Claire completed the steps to solve the system of equations. 4 x minus 2 y = 4. 3 x + 3 y = 21. Step 1 12 x minus 6 y = 12. 6 x + 6 y = 42. Step 2 18 x = 54. Step 3 x = 3. Step 4 4 (3) minus 2 y = 4. 12 minus 2 y = 4. 2 y = negative 8. Y = negative 4. Step 5 Solution is (3, negative 4). Is Claire's solution to the system of equations correct? Explain why or why not.
Answer:
Claire should have gotten –2y = –8 instead of 2y = –8 in step 4.
Step-by-step explanation:
Following the steps taken :
4x - 2y = 4 - - - (1)
3x + 3y = 21 - - - (2)
Multiply (1) by 3 and (2) by 2
12x - 6y = 12 - - - (3)
6x + 6y = 42 - - - (4)
Add (3) and (4)
18x = 54
x = 54/18
x = 3
Put x = 3 in (1)
4(3) - 2y = 4
12 - 2y = 4
-2y = 4 - 12
-2y = - 8 (this is where the mistake lies)
It shouldn't be 2y = - 8 as stated
Answer:
The other dude is right.
Step-by-step explanation:
Somebody please help meee!!!!
Answer:
288.4
Step-by-step explanation:
v=pi r^2 H
Answer:
I think answer is 288.4 plz mark me brainlist
The difference between two numbers is 51 four times the smaller is equal to six more than the larger what are the numbers
Answer:
Smaller #: 19
Larger #: 70
Step-by-step explanation:
Step 1:
We can set the smaller number as x. We can find the larger number by adding 51, hence represented as 51+x.
Step 2:
We can write an equation with the given information. Four times the smaller number is equal to six more than the larger:
[tex]4x=51+x+6\\3x=57\\x=19[/tex]
If the smaller number represented as x is [tex]\fbox{19}[/tex] , then the larger number represented as 51+x would be [tex]\fbox{70}[/tex] .
I hope this helps! Let me know if you have any questions :)
One week, Isabelle bought 2 bags of apples and 3 bags of oranges. The next week, she bought 1 bag of apples and 2 bags of oranges. If a represents the cost of each bag of apples and r represents the cost of each bag of oranges, which expression could Isabelle use to calculate the difference between the amounts she spent each week?
A. 3 a minus r
B. 3 a minus 5 r
C. (2 a minus 3 r) minus (a minus 2 r)
D . (2 a + 3 r) minus (a + 2 r)
Answer:
It should be D.
For this season in baseball, Joseph hit approximately 2 out of every 5 at bats. If he was up at bat 1,000 times this season, estimate the number of hits he had.
Answer:
I estimate he hit 400 bats.
Step-by-step explanation:
I am going to set up a ratio to solve.
Joseph hits about 2 out of every 5 bats, and we want to find out the number of hits we had if he was up to bat 1,000 times.
[tex]\frac{2}{5} = \frac{x}{1000}[/tex]
Cross multiply to solve.
2(1000) = 5(x)
2000 = 5x
Divide by 5 on both sides.
X = 400
I estimate he hit 400 bats.
CAN ANYONE PLEASE HELP ME !!
Answer:
The answer is 9.
Step-by-step explanation:
Sabiendo que la tangente son 4/3 dime el cos y sen estando el angulo en el tercer cuadrante de la circunferencia
Answer:
sen α = - 4/5
cos α = - 3/5
Step-by-step explanation:
tang α = 4/3
De la relación fundamental de la trigonometría sabemos:
sen² α + cos²α = 1
Dividiendo la ecuación anterior por cos² α
sen²α/cos²α + cos²α / cos²α = 1 / cos² α
tang²α + 1 = 1/ cos² α
(4/3)² + 1 = 1/ cos² α ⇒ 16/9 + 1 = 1/ cos² α
1/ cos² α = ( 16 + 9 ) / 9
1/ cos² α = 25/9
cos² α = 9/25
cos α = 3/5
y para calcular el sen α
sen² α = 1 - cos²α
sen² α = 1 - 9/25
sen² α = ( 25 - 9 )/ 25
sen² α = 16/25
sen α = 4 / 5
Ahora bien el angulo α está en el tercer cuadrante, en ese cuadrante tanto el seno como el coseno son negativos.
Respuesta:
sen α = - 4/5
cos α = - 3/5
5−a+4a= anyone know how to solve
Answer:
5 +3a
Step-by-step explanation:
5−a+4a
Combine like terms
5 +3a
Answer:
[tex]5+3a[/tex]
Steps :
All we need to do is add similar elements!
[tex]5-a+4a = 5+3a[/tex]
-
a. 11.2 in.
b. 19.6 in.
c. 25.2 in.
The cost of 2 pounds
of coffee is $0.
True or False
Answer:
false
Step-by-step explanation:
the graph shows that 2 pounds of coffee would be about $4
Answer:
false.
Step-by-step explanation:
because if you look 1 pounds is 2 dollars
A group of friends went to lunch. The bill, before sales tax and tip, was $37.50. A sales
tax of 8% was added. The group then tipped 18% on the amount after the sales tax
was added. What was the amount, in dollars, of the sales tax?
Show your work.
Answer
question continued: what was the total amount the group paid, including tax and tip?
Answer:
Sales tax=3.00, total paid=47.79
Step-by-step explanation:
37.50 x .08=3.00 sales tax
37.50+3.00=40.50 amount with sales tax added
40.50 x .18=7.29 amount of tip
40.50 + 7.29=47.79 total with tip and sales tax
if you subtract 1/2 from a number and multiply the result by 1/2 you get 1/8. what is the number?? (pls provide steps)
Answer:
[tex]Number\ is\ \frac{3}{4}[/tex]
Step-by-step explanation:
Let the number be x
Subtract 1/2 from x = (x - 1/2)
Multiply 1/2 to the result = 1/2(x - 1/2)
The result is 1/8
That is,
[tex]\frac{1}{2}( x - \frac{1}{2}) = \frac{1}{8}\\\\( x - \frac{1}{2}) = \frac{1}{8}\times \frac{2}{1}\\\\(x-\frac{1}{2}) = \frac{1}{4}\\\\x = \frac{1}{4} + \frac{1}{2}\\\\x = \frac{3}{4}[/tex]
Ben is 50 years old. His son, Carl is 24 years old. How many years ago was Ben 3 times as old as Carl?
Answer:
78
Step-by-step explanation:
50 - 24 = 26
26 x 3 = 78
Hope it helps...
The solution to the equation −2(x+11)=−8 is x=
Answer:
-7
Step-by-step explanation:
-2x-22=-8
-2x=-8+22
-2x=14
X=14/-2
X=-7
Wherever necessary.
10. Refer to the table to find the monthly payments necessary to complete parts a -C.
Table of Monthly Payments per $1,000 of Principal
Rale
1 yr
2 yr
3 yr
4 yr
5 ут
10 yr
6.50%
86.30
44.55
30.65
23.71
19.57
11.35
6.75%
86.41
44.66
30.76
23.83
19.68
11.48
7.00%
86.53
44.77
a. What is the monthly payment for a
$3,200 five-year loan with an APR of
9%?
b. Mia borrows$66,000 for four years at
an APR of 7.25%. What is the monthly
payment?
C. What is the total amount of the
monthly payments for a $6,100, two-
year loan with an APR of 8.75%?
Round to the nearest dollar.
30.88
23.95
19.80
11.61
7.25%
86.64
44.89
30.99
24.06
19.92
11.74
7.50% 86.76
45.00
31.11
24.18
20.04
11.87
7.75%
86.87
45.11
31.22
24.30
20.16
12.00
8.00%
86.99
45.23
31 34
24.41
20.28
12.13
8.25%
87.10
45.34
31.45
24.53
20.40
12.27
8.50%
87.22
45.46
31.57
24.65
20.52
12 40
8.75%
87 34
45.57
31.68
24.77
20.64
12 53
9.00%
87.45
45.68
31.80
24.89
20.76
12.67
Answer: 30,000
Step-by-step explanation:
1. The monthly payment for a $3,200 five-year loan with an APR of 9% is $63.
2. The monthly payment is $1,587.
3. The total amount of the monthly payments is $191.
a. From the table, we can see that the monthly payment per $1,000 principal for a five-year loan with a 9% APR is $19.57.
Since the loan amount is $3,200, we can calculate the monthly payment by multiplying the monthly payment per $1,000 principal by the number of thousands in the loan amount:
= $19.57 x (3,200 / 1,000)
= $62.624
= $63.
b. From the table, we can find that the monthly payment per $1,000 principal for a four-year loan with a 7.25% APR is $24.06.
We can calculate the monthly payment by multiplying the monthly payment per $1,000 principal by the number of thousands in the loan amount:
= $24.06 x (66,000 / 1,000)
= $1,586.76
= $1,587.
c. From the table, we can find that the monthly payment per $1,000 principal for a two-year loan with an 8.75% APR is $31.34.
We can calculate the total amount of monthly payments by multiplying the monthly payment per $1,000 principal by the number of thousands in the loan amount:
= $31.34 x (6,100 / 1,000)
= $191.234
= $191.
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I think of a number, I subtract 10 and add 2 . My answer is 20, What was my number
Answer:
x=28Step-by-step explanation:
x-10+2=20 x-8=20 x=20+8 x=28. this is my answerIf mAD = (17x + 2)°, mAC = (7x - 10°), and m∠ABC = (4x + 15)°, find m∠ABC
Please help
Answer:
m<ABC = 51degrees
Step-by-step explanation:
The angle at the vertex is half the difference of the angles at the intercepted arcs. Hence;
m<B = 1/2 (arcAD - arcAC)
<ABC = 1/2(17x + 2 -(7x - 10°))
4x + 15 = 1/2(17x-7x+2+10)
2(4x+15) = 10x+12
8x + 30 = 10x+12
8x-10x = 12-30
-2x = -18
x = 18/2
x = 9
Get m<ABC
m<ABC = 4x + 15
m<ABC = 4(9) + 15
m<ABC = 36 + 15
m<ABC = 51degrees
The measure of angle ∠ABC = 51 degree.
Since we know that,
For a circle,
The angle at the vertex is half the difference of the angles at the intercepted arcs.
Therefore,
m∠ABD = 1/2 (arcAD - arcAC)
⇒ ∠ABC = (1/2)(17x + 2 -(7x - 10°))
⇒ 4x + 15 = (1/2)(17x-7x+2+10)
⇒2(4x+15) = 10x+12
⇒ 8x + 30 = 10x+12
⇒ 8x-10x = 12-30
⇒ -2x = -18
⇒ x = 18/2
⇒ x = 9
Get m∠ABC
⇒ m∠ABC = 4x + 15
⇒ m∠ABC = 4(9) + 15
⇒ m∠ABC = 36 + 15
⇒ m∠ABC = 51 degree
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The ratio of cars to residents on a small island is 1:112. There are 2,912 residents on the island. How many cars are there on the island?
a.
2,800
c.
112
b.
26
d.
52
Answer:
26
Step-by-step explanation:
1:112=113
x:2912=y
Divide 2912 and 112
2912/112=26
1 × 26 = 26
Find The Missing Angle Measure
A. 34
B. 90
C. 6
D. 23
please help me with this
The sum of the 3 inside angles equal 180
To find the missing angle subtract the 2 known angles from 180.
R = 180 - 114 - 32 = 34
R = 34 degrees
A premature infant is gaining 2.5 ounces a day. At that rate, how many days will it take for him to gain 8 ounces
Answer:
3.2 days
Step-by-step explanation:
All you have to do is divide 8 by 2.5
8 ÷ 2.5 = 3.2
(Time expired.) The graph shows the system of equations below.
2 x minus 3 y = negative 6. y = negative one-third x minus 4
Which statement is supported by the graph?
A. The blue line represents the equation 2x-3y=6, and the solution to the system of equations is (–6, –2).
B. The blue line represents the equation 2x-3y=6, and the solution to the system of equations is ( –2, –6).
C. The red line represents the equation 2x-3y=6, and the solution to the system of equations is (2, –4).
D. The red line represents the equation 2x-3y=6, and the solution to the system of equations is (–4, 2).
Answer:
A. The blue line represents the equation 2x-3y=6, and the solution to the system of equations is (–6, –2).
Step-by-step explanation:
Here we have the system:
2x - 3y = -6
y = -(1/3)*x - 4
First, remember that if the slope is negative, then the equation is decreasing.
So, for the second equation, as x increases, y decreases, then the line of the second equation is the red one (because the red one decreases).
So the blue one represents the equation 2x - 3y = -6
Also remember that the solution of a system of equations is the point where the graphs of the equations intersect, here we can see that the intersection happens at the point (-6, - 2)
This means that the solution of the system is (-6, - 2)
From this, we can see that the correct option is:
A. The blue line represents the equation 2x-3y=6, and the solution to the system of equations is (–6, –2).
A: The blue line represents the equation 2x-3y=6, and the solution to the system of equations is (–6, –2).
Find the value of X and Y in the parallelogram
Answer:
[tex]Find~x:-[/tex]
[tex]4x-37=49[/tex]
[tex]4x=49+37[/tex]
[tex]x=21.5[/tex]
[tex]Find ~y:-[/tex]
[tex]y/5=4x-3[/tex]
[tex]y=5(4*21.5-3)[/tex]
[tex]y=415[/tex]
----------------------hope it helps...have a great day!!Help me plzzz please please pleaee
If Ali is x years old, write Omar’s age in terms of x if omar is 6 years younger
Answer:
[tex]\huge\boxed{Answer\hookleftarrow}[/tex]
Ali's age = x
Given that, Omar is 6 years younger than Ali
So, Omar's age = [tex]\large\bold{x - 6}[/tex]
✐ Omar's age in terms of 'x' is x - 6 years.
ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ
# ꧁❣ RainbowSalt2²2² ࿐
Tell us wether the line or segment is best described as a radius, chord, diameter, secant, or a tangent of 0O.
Answer:
AB - secant
DB - diameter
AB - chord
OB - radius
BC - tangent
(In the order they are in the picture)
Step-by-step explanation:
AB - The line goes through the circle and does not go through the center. This fits the definition of a secant, so line AB is a secant.
DB - Segment DB goes through the center and has endpoints on the circle. This fits the definition of a diameter, so DB is a diameter.
AB - Segment AB has endpoints on the circle and does not go through the center. This fits the definition of a chord, so segment AB is a chord.
OB - Segment OB is basically from the center to a point on the circle. This fits the definition of a radius, so segment OB is a radius.
BC - Line BC intersects the circle in only one point and does not go through it. This fits the definition of a tangent, so line BC is a tangent.
PLEASE HELP ME!! ASAP
ANSWER EXPLANATION = BRAINLIEST & FIVE STARS
What is the value of cos Q?
Write your answer as a simplified fraction.
Explanation:
Divide the adjacent side UQ = 28 over the hypotenuse QE = 53 to form the cosine of Q. The adjacent side is the side closest to the reference angle. The hypotenuse is always opposite the right angle.
The fraction 28/53 cannot be reduced further since 28 and 53 have no factors in common other than 1.
Answer:
28/53
Step-by-step explanation:
To find the value of cos(Q), you need to divide the adjacent, 28, and the hypotenuse, 53. Dividing them results to 28/53, and simplified is, I don't think you can simplify that. This answer might not be totally correct.
Just remember in the future,
sin = opposite / hypotenusecos = adjacent / hypotenusetan = opposite / adjacentAnd you can use this link for help
https://www.mathsisfun.com/sine-cosine-tangent.html
Dan had a large piece of wood that was 10 feet
long. He cut the wood into smaller pieces, each
measuring 1/4 foot. How many pieces of wood
dd Dan cut?
Answer:
40 pieces of wood
Step-by-step explanation:
Find how many pieces he cut by dividing 10 by 1/4
10 / (1/4)
= 40
So, Dan cut 40 pieces of wood
Which of the binomials below is a factor of this trinomial?
x^2 + 13x+42
Answer:
x+6 and x+7
Step-by-step explanation:
Given the quadratic equation;
x^2 + 13x + 42
Factorize
x^2+13x+42 = 0
x^2 + 7x + 6x + 42 = 0
x(x+7)+6(x+7) = 0
(x+6)(x+7) =0
Hence the required binomials are x+6 and x+7
If sin(2x + 7)degrees =cos(4x-7)degrees, what is the value of x?
Answer:
x = 15
Step-by-step explanation:
[tex]cosx = sin(\frac{\pi}{2} - x)[/tex]
[tex]sin x = sin y = > x = sin^{-1}(sin y) = y => x = y[/tex]
[tex]sin(2x + 7)^{\circ} = cos(4x - 7)^{\circ}\\\\sin(2x + 7)^{\circ} = sin(\frac{\pi}{2} - (4x - 7))\\\\(2x + 7) = (\frac{\pi}{2}- (4x -7))\\\\2x + 7 = \frac{\pi}{2} - 4x + 7\\\\6x = \frac{\pi}{2}\\\\x = \frac{\pi}{12}[/tex]
x = 15
The attendances y for two movies can be modeled by the following equations, where x is the number of days since the movies opened.
y=-x^2+35x+100 Movie A
y=-5x+275 Movie B
When is the attendance for each movie the same?
After ___ days and after ___ days.
Answer:
After
days and after
days.
By solving a quadratic equation, we will see that the attendance will be the same after 5 days and after 35 days.
When is the attendance for each movie the same?
This will happen for the values of x such that:
y = -x^2 +35x + 100 = y = -5x+275
There says that the attendance for movie A is the same as the one for movie B. So we just need to solve that.
We can write the equation as:
-x^2 +35x + 100 = -5x+275
If we simplify this, we get:
-x^2 + 35x + 100 + 5x - 275 = 0
-x^2 + 40x - 175 = 0
This is a quadratic equation, the two solutions are given by Bhaskara's formula, we will get:
[tex]x = \frac{-40 \pm \sqrt{(40ft)^2 - 4*(-1)*-175)} }{2*-1} \\\\x = \frac{-40 \pm 30}{-2}[/tex]
So the two solutions are:
x = (-40 + 30)/-2 = 5
x = (-40 - 30)/-2 = 35
So, the attendance will be the same after 5 days and after 35 days.
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