints of sides AC , BC , and AB of △ABC. Prove that the area of △MNP is on fourth of the area of △ABC.
Answer:
The area of △MNP is one fourth of the area of △ABC.
Step-by-step explanation:
It is given that the points M, N, and P are the midpoints of sides AC, BC and AB respectively. It means AC, BC and AB are median of the triangle ABC.
Median divides the area of a triangle in two equal parts.
Since the points M, N, and P are the midpoints of sides AC, BC and AB respectively, therefore MN, NP and MP are midsegments of the triangle.
Midsegments are the line segment which are connecting the midpoints of tro sides and parallel to third side. According to midpoint theorem the length of midsegment is half of length of third side.
Since MN, NP and MP are midsegments of the triangle, therefore the length of these sides are half of AB, AC and BC respectively. In triangle ABC and MNP corresponding side are proportional.
[tex]\triangle ABC \sim \triangle NMP[/tex]
[tex]MP\parallel BC[/tex]
[tex]MP=\frac{BC}{2}[/tex]
By the property of similar triangles,
[tex]\frac{\text{Area of }\triangle MNP}{\text{Area of }\triangle ABC}=\frac{PM^2}{BC^2}[/tex]
[tex]\frac{\text{Area of }\triangle MNP}{\text{Area of }\triangle ABC}=\frac{(\frac{BC}{2})^2}{BC^2}[/tex]
[tex]\frac{\text{Area of }\triangle MNP}{\text{Area of }\triangle ABC}=\frac{1}{4}[/tex]
Hence proved.
The area of triangle MNP is one-fourth that of triangle ABC, because M, N, and P are midpoints leading to the smaller triangle being similar to the larger, and thus their area ratio due to the proportional side lengths is 1:4.
Explanation:In Mathematics, proving that the area of △MNP is a fourth of that of △ABC involves the concept of similar triangles and their properties. We know that M, N, and P are the midpoints of BC, AC, and AB. Due to this, triangle MNP is similar to triangle ABC as per the Midpoint theorem. The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides. In this case, the ratio of the sides would be 1:2 (since M, N, P are midpoints).
Therefore, the ratio of their areas (△MNP:△ABC) would be (1⁄2)², which is 1/4. Hence, the area of △MNP is one-fourth of the area of △ABC.
This clearly demonstrates that the area of the smaller triangle formed by the midpoints of a larger triangle equates to a fourth of the total area of the initial triangle.
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If P(A)=0.50, P()=0.40, and P(AuB)=0.15
a=0.55
b=0.65
c=0.90
d=0.75
Answer:
P(A ∩ B) = 0.75 (option d)
Step-by-step explanation:
P(A)=0.50
P(B)=0.40
P(A U B)=0.15
P(A ∩ B)=?
P(A U B)=P(A)+P(B)-P(A ∩ B)
Replacing the given values:
0.15=0.50+0.40-P(A ∩ B)
Adding like terms:
0.15=0.90-P(A ∩ B)
Solving for P(A ∩ B):
Subtracting 0.90 both sides of the equation:
0.15-0.90=0.90-P(A ∩ B)-0.90
Subtracting:
-0.75 = -P(A ∩ B)
Multiplying both sides of the equation by -1:
(-1)(-0.75) = (-1) ( -P(A ∩ B) )
0.75 = P(A ∩ B)
P(A ∩ B) = 0.75
Answer:
d=0.75
Step-by-step explanation:
given ef intersects gh at point D and ef is perpendicular to gh, what is the measure of hdf
Below is an image of what you have described. Since EF intersects GH perpendicularly - all resulting angles will be 90° by the definition of intersection of perpendicular lines.
This is to say that, Angle GDE, GDF, HDF, and HDE are all 90° angles.
Dan made 3 trips to visit his grandmother. He drove a total of 71.10 miles. How many miles did Dan drive on each trip?
Answer:
Dan drove 23.7 miles each trip.
Step-by-step explanation:
If he drove a total of 71.10 miles in three trips and you are trying to find how many miles he drove each trip then you would divide the total miles by the number of trips. You would do, 71.10/3 which is equal to 23.7, which is your answer.
Hope this helps!
What is the value of x?
a. 35 degrees
b. 25 degrees
c. 17 degrees
d. 8 degrees
Which point represents the origin? A.point k B.point m C. point w D.point j
Answer:
Where is the diagram
Step-by-step explanation:
What is an acrostic poem for the word percent
Final answer:
An acrostic poem for the word 'percent' is crafted with each line pertaining to the process and concept of calculating percents, expressed as a part of 100, or ratios with a denominator of 100.
Explanation:
An acrostic poem for the word percent could be:
Perusing numbers, calculations at hand,
Every figure is neatly planned.
Ratios and fractions - they all fit,
Calculations to make you think a bit.
Each part of a hundred, clearly set,
Numerical values that we get,
Twenty, fifty, seventy-five, all to percent we convert and drive.
This acrostic poem takes the word percent and creates a line for each letter that relates to the concept of percentages, which are ratios with a denominator of 100. Calculating percents involves setting up equivalent fractions or converting to decimals and fractions for ease of use in various mathematical situations. An understanding of this concept is essential for mathematical proficiency.
What is the slip of a line that is parallel to the line (0,3) (3,2)
Answer:
The slope is -1/3
Step-by-step explanation:
We can find the slope of a line using the formula
m = (y2-y1)/(x2-x1)
= (2-3)/(3-0)
= (-1/3)
=-1/3
Answer:
m= -1/3
Step-by-step explanation:
Slope is determined from the formula:
y2-y1/x2-x1
Input the corresponding numbers in the formula.
2-3/3-0
-1/3
m= -1/3