There are 35 students on the Step Team to raise a total of 3,500 for uniforms. So far they have raised a total of 1,800. How much more money in dollars, does each member of the Step Team need to raise

The solution to the Raoul's equation x² - 6x - 27 = 0 is x = 9; or x = -3

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

Given the equation:

x² - 6x - 27 = 0

Adding 27 to both sides:

x² - 6x - 27 + 27 = 0 + 27

x² - 6x = 27

Adding to both sides the square of half the coefficient of x, that is 9:

x² - 6x + 9 = 27 + 9

(x - 3)² = 36

taking square root of both sides:

√(x - 3)² = √36

x - 3 = ±6

x = 3 ± 6

x = 3 + 6 or; x = 3 - 6

x = 9; or x = -3

The solution to the Raoul's equation x² - 6x - 27 = 0 is x = 9; or x = -3

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Answer:

Add 3 to both sides

Property: Addition property of equality

Step-by-step explanation:

Action: Add 3 to both sides.

⇒ x - 3 =               12

(cancel out)+ 3     + 3

------------------------ -----

     x    =        15  

The property used:

→ equation is true and the same #is added to each side the resulting equation is true. for any #s a,b,c,if a=b then a+c=b+c.

Answer:

36

Step-by-step explanation:

possibility of slices of pie is 12/24, = 1/2

78 desserts, how much i expect is slices of pie

78*(1/2) = 36

We should expect about 39 of the next 78 desserts sold to be slices of pie.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.com

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

Out of 24 desserts sold, 12 were slices of pie.

Therefore, the proportion of slices of pie sold is 12/24 = 1/2.

To estimate the number of slices of pie in the next 78 desserts sold, we can multiply the proportion of slices of the pie by the total number of desserts sold:

(1/2) x 78 = 39

Therefore,

We should expect about 39 of the next 78 desserts sold to be slices of pie.

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The length and width of the piece of​ metal are 20 and 30 inches respectively.

The term “volume” refers to the amount of three-dimensional space taken up by an item or a closed surface. It is denoted by V and its SI unit is in cubic cm.

Dimension of the rectangle;

Width(w)

Length,L= 10 + w

volume of the box = length  * width * height

Dimension of the box;

length of box, (x + 10) - 4  = x + 6

width of box,(x - 4)

height of box =  2

The volume of the box is 1102 in³;

⇒V=lwh

⇒V=2 (x -4)( x + 6) =

⇒1102 in³ = 2x² + 4x - 48

⇒2x² + 4x - 880 = 0

⇒x  + 2x - 440 = 0

⇒(x + 22)(x - 20) = 0

⇒x = 20

⇒x=-22 (value of the dimesion will not be negative.

The width of an original piece of metal is;

Width,w=20 inches

length,l= 30 inches

Hence. the length and width of the piece of​ metal are 20 and 30 inches respectively.

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for an angle of 780°, we can say that is really a 360° + 360° + 60°, so two full revolutions plus an extra 60°. Check the picture below, with the coterminal in green.

Answer:

i think the answer is 25q - 5 / 4

Given the base edge and the height, the lateral area and surface area of the regular hexagonal prism are 168cm² and 251.138cm² respectively.

For a regular hexagonal prism, the Lateral surface area and the surface area is expressed as follows:

Lateral Area = 6a × h

Surface Area = 6ah + 3√3a²

Where a is base edge and h is height.

Given that;

The Lateral Area of the regular hexagonal prism will be;

Lateral Area = 6a × h

Lateral Area = 6( 4cm ) × 7cm

Lateral Area = 24cm × 7cm

Lateral Area = 168cm²

The Surface Area of the regular hexagonal prism will be;

Surface Area = 6ah + 3(√3)a²

Surface Area = 6(4cm × 7cm) + 3(√3)(4cm)²

Surface Area = 168cm² + 3(√3)16cm²

Surface Area = 168cm² + 83.138cm²

Surface Area = 251.138cm²

Given the base edge and the height, the lateral area and surface area of the regular hexagonal prism are 168cm² and 251.138cm² respectively.

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The domain of the function is x > 0.

The correct option is (B)

Domain of a function is defined by the set of x-values of the graph of a function.

as, domain of a function is defined by the set of x-values of the graph of a function.

From the graph we can see that,

x-values are starts from x > 0 [Since x ≠ 0]

Also, moves towards infinity,

Hence, domain of the function be, (0, ∞) or x > 0

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Answer:

B

Step-by-step explanation:

Answer:

21. x = 18.1

22. x =28.7

Step-by-step explanation:

SOH = sin(theta) = opp/hyp

CAH = cos(theta) = adj/hyp

TOA = sin(theta) = opp/adj

21. You would be using tangent.

tan(theta) = Opp/Adj

tan(32°) = x/29

x = 29 * tan(32°)

x = 18.1

22. You would be using cosine

cos(theta) = Adj/Hyp

cos(43°) = 21/x

x * cos(43°) = 21

x = 21 / cos(43°)

x = 28.7

Use a Calculator to help you solve for those side lengths or degrees.

If you were to search of SOHCAHTOA online and find an image you would be able to see their example problem done using

I am not sure if I am allowed to use an online example image since I got warned for some reason without explanation to the warning.

The probability that a student is a female or major in civil engineering is 62%

At a certain college, 49% of the students are female, and 21% of the students major in civil engineering. Furthermore, 8% of the students both are female and major in civil engineering. What is the probability that a randomly selected female student majors in civil engineering?

Let A represent Female and B represents civil engineering.

The above representation means that the given parameters are:

The required probability is calculated as:

P(A or B) = P(A) + P(B) - P(A and B)

This gives

P(A or B) = 49% + 21% - 8%

Evaluate

P(A or B) = 62%

Hence, the probability that a student is a female or major in civil engineering is 62%

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Answer:

The answer is in the picture.

Step-by-step explanation:

By hand, you can factor it. I did it on a website called Cymath.

Answer:

3x(y - 3)(y + 1)

Step-by-step explanation:

Factor 3x out of 3xy^2

Factor 3x out of -6xy

Factor 3x out of -9x

Factor 3x out of 3x(y^2)+3x(-2y)

Factor 3x out of 3x(y^2-2y) + 3x(-3)

The initial point of vector v if it has a magnitude of 10 and the terminal point (-3,3) is option B (-9,-5).

If we have given a vector v of initial point A and terminal point B

v = ai + bj

then the components form as;

AB = xi + yj

Here, xi and yj are the components of the vector.

Given;

The magnitude of 10 and the terminal point (-3,3).

v = ai + bj

v = [tex]\sqrt{a^2 + b^2}[/tex]

10 =  [tex]\sqrt{a^2 + b^2}[/tex]

AB = (-3 - a)i + (3 - b)j

If we put (-9,-5)then

AB = (-3 - a)i + (3 - b)j

AB = (-3 + 9)i + (3 + 5)j

AB = 6i + 8j

Put the value in the vector magnitude

10 =  [tex]\sqrt{a^2 + b^2}[/tex]

   = [tex]\sqrt{6^2 + 8^2}\\\\\sqrt{36+ 64}\\\\\sqrt{100}[/tex]

10 = 10

Thus, The correct option is B (-9,-5).

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Answer:

The answer is 7

Step-by-step explanation:

To find the volume you multiply the width, height, and the length.

Length= 7/3

width= 3/3

height= 9/3

When you multiply you then have to simplify which is 7/1 or 7.

Mark this correct to help me gain!!

Answer:

18 inches = 1.5 feet

8 inches = 2/3 foot

y = 1.5 + (2/3)x

An x-intercept of the continuous function in the table is (-1, 0)

The x-intercept of a line is the point where the line crossed the x-axis or the  point where the value of y is zero.

From the table, the x-intercept are all the point where the value of f(x) is zero. Hence the Which is an x-intercept of the continuous function in the table is (-1, 0)

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The correct answer is 6 / 7 as it is closer to 1.

The fraction is defined as the division of the whole part into an equal number of parts.

The number near 1 will be calculated as:-

7/ 6 = 1.1666

6 / 7 = 0.8571

Difference of the first ratio from one.

1.1666 - 1  = 0.1666

Difference of the second ratio:-

1 - 0.8571 = 0.1429

So the difference of 6 / 7 is lower than the difference of the fraction 7 / 6 from one.

Therefore the correct answer is 6 / 7 as it is closer to 1.

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Answer:

[tex]6644.672~ m^3[/tex]

Step-by-step explanation:

[tex]\text{Volume} = (18.8)^3~ m^3 = 6644.672~ m^3[/tex]

Answer:

A graph shows zeros to be ±3. Factoring those out leaves the quadratic

 (x-2)² +1

which has complex roots 2±i.

The function has roots -3, 3, 2-i, 2+i.

Step-by-step explanation:

Answer:

See below ~

Step-by-step explanation:

The function is :

f(x) = x⁴ - 4x² - 5

=============================================================

Plotting on a graph :

⇒ Once plotted on graph, check where the line of the function intersects the x-axis

⇒ Those will be the zeros of the function

===========================================================

Solution :

⇒ x = -2.236

⇒ x = 2.236

Answer:

No because Us is powerful country canada is also powerful but U S ever sale to candians

The solution to the triangle is A = 92.0, B = 47.9 and C = 40.1

The figure is not given;

However, the question can still be solved without it

The given parameters are:

a = 31, b = 23, and c = 20

Calculate angle A using the following law of cosine

a² = b² + c² - 2bc * cos(A)

So, we have:

31² = 23² + 20² - 2 * 23 * 20 * cos(A)

Evaluate

961 = 929 - 920 * cos(A)

Subtract 929 from both sides

32 =- 920 * cos(A)

Divide both sides by -920

cos(A) = -0.0348

Take the arc cos of both sides

A = 92.0

Calculate angle B using the following law of sine

a/sin(A) = b/sin(B)

So, we have:

31/sin(92) = 23/sin(B)

This gives

31.0189 = 23/sin(B)

Rewrite as:

sin(B) =23/31.0189

Evaluate

sin(B) =0.7415

Take arc sin of both sides

B = 47.9

Calculate angle C using:

C = 180 - 92.0 - 47.9

Evaluate

C = 40.1

Hence, the solution to the triangle is A = 92.0, B = 47.9 and C = 40.1

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The expression of the translated function g(x) is gotten as; g(x) = 2x² - 3

We are given the function;

f(x) = 2x² + 3

Now, when we translate a function f(x) downwards, the new function becomes;

g(x) = f(x) - a

where a is the amount of units by which the graph was translated.

Thus for translation of 6 units vertically downwards;

g(x) = 2x² + 3 - 6

g(x) = 2x² - 3

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Answer: 103/15

Step-by-step explanation:

We can simplify the right-hand side to be [tex]2 \left(\frac{1}{3}+6 \right)=2 \left(\frac{19}{3} \right)=\frac{38}{3}[/tex].

This means we need to solve:

[tex]\frac{1}{2}(5x-9)=\frac{38}{3}\\5x-9=\frac{76}{3}\\5x=\frac{103}{3}\\x=\boxed{\frac{103}{15}}[/tex]

An equation is formed of two equal expressions. The original height of the water in the pool in feet is 5.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Given the equation, 4.75 = x + (-0.25) can be used to find x, the original height of the water in a pool. Therefore, the height of the fool in the beginning is,

4.75 = x + (-0.25)

4.75 + 0.25 = x

x = 5

Hence, the original height of the water in the pool in feet is 5.

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Answer:

Yes, x = 0 is a solution to the given equation

Step-by-step explanation:

Hi Student!

The goal of this question is to determine x = 0 is a solution of the expression that was provided.  The first step that we must take is input 0 into all of the x's that we have in the expression.  Then we just simplify both sides and determine if the end expression is true and if it is then x = 0 is a solution.

Plug in the values

Simplify both sides

Looking at the final expression, we can see that 1 is indeed equal to 1 and since the expression is true, we can say that x = 0 is a solution of the expression that was provided in the problem statement.

Step-by-step explanation:

Scale factor red to blue meaning 42 to 7

42÷7=6

Scale factor is 6

Perimeter of the blue quadrilateral = ?

If perimeter of red = 204

Then we use this following proportion

[tex]204 \div 42 = x \div 7[/tex]

[tex] \frac{204}{42} = \frac{x}{7} [/tex]

Then we cross multiply

42x=7×204

42x=1428

x=34

Area of the blue quadrilateral = ?

If area of the red quadrilateral = 2880

Then we use the following proportion

[tex]2880 \div 42 = x \div 7[/tex]

[tex] \frac{2880}{42} = \frac{x}{7} [/tex]

Then we cross multiply

42x=2880×7

42x=20160

x=480

Some possible ethical issues to this type of testing that they are subjected to unpleasant and hazardous procedures, as well as stress and injury.

Any well-defined method that yields an observable outcome that cannot be precisely predicted in advance is referred to as a experiment. To avoid any ambiguity or surprise, a experiment must be properly defined.

A) Because human experimentation is immoral, animal research has been employed as a research approach.

However, using animals is unethical because they are subjected to unpleasant and hazardous procedures, as well as stress and injury. The use of non-animal methods to substitute animal methods as much as possible will provide both ethical and technical benefits. Researchers should make the use of non-animal methods for a top priority experiments.

B) Even though the purpose of an experiment is to ensure success in rabbits, this is incorrect in people because action is what will operate properly.

The absence of thyroid-stimulating hormone in rabbit serum is a mistaken notion. As a result, it is preferable to test the drug further, and it was a success. As a result, there will be no dysfunctionality for humans.

Thus, some possible ethical issues to this type of testing that they are subjected to unpleasant and hazardous procedures, as well as stress and injury.

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Por razones trigonométricas, encontramos que las alturas de la torre y el edificio son de aproximadamente 11.548 metros y 31.548 metros, respectivamente.

En esta pregunta debemos utilizar conceptos de trigonometría para determinar la altura de los dos edificios. A continuación, tenemos las siguientes expresiones trigonométricas:

Diferencia entre las alturas del edificio y el torre

20 = r₁ · sin 60°

r₁ ≈ 23.094 m

Ahora determinamos el valor de r₂ mediante identidades trigonométricas:

r₂ = r₁ · (cos 60°/cos 45°)

r₂ = (23.094 m) · (cos 60°/cos 45°)

r₂ ≈ 16.330 m

Finalmente, obtenemos las alturas de cada edificio:

Torre

h = (16.330 m) · sin 45°

h ≈ 11.548 m

Edificio

h' = h + 20 m

h' = 11.548 m + 20 m

h' = 31.548 m

Por razones trigonométricas, encontramos que las alturas de la torre y el edificio son de aproximadamente 11.548 metros y 31.548 metros, respectivamente.

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