What is a necessary step for constructing perpendicular lines through a point off the line?

Volume is a three-dimensional scalar quantity. As per the Cavaleri's principle the volume of both the figures will be the same.

A volume is a scalar number that expresses the amount of three-dimensional space enclosed by a closed surface.

According to Cavalieri's principle, if two figures have the same height and cross-sectional area throughout each point along that height, they have the same volume.

The height of both the objects is 16 cm, also the base area of both the objects is 96 cm². As it can be observed that for both the object there base area is the same through out their height.

Hence, as per the Cavaleri's principle the volume of both the figures will be the same.

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Answer:

C

Step-by-step explanation:

y = 3x - 4

4y = 12x - 4

divide the bottom equation by 4

y = 3x - 4

y = 3x - 1

y = -3

3x - 1 = -3

3x = -2

x = -2/3

(-2/3, -3) is the answer. by this logic, there is a splution so can't be a, the answer is not (0, 4) so not b so it must be c

Answer:

Step-by-step explanation:

Solution,

We use the slope formula, setting x=a :

[tex] \displaystyle{{{{ \lim_{h \to0}}}} \frac{ \frac{2}{x + h} - \frac{2}{x} }{h} = \lim_{h \to0} \frac{ \frac{2}{a + h} - \frac{2}{a} }{h} }[/tex]

[tex] \displaystyle{ \lim_{h \to0} \frac{ \frac{2a - 2(a + h)}{a(a + h)} }{h} = \displaystyle{ \lim_{h \to0} \frac{2a - 2(a + h)}{ha(a + h)} }}[/tex]

[tex] \displaystyle{ \lim_{h \to0} \frac{2a - 2a - 2h}{ha(a + h)} = \displaystyle{ \lim_{h \to0} \frac{ - 2h}{ha(a + h)} }}[/tex]

[tex] \displaystyle{ \lim_{h \to0} \frac{ - 2}{a(a + h)} = - \frac{ 2}{ {a}^{2} } }[/tex]

Therefore, The slope of the curve y=2/x at x=a is -2/a^2.

The missing value of x will be 9.6 mL.

A ratio is a collection of ordered integers a and b represented as a/b, with b never equaling zero. A proportionate expression is one in which two items are equal.

The equation is given below.

12.5 mg : 5 mL = 24 mg : x mL

Then the value of x will be

12.5 / 5 = 24 / x

          x = (24 × 5) / 12.5

          x = 9.6 mL

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Answer:

option b, y = 3/4x - 11

Step-by-step explanation:

Parallel lines have the same slope,

slope = rise / run where the rise is 3 and the run is 4

slope = 3/4

The line is in a upwards trend making the slope positive making choice c and d incorrect

The line passes through (8, -5)

y = 3/4x + b, (x, y)

-5 = 3/4(8) + b

-5 = 6 + b

-5 - 6 = 6 - 6 + b

-5 - 6 = b

-11 = b

y = 3/4x - 11

[tex](5x + 7)(8x + 7) \\ \\ 5x + 7 = 0 \\ \\ 5x = - 7 \\ \\ x = \frac{ - 7}{5} \\ \\ 8x + 7 = 0 \\ \\ 8x = - 7 \\ \\ x = \frac{ - 7}{8} .[/tex]

the values of x are -7/5 and -7/8 .

Hi!

___________________________________________________________

[tex]\rightsquigarrow\circ\boldsymbol{Answer.}\circ\leftharpoonup[/tex]

[tex]\rightsquigarrow\circ\boldsymbol{Explanation}\circ\leftharpoonup[/tex]

Set each factor equal to 0.

[tex]\twoheadrightarrow\sf 5x+7=0[/tex]

[tex]\twoheadrightarrow\sf 8x+7=0[/tex]

[tex]\bullet[/tex] Solve each equation

[tex]\twoheadrightarrow\sf 5x+7=0[/tex]

[tex]\bullet[/tex] Subtract 7 from both sides

[tex]\twoheadrightarrow\sf 5x=-7[/tex]

[tex]\bullet[/tex] Divide both sides by 5

[tex]\underline{\twoheadrightarrow\sf x=-\cfrac{7}{5}}[/tex]

[tex]\bullet[/tex] Now let's solve the second equation

[tex]\twoheadrightarrow\sf 8x+7=0[/tex]

[tex]\bullet[/tex] Subtract 7 from both sides

[tex]\twoheadrightarrow\sf 8x=-7[/tex]

[tex]\bullet[/tex] Divide both sides by 8

[tex]\underline{\twoheadrightarrow\sf x=-\cfrac{7}{8}}[/tex]

[tex]\bullet[/tex] Great job, we found the two possible values

--

Hope that this helped! Best wishes.

[tex]\textsl{Reach far. Aim high. Dream big.}\\\boldsymbol{-Greetings!-}[/tex]

--

Answer:

y≤x²+4x-1.

Step-by-step explanation:

1) to define the equation of the given graph; it is y=x²+4x-1 (its vertex is (-2;-5));

2) to define inequation accorging to the given graph (the area outside of the parabola means ≤).

Answer:

$1710

Step-by-step explanation:

let me know if you want an explanation :))

Answer: 80%

Step-by-step explanation:

Since only 2 out of 10 women dropped out, 10 - 2 = 8

One woman = 10%, 8 x 10% = 80%

The percentage of the women who moved to the next stage is 80%.

Percentage can be described as a fraction out of an amount that is usually expressed as a number out of hundred.

Women who moved to the next stage: 10 - 2 = 8

(8/10) x 100 = 80%

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After taking into consideration the advantages in tax management, it will not be beneficial for Raphael and Martina to get married and avail tax benefits.

The individual taxable incomes of Raphael and Martina after availing the standard deductions will be $33,000 and $3,400 respectively. Now the computation of taxation liabilities will be computed as,

For Raphael, 10% of $33,000= $3,300;

For Martina, 10% of $3,400 = $340.

However, the joint income will be $61,200 and taxation liabilities of Raphael and Martina will be,

[tex]\rm Taxable\ Income = Total\ Income - Standard\ Deduction\\\\\rm Taxable\ Income =61200-24800\\\\\rm Taxable\ Income =\$36400[/tex]

Solving further,

[tex]\rm Joint\ Taxation = (\frac{10}{100}\ x\ 19750) + (\frac{12}{100}\ x\ 16650)\\\\\rm Joint\ Taxation = 1975+1998\\\\\rm Joint\ Taxation = \$3973[/tex]

Now, it can be compared that the joint taxation is higher than the summation of individual taxation of Raphael and Martina, and thus, tax benefits are not enough for Raphael and Martina to get married.

Hence, the tax benefits of Raphael and Martina after getting married are given as above.

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Using the normal distribution, it is found that the girl's score of 10 is higher than 99.62% of the population.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation are given, respectively, by:

[tex]\mu = 6, \sigma = 1.5[/tex].

Her z-score is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{10 - 6}{1.5}[/tex]

Z = 2.67

Z = 2.67 has a p-value of 0.9962.

Hence her score is higher than 99.62% of the population.

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Answer:

Step-by-step explanation:

2 ( x + 3 ) / 4 ( x + 1 )

2 (x + 3) ÷4 (x + 1)

2 (x + 3) ÷ 2×2(x+1)

cancel out the 2 in the numerator with the 2 in the denominator

(x + 3) ÷ 2(x + 1)

x+3 / 2(x+1)

The value of x is 15° and the type of quadrilateral is a rhombus.

Here, we are given,

m∠A = (7x)◦, m∠B = (4x + 5)◦, m∠C =(6x + 15)◦, m∠D = (6x −5)◦

So, we will have

7x+4x+5+6x+15+6x-5=360°

23x+15°=360°

23x=345°

x=345°/23°

x=15°

Hence, the angles of the quadrilateral are:

m∠A = (7x)◦=105°,

m∠B = (4x + 5)◦ =65°

m∠C =105°

m∠D = (6x −5)◦ =85°

Since the diagonal bisects ∠B and ∠D, we get that the quadrilateral is a rhombus.

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The height of the pole is 6.50 meters

To calculate the height of the pole, we will use of the following equivalent ratios.

By Pythagoras theorem, we have:

[tex]x ^2 = 2^2 + 3^2\\\\x ^2 = 4 + 9\\\\x = \sqrt{13}[/tex]

So, we have:

[tex]h = \dfrac{\sqrt{13}^2 }{2} \\\\h = \dfrac{13}{2}\\\\h = 6.5[/tex]

Hence, the height of the pole is 6.50 meters

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Answer:

answer is 5

Step-by-step explanation:

I think so

if yes L I k e

Answer:

40600 = 4.06 × 104.

Step-by-step explanation:

Using a system of equations, the total number of marbles that they have is given by:

A. 27.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

The variables are given as follows:

Eve has two more marbles than Solene, hence:

x = y + 2.

Solene has twice as many marbles as Steve, hence:

Steve has 7 less marbles than eve, hence:

z = x - 7.

Hence:

[tex]\frac{y}{2} = x - 7[/tex]

y = 2(x - 7)

y = 2(y + 2 - 7)

y = 2y - 10

y = 10.

Then:

Hence the total is given by:

T = 12 + 10 + 5 = 27.

Which means that option A is correct.

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Answer:

it is 18 by unknown number

The correct answer is option D.It is the graph that represents two quantities in a proportional relationship.

A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.

As we can see graph D is showing the correct proportionality. We can also create an equation of proportionality as:-

Y = 2x

Put y = 0.5

0.5 = 2 x 0.5 = 1

As we put y=0.5 we get the value of x = 1 as shown in the graph.

Therefore the correct answer is option D.It is the graph that represents two quantities in a proportional relationship.

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Answer:

< $0 --------------$35------ $50>

Step-by-step explanation:

wait that's not the full question but uh I assume that's 30% off $50?

it would be 0.3x50 which is 15 and 50-15 is 35.

the range is 0 - $50 if I'm not mistaken
< $0 -------------------------- $50> scuffed number line
but 35 is somewhere around here?
< $0 --------------$35------ $50>

Answer:

B) 10 cm

Step-by-step explanation:

Hello!

We can use the Pythagorean theorem to solve for the hypotenuse.

Formula: [tex]a^2 + b^2 = c^2[/tex]

We can plug in the values for each leg to solve for the hypotenuse.

The answer is Option B: 10 cm

No, your paycheck is incorrect. The gross salary will be 342.25.

The amount of money paid to any employee without any deductions of the taxes or anything is called as gross salary.

The gross salary will be calculated as follows:-

40x 7.25= $290.00 (base salary)

5x  7.25 = 36.25  (overtime)

.02x 800= 16.00 (commission)

Gross salary will be = 36.25 + 16  + 290 = $324.25

Therefore your paycheck is incorrect. The gross salary will be 342.25.

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Total: 48

DIning Hall: 48(3/8)=18

so theres 30 left for the classes

30/5(#of classes)=6 per class

The attached graph represents the graph of the parallel lines

The equation of the lines are linear equation

A linear equation is represented as:

y = mx + b

Where b represents the y-intercept.

Using the above form of linear equation as a guide, the equations of the lines are

y = -x + 5

y = -x + 2

y = -x - 3

y = -x - 2

Where -5, 2, -3 and -2 are the given y-intercepts and y = -x is the base equation.

Next, we plot the equations on a coordinate grid

See attachment

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Since AC, MN and DB intersect at O, ∠AOM ≅ NOC and ∠MOD ≅ ∠BON by the vertical angles theorem. It is given that ∠BON ≅ ∠NOC, so by the transitive property of congruence, ∠AOM ≅ ∠MOD

An equation is an expression that shows the relationship between two or more numbers and variables.

An angle is formed from the intersection of two or more lines. Types of angles are acute, obtuse and right.

Since AC, MN and DB intersect at O, ∠AOM ≅ NOC and ∠MOD ≅ ∠BON by the vertical angles theorem. It is given that ∠BON ≅ ∠NOC, so by the transitive property of congruence, ∠AOM ≅ ∠MOD

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Answer:

6n+1

Step-by-step explanation:

Eliminate the parenthesis by changing the symbol of each term inside

3+[5n-2+n]

Eliminate the bracket and group similar terms

5n+n+3-2

Simplify terms

6n+1