Solution:
It is given that :
Area of old crate = 8 square feet
Area of the new crate = 12 square feet
Therefore difference in the area = 12 - 8
= 4 square feet
Now the percentage increase in the area of the crate is given by :
[tex]$=\frac{\text{difference in the area of crate}}{\text{original area of crate}} \times 100$[/tex]
[tex]$=\frac{4}{8} \times 100$[/tex]
= 50%
So the percentage increase in space is 50%
Student A spent $9 on a bottle of school glue, a package of colored pencils, and a pencil pouch. Student B
spent $16 on two bottles of school glue, three packages of colored pencils, and a pencil pouch. Student C
spent $17 on a bottle of school glue, two packages of colored pencils, and two pencil pouches.
1. Which augmented matrix best represents the system of linear equations that could be used to
determine the price of each item?
Answer:
Step-by-step explanation:
...
[tex]\left[\begin{array}{ccc}1&1&1\\2&3&1\\1&2&2\end{array}\right] \left[\begin{array}{ccc}G\\C\\P\end{array}\right] =\left[\begin{array}{ccc}9\\16\\17\end{array}\right][/tex] is augmented matrix best represents the system of linear equations that could be used to determine the price of each item
What is Matrix?a matrix is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object.
Student A spent $9 on a bottle of school glue, a package of colored pencils, and a pencil pouch.
Let bottle of school glue=G
a package of colored pencils=C
pencil pouch=P
G+C+P=9
Student B
spent $16 on two bottles of school glue, three packages of colored pencils, and a pencil pouch.
2G+3C+P=16
Student C
spent $17 on a bottle of school glue, two packages of colored pencils, and two pencil pouches.
G+2C+2P=17
[tex]\left[\begin{array}{ccc}1&1&1\\2&3&1\\1&2&2\end{array}\right] \left[\begin{array}{ccc}G\\C\\P\end{array}\right] =\left[\begin{array}{ccc}9\\16\\17\end{array}\right][/tex]
is used to determine the price of each item
Hence [tex]\left[\begin{array}{ccc}1&1&1\\2&3&1\\1&2&2\end{array}\right] \left[\begin{array}{ccc}G\\C\\P\end{array}\right] =\left[\begin{array}{ccc}9\\16\\17\end{array}\right][/tex] is augmented matrix best represents the system of linear equations that could be used to determine the price of each item
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can anyone help with math thanks
Answer:
Step-by-step explanation:
50 - 5 - 18 = 27
27 ÷ 3 = 9
x = 9
If f(x) = 5x - 12, find f(x) when x= - 12
Plz answer
Answer:
-72
Step-by-step explanation:
first replace x with -12 so 5(-12)-12
then simplify which makes it -60-12
finally solve that which gives you -72
hope this helps :)
triangle ABC has vertices at A (-12,-8) B (10,-6) and C (6,14. What is the midpoint of side AC of the triangle?
Step-by-step explanation:
midpoint of AC=(x¹+x²/2,y¹+y²/2)
=(-12+6/2,-8+14/2)
=(-6/2, 6/2)
=(-3,3)
Hey, can someone help me with my math homework?
Evaluate p2 - r2 for p = 10, r = -4 and t = 5.
Answer:
84
Step-by-step explanation:
p^2-r^2= 10^2-(-4)^2
100-16=84
Find the missing value of x in the arithmetic sequence below.
x, 16, 20, 24, 28
Answer:
x=12
Step-by-step explanation:
Answer:
12
Step-by-step explanation:
just find the arithimetic sequence and count backwards have a great day
Consider the function f(x) = x(x-4.
If the point (2+c,y) is on the graph of f(x), the following point will also be on the graph of f(x):
A) (c-2,y)
B) (2-c,y)
(2-c,y) is the answer for the problem.
What is the solution to the system of linear equations graphed below?
On a coordinate plane, 2 lines intersect at (3.5, negative 4).
(3 and one-half, negative 4)
(Negative 4, 3 and one-half)
(0, 3)
(0, negative 4)
Answer: The answer was A,
(3 1/2 , -4 )
For people who are taking the test on edge.
Step-by-step explanation:
Answer:
A is the correct answer
Enter the first four terms.
Answer:
7, 4, 1, and -2.
Step-by-step explanation:
Our recursive rule is:
[tex]f(1)=7\!, f(n)=f(n-1)-3[/tex]
Where n is the nth term.
So, our first term will be f(1). As defined, this is 7.
Our second term will be f(2). We will use the recursive formula. Substituting 2 for n yields:
[tex]f(2)=f(2-1)-3[/tex]
Subtract:
[tex]f(2)=f(1)-3[/tex]
We know that f(1) is 7. Substitute:
[tex]f(2)=7-3=4[/tex]
Hence, the second term is 4.
We will do the same thing for the third term. Substitute 3 for n:
[tex]f(3)=f(3-1)-3[/tex]
Subtracting yields:
[tex]f(3)=f(2)-3[/tex]
We know that f(2) is 4. So:
[tex]f(3)=4-3=1[/tex]
Hence, the third term is 1.
Finally, we will do the same thing. Substitute 4 for n to find the fourth term:
[tex]\begin{aligned} f(4)&=f(4-1)-3 \\ f(4)&=f(3)-3 \\ f(4)&=1-3 \\ f(4)&=-2\end{aligned}[/tex]
Hence, the fourth term is -2.
Therefore, our first four terms are 7, 4, 1, and -2.
Can someone help plz? Jack and Jessica earned the same amount last week. Jack earned $18 per hour and had $41 taken from his check for taxes LaTeX: (18x-41)( 18 x − 41 ). Jessica earned $15 per hour and had $17 deducted from her pay. How many hours did each work in order to get paid the same amount?
Write the equation
Solve for the number of hours
Answer:
the answer is 8
Step-by-step explanation: so first what you want to do is you want to set up the equation 18x-41. then you want to do 15x because of the 15 per hour. then you minus 17. so your equation is 18x-41=15x-17 then the answer to that is 8 hours
ASAP what is the x and y intercept for −4x+7y=3
Answer:
x - (-3/4,0)
y - (0, 3/7)
Step-by-step explanation:
PLEASE THESE 2 HELPPPPPPPPPPPP
Answer:
c and g
Step-by-step explanation:
Line t has an equation of y = -1/2 x + 7. Line u is parallel to line t and passes through
(4, -6). What is the equation of line u?
Answer:
y = -1/2x - 4
Step-by-step explanation:
Let equation of line u be y = mx + c
since line t and line u are parallel, slope/gradient of both lines are the same (aka m = -1/2)
sub (4, -6):
-6 = -1/2(4) + c
c = -4
therefore, equation of line u is y = -1/2x - 4
This is a question on coordinate geometry. If you wish to venture further into it/understand this topic better, you may want to follow my Instagram account (learntionary), where I post some of my own notes on certain topics and also some tips that may be useful to you :)
Kim ate 50% of candies in the bag. If Kim ate 35 candies , how many candies were total in the bag?
Answer:
70 candies
Step-by-step explanation:
35 x 2 = 70
Check:
70/2 = 35
If\ the\ polynomial\ p\left(x\right)\ =\ 2x^3\ +\ ax^{2\ }-\ 7x\ +b,\ p\left(1\right)\ =\ 3\ and\ p\left(2\right)\ =\ 19,\ find\ a\ \&\ b
pls tell fast
Answer:
Value of a =3
Value of b =5
Step-by-step explanation:
[tex]If\ the\ polynomial\ p\left(x\right)\ =\ 2x^3\ +\ ax^{2\ }-\ 7x\ +b,\ p\left(1\right)\ =\ 3\ and\ p\left(2\right)\ =\ 19,\ find\ a\ \&\ b[/tex]
We are given p(1)=3 and p(2)=19
Putting x =1 to find p(1)
[tex]p\left(x\right)\ =\ 2x^3\ +\ ax^{2\ }-\ 7x\ +b\\p(1)=2(1)^3+a(1)^2-7(1)+b\\We \ know \ p(1)=3\\3=2+a-7+b\\3=-5+a+b\\a+b=3+5\\a+b=8[/tex]
Now putting x=2 as p(2)=19
[tex]p\left(x\right)\ =\ 2x^3\ +\ ax^{2\ }-\ 7x\ +b\\p(2)=2(2)^3+a(2)^2-7(2)+b\\We \ know \ p(2)=19\\19=2(8)+4a-14+b\\19=16+4a-14+b\\4a+b=19-16+14\\4a+b=17[/tex]
Solving these equations to find values of a and b
[tex]a+b=8---eq(1)\\4a+b=17---eq(2)[/tex]
Subtract both equations
[tex]a+b=8\\4a+b=17\\-\ \ \ - \ \ \ -\\------\\-3a=-9\\a=\frac{-9}{-3}\\a=3[/tex]
So, value of a =3
Now finding value of b bu putting value of a in equation 1
[tex]a+b=8\\3+b=8\\b=8-3\\b=5[/tex]
So, Value of b =5
What is the value of when x=15
Answer:
Value of what?
Step-by-step explanation:
Put your question DB and I'll answer!
Answer:
x = 15
Step-by-step explanation:
x = 15 means that if you have 1 + x and plug in the 15 for x, 1 + 15 you will get 16.
Note: I'm not quite sure what the question is on this one, but I hope I could help.
Identify the opposite number of -22 7
Answer:
22.7?
Step-by-step explanation:
Please help me out I need this ASAP
Answer:
1. function 2. function 3. function 4. function 5. function 6. not a function
Step-by-step explanation:
Answer:
i think its rise over run
Step-by-step explanation:
Help me ASAP please!
Answer:
∠1 and ∠3
∠6 and ∠8
∠5 and ∠7
Giving out 16 points if you can help me :))
Answer:
g(x)=-6x+5
Step-by-step explanation:
what is value of this expression below when y=3
8y^2-y-8
Answer:
61
Step-by-step explanation:
8x3^2 -3-8
8x9-3-8
72-3-8
72-11
61
How many solutions does the following equation have?
2(3x+5)=5(2x-4)-4x
Answer: None
Step-by-step explanation:
3x - 4y = 32
5x+2y = 10
Answer:
Point Form: ( 4 , − 5 )
Equation Form: x = 4 , y = - 5
Step-by-step explanation:
Solve for the first variable in one of the equations, then substitute the result into the other equation.
Point Form: ( 4 , − 5 )
Equation Form: x = 4 , y = - 5
Answer:
(4, - 5)
Step-by-step explanation:
3x - 4y = 32 ........ (1)
5x + 2y = 10 ....... (2)
(2) × 2 + (1)
13x = 52 ⇒ x = 4
3(4) - 4y = 32 ⇒ y = - 5
(4, - 5)
Convert 21.3 feet per minute to yards per minute.
Answer:
7.1 yard per min
Step-by-step explanation:
what is 0.00000000007234 written in scienific from guysss help mee plss
Answer:
7.234
Step-by-step explanation:
I think this right lol lmk
Answer:
[tex]7.234\times10^{11}[/tex]
Step-by-step explanation:
In order to find the scientific notation of a number you must count the zeros.
[tex]0.00000000007234[/tex]
[tex]zeros=10[/tex]
[tex]7.234\times10^{11} =.00000000007234[/tex]
Remember you have to move the decimal point 11 times to get the decimal to where it is in standard form.
Hope this helps.
Part 1: If we double each side of the second equation, 2x+y=8 we have 4x+2y=16. Explain why the same pair that is the solution to the system is also a solution to this new equation. If needed, you can support your explanation with hanger diagrams, or by inventing a situation that the equations represent.
Part 2: If we add the two equations in the original system, we have 6x+7y=32. Explain why the same (x, y) pair is also a solution to this equation
PLEASE ANSWER FAST
Answer:
Step-by-step explanation:
its the same because when you simplify it the equation is the same
20 pointsBRAINLEST!!!!!!!!!! and PointsAfter an accident, police can use the formula v=25L to estimate the speed, v, in miles per hour, that a car was traveling by measuring the length of the skid marks, L, in feet. Estimate the speed of a car that left skid marks 118 ft long. If the posted speed limit is 45 mi/h, was the car speeding? The speed of a car that left skid marks 118 ft long was about nothing mi/h.
The correct format of the question is
After an accident, police can use the formula [tex]v=2\sqrt{5L }[/tex] to estimate the speed, v, in miles per hour, that a car was traveling by measuring the length of the skid marks, L, in feet. Estimate the speed of a car that left skid marks 118 ft long. If the posted speed limit is 45 mi/h, was the car speeding? The speed of a car that left skid marks 118 ft long was about nothing mi/h.
Answer:
48.6mi/h, Yes the car was speeding.
Step-by-step explanation:
The speed of the car is given by [tex]v=2\sqrt{5L }[/tex]
Skid length (L) = 118ft
V= [tex]2\sqrt{5*118}[/tex]
= 2 [tex]\sqrt{590}[/tex]
= 2*24.3
V = 48.6mi/h
Since the speed limit is 45mi/h and the velocity of this driver is 48.6mi/h it is clear that was speeding by 3.6mi/h over speed limit.
6 to the power 4 simplified
Answer:
1296
Step-by-step explanation:
6x6x6x6
6^4
Answer:
6×6×6×6
Step-by-step explanation:
I hope this helps
what is the value of Y in this triangle
Answer:
5
Step-by-step explanation:
Pythagorean Theorum: a^2 + b^2 = c^2
12^2 + y^2 = 13^2
144 + y^2 = 169
Subtract 144 from both sides
y^2 = 25
Square root both sides
y = 5
Answer:
y = 5
Step-by-step explanation:
Using Pythagoras' identity in the right triangle.
The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is
y² + 12² = 13²
y² + 144 = 169 ( subtract 144 from both sides )
y² = 25 ( take the square root of both sides )
y = [tex]\sqrt{25}[/tex] = 5