Evaluate the expression xy - 3x when x = 4 and y = 5

Let's start with Pattern 1.

SInce the rule is to add 4, we shall add 4 on the first number that is zero.

The pattern 1 shall be:

On the other hand, for Pattern 2, the rule is to add 2. So, let's add 2 on the first number that is 0. Pattern 2 shall be:

Based on these two patterns, we can see that the terms in Pattern 1 are two times the corresponding terms in Pattern 2.

SOLUTION

The function can be derived from the model

So the function becomes

So the fox population in 2008

2008 - 2000 = 8

So our t becomes 8

The population becomes

So the Population = 3985

A) Not a function

A function is a relation which describes that there should be only one output for each input

Step 1

let's check the given ordered pair

we can see that

the input 4 has 2 outputs 6 and 8, so

this is not a function, hence the answer is

A) Not a function

I hope this helps you

From the question, we are given the matrices

We are to find which operation is defined and whic one is not

For the operation

For subtraction operation to be definded

The order of the matrices must be the same

Since the order of M is 4 x 2

And the order of N is 4 x 2

Therefore, the operation M - N is defined

For the operation

Similarly, for the operation to be definded

The order of the matrices must be the same

The oder of matrix L is 2 x 2 while the order of matrix N is 4 x 2

Since the oder of the matrices are not the same then

The operation L - N is not defined

For the operation

For addition operation to be defined, the Order of the matrices must be the same

The order of matrix M is 4 x 2 while the order of matrix P is 2 x 2

Since the order of the matrices are not the same then the operation is not defined

For the operation

For addition operation to be defined, the Order of the matrices must be the same

The order of matrix Q is 2 x 1 while the order of matrix P is 2 x 2

Since the order of the matrices are not the same then the operation is not defined

Recall that a set of ordered pairs A represents a function if:

Now, notice that (3,4) and (3,2) are in the given set of ordered pairs, since

we get that the given set does not correspond to a function.

Answer: Non-function.

Each meter has 100 centimeters, each centimeters has 10 milimeters, so 20 meters has 20.000 milimeters.

You have to write an equation parallel to the line: y=-4x+7 that crosses the point (3,8)

One characteristic that two parallel lines share is that they have the same slope.

The slope for the known line corresponds to the coefficient multiplying the x-term and is m=-4

The line you have to find must have the same slope.

Using the point-slope form you can determine said line. The general structure is:

Where

m is the slope

x₁, y₁ are the coordinates of a point crossed by the line.

Using (3, 8) and m=-4

Now you have to solve it and write it in slope-intercept form. First step is to solve the term in parentheses by applying the distributive propperties of multiplication:

Next pass "-8" to the other side of the equal sign:

The equation for the line parallel to y=-4+7 is y=-4x+20

The rate of emptying the lake is -1/8.

The rate of filling the lake is 1/15

Let t be the time in weeks to empty the lake,

Now, add the given rate to get the total rate of emptying of -1/t.

Thus,

Therefore, it will take 17 weeks and 1 day to empty the lake.

We need to graph on the number line the solution to the compounded inequality

In order to do so, let's work with each inequality separately. The final solution will be the union of the two solutions since it can be one "or" the other.

Step 1

Subtract 6 from both sides of the first inequality:

So, the solution to the first inequality is all real numbers less than 4 (not included). Therefore, we graph this solution using an empty circle:

Step 2

Add 3 to both sides of the second inequality, and then divide both sides by 2:

Thus, the solution to this inequality is all the real numbers greater than 6 (not included: empty circle):

Answer

Therefore, the solution to the compounded inequalities is the union of both solutions:

Applying quadratic formula to the given quadratic equation, we get the solutions as [tex]x=1,-\frac{3}{2}[/tex].

It is given to us that the quadratic equation is -

[tex]-2x^{2} -1x+3=0[/tex] ---- (1)

We have to solve by this by quadratic formula.

From equation (1), we have

[tex]-2x^{2} -1x+3=0\\= > -2x^{2} -x+3=0\\= > -(2x^{2} +x-3)=0\\= > 2x^{2} +x-3=0[/tex]----- (2)

The above equation (2) is in the form of a quadratic equation

[tex]ax^{2} +bx+c=0[/tex]

where, a = 2

b = 1

and, c = -3

Now, using the quadratic formula, we know

[tex]x=\frac{-b+\sqrt{b^{2} -4ac} }{2a}[/tex] and, [tex]x=\frac{-b-\sqrt{b^{2} -4ac} }{2a}[/tex]

Substituting the values of a, b, and c in the above formulas to find the value of x, we get

[tex]x=\frac{-b+\sqrt{b^{2} -4ac} }{2a} and x=\frac{-b-\sqrt{b^{2} -4ac} }{2a}\\= > x=\frac{-1+\sqrt{(-1)^{2} -4*2*(-3)} }{2*2} and x=\frac{-1-\sqrt{(-1)^{2} -4*2*3} }{2*2}\\= > x=\frac{-1+\sqrt{25} }{4} and x=\frac{-1-\sqrt{25} }{4}\\= > x= \frac{-1+5}{4} and x=\frac{-1-5}{4} \\= > x=\frac{4}{4} and x=\frac{-6}{4} \\= > x=1 and x= -\frac{3}{2}[/tex]

Thus, solving the given quadratic equation through quadratic formula, we get the solutions as [tex]x=1,-\frac{3}{2}[/tex].

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x ----> is the smaller number

x+6 ----> is the greater number

the equation is

Total number of kittens = 6

Gray kittens= 1 female+2 males = 3

Black kittens= 2 female+ 1 male =3

Probability of picking one black kitten = black kittens/ total kittens = 3/6 =1/2

We don't know the actual measures of the angles in the diagram but three of them have the same mark. This indicates that the angles are equal.

So the angles ∠EOD, ∠BOC and ∠AOB can be considered congruent.

50%

1) Gathering the data

12 are 6th graders

18 7th graders

6 8th graders

2) Let's add them up at first to get the whole number of students who tutor:

12 +18 +6 = 24 +12 = 36

So we can say that

36 -------------- 100%

The 7th graders: 18 students

So we can write a proportion for that

36-------100%

18 ------- x

36x = 1800 Divide both sides by 36

x =50

3) So the answer is 50% of them are 7th graders.

ANSWER

(2, -7)

EXPLANATION

We want to find which of the ordered pairs is a solution for:

Ordered pairs are usually given in the form (x, f(x)). That is the value of x and the value of the function of x.

We have to put each of the first values in the ordered pairs in the given function and see if it results in the second value.

=> (4, -4)

Not a solution

=> (2, -7)

This is a solution.

=> (10, 3)

Not a solution.

=> (-6, 11)

Not a solution.

The only solution there is (2, -7)

PROBLEM

Total

16 cheddar cheese

8 mozzarella cheese

Solution

He uses

Based on the given information, we can determine the constant and the variable payment.

• He gets $2100 as based salary (never changes, constant).

• The additional $70 depends on ,N ,(variable).

This information can help us build the equation:

Therefore, if he sells 27 copies, then the total payment is:

Answer:

P( 27 ) = $3990

Given

The equations,

4x-3=17, 8(x + 1) = 24, 5(x - 2) = 20, 34 - 7x = 20, 31 - x = 29, 3x +6=21.

To find the solution to each equations.

Explanation:

It is given that,

The equations,

4x-3=17, 8(x + 1) = 24, 5(x - 2) = 20, 34 - 7x = 20, 31 - x = 29, 3x +6=21.

That implies,

1)

Hence, the solution is x=5.

2)

Hence, the solution is x=2.

3)

Hence, the solution is x=6.

4)

Hence, the solution is x=2.

5)

Hence, the solution is x=2.

6)

Hence, the solution is x=5.

Firstly, we need to compare the information ew have from both sides of the equation, the denominators.

The different between the denominator is that the right side has the factor (w + 6), while the lest side does not.

So, sstarting from the expression on the left side, we can introduce the factor (w + 6) into the denominator by multiplying both the numerator and the denominator by this factor:

The order of the factor dont change the result, so we can switch the factors on the denominator to get:

Now, by comparison, we can see that the blank part is the following:

Larry Mitchell invested part of his $22,000 advance at 2% annual simple interest and the rest at 6% annual simple interest if his total yearly interest from both accounts was $760 find the amount invested at each rate

The amount invested at 2%

The amount invested at 6%

Let

x -----> amount invested at 2%

(22,000-x) -----> amount invested at 6%

we have that

x(0.02)+(22,000-x)(0.06)=760

solve for x

0.02x+1,320-0.06x=760

0.06x-0.02x=1,320-760

0.04x=560

x=14,000

(22,000-14,000)=8,000

therefore

The mean value of the sample is 98.1 F and its standard deviation is 0.7 F.

The margin of error of the mean value is given by 0.7/sqrt(751) = 0.7/27.4 = 0.026 (rounded to the nearest thousandth)

Using the Z test, we got: Z = (98.6 - 98.1)/(0.026) = 0.5/0.026 = 196

Therefore, the mean value of the sample is incompatible with 98.6 and we can claim that the mean body temperature is less than it.

Answer:

Triangles ABC and CDA share the side AC, therefore they have three congruent sides. Since AB is congruent to CD and BC is congruent to DA then by the SSS criteria we get that triangles ABC and CDA are congruent.

1) Given that an equilateral triangle has three congruent sides, so we can tell that each side has the following measurement:

Note that since they are congruent then we can tell that.

EXPLANATION:

We must bear in mind that the internal angles of a triangle must add up to 180 degrees.

We will first find values ​​of unknown angles and finally add to find the corresponding measures.

Now to find the measurements given in the exercise; We must take the values ​​found according to what each exercise asks for and add them.

In order to find the mean, we have to multiply each value with its probability and then add al the results:

Now, we add all the results we found on the previous step:

Mean = -0.34 - 11.68 - 0.30 - 1.12 - 1.95

Mean = -15.39

Answer: mean = -15.39

From the given data , the required equation to find the number of popsicles 'p' which Miriam can buy is given by 1.75p +5 = 1.80p + 4.39 is equal to p =12 .

Solution is viable as we can take the nearest round off value to find the number of popsicles.

As given in the question,

Two different companies where Miriam want to spend same amount of her money.

Equation of Food Hub sells is:

1.75p + $5.00

Equation of Foodie eat sells:

1.80p + $4.39

Where p is the number of popsicles

Required relation to get the value of p we have,

1.75p + 5.00 = 1.80p + 4.39

Take like terms on same side we get,

1.80p - 1.75p = 5.00 -4.39

⇒ 0.05p = 0.61

⇒ p = 12.2

⇒ p = 12 (round off number)

Number of popsicles cannot be in decimals.

Solution is viable as we can take the nearest round off value to find the number of popsicles.

Therefore, from the required equation to find the number of popsicles 'p' which Miriam can buy is given by 1.75p +5 = 1.80p + 4.39 is equal to p =12

Solution is viable as we can take the nearest round off value to find the number of popsicles.

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To determine if they are equivalent we equal them and if when simplified they do not show the same values, they are not. That is:

From that, we can see that they are not equivalent fractions.

Cosine theorem:

a= 34ft

b = 20ft

c = 18ft

VABC:

A=126.86º

B=27.07º

C=24.75º

a=34ft

b=20ft

c=18ft

Answer:

To calculate the mean of the set of values with the outlier, we will use the formula below

Concept:

An outlier is an observation that lies an abnormal distance from other values in a random sample of a population.

The mean with the outlier will be

By substituting the value, we will have

Hence,

The mean of the data with the outlier is = 49

Answer:

Concept:

To figure this question out, we will use the trigonometric ratios below

SOH CAH TOA

Using the inverse trigonometric identity,

By simplifying further, we will have that

Hence,

The final answer is