Joe could arrange the eraser in an array by placing 5 rows of 3 erasers each. The multiplication fact for this representation in an array is given by 5 × 3 .
A group of numbers or objects that will follow a predetermined pattern are referred to as an array in mathematics.
An array is a systematic arrangement, frequently in rows, columns, or a matrix, that is most frequently used as a visual aid for multiplying and dividing numbers.A matrix is a rectangular array or table with rows and columns of numbers, symbols, or expressions that is used to represent a mathematical object or an attribute of one.Here Joe has 15 eraser and he placed them on his rectangular bench.
Assuming that the erasers are all uniform , Joe placed them on the bench in an array of 5 rows each containing 3 erasers.
The multiplication fact for this representation in an array is given by
5 × 3 .
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Represent the following sentence as an algebraic expression, where "a number" is the
letter x. You do not need to simplify.
The product of 3 and the difference of 5 and a number.
The sentence "5 is subtracted from the square of a number" represented as an algebraic expression is x² -5.
Algebraic expressions: what are they?
A group of integers or variables combined using the operations +, -, o, or constitute an expression. algebraic expressions with variables, numbers, and mathematical operators, as opposed to arithmetic expressions that simply contain numbers and mathematical operators.Given,
Let the number be x and 3 is subtracted from a number.
Represent it in expression.
Step 2
3 is subtracted from a number means 3 is subtracted from x.
Here we have to subtract 3 from x. It can be represented as = x - 3
Let the number be x.
In this exercise, you're required to write an algebraic expression to represent the word problem (sentence). Also, the number would be denoted by the letter x and no need for further simplification of the algebraic expression.
Translating the word problem (sentence) into an algebraic expression, we have;
Square of a number (x) = x²
Subtracting 5 from the the square of x, we have x² -5 .
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Fill in all missing terms and select all missing descriptions.
Answer:
Add all like terms
12s = 0
s = 0
Step-by-step explanation:
8s + 6 + 4s = 6
12s + 6 = 6
-6 -6
12s = 0
÷12 ÷12
s = 0
I hope this helps!
A large industrial tank holds a maximum of 11,020 gallons of water. There is a drain on the bottom of the tank that allows 29 gallons per minute to drain out of the tank. Suppose the tank is full when the drain opened. How many gallons of water are left in the tank after one minute? Two minutes? Ten minutes? n minutes?
Volume of water in the tank after one minute is 10,991 gallons
Volume of water in the tank after two minutes is 10,962 gallons
Volume of water in the tank after one minute is 10,730 gallons
How to calculate the Flow rate?The given parameters are;
The volume of water the large industrial tank holds, V = 11,020 gallons
The rate of flow out of the tank through the drain on the bottom; Q = 29 gallons per minute
The initial level of water in the tank if the tank is initially filled is; 11,020 gallons
We want to find out the amount of water in gallons left in the tank after one minute.
The volume, V_out, of water that flows out of the tank after a given time, t, is given as follows;
V_out = Q × t
When t = 1 minute, we have;
V_out = 29 * 1
V_out = 29 gallons
The volume of water left in the tank, V_in tank , is given as follows;
V_in tank = V - V_out
Thus, volume left after one minute is;
V_in tank = 11020 - 29
V_in tank = 10991 Gallons
Similarly, after 2 minutes;
When t = 2 minute, we have;
V_out = 29 * 2
V_out = 58 gallons
The volume of water left in the tank, V_in tank , is given as follows;
V_in tank = V - V_out
Thus, volume left after two minutes is;
V_in tank = 11020 - 58
V_in tank = 10672 Gallons
Similarly, after 10 minutes;
When t = 10 minute, we have;
V_out = 29 * 1 0
V_out = 290 gallons
The volume of water left in the tank, V_in tank , is given as follows;
V_in tank = V - V_out
Thus, volume left after ten minutes is;
V_in tank = 11020 - 290
V_in tank = 10933 Gallons
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9x = 7x + 22 need help
Answer:
x=11
Step-by-step explanation:
9x=7x+22
9x-7x=22
2x=22
2x/2=22/2
x=11
What are the approximate x-intercepts for y=(x+4)^2 -7
Answer:
44
Step-by-step explanation:
because if u pit it together 44 is what u get
Two angles are complementary if their sum is 90°. A larger angle measures three degrees less than
twice the measure of the smaller angle. If x represents the measure of the smaller angle and these two
angles are complementary, find the measure of each angle.
Answer:
31 and 59
Step-by-step explanation:
We can figure this out by putting the words into an equation
"three degrees less than twice the measure of the smaller angle"
we know the smaller angle = x, so:
twice the smaller angle=2x
3 degrees less=-3
you then put those into an equation where they all add up to equal 90 and simplify
x+2x-3=90
3x-3=90
3x=93
x=31
you then plug that into the equation we would have for the second angle:
2x-3
2(31)-3
62-3
59
the first angle would be 31 and the second angle would be 59
:D
if 3 equal 8 what will equal 600
Answer:
if 3 equal 8 , then 600 will be 1600.
Rewrite the following statement using a number in scientific notation.
My new music player has a capacity of gigabytes 400. (Recall that giga means billion.)
My new music player has a capacity of _ enter your response here bytes.
(Use scientific notation. Use the multiplication symbol in the math palette as needed.)
4 x 10¹¹
Scientific notation is a way to present extremely large or extremely small numbers in a more understandable way. We are aware that full numbers can go on forever, but we are unable to write such enormous figures on paper. Additionally, a simpler method of representation was required for the numbers that appear at the millions place after the decimal. This makes it challenging to represent a small number of integers in their enlarged form. We therefore employ scientific notations.
400 billion in scientific notation = 4 x 10¹¹
We can complete the sentence as,
My new music player has a capacity of 4 x 10¹¹
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what is (8^5)^4 (answer must include an exponent )
Answer:
[tex]8^{20}[/tex]
Step-by-step explanation:
using the rule of exponents
[tex](a^m)^{n}[/tex] = [tex]a^{mn}[/tex] , then
[tex](8^5)^{4}[/tex] = [tex]8^{5(4)}[/tex] = [tex]8^{20}[/tex]
The perimeter of a rectangle is 32 m. The length is 4 m more than two times the width. Find the length and the width of the rectangle.
The length of the rectangle is 12 meters and its width is 4 meters.
A rectangle is a four sided figure, whose opposite sides are equal and the angle formed by any two adjacent sides is 90 degrees.
Here, we are given that the perimeter of the rectangle is 32 meters.
Let the length of the rectangle be L and breadth or width be B
We known that perimeter of a rectangle = 2(L + B)
Now, it is given that the length is 4 m more than two times the width
⇒ L = 4 + 2B
Thus, the area of the perimeter will be-
Perimeter = 2(4 + 2B + B)
⇒ 32 = 2(4 + 2B + B)
32/2 = 4 + 2B + B
16 = 4 + 3B
16 - 4 = 3B
12 = 3B
or 3B = 12
B = 12/3
B = 4
Thus, the width of the rectangle is 4 meters.
Therefore, L = 4 + 2(4)
L = 4 + 8
L = 12
Thus, the length of the rectangle is 12 meters.
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What number multiplied by 7/9 as a product of one
Answer:
★ How to do :-
Here, we are given with a fraction in which we are asked to find the second number in which we get it's product when multiplied as one. We aren't given with the appropriate first number but it's written in thr form of multiplication. If we multiply those numbers, we'll get the value of the first number. After finding the first number, we shift thr obtained value from LHS to RHS. We should always remember that while shifting the numbers, the sign of the appropriate number changes. So, let's solve!!
\:
➤ Solution :-
{\tt \leadsto 3 \: \bigg( \dfrac{7}{9} \bigg) \times x = 1}⇝3(97)×x=1
First, multiply the numbers on LHS.
{\tt \leadsto \bigg( \dfrac{3}{1} \times \dfrac{7}{9} \bigg) \times x = 1}⇝(13×97)×x=1
First solve the bracket on LHS.
{\tt \leadsto \dfrac{21}{9} \times x = 1}⇝921×x=1
Shift the first fraction from LHS to RHS, changing it's sign.
{\tt \leadsto x = 1 \div \dfrac{21}{9}}⇝x=1÷921
Take the reciprocal of second fraction and multiply both the fractions.
{\tt \leadsto x = \dfrac{1}{1} \times \dfrac{9}{21}}⇝x=11×219
Multiply the fractions now.
{\tt \leadsto x = \dfrac{9}{21}}⇝x=219
\:
{\red{\underline{\boxed{\bf So, \: the \: other \: number \: is \: \dfrac{9}{21}}}}}So,theothernumberis219
\:
Verification :-
{\tt \leadsto 3 \: \bigg( \dfrac{7}{9} \bigg) \times x = 1}⇝3(97)×x=1
Substitute the value of x.
{\tt \leadsto 3 \: \bigg( \dfrac{7}{9} \bigg) \times \dfrac{9}{21} = 1}⇝3(97)×219=1
Multiply the numbers on LHS in the bracket.
{\tt \leadsto \bigg( \dfrac{7 \times 3}{9 \times 1} \bigg) \times \dfrac{9}{21} = 1}⇝(9×17×3)×219=1
Multiply the numerators and denominators.
{\tt \leadsto \dfrac{21}{9} \times \dfrac{9}{21} = 1}⇝921×219=1
Multiply the numbers on LHS.
{\tt \leadsto \dfrac{21 \times 9}{9 \times 21} = 1}⇝9×2121×9=1
Multiply the numerators and denominators.
{\tt \leadsto \dfrac{189}{189} = 1}⇝189189=1
Write the fraction in lowest form on LHS.
{\tt \leadsto 1 = 1}⇝1=1
So,
{\sf \leadsto LHS = RHS}⇝LHS=RHS
\:
Hence verified !!
Please help!!!!!!! thx xxx
Start by dividing both sides by G, giving us
[tex]\frac{F}{G}=\frac{m_{1} m_{2} }{d^{2} } }[/tex]. Multiply both sides by d^2. [tex]\frac{F}{G}(d^{2})=m_{1} m_{2}[/tex].
Finally, divide both sides by m2.
[tex](\frac{F}{G}\div{m_{2}}) (\frac{d^{2} }{m_{2} } )=m_{1}[/tex]
Hope this helps! This was a tough problem for me too.
commencement of business with cash 10000 and goods 5000
The answer to given question is given below in detailed manner.
Business Commencement Date means the first date on which the Company or any Affiliate, licensee or sublicensee of the Company makes a commercial sale of any Product within the Field of Activity in the Territory that would generate a payment to the Partnership or the Class A Limited Partners.
Hence here commencement date is not applicable;
for starting capital required=10000+5000
Now adding commencement of business with cash 10000 and goods 5000 as date commencement is not applied here so we get =15000
The capital account is a liability for business this amount is needed to return to investor one day.
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Answer: The answer to given question is given below:
Step-by-step explanation:
Business Commencement Date means the first date on which the Company or any Affiliate, licensee or sublicensee of the Company makes a commercial sale of any Product within the Field of Activity in the Territory that would generate a payment to the Partnership or the Class A Limited Partners.
hence here
commencement date is not applicable;
for starting capital required=10000+5000
=15000
The capital account is a liability for business
this amount is needed to return to investor one day.
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HELPP!!
Ryan collects rainwater in a barrel for his garden. The barrel is filled with 15 gallons of water. Ryan used 6.8 gallons to water his garden in June and 5 and one-eighth gallons in July. How much water is left in the barrel?
1.) 3.075 gallons
2.) 5.125 gallons
3.) 5.178 gallons
4.) 16.675 gallons
Subtracting the initial amount of water from the amount used, the remaining amount of water is given by:
1.) 3.075 gallons.
How to find the remaining amount of water in the barrel?
To find the remaining amount of water in the barrel, we have to subtract the initial amount by the amount used.
We have that:
The initial amount was of 15 gallons.The amount used was of: 6.8 + 5 + 1/8(relative to the one-eight) = 11.925 gallons.Hence the remaining amount is:
15 - 11.925 = 3.075 gallons.
Which means that option 1 is correct.
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Answer: 3.075 gallons
Step-by-step explanation:
If y= 50 degrees and z=85 degrees, then x in degree is=?
the answer will be 55 degrees. please solve
Answer:
Step-by-step explanation:
You buy a new computer for $1500. The value of the computer decreases by 6% every year. How much is the computer worth after 4 years?
Answer: Your computer will be worth $1,171.12
Step-by-step explanation:
[tex]a_n = 1500(0.94)^4\\a_n=\boxed{1171.12}[/tex]
The length of a rectangle is 1 in. less than 3 times the width. If the perimeter of the rectangle is 46 in., find the length and the width.
[tex] \Large {\mathbb {SOLUTION: }}[/tex]
[tex] \: \: \text{L = 3w - 1}[/tex]
[tex] \: \: \text{P=46}[/tex]
[tex] \: \: \text{2(3w-1) + 2w = 46}[/tex]
[tex] \: \: \text{6w - 2 + 2w = 46}[/tex]
[tex] \: \: \text{8w = 48}[/tex]
[tex] \: \: \text {W = 6 }[/tex]
[tex] \: \: \text{L = 17}[/tex]
[tex] \: \: \text{Applying the inequalities:}[/tex]
[tex] \: \: \text{L>=17 and w=6}[/tex]
[tex] \: \: \text{The perimeter is at least 46.}[/tex]
If y’all can’t se it just zoom in because that’s the best I can get it please help me thank u please don’t comment on my stuff just for points I really need help with this
Answer:
the answer is 42
Step-by-step explanation:
you add 217+153+88=458
500-458=42
Jordan will hike the trail at a rate of 4mph. Write a linear equation to represent the distance Jordan still has to walk after x hours what does the y intercept represent
The linear equation would be y = 18 - 4x which represents the distance Jordan still has to walk after x hours.
The y-intercept represents the total distance Jordan has to walk.
What is the distance?Distance is defined as the product of speed and time.
We have to determine the distance.
So distance = speed× time
Given that his speed is 4 mph and x hours of walking, then:
So distance = 4 × x
Let it Start of the trail: 0 miles
And the end of the trail: 18 miles
The trail length is 18 miles, so if he walked 1 mile, 18 - 1 = 17 miles are left, in general:
⇒ y = 17 - 4(x)
Here y would be the distance Jordan still has to walk.
The y-intercept would be if substitute x = 0, then:
⇒ y = 17- 4(0)
⇒ y = 17
This represents the total distance Jordan has to walk
Hence, the linear equation would be y = 18 - 4x which represents the distance Jordan still has to walk after x hours.
The y-intercept represents the total distance Jordan has to walk.
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.Solve 2x−1<4 or −5x−3>−3 and write the solution in interval notation.
The interval notation is { 5/ 2 < x > 0 }
How to determine the valueGiven the inequalities;
2x−1<4−5x−3>−3To determine the value of x, we have;
2x - 1 < 4
collect like terms
2x < 4 + 1
2x < 5
Make 'x' the subject
x < 5/ 2
−5x −3 > −3
collect like terms
-5x > -3 + 3
-5x > 0
x > 0
Thus, the interval notation is { 5/ 2 < x > 0 }
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Please solve. NO EXPLAINATION NEEDED. I NEED ANSWER FAST
Answer:
11 and 22
Step-by-step explanation:
We can say that BC=2AC.
Since AB=33, AC=11 and BC=22.
all real numbers greater than or equal to 55
The set notation of the numbers is {x | x < 50 ∪ x > 50}
How to determine the set notation of the numbers?The set is given as
The set of all real numbers less than 50 or greater than 50
Let the number be represented by x
So, we have
x less than 50 or x greater than 50
When represented as an inequality, we have
x < 50 or x > 50
Using set notation, we have
{x | x < 50 ∪ x > 50}
Hence, the set notation of the numbers is {x | x < 50 ∪ x > 50}
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Solve the following equation. x/9 = 1Then place the correct number in the box provided.
Answer:
9
Step-by-step explanation:
x/9 = 1
Multiply both sides by 9
x = 9
Also, any number over itself is equal to 1.
Help pleaseee thank you so much
Answer:
It's the nitrogen concentration, since it's the one being decided.
The governor of state A earns $49,485 more than the governor of state B. If the total of their salaries is $288,035, find the salaries of each.
need to find a and b
Answer:
a) $168,760
b) $119,275
Step-by-step explanation:
For this, I believe you do $288,035 - $49,485. This equals $238,550.
Then divide this by 2 to get the salary for state B, which is $119,275 .
$168,760 remains, so it's the salary for state A.
Answer:
Governor of state A = 168,760
Governor of state B = 119,275
Step-by-step explanation:
A = 49485 + B Eq. 1
A + B = 288035 Eq. 2
A = Earns of governor of state A
B = Earns of governor of state B
Replacing Eq. 1 in Eq. 2:
(49485+B) + B =288035
2B + 49485 = 288035
2B = 288035 - 49485
2B = 238550
B = 238550/2
B = 119275
From eq. 1
A = 49485 + 119275
A = 168760
Check:
from eq. 2:
A + B = 288035
168760 + 119275 = 288035
11
Select the decimal that is equivalent to
44
Choose 1 answer:
0.17
0.17
0.25
0.25
None of the above
Answer: None of the above
Step-by-step explanation:
In a salad recipe, the ratio of carrots to broccoli must remain constant. The table below shows some possible combinations of carrots and broccoli.
Salad Ingredients
Carrots
Broccoli
3
9
4
12
6
18
7
21
If only whole vegetables can be used, what is the fewest number of vegetables that can be used to make this salad?
A.1
B.3
C.4
D.12
Answer:
Evaluate the numerical expression. 1/4 - (- 5/8)
Step-by-stepexplanation:
Answer: pretty sure 4
Step-by-step explanation:
took test
yeaswass
Select all figures that have at least one line of symmetry.
Answer:the heart and planet are the only ones
Step-by-step explanation:
the clover looks like maybe but the stem is curved. the planet the line goes verticle through the rings
NO LINKS!! Please help me with these problems. Part 10a1
y = √(x - 2)
Answer:
Domain: [2, ∞)Range: [0, ∞)Continuity: Function is continuous on its domain [2, ∞).Minimum point at (2, 0).Increasing function: (2, ∞)Symmetry: Neither as there is no symmetry about the y-axis and no origin symmetry.Step-by-step explanation:
Given function:
[tex]y=\sqrt{x-2}[/tex]
DomainThe domain is the set of all possible input values (x-values).
As the square root of a negative number cannot be taken, the domain of the given function is restricted.
[tex]x-2\geq 0 \implies x\geq 2[/tex]
Therefore, the domain of the given function is [2, ∞).
RangeThe range is the set of all possible output values (y-values).
As the square root of a negative number cannot be taken, the range of the given function is restricted.
Therefore, the range of the given function is [0, ∞).
ContinuityA function f(x) is continuous when, for every value [tex]c[/tex] in its domain:
[tex]\text{$f(c)$ is de\:\!fined \quad and \quad $\displaystyle \lim_{x \to c} f(x) = f(c)$}[/tex]
Therefore, the function is continuous on its domain [2, ∞).
Maximums and MinimumsStationary points occur when the gradient of a graph is zero.
Therefore, to find the x-coordinate(s) of the stationary points of a function, differentiate the function, set it to zero and solve for x.
[tex]\begin{aligned}y & = \sqrt{x-2}\\& = (x-2)^{\frac{1}{2}\\\implies \dfrac{\text{d}y}{\text{d}x} & = \dfrac{1}{2}(x-2)^{-\frac{1}{2}}\\ & = \dfrac{1}{2\sqrt{x-2}}\\\\\dfrac{\text{d}y}{\text{d}x} & = 0\\\implies \dfrac{1}{2\sqrt{x-2}} &= 0\\\dfrac{1}{2} &\neq 0\end{aligned}[/tex]
Therefore, there are no stationary points.
As the domain is restricted and f(x) ≥ 0, the minimum point of the function is at point (2, 0).
Increasing/Decreasing Function[tex]\textsf{A function is \textbf{increasing} when the \underline{gradient is positive}} \implies \dfrac{\text{d}y}{\text{d}x} > 0[/tex]
[tex]\textsf{A function is \textbf{decreasing} when the \underline{gradient is negative}} \implies \dfrac{\text{d}y}{\text{d}x} < 0[/tex]
Increasing
[tex]\begin{aligned}\dfrac{\text{d}y}{\text{d}x} & > 0 \\ \implies \dfrac{1}{2\sqrt{x-2}} & > 0 \\ \dfrac{1}{\sqrt{x-2}} & > 0\\ \textsf{If $\frac{1}{a} > 0$ then $a > 0$}: \\ \implies \sqrt{x-2} & > 0\\ x-2 & > 0\\ x & > 2\end{aligned}[/tex]
Decreasing
[tex]\begin{aligned}\dfrac{\text{d}y}{\text{d}x} & < 0 \\ \implies \dfrac{1}{2\sqrt{x-2}} & < 0 \\ \dfrac{1}{\sqrt{x-2}} & < 0\\ \textsf{If $\frac{1}{a} < 0$ then $a < 0$}: \\ \implies \sqrt{x-2} & < 0\\ \textsf{As $\sqrt{x}\geq 0$, no solution.}\end{aligned}[/tex]
Therefore:
The function is increasing in the interval (2, ∞).Symmetry[tex]\textsf{A function is \underline{even} when $f(x) = f(-x)$ for all $x$.}[/tex]
[tex]\textsf{A function is \underline{odd} when $-f(x) = f(-x)$ for all $x$.}[/tex]
As there is no symmetry about the y-axis (even symmetry) and no origin symmetry (odd symmetry), the symmetry of the function is neither.
Answer:
Domain: [2, ∞)
Range: [0, ∞)
Continuity: Function is continuous on its domain [2, ∞).
Minimum point at (2, 0).
Increasing function: (2, ∞)
Symmetry: Neither as there is no symmetry about the y-axis and no origin symmetry.
A line passes through ( - 1, - 1) and ( - 3, 5).
What is the equation of the line in slope-intercept form?
Answer:
y= -3x-4.
Step-by-step explanation:
1) the slope-interception form is:
y=slope*x+i, where i - interception;
2) using the given two points it is possible to calculate the slope:
[tex]slope=\frac{5+1}{-3+1}=-3;[/tex]
then the required equation has the form:
y=-3x+i;
3) in order to calculate the 'i', it is enough to substitute the coordinates of the one point into this form of the required equation:
-1=-3*(-1)+i; ⇒ i=-4.
4) finally, the required equation is:
y=-3x-4.
P.S. the suggested way is not the shortest one.
