Answer:
21
Step-by-step explanation:
5x-3x=18+15-9
2x=42 /:2
x=21
Explain in detail with at least two sentences how to represent the product of A and B geometrically given that A=15 + 56i and B = 7 + 4i. Give the coordinate of A • B in polar form.
Answer:
Basically each part of the first complex number gets multiplied by each part of the second complex number. You are multiplying 2 binomials.
(15 + 56i(7 + 4i)
= 105 + 60i + 392i + 224i^2
= 105 + 452i - 224 ( because i^2 = -1)
= - 119 + 452i
Step-by-step explanation:
let me know if this helps!
Let ABC be a triangle such that AB=13 BC=14 and CA=15. D is a point on BC such that AD Bisects
Answer:
Area of triangle ADC is 54 square unit
Step-by-step explanation:
Here is the complete question:
Let ABC be a triangle such that AB=13, BC=14, and CA=15. D is a point on BC such that AD bisects angle A. Find the area of triangle ADC .
Step-by-step explanation:
Please see the attachment below for an illustrative diagram
Considering the diagram,
BC = BD + DC = 14
Let BD be [tex]x[/tex] ; hence, DC will be [tex]14-x[/tex]
and AD be [tex]y[/tex]
To, find the area of triangle ADC
Area of triangle ADC = [tex]\frac{1}{2} (DC)(AD)[/tex]
= [tex]\frac{1}{2}(14-x)(y)[/tex]
We will have to determine [tex]x[/tex] and [tex]y[/tex]
First we will find the area of triangle ABC
The area of triangle ABC can be determined using the Heron's formula.
Given a triangle with a,b, and c
[tex]Area =\sqrt{s(s-a)(s-b)(s-c)}[/tex]
Where [tex]s = \frac{a+b+c}{2}[/tex]
For the given triangle ABC
Let [tex]a[/tex] = AB, [tex]b[/tex] = BC, and [tex]c[/tex] = CA
Hence, [tex]a = 13, b= 14,[/tex] and [tex]c = 15[/tex]
∴ [tex]s = \frac{13+14+15}{2} \\s= \frac{42}{2}\\s = 21[/tex]
Then,
Area of triangle ABC = [tex]\sqrt{(21)(21-13)(21-14)(21-15)}[/tex]
Area of triangle ABC = [tex]\sqrt{(21)(8)(7)(6)}[/tex] = [tex]\sqrt{7056}[/tex]
Area of triangle ABC = 84 square unit
Now, considering the diagram
Area of triangle ABC = Area of triangle ADB + Area of triangle ADC
Area of triangle ADB = [tex]\frac{1}{2} (BD)(AD)[/tex]
Area of triangle ADB = [tex]\frac{1}{2}(x)(y)[/tex]
Hence,
Area of triangle ABC = [tex]\frac{1}{2}(x)(y)[/tex] + [tex]\frac{1}{2}(14-x)(y)[/tex]
84 = [tex]\frac{1}{2}(x)(y)[/tex] + [tex]\frac{1}{2}(14-x)(y)[/tex]
∴ [tex]84 = \frac{1}{2}(xy) + 7y - \frac{1}{2}(xy)[/tex]
[tex]84 = 7y\\y = \frac{84}{7}[/tex]
∴ [tex]y = 12[/tex]
Hence, [tex]y =[/tex] AD = 12
Now, we can find BD
Considering triangle ADB,
From Pythagorean theorem,
/AB/² = /AD/² + /BD/²
∴13² = 12² + /BD/²
/BD/² = 169 - 144
/BD/ = [tex]\sqrt{25}[/tex]
/BD/ = 5
But, BD + DC = 14
Then, DC = 14 - BD = 14 - 5
BD = 9
Now, we can find the area of triangle ADC
Area of triangle ADC = [tex]\frac{1}{2} (DC)(AD)[/tex]
Area of triangle ADC = [tex]\frac{1}{2} (9)(12)[/tex]
Area of triangle ADC = 9 × 6
Area of triangle ADC = 54 square unit
Hence, Area of triangle ADC is 54 square unit.
One number is two less than three times another. If their sum is decreased by two, the result is four. Find the numbers.
The smaller of the numbers is ___ and the larger is ___
Answer: The smaller of the numbers is 2 and the larger is 4.
Step-by-step explanation: 2x3-2=4. 2+4-2=4
Answer:
The bigger number is 1 and the smaller number is also 1
Step-by-step explanation:
One number is 2 less than 3 times another
x + 2 = 3y
If their sum is decreased by 2 the result is 4
(x + 2 + 3y) - 2 = 4
x + 3y = 4
x = 4 - 3y
Substituting value of x, 4 - 3y , in x + 2 = 3y
4 - 3y + 2 = 3y
6 - 3y = 3y
6 = 3y + 3y
6 = 6y
Divide both sides by coefficient of y, 6
y = 1
Substituting value of y, 1 in x + 2 = 3y
x + 2 = 3(1)
x + 2 = 3
x = 3 - 2
x = 1
Problem 1
1.a. Use addition or subtraction to rewrite the equation.
13 POINTS
Enter the new equation as your answer.
7x - 3 = -17
Enter your answer
2.b. Use multiplication or division to rewrite the equation that you entered as an answer in part a.
Enter the new equation as your answer. *
(1 Point)
Enter your math answer
Answer:
7x = -14x = -2Step-by-step explanation:
1. Using the addition property of equality, we can add 3 to both sides of the equation. Then it can be rewritten as ...
7x -3 +3 = -17 +3
7x = -14
__
2. Using the division property of equality, we can divide both sides of the equation by 7. Then it can be rewritten as ...
7x/7 = -14/7
x = -2
_____
Additional comment
Note that we have used these steps to solve the equation, find the value of x that makes it true. We could use different steps to rewrite the equation to almost anything you want:
7x -3 -95 = -17 -95 ⇒ 7x -98 = -112 . . . . . subtract 95 from both sides
12(7x -98) = 12(-112) ⇒ 84x -1176 = -1344 . . . . multiply both sides by 12
The resulting equation is not helpful for finding a solution, but it is an accurate rewrite of the original equation.
Mathematics Free Test 1- 0.75 as a fraction.
Answer: [tex]\frac{3}{4}[/tex]
Step-by-step explanation:
Convert from decimal to fraction.
0.75 = 3/4. That is your answer.
Answer:
3/4 i believe.
Step-by-step explanation:
Sebastian has a bag of 15 blue marbles, 18 red marbles, and 12 yellow marbles. He reaches into the bag three times and pulls out 2 red marbles and a blue marble. What is the probability that he reaches into the bag and pulls out a yellow marble next? A. 1/4 B. 8/21 C. 2/7 D. 5/14
===================================================
Explanation:
Initially there are 15+18+12 = 45 marbles total. He selects 3 marbles (2 reds, 1 blue).
Assuming he doesn't put the three marbles back, this means there are now 45-3 = 42 marbles overall. The yellow count hasn't changed since the first three marbles do not involve yellow. We have 12 yellow out of 42 which leads to the fraction 12/42 to represent the probability of getting yellow.
Reduce 12/42 to get 2/7. You divide both parts by the GCF 6.
-------
Side note: if he did put the marbles back, then the probability of getting yellow would be 12/45 = 4/15
help pls!! 15 points!
Answer:
Third option choice
Step-by-step explanation:
Notice that the angle is in the second quadrant, where the cosine is negative, the sine is positive and the tangent negative. In particular given the value of the cosine you are located at the angle 150 degrees, which gives a sine of 1/2 and a tangent given by [tex]-\sqrt{3} /3[/tex]
Therefore the third option is the correct one.
What’s the difference between evaluating an expression for a given value of a variable and solving an equation?
HELP ME WITH THIS (a+5)(b-3)
Answer:
The answer is ab-3a+5b-15
Step-by-step explanation:
apply de disruptive property by multiplying each term a+5by each term b-3
Hope this helps :)
Answer:
here you go ab-3a+5b-15
n f(x) = 2x , x=5. What is the value of the function?
Samuel was riding in the back seat of the station wagon on the way home after a long and tiring day at the
beach. He fell asleep halfway home. He didn't wake up until he still had half as far to go as he had already
gone while asleep. How much of the entire trip home was Samuel asleep?
Help with diagram please
Answer:
Samuel slept for 1/4 of the distance.
Step-by-step explanation:
The information provided are:
Samuel fell asleep halfway home.He didn't wake up until he still had half as far to go as he had already gone while asleep.Consider that the total distance covered was 1.
Then from the first point we know that Samuel fell asleep after covering a distance of 1/2.
It is provided that he woke up only after covering half of the remaining distance.
That is, he slept for 1/4 of the remaining distance.
Thus, Samuel was asleep for 1/4th of the entire trip home.
idfwuomg1 5000+25000
Answer:
40,000
Step-by-step explanation:
15000+25000=40000
Answer: 40,000
Step-by-step explanation:
25,000 + 15,000 = 40,000
Hope this helps
Plz mark brainliest
Convert 2.7 miles to yards.
Answer:
the answer is 4752
Step-by-step explanation:
*please give me brainliest, i only need four more*
which expression is equivalent to the given expression? (1/7x+6)-(4/7x+3)
Answer:
-2/7x+3
Step-by-step explanation:
1/7x+6-4/7x-3
-3/7x+3
|14| > 14 true or false
Answer:
false
Step-by-step explanation:
since its the absolute value it will be equal to 14
Felicity put down $800 on a used car. She took out a loan to pay off the balance of the cost of the car. Her monthly payment will be $175. After 9 months how much will she have paid for the car? (Consider ALL the money she has paid so far.) *
Answer:
After 9 months she would have paid $2,375
Step-by-step explanation:
All you really need to do is multiply 175 by 9, giving you 1,575, and then add the original $800 down payment.
The shipping cost for order at an online store is 1/10 the cost of the items you order. What is an expression for the total cost of an order of $79? A. 0.10($79) B. $79 + 0.1($79) C. $(79 + 0.10)
Answer:
B. $79 + 0.1($79)
Step-by-step explanation:
Given that;
the shipping cost for an order = 1/10 multiply by the cost of the items bought;
i.e. [tex]\dfrac{1}{10}\times x[/tex]
where
x = cost of items ordered for.
This implies that:
[tex]\implies[/tex] x + 0.1x
The objective is to determine the expression for the total cost of an order which is $79
x = 79
Then, the total cost of an order is
$79 + 0.1($79)
How you solve
-9+[b-8]=-5
your answer is B= 12 your welcome :)
Write 75% as a decimal
Answer:
0.75
Step-by-step explanation:
Answer:
0.75
Step-by-step explanation:
type in calculator
What is the answer to 2log3(x)=4?
Answer:
x ≈ 4.19180
Step-by-step explanation:
[tex]2 log 3(x) = 4[/tex]
[tex]2 log(3)(x) = 4[/tex]
Divide both sides by 2log (3) to isolate x by itself
[tex]\frac{2log(3)(x)}{2log(3)} = \frac{4}{2log(3)}[/tex]
[tex]x = \frac{4}{2log(3)}[/tex]
or x ≈ 4.19180
using a calculator you can write the answer as a rounded number
Which ordered pair is generated from the equation shown below? y = 3x -2
Answer:
hope this helps
Step-by-step explanation:
I don't know I have a similar one but I also don't know that one
Step-by-step explanation:
Four new word processing software programs are to be compared by measuring the speed with which various standard tasks can be completed. Before conducting the tests, researchers note that the level of a person’s computer experience is likely to have a large influence on the test results. Discuss how you would design an experiment that fairly compares the word processing programs while simultaneously accounting for possible differences in users’ computer proficiency.
Answer:
The following are the solution to this question:
Step-by-step explanation:
The average frequency of each of the four new word processing applications, that can be determined as well as the computer expertise of the consumer, which can be calculated as low and medium. Its information could then be displayed in a table of 3×3, and we'll use ANOVA 2 ways to demonstrate those two comparisons.
Find the dimensions of a triangle given the base, height, and area. b=8 inches h=7 inches A=28 square inches
Answer:
Step-by-step explanation:
The formula for the area of a triangle of base b and height h is A = (1/2) (b)(h).
Here A = 28 in^2, so 28 in^2 = (1/2)(8 in)(7 in), or
28 in^2 = 28 in^2
What is the place value of the digit 9 in 45.93
The correct answer is
tenths
Answer:
Thousandth
Step-by-step explanation:
The points P, Q, R and S all lie on the same line segment, in that order, such that the ratio of PQ : QR: RS is equal to 4:2:1. If PS = 14, find PR.
Answer:
PR = 12
Step-by-step explanation:
P-----------Q-----------R----------S
ratio
4:2:1
PS = 14
add the ration = 4 + 2 + 1 = 7
14 / 7 = 2
PQ at 4 x 2 = 8
QR at 2 x 2 = 4
RS at 1 x 2 = 2
------------
14
PR = PQ + QR
PR = 8 + 4
PR = 12
The length of the line segment PR is 12 units.
What is a line segment ?A line segment is a subset of a line which has two endpoints.
According to the given question The points P, Q, R and S all lie on the same line segment PS and the ratio of PQ : QR: RS is equal to 4:2:1.
Assuming PQ = 4x, QR = 2x and RS = x.
We know PQ + QR + RS = PS.
∴ 4x + 2x + x = 14.
7x = 14.
x = 2.
PR = PQ + QR.
PR = 4(2) + 2(2).
PR = 8 + 4.
PR = 12.
learn more about line segment here :
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if PN=29cm and MN=13 , then PM=?
*see attachment for the figure referred to
Answer/Step-by-step explanation:
1. PN = 29
MN = 13
PM = ?
[tex] PN = PM + MN [/tex] (Segment addition postulate)
[tex] PN - MN = PM [/tex] (subtract MN from each side)
[tex] 29 - 13 = PM [/tex] (substitute)
[tex] 16 = PM [/tex]
[tex] PM = 16 cm [/tex]
2. PN = 34, MN = 19, PM = ?
[tex] PN = PM + MN [/tex] (sediment addition postulate)
[tex] PN - MN = PM [/tex] (subtract MN from each side)
[tex] 34 - 19 = PM [/tex] (substitute)
[tex] 15 = PM [/tex]
[tex] PM = 15 cm [/tex]
3. PM = 19, MN = 23, PN = ?
[tex] PN = PM + MN [/tex] (Segment addition postulate)
[tex] PN = 19 + 23 [/tex] (substitute)
[tex] PN = 42 cm [/tex]
4. MN = 82, PN = 105, PM = ?
[tex] PN = PM + MN [/tex] (segment addition postulate)
[tex] PN - MN = PM [/tex] (subtract MN from each side)
[tex] 105 - 82 = PM [/tex] (substitute)
[tex] 23 = PM [/tex]
[tex] PM = 23 cm [/tex]
5. PM = 100, MN = 100, PN = ?
[tex] PN = PM + MN [/tex] (Segment addition postulate)
[tex] PN = 100 + 100 [/tex] (substitute)
[tex] PN = 200 cm [/tex]
Please help me on this one!
Answer:
-1/2
Step-by-step explanation:
The slope of a line parallel is to another line is the same.
So the line in the picture has a slope of -1/2, and since the other line is parallel to the first one, its slope is also -1/2
7 |r/5|=7
solve the equation
Answer:
r=5 or r=−5
Step-by-step explanation:
Answer:
fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffg
Step-by-step explanation:
Pls help me answer word problems about polynomials
Thank you!!!
Three electrons are removed from each of 4 atoms. Write an expression to represent the net change on the charge for the group of atoms.
Answer:
The charge of each electron is -1, so the charge of three electrons is -3. Removing something is denoted by a negative sign. The expression that represents the removal of three electrons from each of four atoms is (-3)(-4).
Step-by-step explanation:
Enjoy
The remaining charge on the group of 4 atoms would be -
q(+) = + 12e.
What are electrons?The electron is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary particles because they have no known components or substructure.Given is that three electrons are removed from each of 4 atoms
Now, the total electrons lost will be = 3 x 4 = 12 electrons.
The remaining charge on the group of 4 atoms would be -
q(+) = + 12e
Therefore, the remaining charge on the group of 4 atoms would be -
q(+) = + 12e.
To solve more questions on electrons, visit the link below -
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