A beam measuring 2 meters can support 172 kilograms
How to determine the weight?The variation is a direct variation.
So, we have:
w = kl
Where k is the constant of variation.
When l = 5, w = 430.
This means that:
430 = 5k
Divide both sides by 5
k = 86
So, we have:
w = 86l
When l = 2, we have:
w = 86 * 2
Evaluate
w = 172
Hence, a beam measuring 2 meters can support 172 kilograms
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Drag the tiles to the correct boxes to complete the pairs. Match each system of inequalities to the graph representing its solution set. y − x > 1 and 2x + y ≤ 2 x + y ≥ -3 and 5x – y ≤ -3 2x – y ≤ -1 and x + 2y < 4 4x – 3y < 12 and x + 3y ≥ 6
The solutions to the systems of inequalities are (0.3, 1.3), (-1, -2), (0.4, 1.8) and (3.6, 0.8)
How to determine the solution to the systems?The graph of the systems of inequalities is not given.
So, I would plot a new graph to answer this question.
The systems of inequalities are given as:
y − x > 1 and 2x + y ≤ 2
x + y ≥ -3 and 5x – y ≤ -3
2x – y ≤ -1 and x + 2y < 4
4x – 3y < 12 and x + 3y ≥ 6
Next, we plot these inequalities on a graph and write out the points of intersection.
From the attached graph, we have:
y − x > 1 and 2x + y ≤ 2 ⇒ (0.3, 1.3)
x + y ≥ -3 and 5x – y ≤ -3 ⇒ (-1, -2)
2x – y ≤ -1 and x + 2y < 4 ⇒ (0.4, 1.8)
4x – 3y < 12 and x + 3y ≥ 6 ⇒ (3.6, 0.8)
Hence, the solutions to the systems of inequalities are (0.3, 1.3), (-1, -2), (0.4, 1.8) and (3.6, 0.8)
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Work out th
e value of x x y x z
Step-by-step explanation:
simple x×x×y×z=x^2×yz=x^2yz
Explain how you would find the area of the shape below.
Answer:
Explained below
Step-by-step explanation:
Area= area of these two triangles+ area of the rectangle+ area of the
=1/4(dh)+ +l.b +
what is the difference between squaring and taking the square root ?
Answer:
Squares are the numbers, generated after multiplying a value by itself. Whereas square root of a number is value which on getting multiplied by itself gives the original value.
Step-by-step explanation:
Hence, both are vice-versa methods. For example, the square of 2 is 4 and the square root of 4 is 2.
What is the solution for p in the equation?
7
p + p + 7 = p +5+4
OAp=1
OB. p=6
OC.
p= -1
OD. p= -6
Step-by-step explanation:
p + p + 7 = p + 5 + 4
2p + 7 = p + 9
2p - p = 9 - 7
p = 2
Melissa wants to make a table representing the area of her vegetable
garden for a variety of different lengths of the tomato patch. she uses
her area expression to create the table.
complete the table by typing the correct answer in each box. use
numerals instead of words. do not round your decimal answers.
The correct numerical values that should be used in completing Melissa's table are:
13√2 or 18.384776 feet.42.25 square feet.12.13466 feet.49 square feet.Note: From the information provided in the table shown in the image attached below, we can deduce that Melissa's vegetable garden has a square shape.
How to calculate the area of a square?Mathematically, the area of a square can be calculated by using this formula;
A = x²
Where:
A is the area of a square.x is the side length of a square.Substituting the given parameters into the formula, we have;
338 = x²
x = √338
x = √2 × √169
x = 13√2 or 18.384776 feet.
For row 2, we have:
A = 6.5²
A = 42.25 square feet.
For row 3, we have:
147.25 = x²
x = √147.25
x = 12.13466 feet.
For row 4, we have:
A = 7²
A = 49 square feet.
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If DE = x + 1, EF = 2x, and DF = 10, what is DE
Answer:
x=3
Step-by-step explanation:
I will assume this is a number line
DE + EF = DF
x+1 + 2x = 10
3x + 1 = 10
3x = 9
x = 3
Find the equation
of the line
that goes through (2,4) and has
a slope of -3.
The equation of the line that goes through (2,4) and has a slope of -3 y = -3x + 10
How to find the equation of a line with slope?The equation of a line can be represented as follows;
y = mx + b
where
m = slopeb = y-interceptTherefore,
y = -3x + b
Let's find b
hence,
4 = -3(2) + b
4 = -6 + b
b = 4 + 6
b = 10
Therefore,
y = -3x + 10
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If g (x) = one-third x and 3 x (StartFraction x Over 3 EndFraction), which expression could be used to verify that (one-third x) (3 x) is the inverse of One-third (3 x)?
The expression that can be used to verify that (one-third x) (3 x) is the inverse of One-third (3 x) is 1/3(3x).
What is an expression?It should be noted that an expression is a collection of symbols that can be used to jointly express a quantity.
From the information given, g(x) = 1/3x + 3x. Here, the expression that can be used to verify that (one-third x) (3 x) is the inverse of One-third (3 x) is 1/3(3x). The inverse in this case is the opposite of the function expressed.
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Answer:
c
Step-by-step explanation:
edge 2022
What numbers between 61 and 107 that is multiple of 5, 8, and 10?
========================================================
Explanation:
We'll need to find the LCM of 5, 8 and 10.
List out the prime factorization of the three numbers.
5 = 1*58 = 2^310 = 2*5The unique prime factors are 2 and 5. The '1' isn't a prime number, so we can ignore it.
The '2' has an exponent of 3 as the largest exponent, meaning 2^3 is part of the LCM. The '5' has the largest exponent of 1. So 5^1 = 5 is also part of the LCM
LCM = 2^3*5 = 8*5 = 40
List out the multiples of 40
40, 80, 120, 160, ...
The number 80 is the only multiple between 61 and 107
which of the following statements best describes the meaning of the y intercept of the line-of best fit in the scatter plot?
9=-7x+7x^2 Helppp please
Answer:
x= 0.21428571428 or x=0.2
Step-by-step explanation:
-7x+7x^2=9 1. simplify 7x^2
-7x+ 7x(7x)=9 2. combine like terms
-7x+49x=9 3. combine like terms
42x=9 4. /42 on both sides
x= 0.21428571428 or x=0.2
What percent is 15 out of 500?
Answer:
3%
Step-by-step explanation:
P% = 15/500
P = 0.03
P% = 0.03 * 100 = 3%
Answer:
15% out of 100 is 15, multiply by 5 and you get 75
HELP ASAPP 10 POINTSSSSS
Answer:
209 cubic mm.
Step-by-step explanation:
Formula for volume of cone:
[tex]V=\frac{1}{3} \pi r^2 h[/tex]
Now let's plug in the values.
[tex]V=\frac{1}{3} \pi 5^2 8[/tex]
[tex]V=\frac{1}{3} \pi 200[/tex]
[tex]V=\frac{200}{3} \pi[/tex]
[tex]V=209.4395...[/tex]
Round to the nearest cubic mm and the volume is 209 cubic mm.
Answer:
209.333
Step-by-step explanation:
→ State the area for the volume for a cone
1/3 × π × r² × h
→ Substitute in the numbers
1/3 × 3.14 × 5² × 8
→ Evaluate
209.333
Grade 11 Math:
Application
3. When Jennifer turned 12 years old, her grandmother gave her $100. Jennifer deposited
the money into a savings account that paid 3.5%/a compounded annually. Since then,
Jennifer’s grandmother has made an automatic deposit of $100 into her account every
year.
a) What is the total amount of the annuity on Jennifer’s 18th birthday? [3 marks]
b) How much of the annuity is interest earned? [1 mark]
The future value of the annuity on Jennifer’s 18th birthday is $655.02
The interest earned is $55.02.
What is the future value of the annuity?An annuity is a fixed payment of money over a specified period of time.
The formula for determining the future value of the annuity is: yearly deposit x annuity factor
Annuity factor = {[(1+r)^n] - 1} / r
Where:
r = interest rate = 3.5%n = number of years = 18 - 12 = 6Future value of the annuity: $100 x [{(1.035^6) - 1} / 0.035} = $655.02
Interest earned = future value - total amount deposited
655.02 - (100 x 6)= $55.02
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In triangle RTS △RTS shown below, point U is on
ST, and point V is on RT so that angle RST UVT∠RST≅∠UVT. If ST=13 VT=5, and RV=13.2, find the length of TU. Figures are not necessarily drawn to scale.
Answer: 7
Step-by-step explanation:
As [tex]\angle T \cong \angle T[/tex] by the reflexive property, we know that [tex]\triangle RST \sim \triangle UVT[/tex] by AA.
Since corresponding sides of similar triangles are proportional,
[tex]\frac{UT}{5}=\frac{13.2+5}{13}\\UT=(5)\left(\frac{13.2+5}{13} \right)=\boxed{7}[/tex]
Consider the graph of the function f(x)=(x−2)12 below. Which statements are true about the function f(x) ? Choose all that are correct. A The minimum value of f(x) occurs at the point x=0 . B The function does not reach a maximum value. C The function is increasing for all values of x larger than 2. D For some values of x , f(x)<0 . E The function is decreasing for all values of x smaller than 2.
The correct statements regarding the function in the graph are given as follows:
B. The function does not reach a maximum value.
C The function is increasing for all values of x larger than 2.
What are the correct statements regarding the function?The function is defined for values of x or 2 and greater, and the function is increasing until infinity(hence it does not reach a maximum value) for all these values, hence statements B and C are correct.
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In ΔDEF, sin D=24/25. What is cos E? [Worth 20 points]
A. 24/25
B. 7/25
C. 25/7
D. 7/24
The value of cos E is [tex]\frac{24}{25}[/tex]. The correct option is A. [tex]\frac{24}{25}[/tex]
TrigonometryFrom the question, we are to determine the value of cos E
From the given information, we have
[tex]sin \ D=\frac{24}{25}[/tex]
By SOH CAH TOA
Opposite = 24
Hypotenuse = 25
Thus, considering the diagram
/EF/ = 24
and
/DE/ = 25
By SOH CAH TOA
[tex]cos \ E =\frac{/EF/}{/DE/}[/tex]
∴ [tex]cos \ E =\frac{24}{25}[/tex]
Hence, the value of cos E is [tex]\frac{24}{25}[/tex]. The correct option is A. [tex]\frac{24}{25}[/tex]
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If your car has a 40 liter gas tank and your car can achieve 26 mpg (miles per gallon), how far can you travel on a full tank
Answer:
270.4 miles
Step-by-step explanation:
First we will convert the 40 liter gas tank into gallons.
There are about 0.26 gallons in 1 liter, so we can find how many gallons are in 40 liters by solving [tex]40 * 0.26[/tex], which equals to [tex]10.4[/tex] gallons.
We can now find how far we can travel on a full tank.
[tex]\mbox{26 miles per gallon } * \mbox{10.4 gallons} = \mbox{270.4 miles}[/tex]
This means we can travel 270.4 miles on a full tank.
That is the answer
- Kan Academy Advance
What is the median of this data set? 15, 14, 6, 10, 7, 15, 7, 8
The median of this set is:
9
A median is:In statistics and probability theory, the median is the value separating the higher half from the lower half of a data sample, a population, or a probability distribution. For a data set, it may be thought of as "the middle" value. The basic feature of the median in describing data compared to the mean is that it is not skewed by a small proportion of extremely large or small values, and therefore provides a better representation of a "typical" value. Median income, for example, may be a better way to suggest what a "typical" income is, because income distribution can be very skewed. The median is of central importance in robust statistics, as it is the most resistant statistic, having a breakdown point of 50%: so long as no more than half the data are contaminated, the median is not an arbitrarily large or small result.
HAVE A NICE DAY!
Answer:
Step-by-step explanation:
Remark
You always have to put the data in order to answer a question like this one.
6 7 7 8 10 14 15
The median is the middle number. In this case it is 8. There are 3 numbers below 8 and 3 numbers above 8, so 8 is the median.
Answer: 8
write the formula of gravitational force between two bodies of mass 'x'and 'y' kept at a distance 'r'
[tex]\huge \orange{F =G.\frac{xy}{r^2}}[/tex]
Step-by-step explanation:
Masses of the bodies are x and yDistance at which they are kept is rWhen two bodies are of masses x and y are placed at a distance r then the gravitational force acting on them is given as:[tex]\huge \purple{F =G.\frac{xy}{r^2}}[/tex]Where G is the gravitational constant.What is the mean of this data set? If necessary, round your answer to the nearest tenth. 11,16,22,28,29,30,31,34,37,38,43,49,56,78,99
Answer:
To find the mean of a given data set, add up all the values then divide by how many numbers ...
Step-by-step explanation:
What is the area of this triangle?
Enter your answer as a decimal in the box. Round only your final
answer to the nearest hundredth.
Answer: 6.64
Step-by-step explanation:
[tex]A=\frac{1}{2}(4.7)(3.2)(\sin 62^{\circ}) \approx \boxed{6.64}[/tex]
help help help help help
Sample red box blue standard deviation 3.868 2.933 then complete each statement. the sample size of the session regarding the number of people would purchase the red box, n the sample size of the session regarding the number of people would purchase the blue box n_{2} is the standard deviation of the sample mean differences is approximately
The confidence Interval is CI = (-1.35, 1.35) and 1.74 is outside of this confidence interval and as such it is statistically significant.
How to find the confidence Interval?Formula for the confidence interval is:
CI = x' ± z(S.E)
where;
x is the mean
z is the critical value.
S.E is the standard error.
We are told that there is no difference between the population and as such; x = 0.
The confidence level is given as 95%.
z-score at 95% confidence level = 1.96.
Standard deviation of the sample mean differences is 0.69. Thus;
S.E = 0.69.
The confidence interval is:
CI = 0 ± (1.96 * 0.69)
CI = (-1.35, 1.35)
1.74 is outside of this confidence interval and as such it is statistically significant.
Complete question is;
I know that the red box has a mean value of 15.11 and the blue box's mean is 16.83. The difference of sample means is 1.74. The red standard deviation is 3.868 and the blue one is 2.933. the standard deviation of the sample mean differences is 0.69. How do I use all this to construct the interval with no difference between the population means.
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Find the solutions to the equation below.
Check all that apply.
6x² +7x-5=0
A. x= -2
B. x = 5
C. x = -5/
D. x = 1/1/2
Ex= 1/3
O F.x= -1/3
x=-5/3 and x=1/2
Step-by-step explanation:
I think you left out some numbers
What is (6 532/1000kg + 7,278g + 5kg 166g) x 8?
Answer:
151.80800 kilograms
Step-by-step explanation:
What’s the difference in these two questions and why did we divide in one and multiple in one ( also why did we divide by8 in question 2)
Answer:
they are different in the equation
42 times 12 divided by 4
Answer:
42×12/4
=42×3
=126
........
2.) which number could not be a value of y if:
y = 4x2-6
a.) 30
b.) 10
c.) -6
d.)-12
The number that could not be a value of y if y = 4x² - 6 is -12.
What is the value of y for a function of f(x)?The value of y for which a function f(x) = y = 4x² - 6 can be determined by knowing the smallest value of y for which x is equal to zero.
So, from the equation y = 4x² - 6, we will replace the value of x with zero to determine the smallest value of y.
i.e.
y = 4(0) - 6
y = 0 - 6
y = -6
Thus, any number smaller than -6 could not be a value of y for the equation y = 4x² - 6.
Therefore, we can conclude that the number that could not be a value of y if y = 4x² - 6 is -12.
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Answer:
-12 is the answer.