Jessica Reads a story about a turtle that swam 16 feet in 24 seconds. She assumes that the time that it takes the turtle to swim a distance of d feet is a proportional relationship. Jessica starts to create the table shown for other times and distances the turtle swam. Enter the missing numbers in the tableto represent the proportional relationship

Answer:

x = -7

x = 5

Step-by-step explanation:

The standard form of quadratic equations is

Ax^2 + Bx + C = 0

The factors need to multiply together to be C and add together to be B.

The two numbers that will multiply together to be -35 and add together to be 2 are -5 & 7.

The factor pairs are (x+7)(x-5). Zero product property means we set each of those factor pairs = 0 and solve.

x + 7 = 0

-7 -7 Subtract 7 from each side to solve

x = -7

x - 5 = 0

+5 +5 Add 5 to each side to solve

x = 5

To solve the equation, factor x²+2x−35 use the formula x² +(a + b) x + ab = (x + a)(x + b). To find a and b, set up a system to be solved.

a + b = 2

ab = −35

Since ab is negative, a and b have opposite signs. Since a+b is positive, the positive number has a greater absolute value than the negative. Show all pairs of integers whose product is −35.

Calculate the sum of each pair.

The solution is the pair that gives sum 2.

Rewrite the factored expression (x + a)(x + b) with the values obtained.

To find solutions to equations, solve x−5=0 and x+7=0.

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Answer:

Its option j.

Step-by-step explanation:

The graph is the graph of y =  |x| moved 1 unit to the right,

Answer:

can you type it out

Step-by-step explanation:

We need to divide every term by itself when changing from standard form to slope intercept form because to change the equation to slope intercept form.

The standard form of an equation is Ax + By = C. This is an equation in which the coefficients of the variables are A and B, and the constant is C. In order to change this equation into slope intercept form, we need to isolate the y variable.

To do this, we need to divide each term by the coefficient of the y variable. This will result in the equation becoming y = mx + b, which is the slope intercept form. By dividing each term by itself, we can ensure that the y variable is isolated, and the equation can now be written in slope intercept form.

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The function y = (e⁻⁽ˣ⁺²⁾) / x + 2  increases along intervals of (-∞, 3) and decreases along (-3, -2), (-2, ∞) and the function y = 2x - 1 / (x - 1)² has no inflection points but  concave downwards along (-∞, 1) ∪ (1 ,∞)

An extremum (or extreme value) of a function is a point at which a maximum or minimum value of the function is obtained in some interval. A local extremum (or relative extremum) of a function is the point at which a maximum or minimum value of the function in some open interval containing the point is obtained.

The function given;

y = (e⁻⁽ˣ⁺²⁾) / x + 2

The extrema and intervals of increase or decrease of this function are

(-1, 1.63) and it increases along (-∞, 3) and decreases along (-3, -2), (-2, ∞)

2. The inflection points and intervals of concavity and convexity of the function

y = 2x - 1 / (x - 1)² are

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The values of x in the first, second, third and fourth triangles are 4 units, 70°, 76° and 80° respectively

To solve this problem, we need some angle geometry knowledge:

For the first triangle:

x = 4 (All sides in a rhombus are identical)

For the second triangle:

The missing side is also equal to x (base of isosceles triangles)

x + x + 40 = 180 (sum of angles in triangle)

2x+40 = 180

2x = 180-40

2x = 140

x = 70°

For the third triangle:

x = 76° (base of isosceles triangles are equal)

For the fourth triangle:

Check the image attached for labeling

m = 180-110 = 70° (angle on a straight line)

y = 70° (base of isosceles triangles are equal)

z = 180-70-70 = 40°

t = 90-40 = 50°

L = 50° (base of isosceles triangles are equal)

Thus, x = 180-50-50 = 80°

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Answer:

The probability is  \(  P( X \ge 2)  =  0.986 \)  

Step-by-step explanation:

From the question we are told that

     The proportion people with  Blood type AB-negative in the world  is p = 0.006

     The sample size is  n =  30

 Generally the distribution of people with  Blood type  AB-negative  follows a binomial distribution  

i.e  

         \(X  \~ \ \ \  B(n , p)\)

and the probability distribution function for binomial  distribution is  

      \(P(X = x) =  ^{n}C_x *  p^x *  (1- p)^{n-x}\)

Here C stands for combination hence we are going to be making use of the combination function in our calculators  

   Generally the probability that at least 2 of them have blood type AB-negative is mathematically represented as

         \( P( X \ge 2) = 1 - P( X <  2 ) \)

         \( P( X \ge 2) = 1 - [P( X = 0  ) + P( X = 1 ) ] \)

=>      \( P( X \ge 2) = 1 - [1  *  1  *  0.8348  ] + [30  *  0.006 *  0.83986 ] \)

=>     \(  P( X \ge 2)  =  0.986 \)  

Step-by-step explanation:

Given: To make smallest 3-digit number of 825.

To find: The smallest 3-digit number of 825.

Solution: We can make the smallest 3-digit number of 825 by separating the numbers and arranging it to ascending order. The given number is 825. ...

Final answer: The smallest 3-digit number of 825 is 258.

hope it helps

Answer:

258

Step-by-step explanation:

We are given 3 numbers:

8 2 5

And we are asked to find the smallest 3 digit number using those 3 digits above.

To make the smallest number, place the numbers in value from least to greatest:

2 5 8

This is your 3 digit number: 258.

Hope this helps! :)

The solution to the system of equations is x = -8/7, y = 4/7 and z = -2/7

The system of equations is given as

2x - y + 2z = -6

-3y + z = -2

2x - 3z = -4

Subtract 2x - 3z = -4 from 2x - y + 2z = -6

This is represented as

(2x - y + 2z = -6) - (2x - 3z = -4)

This gives

- y + 5z = -2

Multiply - y + 5z = -2 by 3

-3y + 15z = -6

Subtract -3y + 15z = -6 from -3y + z = -2

This is represented as

(-3y + z = -2) - (-3y + 15z = -6)

This gives

-14z = 4

Divide by -14

z = -2/7

Substitute z = -2/7 in - y + 5z = -2

- y - 5 * 2/7 = -2

This gives

- y - 10/7 = -2

Rewrite as:

y = 2 - 10/7

Evaluate

y = 4/7

Substitute z = -2/7 in 2x - 3z = -4

2x - 3 * 4/7 = -4

This gives

2x - 12/7 = -4

So, we have:

2x = 12/7 - 4

Evaluate

2x = -16/7

Divide by 2

x = -8/7

Hence, the solution to the system of equations is x = -8/7, y = 4/7 and z = -2/7

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The calculated measure of m∠PNM is 87 degrees

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

The circle

Where, we have

PM = 360 - 64 - 122

Evaluate

PM = 174

Next, we have

m∠PNM = 1/2 * 174

So, we have

m∠PNM = 87

Hence, the measure of m∠PNM is 87 degrees

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Answer:

Number graph ranging from negative three to three on the x axis and negative one to six on the y axis. A line is drawn on the graph that passes through the points (negative three, zero) and (zero, six).

Step-by-step explanation:

Simplified y-4 = 2(x + 1) ⇒ y = 2x + 6

Graphed function on desmos graphing calculator

Matched the through points of option #4, (-3, 0) and (0 ,6) to the graph.

Answer: D. "Number graph ranging from negative three to three on the x axis and negative two to four on the y axis. A line is drawn on the graph that passes through the points (negative one, zero) and (zero, four)."

Step-by-step explanation:

We know that our graph passes through two given sets of points, therefore we can plug in those points to find the correct answer.

Let's test it with choice A. It gives us the points (0,-6) and (3,0). We can plug these into the equation to see if it is true. y-4 = 2(x+1) becomes
-6-4 = 2(3+1), or -10 = 8 which is not true, so we can eliminate it.

Choice B gives us (0,-4) and (1,0) -4-4 = 2(0+1) or -8 = 2, this one is wrong.

Choice C gives us (-1,0), so 0-4 = 2(-1+1) or -4 = 0, this one is also wrong.

Choice D gives us (-3,0) so 0-4 = 2(-3+1) or -4 = -4. This is the only option which has a correct solution, and therefore it is your answer.

A: The differential equation can be expressed in the form f(x ,y) = g(x)h(y) = 0, indicating that it is homogeneous. Divide both sides of the equation by y to observe this, which results in  dy/dx + sin^2(x) = cos^2(x)

B: Since there is just one function y and its derivative dy/dx involved in the equation, it is an ODE.

D: Because there is only one function y and its derivative  dy/dx involved in the equation, first-order differential equations are what it is.

G: The formula for the equation is a(x)y' + b(x)y = c(x), where a(x)=1, b(x) = sin^2(x), c(x) = cos^2(x) . Given that x and the coefficients of y and dy/dx are constants, the equation is linear.

H: The equation may be written as dy / y =  (cos^2(x))dx/(1+sin^2(x)),and it is a candidate for integrating factors because we can multiply both sides by (1+sin^2(x))dx .

I: The variables x and y can be separated by integrating both sides of the equation, which can be represented as  (dy/y) = (cos^2(x))dx/(1+sin^2(x)) + (sin^2(x))dx .

J: The equation is self-sufficient; it is not dependent on any explicit function of t.

       Therefore, the differential equation  dy/dx+sin^2(x)y=cos^2(x)y .A candidate for integrating factors exists in the first-order linear, homogeneous, separable, and autonomous ODE known as y.

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This question discusses Payroll Administration and Management.

Please note that based on the information provided, the weekly gross is K 6,860 the Net Pay is K 4,957  while the monthly Net Pay is K19,828.00.

Payroll Administration and Management is the activity involved in making sure that the compensation and benefits of the employee for the period that they have spent working are well organized, computed, and administered.

The steps to the solution is given below:

1) Note that the information given above is for one week.

The rate per hour is: K125/Hour.

The rate for overtime is 1.5 of the normal rate

Performance Bonus is K45 for every 50 units.

Given the above, the gross pay for the week is:

Normal Pay + Overtime Pay + Performance Bonus Pay.

a) Normal Pay is given as 125 * 40 = K5,000

b) Overtime Pay is given as (125*1.5) * 8 = K 1,500

c) Performance bonus is given as 45 * (400/50) = K360

d) Total Gross therefore is given as 5,000 + 1,500 + 360 = K 6,860

If gross pay is $6,860, Net Pay is calculated by removing deductions.

Deductions are:

Pension fund = 7.5% of K 6,869 = K 514.5

PAYE Tax = 20% of (95% of 6,869) = K 1,310.24 This is because medical aid is non-taxable.

Employee Insurance = 1% of K 6,860= K 68.6

Union Membership = K 10

The Total Deduction, thus, is = 514.5 + 1,310.24 + 68.6 +10 = K 1,903.34

The Net pay =  Gross Pay Less Deductibles

= 6,860 - 1,903

Thus The Net pay = K 4,957 /Week.

Therefore, his monthly net wage will be:

4, 957* 4 = K19,828.00/Month

B) The kind of remuneration method used by company XYZ is

Time Rate System. Under the time rate system, the worker is paid per hour, per day, per week, or per month.

It is normally used for workers who are engaged in highly skilled jobs or highly skilled services, for example, equipment testing, inspection of operations, toolmaking, etc.

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Answer:

Step-by-step explanation:

0.0814 radian / second

Given statement solution is :-  The Vector Calculations and Addition results are as follows:

ü -< -3, -7 > = < -3, -7 >

=< 4, -2 > - < -4, -32 > = < 0, -34 >

< 7, -3 > - < -8, -30 > = < 15, 27 >

< 5, -11 > + < 2, 0, 0, 0 > = < 7, -11, 0, 0 >

And 4 + 20 = 24.

To find the sum of 4 + 20, we simply add the two numbers together:

4 + 20 = 24

As for the given vectors, let's perform the requested calculations:

ü -< -3, -7 > = < -3, -7 >

=< 4, -2 > - < -4, -32 > = < 4 + (-4), -2 + (-32) > = < 0, -34 >

< 7, -3 > - < -8, -30 > = < 7 - (-8), -3 - (-30) > = < 15, 27 >

< 5, -11 > + < 2, 0, 0, 0 > = < 5 + 2, -11 + 0, 0 + 0, 0 + 0 > = < 7, -11, 0, 0 >

Therefore, the Vector Calculations and Addition results are as follows:

ü -< -3, -7 > = < -3, -7 >

=< 4, -2 > - < -4, -32 > = < 0, -34 >

< 7, -3 > - < -8, -30 > = < 15, 27 >

< 5, -11 > + < 2, 0, 0, 0 > = < 7, -11, 0, 0 >

And 4 + 20 = 24.

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The given options, the only value greater than 1 is 1.003. Therefore 0.886, which is less than 1 and makes the inequality true.

The given number sentence is 5.3 × > 5.3, where we need to find the scaling factor that makes the inequality true. To do this, we can divide both sides of the inequality by 5.3. This gives us:

5.3 × x > 5.3 ÷ 5.3 × k

We need to find the value of k that makes the inequality true. Simplifying the right-hand side of the equation, we get:

5.3 ÷ 5.3 × k = k × 1 = k

Substituting this into our equation, we get:

5.3 × x > k

We know that 5.3 × 1 = 5.3, which means that k must be greater than 1 to satisfy the inequality. Among the given options, the only value greater than 1 is 1.003. However, this value would make the inequality too large, so it is not the correct answer.

The correct answer is therefore 0.886, which is less than 1 and makes the inequality true.

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The least common denominator or LCD of ( 2x/ ( x² + x - 20 ) ) and ( 3x / ( x² + 4x - 5 ) ) is ( x + 5 )( x - 4 )( x - 1 ).

The smallest number among all the denominators' common multiples is the least common denominator.

Consider the two fractions,

( 2x/ ( x² + x - 20 ) ) and ( 3x / ( x² + 4x - 5 ) )

The factor of x² + x - 20 are:

x² + x - 20 = x² + 5x - 4x - 20

x² + x - 20 = x( x + 5 ) - 4( x + 5 )

x² + x - 20 = ( x + 5 )( x - 4 )

The factors x² + 4x - 5 are:

x² + 4x - 5 = x² + 5x - x - 5

x² + 4x - 5 = x( x + 5 ) - 1 ( x + 5 )

x² + 4x - 5 = ( x + 5 ) ( x - 1 )

Therefore, the least common denominator is:

LCD = ( x + 5 )( x - 4 )( x - 1 )

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Using bisection, the measure of angle ABD is of m<ABD = 50º.

The bisection of an angle is when the angle is divided into two angles of equal measure.

In the context of this problem, we have that the angle BE bisects the angle DBC, hence the measures of these angles are given as follows:

mDBE = mEBC = 2x + 15.

As shown in the diagram, the entire line forms a ray, meaning that the sum of the measures of the angles is of 180º, hence we can solve for x as follows:

2x + 2(2x + 15) = 180º

2x + 4x + 30 = 180º

6x = 150º

x = 150º/6

x = 25º.

Then the measure of angle ABD is found as follows:

m<ABD = 2x = 2(25) = 50º.

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The following statements are true concerning the values described in columns #1 and column #2. B. The value found in column #1 is less than the value found in column #2.

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree

The equation of curve 1, which is in the shape of a parabola is, when represented in general form

\(y = -2x^2 - 4x + 12\\\\y = -2(x^2 - 2x + 6)\\\\\dfrac{y}{-2} = (x^2 - 2x + 6)\\\\\dfrac{y}{-2} +7=(x+1)^2\)

So,

x+1=0

x= -1

and,

y = 14

Therefore, the Coordinate of a vertex is (-1,14).

The x-coordinate of the vertex of the function \(y = -2x^2 - 4x + 12\) is equal to -1.

The equation of curve 2 , which is in the shape of a parabola is , when represented in general form

\(y = x^2 - 4x + 3\\\\y =( x-2)^2-1\\\\y+1 =( x-2)^2\)

So,

x-2=0

x= 2

and, y+1=0

y= -1

Therefore, the Coordinate of a vertex is (2,-1).

The x-coordinate of the vertex of the function \(y = x^2 - 4x + 3\) is equal to 2.

The following statements are true concerning the values described in columns #1 and column #2. B. The value found in column #1 is less than the value found in column #2.

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Answer:

it will take them 1.71 hours to finish cutting the lawn if they work together.

Step-by-step explanation:

If Marsha cuts the lawn by herself it will take her 3 hours, this mean that in one hour she cuts 1/3 of the lawn.

On the other hand Bob needs one more hour to finish the lawn, this means it takes him 4 hours to cut it and therefore he cuts 1/4 of the lawn per hour.

Now, to know how much they cut by working together we need to sum up the amount of lawn they cut per hour:

Working together in one hour: Marsha's one hour + Bob's one hour

Working together in one hour: \(\frac{1}{3}+ \frac{1}{4}=\frac{4+3}{12}=\frac{7}{12}\)

Therefore, working together they will cut 7/12 in one hour.

Now, to know how long will it take it to cut the entire lawn (which is equivalent to 12/12), we can write this in terms of proportions

Time        Total amount of lawn

1 hour               7/12

x hours             12/12

Solving for x (to know the amount of hours it will take them) we have:

\(x=\frac{12}{12}\)÷\(\frac{7}{12}\)=\(1\)×\(\frac{12}{7}=\frac{12}{7}=1.714\)

Rounded to the nearest hundredth, we have that working together it will take them 1.71 hours to finish cutting the lawn.

Answer:

x = 5

Step-by-step explanation:

We know that BD = 2x - 1 and BC + CD = BD.  Thus, we can set the sum of (x- 3) and 7 equal to 2x - 1 to find x:

BC + CD = BD

x - 3 + 7 = 2x - 1

x + 4 = 2x - 1

x + 5 = 2x

5 = x

Thus, x = 5

Checking the validity of our answer:

We can check that our answer is correct by plugging in 5 for x in x - 3 and 2x - 1 and checking that we get the same answer on both sides of the equation:

5 - 3 + 7 = 2(5) - 1

2 + 7 = 10 - 1

9 = 9

Thus, our answer is correct.

Answer:

There are 14 problems worth 5 points and 15 problems worth 2 points.

Step-by-step explanation:

Hope this helped have a good day :)

Answer:

Step-by-step explanation:

Identify the number of decimal places in each factor.

    0.47

  × 3.2

The number of decimal places in 0.47 is

✔ 2

.

The number of decimal places in 3.2 is

✔ 1

.

The number of decimal places in the product will be the sum of the factors’ decimal places. So the product will have

✔ 3

decimal places.

Step-by-step explanation:

Equation of a line passing through a point (h, k) and slope 'm' will be,

y - k = m(x - h)

If this line passes through a point (-3, 1) and has a slope 2/3 32 .

Therefore, equation of the line will be,

y-1=2/3(x+3)y−1=32(x+3)

y=2/3+2+1y=32x+2+1

y=2/3 x+3y=32x+3

Therefore, equation of the line will be,

y=2/3x+3y=32x+3

P.S (2/3- fraction)

Answer:

51 degrees

Step-by-step explanation:

Complementary angles add up to 90 degrees. This means we can write an equation, where a represents the measure of the acute angle (which we need to find the larger one) and a + 12 is the measure of the larger angle.

a+(a+12)=90

2a+12=90

2a=78

a=39

Now add 12 to a to find the value of the larger angle.

39+12= 51

So the larger angle equals 51 degrees.

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The number of different hands of 3 cards from a set of 52 is given by:

22,100.

The number of different hands is obtained using the combination formula, as the order in which the cards are chosen is not important. If the order was important, then the permutation formula would be used.

The number of different combinations of x objects from a set of n elements is obtained with the formula presented as follows, using factorials of each number.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

In this problem, three cards are taken from a set of 52, hence the values of the parameters are given as follows:

Then the number of hands is obtained as follows:

\(C_{52,3} = \frac{52!}{3!49!} = 22,100\)

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The end behavior of the function q(x) is:

To know the end behavior we need to look at the degree and the sign of the leading coefficient.

If the degree is even, and the leading coefficient is negative, then in both ends the function will tend to negative infinity.

Here we can see that the function is:

q(x) = -2x⁸ + 5x⁶ - 3x⁵ + 50

So, the degree is 8, and the leading coefficient is -2, then the end behavior of the function is:

when x → ∞, q(x) → -∞

when x → -∞, q(x) → -∞

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Answer:

:/

Step-by-step explanation:

:/