What are the roots of the quadratic equation below?
2x² + 8x+7= 0
O A. x = = 2√2
1
O B. x =
-8+√120
8
O
O D. x =
C. x = = 4+√/²
-2+√120

Answer:

Step-by-step explanation:

The maximum and minimum points of the function are (a) (3π/2, -1) (-π/2, -1), (π/2, 3)

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

y = –2 cos (x + π/2) + 1.

Calculating the maximum

Here, we have

y = –2 cos (x + π/2) + 1.

Next, we plot the graph of the function

From the graph of the function, we have the maximum points to be (π/2, 3)

Calculating the minimum

Here, we have

y = –2 cos (x + π/2) + 1.

Next, we plot the graph of the function

From the graph of the function, we have the minimum points to be

(3π/2, -1) (-π/2, -1)

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Answer:

353.48 is the smaller number. the difference between the smaller number and the bigger number is 68.09 so you add the two munbers. 421.67 is the other number.

Step-by-step explanation:

The factored form is (5x+2)(x-4).

What is factorization?

A number, matrix, or polynomial may be broken up or decomposed into factors that, when multiplied together, produce the original number, matrix, etc. This process is known as factorization or factoring.

Here, we have

Given:  5 x squared minus 18 x minus 8

we have to find the factored form.

= 5x² - 18x - 8

= 5x² - 20x + 2x - 8

= 5x(x-4) + 2(x-4)

= (5x+2)(x-4)

Hence, the factored form is (5x+2)(x-4).

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Yes, the expression (64+28+76)/6 makes sense as it represents the average quantity of juice per unit when combining all the shown juices.

To determine whether the expression (64+28+76)/6 makes sense, we need to evaluate the components of the expression and consider whether the mathematical operations are valid.

The expression (64+28+76)/6 represents the sum of three numbers (64, 28, and 76), divided by 6. Let's break it down step by step:

Addition: We have three numbers being added together: 64, 28, and 76. The sum of these numbers is 168 (64 + 28 + 76 = 168).

Division: The sum of the three numbers, 168, is then divided by 6. Division is a valid mathematical operation.

Now, let's analyze whether the expression makes sense in the context of Stephen combining all the juice to make fruit punch. The numbers 64, 28, and 76 may represent quantities of juice (in some units) that Stephen is combining. However, without further information or context, we cannot determine if the expression accurately represents the combination of these juices.

If the numbers 64, 28, and 76 represent quantities of juice in the same units (such as milliliters or liters), then the expression (64+28+76)/6 would represent the average quantity of juice per unit. The result, 168/6, would be 28. This would imply that each unit (e.g., glass or serving) of the fruit punch contains an average of 28 units of juice.

In summary, mathematically, the expression (64+28+76)/6 is valid. However, without additional context regarding the units or quantities being represented, it is not possible to determine whether the expression accurately describes the process of combining the juices to make fruit punch.

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If the random variable x is normally distributed with a mean equal to 0.45 and a standard deviation equal to 0.40, then P(x ≥ .75) is 0.9227.

A z-score describes the position of a raw score in terms of its distance from the mean when measured in standard deviation units. The z-score is positive if the value lies above the mean and negative if it lies below the mean.

Given the problem above, we need to find what the z-score is when P(x ≥ .75).

The formula for calculating a z-score is given by:

\(Z=\dfrac{\text{x}-\mu}{\sigma}\)

Where:

Now,

\(Z=\dfrac{\text{x}-\mu}{\sigma}\)

\(Z=P(\text{x} \geq 0.75) = \huge \text(\dfrac{P(Z \geq (0.75 - 0.45)}{0.40}\huge \text)\)

\(Z= P\huge \text (\dfrac{Z \geq0.30}{0.40}\huge \text)\)

\(Z=P(Z \geq 0.75) = 1 - P(Z < 0.75)\)

\(Z=1 - 0.077337\)

\(Z\thickapprox 0.9227\)

Therefore, the z-score of P(x ≥ .75) is 0.9227.

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The english phrase "Seven less than four times a number" as an algebraic expression is 4x - 7

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

seven less than four times a number

Represent the number with x

So:

four times a number means 4x

So, we have

seven less than 4x

seven less than means - 7

So, we have

4x - 7

Hence, the english phrase as an algebraic expression is 4x - 7

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Complete question

write the english phrase as an algebraic expression. Let x represent the number

Seven less than four times a number

The graph of the system of the inequalities is attached.

To graph the inequalities y < -x - 4 and y ≥ (3/5)x + 4, we can start by graphing the corresponding equations and then shade the appropriate regions based on the inequality signs.

Let's begin with the equation y = -x - 4:

Choose a range of x-values to plot.

For simplicity, let's use x-values from -10 to 10.

Substitute different x-values into the equation to find corresponding y-values.

For example:

When x = -10, y = -(-10) - 4 = 10 - 4 = 6.

When x = 0, y = -(0) - 4 = -4.

When x = 10, y = -(10) - 4 = -10 - 4 = -14.

Plot these points on the coordinate plane and draw a straight line passing through them.

This line represents the equation y = -x - 4.

Next, let's graph the equation y = (3/5)x + 4:

Again, choose a range of x-values to plot. Let's use the same range of -10 to 10.

Substitute different x-values into the equation to find corresponding y-values. For example:

When x = -10, y = (3/5)(-10) + 4 = -6 + 4 = -2.

When x = 0, y = (3/5)(0) + 4 = 0 + 4 = 4.

When x = 10, y = (3/5)(10) + 4 = 6 + 4 = 10.

Plot these points on the coordinate plane and draw a straight line passing through them.

This line represents the equation y = (3/5)x + 4.

Now, let's shade the regions based on the inequalities:

For y < -x - 4, we need to shade the region below the line y = -x - 4.

For y ≥ (3/5)x + 4, we need to shade the region above or on the line y = (3/5)x + 4.

Hence, the region where the shaded regions overlap represents the solution to both inequalities.

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Answer:

x+y=12.96, or 12.96=y=x then you can solve for x and then the other half of the total is the other amount

Answer:

8

Step-by-step explanation:

12.8π=πrl

12.8=1.6*l. (π=πcancel)

l=12.8/1.6

l=8

Answer:

480 cubic feet

Step-by-step explanation:

The volume of any rectangular prism can be found by multiplying together the length, width and height. In this case, 8*6*10=48*10=480 cubic feet. Hope this helps!

Answer:

\(480 {ft}^{3} \)

Step-by-step explanation:

\(area \\ = l \times b \times h \\ = 8 \times 6 \times 10 \\ = 48 \times 10 \\ = 480 {ft}^{3} \)

hope this helps

brainliest appreciated

good luck! have a nice day!

Answer:

Step-by-step explanation:

If you multiply top and bottom of 7/2 by 2 as in (7 *2) / (2 * 2) = 14 /4

If you multiply 7/2 top and bottom by 4, you get 28/8

So 14/4 and 28/8 are both the same as 7/2

The dimensions of the rectangular box are given as follows:

All the dimensions.

The volume of a rectangular prism, with dimensions length, width and height, is given by the multiplication of these dimensions, according to the equation presented as follows:

Volume = length x width x height.

The box's volume is obtained as follows:

54 x 1³ = 128 x (3/4)³ = 54 cubic inches. (the volume of a cube is the side length cubed)

Hence all the options can be the dimensions of the box, as all the options have a multiplication resulting in 54.

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Answer:

y - 2 = 1/2(x - 3)

Step-by-step explanation:

Please let me know if you want me to add an explanation as to why this is the answer/how I got this answer. I can definitely do that, I just wouldn’t want to write it if you don’t want me to :)

hundred thousand place is dtermined by the x

yxy,yyy

tenthousand is determined by the x

yyx,yyy

trial and error

the number must be at least 350000

but less than 355000

the number could be

350,000

351,000

352,000

up to

354,999

any number between

350,000 and 354,999

\(\large\underline{\bf \red{Step \:by\: Step \:Explanation:}}\)

Given two equations are :

We may write them as ,

Multiplying equⁿ (i) by 2 :

⇒ 2(2x + y - 6 ) = 0.

⇒ 4x + 2y - 12 = 0 .....................(iii) .

Subtract equⁿ (ii) from equⁿ (iii) :-

⇒ 4x + 2y - 12 = 0

ㅤ- 4x + 3y - 8 = 0 [ Sign changes ]

__________________

⇒ 5y - 20 = 0.ㅤㅤㅤㅤㅤ

⇒ 5y = 20.

⇒ y = 20/5.

⇒ y = 4

Put this value in (i) to obtain x .

⇒ 2x + y - 6 = 0.

⇒ 2x +4 - 6 = 0.

⇒ 2x - 2 = 0.

⇒2x = 2 .

⇒ x = 2/2.

⇒ x = 1 .

Hence the value of x is 1 & y is 4.

\(\boxed{\purple{\bf\pink{\dag}\:Hence\:the\: correct\: option\:is\:[b]\:(1,4)}}\)

Answer:

so if we take 450 an divide it by 6 you get 75. So take 75 times 18 and you get 1,350 so he would need 1,350 kilograms of rice for 18 people

Step-by-step explanation:

hope this helps :D

Answer: 25%

Step-by-step explanation:

4000 divided by 1600= 4

1/4 = 25%

The intermediate step in completing the square is\($x^2 + 2ax + (a^2) = b - a^2 + (a^2)$\)

To complete the square for the equation \($(x+a)^2=b$\), we can follow these steps:

1. Expand the left side of the equation: \($(x+a)^2 = (x+a)(x+a) = x^2 + 2ax + a^2$\).

2. Rewrite the equation by isolating the squared term and the linear term: \($x^2 + 2ax = b - a^2$\).

3. To complete the square, take half of the coefficient of the linear term, square it, and add it to both sides of the equation:

\($x^2 + 2ax + (a^2) = b - a^2 + (a^2)$\).

4. Simplify the right side of the equation: \($x^2 + 2ax + (a^2) = b$\).

This step can be represented as: \(\[x^2 + 2ax + (a^2) = b - a^2 + (a^2)\]\)

This intermediate step helps us rewrite the equation in a form that allows us to factor it into a perfect square.

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Answer:

60 mins

Step-by-step explanation:

Step-by-step explanation:

Total number of people =3000

Let

the number of fans=17x

The number of staff=3x

\({:}\longrightarrow\)\(\sf 17x+3x=3000 \)

\({:}\longrightarrow\)\(\sf 20x=3000 \)

\({:}\longrightarrow\)\(\sf x={\dfrac {3000}{20}}\)

\({:}\longrightarrow\)\(\sf x=150 \)

500 more fans arrived

Now the new ratio=

\({:}\longrightarrow\)\(\sf {\dfrac {3150}{450}}\)

\({:}\longrightarrow\)\(\sf {\dfrac {1575}{225}}\)

\({:}\longrightarrow\)\(\sf {\dfrac {315}{45}}\)

\({:}\longrightarrow\)\(\sf {\dfrac {63}{9}}\)

\({:}\longrightarrow\)\(\sf {\dfrac {7}{1}}\)

\({:}\longrightarrow\)\(\sf 7:1 \)

\(\therefore\)New ratio of fans to staff is 7:1.

Answer:

12 long sleeved

Step-by-step explanation:

30 / 5 = 6

6 x 2 = 12

Answer:

12

Step-by-step explanation:

The 5 part of the ratio relates to 30 short- sleeved shirts.

Divide by 5 to find the value of 1 part of the ratio

30 ÷ 5 = 6 ← value of 1 part , then

2 parts = 2 × 6 = 12 ← long- sleeved shirts

The answer is:

Work/explanation:

Bear in mind that the sum of all the angles in a triangle is 180°.

Given two angles, we can easily find the third one.

Let's call it x.

Next, we set up an equation:

\(\sf{54+87+x=180}\)

\(\sf{141+x=180}\)

Subtract 141 on each side.

\(\sf{x=180-141}\)

\(\sf{x=39}\)

To evaluate -4.6+7+22+(-7.75) simplifying each term, -4.6+7 = 2.4, 2.4+22 = 24.4, 24.4+(-7.75) = 16.65 so the simplified expression is 16.65 which is a decimal.

A fraction is a mathematical expression that represents a part of a whole. It consists of a numerator (the top number) and a denominator (the bottom number) separated by a horizontal line.

Fractions can be simplified to their lowest form by dividing both numerator and denominator by their greatest common factor.

To evaluate the expression, we need to simplify each term and then add them together. The steps are as follows:

-4.6 + 7 = 2.4 (subtracting 4.6 from 7)

2.4 + 22 = 24.4 (adding 2.4 and 22)

24.4 + (-7.75) = 16.65 (adding 24.4 and -7.75)

So the simplified expression is 16.65.

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