Answer:
-3.5 degrees per hour
[tex] - 3.5t[/tex]
Step-by-step explanation:
The total change is temperature is -12.25 degrees.
The total time is 3.5 hours.
This means that temperature changes by -3.5 degrees per hour (-12.25 degrees ÷ 3.5 hours).
As an expression of hours, simple multiply the coefficient by a variable. I'm assuming the letter t for time (where t is the number of hours):
[tex] - 3.5t[/tex]
Lizzie buys 8 books and pays with a $50 dallor bill.
Alex buys 3 books and pays with a $20 dallor bill.
Lizzie and Alex both get the same amount of change. How much dose one book cost?
The cost of one book is $6.
Step-by-step explanation:
Given,
Lizzie paid for 8 books = $50 bill
Alex paid for 3 books = $20 bill
As the both received same change.
Let,
x represent cost of one book.
y represent the change received.
According to given statement;
50-8x=y Eqn 1
20-3x=y Eqn 2
Putting value of y from Eqn 1 in Eqn 2
[tex]20-3x=50-8x\\-3x+8x=50-20\\5x=30[/tex]
Dividing both sides by 5
[tex]\frac{5x}{5}=\frac{30}{5}\\x=6[/tex]
The cost of one book is $6.
Keywords: linear equation, substitution method
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Which of the following tables represents a function?
Answer:
B seems right
Step-by-step explanation:
A paper company needs to ship paper to a large printing business. The paper will be shipped in small boxes and large boxes. The volume of each small box is 10 cubic feet and the volume of each large box is 22 cubic feet. A total of 21 boxes of paper were shipped with a combined volume of 342 cubic feet. Determine the number of small boxes shipped and the number of large boxes shipped.
10 small boxes and 11 large boxes were shipped.
Step-by-step explanation:
Given,
Total boxes shipped = 21
Total volume of shipped boxes = 342 cubic feet
Volume of each small box = 10 cubic feet
Volume of each large box = 22 cubic feet
Let,
Number of small boxes = x
Number of large boxes = y
According to given statement;
x+y=21 Eqn 1
10x+22y=342 Eqn 2
Multiplying Eqn 1 by 10
[tex]10(x+y=21)\\10x+10y=210\ \ \ Eqn\ 3[/tex]
Subtracting Eqn 3 from Eqn 2
[tex](10x+22y)-(10x+10y)=342-210\\10x+22y-10x-10y=132\\12y=132[/tex]
Dividing both sides by 12
[tex]\frac{12y}{12}=\frac{132}{12}\\y=11[/tex]
Putting y=11 in Eqn 1
[tex]x+11=21\\x=21-11\\x=10[/tex]
10 small boxes and 11 large boxes were shipped.
Keywords: linear equation, subtraction
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Greta and Marge are collecting money for a local charity by taking donations outside of busy
local businesses. Hoping to collect the most money today, Greta gets to her collection spot and
begins collections at 8am. Marge wanted to sleep in so she didn't start collections at her spot
until 11am, by which time Greta had already collected $45.00. If Greta continues to collect
money at a rate of $15 per hour, Marge collects money at a rate of $20 per hour and they each
take a 1 hour break at 2pm, at what time will Greta and Marge have collected the same amount
of money?
Answer:
At 9pm Greta and Marge have collected the same amount of money.
Step-by-step explanation:
Consider the provided information.
Let x represents the number of hours Greta and Marge are both collecting.
It is given that Greta had already collected $45.00 till 11 am.
Greta = 45 + 15x
Marge collects money at a rate of $20 per hour.
Marge = 20x
Greta and Marge have collected the same amount of money.
Thus,
45 + 15x = 20x
45 = 5x
9 = x
Hence, once Marge starts collecting, it would take 9 hours to collect same amount of money.
9 hours after 11am is 8pm. It is given that there is a break time of 1 hour
Hence, at 9pm Greta and Marge have collected the same amount of money.
Helppppp please i need it
-7/8 is less than or greater than -3/4?
Answer:
-3/4
Step-by-step explanation:
The least common denominator is 8.
So you make -3/4 into -6/8 by multiplying 2 in the numerator and denominator.
Now just compare them -6/8 compared to -7/8
-6/8 is bigger since it is closer to 0 (since we are dealing with negative numbers.)
Have a great day!
Find the area of a square if its sides measure 2 2/3m
Answer:
[tex]7\dfrac{1}{9}\ m^2[/tex]
Step-by-step explanation:
If the length of the square side is a units, then the area of the square is
[tex]A=a^2\ un^2.[/tex]
In your case, the side length is
[tex]a=2\dfrac{2}{3}\ m,[/tex]
then the area is
[tex]A=2\dfrac{2}{3}\cdot 2\dfrac{2}{3}\\ \\ \\A=\dfrac{2\cdot 3+2}{3}\cdot \dfrac{2\cdot 3+2}{3}\\ \\ \\A=\dfrac{8}{3}\cdot \dfrac{8}{3}\\ \\ \\A=\dfrac{64}{9}\\ \\ \\A=7\dfrac{1}{9}\ m^2[/tex]
Use the substitution method to solve the system of equations. Choose the
correct ordered pair.
2x + y = 8
y = -x+ 5
O A. (4,1)
O B. (3, 2)
O C. (5,0)
O D. (2,3)
B clearly because u would substitute the x and y with the ordered pairs
What is 16% of 43 minutes? Round answer to tenths place.
Answer: [tex]6.9\ minutes[/tex]
Step-by-step explanation:
Let "x" represents the 16% of 43 minutes.
Once you analize the information given in the exercise, you can identify that 43 minutes is the 100%.
Then, with this data, you can set up the following proportion:
[tex]\frac{100}{43}=\frac{16}{x}[/tex]
Now you must solve for "x". The steps are:
- Multiply both sides of the equation by "x"
[tex](x)(\frac{100}{43})=(\frac{16}{x})(x)\\\\\frac{100x}{43}=16[/tex]
- Multiply both sides by 43:
[tex](43)(\frac{100x}{43})=(16)(43)\\\\100x=688[/tex]
- Divide both sides by 100:
[tex]\frac{100x}{100}=\frac{688}{100}\\\\x=6.88[/tex]
- Rounding to the tenths place:
[tex]x\approx6.9[/tex]
Find the following angle measures.
MZEAD =
mZCAB =
Answer:
m∠EAD = 29°
m∠CAB = 119°
Step-by-step explanation:
m∠EAD = 180 - 61 - 90 = 29°
m∠CAB = 180 - 61 = 119°
Someone please help me with this
Answer:
see explanation
Step-by-step explanation:
(a)
f(0)
Since x = 0 < 5, then
f(0) = x + 4 = 0 + 4 = 4
(b)
f(6)
Since x = 6 meets the condition 5 ≤ x < 7, then
f(6) = 8
what solution is
y=9x+35
y=-8/9x+4/5
Answer:
x=-1539/445, y=1724/445. (-1539/445, 1724/445).
Step-by-step explanation:
y=9x+35
y=-8/9x+4/5
-------------------
9x+35=-8/9x+4/5
9x-(-8/9x)=4/5-35
9x+8/9x=4/5-175/5
81/9x+8/9x=-171/5
89/9x=-171/5
x=(-171/5)/(89/9)
x=(-171/5)(9/89)
x=-1539/445
y=9(-1539/445)+35
y=1724/445
what is the slope of the line that passes through (1,4) and (-3, -3)
Answer: m = 7/4
Step-by-step explanation: Use the slope formula to find the slope m.
Hope this helps you out! ☺
Answer:
7/4
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(-3-4)/(-3-1)
m=-7/-4
m=7/4
a bottle of shampoo has a capacity of 0.43 L. how many milliliiters of shampoo does the bottle contain?
Answer:
0.43 liters = 430 milliliters
Step-by-step explanation:
There are 1000 milliliters in each liter so all you have to do is multiply 0.43 by 1000. :)
Answer:
0.43 liters = 430 milliliters
0.43 liters = 430 milliliters
Step-by-step explanation:
There are 1000 milliliters in each liter so all you have to do is multiply 0.43 by 1000. :)
Simplify -7(-5 + 8x) +11x
Answer:
35 - 45x
Step-by-step explanation:
-7(-5) + -7(8x) + 11x => 35 - 56x + 11x => 35 - 45x
3. Twenty-four students brought their permission slips to attend the class field
trip to the local art museum. If this represented eight tenths of the class, how
many students are in the class? Use a bar diagram to solve arithmetically. Then
use an equation to solve algebraically.
Answer:
x=30
Step-by-step explanation:
ratio: 8:10 as 24:x
8/10=24/x
10x * 8/10= 10x * 24/x
x * 8 = 10 * 24
8x = 240
8x/8 = 240/8
8x/8 = 30
x = 30
quaker oatmeal is a very popular breakfast cereal .If susan wrapped the entire container with out any overlapping paper what is the minimum amount of wrapping paper that she will need
the cylinders hight is 11
and the dimater is 6
Answer:
263.76
Step-by-step explanation:
To answer this question, we need to know the equation for surface area of a cylinder which can be given as Surface Area=2*pi*[tex]R^{2}[/tex]+2*pi*R*H, where R is the radius of the cylinder (also can be calculated as Diameter/2=6/2=3) and H is the height of the cylinder which is given as 11. Considering pi=3.14, the surface area of the cylinder can now be calculated as 2*3.14*[tex]3^{2}[/tex]+2*3.14*3*11=263.76.
Find the slope of 3,6 and 6,9
Hey there!
To find the slope of the two points that you were given, use the slope formula:
[tex]\frac{y2-y1}{x2-x1}[/tex]
y2 is the y value of the second point pair, y1 is the y value of the first point pair, x2 is the x value of the second point pair, and x1 is the x value of the first point pair.
Now, plug in your values:
y2= 9
y1= 6
x2= 6
x1= 3
[tex]\frac{9-6}{6-3}[/tex] = [tex]\frac{3}{3}[/tex] = 1
Therefore, the slope of the two points is 1.
Lui deposited $3,500 into a savings account. The simple interest is 4%. How much interest will the account earn in 2 years?
Answer:
$280
Step-by-step explanation:
Principal = $3,500
Time = 2 Years
Interest Rate = 4%
Interest = Principal x Time x Interest Rate
Interest = $3,500 x 2 x 0.04
Interest = $280
Find f(-5) if f(x) = Ix+1I
Answer:
x = 4
Step-by-step explanation:
f(x) = I x+1 I
when x = -5
f(-5) = I (-5) +1 I
= I -5+1 I
= |-4|
= 4
Answer:
substitute x for -5
f(-5)=|-5+1|
f(-5)=|-4|
however, absolute value is the distance from 0 and so is always positive since you cannot have negative distance.
so f(-5)=4
Which dimensions cannot create a triangle?
three angles measuring 109, 25º, and 1450
three sides measuring 9 m, 15 m, and 9 m
• three angles measuring 40°, 70°, and 650
o three sides measuring 6 cm, 8 cm, and 10 cm
Answer:
three angles measuring 109º, 25º, and 145º cannot create a triangle
three angles measuring 40º, 70º, and 65º cannot create a triangle
Step-by-step explanation:
Verify each dimensions
Part 1) three angles measuring 109º, 25º, and 145º
Remember that the sum of the interior angles of a triangle must be equal to 180 degrees
In this problem we have
[tex]109^o+25^o+145^o=279^o[/tex]
[tex]279^o> 180^o[/tex]
therefore
three angles measuring 109º, 25º, and 145º cannot create a triangle
Part 2) three sides measuring 9 m, 15 m, and 9 m
we know that
The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side
Applying the triangle inequality theorem
1) 9+15 > 9 ---> is ok
2) 9+9 > 15 ---> is ok
therefore
three sides measuring 9 m, 15 m, and 9 m can create a triangle
Part 3) three angles measuring 40º, 70º, and 65º
Remember that the sum of the interior angles of a triangle must be equal to 180 degrees
In this problem we have
[tex]40^o+70^o+65^o=175^o[/tex]
[tex]175^o< 180^o[/tex]
therefore
three angles measuring 40º, 70º, and 65º cannot create a triangle
Part 4) three sides measuring 6 cm, 8 cm, and 10 cm
we know that
The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side
Applying the triangle inequality theorem
1) 6+8 > 10 ---> is ok
2) 8+10 > 6 ---> is ok
3) 6+10 > 8 ---> is ok
therefore
three sides measuring 6 cm, 8 cm, and 10 cm can create a triangle
Answer:
its c i promise
Step-by-step explanation:
the points (3,-2) and (7,r) lie on a line with the slope 3/4. Find the missing coordinate r.
Answer:
the answer is 1
Step-by-step explanation:
X1=3 X2=7
Y1=-2 Y=r
M=y2-Y1/X2-X1
3/4=r-(-2)/7-3
3/4=r+2/4
Cross multiply
4(r+2)=4*3
4r+8=12
collect like terms
4r=12-8
4r=4
divide the by the co efficient of x
r=1
To find the missing coordinate “r” given two points on a line and the slope, we can use the slope formula. Using the given slope and the coordinates of the points, we can set up an equation to solve for the missing value of “r”. By solving the equation, we find “r” is equal to 1.
Explanation:To find the missing coordinate r, we can use the slope formula. The slope m is given as 3/4, and the coordinates of the two points are (3, -2) and (7, r).
We can use the formula: m = (y2 - y1) / (x2 - x1) to find the missing value of r. Substituting the values, we have:
3/4 = (r - (-2)) / (7 - 3)
Solving for r:
3/4 = (r + 2) / 4
Multiplying both sides by 4:
3 = r + 2
Subtracting 2 from both sides:
r = 1
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help me again?- please.
Answer:
Step-by-step explanation:
y - 6 = b
y = b + 6
Answer:
6+b=y
Step-by-step explanation:
If you plug in real values (y=8 and b=2) you can see that at first, you had y-6=b. Basically, 8-6=2. In order to find eight, you would need to reverse the equation to 6+2. The answer is 6+b=y.
Which of the following are solutions to the following equation?
2x^2–98=0
Check all that apply.
Answer:
x=-7
x=7
Step-by-step explanation:
we have
[tex]2x^{2}-98=0[/tex]
Solve for x
Adds 98 both sides
[tex]2x^{2}-98+98=0+98[/tex]
[tex]2x^{2}=98[/tex]
Divide by 2 both sides
[tex]2x^{2}/2=98/2[/tex]
[tex]x^{2}=49[/tex]
take square root both sides
[tex]x=\pm7[/tex]
therefore
The solutions are
x=-7
x=7
What is the value of y in terms of x in the equation 3x+y/2x=15/2 ?
Answer:
y=15x-6x^2
Step-by-step explanation:
3x+y/2x=15/2
y/2x=15/2-3x
y=2x(15/2-3x)
y=15x-6x^2
What is the distance in units from (-15, 20) to (-15, - 3) on the coordinate place
O. 17
!. 23
R. 30
V. 35
Answer:
!. [tex]\displaystyle 23[/tex]
Step-by-step explanation:
Use the Distance Formula:
[tex]\displaystyle \sqrt{[-x_1 + x_2]^2 + [-y_1 + y_2]^2} = D \\ \\ \sqrt{[15 - 15]^2 + [-20 - 3]^2} = \sqrt{0^2 + [-23]^2} = \sqrt{0 + 529} = \sqrt{529} = 23[/tex]
Since we are talking about distance, we ONLY want the NON-NEGATIVE root.
I am joyous to assist you anytime.
Is this true or false 4/3 = 8/9
You are gathering data in the cafeteria, recording which condiments are most popular on students' hamburgers. The data you gather is
A. quantitative.
B. categorical.
C. discrete.
D. bivariate.
An engineering student answered 81 questons correctly on a 90 question test. What percent of the question did she answer correctly?
Answer:
90% of the questions she answered correctly
Step-by-step explanation:
%age = 81/90 * 100= 90 % correctness
The height of a tree is a function of its age example
Answer & Explanation:
To determine the age of a tree, first find its diameter by measuring the circumference of the trunk in inches and then dividing that number by pi. Once you have the tree's diameter, look up the growth factor for the type of tree you're measuring, which is how much width it gains annually.
The height and diameter of a tree is a function of its age.
What is meant by growth rate ?Growth rate of a system is defined as the rate at which the system grows by length, breadth, height, etc.
Here,
The growth rate of a tree represents the age of the tree. The measurement of the height and diameter of the tree is used to calculate the age of the tree. These measurements of height and radius of the tree can be considered as a function of its age.
The method of calculating the age of the tree is,
The circumference at a height above 4.5 feet from the ground is measured(breast height).
Dividing the circumference at breast height with pi(3.14), thus we get the diameter at breast height.
Multiplying the diameter with growth factor will give the age of the tree in years.
Hence,
The height and diameter of a tree is a function of its age.
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