600 joules of work is used to lift a box from the ground to a height of six meters. how much work would have been done if a lever would have been used with an effort arm of 12 meters and a load arm of 6 meters?

The solution of the equation is x = [tex]\frac{\sqrt{3} }{2}[/tex] and - [tex]\frac{\sqrt{3} }{2}[/tex].

Now, According to the question:

What is Quadratic Equation?

The polynomial equation whose highest degree is two is called a quadratic equation or sometimes just quadratics. It is expressed in the form of:

ax² + bx + c = 0

where x is the unknown variable and a, b and c are the constant terms.

The given equation is :

40x² = 30

40x² - 30 =0

Common factor:

10(4x²- 3) = 0

Divide both sides by the same factor

10(4x²- 3) = 0

4x²- 3 = 0

Use the quadratic formula:

x = -b±[tex]\sqrt{b^2-4ac}[/tex]/ 2a

Once in standard form, identify a, b and c from the original equation and plug them into the quadratic formula:

4x²- 3 = 0

a = 4

b = 0

c = -3

x =  -0±[tex]\sqrt{0^2-4(4)(-3)}[/tex]/ 2(4)

By simplify:

x = ±[tex]\frac{4\sqrt{3} }{8}[/tex]

To solve for the unknown variable, separate into two equations: one with a plus and the other with a minus.

x = [tex]\frac{4\sqrt{3} }{8}[/tex]

x = -[tex]\frac{4\sqrt{3} }{8}[/tex]

Rearrange and isolate the variable to find each solution

x = [tex]\frac{\sqrt{3} }{2}[/tex] and - [tex]\frac{\sqrt{3} }{2}[/tex]

Hence, The solution of the equation is x = [tex]\frac{\sqrt{3} }{2}[/tex] and - [tex]\frac{\sqrt{3} }{2}[/tex].

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As a result, the graph illustrating how one face's side width and diameter are linearly associated is the resolution to the given linear equation problem.

One degree is the highest number of levels that can be employed in a linear model. Nonlinearity is the property of any equation having a theoretical extent of at least two. On a map, there is a horizontal line with a straightforward equation. The graph shows the curve that a nonlinear equation produces.

Here,

the side lengths and perimeter of one face are linearly connected.

formula for lines

A regular model is described by the equation y = mx + b.

If b is in fact the y intercept and m is the changing rate, then y and x are variable.

One face's length and perimeter have a linear relationship, as seen by the graph.

As a result, the graph illustrating how one face's edge length or perimeter are linearly associated is the answer to the given linear equation problem.

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Answer:

y = f(x) = a + bx

Step-by-step explanation:

Step-by-step explanation: A linear function is a function of the form f(x) = ax + b, where a and b are real numbers. Here, a represents the gradient of the line, and b represents the y-axis intercept (which is sometimes called the vertical intercept).

Answer:

40

Step-by-step explanation:

total: 56+80+40+24 = 200

(80x100)/200

Answer:

What you first want to do is see what all of the numver of students add up to:

80 + 40 = 120

120 + 24 = 144

144 + 56 = 200

So there are a total of 200 votes. 40 of the 200 vote mystery, so you need to find how many times 40 will go into 200. To find this you can just divide.

200/40 = 5

5% prefer mystery books!

Step-by-step explanation:

Hope it helps! =D

I think I did the math wrong, but just by looking Im pretty sure its 5%

The scale factor is greater than 1.

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Answer:

35

Step-by-step explanation:

a=adult c=children

7a:4c

?a:20c

20 is 5 times more than 4 which I found by doing 20/4

So now we multiply 7 by 5 to get 35

35a:20c

There are 35 adults

The length of BC is 5

The length of AC is 10

From the given information, we are to calculate the length of the given parts of line AC

From the given information,

B is the midpoint of AC

Thus,

We can write that

AB + BC = AC

and

AB = BC

Also, from the given information,

AB = 5

Therefore,

BC = 5

From the equation,

AB + BC = AC

Substitute the values of AB and BC

5 + 5 = AC

10 = AC

AC = 10

Hence, BC = 5 and AC = 10

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The constant of proportionality of the graph is 12.

Proportional relationships are relationships between two variables where their ratios are equivalent. In other words, a proportional relationship is one in which two quantities vary directly with each other.

Proportional relationship can be represented mathematically as follows:

y = kx

where

Therefore, let's use (3, 36) to find the constant of proportionality.

Hence,

y = kx

36 = 3k

divide both sides by 3

3k / 3 = 36 / 3

k = 12

Therefore, the constant of proportionality is 12.

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Answer:

follow me if this helped

Step-by-step explanation:

A kite is a four-sided figure that has two acute angles and two obtuse angles. The angles are formed by the intersection of the diagonals, which are not parallel.

[asy]

size(5cm);

draw((0,0)--(1,1.5)--(3,1)--(2,-0.5)--cycle);

draw((1,1.5)--(2,-0.5));

label("$A$",(0,0),SW);

label("$B$",(1,1.5),NE);

label("$C$",(3,1),SE);

label("$D$",(2,-0.5),NW);

[/asy]

A bow tie shape is another four-sided figure that has two acute angles and two obtuse angles. The angles are formed by the intersection of the diagonals, which are not parallel.

[asy]

size(5cm);

draw((0,0)--(1,1.5)--(2,0)--(1,-1.5)--cycle);

draw((1,1.5)--(1,-1.5));

label("$A$",(0,0),SW);

label("$B$",(1,1.5),NE);

label("$C$",(2,0),SE);

label("$D$",(1,-1.5),NW);

[/asy]

The true statements about the function and its graph are:

The graph of the function is a parabola.

The graph of the function opens up.

The graph contains the point (0, 12)

What is the quadratic function?

A quadratic function is a type of polynomial function of degree 2. It is defined as a function of form f(x) = ax² + bx + c, where a, b, and c are constants and a is not equal to 0. The graph of a quadratic function is a parabola, which is a U-shaped curve that opens up or down, depending on the value of the coefficient a.

The value of f(–10) = x² - 5x + 12 = (-10)² - 5(-10) + 12 = 100 - (-50) + 12 = 62, not 82.

The graph of the function is a parabola.

The graph of the function opens up.

The graph of the quadratic function is a parabola that opens up or down, which depends on the coefficient of x². If the coefficient of x² is positive, the parabola opens up, if it is negative, the parabola opens down. In this case, the coefficient of x² is positive, so the parabola opens up.

The graph contains the point (0, 12)

The graph does not contain the point (20, -8) since the x-coordinate is outside the domain of the function.

Hence,  The true statements about the function and its graph are:

The graph of the function is a parabola.

The graph of the function opens up.

The graph contains the point (0, 12)

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So on solving the provided question we cans say that in the following linear equation values are y = -1, -3 , 3

A linear equation is one that has the form y=mx+b in algebra. B is the slope, and m is the y-intercept. It's usual to refer to the previous clause as a "linear equation with two variables" because y and x are variables. The two-variable linear equations known as bivariate linear equations. There are several instances of linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. It is referred to as being linear when an equation has the form y=mx+b, where m stands for the slope and b for the y-intercept. When an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is referred to as being linear.

here ,

as we know that x = 0

so, y = 3x - 1 = -1

2y - 6x = 4 => y = 2

2y = -x + 6 = y = 3

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Answer:

I believe B, E, and F is the answer

No, number 16 is not representing as a factor of 8. The given statement is false as it is a multiple of 8.

As given in the question,

Given number is equal to 8,

Given factor is equal to 16:

Factors are those numbers which divides the given numbers without leaving any remainder. It exactly divides the given original number.

Here given factor 16 does not divides the given number 8.

Instead 8 divides the the number 16.

here '8' is the factor of the number 16.

And 16 represents as a multiple of 8.

Therefore, the given statement is false and 16 is not considered as a factor of 8 instead it is a multiple of 8.

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Answer: d-20

Step-by-step explanation:

if Mia has $20 less than Brandi, it means Brandi has d dollars, so we subtract Brandi 's money from $20.hope you understood.

Answer:

x = -5

Step-by-step explanation:

Now we have to,

→ find the required value of x.

The equation is,

→ |10x + 50| = 0

Then the value of x will be,

→ |10x + 50| = 0

→ 10x + 50 = 0

→ 10x = 0 - 50

→ 10x = -50

→ x = -50/10

→ [ x = -5 ]

Hence, the value of x is -5.

The principal of account A is $250.26

The principal of account B is $500

The account that would  earn you more interest in the first month is account B

Simple interest is the interest earned on an amount of money in a savings account.

Simple interest = principal x time x interest rate

Principal is the amount deposited

Principal = simple interest / ( time x interest rate)

Principal of account A = 4.88 / (6/12 x 0.039) = $250.26

Principal of account B = 24.75 / (27/12 xx 0.022) =$500

Interest earned in the first month:

Account A =  (1/12) x 250.26 x 0.039 = .81

Account B =  (1/12) x 500 x 0.022 =0.92

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Answer: -c^12+9c^4

Step-by-step explanation:

Answer: 81 c^4 - c^12

Step-by-step explanation:

(9c^2+c^6)(9c^2-c^6)

Step-by-step explanation: (9c^2+c^6)(9c^2-c^6)

This is the difference of squares

(a+b) (a-b) = a^2 - b^2

(9c^2) ^2 - ( c^6)^2

81 c^4 - c^12

The interquartile range (IQR) of this dataset is 8.25, it means that half of the observations fall between 53 and 61.25, while half of the observations fall outside of that range.

IQR stands for Interquartile Range, which is a measure of the variability of a dataset. It is defined as the difference between the third quartile (Q3) and the first quartile (Q1). To calculate the IQR, you first need to order the data set and find the median (middle value) of the dataset, and the Q1 and Q3.

Here is the dataset you provided, in order:

53 53 53 54 55 56 59 60 61 62 63 88

The median of the dataset is: (56+59)/2 = 57.5

Q1 is the median of the lower half of the dataset: (53+53+54)/3 = 53

Q3 is the median of the upper half of the dataset: (60+61+62+63)/4 = 61.25

Now you can calculate the IQR:

IQR = Q3 - Q1 = 61.25 - 53 = 8.25

So the interquartile range of this dataset is 8.25, it means that half of the observations fall between 53 and 61.25, while half of the observations fall outside of that range.

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The correct question should be:

"Find the interquartile range (IQR) of the following dataset

53 53 53 54 55 56 59 60 61 62 63 88"

Sarah's error in the expression 3 so the correct answer is option D

Complete Question: Sarah used properties of operations to write the following three equivalent expressions to.

A. There are no errors. All of the expressions are equivalent.

B. Expression 1. Sarah can’t apply the Distributive Property if there are three addends.

C. Expression 2. Sarah can’t combine -4 and -6. She must combine -4 with 8.

D. Expression 3. Sarah applied the Distributive Property but incorrectly multiplied 1/2 (-6).

Expressions 1, and 2 are equivalent because they are using the distributive property to expand the term within the brackets before applying the 1/2 coefficient.

Expression 3 is not equivalent because it does not use the distributive property and does not have the same terms as the other expressions.

Sarah's error in expression 3 is that she did not use the distributive property and the terms inside the brackets are not the same as the other expressions, hence the results are different.

Therefore, Sarah's error in the expression 3 so the correct answer is option D

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Answer:

168 deg

Step-by-step explanation:

Assuming the increase in temperature in constant during the 3 weeks, we do the following calculations-

8 deg * 7 = 56 deg / week (Since there are 7 days in a week)

56 * 3 = 168 deg in 3 weeks.

There are 21 yellow marbles anita receives

given that

In mathematics, a percentage (from Latin: per centum, "by a hundred") is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%",although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number (pure number); it has no unit of measurement.

The term "percent" is derived from the Latin per centum, meaning "hundred" or "by the hundred". The sign for "percent" evolved by gradual contraction of the Italian term per cento, meaning "for a hundred". The "per" was often abbreviated as "p."—eventually disappeared entirely. The "cento" was contracted to two circles separated by a horizontal line, from which the modern "%" symbol is derived.

at the craft store , Anita bought a bag of yellow and green marble

The bag contained 70 marble,

30% percentage of them were yellow.

now, we need to find How many yellow marble did Anita receive

= 70 * 30%

= 70 * [tex]\frac{30}{100}[/tex]

= 7 *3

= 21

There are 21 yellow marbles anita receives

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The given statement as an expression is 6x + 15 = 6x - 41

From the question, we have the following parameters that can be used in our computation:

A mathematical statement

The mathematical statement is given as

6 times a number plus 15 is equal to 6 times a number minus 41

Represent the number with x

So, we have the following representation

6 times x plus 15 is equal to 6 times x minus 41

is equal to implies =

So, we have:

6 times x plus 15 = 6 times x minus 41

Plus implies +, minus implies - and times *

This gives

6x + 15 = 6x - 41

The question does not require that we solve the expression

So, we leave it at 6x + 15 = 6x - 41

Hence, the required expression is 6x + 15 = 6x - 41

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Answer:

Dilation of 3

Step-by-step explanation:

Note [tex]DE=2[/tex] and [tex]D'E'=6[/tex].

The scale factor is defined as the ratio of the length of the side of the image to the length of the corresponding side of the preimage.

So, the scale factor is [tex]\frac{6}{2}=3[/tex].

The dilation shown in the image is a dilation with a scale factor of 3

The transformation rule for dilation is as follows

(x, y) for a scale factor of r → (3x, 3y)

Dilation is a method of transformation that magnify or shrink the preimage depending on the scale factor

Generally,  transformation rule for dilation is as follows

(x, y) for a scale factor of r → (rx, ry)

Examining the figure, Using side DE as reference we can see that DE is 1 unit

After dilation side D' E' transformed to 3 units, showing an increment of 3.

The dilation is an enlargement and the scale factor is 3

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So on solving the provided question we can say  that factors 8 = 1,2,4,8 factor 20 = 1,2,4,5,10,20

Any natural number other than 1 with just itself and the number 1 as its divisors is considered a prime factor. Actually, 2, 3, 5, 7, 11, and so on are some of the first prime numbers. an amount that has been multiplied to produce another amount. By dividing 15 by 3 and 5, for instance, we get 3 5 = 15. main elements: Prime factors include all factors that are prime but are not composite. A few prime factors of 30 are 2, 3, and 5. Only 2 and 3 are prime factors of 12, so listing 2 twice as 2 2 3 (or 22 3) is necessary to factorize 12. The sum of 2 + 3 is not 12.

here,

factors 8 = 1,2,4,8

factor 20 = 1,2,4,5,10,20

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Total water use in Spain = 810m^3 x 46.5 million = 37,425,000,000 m^3. it is important to be aware of the amount of water used in order to understand and mitigate any potential negative impacts.

1. Given that the per capita water use is 810m^3 and the population of Spain is 46.5 million.

2. Calculate the total water use by multiplying the per capita water use by the population of Spain.

3. Total water use in Spain

= 810m^3 x 46.5 million = 37,425,000,000 m^3

The total water use in Spain is calculated by multiplying the per capita water use (810m^3) by the population of Spain (46.5 million). This yields a total water use of 37,425,000,000 m^3. This number indicates the volume of water used in Spain annually by its citizens. Water use can have a variety of impacts on the environment, such as depletion of water resources, and it is important to be aware of the amount of water used in order to understand and mitigate any potential negative impacts.

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A linear model can be represented by the equation y = mx + b, where y is the dependent variable (megawatt hours generated by hydropower), x is the independent variable (years since 2007), m is the slope of the line, and b is the y-intercept.

To find the slope (m) and y-intercept (b) for this problem, we can use the two points given: (2007, 248) and (2012, 277).

m = (277 - 248) / (2012 - 2007) = 29 / 5 = 5.8

b = 248 - (5.8)(2007) = 248 - 11456 = -11208

So the linear model representing the number of megawatt hours generated by hydropower as a function of the number of years since 2007 is:

y = 5.8x - 11208

where x is the number of years since 2007.

Answer:

[tex]\boxed{\bf u=7}[/tex]

Step-by-step explanation:

[tex]\sf 2u+2.17=16.17[/tex]

Subtract 2.17 from both sides:-

[tex]\sf u+2.17-2.17=16.17-2.17[/tex]

[tex]\sf 2u=14[/tex]

Divide both sides by 2:-

[tex]\sf \cfrac{2u}{2}=\cfrac{14}{2}[/tex]

[tex]\sf u=7[/tex]

Therefore, u = 7

______________________

Hope this helps!

Have a great day!