1. True or False: An equation is a statement that two expressions are equal. 1 point
True
False
Answer:
Its true.
Step-by-step explanation:
An equation is a mathematical statement that two expressions are equal. The solution of an equation is the value that when substituted for the variable makes the equation a true statement.
2
Lena tutors chemistry. For each hour that she tutors, she earns 30 dollars.
Let E be her earnings (in dollars) after tutoring for H hours.
E
Write an equation relating E to H. Then use this equation to find Lena's earnings after tutoring for 19 hours.
Equation:
x
5
?
Lena's earnings for 19 hours: I dollars
Answer:
[tex]E = 30 \times H[/tex]
$570
Step-by-step explanation:
Given that:
For each hour of tutoring, Lena earns 30 dollars.
E is her earning and
H is the number of hours for which she tutors.
To find:
Equation relating E to H.
Solution:
Let Lena tutors for 1 hour, then the earning = 30 dollars
Let Lena tutors for 2 hours, then the earning = 30+30 OR 2[tex]\times[/tex]30 = 60 dollars
Let Lena tutors for 3 hours, then the earning = 30+30 +30 OR 3[tex]\times[/tex]30 = 90 dollars
If Lena tutors for H number of hours, then the earning, E = 30 + 30 + .... + 30 (H times) i.e.
[tex]E = 30 \times H[/tex]
So, the equation that relates E to H is given as:
[tex]E = 30 \times H[/tex]
Now, it is given that she tutors for 19 hours.
Let us put H = 19 hours in the above equation:
[tex]E = 30 \times 19 \\\Rightarrow E = \$570[/tex]
Therefore, the earning for 19 hours of tutoring is 570 Dollars.
Henry can paint a small house in 3 days, Ruby can paint a small house in 4 days, and Charlie can paint a small house in 5 days. How long will it take for Henry, Ruby and Charlie to paint one small house together? Give your answer as a fraction.
Answer:
So it will take them 1 day 6 hours and 39 minutes to paint one small house.
Step-by-step explanation:
Henry can paint 1 small house in 3 days so he can paint 1/3 or .3333 in a day
Ruby can paint 1 small house in 4 days so she can paint 1/4 or .25 in a day
Charlie can paint 1 small house in 5 days so he can paint 1/5 or .2 in a day
Together, that means they pain .3333 + .25 + .2 of a house per day. That's an daily rate of:
.3333 + .25 + .2 = .78333
The portion of the house they clean in x days is .78333x. We'd like to know how long it will take them to paint 100% or 1 of the house. So:
.78333x = 1 Divide each side by .78333
x = 1/.78333
x ≈ 1.277
Let's convert .277 to hours by multiplying by 24
.277 * 24 = 6.65
Let's convert .65 to minutes by multiplying by 60
.65 * 60 = 39
So it will take them 1 day 6 hours and 39 minutes to paint one small house.
Answer:
1.277 days
Step-by-step explanation:
H paint .3333 a day R paint .25 a day Charlie paint .2 a day
.3333 + .25 + .2 = .78333
x is number of days to paint.
.78333x = 1
x = 1/.78333 = 1.277
1.277 days
Is 1.8x10-4 greater than 7.2x10-1and how many times greater
Answer:
ye s1.8x10-4 is greater than 7.2x10-1
Step-by-step explanation:
The number 1.8*10⁻⁴ is smaller, not larger than 7.2*10⁻¹
Is the first number greater than the second?We have two numbers in scientific notation, these are:
1.8*10⁻⁴
7.2*10⁻¹
We want to see if the first one is larger than the second one. This is trivial to notices, because the exponent in the first number is 3 orders of magnitude smaller than the other exponent, then the first number is smaller than the second, not larger.
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If you deposit $200 into a CD (Certificate of Deposit) with an interest rate of 1% for 3 years, how much simple interest will you earn after
THREE years?
O $1
$5
$6
$25
Answer:
$6
Step-by-step explanation:
A=P(1+i.n)
A=200(1+0.01.x 3)
A=206
Thus 206 - 200 = $6
You will earn $6 in interest.
The interest you will earn per year is:
= Interest rate x Amount deposited
= 200 x 1%
= $2
Because it is simple interest, you will earn the same amount of interest every year. In 3 years you will have:
= Interest per year x number of years
= 2 x 3
= $6
You will therefore earn $6 in interest.
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Emilio throws a marshmallow into the air from his balcony. The height of the marshmallow (in feet) is represented by the equation h=−16(t−14)2+49, where t is the time (in seconds) after he throws the marshmallow. What is the maximum height of the marshmallow? Enter your answer as the correct value, including units, like this: 42 meters Be sure to use the correct units from the context of the problem.
Answer:
49 ft
Step-by-step explanation:
h=−16(t−14)^2+49
The path of the marshmallow is an inverted parabola. It has symmetry with respect to its vertical axis.
We take the derivative of the height function.
dh/dt = -32(t - 14)
dh/dt = -32t + 448
We set the derivative equal to zero ti find the value of t corresponding to a maximum value of h.
-32t + 448 = 0
-32t = -448
t = 14
Maximum height occurs at t = 14 seconds.
h=−16(t−14)^2+49
t = 14
h=−16(14−14)^2+49
h = 49
Maximum height is 49 feet.
what is the area of the square length:10 width 15
Answer:
5 I think because don't you divide
Answer 150β
10 times 15
Simplify the expression
8
2
+
9
(
12
÷
3
×
2
)
−
7
. Explain each of your steps.
Answer:
147
Step-by-step explanation:
82+9(12÷3×2)-7
82+9(4×2)-7
82+9(8)-7
82+72-7
154-7
147
Follow PEMDAS
The simplified values of the expression is 97.
How to apply BODMAS rule ?First we will solve what is inside the brackets that too in 1st 2nd and 3rd bracket order then we will divide after that we will multiply then we will add then subtract.
The given equation is
82 + 9 (12 ÷ 3×2) - 7
Here we will follow BODMAS rule
BODMAS stands for Brackets of order division multiplication addition and substraction. In this order we will solve our expression
82 + 9 (12 ÷ 3×2) - 7
= 82 + 9(12 ÷ 6) - 7
= 82 + 9(2) - 7
=82 + 18 - 7
=100 - 7
= 97
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The area is square feet of a rectangular garden can be expressed as the product of the garden's length and
width, or A(x) = 2x2 - 21x + 40. If the width of the garden is (x - 8) feet, what is the length of the garden?
Answer:
(2x-5)feet
Step-by-step explanation:
The area of the rectangular garden A = Length × Width
Given the area A(x) = 2x² - 21x + 40
And the width =x-8 feet
To get the length, we will simply factorise the area function as shown;
You will just factorise the area
Factorizing 2x² - 21x+40
2x² − 21x + 40
2x² -16x - 5x + 40
2x(x - 8) -5(x - 8)
=(2x−5)(x−8)
Hence the length of the garden is
(2x-5)feet
Convert 0.3185° to minutes and seconds
Answer:
Step-by-step explanation:
19 minutes and 16 seconds . because there are 60 minutes in every degree . and 60 seconds in every minute. so, if you take 0.3185 x 60 = 19.11 minutes . —-> 19.11 min. x 60 = 6.6 seconds .
so therefore the answer is 19 min. &’ 16 seconds ur welcome
Answer:
23 min 6 seg
Step-by-step explanation:
0,3185º =
0,3185*60 min = 23,1 min =
23 min + 1/10 de min
1/10 de min = 1/10 * 60 seg = 60/10 = 6 seg
At lunchtime, a cafeteria served a total of 3/8 of a pot of chicken soup and 7/8 of a pot of
onion soup. How many pots of soup were served in all?
Write your answer as a fraction or as a whole or mixed number.
pots
Submit
The total number of pots will be 1¹/₄.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that at lunchtime, a cafeteria served a total of 3/8 of a pot of chicken soup and 7/8 of a pot of onion soup.
The total number of pots will be calculated as:-
E = 3/8 + 7/8
E = 10 / 8
E = 5 / 4
E = 1¹/₄
Hence, the total number of pots will be 1¹/₄.
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Laura has a collection of coins that includes pennies, nickels, dimes, and quarters. The total amount of money she has in dollars can be found using the expression (P + 5N + 10D + 25Q) ÷ 100
Answer:
3.84
Step-by-step explanation:
((24) + 5(12) + 10(10) + 25(8)) ÷ 100 = (24 + 60 + 100 + 200) ÷ 100 Multiply.
= (384) ÷ 100 Add.
= 3.84 Divide.
You want to surround the perimeter of a garden with 35 stones. You need to place a certain number of large and small stones, and for every large
stone, you want to use 4 small stones. Choose the correct equation to find the number of stones for each size. Then solve the equation
OAX + 4x = 35,7 large stones and 28 small stones
O B. X+5x = 35, 7 large stones and 28 small stones
O cx + 4 = 35, 4 large stones and 31 small stones
D. 4x = 35 + x 12 large stones and 23 small stones
Answer: A) x + 4x = 35; 7 large stones and 28 small stones
======================================================
Explanation:
x = number of large stones
4x = number of small stones
x+4x = total number of stones = 35
x+4x = 35 is the equation to solve
-----------
Let's isolate x
x+4x = 35
5x = 35
x = 35/5
x = 7 large stones are needed
4x = 4*7 = 28 small stones are needed
Raphael's Gym has a climbing wall that starts at the gyms basement, 9 feet above the ground level. The wall extends to 21 feet above the ground level. what is the total height of the climbing wall? Represent this situation with a number. Then, explain your answer.
Answer:
The total height of the climbing wall is 12 feet
Step-by-step explanation:
The given parameters are;
The star of the climbing wall = On the gym basement
The height of the gym's basement above the ground level = 9 feet
The height to which the wall extends above the ground level = 21 feet
The total height of climbing the wall = 21 - 9 = 12 feet
The start of the climbing wall is at the gym's basement level which is already 9 feet above the ground level, therefore, given the the height of the wall is 21 feet above ground level, with wall situated already at 9 feet above ground level which gives the total height of the climbing wall will be 21 - 9 feet or 12 feet.
Rectangle with width labeled on the right, width equals 4 and 1 over 2 inches. Below the rectangle, it says, length equals question mark. Inside the rectangle, it says area equals 36 and 3 over 4 square inches.
Answer:
length = [tex]8\frac{1}{6}[/tex] inches
Step-by-step explanation:
A rectangle is a quadrilateral which has opposite sides to be equal.
Area of a rectangle = length × width
Given that: Area = [tex]36\frac{3}{4}[/tex] square inches, width = [tex]4\frac{1}{2}[/tex] inches, length = l. Thus;
[tex]36\frac{3}{4}[/tex] = l × [tex]4\frac{1}{2}[/tex]
[tex]\frac{147}{4}[/tex] = l × [tex]\frac{9}{2}[/tex]
divide both sides by [tex]\frac{9}{2}[/tex],
l = [tex]\frac{147}{4}[/tex] ÷ [tex]\frac{9}{2}[/tex]
= [tex]\frac{147}{4}[/tex] x [tex]\frac{2}{9}[/tex]
= [tex]\frac{49}{6}[/tex]
l = [tex]8\frac{1}{6}[/tex]
Therefore, the length of the rectangle is [tex]8\frac{1}{6}[/tex] inches.
Can someone help me please
Answer:
C
Step-by-step explanation:
I took the test
hope this helps you :)
Mel divided dozens of cookies between 7 classrooms, each
received two dozen. If she had 216 cookies to begin with,
how many dozens did she have left after dividing them up?
Pls help me
Answer:
4 dozen(48)
Step-by-step explanation:
216/dozen(12) =18 dozen(12)
7x2 dozen = 14 dozen
18 dozen - 14 dozen = 4 dozen(48)
Answer:
4
Step-by-step explanation:
Two dozens = 12 × 2 = 24
24 × 7 = 168
216 - 168 = 48
48 ÷ 12 =4
A right triangle and its dimensions are shown in this diagram.
26 meters
10 meters
24 meters
What is the area, in square meters, of the triangle?
Answer: The answer is B
Step-by-step explanation:
I need help understanding mean median
What is the product written in scientific notation? (1.18×10^3)⋅(9.1×10^−6)
Answer:
1.0738 x 10^-2
Step-by-step explanation:
A map is created on the coordinate plan, lori's house is located at ( -3, 7) and Andreas house is located at (-3,-4). Each unit on the map represents 0.2 mile.
Answer: 2.2 miles.
Step-by-step explanation:
I guess that we want to find the distance between Lori's and Andrea's houses.
First, we have the locations:
L = (-3, 7)
A = (-3. -4)
To find the distance (in units) between two coordinate points (a1, a2) and (b1 b2) we can use the formula:
Distance = I (a1, a2) - (b1, b2)I = √( (a1 - b1)^2 + (a2 - b2)^2)
Then in this case we have that:
Distance = √( ( -3 -(-3))^2 + (7 - (-4))^2) = √( 0 + 11^2) = 11
The distance between their houses is 11 units.
And we know that each unit represents 0.2 miles, then 11 units represent 11 times that amount, the distance in miles will be:
D = 11*0.2 miles = 2.2 miles.
4V6+3v2
16
Simplified?
Answer:
195/8v or 24.375v
Step-by-step explanation:
PLEASE HELP ME !!
Instructions: Using the image, find the midpoint of the line segment. Reduce all fractions and enter using a forward slash (i.e. "/").
Answer:
the mid point is ( 3, -1 )
Step-by-step explanation:
the x axis it's 3 and for the y axis is -1
If two point lie in the same plane, then a line containing the lies in the plane. Illustrate.
Answer:
tom
Step-by-step explanation:
2p+1÷5p+6 =1÷7 whats the answer
Answer:
The result can be shown in multiple forms.
Exact Form:
p= - 13/19
Decimal form:
p= - 0.68421052...
What is the solution to the compound inequality 5x + 7 ≥ −8 and 3x + 7 < 19?
Answer:
x[tex]\geq[/tex]-3 and x<4
Step-by-step explanation:
5x[tex]\geq[/tex] -15 and 3x<12
x[tex]\geq[/tex] -3 and x<4
Now you just need to graph it :)
You have four quiz grades. Quiz 1: 17/30, Quiz 2: 17/25, Quiz 3: 38/50, Quiz 4: 18/25 What is your ordinary quiz average?
What is your weighted quiz average?
Answer:
.7 or 70%
Step-by-step explanation:
17/30 + 17/25 + 38/50 + 18/25 = 2.727
2.727 divided by 4 (the amount of addends) = .7
Answer:
68%
Step-by-step explanation:
To find the average quiz grade, you have to add up all the percentages and divide by the numbers of scores you have.
56 + 68 + 76 + 72 = 272
272 ÷ 4 = 68
Hope this helps! <3
need help i don't understand
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1/3 x (15+6) i tried finding the answer but i have no idea
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{7}}}}}[/tex]
Step-by-step explanation:
[tex] \sf{ \frac{1}{3} \times (15 + 6)}[/tex]
Add the numbers : 15 and 6
[tex] \dashrightarrow{ \sf{ \frac{1}{3} \times 21}}[/tex]
Multiply the numerators for the numerator and multiply the denominators for its denominator and reduce the fraction obtained after multiplication into lowest term
[tex] \dashrightarrow {\sf{ \frac{1 \times 21}{3 \times 1}}} [/tex]
[tex] \dashrightarrow{ \sf{ \frac{21}{3} }}[/tex]
[tex] \dashrightarrow{ \sf{7}}[/tex]
Hope I helped!
Best regards! :D
The value of Expression 1/3 x (15+6) on simplification gives 7.
To simplify the expression 1/3 x (15+6),
we start by simplifying the addition inside the parentheses.
=15 + 6
= 21
Now, we can multiply the result by 1/3:
= 1/3 x 21
= 21/3
= 7
Therefore, 1/3 x (15+6) simplifies to 7.
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If 40% of any number is 600 more than its 25%. What is the number?
Answer:
4000
Step-by-step explanation:
40% of the number is 15% more of the number than 15% of the number is. So, 600 is 15% of the number.
600 = 0.15n
600/0.15 = n = 4000
The number is 4000.
__
Check
40% of 4000 is 1600. 25% of 4000 is 1000. 1600 is 600 more than 1000.