Answer:
x ≤ 435
Step-by-step explanation:
Given is the following condition.
The sum of a number and 15 is less than and equal to 450.
So, if the number is x, then we have
x + 15 ≤ 450
⇒ x + 15 - 15 ≤ 450 - 15
⇒ x ≤ 435
Therefore, the solutions of the number are either 435 or less than 435 up to negative infinity. ( Answer )
A 72,000 gallon water tower is being drained. Two thousand gallons are drained in the first hour. How many hours will it take to drain the water tower?
Answer:
To drain the water tower it will take 36 hours.
Step-by-step explanation:
Given:
A 72,000 water tower is being drained, and in an hour 2000 gallons are drained.
Now, to calculate the hours it would take to drain total 72,000 gallons of water, we should divide the gallons of water drained in one hour by total gallons of water in the tower.
Gallons of total water in the tower ÷ Gallons of water drained per hour
[tex]72000\div 2000[/tex]
[tex]=\ 36[/tex]
Therefore, to drain the water tower it will take 36 hours.
Which of the numbers 285, 629, 5490, 7392, 15708, 43695 are divisible by 3 but not by 9.
Answer:
285, 629, 7392, 15708,43695
Step-by-step explanation:
If you add the digits of the number together, it should be divisible by 9. If it isn't, then it must be a multiple of only 3, not 9.
Step-by-step explanation:
We need to find which of the numbers 285, 629, 5490, 7392, 15708, 43695 are divisible by 3 but not by 9.
285
285 ÷ 3 = 95 Divisible
285 ÷ 9 = 31.66 Not divisible.
Correct
629
629 ÷ 3 = 209.67 Not divisible
629 ÷ 9 = 69.89 Not divisible.
Not correct
5490
5490 ÷ 3 = 1830 Divisible
5490 ÷ 9 = 610 Divisible.
Not correct
7392
7392 ÷ 3 = 2464 Divisible
7392 ÷ 9 = 821.33 Not divisible.
Correct
15708
15708 ÷ 3 = 5236 Divisible
15708 ÷ 9 = 1745.33 Not divisible.
Correct
43695
43695 ÷ 3 = 14565 Divisible
43695 ÷ 9 = 4855 Divisible.
Not correct
Divisible by 3 and not by 9 are 285, 7392 and 15708.
The formula for force is f = m⋅a, where f is force, m is mass, and a is acceleration. If a force of 30 Newtons acts upon a 6 kg object, calculate the acceleration of the object. Include proper units and use the fact that one kilogram meter per second squared is known in science as one Newton.
[tex]\Huge{\underline{\underline{\mathttt{Answer \colon}}}}[/tex]
From the Question,Force exerted on the object,F = 30 N Mass of the object,m = 6 Kg To findAcceleration of the object
Since,
[tex] \huge{ \boxed{ \boxed{\texttt{f = ma}}}}[/tex]
[tex] \leadsto \: \sf{a = \frac{f}{m} } \\ \\ \leadsto \: \sf{a = \frac{30}{6} } \\ \\ \huge{ \green{ \leadsto \: \mathtt{f = 5 \: ms {}^{ - 2} } }}[/tex]
Answer:
5 meters per second
Step-by-step explanation:
its basic math people
The sides of an equilateral triangle are 8 units long. What is the length of the altitude of the triangle?
5 StartRoot 2 EndRoot units
4 StartRoot 3 EndRoot units
10 StartRoot 2 EndRoot units
16 StartRoot 5 EndRoot units
Answer:The perimeter of parallelogram PQRS = 2\sqrt{10}+8\sqrt{2} ⇒
2nd answer
Step-by-step explanation:* Lets revise some properties of the parallelogram
- Each two opposite sides are parallel
- Each two opposite sides are equal
- Its perimeter is the twice the sum of two adjacent sides
* Lets solve the problem
∵ PQRS is a parallelogram
∵ The length of side SR is
∵ The length of side QR is
∵ SR and RQ are two adjacent sides
∵ The perimeter of parallelogram PQRS = 2(RQ + SR)
∴ The perimeter of parallelogram PQRS =
∵ =
∵ =
∴ The perimeter of parallelogram PQRS =
Answer:
Option B.
Step-by-step explanation:
It is given that the sides of an equilateral triangle are 8 units long.
Draw an altitude of the triangle.
Altitude of an equilateral triangle is perpendicular bisector.
Let x be the length of the altitude of the triangle.
According to the Pythagoras theorem
[tex]hypotenuse^2=base^2+perpendicular^2[/tex]
Using Pythagoras theorem we get
[tex]8^2=4^2+x^2[/tex]
[tex]64=16+x^2[/tex]
[tex]64-16=x^2[/tex]
[tex]48=x^2[/tex]
Taking square root on both sides.
[tex]\sqrt{48}=x[/tex]
[tex]4\sqrt{3}=x[/tex]
The length of the altitude of the triangle is 4√3 units.
Therefore, the correct option is B.
What is the first step in solving -5x-1/6>3/2
You add 1/6 to both sides
Step-by-step explanation:
Answer:
A is the correct answer
Step-by-step explanation:
Add 1/6 to both sides
Choose the definition for the function.
Please need help badly!!!
Answer:
b
Step-by-step explanation:
Both graphs end or start at at x = 2
The lower graph has an open circle at 2 meaning that x cannot equal 2
Thus y = x + 1 for x < 2
The upper graph has a solid circle at x = 2 meaning that x can equal 2
Thus y = x + 2 for x ≥ 2
Greenfield village is spread across 240 acres of land. Only 37% of the land is used for the exhibits, while the rest of the land consists of forest, rivers and pastures. How many acres are used for exhibits?
88.8 acres are used for exhibits
Step-by-step explanation:
Given
Total area of Greenfield = 24 acres
Percentage of lad for exhibits = 37%
Now,
[tex]Acres\ used\ for\ exhibits = 37\%\ of\ 240\\= \frac{37}{100} * 240\\=0.37*240\\=88.8\ acres[/tex]
Hence,
88.8 acres are used for exhibits
Keywords: Percentage, percent
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There are 6 blades on each windmill. How many total blades are on 7 windmills? Use a five fact to solve
Answer:
42 Blades
Step-by-step explanation:
So 6 blades on each windmill
6=1 Windmill
so 7 windmills
so do
7 times 6 = 42 Blades
The total number of blades in 7 windmills is required.
42 blades are the total number of blades.
The number of blades in 1 windmill is 6 blades
[tex]1\ \text{windmill}=6\ \text{blades}[/tex]
There are 7 windmills
[tex]7\ \text{windmills}=7\times 6[/tex]
Using five fact
[tex]=(5\times 8)+(2\times 1) =42\ \text{blades}[/tex]
The total number of blades of the windmills are 42.
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Delaney would like to make a 10 lb nut mixture that is 60% peanuts and 40% almonds. She has several pounds of peanuts and several pounds of a mixture that is 20% peanuts and 80% almonds. Let p represent the number of pounds of peanuts needed to make the new mixture, and let m represent the number of pounds of the 80% almond-20% peanut mixture.
a) What is the system that models this situation?
b) Which of the following is a solution to the system: 4 lb peanuts and 6 lb mixture; 5 lb peanut and 5 lb mixture; 8 lb peanut and 2 lb mixture? Show your work.
Answer:
{a}p + 0.2m = 6
0.8m = 4
or 5p + m = 30
m = 5
{b} 5 lb peanuts and 5 lb mixture
Step-by-step explanation:
m1 → desired mixture with composition : 60% peanuts and 40% almonds and weight : 10 lb
⇒weight of peanuts in m1 = 60% × 5 = 6 lb
and weight of almonds in m1 is 4 lb
m2 → mixture with composition : 20% peanuts and 80% almonds and weight : m pounds
⇒weight of peanuts in m2 = 0.2m
and weight of almonds in m2 = 0.8m
p → weight (in pounds) of peanuts added to m2 to make m1
{a}
add p pounds of peanuts to m2 to make m1
equating weights of peanuts and almonds:
p + 0.2m = 6
0.8m = 4
{b}
equation gives m = [tex]\frac{4}{0.8}[/tex] ⇒ m = 5 lb
Using this in the [tex]1^{st}[/tex] equation:
p + 1 = 6 ⇒ p = 5 lb
Answer:
a) p + m = 10 and [tex]\frac{p + 0.2m}{0.8m} = \frac{60}{40}[/tex]
b) The mixing amount is 5 lb peanut and 5 lb mixture.
Step-by-step explanation:
Given that p pounds of peanuts and m pounds of the 80% almond and 20% peanut mixture are used to make 10 pounds of 60% peanuts and 40% of almonds mixture.
Now, we can write that p + m = 10 ........ (1)
Now, m pounds of 80% almond and 20% peanut mixture contain 0.2m pounds of peanuts and 0.8m pounds of almonds.
Now, from the condition given it can be written that
[tex]\frac{p + 0.2m}{0.8m} = \frac{60}{40}[/tex] .......... (2)
⇒ [tex]\frac{p + 0.2m}{0.8m} = \frac{3}{2}[/tex]
⇒ 2p + 0.4m = 2.4m
⇒ 2p = 2m
⇒ p = m
Now from equation (1) we get p = m = 5 pounds.
a) Therefore, equations (1) and (2) are the system of equations that models the situation.
b) The mixing amount is 5 lb peanut and 5 lb mixture. (Answer)
Which is the graph of 3x-4y = 6
Note that this is the equation of a line, since you can rewrite it as
[tex]3x-4y=6 \iff 4y=3x-6 \iff y=\dfrac{3}{4}x-\dfrac{3}{2}[/tex]
Now just choose two values for x and compute the correspondent y values:
[tex]x=0 \implies y=-\dfrac{3}{2}[/tex]
So, the line passes through the point (0, -3/2).
[tex]x=2 \implies y=\dfrac{3}{2}-\dfrac{3}{2}=0[/tex]
So, the line passes through the point (2, 0)
Now, draw on a coordinate plane the two points and connect them, and you'll have the line.
You pay $6 in tax on a $30 purchase. What is the tax percent.
Answer:
20%
Step-by-step explanation:
Write the expression in simplest form.
(-11/2 x + 3)-2(-11/4x-5/2
Answer:
The solution of expression in the simplest form is 8
Step-by-step explanation:
Given as :
The expression is written
( [tex]\dfrac{-11 }{2}[/tex]x + 3 ) - 2 ( - [tex]\dfrac{11 }{4}[/tex]x - [tex]\dfrac{5 }{2}[/tex])
Or, ( [tex]\dfrac{-11 }{2}[/tex]x + 3 ) +[tex]\frac{11\times 2}{4}[/tex]x+ [tex]\frac{5\times 2}{2}[/tex]
Now, separate the variable terms
Or, ( [tex]\dfrac{-11 }{2}[/tex] + [tex]\frac{11\times 2}{4}[/tex]) x + 3 + 5
Or, ( 0) × x + 8
or , 0 + 8
∴ 8
The simplest form if expression is 8
Hence The solution of expression in the simplest form is 8 . Answer
Will mark brainliest, complete the two-column proof.
See explanations
Step-by-step explanation:
1. DF≅EF ⇒ Reflexive property
2. ∠1≅∠2 ⇒Given
3.FG bisects ∠DFE ⇒Definition of a bisector
4. FG ≅ FG ⇒Given
5.ΔDFG ≅ΔEFG-SAS Congruence
The reflexive property of congruence simple means that any geometric figure is equal to itself. Line DF equals line FE because triangle ΔDFG≅EFG
A line segment that divides a angle into two equal parts in called an angle bisector. Line segment FG is bisects angle ∠DFE
The Side Angle Side Postulate requires that two sides and included angle of one triangle are congruent to two sides and included angle of another triangle. In this case, angle ∠1 , ∠D and side DF equals ∠2, ∠E and side FE
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A beverage company wanted to see if people in the United States liked their new logo. Which choice best represents a population? Every person in the United States. A selection of logo artists. 3,800 children age 5 - 15
Answer:
Every person in the US.
Step-by-step explanation:
If a selection of logo artists are asked whether they like or not the new logo, their answer will represent only the opinion of a specific group of artists of the US, and this is not the objective of the beverage company,who wants to know if people from the United States like their logo.If 3,800 children age 5-15 are asked whether they like the logo or not, their opinion will only represent the opinion of some children in the US, whose age is between 5 and 15, and again, this is not the objective of the beverage company,who wants to know if people from the United States like their logo.Finally, the population (which by definition includes all the elements under study, in this case, all the people in the US) will be defined by all people in the US: if the company wants to know if people from the US like their new logo, they must take into account that, the population under study is all people, and not a biased selection of it.What is the equation for the line?
Answer:
y=-4x+5
Step-by-step explanation:
the line goes down 4 for every 1 that x changes. the line crosses the y axis at 5.
(this might not be accurate, I can't really see if the line is on the exact point or not)
Answer:
[tex]\displaystyle y = -4x + 5[/tex]
Step-by-step explanation:
Starting from the y-intercept of [tex]\displaystyle [0, 5],[/tex]you do [tex]\displaystyle \frac{rise}{run}[/tex]by either moving four blocks north over one block west or four blocks south over one block east [west and south are negatives].
I am joyous to assist you anytime.
What is the length of the hypotenuse in simplified radical form?(Information needed - long leg is 13, short leg is 5, it is a right triangle)
A. √194
B. 2√97
C. 12
D. 13.93
Answer:
[tex]\large \boxed{\text{A. $\sqrt{194}$}}[/tex]
Step-by-step explanation:
We can use Pythagoras' Theorem.
[tex]\begin{array}{rcl}a^{2} & = & b^{2} + c^{2}\\& = & 5^{2} + 13^{2}\\& = & 25 + 169\\& = & 194\\a & = & \sqrt{194}\\\end{array}\\\text{The length of the hypotenuse is $\large \boxed{\mathbf{\sqrt{194}}}$}[/tex]
Aiden and three of his friends were roasting pumpkin seeds. There were 236 pumpkin seeds. If each person wanted an equal portion, how many pumpkin seeds will each boy get
Answer:
Each boy would get 59 seeds
Step-by-step explanation:
Aiden and his three friends = 4 people
236 divided by 4 = 59
Each boy will get 59 pumpkin seeds.
Explanation:In this problem, Aiden and his three friends are sharing 236 pumpkin seeds equally. To find out how many pumpkin seeds each boy will get, we can divide the total number of seeds by the number of boys.
Divide the total number of pumpkin seeds, 236, by the number of boys, which is 4.
So, each boy will get 236 ÷ 4 = 59 pumpkin seeds.
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Find the solution for 16-x=x+10
Answer:
x=3
Step-by-step explanation:
16-x=x+10
16-x-x=10
16-2x=10
2x=16-10
2x=6
x=6/2
x=3
what is slope of a line that passes through (1,4) (-2,6) plz help
Answer:
-2/3
Step-by-step explanation:
m=(6-4)/(-2-1)=2/-3=-2/3
Can you help me please?
Answer:
C. 3
Step-by-step explanation:
In arithmetic, the range of a set of data is the difference between the largest and smallest values. However, in descriptive statistics, this concept of range has a more complex meaning. The range is the size of the smallest interval which contains all the data and provides an indication of statistical dispersion. It is measured in the same units as the data.
2 - (-1) = 3
6 - 3 = 3
etc...
A nutrition label states that there are 36g of carbonhydrates in each serving. This counts 12% of the daily value. How many grams of carbohydrates are recommended per day?
Can you please show a good explanation like the problem on math on how you did it
300 grams of carbohydrates are recommended per day.
Step-by-step explanation:
Carbohydrates in each serving = 36g
This counts 12% of daily value.
Let,
x be the total daily value.
According to given statement;
12% of x = 36g
[tex]\frac{12}{100}*x=36\\0.12x=36\\[/tex]
Dividing both sides by 0.12
[tex]\frac{0.12x}{0.12}=\frac{36}{0.12}\\x=300\ g[/tex]
300 grams of carbohydrates are recommended per day.
Keywords: percentage, division
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Final answer:
To find the recommended daily amount of carbohydrates, divide the amount per serving (36g) by the daily value percentage (12%) and multiply by 100. The recommended amount is 300 grams of carbohydrates per day.
Explanation:
If a nutrition label states that there are 36g of carbohydrates in each serving and this amount is 12% of the daily value, we can calculate the recommended daily amount of carbohydrates by setting up a simple equation where 36g represents 12%.
To find the full 100%, we divide 36g by 12% and then multiply by 100%.
The calculation steps are as follows:
Divide the amount of carbohydrates in one serving (36g) by the percentage they represent of the daily value (12%). This gives us the amount of carbohydrates per 1% of the daily value.
Multiply the result from step 1 by 100 to find the amount of carbohydrates representing 100% of the daily value, which is the total daily recommended amount.
Calculation:
36g / 12% = 3g per 1% of daily value
3g per 1% * 100 = 300g
Therefore, the recommended daily amount of carbohydrates is 300 grams
10 - 2 +6= 3x (7 + 8)
Answer:
x = [tex]\frac{14}{45}[/tex]
Step-by-step explanation:
10 - 2 + 6 = 3x (7 + 8)
3x (7 + 8) = 10 - 2 + 6
21x + 24x = 8 + 6
45x = 14
x = 14 ÷ 45
x = [tex]\frac{14}{45}[/tex]
Helene invested a total of $1,000 in two simple-interest bank accounts. One account paid 6% annual
interest; the other paid 7% annual interest. The total amount of interest she earned after one year was
$66. Enter and solve a system of equations to find the amount invested in each account. Enter the interest
rates in order as given in the problem. (Hint: Change the interest rates into decimals first.)
x+y = 1,000
0.06
x+ 0.07
y = 66
Helene invested $
at 6% and $
at 7%.
Answer:
Helene invested $ 400 at 6% and $ 600 at 7%.
Step-by-step explanation:
Let
x -----> the amount invested at 6%
y -----> the amount invested at 7%
we know that
The interest earned with the amount invested at 6% plus the interest earned by the amount invested at 7% must be equal to $66
Remember that
[tex]6\%=6/100=0.06\\7\%=7/100=0.07[/tex]
so
[tex]x+y=1,000[/tex] ----> equation A
[tex]0.06x+0.07y=66[/tex] ----> equation B
Solve the system of equations by graphing
The solution of the system is the intersection point both graphs
using a graphing tool
The solution is the point (400,600)
see the attached figure
therefore
Helene invested $ 400 at 6% and $ 600 at 7%.
3. Marissa collected 8 seashells. Her sister Emily
found 7 seashells. The two sisters decided to
put their collection together and give them
all away. Marissa and Emily gave an equal
amount of their seashells to their 5 friends.
How many seashells did each friend receive
Draw more seashells to show how to solve.
Answer:
3
Step-by-step explanation:
There are 15 shells all together
there is 5 friends
15 divided by 5 is 3
Therefore the answer is three
Answer:
Each friend got 3 sea shells
Step-by-step explanation:
8+7=15 then they divided it up equaly to their 5 friends so 15/5=3 so each friend got 3 sea shells
Anyone help with linear inequalities?
Answer:
Yeah I'm here harmony plz tell
Step-by-step explanation:
ScrapBook,you cut a picture into a right triangle for your scrapbook, the lengths of the lago of the triangle are 4 inches and 6 inches is the length of the hypotenuse a rational number
Answer:
hypotenuse is not a rational number
Step-by-step explanation:
In a Right angled triangle , if a, b are the sides and h be the hypotenuse then relationship between them is given by
[tex]h^{2}[/tex] = [tex]a^{2}[/tex] + [tex]b^{2}[/tex]
Here,
a= 4 in. [Given]
b = 6 in. [Given]
Thus ,
[tex]h^{2}[/tex] = [tex]4^{2}[/tex] + [tex]6^{2}[/tex]
[tex]h^{2}[/tex] = 16 + 36
[tex]h^{2}[/tex] = 52.
h = [tex]\sqrt{52}[/tex] = 7.21110255......
Clearly, h is not a rational number
The base of an isosceles triangle is one half as long as each of the congruent sides. The perimeter is 55 in. How long is the base?
Answer:
The base is 11 inches long
Step-by-step explanation:
we know that
An isosceles triangle has two equal sides and two equal interior angles
Let
y -----> is the length of the base of the isosceles triangle
x ----> is the length of each of the congruent sides
The perimeter of the triangle is equal to
[tex]P=y+x+x[/tex]
[tex]P=y+2x[/tex]
we have
[tex]P=55\ in[/tex]
so
[tex]55=y+2x[/tex] ----> equation A
[tex]y=\frac{x}{2}[/tex] ----> equation B
solve the system by substitution
substitute equation B in equation A
[tex]55=\frac{x}{2}+2x[/tex]
solve for x
[tex]55=\frac{5}{2}x[/tex]
[tex]x=55(2)/5\\x=22\ in[/tex]
Find the value of y
[tex]y=\frac{x}{2}[/tex] ----> [tex]y=\frac{22}{2}=11\ in[/tex]
therefore
The base is 11 inches long
Which two mountain peaks combined are 56,190 feet tall?
Answer:
Everest and k2
Step-by-step explanation:
Answer:
its k2 and lhotse
Step-by-step explanation: 28,250 + 27, 940= 56, 190 because 0+ 0 =0
4+5 =9 9+ 2 = 11 carry the 1 8 + 7 +1 = 16 carry the 1 2+2+1 =5 so that equals 56,190 ft
solve the system of equations y=x^2+3-6 y=2x-6
The solutions of the system of equations are (0 , -6) , (-1 , -8)
Step-by-step explanation:
To solve a system of equations, one 1st degree and the other 2nd degree, do that:
Use the 1st degree equation to find one variable in terms of other variableSubstitute this variable in the 2nd degree equation and solve it to find the other variableSubstitute the value of the other variable in the 1st degree equation to find the first variable∵ The system of equations is:
y = x² + 3x - 6 ⇒ (1)
y = 2x - 6 ⇒ (2)
Equate (1) and (2)
∴ x² + 3x - 6 = 2x - 6
- Add 6 to both sides
∴ x² + 3x = 2x
- Subtract 2x from both sides
∴ x² + x = 0
- Take x as a common factor in the left hand side
∴ x(x + 1) = 0
- Equate each factor by 0 to find the values of x
∵ x = 0
∴ The first value of x is 0
∵ x + 1 = 0
- Subtract 1 from each side
∴ x = -1
∴ The second value of x is -1
Substitute each value of x in equation (2) to find the values of y
∵ y = 2(0) - 6
∴ y = 0 - 6 = -6
The first value of y is -6
∵ y = 2(-1) - 6
∴ y = -2 - 6 = -8
∴ The second value of y is -8
∴ The solutions are (0 , -6) , (-1 , -8)
The solutions of the system of equations are (0 , -6) , (-1 , -8)
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A bathtub is filling with water at a rate of 60 liters per minute. How many liters of water are in the bathtub after t minutes? Write your answer as an expression.
Answer:
There are 60t liters of water in the bathtub after t minutes.
After t minutes, [tex]\( 60t \)[/tex] liters of water fill the bathtub.
The amount of water in the bathtub after t minutes can be expressed as the product of the rate of filling (60 liters per minute) and the time (t minutes):
[tex]\[ \text{Amount of water} = \text{Rate of filling} \times \text{Time} \][/tex]
[tex]\[ \text{Amount of water} = 60 \text{ liters/minute} \times t \text{ minutes} \][/tex]
[tex]\[ \text{Amount of water} = 60t \text{ liters} \][/tex]
So, after [tex]\( t \)[/tex] minutes, there will be [tex]\( 60t \)[/tex] liters of water in the bathtub.