Answer:
The length is 89 cm============================
Perimeter equationP = 2(l + w), where
P- perimeter, l- length, w- widthGivenP = 324 cm,w = 73 cmFind the value of l:
324 = 2( l + 73)l + 73 = 324/2l + 73 = 162l = 162 - 73l = 89Answer:
L = 89 cm
Step-by-step explanation:
Formula we use,
→ P = 2(L + W)
Then the value of its length is,
→ P = 2(L + W)
→ 324 = 2(L + 73)
→ 324 = 2L + 146
→ 2L = 324 - 146
→ L = 178/2
→ [ L = 89 cm ]
Hence, the length is 89 cm.
The sum of three consecutive numbers is 33 more than the smallest of the numbers. Find
the numbers.
Answer:
15, 16 and 17
Step-by-step explanation:
Consecutive numbers mean numbers that are separated by 1 from each other. For example 5, 6 and 7 are three consecutive numbers and 5 is the smallest
Let the smallest number be x
Then the next consecutive number is x + 1
The next one after that is x + 2
Sum = x + x + 1 + x + 2 = x + x + x + 1 + 2 = 3x + 3
We are told that this sum is 33 more than the smallest number x
So 3x+3 = x + 33 Subtract x from both sides
3x - x + 3 = x + 33 -x
==> 2x + 3 = 33
Subtract 3 from both sides
==> 2x + 3 - 3 = 33 -3
==> 2x = 30
Divide both sides by 2
==> 2x/2 = 30/2
==> x = 15
So the smallest number is 15 and the three numbers are 15, 16 and 17
Verify by adding 15+16 +17 = 48
15 + 33 = 48 so consistent
A: The three consecutive numbers are 15, 16, 17.
Explanation:
Let x, y, z be the numbers.
x + y + z = x + 33
y = x + 1
z = x + 2
We will solve this system of equations using the substitution method.
x + x + 1 + x + 2 = x + 33
x + x + x - x = 33 - 1 - 2
2x = 30
x = 15
y = 15 + 1 = 16
z = 15 + 2 = 17
Solving for x + y + z = x + 33:
15 + 16 + 17 = 15 + 33
48 = 48
A: 15, 16, 17.
1. I am a number between 120 to 130 and I am divisible by 3, 6 and 9. Who am I?
Answer:
126
Step-by-step explanation:
A number is divisible by 3 if its sum of digits is divisible by 3 (you can do it over and over again until it's one digit!).
A number is divisible by 2 if its last digit is 0, 2, 4, 6 or 8.
A number is divisible by 6 if it is divisible by 2 and by 3.
A number is divisible by 9 if its sum of digits is divisible by 9 (you can do it over and over again until it's one digit!).
So we need a number with last digit 0, 2, 4, 6, or 8 (because it's divisible by 6 hence by 2) and with a sum of digits divisible by 9 (because if it's divisible by 9 it's also divisible by 3).
130 is not divisible by 9, so the first digits must be 12X.
to get a number divisible by 9, we need to add a digit D so that 1+2+D is divisible by 9.
9 - 1 - 2 = 6
126 is divisible by 9 because it's sum of digits is 9. It's also divisible by 6, because it is divisible by 3 and its last digit is 6.
√58 what would be the answer to this?
The square root of 58 is around 7.6
The entire number is, 7.61577310586...
If you double a number and then subtract eight the result is 18. Which equation below could be used to represent the situation?
Answer: 2x - 8= 18
2x - 8=18
2x=26
x= 13
please help me w this
To solve this problem we need to be aware of the concepts of angles in a circle. Also we need to know what is a major angle and what is a minor angle.
That major part of an angle is equal to (360-minor part of the angle).
We know the total angle in a circle is 360°.
Here, ∠SKL=120+2x; ∠JKS=28° and ∠JKL=x+148.
Sum of all the angles will give us 360°.
According to question,
∠SKL+∠JKS+∠JKL=360°
⇒(120+2x)°+28°+(x+148)°=360°
⇒3x+296°=360°
⇒3x=360°-296°
⇒x=[tex]\frac{64}{3}[/tex]
∴ x=21.3
Hence, the value of x is 21.3 in the given problem.
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4.25-1.25x=0 what is x someone help please
Answer:
3.4
Explanation and Check part below
Hope this helps :)
Step-by-step explanation:
Steps
1. Isolate the variable subtract 4.25 since it's positive.
4.25 - 1.25x = 0
- 4.25 - 4.25
- 1.25x = - 4.25
2. Divide by - 1.25 in both sides of equation.
- 1.25x = - 4.25
--------- ---------- <------- fraction bar/ divide
-1.25 -1.25
x = 3.4
Check:
4.25 - 1.25 (3.4) = 0
4.25 - 4.25 = 0
0 = 0
True statement.
The depth of a local river averages 20 ft, which is represented as |−20|. In January, it measured 6 ft deep, or |−6|, and in July, it was 22 ft, or |−22|. What is the difference between depths in January and July
Answer:
the answer is 16 feet
Step-by-step explanation:
Please solve for meeee
Answer: 58 degrees
Step-by-step explanation:
a+b=90 ==> angles a and b are on a right angle which measures 90 degrees.
32+b=90
b=58 degrees
1, Let a = 2i-3j +4k and b = 2i+4k
a) Find the Projection of a "a" long "b"
b) Find the Projection of "b" along "a"
The Projection of "a" along "b" is [tex]\sqrt{20}[/tex] and the Projection of "b" on "a" is [tex]\frac{20}{\sqrt{29} }[/tex]
Given that a = 2i-3j +4k and b = 2i+4k
To find Projection,
Projection of "x" on "Y"=(X vector).(Y unit vecot)
Projection of "a" along "b" = (a vector).(b unit vector)
Projection of "a" along "b" = ( 2i-3j +4k).([tex]\frac{2i+4k}{\sqrt{29} }[/tex])
Projection of "a" along "b" =[tex]\frac{4+16}{\sqrt{20} }[/tex]
Projection of "a" along "b" =[tex]\frac{20}{\sqrt{20} }[/tex]
Projection of "a" along "b" =[tex]\sqrt{20}[/tex]
Projection of "b" along "a" = (b vector).(a unit vector)
Projection of "b" along "a" = ( 2i+4k).([tex]\frac{2i-3j +4k}{\sqrt{29} }[/tex])
Projection of "b" along "a" = [tex]\frac{20}{\sqrt{29} }[/tex]
Therefore,The Projection of "a" along "b" is [tex]\sqrt{20}[/tex] and the Projection of "b" on "a" is [tex]\frac{20}{\sqrt{29} }[/tex]
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the class was required to draw plan for the foundation day. Mary and tess was assigned to draw buildings. mary draw buildings twice as much as tess. if the total buildings are 99, how many buildings was draw by mary and tess
Answer:
Mary drew 66 buildings and Tess drew 33 buildings.
Step-by-step explanation:
Let's label the number of buildings drawn by Mary as x and the number of buildings drawn by Tess as y.
We know there are 99 buildings drawn. This means
99=x+y
We also know that Mary drew twice as many buildings as Tess. We can represent this as
x=2y
Now, let's substitute x for 2y, since that would put us in common terms
99=2y+y
Add common variables together and you get
99=3y
Solve for y by dividing 99 by 3
y=33
We now know that Tess drew 33 buildings, as well as y=33. Substitute y in the equation for how many buildings Mary drew:
x=2(33)
Now we know that Mary drew 66 buildings.
To check our work,
99=x+y
99=66+33
99=99
Answer the following true or false
false is the answer of that Q
The price of a shirt has been discounted by $20. The sale price is $25.95. What percent of the original list price is the discount?
Answer:
that's like 77% off if im reading this right
Step-by-step explanation:
Solve -1/5 [3 - 12 (1/3)^2]
PLEASE HELP QUICK
Answer:
The answer to your problem is -1/3
Step-by-step explanation:
Let me know if you need the steps. Thanks
Bill weighs 240 pounds and is losing two pounds each month . Phil weighs 290 pounds and is losing 4 pounds each month . How many months , m, will it take Bill to weigh the same as Phil
They will weigh the same at twenty-five months.
What is the algebraic expression?Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.
Let the number of months when they will weigh the same would be m
Given that Bill is losing two pounds per month and is currently 240 pounds.
So his model expression of weight would be: 240 - 2m
And Bill is losing four pounds per month and is currently 290 pounds.
So his model expression of weight would be: 290 - 4m
As per the condition, they will weigh the same
⇒ 240 - 2m = 290 - 4m
⇒ 4m - 2m = 290 - 240
⇒ 2m = 50
⇒ m = 25
Therefore, they will weigh the same at twenty-five months.
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The perimeter of the rectangle shown below is 23 feet. What is the missing side length
Answer:
If you could take a picture of the rectangle I could help you answer that. I can't see the rectangle.
What is x in this equation .3=.5x-.7
By solving the linear equation it can be obtained that
The value of x is 2
What is a linear equation?
At first it is important to know about equation
Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.
A one degree equation is known as linear equation.
The given linear equation is
0.3 = 0.5x - 0.7
0.5x = 0.3 + 0.7
0.5x = 1
x = [tex]\frac{1}{0.5}[/tex]
x = 2
The solution of this linear equation is x = 2
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In a room, 9 students have glasses on, while 15 do not. Give the percentage of students wearing glasses. (Round to the nearest tenth of a percent)
Work Shown:
9+15 = 24 students total
9 have glasses, so 9/24 = 0.375 = 37.5% of the class wears glasses.
Two cyclists, 90 miles apart, start riding toward each other at the same time. One cycles 2 times as fast as the
other. If they meet 3 hours later, what' is the speed (in mi/h) of the faster cyclist?
The speed of the faster cyclist is 30 mph.
Two cyclists, distance = 90 miles.
let the speed of one cyclist is = x and
let the speed of the other cyclist = 2x
time after which both the cyclists will meet = 3 hours.
Since they are travelling towards each other the effective speed = 2x ₊ x
= 3x
we know that time = distance/speed
3 = 90/3x
3x = 30
x = 10 mph speed of one cyclist.
speed of the other cyclist will be 3x = 3 × 10 = 30 mph
The speed of the fastest cyclist is 30 mph.
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While training for an athletic event, Julian's daily calorie intake increased from 2,500 to 7,000. What is the absolute increase in Julian's daily calorie intake?
What percent of 32 is 4?
A 12.5%
B 1.28%
of 32 is 4?
C 0.125%
D 8%
Answer:
A
Step-by-step explanation:
12.5% is 4 of 32. Devide 4 by 32 you get the 0125
Answer:
A 12.5%
Step-by-step explanation:
let p be the percentage that 4 represents.
[tex]32\longrightarrow 100 \%\\4 \longrightarrow \text{p} \%[/tex]
Then
[tex]p=\frac{4}{32} \times 100[/tex]
[tex]= 0.125 \times 100[/tex]
[tex]=12.5[/tex]
How many times larger is 6.945 × 1010 than 1.5 × 108?
463
216
21.6
4.63
Answer:
The only answer is 46.3. I'm not sure whether or not you mixed up one of the decimals, but this is the only answer out of the others.
I hope this helps.
The number 6.945 × 10¹⁰ is 463 times more than 1.5 × 10⁸. As a result, option A is right and the other choices are false.
What is a Fraction?A fraction is a number that, when stated mathematically, designates a component of a whole. A fraction is a portion or division of any whole, which could be any number, a specific sum, or an actual object.
The horizontal bar known as the fractional bar divides the numerator and denominator of every fraction into these two halves.
There are several types of fractions, some of them are :
Proper fractionImproper fractionUnit fractionMixed fractionEquivalent fractionAccording to the question,
(6.945 × 10¹⁰) / (1.5 × 10⁸)
= 463
Hence, it is concluded that 6.945 × 10¹⁰ is 463 times more than 1.5 × 10⁸.
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A population of mold decays at a rate of 30 mold spores per day. If the initial population of mold spores is 1560 spores, how many days will it take for the population to be less than 1000 mold spores?
By using a linear equation, we can see that after the 19 day the population will be less than 1000 mold spores.
How many days will it take for the population to be less than 1000 mold spores?We know that the population decays at a rate of 30 spores per day, and we have an initial population of 1560 mold spores.
Then, the population of spores after x days is given by the linear equation:
P(x) = 1560 - 30*x
The population will be exactly 1000 spores when:
P(x) = 1000 = 1560 - 30*x
We need to solve that for x.
30x = 1560 - 1000 = 560
x = 560/30 = 18.67
So after 18.67 days the population is 1000, this means that after the 19 day the population will be less than 1000 mold spores.
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A student on the track team runs 45 minutes each day as a part of her training. She begins her workout by running at a constant rate of 8 miles per hour for 푎 minutes, then slows to a constant rate of 7.5 miles per hour for 푏 minutes. Which equation describes the relationship between the distance she runs in miles, 퐷, and her running speed, in miles per hour?
D = RT would be the fundamental equation to answer this, which is
Distance in D
Rate is R (speed)
It is now.
We can determine the individual distances for the two legs of the whole to determine the overall distance D.
Initial Leg:
R = 8
T = a
D = 8a
8(45 – b) + 7.5b =D
What is the formula for rate and distance?
Use the formula d = st to determine speed, distance, or time. Distance is equal to speed multiplied by time. Given two known numbers, the Speed Distance Time Calculator can solve for the unknown sdt value.
Units of seconds (s), minutes (min), hours (hr), or hours, minutes, and seconds can be used to input or solve for time (hh:mm:ss). Time format shortcuts are shown below.
Use the formula d = st, or distance equals speed times time, to find the distance.
Distance Equals speed x time
Since both reflect a certain amount of distance per unit of time, such as miles per hour or kilometers per hour, rate and speed are comparable. If speed s and rate r are equal, then r = s = d/t. The corresponding formula is d = rt, which denotes Rate times time are equivalent to distance.
Distance = Rate x Time
Use the speed formula, s = d/t, which states that speed is equal to distance divided by time, to solve for speed or rate.
speed equals distance/time.
Use the time formula, t = d/s, which states that time is equal to distance divided by speed, to solve for time.
Time = Speed/Distance
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x^x = 2^2048
solve for x
x=256
[tex] {256}^{256} = ( { {2}^{8} })^{256} = {2}^{8 \times 256} = {2}^{2048} [/tex]
It is so hot that Craig's cousins ask him to make creamy mango smoothies. First, Craig blends 5 cups of mango, 1 quart of yogurt, and 3 cups of crushed ice. Then, he divides the smoothie evenly among 6 large glasses. How many cups of smoothie does he put in each glass?
Answer:
2 Cups
Step-by-step explanation:
First of all you need to add all of the ingredients together, which would total 12 cups of smoothie. Also important to add is that 1 quart is 4 cups. Then you have 12/6 which equals 2!
The cups of smoothie in each glass is 2 cups.
How many cups of smoothie is in each glass?In order to determine the number of cups of smoothie that would be put in each glass, it should be ensured that the measures of the ingredients are in the same unit.
The first step is to determine the total cups of smoothie that Craig makes.
In order to determine the total cups, quart has to be converted to cups
1 quart = 4 cups
Total number of cups = 5 + 4 + 3 = 12 cups
The next step is to determine the cups in each glass.
Cup of smoothie in each glass = total number of cups of smoothie / total number of large cups
12 / 6 =2 cups.
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A spinning disk with radius 10 cm rotates at 120 rpm.
1. Find the angular speed:
2. Find the linear speed of a point on the edge of the disk:
1) The angular speed is approximately 12.566 radians per second.
2) The linear speed of a point on the edge of the disk is 1.257 meters per second.
What are the angular speed and the linear speed of a spinning disk?
1) Herein we have a disk that spins at constant angular speed (ω), in radians per second, whose magnitude is found dimensional analysis and unit conversions:
ω = 120 rev / min × (2π rad / 1 rev) × (1 min / 60 s)
ω ≈ 12.566 rad / s
The angular speed is approximately 12.566 radians per second.
2) The linear speed (v), in meters per second, on the edge of the disk is described by the following formula:
v = R · ω
Where R is the radius of the spinning disk, in meters.
If we know that R = 0.1 m and ω ≈ 12.566 rad / s, then the linear speed is:
v = (0.1 m) · (12.566 rad / s)
v = 1.257 m / s
The linear speed of a point on the edge of the disk is 1.257 meters per second.
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What are the solutions to this linear system?
Building systems of equations, we have that:
a) The price of a cow is of 1200 coins, the price of a sheep is of 500 coins and the price of a pig is of 300 coins.
b) The system of equations is composed by the equations given below.
x + 9 + 4 = 15.7 + y + z = 15.t + 1 + w = 15.x + 7 + t = 15.9 + y + 1 = 15.4 + z + w = 15.x + y + w = 15.4 + y + t = 15.What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
For item a, the variables are given as follows:
Variable x: Price of a cow.Variable y: Price of a sheep.Variable z: Price of a pig.Considering that a sell is positive money and a buy negative, and the text, the equations are given as follows:
2x + 5y - 13z = 1000.3x - 9y + 3z = 0.-5x + 6y + 8z = -600.Using a calculator, the solutions are given as follows:
x = 1200, y = 500, z = 300.
Hence:
The price of a cow is of 1200 coins, the price of a sheep is of 500 coins and the price of a pig is of 300 coins.
For item b, all missing values are variables, given by:
x, y, z, t and w.
From the sum of the rows:
x + 9 + 4 = 15.7 + y + z = 15.t + 1 + w = 15.From the sum of the columns:
x + 7 + t = 15.9 + y + 1 = 15.4 + z + w = 15.From the diagonals:
x + y + w = 15.4 + y + t = 15.The system is composed by all these equations.
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as a contractor to make a hole 4 5/8 inches diameter. express the mixed number as an improper fraction.
The mixed number as an improper fraction is 37/8
How to express the mixed number as an improper fraction?The diameter is give as:
Diameter = 4 5/8
Next we convert the above number to an improper fraction
The numerator is calculated as
Numerator = 8 * 4 + 5
This gives
Numerator = 37
Hence, the mixed number as an improper fraction is 37/8
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Multiplication Burrito
In the multiplication problem below,
find the 2 remaining digits in the
4-digit product. In other words, find
A and B.
X
008
A B 66
A=;B=_
Solve the equation and determine the solution(s) or any extraneous solution.
Answer:
Solution: x = 9 Extraneous solution: x = 1
Step-by-step explanation:
Given equation:
[tex]\sqrt{4x}=x-3[/tex]
Square both sides:
[tex]\implies \left(\sqrt{4x}\right)^2=\left(x-3\right)^2[/tex]
[tex]\implies 4x=x^2-6x+9[/tex]
Subtract 4x from both sides:
[tex]\implies 4x-4x=x^2-6x+9-4x[/tex]
[tex]\implies 0=x^2-10x+9[/tex]
[tex]\implies x^2-10x+9=0[/tex]
Split the term in x:
[tex]\implies x^2-x-9x+9=0[/tex]
Factor the first two terms and the last two terms separately:
[tex]\implies x(x-1)-9(x-1)=0[/tex]
Factor out the common term (x - 1):
[tex]\implies (x-9)(x-1)=0[/tex]
Apply the zero-product property:
[tex](x-9)=0 \implies x = 9[/tex]
[tex](x-1)=0 \implies x=1[/tex]
Substitute the found values of x into the original equation to verify the solutions:
[tex]\begin{aligned}x=9 \implies \sqrt{4 \cdot 9} & = 9-3\\\sqrt{36} & = 6\\6 & = 6\end{aligned}[/tex]
[tex]\begin{aligned}x=1 \implies \sqrt{4 \cdot 1} & = 1-3\\\sqrt{4} & = -2\\ 2 & = -2\end{aligned}[/tex]
Therefore, the only valid solution is x = 9:
Solution: x = 9Extraneous solution: x = 1Extraneous solution: A solution from the process of solving the equation that is not a valid solution to the original equation.
