Which equation is equivalent to x2 + 36x= 88?

Answer: choice D 1/2

Step-by-step explanation:

Events A and B are independent if the equation P(A∩B) = P(A) · P(B) holds true.

so

1/6=1/3*p(A)

p(A)=1/2

The exact value of x is √1156 and it follows the Pythagorean triple

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

Legs of the right triangle = 16 and 30

Using the pythagoras theorem, we have

Hypotenuse^2 = the sum of the squares of the other lengths

So, we have

x^2 = 16^2 + 30^2

When evaluated, we have

x^2 = 1156

This gives

x = √1156

Hence, the exact value is √1156

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Answer:

5 groups of 36 with one group with 37.

Hope this helps!

Step-by-step explanation:

35 students × 3 classes = 105 total number of third graders

105 third graders + 112 fourth graders = 217 total number of students

217 students ÷ 6 groups = 36.16666... students in each group

Because students cannot be decimals or fractions and have to be whole, there will be 5 groups of 36 with a 6th group with 37 students.

36 + 36 + 36 + 36 + 36 + 37 = 217

El cuervo está parado en una rama con un trozo de queso en el pico debido a que tenía la intención de reservarlo para otra ocasión. No obstante lo pierde por creer en el zorro.

El cuervo estaría parado en una rama de un árbol con un trozo de queso en el pico debido a que le gustaba reservar comida para tener provisiones disponible para ocasiones futuras. No obstante, en la fábula se menciona que se encuentra con el zorro que tiene el proposito de quitarle el trozo de queso.

Para ello, el zorro comienza a adular al cuervo para que cante y este cae en la trampa, soltando el trozo de queso. Luego de esto, el zorro toma el trozo de queso y se va.

Nota: Esta pregunta está incompleta debido a que tiene información faltante. A continuación se menciona la información faltante.

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Answer

Option C is correct.

There are 21 green and red marbles combined.

Explanation

There are 30 marbles in the bag

40% are red

40% of 30 marbles = 0.4 × 30 = 12 red marbles.

30% are green

30% of 30 marbles = 0.3 × 30 = 9 green marbles.

30% are blue

30% of 30 marbles = 0.3 × 30 = 9 blue marbles.

The question then asks us to compute how many marbles are green and red combined.

There are 9 grren marbles and 12 red marbles, that is, there are (9 + 12) = 21 green and red marbles combined.

Hope this Helps!!!

Answer:

$275

Step-by-step explanation:

25600-2500=23100 how much is left to pay

7*12=84 months left till college

23100/84=275 he would have to save per month

The 14th term of the geometric sequence will be -1220703125.

What is geometric sequence?

The sequence where each word is varied by another by a common ratio is known as a geometric progression or geometric sequence. When we add a constant (which is not zero) to the term before it, the sequence's subsequent term is created. The following symbols stand in for it: a, ar, ar2, ar3, ar4, etc.

Geometric Progression (GP), a form of sequence in mathematics, is a series in which each subsequent term is created by multiplying each preceding term by a set integer, known as a common ratio. A geometric sequence of integers that follows a pattern is another name for this development.

\(1*(-5)^{13}\)The terms are given, 1,-5,25

a = 1

r = -5/1 = -5

The 14th term will be= \(ar^{13}\)

= \(1*(-5)^{13}\)

= -1220703125

Hence, the 14th term of the geometric sequence will be -1220703125.

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d=√((x2-x1)²+(y2-y1)²)

using above formula,

AB= 4.47

BC= 5

CD = 4.47

DA = 5

Area = L×B = 5 × 4.47 = 22.35 sq unit.

See alternative y coordinates are equal so this is rectangle

AD

BC

AB

CD

Area

Answer:

f ( - 2 ) = - 2

Step-by-step explanation:

Step 1:

f ( x ) = 3x + 4        Equation

Step 2:

f ( - 2 ) = 3 ( - 2 ) + 4     Input x value

Step 3:

f ( - 2 ) = - 6 + 4       Combine Like Terms

Answer:

f ( - 2 ) = - 2          Combine Like Terms

Hope This Helps :)

3) The equation of the linear model would be y = 7.5x+60.

4) If Adam studies for 6 hours then his score would be 88.

What is the Linear equation?

An algebraic equation with only a constant and a first-order (linear) term is said to be linear if it has the formula y = mx + b, where m is the slope and b is the y-intercept. The above is occasionally referred to as a "linear equation with two variables," where y and x are the variables.

y = mx + c

where m denotes the slope.

The y-intercept is represented by the constant c. (Where x is zero)

In our instance, y-intercept equals 60.

The line's equation will therefore be:

y = mx + 60

y = mx + 60

There are given the line's coordinates (4, 90). These considerations will thus satisfy the equation.

90 = 4*m + 60

4.m = 30 m = 7.5 m = 7.5 y = 7.5x + 60 y = 7.5 * 6 + 60 y = 45 + 60 y = 105 is

y = 7.5x + 60.

If Adam's study for 6 hours then his score would be

y = 7.5x + 60.

y = 7.5(6) + 60

y = 105

Hence,

3) The equation of the linear model would be y = 7.5x+60.

4) If Adam studies for 6 hours then his score would be 88.

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\(\begin{array}{ccll} \stackrel{guys}{good}&\stackrel{guys}{bad}\\ \cline{1-2} 15&4\\ 75&x \end{array}\implies \cfrac{15}{75}=\cfrac{4}{x}\implies \cfrac{1}{5}=\cfrac{4}{x}\implies x = 20\)

Number of bad guys = 12

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.

Given,

Ratio of good to bad guys = 15:4 = 15/4

No. of good guys = 75

Let the no. of guys be x

⇒ 15:4 = 75:x

⇒ 15/4 = 75/x

Cross multiplying

15 x = 75×4

x = (75/15)×4

No. of bad guys = (75/15)×4

                           = 3 × 4

No. of bad guys = 12

Hence, there are 12 bad guys.

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Answer:

7

Step-by-step explanation:

13.07 minus 6.07 is 7

7 divided by 1 is 7

ans is 7

The correct expression is 5/a = 1. There is no need to introduce an additional variable "x".

In such a fraction, the value that appears above the horizontal line is referred to as the numerator.

It represents the number of pieces removed from the whole. The denominator of a fraction is the numerical value that comes before the brings together various.

The error in the reasoning is that it assumes that multiplying the second fraction by "x" will result in an equivalent expression to 5/a. However, this is not necessarily true.

To correct the error, we can use the property of reciprocals, which states that if a/b = c/d, then b/a = d/c. Using this property, we can rewrite the given equation as:

a/5 = b/3

5/a = 3/b (multiplying both sides by 5/a)

5/a = (b/3) * (3/b) (multiplying both sides by the reciprocal of b/3)

5/a = 1

Therefore, the correct expression is 5/a = 1. There is no need to introduce an additional variable "x".

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Point Y is (6, -1)

Subtract 6 from the y coordinate in point y since it is translated down. keep the x coordinate since it is only being translated up and down, or by the y axis

In order to find the height of 2 different 3-D shapes, we must identify which dimension represents the height for each individual shape and then add them together.

The first thing is that we must identify which dimension represents the height for each individual shape, for instance, if one shape is a rectangular prism, its height would be the length of one of its sides.

After we identified the height for each shape, you can add them together to get the total height of the composite figure, but, we must understand that this method assumes that the two shapes are stacked vertically on top of each other with their bases aligned.

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Answer:

Becky is 7 years old.

Step-by-step explanation: Let b - Becky's age ; Equation - 3b = 21. Divide both size by 3 to isolate the variable.

Answer:

Becky's 7 seven years old

Step-by-step explanation:

If 21 = 3x

x = 21/3

x = 7

Hope this helps :)

Pls brainliest...

Answer:

\((x - 12)(x +11)\)

Step-by-step explanation:

Hello!

We can factor by grouping. Find two numbers that multiply to -132 and add to -1.

The factored form is \((x - 12)(x +11)\).

Answer: 519 120

Step-by-step explanation:

84*84=7056

7056/7=1008

1008*515=519 120

Answer:

256 miles

Step-by-step explanation:

1 cm = 8 miles

32 cm = x miles

32 * 8 = 256 miles

a. The  slope of the curve at the point (4,16)   is approximately 1.165, and at the point (16,4)  is approximately -0.496.

b. The   curve has a horizontal tangent line at the points(0,0) and (3,27).

c. The   curve has a vertical tangent lineat the points (0,0) and (65/2, (65/2)³).

a. To find the   slope of the curve given by the equation x³ + y³ - 65xy = 0 at the points (4,16) and (16,4),we can differentiate the equation implicitly with respect to x and solve for dy/dx.

Differentiating the equation with respect to x, we have  -

3x² + 3y²(dy/dx) - 65y - 65x(dy/dx) = 0

To find the slope at a specific point, substitute the x and y coordinates into the equation and solve for dy/dx.

For the point (4,16)  -

3(4)² + 3(16)²(dy/dx) - 65(16) - 65(4)(dy/dx) = 0

48 + 768(dy/dx) - 1040 - 260(dy/dx) = 0

508(dy/dx) = 592

(dy/dx) = 592/508

(dy/dx) ≈ 1.165

For the point (16,4)  -

3(16)² + 3(4)²(dy/dx) - 65(4) - 65(16)(dy/dx) = 0

768 + 48(dy/dx) - 260 - 1040(dy/dx) = 0

(-992)(dy/dx) = 492

(dy/dx) = 492/(-992)

(dy/dx) ≈ -0.496

Thus, the slope of the   curve at the point (4,16) isapproximately 1.165, and at the point (16,4) is approximately -0.496.

b. To find the point where the curve has   a horizontal tangent line, we need to find the x-coordinate(s)where dy/dx equals zero.

This means   the slope is zero and the tangent line is horizontal.

From the derivative we obtained earlier  -

3x² + 3y²(dy/dx) - 65y - 65x(dy/dx) = 0

Setting dy/dx equal to zero  -

3x² - 65y = 0

Substituting y = x³/65 into the equation  -

3x² - 65(x³/65) = 0

3x² - x³ = 0

Factoring out an x²  -

x²(3 - x) = 0

This equation has two solutions  -  x = 0 and x = 3.

hence, the curve has a horizontal   tangent line at the points(0,0) and (3,27).

c. To find the point where the curve has a vertical tangent line, we need to find the x-coordinate(s)   where the derivative is undefinedor approaches infinity.

From the derivative  -

3x² + 3y²(dy/dx) - 65y - 65x(dy/dx) = 0

To find the vertical tangent line, dy/dx should be undefined or infinite. This occurs when the denominator of dy/dx is zero.

Setting the denominator equal to zero:  -

65x = 65y

x = y

Substituting this condition back into the original equation  -

x³ + x³ - 65x² = 0

2x³ - 65x² = 0

x²(2x - 65) = 0

This equation has two solutions  - x = 0 and x = 65/2.

Therefore, the curve has a vertical tangent line   at the points (0,0)

and(65/2, (65/2)³).

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The United States' decision to remain neutral was motivated by its over $1 billion in annual trade with Europe.

Early 20th-century American trade with Europe helped the US remain neutral by enabling it to maintain business ties with both the Allied and Central Powers.

The US was able to avoid taking a political stance and maintain its neutral status by supplying goods to both sides of the conflict. Additionally, trade helped the US maintain its economic stability because it would have been detrimental to the nation's economy to break off trade with one party.

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With the concept of proportion and time unit conversion from minutes to seconds, The answer is 1980 feet is travelled in one minute.

Proportion refers to the relationship between two or more quantities or values, often represented as a ratio or fraction. It can also refer to the relative size or scale of something in relation to something else. In mathematics, a proportion is an equation that states that two ratios are equal. For example, "the ratio of apples to oranges is 2:3" can be written as the proportion "2/3 = x/y," where x and y represent the number of apples and oranges. In statistics, a proportion is a measure of the frequency with which an event occurs, often expressed as a decimal or percentage.

Speed is a scalar quantity that measures how fast an object is moving. It is often represented by the symbol "v" and is typically measured in units of distance per time, such as meters per second (m/s) or miles per hour (mph). Speed is defined as the magnitude of an object's velocity, which is a vector quantity that also includes information about the direction of motion. For example, an object that is moving at a constant speed of 50 miles per hour to the north has a velocity of 50 mph to the north. Speed can also be calculated by dividing the distance traveled by the time it took to travel that distance, such as speed = distance / time.

car travels 66feet in 2 seconds.

car travels 66/2 feet in 1 seconds.

1 minute = 60 seconds

in 1 minute, car travels 33*60 = 1980 feet.

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Answer:

Step-by-step explanation:

The general equation of a circle can be expressed as (x-a)²+(y-b)² = r² where (a,b) is the centre of the circle and r is the radius.

To show that the equation x² + y² +6y + 2 = 0 represents a circle, we need to write it in the format above using the completing the square method.

Given x² + (y² +6y) + 2 = 0

First we need to complete the square of the square in parenthesis by adding the square of half of the coefficient of y i.e \((\frac{1}{2}*6) ^2\) to the equation and adding the constant to the other side of the equation as well.

x² + (y² +6y) + 2 = 0

\(x^2+(y^2+6y+(\frac{1}{2}*6) ^2)+2 = 0+(\frac{1}{2}*6) ^2\\x^2+(y^2+6y+(3) ^2)+2 = 0+3 ^2\\x^2+(y^2+6y+9)+2 = 0+9\\x^2+(y+3)^2+2 = 9\\x^2+(y+3)^2+2-2 = 9-2\\x^2+(y+3)^2 = 7\\(x-0)^2+(y+3)^2 = 7\\\)

Hence the equation represents a circle with centre C at (0, -3) and radius of √7

Answer:

The answer is B (\(\sqrt[6]{2}\))

You have guessed it correctly

Answer:

229.50 ÷ 8.50= 27 people

a. The answer is: The fewest number of multibase blocks required to represent 20 longs in base seven is 2 flats.

b. The answer is: The fewest number of multibase blocks required to represent 10 longs in base three is 3 flats and 1 unit.

a. To represent 20 longs in base seven, we need to find the fewest number of multibase blocks required.

In base seven, we have the following conversions:

1 long = 1 unit

1 flat = 10 units

1 block = 10 flats

To represent 20 longs, we can use 2 flats (each flat representing 10 units) and 0 units since there are no remaining units.

So, the fewest number of multibase blocks required would be 2 flats.

Therefore, the answer is: The fewest number of multibase blocks required to represent 20 longs in base seven is 2 flats.

b. To represent 10 longs in base three, we need to find the fewest number of multibase blocks required.

In base three, we have the following conversions:

1 long = 1 unit

1 flat = 3 units

1 block = 3 flats

To represent 10 longs, we can use 3 flats (each flat representing 3 units) and 1 unit since there is one remaining unit.

So, the fewest number of multibase blocks required would be 3 flats and 1 unit.

Therefore, the answer is: The fewest number of multibase blocks required to represent 10 longs in base three is 3 flats and 1 unit.

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Answer:

Step-by-step explanation:

3 sinθ=3 cos 2θ

sin θ=cos 2θ

sinθ=1-2sin² θ

2sin²θ+sin θ-1=0

2sin²θ+2sinθ-sinθ-1=0

2sin θ(sin θ+1)-1(sin θ+1)=0

(sin θ+1)(2 sin θ-1)=0

sin θ=-1=-sin 90=sin (180+90)

θ=270

or sin θ=1/2=sin 30,sin (180-30)

θ=30,150

solution set is {30,150,270}