6. Multiply: (x – 4)(x + 5)

(a) x2 + 5x - 20,

(b) x2 - 4x - 20,

(c) x2 - x - 20,

(d) x2 + x - 20.​

a) The amount of water in the pool after 2 hours can be calculated using the equation.

Water in pool = 10L/hour × 2 hours = 20L.

b) The pool will be 80L when the equation is satisfied: 80L = 10L/hour × Time.

Solving for Time, we find Time = 8 hours.

c) Part b) is linear.

a) To calculate the amount of water in the pool after 2 hours, we can use the equation:

Water in pool = Water filling rate × Time

Since the pool gets filled up with 10L of water per hour, we can substitute the values:

Water in pool = 10 L/hour × 2 hours = 20L

Therefore, after 2 hours, there will be 20 liters of water in the pool.

b) To determine the number of hours it takes for the pool to reach 80 liters, we can set up the equation:

Water in pool = Water filling rate × Time

We want the water in the pool to be 80 liters, so the equation becomes:

80L = 10 L/hour × Time

Dividing both sides by 10 L/hour, we get:

Time = 80L / 10 L/hour = 8 hours

Therefore, it will take 8 hours for the pool to contain 80 liters of water.

c) Part b) is linear.

The equation Water in pool = Water filling rate × Time represents a linear relationship because the amount of water in the pool increases linearly with respect to time.

Each hour, the pool fills up with a constant rate of 10 liters, leading to a proportional increase in the total volume of water in the pool.

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Answer:

x=0 & x=2

Step-by-step explanation:

To find when f(x)=g(x), then look for a value that is the same for both functions in the table. 0 occurs twice for the same x value. 0 also appear twice for the x value 2. This is when they are equal. The solution is x=0 and x=2

Answer:

The Mets had 8, and the Dodgers had 11

Step-by-step explanation:

8 + 11 = 19

11 is 3 more than 19

Answer:

Dodgers 11 - Mets 8

Step-by-step explanation:

The Dodgers hit a couple homers probably,

Mets hit runs that are equal to 2 grand slams,

Dodgers 11

Mets 8

Answer:

22 + 63 = 20 + 65

Step-by-step explanation:

Hope this helps!

Answer:

22 + 63 is the same as 20 +  65

Step-by-step explanation:

Hope this helped!

To write the equation of a line in slope-intercept form (y = mx + b), we need to find the slope of the line (m) and the y-intercept (the point where the line crosses the y-axis, which is represented by b).

We can use the point-slope formula to find the equation of the line that passes through the points (-2,-2) and (5,12):

y - y1 = m(x - x1)

Where (x1, y1) is a point on the line, and m is the slope of the line.

Plugging in the values for the given points and solving for m, we get:

m = (12 - (-2)) / (5 - (-2))

= 14 / 7

= 2

Now that we have the slope, we can use either of the given points to find the y-intercept (b). Let's use the point (-2,-2):

y = mx + b

-2 = 2(-2) + b

-2 = -4 + b

b = -2 + 4

b = 2

Therefore, the equation of the line in slope-intercept form is:

y = 2x + 2

This is the equation of the line that passes through the points (-2,-2) and (5,12).

Answer:

23/3 OR 7 and 2/3

Answer:

41

Step-by-step explanation:

4x +5 = 7x -22

5 = 3x -22

27 = 3x

x = 27/3

x = 9

4(9) + 5 = RS

36+ 5 = RS

RS = 41

Answer:

RS=41

Step-by-step explanation:

Because RT intersects the midpoint of QS, from doing some geometry we know that QRT and SRT are congruent triangles. Thus, RS=RQ because of cpctc

so, we can make the equation:

4x+5=7x-22

simplify

3x=27

x=9

now, plug that into 4x+5, and we get 36+5, or 41. RS=41

The weight of the solution is 13 1/3 ounces.

Each container can contain 5/12 ounces.

The number of container required can be determined as,

Thus, the requried number of containers is 32.

The number of hours the student should record on the nighttime picture to complete a day-night cycle = 13 hours

The correct answer is an option (c)

We need to find the number of hours the student should record on the nighttime picture to complete a day-night cycle.

From the following pictures we can observe that, the sunrise time is 7:10 A.M. and the sunset timing is 6:10 P.M.

This means that thet daytime is of 11 hours (from 7:10 A.M. to 6:10 P.M.)

We know that the number hours in a day = 24

Let us assume that x represents the nighttime hours.

From this situation we get an equation,

x = 24 - 11

x = 13 hours

And the nighttime cycle would be:

from 6:10 P.M. to 7:10 A.M.

Therefore, the required number of hours = 13 hours

The correct answer is an option (c)

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Find the complete question below.

Answer:

85 square inches

Step-by-step explanation:

\(5*5=25\)

\(5*6=30*2=60\)

\(25+60=85\)

Hope this is helpful

Answer:

x = 42 and y = 92

Step-by-step explanation:

Since there are parallel lines, then

x = 42 ( Alternate angles )

The external angle of a triangle is equal to the sum of the 2 opposite interior angles.

134° is an external angle to the triangle, thus

x + y = 134 , that is

42 + y = 134 ( subtract 42 from both sides )

y = 92

----------------------------------------------------

(b)

The sum of the interior angles of a polygon are

sum = 180° (n - 2) ← n is the number of sides

Here n = 7, thus

sum = 180° × 5 = 900°

The 80th percentile for the number of hours spent studying each day is 7.07 hours.

A data set with a normal distribution has the majority of its values clustered in the middle of the range, while the remainder taper off symmetrically toward either extreme. The term "standard deviation" refers to the degree of dispersion of the data from the mean. Data are grouped around the mean when the standard deviation is low, and are dispersed when the standard deviation is high.

The percentage of scores below a given value is shown by percentiles. They provide information about how a score compares to other scores.

Given Data :

Mean time (u) = 6.4 hour

Standard Deviation = 0.80 hour

It is given that the probability distribution is normal.

The formula for the z-score is z =( x- mean)/standard deviation

For the 80th percentile,  the z value from the z table is 0.842.

We have,

0.842 = (x - 6.4)/0.8

0.842*0.8 = x - 6.4

0.6736 =x - 6.4

x = 0.6736 + 6.4

x = 7.0736

x = 7.07

Hence, the 80th percentile for the number of hours spent studying each day is 7.07 hours.

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Answer:

Answer is C noumber

Step-by-step explanation:

We know that a combination is a collection of the items where the order doesn't matter. It is a way to calculate the total outcomes of an event where order of the outcomes does not matter. It is denoted by C(n,k) or (n,k) or (n/k).

The formula for the number of combinations of n things taken r at a time is given by :-

C(n,k)=(n/k)=\frac{n!}{k!(n-k)!}C(n,k)=(n/k)=

k!(n−k)!

n!

Hence, C is the right option.

Answer: D, 36in.

Step-by-step explanation:

Answer:

184.26

Step-by-step explanation:

28.275 + 60 + 96 = 184.26

The value of the angle x will be equal to x = 61°

The circle is defined as the locus of the point traces around a fixed point called the centre and is equidistant from the out trace.

Given that:-

The value of the angle will be calculated as:-

We know that A tangent to a circle forms a right angle with the circle's radius, at the point of contact of the tangent, therefore ∠OQP=90°.

Now, using the angle sum property in ΔOPQ, we have

∠OPQ  + ∠PQO  +  ∠QOP = 180°

Substituting the given values, we get

29    +    90    +   x   =   180

119    +    x     =  180

x  =  61°

Therefore, the value of x is 61 degrees.

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Answer:

147 square yards

Step-by-step explanation:

hope this helps:)))

Answer:

78 sq. yards

Step-by-step explanation:

surface area of cuboid =2(lb + bh + lh)

length= 5 yards

breadth=3 yds

height =3yds

=2(5×3+3×3+5×3)

=2(15+9+15)

=78 sq. yards

The equations (x,y) | x + y > 1 and y (1/2)x + 2 have these solutions as their solutions.

To solve the system of inequalities without using graphs, we can use algebraic methods. First, we can rearrange the second inequality to slope-intercept form y < (1/2)x + 2.

This inequality represents a line with slope 1/2 and y-intercept 2. Next, we can identify the region of the coordinate plane that satisfies the first inequality, x + y > 1. This region is above the line x + y = 1. To check which side of the line satisfies the inequality, we can test a point, such as (0,1),

0 + 1 > 1

This is true, so the region above the line x + y = 1 satisfies the inequality.

Finally, we can combine the regions from the two inequalities to find the solution set. The solution set is the region above the line x + y = 1 and below the line y = (1/2)x + 2.

Therefore, the solution set can be expressed as,

{(x,y) | x + y > 1 and y < (1/2)x + 2}.

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Complete question - solve the given system of inequalities in two variables.

x + y > 1

y < 1/2x + 2

The total derivative of a function is not necessarily one-to-one. The total derivative represents the change in a function with respect to all of its input variables.

If a function has multiple input variables, the total derivative is a matrix, called the Jacobian matrix, whose entries represent the partial derivatives of the function with respect to each input variable.

A function with a non-invertible Jacobian matrix is not one-to-one, since multiple input values can result in the same output value. For example, consider the function f(x,y) = (x^2, y^2). The total derivative of f is given by the Jacobian matrix:

| 2x 0 |

| 0 2y|

This matrix is non-invertible when x=0 or y=0, since it has a determinant of zero. Thus, the function f is not one-to-one when x=0 or y=0.

In terms of polynomials, the total derivative is important for determining whether a polynomial has multiple roots. A root of a polynomial is a value of the input variable that causes the polynomial to equal zero. If a polynomial has multiple roots, it is not one-to-one, since different input values can result in the same output value.

The total derivative of a polynomial can be computed using the power rule of differentiation. For example, consider the polynomial p(x) = x^3 - 6x^2 + 11x - 6. The total derivative of p with respect to x is:

p'(x) = 3x^2 - 12x + 11

If p'(x) has multiple roots, then p(x) has multiple roots as well. In this case, p'(x) has roots at x=1 and x=11/3, so p(x) has multiple roots at x=1 and x=3. Thus, the total derivative is useful for identifying when a polynomial is not one-to-one.

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Is total derivative  is one-to-one? explain the significance of this result in terms of the derivative on polynomials.

Answer:

The pile is 2 feet high.

Step-by-step explanation:

There are 6 blocks, each block is 4 inches in height. That means the total height is:

6×4=24 inches

Because the question asked for the answer in feet, you have to convert the 24 inches into feet:

24 inches=2 feet

Answer:

The total number of students that are in Ms. Cunningham's class is 30 students

Step-by-step explanation:

the number of boys are represented by X
18 divided by 3 is 6
2 times 6 is 12.
12 plus 18 is 30.

Total number of students = 12 + 18 = 30

Answer:

I believe your equation is \(y=\frac{4}{5} x-2\)

Step-by-step explanation:

Using the rise over run formula, you get the slope as 4/5. Then, you look for the y-intercept, which turned out to be -2.

Answer:

Equation: 3x - 11 = 85

Solution: x = 32

Step-by-step explanation:

3x - 11 = 85

You will have to do the opposite to the equation shown on the screen.

3x = 96 (85 + 11)

x = 32 (96 / 3)

he number of ways the friends can choose seats without sitting next to each other is 7! - 4! = 5040

If there are 5 seats open in a row and no restrictions on the seating arrangement, each friend can choose one seat independently. Therefore, the total number of ways the friends can choose seats is 5 factorial (5!) which is equal to 5 × 4 × 3 × 2 × 1 = 120.

(b) If there are 7 seats open in a row and no restrictions on the seating arrangement, each friend can choose one seat independently. Therefore, the total number of ways the friends can choose seats is 7 factorial (7!) which is equal to 7 × 6 × 5 × 4 × 3 × 2 × 1 = 5040.

(c) If two friends are required to sit next to each other, we can treat them as a single entity. This reduces the problem to arranging four entities (three individual friends and one pair of friends) and three empty seats. The total number of ways the friends can choose seats is then 4 factorial (4!) which is equal to 4 × 3 × 2 × 1 = 24.

(d) If two friends are required to not sit next to each other, we can count the complement of the situation in part (c). There are 7 factorial (7!) total seating arrangements without any restrictions. From part (c), we found that there are 4 factorial (4!) seating arrangements where the two friends sit next to each other. - 24 = 5016.

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We will have the following:

We will determine the decrease after 9 minutes as follows:

Here each unit in the exponent represent each half life period.

So, after 9 minutes (3 sets of the half life) there wil be 12 grams of it.

Answer:

the time is the independent quantities and the dependent one is the mass of the turkey

Step-by-step explanation:

the reason is that the mass is the one determining the time but the time per pound is not going to change their for you can say with confidence that this is the answer.  

  hope you can learn from this response

15 hours - 36 caterpillars

x hours - 54 caterpillars

\(54x=15\cdot36\\54x=540\\x=10\)

10 hours

Answer: It would take 54 caterpillars 10 hours to eat the same bush.

Step-by-step explanation: The rate at which the caterpillars eat the bush is proportional to the number of caterpillars. In other words, if you have more caterpillars, they will eat the bush faster.

So, if 36 caterpillars can eat a bush in 15 hours, we can calculate the rate at which one caterpillar eats the bush by dividing the total time by the number of caterpillars:

Rate of 1 caterpillar = 15 hours / 36 caterpillars = 0.4167 hours/caterpillar

Now, to find out how long it would take for 54 caterpillars to eat the bush, we divide the total time by the new number of caterpillars, using the rate we just calculated:

Time for 54 caterpillars = 15 hours / (54 caterpillars / 36 caterpillars) = 10 hours.

So, it would take 54 caterpillars 10 hours to eat the same bush.

Answer:

3×6 + 3×6 =36

Step-by-step explanation:

3 multiply 3+3 = 3*6 =18×2 =36

Answer:

Step-by-step explanation:

=3(3+3)+3(3+3)

=3x6+3x6

=18+18

=36

I hope this helps

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