What are the solutions of the equation x4 + 95x2 – 500 = 0? Use factoring to solve.


x=+- sqrt 5 and x = ±10
x=+- sqrt i5 and x = ±10i
x=+- sqrt 5 and x = ±10i
x=+- sqrt i5 and x = ±10

Answer:

A. The ball is at the same height as the building between 8 and 10 seconds after it is thrown.

C. The ball reaches its maximum height about 4 seconds after it is thrown

Step-by-step explanation:    • The ball is at the same height as the building between 8 and 10 seconds after it is thrown. TRUE - the height is zero somewhere in that interval, hence the ball is the same height from which it was thrown, the height of the roof of the building.

• The height of the ball decreases and then increases. FALSE - at t=2, the height is greater than at t=0.

• The ball reaches its maximum height about 4 seconds after it is thrown. TRUE - the largest number in the table corresponds to t=4.

• The ball hits the ground between 8 and 10 seconds after it is thrown. FALSE - see statement 1.

• The height of the building is 81.6 meters. FALSE - the maximum height above the building is 81.6 meters. Since the ball continues its travel to a distance 225.6 meters below the roof of the building, the building is at least that high.

The equation representing this situation is expressed as [tex]\[ 10h + 8 = 48 \][/tex] and

Demi received 4 hours of tutoring services.

Let's denote the number of hours Demi received tutoring services as [tex]\( h \).[/tex]

The equation representing this situation can be expressed as:

[tex]\[ 10h + 8 = 48 \][/tex]

Now, let's solve for [tex]\( h \):[/tex]

[tex]\[ 10h = 48 - 8 \][/tex]

[tex]\[ 10h = 40 \][/tex]

[tex]\[ h = \frac{40}{10} \][/tex]

[tex]\[ h = 4 \][/tex]

So, Demi received 4 hours of tutoring services.

To find the equation representing the situation, we need to consider the total cost Demi paid. She paid $10 per hour for tutoring services, so the cost for the tutoring service itself is [tex]\( 10h \),[/tex] where [tex]\( h \)[/tex] represents the number of hours of tutoring. Additionally, she paid $8 for books and supplies, which is a fixed cost regardless of the number of hours. Therefore, we add $8 to the cost equation. This gives us [tex]\( 10h + 8 = 48 \).[/tex]

Next, we solve this equation to find the value of [tex]\( h \),[/tex] which represents the number of hours of tutoring. We subtract 8 from both sides to isolate the term [tex]\( 10h \),[/tex] giving us[tex]\( 10h = 40 \)[/tex]. Then, we divide both sides by 10 to solve for [tex]\( h \),[/tex] which gives us[tex]\( h = \frac{40}{10} = 4 \).[/tex]

So, Demi received 4 hours of tutoring services.

Complete question:

For her tutoring services, Thuy charged Demi $10 per hour and $8 for books and supplies. Demi paid a total of $48.00. Which equation represents this situation?

To find the area of a segment of a circle, we can use the formula A = (r^2/2)(θ - sinθ), where r is the radius and θ is the central angle in radians. In this case, the arc measure is 120 degrees and the chord length is 8√3 inches. By plugging in the values and following the steps, we can find that the area of the segment is 3840 - 16√3 square inches.

To find the area of a segment of a circle, we need to know the measure of the arc and the length of the chord. In this case, the arc measure is 120 degrees and the chord length is 8√3 inches. To find the area, we can use the formula A = (r^2/2)(θ - sinθ), where r is the radius and θ is the central angle in radians.

First, we need to find the radius by using the length of the chord. The formula for the radius is r = 2c/sinθ, where c is the length of the chord and θ is the central angle in degrees. Plugging in the values, we get r = 8√3/(2sin60) = 4√3/sin60 = 4√3/(√3/2) = 8 inches. Now we can find the area using the formula A = (r^2/2)(θ - sinθ). Plugging in the values, we get A = (8^2/2)(120 - sin120) = 32(120 - √3/2) = 3840 - 16√3 square inches.

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The length of the side opposite the[tex]\( 30^\circ \)[/tex] angle is 22 units.

To find the length of the side opposite the \( 30^\circ \) angle in a right triangle with a hypotenuse of 44, we can use the sine function:

1. Identify the Known Angle and Hypotenuse: We have an angle of[tex]\( 30^\circ \)[/tex] and a hypotenuse of 44.

2. Use the Sine Function: Since sine relates the opposite side and the hypotenuse in a right triangle, we use the sine function for the [tex]\( 30^\circ \)[/tex] angle.

[tex]\[ \sin(30^\circ) = \frac{\text{opposite}}{44} \][/tex]

3. Sine of 30 Degrees: The sine of [tex]\( 30^\circ \)[/tex] is a known value, which is [tex]\( \frac{1}{2} \).[/tex]

4. Calculate the Opposite Side: Use the sine value to find the opposite side:

[tex]\[ \text{opposite} = 44 \cdot \sin(30^\circ) = 44 \cdot \frac{1}{2} \][/tex]

5. Result: The length of the side opposite the[tex]\( 30^\circ \)[/tex] angle is therefore:

[tex]\[ \text{opposite} = 22 \][/tex]

Final answer:

The truck driver can travel 700 miles on 35 gallons of gas.

Explanation:

In order to determine the distance the truck driver can travel on 35 gallons of gas, we can set up a proportion using the information provided.

The truck driver can travel 560 miles on 28 gallons of gas, so we can set up the proportion:

= 560 miles / 28 gallons

= x miles / 35 gallons.

Cross-multiplying and solving for x, we find that x = 700 miles.

Therefore, the truck driver can travel 700 miles on 35 gallons of gas.

The student asked for the four smallest positive angles where cosine equals ½. By using the unit circle, the angles of 60° and 300° are identified as solutions, with their general solutions given by θ = π/3 + 2kπ and θ = 5π/3 + 2kπ. The four smallest positive answers are thus 60°, 300°, 420°, and 660°.

The student is asking for the four smallest positive angles θ for which the cosine is equal to ½. To find these angles, it helps to recall the unit circle and the fact that the cosine of an angle corresponds to the x-coordinate of a point on the unit circle. The angles with a cosine of ½ in the first 360° (or 2π radians) are those where the corresponding points on the unit circle are at (½, √3/2) and (½, -√3/2). These points correspond to angles of 60° (or π/3 radians) and 300° (5π/3 radians) respectively. However, these are not the only solutions when considering multiple rotations around the circle.

The general solutions for cosine equaling ½ in terms of radians are given by:

The four smallest positive solutions correspond to setting k=0 and k=1 in the above equations, yielding the angles:

Note that these angles are measured in degrees for simplicity, but they can be converted to radians by using the equivalence 180° = π radians. To convert these angles to radians, simply divide by 180 and multiply by π.

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The final velocity of the sprinter is 7.23 meters per second.

Acceleration of any object is defined as the variation in the speed of the object with the variation of time. Acceleration is a vector term and to define it we require both the magnitude and the direction. The unit of acceleration can be m / sec², miles / sec², etc.

Given that a sprinter starts from rest, and accelerates at 1.87 m/s² over a distance of 14.0 m.

The final velocity will be calculated by the equation of the motion formula as below,

V² = u² + 2as

V² = 2 x 1.87 x 14

V² = 52.36

V = √52.36

V = 7.23 meter per second

Hence, the final velocity is 7.23 meters per second.

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Answer:

It's 14 inches on Ed

Step-by-step explanation:

Final answer:

The volume of the sphere is given as 1372π/3 cubic inches. Using the volume formula for a sphere, V = (4/3)πr³, we calculate the radius and then double it to find the diameter, which is 14 inches.

Explanation:

The student asks for the diameter of the great circle of a sphere, given its volume is 1372π/3 cubic inches. To find this, we'll make use of the formula for the volume of a sphere, V = (4/3)πr³, where V represents the volume and r is the radius of the sphere.

Let's start by equating the given volume to the volume formula:

1372π/3 = (4/3)πr³

Cancelling out π and the fraction (4/3) on both sides, we get:

1372/4 = r³

This simplifies to:

343 = r³

Taking the cube root of both sides gives us the radius:

r = ∛343

r = 7 inches

The diameter of the sphere is twice the radius, so:

diameter = 2r = 2 × 7 = 14 inches

Therefore, the diameter of the great circle of the sphere is 14 inches.

Answer: it would be (D)

Step-by-step explanation:

Solution to y = 3x - 1: B. (2, 5)

Matching equation for "The sum of -4x and 2 is 9": A. -4x + 2 = 9

Solve x - 6 = -18: A. x = -12

Solve 4x + 3 = 47: A. x = 11

Let's solve each of the given equations one by one:

Solution to y = 3x - 1:

The equation y = 3x - 1 represents a linear relationship between x and y with a slope of 3 and a y-intercept of -1. To find the solution, we can substitute the given options for x and see which one satisfies the equation:

A. (4, 1): 1 = 3(4) - 1 => 1 = 12 - 1 => 1 = 11 (Not a solution)

B. (2, 5): 5 = 3(2) - 1 => 5 = 6 - 1 => 5 = 5 (This is a solution)

C. (4, 3): 3 = 3(4) - 1 => 3 = 12 - 1 => 3 = 11 (Not a solution)

D. (0, -3): -3 = 3(0) - 1 => -3 = 0 - 1 => -3 = -1 (Not a solution)

So, the solution is B. (2, 5).

Matching equation for "The sum of -4x and 2 is 9":

The statement can be translated into the equation: -4x + 2 = 9. So, the correct equation is A. -4x + 2 = 9.

Solving x - 6 = -18:

To solve for x, add 6 to both sides of the equation:

x - 6 + 6 = -18 + 6

x = -12

So, the solution is A. x = -12.

Solving 4x + 3 = 47:

To solve for x, subtract 3 from both sides of the equation:

4x + 3 - 3 = 47 - 3

4x = 44

Now, divide both sides by 4 to isolate x:

(4x)/4 = 44/4

x = 11

So, the solution is A. x = 11.

In summary, the solutions to the given equations are:

B. (2, 5)

A. -4x + 2 = 9

A. x = -12

A. x = 11

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Answer: She earned $ 4 for each package delivered.

Step-by-step explanation:

Since, her total rate of earning = $ 12.50 per hours,

And, she worked for 8 hours.

⇒ She earned in 8 hours = 8 × 12.50 = $ 100

According to the question,

She delivered 25 packages in 8 hours.

⇒ 25 packages = 8 hours

⇒ 25 packages = $ 100

⇒ 1 package = $ 4

Thus, she earned 4 dollars for each package.

To calculate the discount amount on an item with a regular price during a sale of 40% off, use the function d(p) = 0.40 x p.

The question involves creating a mathematical function to calculate the amount of discount during a sale. The store is offering a 40% discount on items, so to find the discount amount d on an item with a regular price p, we can write the function as d(p) = 0.40 * p. Here, p represents the regular price of the item, and d represents the discount amount in dollars that will be subtracted from the regular price.

Answer:

The answer is -8

Hope this helps :)

Answer:

a.

Step-by-step explanation:

took quiz

The missing reason in the geometric proof for step 4 is that all sides of a square are congruent. This property is part of the definition of a square and justifies the statement AB ≅ BC ≅ CD ≅ DA.

The missing reason in the proof is: "all sides of a square are congruent" Option a.

This reason is necessary to establish statement 4: "AB ≅ BC ≅ CD ≅ DA". It's a critical property of a square that all its sides are congruent to each other. Once you establish this, you can proceed with statement 5 using SAS (Side-Angle-Side) congruence to prove △BAD ≅ △ABC, and then finally, using Corresponding Parts of Congruent Triangles are Congruent to conclude BD ≅ AC.

Here is the corrected step:

The probability of picking a pair of red socks is 1/5.

Probability is the chance of occurrence of a certain event out of the total no. of events that can occur in a given context.

Given, There are 5 red socks, 2 white socks and 3 blue socks in a basket.

So, The no. of sample space N(S) = 5 + 2 + 3 = 10.

Now pair of red socks means 2 red socks let it be N(A).

∴ The probability of picking a pair of red socks P(A) = N(A)/N(S).

P(A) = 2/10.

P(A) = 1/5.

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There are 432 total barns when multiplying 48 chicken farms by 9 barns per farm. For question number 27, without knowing the number of mice per barn, we cannot determine the exact number of cats needed to control the grain destruction.

To determine the number of total barns if there are 48 chicken farms near an Ohio town and each farm has 9 barns, we simply need to multiply the number of farms by the number of barns per farm. This can be represented by the equation: 48 farms times 9 barns/farm = 432 barns. Therefore, there are 432 total barns.Now, addressing the second question (Number 27): To calculate the number of cats required to control the destruction of stored grain by mice, we need to find out how many mice are in each barn, and then see how many cats are needed to kill that number of mice. A mouse eats 521 ikats of grain each year, and if we are to prevent the destruction of grain in each of the 24 barns, we need to find out how many mice a single cat can kill in a year, and then divide the number of mice by this figure.If one cat kills 96 mice a year, and assuming each barn has the same number of mice, then for one barn: Total mice killed in one barn/year = Number of cats times 96 mice/cat/year. Therefore, to find the number of cats needed: Number of cats = Total mice in one barn/year extdiv 96 mice/cat/year. Without the number of mice, we cannot complete the calculation. More information on the number of mice per barn is required to give a definitive answer.

Answer:  the correct option is

(a) If x – 5 ≠ 10, then 4x + 1 ≠ 61.

Step-by-step explanation:  We are given to select the correct inverse of the conditional statement p → q if

p : x – 5 =10  and  q : 4x + 1 = 61.

We know that

the inverse of a conditional statement p → q is given by "not p → not q".

Therefore, the inverse of the given statement is

not p → not q

that is, if  x – 5 ≠ 10, then 4x + 1 ≠ 61.

Thus, the required inverse is " x – 5 ≠ 10, then 4x + 1 ≠ 61."

Option (a) is CORRECT.

Answer with Step-by-step explanation:

a. 0.34 × 6=2.04

b. 0.11 × 4=0.44

c. 17 × 0.07=1.19

d. 28 × 0.003= 0.084

e. 3.8 × 5=19

f. 5.931 × 7=41.517

g. 14.07 × 13=182.91

h. 3.005 × 32=96.16

i. 0.8 × 0.3=0.24

j. 0.45 × 0.05=0.0225

k. 0.09 × 0.02=0.0018

l. 0.074 × 0.08=0.00592

m. 2.3 × 0.9=2.07

n. 7.25 × 0.3=2.175

o. 4.53 × .003=0.01359

p. 53.67 × 0.056=3.00552

q. 1.1 × 3.7 =4.07

r. 3.76 × 18.9 =71.064

s. 4.57 × 6.1 =27.877

t. 24.13 × 1.48=35.7124