Answer:
[tex]\boxed{\boxed{\sf x=-3}}[/tex]
Step-by-step explanation:
[tex]\sf y = -3x - 2[/tex]
[tex]\sf y=7[/tex]
We'll substitute y into the equation:
[tex]\sf 7 = -3x - 2[/tex]
Switch sides:
[tex]\sf -3x-2=7[/tex]
Add 2 to both sides
[tex]\sf -3x-2+2=7+2[/tex]
[tex]\sf -3x=9[/tex]
Divide both sides by -3:
[tex]\sf \cfrac{-3x}{-3}=\cfrac{9}{-3}[/tex]
[tex]\sf x=-3[/tex]
Therefore, the value of x/solution is -3
________________________________________
Answer:
The value of x is
✔ –3
The solution to this system of equations is
✔ (–3, 7)
Step-by-step explanation:
if z1= 3+3i and z2=7(cos(5pi/9) + i sin (5pi/9)), then z1/z2= blank
[tex]z1=\stackrel{a}{3}+\stackrel{b}{3}i~~ \begin{cases} r = \sqrt{a^2+b^2}\\ r = \sqrt{18}\\[-0.5em] \hrulefill\\ \theta =\tan^{-1}\left( \frac{b}{a} \right)\\ \theta =\frac{\pi }{4} \end{cases}~\hfill z1=\sqrt{18}\left[\cos\left( \frac{\pi }{4} \right) i\sin\left( \frac{\pi }{4} \right) \right] \\\\[-0.35em] ~\dotfill[/tex]
[tex]\cfrac{z1}{z2}\implies \cfrac{\sqrt{18}\left[\cos\left( \frac{\pi }{4} \right) i\sin\left( \frac{\pi }{4} \right) \right]} {7\left[\cos\left( \frac{5\pi }{9} \right) i\sin\left( \frac{5\pi }{9} \right) \right]} \\\\[-0.35em] ~\dotfill\\\\ \qquad \textit{division of two complex numbers} \\\\ \cfrac{r_1[\cos(\alpha)+i\sin(\alpha)]}{r_2[\cos(\beta)+i\sin(\beta)]}\implies \cfrac{r_1}{r_2}[\cos(\alpha - \beta)+i\sin(\alpha - \beta)] \\\\[-0.35em] ~\dotfill[/tex]
[tex]\cfrac{z1}{z2}\implies \cfrac{\sqrt{18}}{7}\left[\cos\left( \frac{\pi }{4}-\frac{5\pi }{9} \right)+i\sin\left( \frac{\pi }{4}-\frac{5\pi }{9} \right) \right] \\\\\\ \cfrac{\sqrt{18}}{7}\left[\cos\left( \frac{-11\pi }{36} \right) +i\sin\left( \frac{-11\pi }{36} \right) \right]\implies \cfrac{\sqrt{18}}{7}\left[\cos\left( \frac{83\pi }{36} \right) +i\sin\left( \frac{83\pi }{36} \right) \right] \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \cfrac{z1}{z2}\approx 0.348~~ + ~~0.496i~\hfill[/tex]
The value of z1/z2 is √18/ 7 (cos ( 11π/36 ) - isin ( 11π/36 )).
What is complex number?"A complex number is the sum of a real number and an imaginary number and it is of the form x + iy and is usually represented by z".
For the given situation,
z1= 3+3i and
z2= 7(cos(5π/9) + i sin (5π/9))
To divide the complex numbers, both should be in same form.
Convert z1 in polar form.
z is of the form x+iy, so, r=[tex]\sqrt{x^{2}+y^{2} }[/tex]
⇒[tex]r=\sqrt{3^{2}+3^{2} }[/tex]
⇒[tex]r=\sqrt{18}[/tex]
θ = [tex]tan^{-1}(\frac{b}{a} )[/tex]
⇒[tex]tan^{-1}(\frac{3}{3} )[/tex]
⇒[tex]tan^{-1}(1)[/tex]
⇒[tex]45[/tex]°
The polar form is of the form, z= r (cosθ + i sinθ),
⇒ z1 = [tex]\sqrt{18}[/tex] (cosπ/4 + isinπ/4)
The formula for dividing complex number is
z1/z2 = r1(cos θ1 + isin θ1) / r2(cos θ2 + isin θ2)
⇒ z1/z2 = r(cosθ + isinθ)
where, r = r1/r2 and θ = (θ1 - θ2)
z1/z2 = [tex]\sqrt{18}[/tex] (cos π/4 + isin π/4) / 7 (cos 5π/9 + isin 5π/9)
⇒ r = [tex]\sqrt{18}[/tex] / 7 and
θ = (π/4 - 5π/9 )
⇒ θ = (-11π/36)
cos(-θ) = cos θ
⇒cos( -11π/36 ) = cos ( 11π/36 )
sin(-θ) = -sin θ
⇒ sin ( -11π/36 ) = -sin ( 11π/36 )
Thus, z1/z2 = [tex]\sqrt{18}[/tex] / 7 (cos ( 11π/36 ) - isin ( 11π/36 ))
Hence we can conclude that the value of z1/z2 is
√18/ 7 (cos ( 11π/36 ) - isin ( 11π/36 )).
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Today is my birthday. My age today, in months, is 72 times my age 5 years ago,
in years. My age today, in years, is
Answer:
Happy Birthday!
Step-by-step explanation:
y= 3/4x + 3 Find the y and x intercept
[tex]y - intercept = 3[/tex]
[tex]x - intercept = - 4[/tex]
What is the prime factorization of 24?
1. 2x2x2x3
2. 2x2x3
3. 8x3
4. 6x4
Answer:
1. 2x2x2x3
Step-by-step explanation:
Let's do process of elimination.
2. 2x2x3
2x2=4 4x3=12
2 is false.
3. 8x3
8x3=24
3 is true, but 8 is not a prime number.
4. 6x4
6x4=24
4 is true, but 6 is not a prime number.
This leaves 1. 2x2x2x3.
1. 2x2x2x3
2x2=4 2x3=6 6x4=24
1 is true, and 2 and 3 are prime numbers. So, the answer is 1.
-hope it helps
Answer:
1. 2x2x2x3
Step-by-step explanation:
Prime factorization is defined as a way of finding the prime factors of a number, such that the original number is evenly divisible by these factors.
[tex]24\:\mathrm{divides\:by}\:2\\\\\quad \:24=12\cdot \:2[/tex]
[tex]12\:\mathrm{divides\:by}\:2\\\\\quad \:12=6\cdot \:2[/tex]
[tex]6\:\mathrm{divides\:by}\:2\quad\\\\ \:6=3\cdot \:2[/tex]
[tex]2, 6\:\mathrm{divides\:by}\:2\quad \\\\\:6=3\cdot \:2[/tex]
Find the measure of the angle marked and indicated in bold
I need help with this, i did part of it but i'm desperate
Answer:
Let's add more steps.
step 6: angle AEB measures 360 - 90 -90 - 70 - 39 = 71° Reason, AECF is a quadrangonal and three of its angle measures 90, 90, and (70+39)
step 7: angles AEB and ABE are congruent: reason triangle ABE is isosceles since AE is conruent to AB
step 8 Angle BAE measures 180 -71-71 = 38°: by difference from the sum of the internal angles.
step 9: Angle BAD measures 90 - BAE = 90 - 38 = 52° Reason angles BAD and BAE are complementary.
QED
Multiply. Write the answer in simplest form. 3/7 x 2 5/6
193/42
3×6+25×7÷4218+175÷42193/42clothing store sells t shirt in only three colors red blue green the colors are in the ratio of 3:4:5 if the store has a total of 60 how many blue t shirt
Answer:
Step-by-step explanation:
red/blue = 3/4 and you get blue/green = 4/5
= 60/4 = 15
you have 15 red shirts, 20 blue shirts, and 25 green shirts.
15/20 = 3/4
20/25 = 4/5
if you simplify 15/20, you will see that it is equivalent to 3/4
if you simplify 20/25, you will see that it is equivalent to 4/5.
A scuba diver wants to dive more than 2/12 times her previous deepest dive. That means she has to dive at least 70 feet below the surface of the ocean. This dive is represented by the inequality 2/12p<−70, where p is the distance below the surface of her previous deepest dive.
Select from the drop-down to correctly interpret the solution of this inequality.
The scuba diver's previous deepest dive was
Choose...
feet below the surface of the ocean.
The distance below the surface of her previous deepest dive is 420 feet
Given the inequality expression representing the dive given as:
2/12p<−70We are to get the solution to the inequality expression;
Given;
2/12p<−70
Multiply both sides by 12:
2p < 70 * 12
2p < 840
Divide both sides by 2
2p/2 < 840/2
p < 420
Hence the distance below the surface of her previous deepest dive is 420 feet
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Answer:
2 1/2p<-70
the answer is deeper than 28
Step-by-step explanation: I took the test
If △CFE≅△PTR, complete each of the following statements:
CE¯¯¯¯¯¯¯¯ ≅
TR¯¯¯¯¯¯¯ ≅
∠P ≅∠
∠F ≅∠
△FEC ≅△
△RPT ≅△
Based on the definition of congruent triangles, the statements will be completed as follows:
CE ≅ PRTR ≅ FE∠P ≅ ∠C∠F ≅ ∠T△FEC ≅ △TRP△RPT ≅ △ECFRecall the following about Congruent Triangles:
The three angles of one triangle is congruent to the three corresponding angles in another triangle if both triangles are congruent triangles.The three sides of one triangle is congruent to the three corresponding sides in another triangle if both triangles are congruent triangles.Given that △CFE≅△PTR, thus:
CE corresponds to PR, therefore CE ≅ PRFE corresponds to TR, therefore FE ≅ TRCF corresponds to PT, therefore CF ≅ PT∠P corresponds to ∠C, therefore ∠P ≅ ∠C∠T corresponds to ∠F, therefore ∠T ≅ ∠F∠R corresponds to ∠E, therefore ∠R ≅ ∠EThus, based on the definition of congruent triangles, the statements will be completed as follows:
CE ≅ PRTR ≅ FE∠P ≅ ∠C∠F ≅ ∠T△FEC ≅ △TRP△RPT ≅ △ECFLearn more about congruent triangles on:]
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Practice using angle relationships.
Assignment
J
What is the measure of JKL?
* 60°
96°
O 80°
O 110°
O 120°
240
H
K L
Answer:
120
Step-by-step explanation:
24 + 96 = 120
Hope this helps!
what is 0.128 as a fraction
[tex]0.128 \\ = \frac{128}{1000} \\ = \frac{16}{125} [/tex]
Hope you could get an idea from here.
Doubt clarification - use comment section.
Answer:
16/125
Step-by-step explanation:
Write 0.128 as
0.128/1
Multiply both numerator and denominator by 10 for every number after the decimal point
(0.128 × 1000)/(1 × 1000) = 128/1000
Reducing the fraction gives
16/125
A group of pupils calculated their average score for a Mathematics
test. If one of them scored 9 marks more, their average score would
be 81. If one of them scored 3 marks less, their average score would
be 78. How many pupils were there in the group?
Answer: 4
Step-by-step explanation: +9-(-3)=12
81-78=3
so 12/3=4
Consider the equation of a circle x^2-2x+y^2-4y-4=0. If the line 2x-y+a=0 is its diameter. Then find the value of a.
Answer:
a=0
Step-by-step explanation:
x²-2x+y²-4y-4=0
(x²-2x+1)+(y²-4y+4)-9=0
(x-1)² + (y-2)² = 3²
Center: (1,2) radius: 3
(1,2) on line 2x-y+a=0
2*1 - 2 + a = 0
a = 0
YOU’RE GETTING A BRAINLIST IF YOU ANSWER THESE:
If you and I meet halfway between the fountain and the restrooms what are the coordinates of our meeting place?
If my cat and your dog meet halfway between the ball field and the swings what are the coordinates of their meeting place?
Now to the nearest yard how far are you and I to our pets after arriving to our meeting place?
Answer:
(0.5,-0.5)(0.5,0.5)2 yardsWILL BRAINLIST IF YOU GET CORRECT AND HURRY
A pair of linear equations is shown below: y = −3x + 5 y = x + 2 Which of the following statements best explains the steps to solve the pair of equations graphically? (4 points)
A: On a graph, find the point of intersection of two lines, the first line has y-intercept = 5 and slope = −3, and the second line has y-intercept = 2 and slope = 1.
B: On a graph, find the point of intersection of two lines, the first line has y-intercept = −3 and slope = 5, and the second line has y-intercept = 1 and slope = 2.
C: On a graph, find the point of intersection of two lines, the first line has y-intercept = −5 and slope = 3, and the second line has y-intercept = −2 and slope = −1.
D: On a graph, find the point of intersection of two lines, the first line has y-intercept = 3 and slope = −5, and the second line has y-intercept = −1 and slope = −2.
Answer:
answer is b
Step-by-step explanation:
HELP ME FAST PLZZ
Wendy has 5 1/3 of ribbon.
Part A: How many 2/3 -foot pieces can Wendy cut from the 5 1/3 feet of ribbon? Show your work. (5 points)
Part B: Using the information in Part A, interpret the meaning of the quotient in terms of the two fractions given. (5 points)
Answer:
Part A: 8 ribbons
Part B: see below
Step-by-step explanation:
first 5 1/3 = 16/3
[tex] \frac{16}{3} \div \frac{2}{3} \\ = \frac{16}{3} \times \frac{3}{2} \\ = \frac{48}{6} = 8[/tex]
the answer is 8 dude!
One bridge in Maryland is 6,946 meters
long. It is 46 times as long as another
nearby bridge. How long is the shorter
bridge? Explain.
Answer:
151 meters
Step-by-step explanation:
6946/46=151 meters
Answer:
Step-by-step explanation:
If you want to be formal, let the shorter bridge = x
46x = 6946 Divide by 46
x = 6946/46
x = 151
So the shorter bridge is 151 meters long.
Select the correct answer.
Which phrase best describes the relationship indicated by the scatter plot?
a. constant Correlation
b. negative Correlation
c. Positive correlation
d. no correlation
Answer:
no correlation
Step-by-step explanation:
they arent in a line
The phrase that best describes the relationship indicated by the scatter plot is D. No correlation
What is a Scatter Plot?This refers to the use of dots to represent values for two different numeric variables.
Hence, we can see that the best description that can be used to show the relationship in the scatter plot is option D which is no correlation because they are not in a line.
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What is the slope of the line?
Answer:
[tex] - \frac{2}{3} [/tex]
Step-by-step explanation:
Pick two points on the graph: (4, -5) and (1, -3)
[tex]\boxed{ slope = \frac{y _{1} - y_2 }{x_1 - x_2} }[/tex]
Slope
[tex] = \frac{ - 5 - ( - 3)}{4 - 1} [/tex]
[tex] = \frac{ - 5 + 3}{3} [/tex]
[tex] = - \frac{2}{3} [/tex]
can anyone please tell me how to do this
Hello there, this problem is just basic addition, here is what it would look like
[tex]52.31+25.90[/tex]
Solve it and we get 78.21
Amount earned on Saturday = $ 52.31
Amount earned on Sunday = $ 25.90
Total amount earned
= $ 52.31 + $ 25.90
= $ 78.21
Therefore, Tara earned $ 78.21 in total. Hope this helps.
Have a nice day.
Marc drove 312.8 miles on 12.5 gallons of gas. What was the car’s average mileage miles per gallon for the distance.
Answer:
25.024 mi/gal
Step-by-step explanation:
To find miles per gallon, divide miles by gallons.
(312.8 mi)/(12.5 gal) = 25.024 mi/gal
A coin is tossed and the spinner is spun one possible outcome is H3 (heads, 3). What is the sample space for the experiment?
Supposing a spinner with 4 sides, the sample space is:
{H1, H2, H3, H4, T1, T2, T3, T4}
The sample space is the set that contains all possible outcomes for an experiment.
In this problem:
For the coin, there are two possible outcomes: H or T.Supposing the spinner has 4 sides, there are four possible outcomes: 1, 2, 3, or 4.Hence, the sample space is:
{H1, H2, H3, H4, T1, T2, T3, T4}
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A baby is 3 weeks and 4 days old. What it's is age in days?
Work Shown:
1 week = 7 days
3 weeks = 21 days .... multiply both sides by 3
3 weeks + 4 days = 21 days + 4 days = 25 days
A car is traveling at 25 miles per hour during rush hour. How far does the car travel in
2 minute and 45 seconds?
Answer: 1.14583333333 miles
Step-by-step explanation: divide 25/21.81818181818182
The car will travel 1.15 miles in 2 minutes 45 secs
if a car is traveling at 25 miles per hour, the amount of time the car travels in secs is 3600secs
25 miles = 3600secs
To get the distance traveled in 2 minutes 45 secs, we can write;
x = 165 secs
Divide both expressions
25/x = 3600/165
3600x = 25 * 165
3600x = 4125
x = 1.15 miles
Hence the car will travel 1.15 miles in 2 minutes 45 secs
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If the letters in the word NEIGHBOR are
randomly rearranged, what is the probability
that the arrangement ends with the letter B?
There are 28 girls and 21 boys in a class. What is the ratio, in simplest terms, of the number of girls to the number of boys? (show the work please)
Answer: The simplified ratio is 4:3
Step-by-step explanation:
To find the ratio of the number of girls to the number of boys, we can divide the number of girls (28) by the number of boys (21) to get:
28 ÷ 21 = [tex]\frac{28}{21}[/tex]
Next, we can simplify the fraction further to get [tex]\frac{4}{3}[/tex], which equals 4:3.
references on kinetic energy will give brainlist! in own words NO PLARISM!!!!!!!!!!!
Answer:
See below
Step-by-step explanation:
Kinetic energy is basically energy that an object has while it moves. For example, a ball rolling down a hill will have kinetic energy as it rolls, or a bullet shot out of a gun.
If Alex is 14 years old, and Ben is 17 years old, in how many years will the sum of their ages be 169 years?
Answer:
69 years
Step-by-step explanation:
Sum of Alex's and Ben's current age
= 14 +17
= 31 years
For every year, Alex and Ben will each be one year older. Thus, 2 years would be added to the sum of their ages with each passing year.
Difference in the sum of their ages
= 169 -31
= 138 years
Number of sets of 2 years
= 138 ÷2
= 69
Thus, the sum of their ages will be 169 in 69 years.
The mass of 100 tins of corned beef is 34 g. What is the mass, in grams (g), of 1 tin of corned beef?
Answer:
solution
100 tins of corned beef =36 g
1 tin of corned beef = 36÷100=0.36
so, 1 tin of corned beef is 0.36 g.