Identify the perimeter and area of an equilateral triangle with height 9 cm. Give your answer in simplest radical form. PLEASE HELP!!

Answer:

Part 1. [tex]\dfrac{x+1}{2x}=\dfrac{x^2-7x+10}{4x}.[/tex]

Part 2. Solutions: [tex]x_1=1,\ x_2=8.[/tex]

Extraneous solution: [tex]x=0.[/tex]

Step-by-step explanation:

Part 1. You are given the equation

[tex]\dfrac{1}{2}+\dfrac{1}{2x}=\dfrac{x^2-7x+10}{4x}.[/tex]

Note that

[tex]\dfrac{1}{2}+\dfrac{1}{2x}=\dfrac{x+1}{2x},[/tex]

then the equation  rewritten as proportion is

[tex]\dfrac{x+1}{2x}=\dfrac{x^2-7x+10}{4x}.[/tex]

Part 2. Solve this equation using the main property of proportion:

[tex]4x\cdot (x+1)=2x\cdot (x^2-7x+10),\\ \\2x(2x+2-x^2+7x-10)=0,\\ \\2x(-x^2+9x-8)=0.[/tex]

x cannot be equal 0 (it is placed in the denominator of the initial equation and denominator cannot be 0), so [tex]x=0[/tex] is  extraneous solution to the equation.

Thus,

[tex]-x^2+9x-8=0,\\ \\x^2-9x+8=0,\\ \\x_{1,2}=\dfrac{9\pm\sqrt{(-9)^2-4\cdot 8}}{2}=\dfrac{9\pm7}{2}=1,\ 8.[/tex]

Part A: i forgot the question but i know its the third option (c)

Part B:

Solve the original equation by solving the proportion.

The solutions are: (1,6)

Part c:

Name the extraneous solution(s) to the equation

answer: Neither

These are for edu2020

The perimeter of a rectangle is found by multiplying the length by 2 and then adding that to the width multiplied by 2.

The length is 7, multiplied by 2 = 7x2 = 14.

Subtract that from the total perimeter:

42 - 14 = 28

The length of the 2 widths is equal to 28, to find the length of 1 width, divide that by 2:

Width = 28 / 2 = 14

The width is 14 feet.

Answer:

Step-by-step explanation:

Alicia was rock climbing. She climbed to a height of 30 ft. Next , she climbed down 18 ft. Finally she climbed up another 55 ft. Write an addition expression to describe this situation then find the sum of your addition expression to determine Alicia's elevation.

We are given that revenue of Tacos is given by the mathematical expression [tex]-7x^{2}+32x+240[/tex].

(A) The constant term in this revenue function is 240 and it represents the revenue when price per Taco is $4. That is, 240 dollars is the revenue without making any incremental increase in the price.

(B) Let us factor the given revenue expression.

[tex]-7x^{2}+32x+240=-7x^{2}+60x-28x+240\\-7x^{2}+32x+240=x(-7x+60)+4(-7x+60)\\-7x^{2}+32x+240=(-7x+60)(x+4)\\[/tex]

Therefore, correct option for part (B) is the third option.

(C) The factor (-7x+60) represents the number of Tacos sold per day after increasing the price x times. Factor (4+x) represents the new price after making x increments of 1 dollar.

(D) Writing the polynomial in factored form gives us the expression for new price as well as the expression for number of Tacos sold per day after making x increments of 1 dollar to the price.

(E) The table is attached.

Since revenue is maximum when price is 6 dollars. Therefore, optimal price is 6 dollars.

Answer:

Option d is correct.

no , because y does not vary directly with x.

Step-by-step explanation:

Direct variation states that a relationship between any two variables in which one is a constant multiple of the other.

in other way, when one of the  variable changes then the other changes in proportion to the first.

If y is directly proportional to x i.e,  [tex]y \propto x[/tex]

then the equation is of the form;

[tex]y = kx[/tex] where k is the constant of Variation.

From the table:

Consider any values of x and y:

Let x = 4 and y = 28

then by definition of direct variation solve for k;

28 = 4k

Divide both sides by 4 we get;

k = 7

Then the equation become: y = 7x           .....[1]

Check whether the other data follows this equation or not,

x = 6 and y = 48

Substitute in equation [1];

48 = 7(6)

48 = 42 False

Also, for;

x = 8 and  y= 72

72 = 7(8)

72 = 56  False

⇒ y= 7x does not follows the data of the given table.

Therefore, y does not vary directly with x.

Answer:

( -1,-5 )

Step-by-step explanation:

We have the co-ordinates A( -3,3 ), B( -1,7 ) and C( 3,3 ).

We will find the orthocenter using below steps:

1. First, we find the equations of AB and BC.

The general form of a line is y=mx+b where m is the slope and b is the y-intercept.

Using the formula of slope given by [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1} }[/tex], we will find the slope of AB and BC.

Now, slope of AB is [tex]m=\frac{7-3}{-1+3}[/tex] i.e. [tex]m=\frac{4}{2}[/tex] i.e.  [tex]m=2[/tex].

Putting this 'm' in the general form and using the point B( -1,1 ), we get the y-intercept as,

y = mx + b i.e. 1 = 2 × (-1) + b i.e. b = 3.

So, the equation of AB is y = 2x + 3.

Also, slope of BC is [tex]m=\frac{3-7}{3+1}[/tex] i.e. [tex]m=\frac{-4}{4}[/tex] i.e. [tex]m=-1[/tex].

Putting this 'm' in the general form and using the point B( -1,1 ), we get the y-intercept as,

y = mx + b i.e. 1 = (-1) × (-1) + b i.e. b = 0.

So, the equation of BC is y = -x.

2. We will find the slope of line perpendicular to AB and BC.

When two lines are perpendicular, then the product of their slopes is -1.

So, slope of line perpendicular to AB is [tex]m \times 2 = -1[/tex] i.e. [tex]m=\frac{-1}{2}[/tex]

So, slope of line perpendicular to BC is [tex]m \times (-1) = -1[/tex] i.e. m = 1.

3. We will now find the equations of line perpendicular to AB and BC.

Using the slope of line perpendicular to AB i.e. [tex]m=\frac{-1}{2}[/tex] and the point opposite to AB i.e. C( 3,3 ), we get,

y = mx+b i.e. [tex]3=\frac{-1}{2} \times 3 + b[/tex]  i.e. [tex]b=\frac{9}{2}[/tex]

So, the equation of line perpendicular to AB is [tex]y=\frac{-x}{2} +\frac{9}{2}[/tex]

Again, using the slope of line perpendicular to BC i.e. m = 1 and the point opposite to BC i.e. A( -3,3 ), we get,

y = mx + b i.e. 3 = 1 × -3 + b i.e. b = 6.

So, the equation of line perpendicular to BC is y = x+6

4. Finally, we will solve the obtained equations to find the value of ( x,y ).

As, we have y = x+6 and  [tex]y=\frac{-x}{2}+\frac{9}{2}[/tex]

This gives,  [tex]y=\frac{-x}{2}+\frac{9}{2}[/tex] → [tex]x+6=\frac{-x}{2} +\frac{9}{2}[/tex] → 2x+12 = -x+9 → 3x = -3 → x = -1.

So, y = x+6 → y = -1+6 → y=5.

Hence, the orthocenter of the ΔABC is ( -1,5 ).

Answer:

Actually, the equation is

power (in Watts) = I² * r

I - current in amps and r - resistance in watts

Solving this for the current (I)

I = square root (power / resistance)

I = square root (15 / 100)

I = square root (.15)

I = 0.3872983346 amps

answer is B

Step-by-step explanation:

The current in the circuit is approximately 0.39 amperes, which is option B.

The power in an electrical circuit can be calculated using the formula:

P = I^2 * R

Where:

P = Power (in watts)

I = Current (in amperes)

R = Resistance (in ohms)

In your case, you have:

P = 15 watts

R = 100 ohms

You want to find the current (I), so rearrange the formula to solve for I:

I = sqrt(P / R)

I = sqrt(15 watts / 100 ohms)

I = sqrt(0.15 A^2)

I = 0.39 A (approximately)

So, the current in the circuit is approximately 0.39 amperes, which is option B.

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Answer:

Well some places are more expensive. This will effect the prices of utilities because some places have a higher expense of living because of the lack of certain materials or because of the desirable location. For example, although living in Hawaii was beautiful, it was extremely expensive for everyday items because most things needed to be shipped and because of constant tourism.

The factor for dependency of Utility Cost shown below.

The cost of using utilities like power, water, waste disposal, heating, and sewage is known as a utilities expense. During the reporting period, the costs are incurred, computed, and accumulated for, or a payment is made.

Given:

Due to climate and fluctuating utility prices, location might affect your utility expenditures. The expense of heating would be higher in an extremely cold climate than in a warmer one.

Certain locations are more pricey. The cost of utilities will be impacted because some regions have a greater cost of living due to a shortage of specific materials or a desirable location.

For instance, even though Hawaii was a wonderful place to live, the cost of basic necessities was very high due to the frequent tourism and the fact that the majority of goods had to be shipped.

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If

[tex]ax^2+bx+c=(Ax+B)(Cx+D)[/tex]

then

[tex]ax^2+bx+c=ACx^2+(AD+BC)x+BD[/tex]

[tex]\implies a=AC[/tex]

If [tex]a[/tex] is known and Jimmy wants to find [tex]A[/tex], then he has to know the value of [tex]C[/tex].

Answer:

possible value of A are 1, 2, 4

Step-by-step explanation:

Jimmy is trying to factor the quadratic equation ax^2 + bx + c = 0.

He assumes that it will factor in the form ax^2 + bx + c = (Ax + B)(C x + D)

Given a=4

We need to find the value of A

When we do factoring we use the factors of the numbers

(Ax+B)(Cx+D) is ACx^2 + ADx + BCx + BD

[tex]ax^2 + bx + c =ACx^2 + ADx + BCx + BD[/tex]

When a=4  then AC is also 4

A* C = 4

1 * 4= 4

2 * 2= 4

4 * 1 = 4

So possible value of A are 1, 2, 4

Answer:

50+2p=C

Step-by-step explanation:

Answer: Our required equation to find the total cost of his monthly membership to the gym  would be [tex]C=50+2p[/tex]

Step-by-step explanation:

Let C be the total cost for your monthly membership.

Let p be the number of times you used the pool in one month.

Cost of every time he want to use the pool = $2

Monthly fee = $50

According to question, it becomes,

[tex]C=50+2p[/tex]

Hence, our required equation to find the total cost of his monthly membership to the gym  would be [tex]C=50+2p[/tex]

Answer: The second equation (2y=4x+6) can be divided by 2 to get y=2x+3. Since this is the same equation as the first one, there are infinite solutions.

Answer:

D.)

Step-by-step explanation:

The zero's are referencing when y=0, note that when y=0 they are talking about the x-intercepts.  You can graph the function and see when the graph crosses the x-axis or solve for the x-values.  I will solve it via factoring and so:

[tex]f(x)=x^2+5x+6[/tex]

Multiply the outer coefficients, in this case 1 and 6, and 1×6=6.  Now let's think about all the factors of 6 we have: 6×1 and 2×3.  Now is there a way that if we use any of these factors and add/subtract them they will return the middle term 5?  Actually we can say 6-1=5 and 2+3=5.  Let's try both.

First let's use 6 and -1 and so:

[tex]x^2+5x+6\\\\x^2+6x-x+6\\\\x(x+6)-1(x-6)[/tex]

Notice how we have (x+6) and (x-6), these factors do not match so this is incorrect.

Now let's try 2 and 3 and so:

[tex]x^2+5x+6\\\\x^2+3x+2x+6\\\\x(x+3)+2(x+3)\\\\(x+2)(x+3)[/tex]

Notice how the factors (x+3) matched up so this is a factor and so is (x+2), now to solve for the zero's let's make f(x)=0 and solve each factor separately:

Case 1:

[tex]f(x)=x+2\\\\0=x+2\\\\x=-2[/tex]

Case 2:

[tex]f(x)=x+3\\\\0=x+3\\\\x=-3[/tex]

So your zero's are when x=-2 and x=-3.

D.) x=-3 and x=-2 because the graph crosses the x-axis at -3 and -2.

~~~Brainliest Appreciated~~~

Answer:

The answer is C) Remote Interior Angle

Step-by-step explanation:

The name of an interior angle of a triangle that is not adjacent to a given exterior angle of the triangle is the remote interior angle. Getting the values of each sides help you come up with the remote interior and exterior angles.

Answer:

1.75 h

Step-by-step explanation:

t = k/w

k = 28

t = 28/w

If w = 16,

t = 28/16

t  = 1.75 h

It will take 16 workers 1.75 h to complete the job.

Answer:

correct choice is 1st option

Step-by-step explanation:

Two given triangles have two pairs of congruent sides: one pair of length 7 units and second pair of length 8 units. The third side is common, i.e the lengths of third sides are equal too.

Use SSS theorem that states that if three sides of one triangle are congruent to three sides of another triangle, then these two triangles are congruent.

Thus, given triangles are congruent by SSS theorem.

Answer: Geometric , convergent

Step-by-step explanation:

Given sequence is    {  12 + ( -8 )  + 16/3 + ( - 32/9 ) + 64/27 + . . .  . . . . }

To check whether the sequence is arithmetic , we first find difference of first two terms then find difference of third and second term .

If we get both the difference same , then it is arithmetic .

d₁   =   - 8 - ( 12 ) =  - 20

           16                              40

d₂  =   ------     - ( - 8 )  =    ------------

             3                                3

Common difference is not same , thus it is not arithmetic .

To check whether sequence is geometric , we divide second by first term and then third by second term . If we get the same ratio , then it is geometric .

             -8              - 2

r₁   =   ----------- =   ----------

             12                3

            16/3           16                     -2

r₂   =   ---------- =    ----------    =    -----------

            - 8              3 * ( -8)              3

Thus common ratio is same , so it is geometric .

Now we need to check whether it is convergent or divergent .

We have an infinite geometric series .

It is convergent if | r | < 1 , that is common ratio is less than 1 .

We have | r |  = | - 2/3 |  = | - 0.66 |  = 0.66 < 1 .

Thus the  geometric series converges .

Thus given series is geometric , convergent .

Third is the correct option .

Answer:

Convergent and Divergent Sequences and Series Practice.

1. The sequence diverges; the series diverges.
2. geometric, divergent
3. 3/5 and -1/6

Convergent and Divergent Sequences and

Series
1. 1/5 and 2/3

2.geometric, convergent

3. arithmetic, divergent

Step-by-step explanation:

You’re welcome

Answer: y = {5, 4, 8}

Step-by-step explanation:

f(x) = 4 + x²

f(-1) = 4 + (-1)²

      = 4 + 1

      = 5

f(0) = 4 + (0)²

      = 4 + 0

      = 4

f(1) = 4 + (1)²

      = 4 + 1

      = 5

f(2) = 4 + (2)²

      = 4 + 4

      = 8

Put the values from domain to the equation of the function.

f(x) = 4 + x²

f(-1) = 4 + (-1)² = 4 + 1 = 5

f(0) = 4 + 0² = 4 + 0 = 4

f(1) = 4 + 1² = 4 + 1 = 5

f(2) = 4 + 2² = 4 + 4 = 8

Answer:

Use desmos it is really helpful

[tex]The\:Answers\:Are:[/tex]

[tex]A.\:If\:\:UV=KL \:\:And\:\:KL=6,\:Then\:\:UV = 6,\:True[/tex]

[tex]C.\:Angle\:ABC\:Is\:Congruent\:To\:ABC,\:True[/tex]

[tex]\mathrm{E.\:If\:Angle\:DE F\:Is\:Congruent\:To\:Angle\:HJK,\:Then\:Angle\:HJK\:Is\:Congruent\:To\:Angle\:DE F},\:True[/tex]

[tex]The\:Questions\:B\:And\:C\:Are\:False[/tex]

[tex]\mathrm{Hope\:This\:Helps!!!}[/tex]

[tex]\mathrm{Please\:Mark\:Brainliest!!!}[/tex]

[tex]\mathrm{-Austint1414}[/tex]

Answer:

The length of the string is 32.56 feet  (Approx) .

Step-by-step explanation:

As given

A kite is 37 feet in the air and string forms an angle of 62 degrees .

Now by using the trignometric identity.

[tex]sin\theta = \frac{Perpendicular}{Hypotenuse}[/tex]

As shown in the figure given below.

[tex]\theta = 62^{\circ}[/tex]

Perpendicular = AB

Hypotenuse = AC = 37 feet

Put in the identity .

[tex]sin\ 62^{\circ} = \frac{AB}{AC}[/tex]

[tex]sin\ 62^{\circ} = \frac{AB}{37}[/tex]

[tex]sin\ 62^{\circ} = 0.88\ (Approx)[/tex]

Put in the identity

[tex]0.88 = \frac{AB}{37}[/tex]

AB =  0.88 × 37

AB = 32.56 feet  (Approx)

Therefore the length of the string is 32.56 feet  (Approx) .

Answer:

B)She should accept because the probability of Door C being the Grand Prize increased.

Hope you do well on the rest of the test!

Answer:

5x

Step-by-step explanation:

Answer:

The daily rental rate is 75 dollars

The cost per mile is .14

The cost for the mileage is .14m

The total cost per day  is .14m+75

Step-by-step explanation:

cost = 75 + 0.14m

Let's rewrite this in the form  

y= mx+b

 where m is the slope and b is the y intercept

cost = .14m +75

The daily rental rate is 75 dollars

The cost per mile is .14

The cost for the mileage is .14m

The total cost per day  is .14m+75

Answer:

We have the equation y - 4 = (-2)( x - 0 );

Then, y - 4 = -2x;

Finally, y = -2x + 4;

The correct answer is B) y = -2x + 4;

Step-by-step explanation:

The equation for the line with a slope of -2 and crossing the y-axis at (0,4) is y = -2x + 4.

To find an equation for a line that crosses the y-axis at (0,4) with a slope of -2, we can use the slope-intercept form of a line, which is y = mx + b, where m is the slope and b is the y-intercept. Since we are given that the slope (m) is -2 and the y-intercept (b) is 4, the equation of the line is y = -2x + 4.

The point slope formula is

y-y1=m(x-x1)

M represents slope and (y1, x1) are the coordinates to your point.

From this question we know the slope is -1/7 so you plug that in to the formula which will give you

Y-y1=-1/7(x-x1)

There isn’t a point attached to this question so let’s make up a point and say it’s (1,7). You plug this into the equation to get

Y-7=-1/7(x-1)

This is your equation.

Answer:

8 adults

Step-by-step explanation:

The proper equation to find the number of adults is as follows...

(1 x 5) +(10x) = 85

Since there is only one child will will have 1 ticket for a child. hint ( 1 x 5)

Since we need to find the total number of adults at the movie group we will put (10x)

Since the total cost is 85 we will have it equal to $85

Now time to solve

5 + 10x = 85

first subtract 5 from both sides ( 5 - 5 ) and ( 85 - 5 )

10x=80

Now divide both sides by 10 ( 10x/10 ) and 80/10

x=8

So there are 8 adults.

Answer:-5

Step-by-step explanation:

2x+7-x+12=14

x+19=14

x=-5

Answer:

x=-5

Step-by-step explanation:

Ok so, (2x+7)+(-x+12)=14

solve the equation, by opening the parantheses.

2x+7+-x+12=14

x= -5

Answer:

The total inventory is 200 + 300 + 400 + 100 = 1000.

Step-by-step explanation:

If 300 units remained, the we calculate the cost of the 700 sold via LIFO. These 700 units include the 100 units at $12.00, the 400 units at $11.00, and 200 units at $10.00 (out of the 300 purchased). This is a total cost of 100*12 + 400*11 + 200*10 = 1200 + 4400 + 2000 = $7600.

The required quadratic equation is [tex]2x^{2} -20x+48[/tex].

Given roots of quadratic equation are 4 and 6.

Also given here leading coefficient is 2.

We know that, the formulae for forming quadratic equation when its roots are given is as follows: [tex]x^{2} -(\alpha +\beta )x+\alpha \beta[/tex]

Here [tex]\alpha and \beta[/tex] are the roots of the quadratic equation.

Let [tex]\alpha =4 and \beta = 6[/tex]

Putting the value of [tex]\alpha and\beta[/tex] in the above formulae we get,

[tex]x^{2} -(4+6)x+4\times6[/tex]

[tex]x^{2} -10x+24[/tex]

But remember here 2 is the leading coefficient of the quadratic equation with roots 4 and 6 (given in question),so we have to multiply the equation by 2 to get the final answer.

So, [tex]2(x^{2} -10x+24)[/tex]

[tex]2x^{2} -20x+48[/tex].

Hence the required quadratic equation is [tex]2x^{2} -20x+48[/tex].

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