(x-1)²-25=0
Factor by using the difference between two squares

Answer:

(- 2, - 7 )

Step-by-step explanation:

Under a reflection in the x- axis

a point (x, y ) → (x, - y ), thus

P(- 2, 7 ) → P'(- 2, - 7 )

Answer:22

Step-by-step explanation:

Answer:maximize p = profit = 2 L + 1 C >/= 25

L >/= 5

C>/=5

start with L = 5

10+C >/= 25

C >/= 15

if L = 6

12 + C >/= 25

C >/= 13

so

L 7, C 11

L 8 ,C 9

L 9 , C 7

L 10, C 5

are your MINIMUM combinations. Of course you can always sell more

Step-by-step explanation:

The x-coordinate of the point of intersection for given equations is 2

Step-by-step explanation:

Given equations are:

[tex]2x+y = 7\ \ \ Eqn\ 1\\10x-7y = -1\ \ \ Eqn\ 2[/tex]

The point of intersection is the solution of the system of equations

as we have to find the x-coordinate we will use elimination method to eliminate y

So,

Multiplying equation 1 with 7

[tex]7(2x+y) = 7(7)\\14x+7y = 49\ \ \ \ Eqn\ 3[/tex]

Adding equation 2 and 3

[tex](14x+7y) + (10x-7y) = 49-1\\14x+10x+7y-7y = 48\\24x = 48[/tex]

Dividing both sides by 24

[tex]\frac{24x}{24} = \frac{48}{24}\\x = 2[/tex]

The x-coordinate of the point of intersection for given equations is 2

Keywords: Linear equations, simultaneous equations

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Answer:

11m

Step-by-step explanation:

2(5m)+m=10m+m=11m

Answer:

[tex]y=-5(x-0)^2+5[/tex]

Step-by-step explanation:

Given height of parabola is [tex]5\ m[/tex].

And [tex]2\ m[/tex] wide at ground level.

Also, the parabola opens down.

Let us assume the parabola is aligned on Y-axis

As the height of parabola is [tex]5\ m[/tex]. The maximum height of parabola is achieved when [tex]x=0[/tex].

So, the vertex of parabola is [tex](0,5)[/tex].

The equation of parabola having vertex [tex](h,k)[/tex] is.

[tex]y=a(x-h)^2+k[/tex].

Plugging the vertex of parabola

[tex](h,k)[/tex] [tex]=[/tex] [tex](0,5)[/tex].

[tex]h=0\ and\ k=5[/tex]

[tex]y=a(x-0)^2+5[/tex]

It is given that parabola is [tex]2\ m[/tex] wide at the ground.

As the parabola is aligned on Y-axis. So, distance between X-intercept is [tex]2\ m[/tex].

The X-intercept would be [tex](-1,0)\ and\ (1,0)[/tex]

Plugging [tex](1,0)[/tex] in the equation [tex]y=a(x-0)^2+5[/tex]

[tex]0=a(1-0)^2+5\\\\-5=a(1)^2\\\\-5=a[/tex]

Now, we get [tex]a=-5[/tex] and having vertex [tex]h=0\ and\ k=5[/tex].

So, the equation of parabola is

[tex]y=a(x-h)^2+k[/tex].

[tex]y=-5(x-0)^2+5[/tex]

Answer:

$1862 ÷9=$207(each lot)

$207 ×4=$828

Answer:

Step-by-step explanation:

-2(x+3)=-10

Open the bracket

-2x - 6 = -10

Collecting like terms

-2x = -10 + 6

-2x = -4

Dividing through by -2

x = -4/-2

x = 2

Answer:

length is 28 meters

width is 15 meters

Step-by-step explanation:

Write out formulas and assign variables:

Width: w

Length: l = 2w - 2

Here is a diagram:

            2w - 2              

|                                     |  w

|_________________|

The perimeter formula for rectangle is P = 2(l +w). Substitute the perimeter and the formula for length into the formula.

P = 2(l +w)

86 = 2(2w - 2 + w)       Simplify inside the brackets

86 = 2(3w - 2)            Divide both sides by 2

43 = 3w - 2              Add 2 to both sides

45 = 3w                  Divide both sides by 3

w = 45/3               Variable on left side is standard formatting

w = 15                 Width of basketball court

Substitute width into the length formula to fin length.

l = 2w - 2

l = 2(15) - 2

l = 30 - 2

l = 28           Length of basketball court

Therefore the length is 28 meters and the width is 15 meters.

The dimensions of the basketball court are 28 meters in length and 15 meters in width.

We need to find the dimensions of the rectangular court where the length (L) is 2 meters less than twice the width (W), given that the perimeter is 86 meters. We can set up the equations as follows:

First, substitute the value of L from the first equation into the second equation:

Simplify and solve for W:

Now, find the length (L):

Thus, the dimensions of the court are 28 meters in length and 15 meters in width.

Answer:

g(x) = - (x² + 3x + 2) = - x² - 3x - 2

Step-by-step explanation:

The graph represents the function f(x) = x² + 3x + 2.

Now, g(x) is the function which is obtained by reflecting f(x) across the x-axis.

While a graph of a function reflects across x-axis then its y-values will change sign for a fixed value of x.  

Therefore, the function g(x) will be given by  

g(x) = - (x² + 3x + 2) = - x² - 3x - 2 (Answer)

Answer:

[tex]x<-3[/tex]

Step-by-step explanation:

Given inequality:

[tex]4-3x>13[/tex]

In order to represent the solution on the number line, we will first solve the given inequality.

We have

[tex]4-3x>13[/tex]

Subtracting both sides by 4.

[tex]4-3x-4>13-4[/tex]

[tex]-3x>9[/tex]

Dividing both sides by -3.

[tex]\frac{-3x}{-3}<\frac{9}{-3}[/tex] [On dividing both sides by a negative number the sign of the inequality reverses.]

[tex]x<-3[/tex]

So, solution of this inequality will range from -3 to -∞

The number line is represented below.

16π

Step-by-step explanation:

The area within a circle is given by the formulae;

πr²

Since this circle is part of a full circle will multiply the area by teh appropriate fraction;

90/360 = ¼

¼ πr²

r = 8 according to the illustration

¼ π*8²

1/4 * π * 64

= 16π

Area = 16π

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Answer:

8x+24

Step-by-step explanation:

8(x+3)=8x+24

The perimeter of rectangle is 16x-2y+4.

Step-by-step explanation:

Given dimensions are;

Length = 5x-y

Width = 3x+2

We know that;

Perimeter of rectangle = 2(Length + Width)

Perimeter of rectangle = [tex]2(5x-y+3x+2)[/tex]

Perimeter of rectangle = [tex]2(8x-y+2)[/tex]

Perimeter of rectangle = [tex]16x-2y+4[/tex]

The perimeter of rectangle is 16x-2y+4.

Keywords: rectangle, perimeter

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Answer:

Domain: (-∞,∞)

Range: {3}

Step-by-step explanation:

The domain is the x-values of the function, and the range is the y value of the function.

F(x)=3 is really just a fancy way of saying y=3. The range is 3.

Since the function makes a horizontal line, the domain is ∞.

Answer:

Therefore the choice is

a) AD/AB=AB/AC

Step-by-step explanation:

In  Δ ADB and Δ ABC  

∠A ≅ ∠A    …………..{Reflexive Property}

∠ ADB ≅ ∠ ABC      ..............{ measure of each angle is 90° given }

Δ ADB ~ Δ ABC ….{Angle-Angle  Similarity test}

If two triangles are similar then their sides are in proportion.

[tex]\frac{AD}{AB} =\frac{AB}{AC}\ \textrm{corresponding sides of similar triangles are in proportion}\\[/tex]  

Therefore the choice is

a) AD/AB=AB/AC

Answer:

Therefore the choice is

a) AD/AB=AB/AC

Step-by-step explanation:

In  Δ ADB and Δ ABC  

∠A ≅ ∠A    …………..{Reflexive Property}

∠ ADB ≅ ∠ ABC      ..............{ measure of each angle is 90° given }

  Δ ADB ~ Δ ABC ….{Angle-Angle  Similarity test}

If two triangles are similar then their sides are in proportion.

Therefore the choice is

a) AD/AB=AB/AC

Answer:

0.

Step-by-step explanation:

We can do this by substitution of -2  The numerator will tend to 0.

The denominator  will always be positive so the limit is 0.

Answer:

The value of log  43is 1.633

Step-by-step explanation:

Explanation:

Suppose you know that:

[tex]\begin{array}{l}{\log 2 \approx 0.30103} \\{\log 3 \approx 0.47712}\end{array}[/tex]

Then note that:

[tex]43=\frac{129}{3} \approx \frac{128}{3}=\frac{2^{7}}{3}[/tex]

So

[tex]\log 43 \approx \log \left(\frac{2^{7}}{3}\right)=7 \log 2-\log 3 \approx 7 \cdot 0.30103-0.47712=1.63009[/tex]

We know that the error is approximately:

[tex]\log \left(\frac{129}{128}\right)=\log 1.0078125=\frac{\ln 1.0078125}{\ln 10} \approx 0.00782 .3=0.0034[/tex]

So we can confidently give the approximation:

[tex]\log 43 \approx 1.633[/tex]

Answer:

1.6

Step-by-step explanation:

It's 1.633, when you round to the nearest tenth, it's B) 1.6

3 + 8x = 19 is the equation for given sentence three more than eight times a number is equal to 19

Solution:

Given sentence is:

Three more than eight times a number is equal to 19.

We have to translate the sentence into an equation

Let us first break the sentence and find out the equation

Let "x" be the required number

Given that, Three more than eight times a number is equal to 19.

Here "more than" represents addition

"times" represents multiplication

eight times a number = [tex]8 \times x[/tex]

So the required equation is:

Three more than eight times a number is equal to 19

[tex]3 + 8 \times x = 19\\\\3 + 8x = 19[/tex]

Thus the required equation for given sentence is found

Answer:

16. B

17. B

Step-by-step explanation:

16. The intercept form of the parabola is

[tex]y=a(x-x_1)(x-x_2),[/tex]

where [tex]x_1, x_2[/tex] are two x-intercepts.

In your case,

[tex]x_1=2\\ \\x_2=-8[/tex]

so

[tex]y=a(x-2)(x-(-8))\\ \\y=a(x-2)(x+8)[/tex]

To find a, substitute coordinates of the point (-6,-4) parabola is passing through

[tex]-4=a(-6-2)(-6+8)\\ \\-4=-16a\\ \\a=\dfrac{1}{4}[/tex]

and

[tex]y=\dfrac{1}{4}(x-2)(x+8)[/tex]

17. The vertex form of the parabola equation is

[tex]-2p(y-k)=(x-h)^2,[/tex]

where (h,k) are the coordinates of the vertex and sign "-" because parabola goes down.

In your case, vertex is (2,3), so

[tex]-2p(y-3)=(x-2)^2[/tex]

The vertex is 3 units from the focus, then

[tex]\dfrac{p}{2}=3\\ \\p=6[/tex]

The equation of the parabola is

[tex]-2\cdot 6(y-3)=(x-2)^2\\ \\y=-\dfrac{1}{12}(x-3)^2+3[/tex]

Answer:

The value of x is 22.

Step-by-step explanation:

We are given that,

12 less triple the difference of x and 10 is 24.

So, according to question :

  3(x - 10) - 12 = 24

Adding '12' on both sides of the above equation, we get

  3(x -10) - 12 + 12 = 24 + 12

⇒3(x - 10) = 36

Dividing the above equation by '3', we get

  3(x - 10) ÷ 3 = 36 ÷ 3

⇒x - 10 = 12

Now, adding '10' on both sides of the above equation, we get

  x - 10 + 10 = 12 + 10

⇒x = 22

So, the value of x is 22.

Answer:

Please see pic

Step-by-step explanation:

Go two places to the right (on x axis), then four places down (on y axis)

Sorry it would not let me attach a pic

Answer: 26.5 mph, or miles per hour

265/10 = 26.5

Answer: 26.5 mph

Step-by-step explanation: We need to divided 265 miles by 10 hours

265/10

Answer: 26.5 mph

Hope this helps!

Answer:

n will be 6

Step-by-step explanation:

3×n=2×9

substitute n=6 in the above equation

3×6=2×9

18=18

N is 6

In this question, we're trying to make an equation for the given scenario and answer a couple of leading questions.

We know that Aiko types at a rate of 70 words per minute

We would represent this as 70x

x = minutes

We are also given more information that he types 210 words in 3 minutes, that still follows our "70x" scenario.

So our equation would be:

y = 70x

The slope of the linear equation would be 70 or 70/1

The slope would be 70 because this is the change that's happening each minute.

A point on a graph would be at (1 , 70)

You would put this equation into a graph, and you would grab a point that's on the linear line. I'll insert a picture of the graph

The linear equation would be written as: y = 70x

The beginning point would be at 0, since Aiko doesn't type anything for 0 minutes.

Answer:

1 The slope of the linear equation is  70

2 One point on the graph of a linear equation will be 3, 210

3,This linear equation can be written as  y-210=70(x-3)

Step-by-step explanation:

Answer:

x = 3

Step-by-step explanation:

The last two parts of the function help see where the curve is and where the vertical asymptote would be. The (x-3) says that it was moved 3 units to the right, and the -5 says that it was moved 5 units down:

                                                 /\        *  ]

                                                  |         *  [

                                                  |         *  ]

                                                  |         *  [

             <--|--|--|--|--|--|--|--|-- |--|--|--|--|--3*-]-|--|--|--|--|--|--|--|--|-->

                                                  |        *   [

                                                  |       *    ]

                                                  |*5         [

                                                  \/           ]        

So the vertical asymptote would be where it crosses the x-axis and then goes straight up: 3    

[

]   = vertical asymptote

[

__________________________________

*

*   = function graphed

*

__________________________________

(By the way, I got this correct on my quiz!)

Hope this helps!

The vertical asymptote of the given function h(x)=6log4(x−3)−5 is x=3.

The vertical asymptote of a function is the value of x at which the function approaches infinity or negative infinity. For a logarithmic function h(x)=a*logb(x−c)−d, the vertical asymptote is x=c. Consequently, in the given function h(x)=6log4(x−3)−5, the vertical asymptote is x=3.

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Answer:

Multiples of 2 are {2,4,6,8,10,12,14,16,...} Multiples of 4 are {4,8,12,16,.......) Hence common multiples are {4,8,12,16,...} and Lowest Common Multiple is 4 .

Step-by-step explanation:

To find common multiples of 2 and 4, list the multiples of each and identify the common elements. For 2 and 4, these are 4, 8, 12, and 16.

Finding Common Multiples of 2 and 4

To find common multiples of 2 and 4, we start by listing the multiples of each number.

→ Multiples of 2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, ...

→ Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, ...

Next, we look for common multiples from these lists.

→ 4: divisible by 2 and 4

→ 8: divisible by 2 and 4

→ 12: divisible by 2 and 4

→ 16: divisible by 2 and 4

Therefore, four common multiples of 2 and 4 are 4, 8, 12, and 16.

Step-by-step explanation:

Solve the system via elimination (add the equations):

-10y + 9x = -9

+ (10y + 5x = -5)

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

14x = -14

x = -1

Plug in the value for 'x' into the second equation:

-10y + 5(-1) = -5

Solve for y:

-10y - 5 = -5

--> -10y = 0

--> y = 0

x = -1

y = 0

Answer:

  y = 3(x -4)^3 -3

Step-by-step explanation:

As you know, the transformations are

  g(x) = (vertical stretch factor) · f(x - (right shift)) +(vertical shift)

For the given transformations, the equation becomes ...

  y = 3(x -4)^3 -3

The equation of y=x^3 with the given transformations is y = 3(x - 4)^3 - 3.

The equation of y = x^3 after the given transformations is y = 3(x - 4)^3 - 3.

The vertical stretch by a factor of 3 means that all y-values will be multiplied by 3, so the equation becomes y = 3x^3.

The horizontal shift 4 units to the right means that x-values will be replaced by (x - 4), so the equation becomes y = 3(x - 4)^3.

The vertical shift 3 units down means that all y-values will be decreased by 3, so the equation becomes y = 3(x - 4)^3 - 3.

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There are 3 dollars per hour per babysitting job for they will get the same amount.

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

Jill babysits and makes x dollars per hour plus a $5 transportation charge. Samantha babysits and makes two thousand dollars per hour extra transportation cost of $10

As per the given question, the required system of equations would be as:

Jill: y = 8 - 5

8- 5 = 3

y = 3 dollars per hr per babysitting job

Samantha: 2y = 16 -10

2y = 6

2/2 = 6/2

3 dollars per hr per babysitting job

They will get the same amount regardless of how many hours they babysit

Thus, there are 3 dollars per hour per babysitting job for they will get the same amount.

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Answer:

[tex]\large \boxed{\text{101 pieces}}[/tex]

Step-by-step explanation:

1. Calculate the area of the floor

The formula for the area of a trapezoid is  

A = ½(a + b)h,

where a and b are the lengths of the parallel sides and h is the distance between them.

However, we are not given the value of h, so we must use Brahmagupta's formula.

If the four sides are a, b, c, and d, the area A is

[tex]A = \sqrt{(s - a) (s - b) (s - c) (s - d)}[/tex]

where s is the semiperimeter

[tex]s = \frac{1}{2}(a + b + c + d)[/tex]

Data:

a = 13 ft

b = 16 ft

c = 13 ft

d = 26 ft  

(a) Calculate the semiperimeter

[tex]\begin{array}{rcl}s & = & \sqrt{(s - a) (s - b) (s - c) (s - d)}\\\\ & = & \frac{1}{2}(13 + 16 + 13 + 26)\\\\ & = & \frac{1}{2}(68)\\\\ & = & 34\\\end{array}[/tex]

(b) Calculate the area

[tex]\begin{array}{rcl}A & = &\sqrt{(s - a) (s - b) (s - c) (s - d)}\\\\& = &\sqrt{(34 - 13) (34 - 16) (34 - 13) (34 - 26)}\\\\& = &\sqrt{21 \times 18 \times 21 \times 8}\\\\& = & \sqrt{63504}\\\\ & = & \mathbf{252}\\\end{array}[/tex]

The area of David's floor is 252 ft².

2. Calculate the number of pieces of material

[tex]\text{No. of pieces} = \text{252 ft}^{2} \times \dfrac{\text{1 piece}}{\text{2.5 ft}^{2}} = \textbf{100.8 pieces}\\\\\text{David can't buy a fraction of a piece, so he must buy $\large \boxed{\textbf{101 pieces}}$}[/tex]