(3,4)(4,-3)(7,4)(3,8)
Is it a function ?

The roots of the quadratic equation 0 = 2x² + 12x-14 is (C) x=-7 and x=1.

Any equation in algebra that can be written in the standard form where x stands for an unknown value and a, b, and c stand for known values is said to be a quadratic equation.

In general, it is assumed that a > 0; equations with a = 0 are regarded as degenerate since they become linear or even simpler.

So, the roots of 0 = 2x² + 12x-14 are:

2x² + 12x-14  = 0

2x² + 14x - 2x -14

2x(x + 7) - 2(x + 7)

(2x - 2) (x + 7)

Now, use the zero product property as follows:

2x - 2 = 0

2x = 2

x = 2/2

x = 1

And

x + 7 = 0

x = -7

Therefore, the roots of the quadratic equation 0 = 2x² + 12x-14 is (C) x = -7 and x = 1.

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Correct question:

What are the roots of the quadratic equation 0 = 2x² + 12x-14?

a. 1,6, -7

b. 2,12,-14

c. -7,1

d. -1,7

Answer:

Hence he travels 45 km

Step-by-step explanation:

*Image*

Answer:

y=1/5x-2

Step-by-step explanation:

y+1=1/5x(x-5)

y+1=1/5x-1

y=1/5x-2

hope that helps :)

Answer:

1. 5/3 is not equal to 3/5.

2. 7-(4+3) is equal to (4+3)-7

3. (x + y) + 1 is equal to x + (y + 1)

Step-by-step explanation:

1. 5/3 and 3/5 are completely different fractions and when you switch the denominator and the numerator you get a different fraction: 5/3 = 1 2/3, 3/5

2. If you solve both of them, they are equal because 7-7 = 7-7

3. This is equal due to the associative addition property, which means that when the addition of three or more numbers, the total/sum will be the same, even when the grouping of addends are changed.

Plz mark brainliest thx

#1

\(\boxed{\dfrac{a}{b}=\dfrac{b}{a},a=b}\)

Here 5\(\neq 3\)

Hence inequality holds

#2

\(\\ \sf\longmapsto 7-(4+3)=(4+3)-7\)

\(\\ \sf\longmapsto 7-7=7-7\)

\(\\ \sf\longmapsto 0=0\)

Equality holds

#3

\(\\ \sf\longmapsto (x+y)+1=x+(y+1)\)

Equality holds

Done

In order to simplify and verify trig identities, one needs to use the rules of trigonometry and algebra to manipulate the equation until it is in a simplified form.

The most common trig identities to remember include the Pythagorean identity, reciprocal identities, quotient identities, and sum and difference identities. When simplifying an equation, it is important to remember to include the negative sign when necessary and to factor out any common factors.

After simplifying, it is important to verify the equation. This can be done by plugging in known values for the variables and verifying that the equation is true. By utilizing the rules of trigonometry and algebra, one can simplify and verify trig identities. This process is essential for working with trigonometric functions.

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Answer:

im not shure if your asking for an answer but here is this

Solution

Step-by-step explanation:

The midpoint formula is as follows

\(M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})\)

Plug in the information we know.

\((1,-2)=(\frac{7+x_2}{2},\frac{2+y_2}{2})\)

Solve for \(x\)

\(1=\frac{7+x_2}{2}\)

\(2=7+x_2\)

\(x_2=-5\)

Solve for \(y\)

\(-2=\frac{2+y_2}{2}\)

\(-4=2+y_2\)

\(y_2=-6\)

The other endpoint of the segment is \((-5,-6)\)

Hope this helps.

頑張って!

Mr. Li should pay approximately $3,807.33 at the end of each month for his $150,000 car loan with an 18% annual rate, repaid in 5 years.

To find the monthly repayment Mr. Li should pay for his car loan, we will use the following terms:
Loan amount (P): $150,000
Annual interest rate (r): 18%
Loan term (n): 5 years.

Monthly installments
First, let's convert the annual interest rate to a monthly rate:
Monthly interest rate \((R) = (1 + r)^(1/12) - 1\)
\(R = (1 + 0.18)^(1/12) - 1\) ≈ 0.013685
Next, we need to find the total number of monthly payments:
Total monthly payments (N) = n * 12 (since there are 12 months in a year)
N = 5 * 12 = 60.
Now, we can calculate the monthly repayment using the formula for the loan payment:
Monthly repayment\((M) = P * (R * (1 + R)^N) / ((1 + R)^N - 1)\)
\(M = 150,000 * (0.013685 * (1 + 0.013685)^60) / ((1 + 0.013685)^60 - 1)\)
M ≈ $3,807.33

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Using the Pythagorean Theorem, it is found that the value of k is of k = 2.

The problem gives a right triangle in which:

The Pythagorean Theorem relates the length of the legs \(l_1\) and \(l_2\) of a right triangle with the length of the hypotenuse h, according to the following equation:

\(h^2 = l_1^2 + l_2^2\)

Hence, the value of k can be found as follows:

k² + (5.24)² = (5.61)²

k² = (5.61)² - (5.24)²

k = sqrt((5.61)² - (5.24)²)

k = 2.

The value of k is of k = 2.

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By taking the quotient between the two values, we will see that 17^6 is 289 times larger than 17^4

To find this we just need to take the quotient between the two expressions.

Remember that the quotient of two powers with the same base is:

\(\frac{x^n}{x^m} = x^{n - m}\)

So here we need use that rule.

We will get the quotient:

\(\frac{17^6}{17^4} = 17^{6 - 4} = 17^2 \\\\17^2 = 289\)

Then we can see that 17^6 is 289 times larger than 17^4

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Answer:

289 units

Step-by-step explanation:

To find out how many times larger 17^6 is than 17^4, we need to calculate the ratio of the two values. This can be done by dividing 17^6 by 17^4.

17^6/17^4 = (17^2)^3/17^4

Simplifying this, we get:

= 17^(2x3)/17^4

= 17^6/17^4

= 17^(6-4)

= 17^2

So, 17^6 is 289 times larger than 17^4 (17^2 = 289). This means that if 17^4 is represented by one unit, 17^6 would be represented by 289 units.

Answer:

Pretty Sure it’s 20mph

Step-by-step explanation:

X/20=x-10/30

30x=20x-200

30x=20x-200

-20x

10x=-200

Divied by ten on both sides.

x=-20

20mph

Answer:can’t read it

Step-by-step explanation:

Can you take a pic closer to the screen?

The translation 1 unit left of f ( x ) =–7x+10  then g(x) is -7x + 3.

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in its range(involving values of y) or in its domain(involving values of x).

The up and down movements are in the vertical direction by the y coordinate.

The left and right movements are in the horizontal direction by the x coordinate.

When translating a graph, adding units moves the graph to the left, and eliminating units moves the graph to the right.

hence we say that;

f(x) = –7x+10

g(x) = f(x + 1)

= –7(x + 1)+10

= -7x - 7 + 10

= -7x + 3

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Answer:

In The Function of Form, internationally acclaimed architect, Farshid Moussavi, provides a provocative critique of the historically opposing relationship between function and form to reveal the contradiction at the heart of modernism.

Step-by-step explanation:

Answer: A function of the form is a special relationship where each input has a single output like f(x)=x/2 its a function because of the input value

Step-by-step explanation:

a function can be solve this way

f(2)=1

f(16)=8

ect

hope this helps

Answer:

5 hours

Step-by-step explanation:

To figure this out we will do the total she earned yesterday divided by the hours she worked. So, 84/7=12. So know we know how much she earns in an hour, $12. So if she is earn $60 today then we should do 60/12 to figure out how many hours she worked. 60/12=5. So she worked 5 hours.

I hope this helps!!!

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Upon calculating the sum up to the appropriate term, we find that the sum is approximately 0.0713. So, the correct answer is a. 0.0713

It seems like there is a typo in the series notation. I assume the series you are referring to is ∑(2(-1)^n-1)/(12n^2 + 1) from n=1 to infinity. In this case, we can determine the sum using a well-known function and round the answer to four decimal places. Since the given series is an alternating series, we can use the Alternating Series Estimation Theorem to determine an approximation for the sum. The theorem states that if the absolute difference between consecutive terms is decreasing and the limit of the terms as n approaches infinity is zero, the approximation for the sum is accurate up to the first term that is less than or equal to the desired error bound (in this case, 0.0001). For this series, we can see that the absolute difference between consecutive terms decreases as n increases and the limit as n approaches infinity is zero. So, we can find the smallest value of n for which the term is less than or equal to 0.0001 and calculate the sum up to that term.

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Answer: =−13x+21

Step-by-step explanation: Hope this help :D

Let's simplify step-by-step.

x−7(2x−3)

Distribute:

=x+(−7)(2x)+(−7)(−3)

=x+-14x+21

Combine Like Terms:

=x+−14x+21

=(x+−14x)+(21)

=−13x+21

2

3x. + 63x + 9x + 189

Step-by-step explanation:

Use distributive law, in other words multiply the first bracket terms by the second bracket terms

ATQ

\(\\ \tt\hookrightarrow 12+2.5r=95.75\)

\(\\ \tt\hookrightarrow 2.5r=95.75-12=83.75\)

\(\\ \tt\hookrightarrow r=83.75/2.5\)

\(\\ \tt\hookrightarrow r=33.5\)

The completed operations with the values of the exponents are:
1041 = 10^8
1010−4105 = 10^16

To complete the operations and fill in the value of the exponent for the result, let's break it down step by step:

1041 = 10(103)(105)

Here, we are multiplying 10 by 103 and then multiplying the result by 105. To find the exponent, we add the exponents when multiplying.

So, the exponent for the result is 3 + 5 = 8.

Therefore, the expression simplifies to 108.

1010−4105 = 10(104)4

In this case, we have 10 raised to the power of 104, and then we raise the result to the power of 4. When raising a power to another power, we multiply the exponents. So, the exponent for the result is 4 * 104 = 416. Hence, the expression simplifies to 1016.

Therefore, the completed operations with the values of the exponents are:

1041 = 10^8
1010−4105 = 10^16

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Answer:

14 square units

Step-by-step explanation:

Answer:

0.5 X 6 X 2 = 6 square units

Answer:

(3,1)

Step-by-step explanation:

When a point is reflected across the y axis, the sign of its x coordinate flips. Since point A is at (-3,-5), when it is reflected across the y axis its new position will be (3,-5). Now, point A is 3 units from the line y=-2, meaning that when it is reflected across it will be 3 units away from the other direction. (-2+(3))=1, meaning that the final coordinates of point A are (3,1). Hope this helps!

Let L be the linear operator in R2 defined by L(x) = (3x1 - 2x2, 9x1 - 6x2)T. The bases of the kernel and image of L are to be determined. To find the bases of the kernel and image of L, we first recall the definitions of kernel and image of a linear operator. Definition of Kernel: Let T be a linear operator on a vector space V. Then the kernel of T, denoted as ke T, is the subspace of V that consists of all vectors that are mapped to the zero vector of the range of T. Definition of Image: Let T be a linear operator on a vector space V. Then the image of T, denoted as im T, is the subspace of the range of T consisting of all vectors that are mapped by T to some vectors in the range of T. The kernel and image of L are given as follows. Kernel of L: For L(x) = (3x1 - 2x2, 9x1 - 6x2)T to be zero vector, we must have 3x1 - 2x2 = 0 and 9x1 - 6x2 = 0, which implies that x1 = (2/3)x2.

Therefore, a typical element of the kernel of L can be expressed as (x1, x2)T = (2/3)x2(1, 3)T, where x2 is a scalar. Hence, a basis for the kernel of L is {(1, 3)T}. Image of L: The image of L is the subspace of R2 consisting of all vectors that can be expressed in the form L(x) = (3x1 - 2x2, 9x1 - 6x2)T, where x is any vector in R2. It follows that any vector in the image of L is of the form (3x1 - 2x2, 9x1 - 6x2)T = x1(3, 9)T + x2(-2, -6)T. Therefore, a basis for the image of L is {(3, 9)T, (-2, -6)T}.Hence, the bases of the kernel and image of L are as follows. Kernel: {(1, 3)T}Image: {(3, 9)T, (-2, -6)T}.

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Answer:

5.7x10^-8

Step-by-step explanation:

Move the decimal 8 places to the right.

Hope this helps

Answer:

its B

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

The part of the statement following "if" is called the antecedent, and the part of the statement following "then" is called the consequent in conditional statements.

The if statement evaluates the test expression inside the parenthesis ().

If the test expression is evaluated to true, statements inside the body of if are executed.

If the test expression is evaluated to false, statements inside the body of if are not executed.

The part of the statement following "if" is called the antecedent, and the part of the statement following "then" is called the consequent in conditional statements.

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In conditional statements, the part of the statement following 'if' is called the antecedent.

The antecedent is the condition that needs to be true for the consequent to occur.

The consequent is the part of the statement that follows 'then.'

An antecedent is a noun or pronoun that denotes a specific being, place, object, or clause.

It's also referred to as a referent. Without an antecedent, a sentence may be insufficient or nonsensical since it is

required to establish what or to whom a pronoun in a sentence is referring.

In summary, a conditional statement is structured as "if (antecedent) then (consequent)."

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Answer -2

Step-by-step explanation:

Problem 4.2

We're told that y = 2x is the equation of the tangent line through point Q.

Plug this into the equation of the circle (that was given at the very top of the page). Solve for x.

x^2 + y^2 - 18x - 6y + 45 = 0

x^2 + (2x)^2 - 18x - 6(2x) + 45 = 0 ... every "y" replaced with "2x"

x^2 + 4x^2 - 18x - 12x + 45 = 0

5x^2 - 30x + 45 = 0

5(x^2 - 6x + 9) = 0

5(x-3)^2 = 0

(x-3)^2 = 0

x-3 = 0

x = 3

This then means y = 2x = 2*3 = 6

The coordinates of point Q are (x,y) = (3,6)

----------

===========================================================

Problem 4.3

We first need to find the location of point S. That will involve solving this system of equations

\(\begin{cases}x-2y+12=0\\y = 2x\end{cases}\)

which represent the equations of lines SR and QS in that exact order.

Like before, we'll apply substitution to solve for x.

x-2y+12 = 0

x-2(2x)+12 = 0

x-4x+12 = 0

-3x+12 = 0

12 = 3x

12/3 = x

4 = x

x = 4

Which leads to y = 2x = 2*4 = 8

Point S is located at (4,8)

Point R is given to be located at (6,9)

Apply the distance formula for these two points to find the length of SR (aka the distance from S to R).

\(S = (x_1,y_1) = (4,8)\\\\R = (x_2,y_2) = (6,9)\\\\d = \text{Length of SR, aka distance from S to R}\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(4-6)^2 + (8-9)^2}\\\\d = \sqrt{(-2)^2 + (-1)^2}\\\\d = \sqrt{4 + 1}\\\\d = \sqrt{5}\\\\d \approx 2.236068\\\\\)

The exact length is \(\sqrt{5}\) and that approximates to roughly 2.236068 units.

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Exact length = \(\sqrt{5}\) units

Approximate length = 2.236068 units