41 = 5x + 35 and 3 = 4x + 10. Find the measure of x, 21 and 22.
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The linear equation that is modeled by the table is:

y = 2x + 1

A general linear equation is written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

If the line passes through two points (x1, y1) and (x2, y2), then the slope is:

a = (y2 - y1)/(x2 - x1)

Here we can use the first two points on the table (-3, -5) and (-1, -1), we will get the slope:

a = (-1 + 5)/(-1 + 3)

a = 4/2 = 2

Then the line is something like:

y = 2x + b

To find the value of b we can use one of the points (-3, -5), replacing these values we will get:

-5 = 2*-3 + b

-5 = -6 + b

-5 + 6 = b

1 = b

Then the linear equation is:

y = 2x + 1

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The limit lim (tan(2x) / (6x sec(3x))) as x approaches 0 is 1/3, which corresponds to option C.

To find the limit lim (tan(2x) / (6x sec(3x))) as x approaches 0, we can use L'Hopital's rule, which states that if the limit of the ratio of two functions' derivatives exists, then that limit is equal to the limit of the ratio of the original functions.

First, let's find the derivatives of the numerator and denominator:
d(tan(2x))/dx = 2 * sec^2(2x)
d(6x sec(3x))/dx = 6 sec(3x) + 18x sec(3x) tan(3x)

Now, let's apply L'Hopital's rule and find the limit of the ratio of the derivatives as x approaches 0:
lim (2 * sec^2(2x) / (6 sec(3x) + 18x sec(3x) tan(3x))) as x -> 0

At x = 0, we have:
2 * sec^2(0) / (6 sec(0) + 0) = 2 * 1 / (6 * 1) = 2/6 = 1/3

So, the limit lim (tan(2x) / (6x sec(3x))) as x approaches 0 is 1/3, which corresponds to option C.

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The solution of the equation 3z minus 2 is equal to 46 is 16.

The given equation '3z minus 2 is equal to 46' can be written as

    3z - 2  =   46

Now solving for z because the value of z will give the required solution of the given equation. So now finding the z from the equation:

   3z = 46  + 2

   3z =  48

   z = 48/3

   z = 16

The value of the z is 16 which represents the solution of the given equation i.e 3z minus 2 is equal to 46.

Therefore it is concluded that the solution of the equation 3z minus 2 is equal to 46 is 16.

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Answer:

62

Step-by-step explanation:

another way to write this is

x - 12 = 50

the answer is 62

62 - 12 = 50

Answer:

k = - \(\frac{3h}{h+1}\)

Step-by-step explanation:

Given

h(k + 6) = 3h - k ← distribute parenthesis on left side

hk + 6h = 3h - k ( add k to both sides )

hk + k + 6h = 3h ( subtract 6h from both sides )

hk + k = - 3h ← factor out k from each term on the left side

k(h + 1) = - 3h ( divide both sides by (h + 1) )

k = - \(\frac{3h}{h+1}\)

by solving this equation, the value of y = (x²+1)/(1-x²)

Equation can be used to represent relationships between variables and to solve problems. They are written using an equal sign (=) and can include numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division.

To make y the subject of the equation x = √((y-1)/(y+1)),

x = √[(y-1)/(y+1)]

we can square both sides:

x² = (y-1)/(y+1)

Next, we can multiply both sides by (y+1) to get rid of the fraction:

x² × (y+1) = y-1

x²y + x² = y - 1

Rearranging the terms:

x² + 1 = y - x²y

x² + 1 = y(1 - x²)

Divide both side by (1-x²) we get

y = (x²+1)/(1-x²)

So, y is the subject of the equation is y = (x²+1)/(1-x²)

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Answer: The answer is 1/4.

Step-by-step explanation:

The situation that describes the use of an ATM is option C, where Abby entered a PIN to begin a transaction and received an amount of cash.

An ATM, or Automated Teller Machine, is a self-service banking machine that allows users to perform various financial transactions, including withdrawing cash, depositing money, checking account balances, and transferring funds. To use an ATM, the user typically needs to have a debit card or ATM card linked to their bank account, and they need to enter a unique Personal Identification Number (PIN) to access their account.

Once the user enters the correct PIN, they can choose the type of transaction they want to perform, such as withdrawing cash, and the machine dispenses the requested amount of cash.

Therefore, option C is the correct answer that describes the use of an ATM.

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The given relation is function, because the curve of y = p(x) has its exist for every x in its domain(-6, 3) and the range of the function is lies between (-1, 9).

Functions is the relationship between sets of values. e g y=f(x), for every value of x there is its exists in set of y. x is independent while Y is dependent variable.

As Clearly the shows in the graph the structure is decreasing, increasing and then decreasing. And implies, curve is continuous in its limits and for every x (-6,3) there is exist in range of y(-1, 9).

Thus, The given relation is function, and domain is (-6, 3) and the range of the function is lies between (-1, 9).

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The amount of money left with Dalton on gift card is given by the equation

9.95 + m = 25

Given data ,

Let the total amount of money on the gift card be = $ 25

Now , the amount of money spent on restaurant = $ 9.95

So , the amount of money left is

m = 25 - 9.95

On simplifying the equation , we get

m = $ 15.05

Hence , the amount left is m = $ 15.05

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Answer:

Find the answers in the explanation

Step-by-step explanation:

The given function is

f(x)=475-15x

A.) To find f^-1 and explain what it represents in this situacions, let f(x) = y. That is,

Y = 475 - 15x

Interchange y and x and make y the subject of formula

X = 475 - 15y

-15y = x - 475

Y = 475/15 - x/15

Y = (475 - x) / 15

Therefore,

f^-1(x) = (475 - x) / 15

If the function depreciates the smartphone, then, the inverse function will appreciate it.

When will the deprecated value of smart phone be less than $100.00

Substitute 100 for f(x) and find x

100 = 475 - 15x

-15x = 100 - 475

-15x = - 375

X = 375/15

X = 25

Therefore, the deprecated value of smart phone be less than $100.00 in the next 26 months.

what does x represent in f^-1(x) =30?

X represent the number of months for the smartphone appreciations

What is the value of x?

Substitute the inverse function for 30 and make x the subject of formula in the equation

f^-1(x) = (475 - x) / 15

30 = (475 - x) / 15

Cross multiply

450 = 475 - x

X = 475 - 450

X = 25 months

Graph f(x) and f^-1 (x) on the same coordinate

Answer:

About 2 seconds

Step-by-step explanation:

25/12

2.0833333333333333333333333333333333333333333333333333333333333333................

The correct option is C. Length = 24 feet, width = 18 feet

To measure a rectangular room, use a tape measure, pencil and paper to record the length and width of the room. Then multiply these numbers to get the total area of the room.

The calculation is as follows:

Since 2cm = 6 feet

So,

The length is = 4(6) = 24 feet

And, the width be = 3(6) = 18 feet

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A scale drawing of Julie's living room is shown below:

A rectangle is shown. The length of the rectangle is labeled as length equal to 8 cm, and the width is labeled as width equal to 6 cm.

If each 2 cm on the scale drawing equals 4 feet, what are the actual dimensions of the room?

A)Length = 16 feet, width = 12 feet

B)Length = 10 feet, width = 8 feet

C)Length = 32 feet, width = 24 feet

D)Length = 14 feet, width = 12 feet

Answer:

Tyler owes $250 and both $180 and $70 are positive.

Step-by-step explanation:

Tyler owes $180.

Tyler's brother owes $70 more than him.

180 + 70 = 250

Tyler owes the bank $250.

Answer:

Step-by-step explanation:

Using the formula for calculating heat energy H = mcΔT

m = mass of the aluminum (in g/kg)

c = specific heat capacity of aluminum

ΔT = change in temperature = T - Ti (in °C)

T is the final temperature

Ti is the initial temperature

Given m = 100.0g,  c = 0.931096J/g °C, Ti = 20°C, H = 1100J T = ?

Substituting the given values into the formula;

1100 = 100*0.931096 (T - 20)

1100 = 93.1096T - 1862.192

93.1096 T = 1100+1862.192

93.1096 T  = 2962.192

T = 2962.192/93.1096

T = 31.81°C

The final temperature of the metal is 31.81°C

Answer:

31.81c

Step-by-step explanation:

1100 = 100*0.931096 (T - 20)

1100 = 93.1096T - 1862.192

93.1096 T = 1100+1862.192

93.1096 T  = 2962.192

T = 2962.192/93.1096

T = 31.81°C

We assume that G is a connected planar graph with no vertex of degree <= 5. We will use e <= 3v - 6 to prove that G is not a planar graph. By handshaking lemma, we know that 2e = sum of degrees of all vertices. Let d be the maximum degree of G.

Qa. Contrapositive of an implication is a new implication formed by negating both the hypothesis and the conclusion.

The contrapositive of the implication "If G is a connected planar graph, then G has at least one vertex of degree <= 5" is "If G has no vertex of degree <= 5, then G is not a connected planar graph."

Qb. Proof: We assume that G is a connected planar graph with no vertex of degree <= 5.

We will use e <= 3v - 6 to prove that G is not a planar graph. By handshaking lemma, we know that 2e = sum of degrees of all vertices.

Let d be the maximum degree of G. Since G has no vertex of degree <= 5, then d >= 6.

Thus, the sum of degrees of all vertices in G is greater than or equal to 6v/2, which is equal to 3v.

Hence, 2e >= 3v.

Substituting this inequality in e <= 3v - 6, we get 2e >= 3e - 6, which implies that e >= 6.

Since e >= 6, it follows that G is not planar.

Qc. Proof: We use proof by induction on the number of vertices of G. For a graph with one vertex, the statement is trivially true.

For a graph with n > 1 vertices, assume that every planar graph with at most n - 1 vertices can be colored with 6 (or less) colors.

Let G be a planar graph with n vertices.

By part (a), there exists a vertex v of G with degree <= 5.

We remove v and all its edges from G to get a new graph G' with n - 1 vertices.

By the induction hypothesis, we can color G' with 6 (or less) colors.

We add back v and its edges to G.

Since v has degree <= 5, at most 5 colors are used on its adjacent vertices.

We use a new color for v.

Thus, G can be colored with 6 (or less) colors.

Therefore, by induction, the statement is true for all planar graphs.

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Answer:

its 9.2

Step-by-step explanation:

Well i counted 7 units (x-axis) and 6 units (y axis). 6 squared is 36 and 7 squared is 49. Add them together and get 85. Square root 85 and youll get 9.21954445729. Round it to the nearest tenths and get 9.2

Answer: Inequality notation is < or ≥.

Step-by-step explanation:

EQUATION ONE: -5x + 7 > 47, x < -8

EQUATION TWO: -5x + 7 ≤ -43, x ≥ 10

Answer:

A, -11

Step-by-step explanation:

f(x)=-3x(-2)+1

=-3(4)+1

=-12+1

=-11

Step-by-step explanation:

f(x)=3x²+1

f(-2)=3(-2)²+1

= -12+1

=-13 ans

The domain of the given function is x≤-2

Function, in mathematics, is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given here: The function f(x)=-√(√-4x)²

Simplifying the expression we get

f(x)=-√(√-4x)²

f(x)= -√-4x

   Case 1) If the domain of x is greater than 2 then we have

f(3)=-√-12 which is a complex number and thus is not possible.

Case2 id x≤-2

then we have

f(-2)=-√8 which is not complex

Thus the feasible domain of the function is given by x≤-2

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Answer: 48 and 12.

Step-by-step explanation:

Let the smaller number is x. Hence, the larger number is 4*x.

The difference between 2 number is 36.

So,

4*x-x=36

3*x=36\ |:3

x=12.

4*x=12*4

4*x=48.

Good luck an' have a nice day!

Therefore, In the figure, a∥b  angle m∠7 = 34° .

An angle is a figure in Euclidean geometry made up of two rays that share a vertex, or common terminus, and are referred to as the sides of the angle. Angles of two rays lie in the plane containing the rays. Angles can also result from the intersection of two planes. Dihedral angles are the name given to them.

Here,

Given that a and b are parallel lines,

∠3 and ∠7  are corresponding angles and congruent

m∠3 = 34°

thus ,m∠7 =m∠3 = 34°

so, m∠7 = 34°

Therefore, In the figure, a∥b  m∠7 = 34° .

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Step-by-step explanation:

the correct answer is option a 6a-7

Answer:

31

Step-by-step explanation:

We just have to calculate 87 - 56 which is 31 so the answer is 31 sunflowers.

Answer:

31

Step-by-step explanation:

Since we know that we started with a higher number than we ended with, it is obvious that this is a subtraction problem. Then, we simply have to find the difference by subtracting 87 by 56 (87 - 56 = x). After the calculation, we see that the answer is 31 (87 - 56 = 31).

Given:

A line passes through (1,-2) and is perpendicular to \(-4x+7y=21\).

To find:

The equation of that line.

Solution:

We have, equation of perpendicular line.

\(-4x+7y=21\)

Slope of this line is

\(m_1=-\dfrac{\text{Coefficient of x}}{\text{Coefficient of y}}\)

\(m_1=-\dfrac{-4}{7}\)

\(m_1=\dfrac{4}{7}\)

Product of slope of two perpendicular lines is -1.

\(m_1\times m_2=-1\)

\(\dfrac{4}{7}\times m_2=-1\)

\(m_2=-\dfrac{7}{4}\)

Now, slope of required line is \(-\dfrac{7}{4}\) and it passes through (1,-2). So, the equation of line is

\(y-y_1=m(x-x_1)\)

where, m is slope.

\(y-(-2)=-\dfrac{7}{4}(x-1)\)

\(4(y+2)=-7(x-1)\)

\(4y+8=-7x+7\)

\(4y+7x=7-8\)

\(7x+4y=-1\)

Therefore, the equation of required line is \(7x+4y=-1\).

Factorial design are useful in testing theories because they enable researchers to investigate a theory's construct validity. so the correct answer  is option  (a).

A key technique for identifying the impact of numerous variables on a response is the factorial design. Traditionally, experiments are planned to ascertain how one variable affects just one response.

The corpus of knowledge supporting the analysis and application of test results. The definition and measurement of reliability are of primary relevance. Classical test theory, generalizability theory, and item response theory are examples of theoretical frameworks.

a) They enable academics to investigate a theory's construct validity.

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Step-by-step explanation:

\(y = 3(4 - 2) + 5.5 \\ y = 3(2) + 5.5 \\ y = 11.5\)

If sin θ = 45 4 5 and 2 π 2 < θ < 32 3 π 2 , the value of tan(θ) is 1125/sqrt(23).

First, we need to find the value of cos(θ) since we know sin(θ).

sin²(θ) + cos²(θ) = 1

cos²(θ) = 1 - sin²(θ)

cos(θ) = sqrt(1 - sin²(θ))

cos(θ) = sqrt(1 - (45/4)^2/5^2)

cos(θ) = sqrt(1 - (2025/1600))

cos(θ) = sqrt(575/1600)

cos(θ) = sqrt(23)/20

Now, we can find the value of tan(θ).

tan(θ) = sin(θ)/cos(θ)

tan(θ) = (45/4)/sqrt(23)/20

tan(θ) = (45/4) * (20/sqrt(23))

tan(θ) = (225/2) * (1/sqrt(23))

tan(θ) = (225/2) * (sqrt(23)/23)

tan(θ) = 1125/sqrt(23)

Therefore, the value of tan(θ) is 1125/sqrt(23).

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Answer:

x=1

Step-by-step explanation:

you have -3x+4  and your left with  one whole number when you put -3 and 4 together

Answer: B

Step-by-step explanation:

The answer is 9x^2 + 14xy -19y^2