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The steps Sergey could use to solve the quadratic equation by completing the square is 5(x2 + 4x) = –7

We should know that in completing the square method both sides of the equation are made perfect squares.

The given equation is 5x²+20x-7=0

Solving this equation by completing the square method we have

5(x²+4x+4)=-7

This means that (x+2)=±√27/5

Simplifying further we have

5(x²+4x)=7

Then expanding to make ²HS a perfect square we have

5(x²+4x+4)=7+20

This means that 5(x²+4x)=-7

Therefore the step he could use is 5(x²+4x)=-7\

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Answer:

p(B) = 4/32 = 1/8

p(G) = 6/32 = 3/16

We have the following equation:

since we need P, we must move k and V to the left hand side as

By substituting the given values, we get

that is, P is equal to 2.

Answer:

33.53

Step-by-step explanation:

OB is a radius of the circle, and OC is also a radius of the circle, so both are equal length.  That makes ΔOBC an isosceles triangle.

If we cut ΔOBC in half, the angle formed is 125° / 2 = 62.5°.

Therefore:

sin 62.5 = (x/2) / 18.9

x = 37.8 sin 62.5

x ≈ 33.53

Answer:

33.5

Step-by-step explanation:

Step-by-step explanation:

I assume you are looking for the height of p-gram?

Rectangle area  =   7 in x 8 in = 56 in^2

Parallelogram area = base * height

                  56 in^2 = 5.6 in * height

               height = 10 in

Answer:

*A*

jog > 2 km

pushups > 25

pullups > 10

*B*

yes you would because

2500m > 2km  2500 meters is greater than or equal to 2 kilometers? check

30 pushups > 25 pushups  **** 30 push ups is more than or equal to 25

push ups? check

20 pullups > 10 pullups   20 pullups greater than or equal to 10 pullups? check.

Since you do more than what the requirment standards are you will pass your test.

Step-by-step explanation:

Answer:

29. \(\frac{1}{3}\)

30. a) 32

b) Yes, the ratio will change 1 : 2.

Step-by-step explanation:

Question 29.

Given that:

Number of gold medals won by France = 11

Number of silver medals won by France = 9

Number of bronze medals won by France = 13

To find:

The ratio of gold medals won to the total number of medals won by France.

Solution:

First of all, we need to find the total number of medals won by France.

Total number of medals won = 11 + 9 + 13 = 33

The required ratio can be found as:

\(\dfrac{\text{Number of gold medals won}}{\text{Total number of medals won}}\\\Rightarrow \dfrac{11}{33}\\\Rightarrow \bold{\dfrac{1}{3}}\)

Question 30:

Number of girls = 20

Ratio of boys to Ratio of girls = 3 : 5

a. Total number of students in the class?

First of all, we need to find the number of boys in the class then we will add the value to the number of girls to get the answer.

Let the number of boys = \(x\)

As per the ratio, we can write:

\(\dfrac{3}{5 } = \dfrac{x}{20}\\\Rightarrow x = 12\)

Total number of students = 20 + 12 = 32

b. Four number of boys and four girls are moved to other class.

Number of boys left = 12 - 4 = 8

Number of girls left = 20 - 4 = 16

New ratio = 8 : 16 = 1 : 2

Therefore, the ratio got changed to 1 : 2.

The area of the triangle in the image is 24 square centimeters.

Remember that the area of a triangle of base B and height H is given by:

A = B*H/2

On the diagram, we can see that the base of the triangle is 8cm, and the height is 6cm, then we can replace these two values in the formula above, then we will get:

A = 8cm*6cm/2

A = 8cm*3cm

A = 24cm²

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The probability that the slope of the line determined by p and the point (5/8, 3/8) is greater than or equal to 1/2 is 5/8.

Let the coordinates of point p be (x,y). Then, the slope of the line determined by p and the point (5/8, 3/8) is:

For the slope to be greater than or equal to 1/2, we must have:

Solving for y, we get:

Graphing this inequality on the unit square, we see that the region satisfying this inequality is a trapezoid with vertices (5/8,3/8), (1,1/2), (1,1), and (3/4,1).

The area of this trapezoid is (1/2)*((5/8 - 3/4) + (1 - 5/8) + (1 - 1/2) + (3/8 - 3/16)) = 5/16.

The area of the unit square is 1, so the probability we seek is 5/16.

Hence, the answer is 5/16 written as a fraction in its simplest form, which is 5/16.

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The outcomes that are contained in the events are

1 - P(X) = 4/5 and 1 - P(X) is the same as P(Not X)

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

X = gray colours

Given that

gray colours = 3 and 10

We have

X = 3 and 10

Not X =1, 2, 4, 5, 6, 7, 8

The probability is then calculated as

P(X) = 2/10 = 1/5

For P(Not X), we have

P(Not X) = 1 - 1/5 = 4/5

In (a), we have

P(Not X) = 1 - 1/5 = 4/5

This means that

P(Not X) = 1 - P(X)

So, the solution is

1 - P(X) = 4/5

Using the above (a) and (b) as a guide, we have the following:

1 - P(X) is the same as P(Not X)

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Answer:

(-5,-2)

Step-by-step explanation:

To find the mid-point the formula is;

\((x_1+x_2)/2 ,(y_1+y_2)/2\)

In this case point A (3,-8) , mid-point (-1,-5), point B (x,y)

Thus (3+x)/2 = -1  

        3+x=-2

            x= -2-3 = -5

And

      ( -8+y)/2 = -5

      -8 + y = -5*2

       -8 +y = -10

             y= -10 +8 = -2

Hence point B coordinates are: (-5, -2)

Check below, please

1) Let's find out the sum of 503 + 10 mentally through this modeling:

500 + 10 +3 = 513

That 5 hundred will remain

The Tens place won't change 1

The unit's place won't change.

2) Another model to find out 503 +100 is

500 + 100 + 3 = 603

The hundreds place will add up to 600

The tens place won't change

The units place will change

Answer:

2520

Step-by-step explanation:

2520

Answer:

There are a total of 20 presents, and 3 of them contain gems. Therefore, there are 20 - 3 = 17 presents that do not contain gems.

The probability of randomly selecting a present that does not contain a gem is 17/20 = 0.85 or 85%.

hope it helps you...

Answer:

39000meter

hope it will help you

Answer:

A visit must be of at least 42.39 minutes to put a shopper in the longest 10 percent.

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean of 27.8 minutes and a standard deviation of 11.4 minutes.

This means that \(\mu = 27.8, \sigma = 11.4\)

How long must a visit be to put a shopper in the longest 10 percent?

The 100 - 10 = 90th percentile, which is X when Z has a p-value of 0.9, so X when Z = 1.28.

\(Z = \frac{X - \mu}{\sigma}\)

\(1.28 = \frac{X - 27.8}{11.4}\)

\(X - 27.8 = 1.28*11.4\)

\(X = 42.39\)

A visit must be of at least 42.39 minutes to put a shopper in the longest 10 percent.

6/8 is an equivalent fraction to 3/4; 2/6 is equivalent to 1/3; 6/9 is equivalent to 2/3; 10/25 is equivalent to 2/5; 4/16 is equivalent to 1/4; the fraction of 1/3 is equivalent to 2/6; 8/16 is an equivalent fraction to 2/4.

A fraction can be referred to or considered as a divisional representation of a whole number or a percentage, usually represented as a bigger numerical. A fraction denotes the representation of a number in such a way that the meaning or the accuracy of the number is not disturbed, but is shown differently. The fractions equivalent to each other have been mentioned above.

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Answer:

the berry-scented pillar candle

Step-by-step explanation:

khan academy

we would expect m to be positive.

In this case, we're considering a formula of the form y = mx + b, where y represents the cost of a four-year college x years after 2010. The variable m represents the coefficient of x, which determines the slope of the line.

Since we're discussing the cost of college, it's reasonable to expect that it generally increases over time. Therefore, we would expect the coefficient m to be positive. A positive value of m indicates that as the number of years after 2010 increases (x), the cost of college (y) will also increase.

If m were negative, it would imply a decreasing cost over time, which is less likely for a four-year college. If m were zero, it would indicate that the cost remains constant regardless of the number of years after 2010, which is also unlikely given the rising trend in college costs.

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We have to find the values for the function:

y = | x - 2 | + 5 [1],

a) When x = 5, and check if the result is y = 8.

b) When x = -2, and check if the result is y = 0.

The function | x | is called absolute value function. And, for this function, we have that:

| x | = x

| -x | = x

Having all this information, we are ready to solve the question:

a) When x = 5, we have

y = | x - 2 | + 5

y = | 5 - 2 | + 5

y = | 3 | + 5

y = 3 + 5

y = 8.

Since we have that y = 8 when x = 5, the point is on the graph represented by the function [1]. Conclusion: the point (5, 8) is on the graph.

b) We can follow the same procedure as before:

When x = -2, we have

y = | x - 2 | + 5

y = | -2 - 2 | + 5

y = | -4 | + 5

y = 4 + 5

y = 9

Thus, for x = -2, the value for y = 9. We have the point (-2, 9), and not the point (-2, 0).Therefore, the point (-2, 0) is not on the graph.

The truck driver would deliver 105 packages in a 7 hours day

An equation is an expression that shows how numbers and variables are related to each other using mathematical operators.

Let y represent the number of packages delivered by the truck driver in x hours. Using the point (1, 15) and (4, 60). Hence, the equation is:

y - 15 = [(60-15)/(4-1)](x - 1)

y = 15x

For a 7 hour day (x = 7):

y = 15(7) = 105

The driver would deliver 105 packages in 7 hours

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tan graph and its tax because tax=0

Answer:

It's 18.37

Step-by-step explanation:

I'm smart trust me.

Answer:

26

Step-by-step explanation:

One leg measures 7.

One leg measures 8.

a² + b² = c²

7² + 8² = c²

c² = √113 = 10.630 = 11

perimeter = 7 + 8 + 11

perimeter = 26

Answer:

5

Step-by-step explanation:

The two pairs of integers that satisfy the given conditions are (-3, 8) and (5, 24).

To solve the system of equations, let's assign variables to the two integers. Let the first integer be represented by 'x' and the second integer by 'y'.

According to the given information:

a. Fourteen more than twice the first integer gives the second integer:

This can be expressed as: 2x + 14 = y

b. The second integer increased by one is the square of the first integer:

This can be expressed as: y + 1 = x^2

Now, we have a system of equations:

1) 2x + 14 = y

2) y + 1 = x^2

To solve this system, we can substitute the value of 'y' from equation 1) into equation 2):

2x + 14 + 1 = x^2

2x + 15 = x^2

Rearranging the equation, we have:

\(x^2 - 2x - 15 = 0\)

Factoring the quadratic equation, we get:

(x - 5)(x + 3) = 0

Setting each factor equal to zero:

x - 5 = 0   -->   x = 5

x + 3 = 0   -->   x = -3

Substituting the values of 'x' back into equation 1), we can find the corresponding values of 'y':

For x = 5:

2(5) + 14 = y

10 + 14 = y

y = 24

For x = -3:

2(-3) + 14 = y

-6 + 14 = y

y = 8

Therefore, the two pairs of integers that satisfy the given conditions are (-3, 8) and (5, 24).

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The canister holds 80 cups and they need 84 cups of flour to make a dozen pizzas. So, the cooks cannot make a dozen pizzas without refilling the canister. The solution has been obtained by using unitary method.

What is the unitary method?

The unitary technique is used to first calculate the value of each individual unit, and only then is the value of the necessary quantity of units calculated.

We are given that a pizzeria stores flour in a 5-gallon container. We assumed that 16 cups make 1 gallon.

So, number of cups that will make 5 gallon is 16 * 5 = 80 cups

Since, each pizza they make uses 7 cups of flour. So, for making 12 pizzas, they require 12 * 7 = 84 cups of flour.

Hence, the cooks cannot make a dozen pizzas without refilling the canister.

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