Solve the following system of equations graphically. Select the graph that shows the correct solution of the system. 2x +y =3 3y= x - 12
Answer:
The second figure is the correct figure.
Step-by-step explanation:
Graph (ii) is solution of system of equation.
We have to given that,
System of equations are,
2x + y = 3
3y = x - 12
Now, Solve the equations and find the solution,
Here, Equations are,
2x + y = 3 .. (i)
3y = x - 12 .. (ii)
From (i);
y = 3 - 2x
Substitute in (ii);
3 (3 - 2x) = x - 12
9 - 6x = x - 12
9 + 12 = 6x + x
7x = 21
x = 3
And from (i);
2 × 3 + y = 3
6 + y = 3
y = - 6 + 3
y = - 3
Hence, Solution is, (3, - 3).
So, Graph shown in option (ii) has intersection point (3, - 3)
Thus, Graph (ii) is solution of system of equation.
Learn more about systems of equations at:
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x^2+4x+y^2-10y+20=30 find the center of the circle by completing the square
Answer:
a). Center of the circle = (-2, 5)
b). Equation of the line ⇒ y = [tex]-\frac{4}{5}x+\frac{58}{5}[/tex]
Step-by-step explanation:
Equation of the circle is,
x² + 4x + y²- 10y + 20 = 30
a). [x² + 2(2)x + 4 - 4] + [y²- 2(5)y + 25] - 25 + 20 = 30
[x² + 2(2)x + 4] - 4 + [y² - 2(5)y + 25] - 25 + 20 = 30
(x + 2)² + (y - 5)²- 29 + 20 = 30
(x + 2)² + (y - 5)²- 9 = 30
(x + 2)² + (y - 5)² = 39
By comparing this equation with the standard equation of a circle,
Center of the circle is (-2, 5).
b). A point (2, 10) lies on this circle.
Slope of the line joining this point to the center (-2, 5),
[tex]m_{1}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
= [tex]\frac{10-5}{2+2}[/tex]
= [tex]\frac{5}{4}[/tex]
Let the slope of the tangent which is perpendicular to this line is '[tex]m_{2}[/tex]'
Then by the property of perpendicular lines,
[tex]m_{1}\times m_{2}=-1[/tex]
[tex]\frac{5}{4}\times m_{2}=-1[/tex]
[tex]m_{2}=-\frac{4}{5}[/tex]
Now the equation of the line passing though (2, 10) having slope [tex]m_{2}=-\frac{4}{5}[/tex]
y - y' = [tex]m_{2}(x-x')[/tex]
y - 10 = [tex]-\frac{4}{5}(x-2)[/tex]
y - 10 = [tex]-\frac{4}{5}x+\frac{8}{5}[/tex]
y = [tex]-\frac{4}{5}x+\frac{8}{5}+10[/tex]
y = [tex]-\frac{4}{5}x+\frac{58}{5}[/tex]
Therefore, equation of the line will be, y = [tex]-\frac{4}{5}x+\frac{58}{5}[/tex]
If the temperature is 20c what is it in Fahrenheit.
Answer:
The answer is 68 degrees Fahrenheit.
Step-by-step explanation:
The equation to convert Celsius to Fahrenheit is (C × 9/5) + 32.
So, first we calculate Celsius times 9/5. 20×9/5 = 36.
Then, we add 36 and 32 together. 36+32= 68
So, 68 is your answer.
Can someone help me solved this problem plz need help ASAP! Show de steps plz! I really need help
Answer:
a) 3
b) -4
c) -1/3
d) -2
e) -4/3
Step-by-step explanation:
a) 6w=2 , w=6/2 , ie. w= 3
b) 6+w=2 ,w=2-6 , ie. w= -4
c) 6w+2= 0, 6w= 0-2 , 6w= -2 , w= -2/6, ie. w= -1/3
d) 6w+2= -10, 6w= -10-2, 6w= -12, w= -12/6 , ie. w= -2
e) 6w+2= 12w+10, 6w-12w = 10-2 ( here we interchanged the digits to get the variables or you can say the terms having variables in this case 'w' to the same side. hereby changing the sign from '+' to '-')
so
6w-12w = 10-2 ,-6w=8, w= -8/6, ie. w= -4/3
You can check your answers by substituting with the answers in place of the variable and check if the equation is solved.
Tell me if this was helpful
CD and EF are parallel lines. AB is a straight line
Answer:
x =42
q = 135°
p + q + r = 225°
Step-by-step explanation:
a)
Since, AB and BC are perpendicular lines.
[tex] m\angle ABC = 90\degree \\
\therefore 24\degree + x\degree + 24\degree = 90\degree \\
\therefore x\degree + 48\degree = 90\degree \\
\therefore x\degree = 90\degree - 48\degree \\
\huge \red {\boxed {\therefore x = 42}} \\[/tex]
b) (i)
Since, CD and EF are parallel lines and AB is a straight line.
[tex] \therefore q = 135\degree... (vertical \: \angle 's) \\\\
p + 135\degree = 180°..(straight\: line \: \angle' s) \\
p = 180\degree - 135\degree \\
\huge \purple {\boxed {p = 45\degree}} \\
\because r = p ... (vertical \: \angle 's) \\
\huge \purple {\boxed {r = 45\degree}} \\
p + q + r = 45\degree + 135\degree + 45\degree \\
\huge \purple {\boxed {p + q + r = 225\degree }}\\[/tex]
Five times one number minus two times a second number is 11. Three times the first number minus two times the second number is 1. what are the numbers?
Answer:
first number is 5
second number is 7
Step-by-step explanation:
let x and y represent the first and second number
5x - 2y = 11 ........ equation 1
3x - 2y = 11.......... equation 2
so by elimination, equation 1 minus equation 2
5x - 3x - 2y - 2y = 11 - 1
2x = 10
x = 5
therefore the first number is 5
put x = 5 into equation 1
5x - 2y = 11
5(5) - 2y = 11
25 - 2y = 11
-2y = 11 - 25
-2y = - 14
y = 7
therefore the second number is 7
hope it helps .
Can someone please help me :(
Answer:
Step-by-step explanation:
ok its AAS because if you see the most aperent thing on the trangle is that
Answer:
AAS
Step-by-step explanation:
The two triangles are congruent because they have two equal angles and one side
Which describes unit rates? Check all that apply.
-Nadia pays $30 for 2 baseball tickets.
-A certain type of sailboat travels at 7 nautical miles per hour.
-The cost of 3 hot chocolates is $2.
-A summer camp provides 3 meals for each camper.
Answer 2,4 are all described as unit rates a unit rate is anything that has per or each in it so a certain type of boat travels at 7 hours PER mile so we know question 2 is correct and 3 is a unit rate because it has each in it A summer camp provides 3 meals for EACH camper. That’s why the answer is 2 and 4
Factor −1/9 out of −1/9x−3.
Answer:
-1/9 (x+27)
Step-by-step explanation:
Divide the whole expression by -1/9.
-1/9x becomes x
-3 becomes + 27
3
7 2 4 7
5 7 1
1 8 8
What is the range?
Answer: 5
Step-by-step explanation:
Range means the difference between the largest and smallest values. Which would be 3 and 8.
Solve the following inequality. Then place the correct answer in the box provided. Answer in terms of a mixed number.
2(P +1) + 3(P + 2 ) > 2
Answer: [tex]-1\frac{1}{5}[/tex]
Step-by-step explanation:
[tex]2(P +1) + 3(P + 2 ) > 2[/tex]
Distribute 2 and 3
[tex]2P+2+3P+6>2[/tex]
Combine like terms;
[tex]5P+8>2[/tex]
Subtract 8
[tex]5P>2-8[/tex]
[tex]5P>-6[/tex]
Divide by 5
[tex]P>-\frac{6}{5}[/tex]
Convert to a mixed number by dividing. However, when we have the numerator greater than the denominator, we must find a way to make the numerator lower. We can achieve this by separating it into 2 fractions.
[tex]-\frac{6}{5}=-\frac{5}{5}-\frac{1}{5}[/tex]
When we do this, we can see that 5/5 = 1
[tex]-1-\frac{1}{5}=-1\frac{1}{5}[/tex]
rearrange to make x the subject a= 4x/t -p
Answer:
x = [tex]\frac{t(a+p)}{4}[/tex]
Step-by-step explanation:
Given
a = [tex]\frac{4x}{t}[/tex] - p ( isolate term in x by adding p to both sides )
a + p = [tex]\frac{4x}{t}[/tex] ( multiply both sides by t )
t(a + p) = 4x ( divide both sides by 4 )
[tex]\frac{t(a+p)}{4}[/tex] = x
Clothing price (100 percent) is 26 dollars and 50 cents, Added tax is 5 percent, and total cost is blank. Darrien purchases some clothes for a total of $26.50, before tax. Sales tax in his state is 5 percent. What is the total price he has to pay for the clothes? Step 1: (Original Price)(Tax Percent) = Amount of Tax Step 2: Original Price + Amount of Tax = $
ANSWER PLS
Answer:
$27.83
Step-by-step explanation:
If Darrien spends 26.50, multiply that by 0.05 (26.50×0.05) which is 1.325 which rounds to 1.33. $1.33 is the amount of tax he has to add. For the full price you would do 26.50+1.33 to get 27.83.
Answer:
The answer is 27.83
Step-by-step explanation:
Thank the person above me.
People pay to visit a stately home [tickets age 16 and over : £18.60 ..under 16:£12.80] 155 people pay and 49 of these people are under 16. How much money is collected
Answer: £2598.80
Step-by-step explanation:
Let those under 16 be x
Those over 16 be y
49 + y = 155
y = 155-49
y = 106 = over 16
for over 16, y * 18.60
= 106 * 18.60 = 1971.60
For under 16, x * 12.80
= 49 * 12.80 = 627.20
Which equation is equivalent to 4 x = t + 2
Answer:
Its supposed to be x = s
like its in the picture
So we divide both sides by 4
we get t+2 / 4
That means the answer is C
Answer:
the correct answer for this question is c. s= t+2/4
source. edge.
Three friend went out to eat pizza. Their pizza costs 15.63 and drinks cost 1.29 each. Salad costs 2.45. If they plan to share the cost of the pizza.How much will each person pay? Plz helppp
Answer:
Friend 1: $11.53 Frind 2: $5.21 Friend 3: $5.21
Step-by-step explanation:
15.63/3=5.21
One friend pays for the rest.
1.29*3=$3.87=drinks
salad=$2.45
5.21+3.87+2.45=11.53
A basket ball that has a diameter of 20cm is placed in a box so that it touches all inner sides of a box. What is the volume NOT occupied by the ball when it is placed in the box?
Please help me asap
Answer:
3811.21
Step-by-step explanation:
volume of sphere is 4188.79 using the formula for the volume of a sphere.
volume of the box is=20x20x20=8000
8000-4188.79=3811.21
At the start of the week, Ladasha’s checking account had a balance of $34. She deposited $50 each day for three days. She made a $60 withdrawal on the fourth day. Ladasha also wrote a check for $22. Explain how you can write an expression to show the account balance at the end of the week.
Step-by-step explanation: The account started at $34. Three $50 credits were added. Indicate the withdrawal by subtracting $60 or adding –$60. The check is also represented by subtracting $22 or by taking the additive inverse and adding –$22.
Sample Response: The account started at $34. Three $50 credits were added. Indicate the withdrawal by subtracting $60 or adding –$60. The check is also represented by subtracting $22 or by taking the additive inverse and adding –$22.
Hi can any one please help me to do this I have no idea about it please help me
Answer:
188.4cm³
Step-by-step explanation:
Joe went shopping yesterday. He saw a new Wii game that costs $55.00. It was on sale for 20% off. How much did Joe pay for the game after the discount? (don't include tax)
Answer:
the answer is 1100
Step-by-step explanation:
you will do... 5500*20/100
Evaluate 10x^2y^–2 for x = –1 and y = –2.
Answer:
10
Step-by-step explanation:
10x^2y^-2
10(-1)^2(-2)^2=10
What is a equivalent expression to $3.79 x 2 = $7.58
Answer: $7.58/2=$3.79
Step-by-step explanation:
Wendy and her friend Sandra went to dinner. Their total food bill was $25.00. The tax was 7%. How much was the tax? How much was the bill including the tax?
Answer:
the answer is 175
Step-by-step explanation:
you will do 2500*7/100
What is 0.25 as a percent?
Answer:
Step-by-step explanation:
25%
the numbers after the decimal formes a percent
0.x
x = x_%
Answer:
25%
Step-by-step explanation:
25 x 100 you move the decimal point two places to the right.
So you end up with 25%
I really hope this helps.
what is the area of the circle?
Answer:
Area =28.27
Step-by-step explanation:
Answer:
The area of circle:
[tex]A \approx 28.27[/tex] [tex]m^2[/tex]
Step-by-step explanation:
To find the area of circle, you need this formula:
[tex]A = \pi r^2[/tex]
-After have the formula set up, use the given radius for the formula:
[tex]A = \pi 3^2[/tex]
-Then, you solve:
[tex]A = \pi \times 3^2[/tex]
[tex]A = \pi \times 9[/tex]
[tex]A = 9\pi \approx 28.27[/tex] [tex]m^2[/tex]
-So, the area of a circle is [tex]28.27[/tex] [tex]m^2[/tex] .
c) work out the value of 3² + 2³
d) work out the value of 2⁴ - 3²
Answer:
a) 2^6 = 2 x 2 x 2 x 2 x 2 x 2 = 64
b) 7^4 = 7*7*7*7 = 2401
c) 3^2 + 2^3
= 9 + 8
= 17
d) 2^4 - 3^2
= 16 - 9
= 7
what is the discriminant of the equation 2x^2-4x+1=0
Answer:
8 i think
Step-by-step explanation:
Answer:
8
Step-by-step explanation:
2x^2-4x+1=0
This is written in the form
ax^2 +bx+c =0
a=2 b = -4 c =1
The discriminant is
b^2 -4ac
(-4)^2 -4(2)(1)
16 - 8
8
The discriminant is 8
in your own words what is a polygon
Step-by-step explanation:
A polygon is a shape with at least three straight lines and angles
Select the correct answer.
What is the simplest form of the ratio 11 : 16?
A.
1:6
B
5:8
c.
11.16
D.
22:32
Answer:
C
Step-by-step explanation:
The ratio 11:16 cannot be simplified
Answer:
Its already in simplest form
Step-by-step explanation:
You can think of it as a fraction. you cant divide 11 by anything besides 1 and itself. 11 doesnt go into 16 at all, completely. So the ratio cant be simplified
You roll a twelve-sided die (having values one through twelve on its faces). What is the probability that the value of the roll will be a composite number?
show work pls!
help pls!
Step-by-step explanation:
Probability
Probability is a measure of the likelihood that an event will happen.
When dealing with probability, the outcomes of a process are the possible results. For example, when a die is rolled, the possible outcomes are 1, 2, 3, 4, 5, and 6. In mathematical language, an event is a set of outcomes, which describe what outcomes correspond to the "event" happening. For instance, "rolling an even number" is an event that corresponds to the set of outcomes {2, 4, 6}. The probability of an event, like rolling an even number, is the number of outcomes that constitute the event divided by the total number of possible outcomes. We call the outcomes in an event its "favorable outcomes".
Probability =
