Arrange in column then perform the indicated operations. 75 - 26.5731 =

△ABC is congruent to △CDA (△ABC ≅ △CDA) under (A) SAS condition.

So, to prove that △ABC ≅ △CDA as follows:

So, △ABC ≅ △CDA under SAS condition.

Therefore, △ABC is congruent to △CDA (△ABC ≅ △CDA) under (A) SAS condition.

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The equation of the parallel line is y = m(x-a) + b.

The equation of the perpendicular line is y = (-1/m)(x-a) + b.

Let the equation of the given line be y = mx + c.

Let the coordinates of the passing point be (a, b).

We need to find the equation of the parallel line.

The slope will remain the same.

y = mx + c'

The line passes through (a, b).

b = ma + c'

y = mx + (b-ma)

y = m(x-a) + b

We need to find the equation of the perpendicular line.

The slope will be the negative reciprocal.

y = (-1/m)x + c"

The line passes through (a, b).

b = (-1/m)a + c"

y = (-1/m)x + (b+a/m)

y = (-1/m)(x-a) + b

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Answer: 6.4

Step-by-step explanation:

Answer:

the 61 curv should lead to ars so the answer is ars

• Given Function A:

You need to remember that, by definition, the value of "y" is zero when the function intersects the x-axis.

Therefore, you need to set up that:

Substitute this value into the function and then solve for "x", in order to find the x-intercept:

• Given that Function B passes through these points:

You need to determine the equation of the line, in order to find the x-intercept using it.

The Slope-Intercept Form of the equation of a line is:

Where "m" is the slope of the line and "b" is the y-intercept.

By definition, the value of "x" is zero when the function intersects the y-axis. Therefore, knowing the first point given in the exercise (whose x-coordinate is zero), you can determine that, for this line:

Substitute "b" and the coordinates of the second point into this equation:

And then solve for "m":

Therefore, the equation of Function B in Slope-Intercept Form is:

Now you can find the x-intercept by using the procedure used for Function A:

You know that:

Hence, the answer is: Third option.

Step-by-step explanation:

To get more than a dollar, Bob needs to earn at least 110 cents. Bob already has 20 cents. He needs to get 9 right to earn over a dollar.

If Bob gets 9 right, Bob would earn 90 cents more. 90 + 20 = 110 cents = $1.1

Algebraic Expression: An algebraic expression in mathematics is an expression which is made up of variables and constants, along with algebraic operations (addition, subtraction, etc.). Expressions are made up of terms

Bob correctly answered 12 questions, so

Bob mis-answered 20 questions.

Let x be the number of questions that he correctly answered.

Let y be the number of questions that he answered incorrectly.

Bob's mother promised to give him 10 cents for each accurate response. This implies that he would receive $10x for correctly answering x questions.

Bob's mother informed him that she would deduct $5 for each incorrect response. This implies that if he answers y questions incorrectly, Bob will forfeit.

- $5y.

Bob completed 32 problems, which indicates that

x + y = 32

After solving 32 tasks, Bob received 20 cents, which indicates that

10x - 5y = 20 - - - - - - - - -1

When x = 32 - y is substituted into equation 1, it produces

10(32 - y) - 5y = 20

320 - 10y - 5y = 20

- 10y - 5y = 20 - 320

- 15y = - 300

y = - 300/ -15 = 20

Substituting y = 20 into x = 32 - y, it becomes.

x = 32 - 20 = 12

To get more than a dollar, Bob needs to earn at least 110 cents. Bob already has 20 cents. He needs to get 9 right to earn over a dollar.

If Bob gets 9 right, Bob would earn 90 cents more. 90 + 20 = 110 cents = $1.1

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Step-by-step explanation:

when an object gains height, Kinetic energy in the object is converted to gpe. gpe = mgh

when an object loses height and falls down, the object is accelerated by gravity (free fall) therefore, gains velocity which means the gpe is converted to kinetic energy.

kinetic energy = 1/2 × m × v²

this is applicable only when the mass is constant.

hope it helps. :)

Answer:

it is important to regroup correctly so that you don't get the wrong answer instead of the right one

Answer:

Step-by-step explanation:

According to quadratic formula:

y = - b  ±  √ b²- 4ac / 2a

y = - (-5) ± √ -5²- 4(2x-12) / 2(2)

y = 5 ± √ 25 - 4(-24) / 4

y = 5 ± √ 25 - (-96) / 4

y = 5 ± √ 121 / 4

y = 5 ± √ (11)² / 4

y = 5 ± 11 / 4

Now either,

y = 5 + 11 / 4

y = 4

Or,

y = 5 - 11 / 4

y = -3/2 = -1.5

Given that a polynomial function [tex]f(x)[/tex] has,

And we need to find [tex]f(x)[/tex]

as we know that if a polynomial has zeroes as [tex]\alpha[/tex] , [tex]\beta[/tex] and [tex]\gamma[/tex] , then the cubic polynomial is given by,

[tex]\longrightarrow f(x)=k (x-\alpha)(x-\beta)(x-\gamma)\\ [/tex]

where ,

Now substitute the given zeroes, as ;

[tex]\longrightarrow f(x)=2[ (x-2)(x-\sqrt3)(x+\sqrt3)]\\ [/tex]

[tex]\longrightarrow f(x)= 2[(x-2)\{ x^2-(\sqrt3)^2\}][/tex]

[tex]\\\longrightarrow f(x)= 2[ (x-2)(x^2-3)]\\ [/tex]

[tex]\longrightarrow f(x)=2[ x(x^2-3)-2(x^2-3)]\\ [/tex]

[tex]\longrightarrow f(x)= 2[ x^3-3x -2x^2+6]\\ [/tex]

[tex]\longrightarrow \underline{\underline{ f(x)= 2x^3-4x^2-6x+12}}[/tex]

and we are done!

Answer:

[tex]f(x)=2x^3-4x^2-6x+12[/tex]

Step-by-step explanation:

Given characteristics of the polynomial:

As the polynomial has 3 roots, it is a cubic polynomial.

[tex]\boxed{\begin{minipage}{6 cm}\underline{Intercept form of a cubic polynomial}\\\\$y=a(x-r_1)(x-r_2)(x-r_3)$\\\\where:\\ \phantom{ww}$\bullet$ $r_n$ are the roots. \\ \phantom{ww}$\bullet$ $a$ is the leading constant.\\\end{minipage}}[/tex]

Substitute the given leading coefficient and roots into the formula:

[tex]f(x)=2(x-2)(x-\sqrt{3})(x+\sqrt{3})[/tex]

Expand to standard form:

[tex]\implies f(x)=2(x-2)(x+\sqrt{3}x-\sqrt{3}x-3)[/tex]

[tex]\implies f(x)=(2x-4)(x^2-3)[/tex]

[tex]\implies f(x)=2x^3-6x-4x^2+12[/tex]

[tex]\implies f(x)=2x^3-4x^2-6x+12[/tex]

We can see here, from the first term to the second term, we minus 2. From the second term to the third term, we minus 2.

So, we're constantly reducing by an amount, therefore making this sequence an arithmetic sequence.

The common difference, said above, is -2 (since if the terms are getting smaller the common difference is a negative number.)

Answer:

8.18

Step-by-step explanation:

Answer:

8.18

Step-by-step explanation:

8.50

-0.32=8.18

you subtract 0.32 from 8.5 meaning you are going to add a zero on 8.5 because the number that you are subtracting has two numbers after the decimal point

In linear equation, $5.26  is her hourly wage .

What is linear equation in math?

Serita worked 6 h and earned $31.50.

1 hour of wage of serita = $31.50/6

                                       = $5.26

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let us find the slope using 2 points

Therefore let us find y

Answer:

The limit from the left does not equal the limit from the right.

Answer:

20 problems.

Step-by-step explanation:

She has 100 - 65 = 35% of her problems left.

35% is equivalent to 7 problems,

so, 100% = 7 * 100/35

               = 100/5

              = 20 problems

Answer:

$370

Step-by-step explanation:

20m times 18.5per m

20x18.5=$370

Answer:

Rs370

Step-by-step explanation:

Here,

1m= Rs18.50

Therefore, 20m = 20*18.50

= 370

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If 12 out of 18 students prefer summer sports, then the fraction of students prefer winter sports is 33.33%

Total number of students = 18

The number of student prefer summer sports = 12

Then the number of student who prefer winter sports = Total number of students - The number of student prefer summer sports

= 18 - 12

= 6 students

The percentage is number that can be represented as the fraction of 100.

It is denoted by the percentage sign "%"

Then the fraction of students who prefer winter sports = (Number of student who prefer winter sports /Total number of students )×100

= (6/18) × 100

= 33.33%

Hence, if 12 out of 18 students prefer summer sports, then the fraction of students prefer winter sports is 33.33%

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Answer:

Step-by-step explanation:

To solve this, find the value of n to one side of the equation.

N is a variable.

Variable is a quantity that can assume any of a set of values.

3n-4=11

First, you add by 4 from both sides.

[tex]\sf{3n-4+4=11+4}[/tex]

Solve.

[tex]\sf{11+4=15}[/tex]

[tex]\sf{3n=15}[/tex]

Then, you divide by 3 from both sides.

[tex]\sf{\dfrac{3n}{3}=\dfrac{15}{3} }[/tex]

Solve.

15/3=5

[tex]\Rightarrow \boxed{\sf{n=5}}[/tex]

As a result, the solution is n=5, which is our answer.

I hope this helps, let me know if you have any questions.

Answer:

cosecxsecx

Step-by-step explanation:

[tex]\hookrightarrow tanx+cotx\\\\\hookrightarrow \frac{sinx}{cosx} +\frac{cosx}{sinx} \\\\\hookrightarrow \frac{sin^{2}x+cos^{2}x }{sinxcosx} \\\\\hookrightarrow \frac{1}{sinxcosx} \\\\\hookrightarrow cosecxsecx[/tex]

Answer: x=0   x=2   x=-1

Step-by-step explanation:

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

Answer:

Factored form: x(x-2)(x+1)=0

Solutions: x=0, x=2, x=-1

Step-by-step explanation:

[tex]x^{3} -x^{2} -2x=0\\[/tex]

[tex]x(x^{2} -x-2)=0\\\left \{ {{x=0} \atop {x^{2}-x-2 =0}} \right. \\\left \{ {{x=0} \atop (x-2)(x+1)=0}} \right. \\x=0,x=2,x=-1[/tex]

Santiago needs to invest  50467.3 dollars for the value of the account to reach $81,000 in 16 years at a rate of 3.3%.

Simple interest is often a predetermined percentage of the principle amount borrowed or lent paid or received over a specific time period.

Borrowers are required to pay interest on interest in addition to principal since compound interest accrues and is added to the accrued interest from prior periods.

Given Santiago is going to invest in an account paying an interest rate of 3.3% compounded annually for the value of the account to reach $81,000 in 16 years.

We know the formula of compound interest which is A = P(1 + r/100)ⁿ,

where A = Amount, P = Principle, n = Time in years and r = rate percentage.

∴ 81000 = P( 1 + 3.3/100)¹⁶.

81000 = P( 1 + 0.03)¹⁶.

81000 = P( 1.03)¹⁶.

81000 = P×1.605.

P = 81000/1.605

P = 50467.3 dollars.

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Answer:

1. Angle A + Angle C = 180 degrees, hence Angle B cannot have a value is ABC is a triangle

2. If Angle A = 90 and Angle C = 90, line AB is parallel to AC and therefore these two lines cannot touch and form a triangle

Step-by-step explanation:

Answer:A triangle can’t have two right angles.

Step-by-step explanation: Three angles inside of a triangle have to sum to 180°. In this triangle the sum of angels will be greater than 180° which is not possible.

In one revolution, cycle travels 18.84 feet.

A problem can be resolved using the unitary method by first calculating the worth of a single unit, and then multiplying that amount to find the required value. A single or unique unit is referred to as unitary. Determining values in relation to a single unit is the goal of this strategy. For instance, we can use the unitary technique to determine how many kilometers a car will go on one litre of gas if it travels 44 km on two litres of fuel. With the unitary method, you first determine the value of a single unit before determining the value of the necessary quantity of units.

Radius = 3 feet

If r is the radius of the wheel (including the tire), then the circumference of the wheel = 2πr

= 2 x 22/7 x 3 feet

= 18.84 feet

In one revolution, cycle travels 18.84 feet.

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Step 1

Given;

Required; To determine where 1 banana went if 29 bananas are accounted for.

Step 2

Here is the break down; the balance should be like this;

Hence, there is no extra 1 banana, The monkeys spent 27 bananas of which the bellboy took 2 bananas and 25 bananas went to the room, and 3 bananas where returned to them. A total of 30 bananas

Answer:

I believe yes.

Step-by-step explanation: