[tex]\bold{\huge{\pink{\underline{ Solution }}}}[/tex]
[tex]\bold{\underline{ Given }}[/tex]
We have given two linear equations that is 2x - 3y = -6 and x + 3y = 12 .[tex]\bold{\underline{ To \: Find }}[/tex]
We have to find the value of x and y by elimination method.[tex]\bold{\underline{ Let's \: Begin }}[/tex]
[tex]\sf{ 2x - 3y = -6 ...eq(1)}[/tex]
[tex]\sf{ x + 3y = 12 ...eq(2)}[/tex]
Multiply eq( 2 ) by 2 :-
[tex]\sf{ 2( x + 3y = 12 )}[/tex]
[tex]\sf{ 2x + 6y = 24 }[/tex]
Subtract eq(1) from eq(2) :-
[tex]\sf{ 2x + 6y -( 2x - 3y) = 24 -(-6)}[/tex]
[tex]\sf{ 2x + 6y - 2x + 3y = 24 + 6 }[/tex]
[tex]\sf{ 9y = 30 }[/tex]
[tex]\sf{ y = 30/9}[/tex]
[tex]\sf{\red{ y = 10/3}}[/tex]
Now, Subsitute the value of y in eq( 1 ):-
[tex]\sf{ 2x - 3(10/3) = -6 }[/tex]
[tex]\sf{ 2x - 10 = -6 }[/tex]
[tex]\sf{ 2x = -6 + 10}[/tex]
[tex]\sf{ x = 4/2}[/tex]
[tex]\sf{\red{ x = 2}}[/tex]
Hence, The value of x and y is 2 and 10/3
Frederick asked a bank teller to cash a $390 check using $20 and $50 bills. If the teller gave
him 15 bills, how many of each did he receive?
12 of $20 and 3 of $50 totally didnt edit it... lolol..
Answer:
12 $20 Bills & 3 $50 Bills
Step-by-step explanation:
Because if the total is $390, Then if you get 10 $20 Bill that would equal $200 Bills and if you get 2 $50 Bills then you would get $100. Add the $200 Bills & the $100 Bills you get $300 Bills.
Then you get 1 $50 Bill and 2 $20 Dollar Bills you get $90 Bills.
Add $300 Bills with $90 Bills and you get $390.
If you add the number of bills handed it would be 15.
Use the long division method to find the result when 4x3 + 4x2 + 19x + 9 is
divided by 2x + 1.
Answer:
47x+42/2
Step-by-step explanation:
simplify 9/2
((19x+20)+(9/2×x))+1
(47x+40)/2+1
(47+42)/2
This circle is centered at the origin, and the length of its radius is 4. What is
the circle's equation?
What is 5/6 - 3/8 ?
? Choose the answer in the most simplified form.
A. 1 / 3
B. 9/16
C. 1/12
D. 11/24
Answer:
D. 11/24
Step-by-step explanation:
→ [tex]\frac{5}{6} -\frac{3}{8}[/tex]
→ [tex]\frac{40-18}{48}[/tex]
→ [tex]\frac{22}{48}[/tex]
→ [tex]\frac{11}{24}[/tex]
Answer:
D is the answer
Step-by-step explanation:
[tex]\frac{5}{6} - \frac{3}{8} \\[/tex]
find a common factor between 6 and 8, thats 24.
(multiply the first fraction by 4, second by 3, both numerator and denominator)
Becomes:
[tex]\frac{20}{24} - \frac{9}{24}[/tex]
Then subtract the numerators, keeping the denominators the same:
20 - 9 = 11;
So the answer is:
[tex]\frac{11}{24}[/tex]
Evaluate (-A) 2 for A = 5, B = -4, and C = 2.
Answer:
=-10 or 25 depending on the placing of the 2
Step-by-step explanation:
(-A)2=(-5)x2=-10
(-A)^2=(-5)x(-5)=25
help asap (image below!!)
Answer:
D
......................
I need help with my fractions
Answer:
1 1/2
Step-by-step explanation:
2/3 + 5/6 = 32 = 1 12 = 1.5. Spelled result in words is three halves (or one and one half).
Answer only 22 please
Answer:
147.3°
Step-by-step explanation:
[ 180 × ( n - 2 ) ] ÷ 11
= [ 180 × ( 11 - 2 ) ] ÷ 11
= ( 180 × 9 ) ÷ 11
= 1620 ÷ 11
= 147.273°
Solve ABC where ∠C = 90°, a = 15 cm, and b = 7 cm.
Answer:
c ≈ 16.55cm ; ∠A = 65 degrees ; ∠B = 25 degrees
Step-by-step explanation:
Because of the Pythagorean theorem, we can solve for c.
This theorem states: a^2 + b^2 = c^2
Since there can only be 180 degrees in a triangle, angle C must be our largest angle. This means that side c is our hypotenuse (the longest side).
Using all of this information, we can say that 15^2 + 7^2 = c^2.
Simplifying that equation, we get that 274 = c^2.
In order to find c, we must square root both sides, and we find that c is about 16.55 cm long.
Using SOHCAHTOA, we know that the tan(∠B)=[tex]\frac{7}{15}[/tex]. Therefore, the arctan ([tex]\frac{7}{15}[/tex]) = ∠B.
Once you find that ∠B is about 25 degrees, you can add ∠B and ∠C together and subtract that from 180 to find ∠A.
∠A = 65 degrees.
Which expression is equivalent to
(3/2p+1)(1/2p+3)
Answer:
3/4p²+5p+3
Step-by-step explanation:
[tex]\dfrac{3}{4}p^2+5p+3[/tex] is the correct answer on simplifying [tex]\left(\dfrac{3}{2}p+1\right)\left(\dfrac{1}{2}p+3\right)[/tex].
SimplificationSimplification of expression is to get an expression in the rearranged form.
How to simplify the arithmetic expression?Simplify the given expression as-
[tex]\left(\dfrac{3}{2}p+1\right)\left(\dfrac{1}{2}p+3\right)=\dfrac{3}{4}p^2+3\times \dfrac{3p}{2}+\dfrac{p}{2}+3\\=\dfrac{3}{4}p^2+5p+3[/tex]
Thus, option C is the correct answer.
Learn more about arithmetic expression here- https://brainly.com/question/17722555
#SPJ2
HELP ME PLEASE!!! A ball is thrown in the air from a platform that is 112 feet above ground level with an initial vertical velocity of 32 feet per second. The height of the ball, in feet, can be represented by the function shown where t is the time, in seconds, since the ball was thrown.
h(t)=−16t2+32t+112
Which of the following equations shows the function rewritten in the form that would be best used to identify the maximum height of the ball?
Question 16 options:
h(t)=−16(t−2)2+112
h(t)=−16(t−1)2+80
h(t)=−16(t−1)2+96
h(t)=−16(t−1)2+128
The ball thrown upwards follows a parabolic path
The equation that shows the function rewritten in the form that would be best used to identify the maximum height of the ball is [tex]h(t)=-16(t-1)^2+128[/tex]
How to determine the equivalent equationThe equation is given as:
[tex]h(t)=-16t^2+32t+112[/tex]
Factor out -16
[tex]h(t)=-16(t^2-2t)+112[/tex]
Express the bracket as a perfect square expression
[tex]h(t)=-16(t^2-2t + 1 - 1)+112[/tex]
Factor out -4
[tex]h(t)=-16(t^2-2t + 1)+112 + 16 * 1[/tex]
[tex]h(t)=-16(t^2-2t + 1)+128[/tex]
Express as a perfect square
[tex]h(t)=-16(t-1)^2+128[/tex]
Hence, the equivalent expression is [tex]h(t)=-16(t-1)^2+128[/tex]
Read more about parabolas at:
https://brainly.com/question/4061870
A polling company is trying to estimate the percentage of adults that consider themselves happy. A confidence interval based on a sample size of 360 has a larger than desired margin of error. The company wants to conduct another poll and obtain another confidence interval of the same level but reduce the error to one-third the size of the original sample. How many adults should they now interview
Reducing the sample size to one-third, increases the error by √3.
Margin of ErrorThe margin of error is given by:
[tex]E=z_\frac{\alpha}{2} *\frac{\sigma}{\sqrt{n} } \\\\where\ z_\frac{\alpha}{2} \ is \ the \ confidence\ level\ z\ score, \sigma\ is \ mean\ and\ n\ is\ sample\ size.\\\\n=360, hence:\\\\E=z_\frac{\alpha}{2} *\frac{\sigma}{\sqrt{360} } \\\\E=0.0527(z_\frac{\alpha}{2} *\sigma)\\\\For\ n = 1/3 * 360=120:\\\\\\E=z_\frac{\alpha}{2} *\frac{\sigma}{\sqrt{120} } \\\\E=0.09122(z_\frac{\alpha}{2} *\sigma)[/tex]
Reducing the sample size to one-third, increases the error by √3.
Find out more on Margin of Error at: https://brainly.com/question/10218601
How do I do this I am confused
pls help! how would I solve this problem ?The figures shown are similar. Find the lengths of x, y, and z.
9/25
start fraction, 9, divided by, 25, end fraction of Polly's co-workers prefers tea over coffee.
What percent of Polly's co-workers prefer tea over coffee?
Answer: To convert a fraction to a percentage you multiply by 100.
(9 / 25) * 100
= 9 * 100/25
= 9 * 4
= 36% answer
Step-by-step explanation:
QUESTION
WORTH
20 POINTS!!! HELP ASAP PLEASE
why am i alive
Answer:
Cause you were born, as simple as that. Plenty of people deal with harsh life.
Step-by-step explanation:
That's not a math question BUT
If the question is why am I alive, I will answer it.
Although i am not a Christian(I deeply respect those who are, though),
I still believe there is an unnatural force that
selected you to be born and experience life for yourself.
If you are thinking about killing yourself, please call 800-273-8255
To which linear equations is the coordinate a solution?
Select two options.
y = 2x + 13
y=-x-2
y = 3x - 5 2. >4 -2 2. 4
y=-x+6 -2 .
y=-2x-2
The linear equation y = -x - 2 and y = 2x + 13 form the solution (-5, 3)
Linear equation
A linear equation is in the form:
y = mx + b
where y, x are variables, m is the rate of change and b is the y intercept.
Given the coordinate (-5, 3) as a solution.
The linear equation y = -x - 2 satisfies this this equation because 3 = -(-5) -2
Also, the linear equation y = 2x + 13 satisfies this this equation because 3 = 2(-5) + 14
Find out more on Linear equation at: https://brainly.com/question/14323743
Answer:
View attached graph
Step-by-step explanation:
y = 2x + 13 and y = -x - 2
Hope this helps!
A 60 ounce glass bottle of juice sells for $4. 20 while a 1. 5 liter of the same juice sells in a plastic bottle for $3. 6. Compare the unit prices of the juice for the two containers. (1 liter is approximately 34 ounces) a. The juice in the glass bottle is 1 cent cheaper per ounce. B. The juice in the plastic bottle is 1 cent cheaper per ounce. C. The juice in the glass bottle is 10 cents cheaper per ounce. D. The juice in the plastic bottle is 10 cents cheaper per ounce. Please select the best answer from the choices provided A B C D.
The triangle shown is reduced to form a similar triangle that is 40% smaller than its current size. Find the perimeter of the triangle.
Step-by-step explanation:
6x+2x+10+8x-30= 16x-20= 4(x-5)
40% of perimeter = 1.6(x-5)
how do you solve this problem ??
Answer:
[tex]x=3c\sqrt{a} -b^2[/tex]
Step-by-step explanation:
[tex]\sqrt{a} =\dfrac{x+b^2}{3c}[/tex]
Multiply both sides by 3c:
[tex]\implies \sqrt{a} \cdot 3c=\dfrac{(x+b^2) \cdot 3c}{3c}[/tex]
[tex]\implies 3c\sqrt{a} =x+b^2[/tex]
Subtract [tex]b^2[/tex] from both sides:
[tex]\implies 3c\sqrt{a} -b^2=x+b^2-b^2[/tex]
[tex]\implies 3c\sqrt{a}-b^2=x[/tex]
Switch sides:
[tex]\implies x=3c\sqrt{a} -b^2[/tex]
Danieli bought 2 1/2 yards of fabric to make a costume what is the length of the fabric in feet and inches show your work
Answer:
7.5 feet and 90 inches
Step-by-step explanation:
you take 2.5 and multiply it by 3 because there are 3 feet in a yard to get 7.5. then take 7.5 and multiply it by 12 to get 90 inches
What is the first term of the arithmetic sequence?.
Answer: -4
second part is x=3 y=10 z=17
Step-by-step explanation:
edge 2023
PLEASE HELP & SHOW WORK PLS..
given that (x-2) is a factor of (x³-8) ,what is the other factor?
Answer:
[tex]x^2+2x+4[/tex]
Step-by-step explanation:
This expression can also be written as a difference of cubes:
[tex]x^3-2^3[/tex]
A important formula to remember is:
[tex]a^3-b^3=(a-b)(a^2+ab+b^2)[/tex]
We can use this to factor this expression:
[tex]x^3-2^3=(x-2)(x^2+2x+4)[/tex]
Therefore the other factor is:
[tex]x^2+2x+4[/tex]
The following triangular prism has a base that is a right triangle.
Draw or describe the net of this triangular prism. Make sure to include the dimensions of each part of the net. Use your net to calculate the surface area of the prism.
Answer:
The Answer is 175.86 cm^2
Step-by-step explanation:
4.3*5.2/2*2=22.36 cm^2
6.75*10=67.5 cm^2
10*4.3*2=86 cm^2
86+22.36+67.5=175.86 cm^2
Hoped this helped ^^
= 234.02
10 x 6.75 = 67.5 x 3 202.5
4.3 x 5.2 = 21.84 square root = 4.67
6.7/2 = 2 = 3.375
3.375 x 4.67 = 15.76
15.76 x 2 = 31.52
202.5 + 31.52 = 234.02
Model of car driven… is it qualitative or quantitative?
Answer:
ok so
Step-by-step explanation:
ok so if theres numbers its qualitative if it has to do with how it drives is quantitative
Can someone please help me I’m stuck on this.
Round 0.3391 to
the thousandths place.
Answer:
.3390 or just .339
Step-by-step explanation:
Write the ratio the 3 ways learned. A recipe uses 5 cups of water for
every 3 cups of flour.
Answer:
5:3
3:5
5 for 3
Step-by-step explanation:
Because for every 5 cups you get 3 cups
How do I do number 1
{twenty symbols text.... }
Can u answer3 3/4 + 2 5/7
Answer:
[tex]6\frac{13}{28}[/tex]
Step-by-step explanation:
Add:
[tex]3\frac34 + 2\frac57[/tex][tex]\frac{15}{4} + \frac{19}{7}[/tex][tex]\frac{105}{28} + \frac{76}{28}[/tex][tex]\frac{181}{28}\\[/tex][tex]6\frac{13}{28}[/tex]-Chetan K