A science teacher ordered S2278 worth of microscopes and dissection kits for the new science lab. A total of
26 microscopes and 56 dissection kits were ordered. A microscope costs three times as much as a dissection
kit. Write a system of linear equations that represents this situation. What is the cost of each item?
Answer:
[tex]26M + 56D = 2278[/tex] ---- equation 1
[tex]M = 3D[/tex] ---- equation 2
A microscope costs S51 and a dissection kit costs S17
Step-by-step explanation:
Given
Represent microscope with M and Dissection kits with D
Cost:
[tex]M = 3D[/tex]
[tex]Total = 2278[/tex]
Required
Represent as an equation:
To do this, we represent the equation in terms of cost and quantity
In terms of cost, we have:
[tex]26M + 56D = 2278[/tex] ---- equation 1
and
[tex]M = 3D[/tex] ---- equation 2
Substitute 3D for M in equation 1
[tex]26*3D + 56D = 2278[/tex]
[tex]78D + 56D = 2278[/tex]
[tex]134D = 2278[/tex]
Divide both sides by 134
[tex]D = \frac{2278}{134}[/tex]
[tex]D = 17[/tex]
Substitute 17 for D in [tex]M = 3D[/tex]
[tex]M = 3 * 17[/tex]
[tex]M = 51[/tex]
Hence:
A microscope costs S51 and a dissection kit costs S17
1. What is the solution to the equation modeled below?
Answer:
3.67
Step-by-step explanation:
the equation is 3x + 5= 16
do 16 - 5 to get 11
next do 11 divided by 3 to get 3.67
hope this helps :)
this answer may be incorrect because the answer was really 3.66666666667
In the diagram, AB= DC and AC= DB. Why does m
Answer:
why does m what????
Step-by-step explanation:
Mike has a recipe that feeds one person that calls for 3/8 teaspoon
of salt. How much salt is needed to make the recipe if he needs to cook
the recipe for 5 people? ASAP correct answers only
a. 3/40 teaspoon c. 1 teaspoon
b. 15/40 teaspoon d. 1 7/8 teaspoons
Answer:
D
Step-by-step explanation:
You can multiply the numerator by 5 to get the answer of 15/8 which when simplified comes to 1 7/8 teaspoons. 8 goes into 15 one time with 7 left over
Hope i explained everything thoroughly!
5x-6
3x +2
5yº
Only enter the number. What is the value of x?
Answer:
4
Step-by-step explanation:
if AB || CD and AC = BD, is ACD = CAB?
A group of 8 friends went to lunh and Spent a total of $76 which included the food bill in the tip of $16 they decide to split the bill into evenly among themselves
Answer:
The equation 1/8(x+16)=76/8 represents the situation, where x is the food bill.
The solution x=60 represents the total food bill.
Step-by-step explanation:
As in the question it is mentioned that there is eight group of friends and the total amount incurred is $76 that also involved $16
Now let us assume the food bill be x
So the equation would be
(x + 16) ÷ 8 = 76 ÷ 8
(x + 16) ÷ 8 = 9.5
x + 16 = 9.5 × 8
x = 76 -16
x = 60
So, the bill of food is 60
As per the given options, the above two statements should be selected
7. Two people enter a whispering gallery t want to know where they should stand so they can hear other people whisper. The gallery is too fast wide and the vertical distance from their head to the peak of the ceiling is 30ft.
Answer: Just get closer
Step-by-step explanation:
Walk next to someone to hear them left foot right foot towards them.
Please help. Questions in the picture.
Answer:
Step-by-step explanation:
(2 , 0) ; (0, 1)
Slope = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\[/tex]
[tex]= \frac{1-0}{0-2}\\\\=\frac{1}{-2}\\\\\\=\frac{-1}{2}[/tex]
m = -1/2 ; (2 , 0)
Equation of the line : y - y1 = m(x - x1)
[tex]y - 0 = \frac{-1}{2}(x-2)\\\\ y = \frac{-1}{2}x - 2*\frac{-1}{2}\\\\\\ y = \frac{-1}{2}x+1[/tex]
slope = (-1/2)
y - intercept = 1
The standard diameter of a golf ball is 42.67 mm. A golf ball factory does quality control on the balls it manufactures. Golf balls are randomly measured to ensure the correct size. One day, an inspector decides to stop production if the discrepancy in diameter is more than 0.002 mm. Which function could represent this situation?
f(x ) = x – |42.67|
f(x ) = |x| – 42.67
f(x ) = |42.67 – x|
f(x ) = 42.67 – |x|
Answer:
c
Step-by-step explanation:
The function that could represent this situation is f(x ) = |42.67 – x| (Option C).
What quality control?The process of quality control helps a producer to ensure that the correct standard is maintained in the production of goods. It involves the testing of products to ensure that they conform to specifications.
Now we are told that factory wants to ensure that the discrepancy in diameter is not more than 0.002 mm. Since the discrepancy could be above or below the given value then it follows that the function that could represent this situation is f(x ) = |42.67 – x| (Option C).
Learn more about quality control:https://brainly.com/question/1674784
#SPJ9
Which are characteristics of the graph of the function f(x) = (x + 1)2 + 2? Check all that apply.
The domain is all real numbers.
The range is all real numbers greater than or equal to 1.
The y-intercept is 3.
The graph of the function is 1 unit up and 2 units to the left from the graph of y = x2.
The graph has two x-intercepts. HELP 40 POINTS
Answer:
A and C
Step-by-step explanation:
Answer:
A and C
Step-by-step explanation: hope it helps ^w^
A(n)______ dot on the graph of an inequality shows that the points IS a solution of the inequality.
A) flat
B) open
C) closed
D) invisible
Answer:
c because an open doesnt mean its guaranteed but it starts at closed.
Lastly solve |5x-7|= -3
Answer:
there is no number to plug into x cause you can't have a negative number if it is absolute value cause that makes everything positive
Help
This is easy but I am DUMB
Answer:1. The third stage it did the addition first not the division and number two the first stage u need to do the problem on the parenthesis first .
Step-by-step explanation:
The first five terms of an arithmetic sequence are 8, 13/2, 5, 7/2, and 2. Which function, f(x), could be used to describe the xth term of the sequence?
Answer:
f(x) = 8 - 1.5x
Step-by-step explanation:
Here, we want to write a function that can be used to describe the x th term of the sequence
Mathematically, this can be calculated by looking at the numbers in the sequence
The difference between each successive term
is -1.5 ( 6.5-8, 3.5 -5)
So the formula for then x th term will be;
f(x) = 8 - 1.5x
where x refers to the number of the term , for example the 4th term
Answer:
-1.5x+9.5
Step-by-step explanation:
-1.5(1)+9.5=8
-1.5(2)+9.5=6.5
-1.5(3)+9.5=5
and so on....
the difference between two numbers is 3. their sum is 13. find the numbers
Answer:
8 and 5
Step-by-step explanation:
8 plus 5 is 13 and 8 minus 5 is 3
Please help me!! Thank youu
Answer:
6.5x and 3.05x were adding incorrectly.
Step-by-step explanation:
The answer to adding those two numbers would be 9.55x
Answer:
error is in step A. 6.5x and 3.05x do not combing to 10x. instead, it should be 9.55x
Please answer FAST i need your help and when you put your answers put them like
1.
2.
3.
4.
5.
Step-by-step explanation:
3.5
1
-7.14
1
1/5
6.5
sorry if this and are wrong
el área de un terreno rectangular es de 616 metros cuadrados si el largo del terreno mide 6 m más que el ancho cuáles son sus dimensiones
Answer:
length 28, width 22
Step-by-step explanation:
28 - 22 = 6, 28 x 22 = 616
find one arithmetic means between 2 and 32? step-by-step
Answer:
17
Step-by-step explanation:
An arithmetic mean is the average of the 2 given numbers, that is
mean = [tex]\frac{sum}{count}[/tex] = [tex]\frac{2+32}{2}[/tex] = [tex]\frac{34}{2}[/tex] = 17
Which could be the missing first term of the expression that, when fully simplified, would be a binomial with a degree of 4? Select three options.
________ – 5xy3 + 9x2y
0
5xy3
9x2y
8y4
4xy3
Answer:
Yo The answer is A,C,E or 0, 9x2y, and 4xy3
Step-by-step explanation:
Got it right on Edge. Good luck
Answer: A, C, E
Step-by-step explanation:
Alex and Freddy collect stamps. The number of stamps in Alex’s collection is in ratio 3:5 to the number of stamps in Freddy’s collection. If Freddy gives Alex 10 stamps, the ratio will change to 7:9. How many stamps are in both collections together?
In 2015 the population of 895 quail increases at an annual rate of 3.5%. In writing an
exponential function to model the quail population, using f(t) = a(b)+ what is the value
of a
?
and b =
Please help!!
Answer:
y=895•1.07^x Y is the population of quails and X is the amount of years that have passed.
Step-by-step explanation:
hope this helps
What is x- value of point A
Answer:
5
Step-by-step explanation:
I really need a 100 I'm felling in all my classes, please
Select the fraction that is equivalent to one-sixth.
Answer:
There is no picture, or diagram with the question, but 1/6 = 2/12
Answer:
2/12
Step-by-step explanation:
1/6 * 2 = 2/12
Multiply both numerator and denomanotor
how do i find my sister's math question she just posted how do i find it
Answer:
You can find it on her profile, in the questions section.
Step-by-step explanation:
Tap her profile picture, which will take you to her profile.
Tap the questions bar, which should lead you to all questions she has posted.
Lastly, tap the question you want! It should show you the date or time it was posted.
A brainiest is this doggo's bone!
7x-11>3
Solve and graph for X
Beep help please ASAP
You want to apply two coats of paint to walls that are 8 ft high in a room that is 7 11/12 feet wide and 9 5/6 feet long. One gallon of paint covers 350 square feet.
Answer:
Paint required will be 2.06gallons
Step-by-step explanation:
The given dimensions are
Height - 8ft
Width - 7 [tex]\frac{11}{12}[/tex] = 7.9ft
Length - 9. 83ft
To calculate the the amount of paint required to paint the walls we need to find the area of the walls
wall 1 = height * width of room= 8 * 7.9 = 63.28[tex]ft^2[/tex]
wall 2 = height * length = 8*9.83 = 78.64 [tex]ft^2[/tex]
The total area of the 4 walls will be = 2*(63 .28+78.64)= 283.84[tex]ft^2[/tex]
ceiling area = 77.66[tex]ft^2[/tex]
total area to be painted = 283.84 + 77.66 = 361.50[tex]ft^2[/tex]
One gallon of paint covers 350 [tex]ft^2[/tex] of area
so 361.50 [tex]ft^2[/tex] area will be covered by = 361.5/350 = 1.03gallons of paint
also we need two coating so the paint required will be = 1.03 * 2 =2.06gallons
Is 11/5 rational or irrational ?
Answer:
Step-by-step explanation:
Rational number. An rational number is simply a number of arithmetic: a whole number, fraction, mixed or decimal; together with its negative image.
after giving 8 apples to her friend, John finds notices that two third of the remainder is 12.how many appledid she have all tigether
Answer:
26
Step-by-step explanation:
It started with x apples.
8 were given away.
Now there are x - 8 apples.
Two thirds of the remainder is (2/3)(x - 8).
That is equal to 12.
(2/3)(x - 8) = 12
x - 8 = 18
x = 26
There were originally 26 apples.
Answer:
26, if I understood the question correctly.
John has an amount of apples, gave 8 to her friend, and noticed that two thirds of the remainder is a dozen.
Step-by-step explanation:
If 2/3 of the remainder is 12, then we can set this up as an algebraic equation to see what the remainder started with.
x*2/3=12
Now we can see that we need to divide the 2/3 to get the answer for what x is equal to.
[tex]x=12/(\frac{2}{3} )[/tex]
To divide fractions, you multiply by the reciprocal, (or the fraction upside down)
[tex]x=12*(\frac{3}{2})[/tex]
When we multiply 12 by 3/2, we get 36/2, and when we reduce, we get 18.
If the entire remainder is 18, then the original total would be 18 plus the 8 that John gave to her friend.
18+8=26
Kind of a strangely worded question, I hope I understood correctly