2. What is a solution of x2 + 6x = -5? (1 point)x= -6x=-1Ox=1x=6

Answer:

unknown

Step-by-step explanation:

Answer:

541.5 ksh

Step-by-step explanation:

The rate at which the volume of the cylinder is changing is 600 mm^3/min, and the rate at which the surface area is changing is 240π mm^2/min.

To find the rate at which the volume and surface area of the cylinder are changing, we can use the given formulas for volume and surface area and differentiate them with respect to time. Let's calculate the rates at the moment when the radius of the base is 10 mm.

Given:

Radius rate of change: dr/dt = 3 mm/min

Height: h = 20 mm

Radius: r = 10 mm

Volume of the cylinder (V) = \(r^2h\)

Differentiating with respect to time (t), we have:

dV/dt = 2rh(dr/dt) + \(r^2\)(dh/dt)

Since the height of the cylinder is constant, dh/dt = 0.

Substituting the given values:

dV/dt = 2(10)(20)(3) + (10^2)(0)

dV/dt = 600 + 0

dV/dt = 600 mm^3/min

Therefore, the rate at which the volume of the cylinder is changing at the given moment is 600 mm^3/min.

Surface area of the cylinder (SA) = 2πrh + 2π\(r^2\)

Differentiating with respect to time (t), we have:

dSA/dt = 2πr(dh/dt) + 2πh(dr/dt) + 4πr(dr/dt)

Again, since the height of the cylinder is constant, dh/dt = 0.

Substituting the given values:

dSA/dt = 2π(10)(0) + 2π(20)(3) + 4π(10)(3)

dSA/dt = 0 + 120π + 120π

dSA/dt = 240π mm^2/min

Therefore, the rate at which the surface area of the cylinder is changing at the given moment is 240π mm^2/min.

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FOR ARITHMETIC

\(lhs = 9 - 4 \\ lhs = 5 \\ rhs = 4 - 1 \\ rhs= 3 \\ \\ lhs \: not = rhs\)

SINCE THERE IS NO COMMON DIFFERENCE LET US TEST FOR A GEOMETRIC SEQUENCE.

\(lhs = \frac{9}{4} \\ \\ rhs = \frac{4}{1} \\ rhs = 4 \\ \\ lhs \: not = rhs\)

THERE IS NO COMMON DIFFERENCE NOR A COMMON RATION THIS MEANS THAT THE SEQUENCE IS NEITHER AN ARITHMETIC NOR A GEOMETRIC SEQUENCE.

THE OPTION IS A.NEITHER.

Answer:

  9) D: (-4, 4]; R: [-6, -4]

  10) D: [-5, -5]; R: (-7, ∞)

Step-by-step explanation:

You want the domain and range of the relations shown on the given graphs.

The domain of a relation is the set of x-values for which it is defined. An open circle indicates that point is not included in either the domain or range.

The range of a relation is the set of y-values that the relation produces. An open circle indicates the y-value at that point is not in the range.

The graph has an open circle at x = -4 on the left, and a solid dot at x = 4 on the right. All of the x-values between these have corresponding y-values.

The domain is (-4, 4].

The bottom (minimum) of the curve lies on the line y = -6, so that is the lowest value in the range. The relation produces all y-values between -6 and -4. The solid dot at (4, -4) means -4 is included in the range.

The range is [-6, -4].

The vertical line at x=-5 means -5 is the only value in the domain.

The domain is [-5, -5].

The vertical line extends upward from an open circle at y = -7. The open circle means -7 is not part of the range.

The range is (-7, ∞).

Answer:

9)  Domain:  (-4, 4]

    Range:  [-6, -4]

10)  Domain:  [-5]

    Range:  (-7, ∞)

Step-by-step explanation:

Definitions

An open circle indicates the value is not included in the interval.

A closed circle indicates the value is included in the interval.

An arrow shows that the function continues indefinitely in that direction.

Interval notation

( or ) : Use parentheses to indicate that the endpoint is excluded.

[ or ] : Use square brackets to indicate that the endpoint is included.

Domain & Range

The domain is the set of all possible input values (x-values).

The range is the set of all possible output values (y-values).

From inspection of the graph, the minimum x-value is x = -4 and the maximum x-value is x = 4.

There is an open circle at endpoint (-4, -4).  Therefore, x = -4 is not included in the domain.

There is an closed circle at endpoint (4, -4).  Therefore, x = 4 is included in the domain.

Therefore, the domain of the relation is restricted:  (-4, 4]

From inspection of the graph, the minimum y-value is y = -6 and the maximum y-value is y = -4.

This maximum value is included in the range since there is a closed circle at (4, -4).

Therefore, the range of the relation is restricted:  [-6, -4]

From inspection of the graph, the line is a vertical line at x = -5.

Therefore, the domain of the relation is restricted to x = -5:  [-5]

From inspection of the graph, the minimum y-value is x = -7.  

This minimum value is not included in the range since there is an open circle at (-5, -7).

There is an arrow on the other endpoint of the line, indicating that the line continues indefinitely in that direction.

Therefore, the range of the relation is restricted:  (-7, ∞)

Answer:

30

Step-by-step explanation:

b×h

6×5=30

gggffcguhh

Answer:

a. 5

b. 36

c. 1/3

d. 1/6

Step-by-step explanation:

a. The answer is five because 9 people bike and 4 people walk and 9-4 is equal to 5

b. The is answer is 36 because 12 people walked, 9 people biked, 4 people walked, 6 people used a motorcycle and 5 people used a cab and 12+9+4+6+5=36

c. The answer is 1/3 because 12 people walked to school and there are 36 people in the class so 12/36 people walked to school, which can be simplified to 1/3.

d. The answer is 1/6 because 6 people used a motorcycle to go school and there are 36 people in the class so 6/36 people used a motorcycle which is equal to 1/6

Answer:

k=1/5

Step-by-step explanation:

y=kx so

1=1/5(5) yes

3=1/5(15)yes

5=1/5(25)yes

7=1/5(35)yes

Answer:

5×5=25

8×5÷2=20

25+20= 45

area of a composite 45

Answer:

10 hours

Step-by-step explanation:

380 - 80 = 300

30 : 1 = 300 : x

x = 300 / 30

x = 10

ANSWER

7.2

EXPLANATION

We want to find 6% of $120.

This means that we want to find 6 out of 100 multiplied by 120 (since per cent means per 100).

That is:

That is the answer.

The compound amount after 3 years is $2275.22.

In this case, you are given:

Principle = $2,000

rate = 0.0353

time = 3

You need to find A, the compound amount after 3 years.

To do this, you need to plug in the values of P, r and t into the formula and use a calculator:

A=P×e^rt

A=2000×(e)^0.0353×3

A≈2275.22

Therefore, by the compound interest the answer will be $2275.22.

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Answer:

4 5/8

Step-by-step explanation:

Rewriting our equation with parts separated

=4+12+18

Solving the fraction parts

12+18=?

Find the LCD of 1/2 and 1/8 and rewrite to solve with the equivalent fractions.

LCD = 8

48+18=58

Combining the whole and fraction parts

4+58=458

Answer:

Step-by-step explanation:

Given formula:

To solve for k, multiply both sides by 2 and divide by x²:

Answer:

\(\sf\longmapsto \: k = \frac{2E}{x {}^{2} } \)

Step-by-step explanation:

The formula given is :

\(\sf\longmapsto \: E = \frac{1}{2} kx²\)

Now, multiply (×) both sides by 2 and divide (÷) by x^2

\(\sf\longmapsto \: 2E = kx²\)

\(\sf\longmapsto \: k = \frac{2E}{x {}^{2} } \)

The volume of the solid obtained by rotating the region bounded by the curve y = 1 - (x - 5)² in the first quadrant about the y-axis is 51π cubic units.

To find the volume of the solid obtained by rotating the region bounded by the curve y = 1 - (x - 5)² in the first quadrant about the y-axis, we can use the method of cylindrical shells.

The formula for the volume using cylindrical shells is:

V = 2π ∫ [a, b] x * h(x) dx

Where:

- V is the volume of the solid

- π represents the mathematical constant pi

- [a, b] is the interval over which we are integrating

- x is the variable representing the x-axis

- h(x) is the height of the cylindrical shell at a given x-value

In this case, we need to solve for x in terms of y to express the equation in terms of y.

Rearranging the given equation:

x = 5 ± √(1 - y)

Since we are only interested in the region in the first quadrant, we take the positive square root:

x = 5 + √(1 - y)

Now we can rewrite the volume formula with respect to y:

V = 2π ∫ [c, d] x * h(y) dy

Where:

- [c, d] is the interval of y-values that correspond to the region in the first quadrant

To determine the interval [c, d], we set the equation equal to zero and solve for y:

1 - (x - 5)² = 0

Expanding and rearranging the equation:

(x - 5)² = 1

x - 5 = ±√1

x = 5 ± 1

Since we are only interested in the region in the first quadrant, we take the value x = 6:

x = 6

Now we can evaluate the integral to find the volume:

V = 2π ∫ [0, 1] x * h(y) dy

Where h(y) represents the height of the cylindrical shell at a given y-value.

Integrating the expression:

V = 2π ∫ [0, 1] (5 + √(1 - y)) * h(y) dy

To find h(y), we need to determine the distance between the y-axis and the curve at a given y-value. Since the curve is symmetric, h(y) is simply the x-coordinate at that point:

h(y) = 5 + √(1 - y)

Substituting this expression back into the integral:

V = 2π ∫ [0, 1] (5 + √(1 - y)) * (5 + √(1 - y)) dy

Now, we can evaluate this integral to find the volume

V = 2π ∫ [0, 1] (5 + √(1 - y)) * (5 + √(1 - y)) dy

To simplify the integral, let's expand the expression:

V = 2π ∫ [0, 1] (25 + 10√(1 - y) + 1 - y) dy

V = 2π ∫ [0, 1] (26 + 10√(1 - y) - y) dy

Now, let's integrate term by term:

\(V = 2\pi [26y + 10/3 * (1 - y)^\frac{3}{2} - 1/2 * y^2]\)] evaluated from 0 to 1

V = \(2\pi [(26 + 10/3 * (1 - 1)^\frac{3}{2} - 1/2 * 1^2) - (26 * 0 + 10/3 * (1 - 0)^\frac{3}{2} - 1/2 * 0^2)]\)

V = 2π [(26 + 0 - 1/2) - (0 + 10/3 - 0)]

V = 2π (25.5)

V = 51π cubic units

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The measure of the missing side length from the given figure is 11 feet.

The right angle is created when two straight lines cross at a 90° angle or when they are perpendicular at the intersection.

It is referred to as a right angle if the angle formed by two rays exactly equals 90 degrees, or π/2.

The adjacent angles are right angles if a ray is positioned so that its terminus is on a line and they are equal.

In the given figure, assuming that all the intersecting sides meet at right angles.

So, the opposite sides are parallel to each other.

Let x be the length of missing side.

Thus, The length of missing side = Sum of length of parallel sides

Now, x= 5+6

= 11 feet

Therefore, the length of side missing is 11 feet.

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Answer: 162°

Step-by-step explanation:

To find the answer to this question, we need to find what 45% of 360 degrees (a circle) is.

First, a percent divided by 100 becomes a decimal.

       45% / 100 = 0.45

Next, "of" means multiplication in mathematics.

       0.45 * 360 = 162

The central angle will be 162°.

The expression can be simplified to obtain as 9 + 6t.

An algebraic expression can be obtained by doing mathematical operations on the variable and constant terms.

The variable part of an algebraic expression can never be added or subtracted from the constant part.

The given algebraic expression is 9 + 12t – 6t.

It can be simplified as follows,

9 + 12t – 6t

Here 9 is a constant.

And, the terms 12t and 6t have the same variable t.

Which implies they are like terms.

Since the like terms in an expression can be added to subtracted, the given expression can be simplified as below,

9 + 12t – 6t

⇒ 9 + 6t

Hence, the simplification of the given expression results as 9 + 6t.

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Answer:

B

Step-by-step explanation:

Look at the X and Y coordinates carefully. X and Y coordinates are swapped and Y coordinate got negative sign.

The average speed of the truck travelling for Johannesburg to Capetown is  0.121995 kilometers / hour

The distance is given as 1.59 km

The time taken is 13 hours 2 minutes.

First we need to convert all values in to a singular metric

1.59km = 1590 meters
13 hours 2 minutes = 782 minutes

average speed = distance/time

Average speed = 1590/782

= 2.0332480818 meters/min

Converting back to Km/H we have

average speed = 0.121995 kilometers per hour

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The first step is to make a sketch of the triangle

The altitude (h= BD) of the triangle divides it into two similar right triangles and the hypothenuse, AC, into two line segments n= AD and m= DC.

The relationship between the altitude and the parts of the hypothenuse follows the ratios:

So, the first step is to determine the altitude of the triangle. To do so, you have to work with ΔABD, "h" is one of the sides of the triangle. Using the Pythagorean theorem you can determine the measure of the missing side:

Write the expression for the missing side:

Replace c=6 and a=2

Now that we have determined the value of the altitude, we can calculate the value of m

Write the expression for m:

-Multiply both sides by m to take it from the denominators place:

-Multiply both sides of the equal sign by the reciprocal of n/h

Replace the expression with h=4√2 and n=2 and calculate the value of m

So DC=m= 16cm and AD=n= 2cm, now you can determine the measure of the hypothenuse:

The hypothenuse is AC=18cm

Answer:

x = 5

Step-by-step explanation:

Given g(x) = - x + 5 and g(x) = 0 , then equate the right sides

- x + 5 = 0 ( subtract 5 from both sides )

- x = - 5 ( multiply both sides by - 1 )

x = 5

The area of the triangle, when a = 2 and c = 3, is 1512 square centimeters.

We must apply the formula for the area of a triangle, which is provided by: to determine the triangle's area.

(1/2) * Base * Height = Area

We can enter the values of a = 2 and c = 3 into the formula given that the base length is 3ac2 and the height is 2 centimetres greater than the base length.

Base length =\(3ac^2 = 3 * 2 * (3^2) = 3 * 2 * 9 = 54\) centimeters

Height is calculated as Base Length + 2 (54 + 2 = 56 centimetres).

Using these values as a substitute in the formula, we obtain:

Area =\((1/2) * 54 * 56 = 1512\) square centimeters

centimetres square

It's crucial to understand that the calculation assumes the triangle is a right triangle with the specified base and height and that the given values of a and c are accurately used in the formula.

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Answer:

If M is the midpoint of AB, then MB is half of AB:

6x + 40 = 2(2x - 30)

6x + 40 = 4x - 60

-4x          -4x

2x + 40 = -60

     -40     -40

2x/2 = -100/2

x = -50

AB = 6(-50) + 40 = -300 + 40 = -260

MB = 2(-50) - 30 = -100 - 30 = -130

Answer:

\(y=5x^2-80x+324\)

Step-by-step explanation:

The value of x is approximately 36.87 degrees.

The alternate internal angles APQ and QSR, as well as the vertical angles APQ and BPS, are congruent in the diagram. As a result, we have:

APQ = BPS, APQ = QSR, etc.

As there are 180 degrees in total between all of the angles in a straight line, we can write:

BPS + QSR equals 180.

When we replace the first equation, we obtain:

QSR + APQ = 180

But, since we are aware that APQ and QSR are congruent, we can write:

2∠APQ = 180

If we simplify, we get:

∠APQ = 90

Due to the complementarity between APQ and DPQ, we have:

∠DPQ = 90 - x

Triangle DPQ can be written using the sine rule as follows:

PQ = PQD / PD = sin(DPQ) / PQ

Inputting the values provided yields:

Sin(x - 90) / 10 = Sin(x - 60) / 8

If we simplify, we get:

cos(x) = 4 / 5

When we calculate the inverse cosine of both sides, we obtain:

x = cos^-1(4/5) ≈ 36.87

Hence, x has a value of almost 36.87 degrees.

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Answer:

$1625

Step-by-step explanation:

Answer:

1495

Step-by-step explanation:

2*1.15*650

Answer: 3

Step-by-step explanation:

The tenths place in this number:

2 = tens place

1 = ones place

.

3 = tenths place

4 hundredths place

Answer is 3.

Look at each place value. The number shows you how much of each are there.

Tenths is the first column after the decimal point and it says 3.