Given:
The system of equations is
[tex]8x+9y=36[/tex]
[tex]3x+4y=16[/tex]
To find:
The solution of the given system of equations using the substituting method.
Solution:
We have,
[tex]8x+9y=36[/tex] ...(i)
[tex]3x+4y=16[/tex] ...(ii)
From (ii), we get
[tex]3x=16-4y[/tex]
[tex]x=\dfrac{16-4y}{3}[/tex] ...(iii)
Putting this value in (i), we get
[tex]8\left(\dfrac{16-4y}{3}\right)+9y=36[/tex]
Multiply both sides by 3.
[tex]8(16-4y)+27y=108[/tex]
[tex]128-32y+27y=108[/tex]
[tex]-5y=108-128[/tex]
[tex]y=\dfrac{-20}{-5}[/tex]
[tex]y=4[/tex]
Putting y=4 in (iii), we get
[tex]x=\dfrac{16-4(4)}{3}[/tex]
[tex]x=\dfrac{16-16}{3}[/tex]
[tex]x=\dfrac{0}{3}[/tex]
[tex]x=0[/tex]
Therefore, the solution of given system of equations is (0,0).
Which choices are equivalent to the expression below?
Answer:
b d and e
Step-by-step explanation:
just simplify or modify each answer and you'll see which equate to 4 root 6. takes 2 mins.
help my peleas
[tex]25 = {c}^{2} [/tex]
Answer:
5
Step-by-step explanation:
[tex]c^{2}[/tex] = 25
[tex]\sqrt{c} = \sqrt{25}[/tex] /take square root of both sides
c = 5 /square root of 25 is 5
Someone help me Please!!!
Answer: (-2, -1) and (3, 14).
Step-by-step explanation:
[tex]\left \Bigg \{ { \bigg{y=x^{2} +2x-1} \atop \bigg {y-3x=5}} \right. ; \left \Bigg \{ { \bigg{y=x^{2} +2x-1} \atop \bigg {y=5+3x}} \right.[/tex]
x² + 2x - 1 = 5 + 3x
x² + 2x - 1 - 5 - 3x = 0
x² - x - 6 = 0
[tex]General formula\\\\x=\dfrac{-b \pm \sqrt{b^{2}-4ac } }{2a} \\\\a=1; \: \: b=-1; \: \: c=-6\\\\x=\dfrac{1 \pm \sqrt{(-1)^{2}-4 \cdot1 \cdot (-6)} }{2 \cdot 1}=\dfrac{1 \pm\sqrt{25} } {2} =\dfrac{1 \pm5}{2} \\\\x_{1} = -2\\x_{2} =3[/tex]
y = 5 + 3x
y₁ = 5 + 3 * (-2) = -1
y₂ = 5 + 3 * 3 = 14
The pair of points representing the solution set of this system of equations is (-2, -1) and (3, 14).
How are the triangles congruent? A) not congruent B) ASA C) SAS D) AAS
Answer:
A) not congruent. You only know one side and one angle to be congruent.
Step-by-step explanation:
pls help me with this multiple choice !
Answer:
Step-by-step explanation:
Cdd
Answer:
B
Step-by-step explanation:
[tex] \tan(60) = \frac{n}{46} \\ n =46 \sqrt{3} \\ \cos(60) = \frac{46}{m} \\ m = 92[/tex]
What is an equation of the line that passes through the points (-4,3)
and (-8,0)?
Answer:
Step-by-step explanation:
Slope of line passing through (-4, 3) and (-8, 0) = (3-0)/(-4-(-8)) = 3/4
Point-slope equation for line of slope ¾ that passes through (-8, 0):
y-0 = ¾(x+8)
Answer please nowwwwwwe
At Keller's Bike Rentals, it costs $34 to rent a bike for 9 hours. How many dollars does it cost per hour of bike use?
Answer: $3.77
Step-by-step explanation:
What does 2.8- 4.4n- 2n + 7 equal?
Answer:
2.8- 4.4n- 2n + 7 = -6.4n + 9.8
Step-by-step explanation:
combined like term:
-4.4n - 2n = -6.4n
2.8 + 7 = 9.8
so all you do is combined together and got -6.4n + 9.8
i believe it equals 9.8-6.4n
sorry, im not very good at explaining how i solved it!! D:
but i hope this helped you out :)
I NEED HELP ASAP!!!!!
Solve the equation and show your work.
Here's the problem: 4x + 3x - 3(4x - 8) = 14
Step 1.) Eliminate parentheses by distributing the -3.
Step 2.) Collect any like terms on the left side of the equation.
Step 3.) Subtract 24 from both sides of the equation.
Step 4.) Divide both sides of the equation by -5.
Answer:
Step-by-step explanation:
x=2
17)
In the coordinate plane, the endpoints of a line segment are (-12, 9) and (16, -5). What is the midpoint of the line segment?
A
(2, 2)
B
(-2,2)
(4.-2)
D
The value of Maggie's car decreased by 10% since last year, when she bought it. If the car is now worth $21,000.00, how much was the car worth when she bought it?
Answer
$23,333
Step-by-step explanation:
100% - 10% = 90%
90% = 0.90
21000/.90 = $23,333
Kirk wanted to open a savings account with the $2,000 he had earned over the summer. If the bank’s interest rate is 5%, how much will he have in 2 years? Show your work.
Answer:
$2205
Step-by-step explanation:
The formula is (2000*1.05^2) which is 2205
Can someone help me with this?
Answer:
Step-by-step explanation:
Quadrilateral EFGH is a rectangle.
Therefore, measure of all interior angle of the rectangle = 90°
7). m∠FEG + m∠GEH = 90°
57° + m∠GEH = 90°
m∠GEH = 90° - 57°
m∠GEH = 33°
Diagonal of the rectangle are equal in measure and bisect each other.
8). m(FH) = m(FK) + m(KH)
= 32 + 32 [Since, FK ≅ KH]
= 64
9). m∠FGH + m∠EFG = 90° + 90°
= 180°
MNOP is a Rhombus, so the diagonals will be perpendicular and bisect each other.
10). m∠MRN = 90°
11). m(PR) = 12
Therefore, m(RN) = 12
"Diagonals of a rhombus bisect the opposite angles"
12). m(∠PON) = 124°
Therefore, m(∠POM) = 124°
"ABCD is an isosceles Trapezoid"
13). Therefore, ∠C ≅ ∠D
14). AB║CD
15). AD ≅ BC
Andre paid $17,520 for a new car. He will make equal payments each month for 4 years. What will be Andre’s monthly car payment?
Answer:
$12
Step-by-step explanation:
because,
365=year
365*4= 1460
17,520/1460=$12
A local car dealership is holding a year-end event because new car models have just been released. Declan has $35,000 to spend on a car. The car Declan decides to buy for his family costs $35,000. However, it is part of the year-end event, which means he receives a 15% discount on the new car. Declan plans to put the money he saves on the car into a new bank account. The bank account has a yearly simple interest rate of 4%, paid at the end of each year. If Declan does not add any other money to this bank account, it will take
Answer:
6 years
Step-by-step explanation:
The computation of the time period is given below:
As we know that
Future value = Present value × (1 + rate of interest)^time period
$6,720 = ($35,000 × 15%) × (1 + 0.04)^time period
$6,720 = $5,250 × 1.04^time period
1.28 = 1.04^time period
So, the time period is 6.29 years i.e. 6 years
hence, the time that should be taken is 6 years
A triangle has a height of 24km and a base of 18km. What is the area of the figure?
Answer:
216 square km
Step-by-step explanation:
24 x 18 / 2 =
432 / 2 =
216 km square
Hope that helps!
Answer:
225 [tex]km^{2}[/tex]
Step-by-step explanation:
h is 60% of m.
Also, r is 75% ofm.
Work out h as a percentage of r.
Answer:
h=0.6m
r=0.75m
h=0.6m/0.75m*100 percent of r.
h=6000/75% of r
h=80% of r
Step-by-step explanation:
The expression of h as a percentage of r would be as; 80% of r.
What is the percentage?A percentage is a minimum number or ratio that is measured by a fraction of 100.
WE are given that h is 60% of m.
Also, r is 75% of m.
WE need to find out h as a percentage of r.
Therefore, h=0.6m
r=0.75m
Now we can write as;
h = 0.6m/0.75m x 100 percent of r.
h = 6000/75% of r
h = 80% of r
Hence, the expression of h as a percentage of r would be as; 80% of r.
Learn more about percentages;
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1. The graph of a LINEAR FUNCTION is a _______
A. Parabola
B. Point
C. Line
D. Circle
2. Which of the following are linear equations in two variables?
(a.) 2x + 3y = 12
(b.) x² +3y=4
(c.) y= 3x² -4
(d.) y² =16
3. Which of the following linear equations is in Standard form? (Ax + By =C)
A. Y= 7x + 3
B. 3x –5y= -5
C. - x + 7y =2
D. 4y -x = 0
4. What is the value of y in the equation
x -2y =4 given that x=8?
A. -4
B. -2
C. 2
D. 4
5. in the equation 2x + 3y = 7‚ when y=1, which would be the corresponding value of x?
A. -2
B. 0
C. 2
D. 4
6. which of the following ordered pairs is a
solution to the linear equation x-2y = 12?
A. (16,2)
B. (-8, -1)
C. (14,-1)
D. (4,-3)
7. which of the following is NOT a solution of the linear equation 3x -5y =-2?
A. (2,1)
B. (1, 1)
C. (6,4)
D. (16,10)
8. the steepness of the line also known as rise over run is called
A. linear equation
B. linear function
C. linear inequality
D. slope
9. which of the following equation is to be used in finding for slope of the given linear equation standard form?
A. m=A/ B
B. m= -A/B
C. m= B/-A
10. find the slope of the line that corresponds to the equation y=7x–5.
A. –5
B. 7x–5
C. 7
D. 7x
11. in the equation y= -2x +6, what is the slope?
A. -2
B. -1
C. 2
D. 6
12. in the equation y= 3x – 2, what is the y- intercept?
A. 3
B. -3
C. 2
D. -2
13. which of the following linear equations
is in slope-intercept form? (y=mx + b)
A. y= 9x – 23
B. x=3y+10
C. 2x+2y=2
D. x+7y=1
14. which of the following linear equations is in standard form? (Ax + By =C)
A. –x+7y=14
B. y=7x–14
C. 8y–x=16
D. 2x–9y=–6
15. which of the following is the standard form of y=11x+3 ?
A. 11x–y=3
B. –11x+y=–3
C. –11x+y=3
D. 11x–y=–3
=mclm=
Answer:
1.Line
2.A
3. c
4.2
5.2
6. a
7.A
8.Slope
9.C
10.B
11.D
Step-by-step explanation:
Which expression is equivalent to 2.2m2 – 3.5(4m – 1.4) + 3.6(8m2 – 4.5m)?
Answer:
31m2−30.2m+4.9
Step-by-step explanation:
An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
The equivalent expression to 2.2m² – 3.5(4m – 1.4) + 3.6(8m² – 4.5m) is
31m² - 30.2m - 4.9
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
2.2m² – 3.5(4m – 1.4) + 3.6(8m² – 4.5m)
Remove the parenthesis.
2.2m² - 3.5 x 4m - 3.5 x 1.4 + 3.6 x 8m² - 3.6 x 4.5m
2.2m² - 14m - 4.9 + 28.8m² - 16.2m
Combine the like terms.
31m² - 30.2m - 4.9
Thus,
The equivalent expression to 2.2m² – 3.5(4m – 1.4) + 3.6(8m² – 4.5m) is
31m² - 30.2m - 4.9
Learn more about expressions here:
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adam hikes from bridgetown to lakeville. Gina starts at the same time, and hikes from Lakeville to Bridgetown on the same road. Their hikes are represneted on the graph below.
Answer:
45
Step-by-step explanation:
how can I find the smallest division of a measurement without a ruler? for eg. 12.45cm, what's the smallest division?
Answer:
Step-by-step explanation:
mm
Which statement below is an example of the
Associative Property of Addition?
A. 7+(3+5)= 7+(5+3)
B.9+(11 + 6) = (9 +11) + 6
C. 3(6+5) = 3.6+3.5
D. 12(8 + 4) = 12(8) + 12(4)
Answer:
B
Step-by-step explanation:
Let say, a=9,b=11,c=6
Then associative properties says that every element is related to each other, here "b" associates a &c.
Therefore, a is related to b+c
c is related to a+b
What is the value of y when x = 4?
Answer:
I think there is no y-intercept bc all they give you is x ( don't even have slope either) but I could be wrong...sorry
Q8.
a. xy = 24, since (3)(8) = 24
b. 4y = 24
Y = 24 ÷ 4
Y = 6
NB: I think I figured it out ^-^ I hope this helps!
Find the gradient of the line segment between the points (1,2) and (3,-10)
Pleaseee helpp answer correctly !!!!!!!! Will mark Brianliest !!!!!!!!!!! P equals what ??????
Answer:
P = 2t + 2u + 2v + 4w
Step-by-step explanation:
[tex]P =t + t + u + u + v + v \\ + w + w + w + w \\ \\ P = 2t + 2u + 2v + 4w \\ [/tex]
Simplify.
56bc
64cd
I need ASAP
Answer:
8c(7b + 8d)
Step-by-step explanation:
Supposing that you are ADDING these terms, you have 56bc + 64cd. This can be factored as follows: 56bc + 64cd = 8c(7b + 8d)
Write two expresiones that are equivalent to -5/4x - 3/4
Answer:
Two expressions that are equal to [tex]-\frac{5}{4} x - \frac{3}{4}[/tex] is -([tex]\frac{5}{4} x + \frac{3}{4}[/tex]) and [tex]\frac{1}{4}[/tex] (-5x - 3)
Step-by-step explanation:
Both expressions use the distributive property and take out -1 and [tex]\frac{1}{4}[/tex] from each expression to form equivalent expressions to [tex]-\frac{5}{4} x - \frac{3}{4}[/tex].
Find the volume of this cylinder.
Give your answer to 1 decimal place.
11 cm
10
14 cm
Cylinder's volume = 1330.5 cm^3
Step-by-step explanation:
radius, r = diameter, d / 2
= 11/2
= 5.5 cm
Volume = π r^2 h
= π × 5.5^2 × 14
= 423.5π
= 1330.5 cm^3
PLLLLZxxXXZZ I REALLY NEED HELP DONT ANSWER RANDOM THINGS PLZ
Answer:
its B
Step-by-step explanation:
Answer:
i got A for both of them ^^
for #1 you would do 8(1/2÷2)-(1/4+4)
and for #2 its 7(2.5) - (12/3+6)