Chelsea is solving a quadratic equation. She wants to find the value of x by taking the
square root of both sides of the equation. Which equation allows her to do this?

x2 + 10x + 16 = 25
x2 + 12x + 36 = 17
X2 + 5x + 25 = 64
x2 + 16x + 4 = 18

Answer:

469.42 ft²

Step-by-step explanation:

         w/sin27 = 38/sin40

                   w = sin27*38/sin40

                    w = 26.84 ft

            ∡X = 180 - 27- 40 = 113º

              A = 0.5*(26.84)*(38)*sin(113)

            A = 469.42 ft²

Answer:

They are both equal to 7.07

Step-by-step explanation:

Using SohCahToa to find x you use the opposite and the hypotenuse if you use the 45 degree angle.

Now you use sin(45)=x/10

x=7.07

Now using SohCahToa to find y you use hypotenuse and adjacent, if using the 45 degree angle.

Now you use cos(45)=y/10

y=7.07

Answer: side y=7.1

side x= 7.1

Step-by-step explanation:

[tex]sin(45)=\frac{x}{10}[/tex]

[tex]x=7.07...[/tex]

[tex]cos(45)=\frac{y}{10}[/tex]

[tex]y=7.07...[/tex]

Answer:

Step-by-step explanation:

Let the first number be x

Let the second number be y

For the first equation

One number is 7 less than 3 times the second number is written as

x = 3y - 7

For the second equation

The sum of the two numbers is 29

So we have

x + y = 29

Substitute the first equation into the second one

That's

3y - 7 + y = 29

4y = 29 + 7

4y = 36

Divide both sides by 4

Substitute y = 9 into x = 3y - 7

That's

x = 3(9) - 7

x = 27 - 7

The numbers are 20 and 9

Hope this helps you

As an approximate decimal, this is 0.5556 which converts to 55.56%

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

Explanation:

Let's say there are 100 households (just for the sake of simplicity). We are told that 90% of them have answering machines. So that means 90 households have answering machines. In addition, 50 households have answering machines and call waiting. Those 50 households are part of the 90 mentioned previously.

We then select a house at random. Someone tells us (or we have some kind of prior knowledge) that whichever house is selected, they have an answering machine. We can ignore the 10 households that don't have an answering machine. Out of those 90 households, 50 have both features. So 50/90 = 5/9 is the probability of getting a household with both features.

The answer would be 1/2 or 50% if we didn't have the prior knowledge of the household having an answering machine. But with this prior knowledge, the conditions change and so does the probability.

----------------

You could also compute 0.50/0.90 to get the same answer.

Answer:

1/3(x+5)

Step-by-step explanation:

f(x) = 3x-5

y = 3x-5

Exchange x and y

x = 3y-5

Solve for y

Add 5 to each side

x+5 = 3y

Divide each side by 3

1/3 ( x+5) = 3y/3

1/3 ( x+5) = y

The inverse is 1/3(x+5)

Answer:

[tex]f^{-1}(x)=\frac{x+5}{3}[/tex]

Step-by-step explanation:

[tex]f(x)=3x-5[/tex]

[tex]\mathrm{We \: need \: to \: find \: the \: inverse \: of \: the \: function.} \\ \mathrm{The \: inverse \: of \: a \: function \: reverses \: the \: original \: function.}[/tex]

[tex]\mathrm{Plug \: f(x) \: as \: y.}[/tex]

[tex]y=3x-5[/tex]

[tex]\mathrm{Solve \: for \: x.}[/tex]

[tex]\mathrm{Add \: 5 \: to \: both \: sides \: of \: the \: equation.}[/tex]

[tex]y+5=3x[/tex]

[tex]\mathrm{Divide \: both \: sides \: of \: the \: equation \: by \: 3.}[/tex]

[tex]\frac{y+5}{3} =x[/tex]

[tex]\mathrm{Switch \: variables.}[/tex]

[tex]\frac{x+5}{3} =y[/tex]

[tex]\mathrm{Plug \: y \: as \: f^{-1}(x).}[/tex]

[tex]f^{-1}(x)=\frac{x+5}{3}[/tex]

Answer:

336m^2

Step-by-step explanation:

The triangle area is half of base times height so: 1/2*8*12=48m^2

There are 4 triangles so 48*4=192

Then the square base area is side times side so: 12*12=144m^2

Then surface area of model is 192m^2+144m^2=336m^2

Answer:

336 m²

Step-by-step explanation:

We can find the surface area of this pyramid by finding the surface area of one of the sides, multiplying it by 4 (as there are 4 sides to the pyramid) then adding it to the surface area of the base.

Each side of this (excluding the base) is a triangle, and to find the area of a triangle we use the equation [tex]\frac{b \cdot h}{2}[/tex].

[tex]\frac{12 \cdot 8}{2}[/tex]

[tex]\frac{96}{2}[/tex]

48.

So, one side of this is 48. Multiplying it by 4 gets us 192.

Now we have to add the area of the base. The area of the bass is a square with side lengths of 12, so we can square 12 to get the area of the bass. 12² = 144.

Now let's add these numbers:

192+144 = 336

So, 336 m² is what this comes out to.

Hope this helped!

To generate a point, you plug in a number for x to get the corresponding y value.

If x = 0 for instance, then the y value is...

y = x^2 - 4

y = 0^2 - 4 ... x is replaced with 0

y = 0 - 4

y = -4

So x = 0 and y = -4 pair up to get the point (0,-4). This is the y intercept as the parabola crosses the y axis here. It turns out that this is also the vertex point as it is the lowest point on the parabola.

----------------

If x = 1, then,

y = x^2 - 4

y = 1^2 - 4

y = 1 - 4

y = -3

meaning (x,y) = (1,-3) is another point on this line.

----------------

Repeat for x = 2

y = x^2 - 4

y = 2^2 - 4

y = 4-4

y = 0

Since we got a y output of 0, we have found an x intercept located at (2,0). The other x intercept is (-2,0).

-------------------

The idea is to generate as many points as possible. Plot all of the points on the same xy coordinate grid. Then draw a curve through those points the best you can. You should get what you see in the diagram below. I used GeoGebra to make the graph. Desmos is another handy tool I recommend.

Note: the more points you generate, the more accurate the graph will be

Answer:

[tex]\frac{x3 + 5x2 + 4x + 4}{x}[/tex]

Step-by-step explanation:

x2+5x+ 4/x+4

Answer:

None

Step-by-step explanation:

You wrote:

"Determine what type of quadrilateral ABCD is, given the following points. A(0,0) B(5,0) C(0,4) D(5,4) Parallelogram, Rectangle, Rhombus, or Square"

According to what you wrote, you don't have any of the listed quadrilaterals.

ABCD (in that precise order) is not a simple polygon according to the coordinates of the points since there is an internal intersection of sides.

ABDC, though, is a rectangle.

The quadrilateral with points A(0,0), B(5,0), C(0,4) and D(5,4) is a rectangle, option B is correct.

To find the type of quadrilateral find the length of four sides:

For A(0,0) and B(5,0)

AB=√(5-0)²+(0-0)²

AB=5 units

For  B(5,0) and D(5,4)

BD=√(5-5)²+(4-0)²

BD=√16

BD=4 units

For C(0,4) and D(5,4):

BD=√(5-0)²+(4-4)²

=5 units

For A(0,0) and C(0,4):

AC=√(0-0)²+(4-0)²

= 4 units.

In the quadrilateral the opposite sides are equal, so it is a rectangle.

Hence, the quadrilateral is a rectangle. Option B is correct.

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Complete question:

Determine what type of quadrilateral ABCD is, given the following points. A(0,0) B(5,0) C(0,4) D(5,4)

(A) Parallelogram

(B) Rectangle

(C) Rhombus
(D)Square

Answer:

[tex]\boxed{\sf Average \ Speed = 54\ km/hr}[/tex]

Step-by-step explanation:

Given:

Distance = S = 18 km

Time = t = 20 min = 20/60 = 0.33 hours

Required:

Average Speed = <v> = ?

Formula:

Average Speed = Total Distance Covered / Total Time Taken

Solution:

A . S = 18 / 0.33

A.S = 54 km/hr

Answer:

0.9km/minute

or

54km/hour

Step-by-step explanation:

18km in 20 minutes = 18km/20min

18km/20min = 0.9km/min

1 hour = 60 minutes

20 minutes = 20/60 = 0.3333 hours

18km/20mins = 18km/0.3333hours = 54km/hour

Answer:

A.

Step-by-step explanation:

We are given the two points (2,7) and (4,-1).  In order to determine the linear equation, we need to find the slope and the y-intercept. First, find the slope m. Let (2,7) be x1 and y1, and let (4,-1) be x2 and y2:

[tex]m=\frac{y_2-y_1}{x_2-x_1} =\frac{-1-7}{4-2}=-8/2=-4[/tex]

Thus, the slope is -4.

Now, to find the y-intercept, we can use the point-slope form. Recall that the point slope form is:

[tex]y-y_1=m(x-x_1)[/tex]

Where (x1, y1) is a coordinate pair and m is the slope.

Use either of the two coordinate pair. I'm going to use (2,7). Substitute them for x1 and y1, respectively:

[tex]y-(7)=-4(x-(2))\\y-7=-4x+8\\y=-4x+15[/tex]

This is also slope-intercept form. The answer is A.

Answer:

A. y=-4x+15

Step-by-step explanation:

First, you want to find the slope by using the formula

[tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

The first step is to put in the right numbers,

[tex]\frac{-1-7}{4-2}[/tex]

Then, subtract the numbers accordingly

[tex]\frac{-8}{2}[/tex]

Then simplify

[tex]\frac{-4}{1}[/tex] or -4

The next step is finding the y-intercept, you can do this by drawing it out or using the formula (i will be using the point (2,7) where y is 7 and x is 2)

y=-4x+b   Plug in the values

7=-4(2)+b   Multiply

7=-8+b   add 8 to both sides to isolate the variable

15=b

so y=-4x+15

Hope this helps, if you have any questions, feel free to ask.

Have a good day! :)

Answer:

y = -x/4 + 9/2

Step-by-step explanation:

The diagonal AC is the perpendicular bisector of BD.

The centre of the square, P, through which both diagonal pass through is at the average of the coordinates of B(2,6) and D(0,-2)

P ((2+0)/2, (6-2)/2) = P(1,2)

The slope of BD,

m = (yd-yb)/(xd-xb) = (-2-6)/(0-2) = -8/-2 =4

Slope of AC

m' = -1 / m = -1/4

Using the point slope form of the line AC, slope m' through P(1,2)

y-yp = m'(x-xp)

y-2 = -(1/4)(x-1)

Simplify and isolate y

y = -x/4 + 1/4 +2 = -x/4 + 9/2

Answer: [tex]y=\frac{2}{5}, \frac{6}{5}[/tex]

Step-by-step explanation:

When answering a problem like this, you first isolate the absolute value.  TO do this, first subtract 8 from both sides, to get –2|4–5y|=-4.  Then divide both sides of the equation to get |4–5y|=2.  The next thing you do is split the equation into 4-5y=2 and 4-5y=-2, because the contents of the absolute value could be negative or positive, and simplifying both into y = 2/5, and y = 6/5y.

Hope it helps <3

Answer:

False

Step-by-step explanation:

[tex]y = x^2-3x+8[/tex]

Y-intercept is when x = 0

So, Putting x = 0 in the above equation

[tex]y = (0)^2-3(0)+8\\y = 0-0+8\\y = 8[/tex]

So, y-intercept = 8

y-intercept = -3 is a false statement.

Answer:

[tex]\boxed{false}[/tex]

Step-by-step explanation:

The y-intercept is when the value of x is 0.

Let x = 0

y = 0² - 3(0) + 8

y = 0 - 0 + 8

y = 8

The y-intercept is 8.

I think it is C. Pls comment right or wrong!

The equation 2(x + 5) = 40 is true for the value x = 15 which is the correct answer would be option (C)

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

To determine the required equation which is true for the value x = 15

We have to simplify the given equations and solve for x.

A. 2(x + 3) = 40

⇒ 2x + 6 = 40

⇒ 2x = 40 - 6

⇒ 2x = 34

⇒ x = 34/2

⇒ x = 17

B. 2(x − 5) = 30

⇒ 2x - 10 = 30

⇒ 2x = 30 + 10

⇒ 2x = 40

⇒ x = 20

C. 2(x + 5) = 40

⇒ 2x + 10 = 40

⇒ 2x = 40 - 10

⇒ 2x = 30

⇒ x  = 15

Hence, the equation 2(x + 5) = 40 is true for the value x = 15 which is the correct answer would be option (C)

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Answer:

3/14

Step-by-step explanation:

En esta pregunta, nos preocupa calcular la fracción de los estudiantes que no asisten a los talleres.

Para obtener la fracción que no asiste a los talleres, lo que debemos hacer es sumar las fracciones de cada uno de los talleres y restar el total de 1.

Matemáticamente eso sería;

1- (2/7 + 1/10 + 2/5)

Agregando los términos en el paréntesis, tenemos;

(20+ 7 + 28) / 70 = 55/70 = 11/14

Restando esto de 1, tenemos; 1-11 / 14 = 3/14

Answer:

-25 and -23

Step-by-step explanation:

The arithmetic sequences are the same so we will have the same formula for each of them. The first term (a₁) is 3 and the common difference (d) is -2.

Explicit formula: aₙ = a₁ + (n - 1) * d

Our formula is aₙ = 3 + (n - 1) * (-2) = -2n + 5

a₁₅ = -2 * 15 + 5 = -25

a₁₄ = -2 * 14 + 5 = -23

Answer: -25 and -23

Step-by-step explanation:

Answer:

y<=-x+3 and y<=2x+1

Step-by-step explanation:

y=-x+3 is the orange line. The shaded region is below so its y<-x+3

y=2x+1 is the blue line. The shaded region is below so y<2x+1

Answer:

use factoring x (see attachment)

-8 x 7 = -56

-8 + 7 = -1

(x - 8)(x + 7) = 0

x = 8, -7

hope this helps :)

Answer:

Option B. an = 3• 6ⁿ¯¹

Step-by-step explanation:

The following data were obtained from the question:

First generation = 3

2nd generation = 1st generation x 6

2nd generation = 3 x 6 = 18

3rd generation = 2nd generation x 6

3rd generation = 18 x 6 = 108

Therefore, we can thus form a sequence as:

3, 18, 108

Since the 2nd term is obtained by multiplying the previous term (i.e the 1st term) by 6 and also, the 3rd is obtained by multiplying the 2nd by 6, the sequence is a geometric progression.

Thus,

The common ratio (r) = 6

The first term (a) = 3

The nth term (an) =?

The nth term of geometric progression is given as

an = arⁿ¯¹

Inputing the value of the first term (a) and common ratio (r) into the above equation, we obtained:

an = arⁿ¯¹

an = 3• 6ⁿ¯¹

Therefore, the explicit formula which can be used to find the number of rabbits in the nth generation is

an = 3• 6ⁿ¯¹

Answer:

1,110

Step-by-step explanation:

calculator

Answer:

No

Step-by-step explanation:

The sum of two random sides of a triangle must be bigger than the third side and their differences must be smaller than the third side

For example

3 - 4 - 5 can be made into a triangle because 3 + 4 > 5 and 4 - 3 < 5

Answer:6/16 or 3/8

Step-by-step explanation:

I did it

Answer: 3/16

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given,

Cost price ( CP ) = 12

Selling price ( SP ) = 15

Since, CP < SP , she made a profit

Actual profit = SP - CP

plug the values

[tex] = 15 - 12[/tex]

Subtract the numbers

[tex] = 3[/tex]

Profit = 3

Now,

Profit percent = [tex] \frac{actual \: profit}{cost \: price} \times 100[/tex] %

Plug the values

[tex] = \frac{3}{12} \times 100[/tex] %

Calculate

[tex] = 25[/tex] %

Hope this helps...

Best regards!!

Answer:

25%

Step-by-step explanation:

Cost Price: ₦12

Selling Price: ₦15

Profit: ₦15 - ₦12 = ₦3

Profit Percentage = [tex]\frac{profit}{cost price}[/tex]  ×  [tex]\frac{100}{1}[/tex]

Profit Percentage = [tex]\frac{3}{12}[/tex] × [tex]\frac{100}{1}[/tex]

Profit Percentage = [tex]\frac{1}{4}[/tex] × [tex]\frac{100}{1}[/tex] = 25%

Final Answer = 25%

Answer:

2 triangles are possible.

Step-by-step explanation:

Given

a=6

b=10

[tex]\angle[/tex]A=33°

To find:

Number of triangles possible ?

Solution:

First of all, let us use the sine rule:

As per Sine Rule:

[tex]\dfrac{a}{sinA}=\dfrac{b}{sinB}[/tex]

And let us find the angle B.

[tex]\dfrac{6}{sin33}=\dfrac{10}{sinB}\\sinB = \dfrac{10}{6}\times sin33\\B =sin^{-1}(1.67 \times 0.545)\\B =sin^{-1}(0.9095) =65.44^\circ[/tex]

This value is in the 1st quadrant i.e. acute angle.

One more value for B is possible in the 2nd quadrant i.e. obtuse angle which is: 180 - 65.44 = [tex]114.56^\circ[/tex]

For the value of [tex]\angle B = 65.44^\circ[/tex], let us find [tex]\angle C[/tex]:

[tex]\angle A+\angle B+\angle C = 180^\circ\\\Rightarrow 33+65.44+\angle C = 180\\\Rightarrow \angle C = 180-98.44 = 81.56^\circ[/tex]

Let us find side c using sine rule again:

[tex]\dfrac{6}{sin33}=\dfrac{c}{sin81.56^\circ}\\\Rightarrow c = 11.02 \times sin81.56^\circ = 10.89[/tex]

So, one possible triangle is:

a = 6, b = 10, c = 10.89

[tex]\angle[/tex]A=33°, [tex]\angle[/tex]A=65.44°, [tex]\angle[/tex]C=81.56°

For the value of [tex]\angle B =[/tex][tex]114.56^\circ[/tex], let us find [tex]\angle C[/tex]:

[tex]\angle A+\angle B+\angle C = 180^\circ\\\Rightarrow 33+114.56+\angle C = 180\\\Rightarrow \angle C = 180-147.56 = 32.44^\circ[/tex]

Let us find side c using sine rule again:

[tex]\dfrac{6}{sin33}=\dfrac{c}{sin32.44^\circ}\\\Rightarrow c = 11.02 \times sin32.44^\circ = 5.91[/tex]

So, second possible triangle is:

a = 6, b = 10, c = 5.91

[tex]\angle[/tex]A=33°, [tex]\angle[/tex]A=114.56°, [tex]\angle[/tex]C=32.44°

So, answer is : 2 triangles are possible.

Answer: 0.49 ± 0.0237

Step-by-step explanation: A interval of a 99% confidence interval for the population proportion can be found by:

[tex]p_{hat}[/tex] ± z.[tex]\sqrt{\frac{p_{hat}(1-p_{hat})}{n} }[/tex]

[tex]p_{hat}[/tex] is the proportion:

[tex]p_{hat}[/tex] = [tex]\frac{1455}{2957}[/tex]

[tex]p_{hat}[/tex] = 0.49

For a 99% confidence interval, z = 2.576:

0.49 ± 2.576.[tex]\sqrt{\frac{0.49(1-0.49)}{2957} }[/tex]

0.49 ± 2.576.[tex]\sqrt{\frac{0.49*0.51}{2957} }[/tex]

0.49 ± 2.576.(0.0092)

0.49 ± 0.0237

For a 99% confidence interval, the proportion will be between 0.4663 and 0.5137 or 0.49 ± 0.0237

Answer:

7.1%

The percentage increase is 7.1%

Step-by-step explanation:

Percentage increase %∆P is the percentage change in the price.

Percentage increase %∆P = ∆P/Pr × 100%

Where;

∆P = change in sales price = $241,500-$225,400

Pr = regular price = $225,400

Substituting the given values;

%∆P = (241,500-225,400)/225,400 × 100%

%∆P = 7.142857142857% = 7.1%

The percentage increase is 7.1%

Answer:

6x - 5y = 15 and x + 2y = 0

Step-by-step explanation:

Here we are given the following equations:

i) x-2y= 4

ii) 4x+5y= 8

iii) 6x-5y=15

iv) x+2y=0

Required:

Which system of equations has a solution of approximately (1.8, –0.9).

To find the approximate equations, substitute x and y for  1.8 and  -0.9 into all the equations respectively and check the resulting values

i) Substitute (1.8, -0.9) in x-2y= 4:

1.8 - 2(-0.9) = 4.

1.8 + 1.8 = 4.

3.6 ≠ 4.

ii) Substitute (1.8, -0.9) in 4x+5y= 8

4(1.8) + 5(-0.9) = 8

7.2 - 4.5 = 8.

2.7 ≠ 8.

iii) Substitute (1.8, -0.9) in 6x-5y=15

6(1.8) - 5(-0.9) = 15.

10.8 + 4.5 = 15

15.3 ≠ 15.

This equation has a solution that is close, therefore it is correct.

iv) Substitute (1.8, -0.9) in x+2y=0

1.8 + 2(-0.9) = 0.

1.8 - 1.8 = 0.

0 = 0.

x + 2 y = 0 has the exact value, therefore it is also correct.

The system of equations that has a solution of approximately (1.8, –0.9) are:

x+2y=0 and 6x-5y=15

Answer:

the correct answer is A

Step-by-step explanation: