What is the area of this triangle?
8cm
6cm
2cm

Answer:

Step-by-step explanation:

The slope of the line y = -5x-4 is -5 or -5/1 so the slope of the perpendicular line is +1/5 eg…

y = x/5 + c

To find c we substitute x=15, y=-2

-2 = 15/5 + c

-2 = 3 + c

C = -5

So the equation is

Y = x/5 - 5

The expression of [tex]3-2tan^2x\\[/tex] in terms of [tex]cosx[/tex] is [tex]3-2(\frac{1-cos^2x}{cos^2x})[/tex]. Similarly, any tirigonometric equation can be convereted into other forms of trigonometric functions.

What is trigonometric functions?

Denoting the relation between a right-angled triangle's angle and sides are trigonometric functions, which are periodic functions.

Consider the given expression.

[tex]3-2tan^2x\\[/tex]

Now, substitute [tex]\frac{sinx}{cosx}[/tex] for [tex]tanx[/tex] as follows:

[tex]3-2tan^2x=3-2(\frac{sinx}{cosx})^2\\=3-2(\frac{sin^2x}{cos^2x})[/tex]

Now, all the terms are converted into cos x except the sin x terms in the numerator. Hence, using the relation between sin x and cos x. Substitute [tex]1-cos^2x[/tex] for [tex]sin^2x[/tex].

[tex]3-2tan^2x=3-2(\frac{1-cos^2x}{cos^2x})[/tex]

Now, all the terms are in cos x. Hence, the expression of [tex]3-2tan^2x\\[/tex] in terms of [tex]cosx[/tex] is [tex]3-2(\frac{1-cos^2x}{cos^2x})[/tex]. In the similar way any function can be conveted into other trigonometric functions.

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Answer:

113

Step-by-step explanation:

Finding a remainder seems like you should be dividing. Remember everything is a shortcut for something else in math. So first you learn Long Division, but that's too much writing, so then you learn Synthetic Division, but there's an even shorter shortcut. It is called Remainder Theorem. If you just substitute 3 (because x-3 in the question) into the function, and you calculate it, you get the remainder.

f(x) = 4x^3 + 5

f(3) = 4(3)^3 + 5

f(3) = 4(27) + 5

= 108 + 5

= 113

See image.

Answer:

i think it might be c

Step-by-step explanation:

a) 88 unique special dinners are there if there are 8 appetizers and 11 entrees.

b) 84 unique special dinners are there if there are 12 appetizers and 7 entrees.

Given that,

In a typical Chinese restaurant, the Special Dinner is frequently offered, allowing the customer to select one appetizer and one entrée.

We have to find

a) How many unique special dinners are there if there are 8 appetizers and 11 entrees.

b) How many unique special dinners are there if there are 12 appetizers and 7 entrees.

We solve

a) We just multiply

8×11=88

b) 12×7=84

Therefore, a) 88 unique special dinners are there if there are 8 appetizers and 11 entrees.

b) 84 unique special dinners are there if there are 12 appetizers and 7 entrees.

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The number of minutes in total that the three swimmers spent in completing the race is; 4.12795 minutes

We are given;

Time taken by Martin to finish swimming = 78.934 seconds

Time taken by Abby to finish swimming = 83.978 seconds

Time taken by the last teammate to finish the race = 84.765 seconds

Thus;

Total time taken by the three swimmers to finish the race = 78.934 + 83.978 + 84.765 = 247.677 seconds

Now, we want to know the total time they spent in minutes and we know that the unit of conversion is;

60 seconds = 1 minute

Thus;

247.677 seconds = (247.677 * 1)/60 = 4.12795 minutes

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Answer:

Step-by-step explanation:

The number of pack of cards sold at the state of Arkansas is 8100.

For the values given in question.

The tax on playing card in state of Arkansas = 6 cents per pack.

Total revenue generated =  $48600.

Divide total revenue by one pack price to get the number of packs.

Number of pack = Total revenue/price of each pack

Number of pack =  $48600/6

$48600.Number of pack = 8100

Thus, the number of pack of cards sold at the state of Arkansas is 8100.

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Answer:

(7,5)

Step-by-step explanation:

[tex]-3y+4x=13 \implies -15y+20x=65 \\ \\ -5y-6x=-67 \implies 15y+18x=201 \\ \\ \therefore 38x=266 \implies x=7 \\ \\ \implies -3y+4(7)=13 \implies y=5 \\ \\ \therefore (7,5)[/tex]

Answer:

Step-by-step explanation:

Percent increase is the percent of the increased value over the initial value.

In our case the increase is represented by the difference of values and the initial value is Value 1.

So the matching choice is D.

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

Answer choices in the comment:

The numerical coefficient is -7

From the question,  the expression is given as

-7x

Considering an expression given as

Ax

The numerical coefficient of the above expression is A

When compared to the expression -7x, we have

The numerical coefficient is -7

So, we can conclude that the numerical coefficient of -7x is -7

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Answer:

-7

Step-by-step explanation:

The numerical coefficient is -7

Answer:

The error made is that the ASA theorem cannot be used here because the congruent side is not directly in between the two congruent angles in either triangle. Really, the information we are given is Angle-Side-Side, not Angle-Side-Angle, and this is not a congruence theorem unless the triangles given are right triangles.

The value of x is 4 for the isosceles triangle has a base that measures x+2 with legs that measure 4x-3 and 2x+5.

Therefore, an isosceles triangle has two equal sides as well as two equal angles. An equilateral triangle is one in which all of its sides are equal, and a scalene triangle is one in which none of its sides are equal. The characteristics of an isosceles triangle are as follows: There is agreement between two sides. The base of an isosceles triangle refers to the third side of the triangle, which is unequal to the other two sides. The two angles that are opposite the equal sides line up perfectly.

Here,

Since the adjacent sides of isosceles triangles are equal,

4x-3=2x+5

4x-2x=5+3

2x=8

x=4

The isosceles triangle has a base that measures x+2 and legs that measure 4x-3 and 2x+5, so x is equal to 4.

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Answer:

First step, correct answer is (3,1)

Step-by-step explanation:

1.it should be x+2(3x-8)=5

2. x+6x-16=5

3.7x=21

4. 7x/7=21/7

5. x=3

then you can eitheir take x+2y=5 or y=3x-8 i suggets taking second option as it is easier, just input values for x in

)  3x-8=y

6. 3(3)-8= 1

7. x=3, y=1

Answer:

5 feet.

Step-by-step explanation:

if we see that 3 feet is the model and 15 feet is the actual, we find the ratio is 3:15 or 1:5. since the width is 1 foot, then we see the actual is 5 feet long.

Each person need to pay $ 80.88345.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

Bill without tax = 105.73

Tax = 6%

So, bill amount after tax = 105. 73 + 105. 73 x 6/100

                                        = 105.73 + 6.3438

                                        = $112.0738

Addition of 20% tip = 112.0738 + 211.46 = $323.5338.

If the amount is divided among 4 people, each will pay

= 323.5338/4

= $ 80.88345

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Answer:

Theres nothing to see?

Step-by-step explanation:

Answer:

First is one value of x

Second is no values of x

Third is all values of x

Step-by-step explanation:

Please give brainliest!

Answer: The answer is C: No solution

Step-by-step explanation:

By squaring the other side (to therefor remove the square off X) you get [tex]x-3=x+6\sqrt{x} +9[/tex]

You then cancel out the equal terms, in this case x, to reach the equation:

[tex]-3=6\sqrt{x} +9[/tex]

This equation, has no solution, as the left side is always negative, and the right side will always be positive, making any statement for x false.

The length AB of rectangle in terms of x is (4 + x) and values of a and b are 10 and 4.

The side AB measures (4 + x). Hence, the length of AB in terms of x is (4 + x).

The area of rectangle is calculated by the formula-

Area = length × breadth

Keep the values in formula -

28 = (4 + x) (6 + x)

Performing multiplication of both brackets with each other

28 = 24 + 4x + 6x + x²

Solving and rewriting the equation

x² + 10x = 4

Equation in question - x² + ax = b

Comparing both the equations, we get a = 10 and b = 4.

Thus, length of AB is (4 + x) and value fo a is 10 and b is 4.

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The probability of getting a number greater than 4 when the dice is rolled 20 times is 7.

The number on dice greater than 4 is 2 (that is 5 and 6 on dice) thus the probability of getting a number greater than 4 is

P = 2/6

P = 1/3

This is the probability if the dice were rolled once but if the dice were rolled 20 times thus the probability, in this case, needs to be multiplied by 20  

P = 1/3*20

P = 6.66

equivalents to 7

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They bought  15 acres at $ 4000 per acre and  8 acres at  $6300 per acre

Let,

They bought x acres at $ 4000

and ( 23-x ) acres at $ 6300

From information,

By using algebra,

4000x + 6300(23-x) = 110,400

4000x - 6300x+ 144900 = 110,400

-2300x = 110,400-144900

- 2300x  = - 34500

x =34500 /2300

x = 15

x = 15

They bought 15 acres at $ 4000 per acre

(23 - 15 ) = 8 acres at  $6300 per acre

Hence, they purchased 8 acres for $6300 per acre and 15 acres for $4,000 each.

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The blanks are -2 and 0.5 respectively, by solving the expression (8 - 2x) *(-0.25x)

What does the term Algebraic Expression means?

In mathematics, an algebraic expression is an expression composed of variables and constants as well as algebraic operations (addition, subtraction, etc.). Terms combine to form expressions.

Solution:

Given the expression, we need to solve it by using the properties of basic multiplication.

= (8 - 2x)*(-0.25x)

= (8*(-0.25x)) + (-2x * (-0.25x))

= -2x + 0.5[tex]x^{2}[/tex]

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The table for the linear equation is summarized below:

d                         t

3                        13

4                        18

5                        23

6                        28

In this problem we have a two-column table associated to a linear function, the first column of the table represent a set of values of the domain (d) of the function and the second column of the table is for the set of values of the range (t) of the same. We need to fill the second column of the table with the values associated with the range:

d = 3

t = 5 · 3 - 2

t = 15 - 2

t = 13

d = 4

t = 5 · 4 - 2

t = 20 - 2

t = 18

d = 5

t = 5 · 5 - 2

t = 25 - 2

t = 23

d = 6

t = 5 · 6 - 2

t = 30 - 2

t = 28

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The missing expression in step 2 should be [(6² + 2)/0.5] - 14.8 ÷ 8.

The missing expression in step 6 should be 76 - 1.85.

In order to evaluate this expression, we would apply the PEMDAS rule, where mathematical operations within the parenthesis are first of all evaluated, followed by exponent, and then multiplication or division from the left side of the expression to the right. Lastly, the mathematical operations of addition or subtraction would be performed from left to right.

For step 1, we have the following:

[(6² + 2)/|-0.5|] - 14.8 ÷ 8.

In step 2, we would take the absolute value of -0.5:

[(6² + 2)/0.5] - 14.8 ÷ 8.

Therefore, we would have the quantity of the sum of six squared (6²) plus two (2) divided by 0.25, minus 14.8 ÷ 8

In step 3, we would take the exponent of 6:

[(36 + 2)/0.5] - 14.8 ÷ 8.

In step 4, we would add 36 and 2 together:

[(38)/0.5] - 14.8 ÷ 8.

In step 5, we would divide 38 by 0.5:

76 - 14.8 ÷ 8.

In step 6, we would divide 14.8 by 0.5:

76 - 1.85

In step 7, we would subtract 1.85 from 76 as follows:

Solution = 76 - 1.85 = 74.15.

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Step-by-step explanation:

[tex]6(8v - 7) - 10 \\ 48v - 42 - 10 \\ 48v - 52[/tex]

The system of equations best represented by the graph are 4x + y = 6 and −2x + y = −5

The solution of the equations plotted in the graph can be found by checking the point of intersection of the lines

By examining the given graph we can guess the x and y values of the point of intersection. We need to guess because we do not have a means of getting the exact value from the graph. I guess x = 1.9 and y = -1.4

In order to find the system of equations represented by the graph, we need to solve the equations given in the option and check which one gives us  x and y values close to what we guessed from the graph

By Solving 4x + y = 6 and −2x + y = −5:

4x + y = 6          (1)

−2x + y = −5      (2)

Using elimination, subtract (2) from (1), this gives:

6x = 11            

x = 11/6 = 1.83

Put x = 11/6 into (1):

4(11/6) + y = 6

y = 6 - 4(11/6)

y = 6 -44/6 = -4/3 = -1.33

Since these calculated values are very close to the guessed values

Therefore, 4x + y = 6 and −2x + y = −5 are the system of equations best

represented by the graph. So option A is the answer

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Answer:

see explanation

Step-by-step explanation:

(a)

given y is inversely proportional to x² then the equation relating them is

y = [tex]\frac{k}{x^2}[/tex] ← k is the constant of variation

to find k use any ordered pair from the table

using (2, 4 ) , then

4 = [tex]\frac{k}{2^2}[/tex] = [tex]\frac{k}{4}[/tex] ( multiply both sides by 4 )

16 = k

y = [tex]\frac{16}{x^2}[/tex] ← equation of variation

(b)

when y = 25 , that is

25 = [tex]\frac{16}{x^2}[/tex] ( multiply both sides by x² )

25x² = 16 ( divide both sides by 25 )

x² = [tex]\frac{16}{25}[/tex] ( take square root of both sides )

x = ± [tex]\sqrt{\frac{16}{25} }[/tex] = ± [tex]\frac{4}{5}[/tex]

the positive value of x is then [tex]\frac{4}{5}[/tex]

The given quadrilateral PONY is rotated to 180° as P'O'N'Y' and its coordinates are:

So, rotate the given quadrilateral at 180° as follows:

Given quadrilateral: PONY

Rotate to 180° and plot as follows:

Quadrilateral after rotation: P'O'N'Y'

(Refer to the graph attached below)

Therefore, the given quadrilateral PONY is rotated to 180° as P'O'N'Y', and its coordinates are:

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Answer:

P': (2, -7)

O': (2, -3)

N': (6, -3)

Y': (5, -6)

Step-by-step explanation:

The equation for the linear equation parallel to BC is:

y = (2/3)*x - 19/3

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:

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

And two lines are parallel if both lines have the same slope and different y-intercept.

So if we want to et a line parallel to BC whose endpoints are (1, 3) and ( 4, 5), the slope should be:

slope = (5 - 3)/(4 - 1) = 2/3

So our line is like:

y = (2/3)*x + b

And this must pass through (2, -5)

Replacing these values we get:

-5 = (2/3)*2 + b

-5 - 4/3 = b

-15/3 - 4/3 = b

-19/3  =b

Then the linear equation is:

y = (2/3)*x - 19/3

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