Today, the mountain that contains Mount Rushmore is approximately 5,675 feet high. The height of the mountain is 622.5 feet less than 1.1 times its height before construction began.

The equation to find the height of the mountain prior to construction, represented by the variable h, is

1.1h – 622.5 = 5,675

Solve an equation to find the height of the mountain prior to construction, represented by the variable h.



h =
feet

sin y =12/13 but can't find cos x as sin x can't exceed from 1.

It can be solved by using identities of trigonometry.

What are the  trigonometric identities?

These are the equivalent ways to define trigonometric functions.

Basic identities are:

sin²x + cos²x = 1

1 + tan²x = sec²x

1 + cot²x = cosec²x

For cos x:
cos²x = 1 - sin²x

          = 1 - (5/3)²

          = 1- (25/9)

          = -16/9

i.e. not possible

For sin y:

sin²y = 1 - cos²y

         = 1 - (5/13)²

         = 1 - 25/169

         = 144/169

So, sin y = ±(12/13)

but as mentioned x and y are in 1st quadrant ,

so, sin y = 12/13.

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The Solution for the given quadratic equation is Cosx = 1 and Cosx = -3 .

In the question ,

it is given that ,

the quadratic equation is cos²x + 2 cosx - 3 = 0 ,

let cosx = a ,

So , the equation becomes , a² + 2a - 3 = 0

writing the factors using the splitting the middle term method ,

we get ,

a² [tex]+[/tex] 3a -a - 3 = 0

a(a + 3) -1(a [tex]+[/tex] 3) = 0

(a - 1)(a [tex]+[/tex] 3) = 0

which means a - 1 = 0      or    a + 3 = 0

a [tex]=[/tex] 1    or     a [tex]=[/tex] -3 ,

Substituting a = cosx , we get

cosx [tex]=[/tex] 1   or cosx [tex]=[/tex] -3 ,

Therefore , The Solution for the given quadratic equation is Cosx = 1 and Cosx = -3 .

The given question is incomplete , the complete question is

Solve the given quadratic equation for Cosx , cos²x + 2 cosx - 3 = 0 .

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The dynamic power consumption of your chip if it has an area of 70 mm² and runs at 450 MHz at vdd = 0.9V is 1.08 W.

It is given that,

The average activity factor = 0.1

The Average switching capacity = 450 pF/mm²

We know that,

              p = aCV²f

putting the values in the above equation:

   = 0.1× (450e⁻¹² × 70) × (0.9)² × 450e⁶

   = 1.08 W

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The set of ordered pairs that represent dilation factor of -3 is

c. A' (-3, -18) B' (-18, -18) C' (-3, -6)

Dilation is a method of transformation that magnify or shrink the preimage depending on the scale factor

The transformation rule for dilation is as follows

(x, y) for a scale factor of r → (rx, ry)

From the graph the coordinates are read and following the given transformation rule we have

preimage                           image

A (1, 3)   → (2 * -3, 4 * -3) →   A' (-3, -8)

B (6, 6)  → (4 * -3, 4 * -3) →    B' (-18, -18)  

C (1, 6)  → (3 * -3, 2 * -3) →    C' (-3, -6)

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Answer:

x ≥ 5

Step-by-step explanation:

3x - 8 ≥ 7 ( add 8 to both sides )

3x ≥ 15 ( divide both sides by 3 )

x ≥ 5

Answer:

[tex]\textsf{1.} \quad (x-1)^2=12(y+2)[/tex]

     See attachment 1.

2.  See attachment 2.

Step-by-step explanation:

Given values:

As the x-value of the vertex and focus is the same, the parabola has a vertical axis of symmetry.

The focus is always on the inside of the parabola.

Since p represents the distance from the vertex to the focus, and the distance from the vertex to the focus is 1 - (-2) = 3, then p = 3.

If p > 0, the parabola opens upwards, and if p < 0, the parabola opens downwards.  Therefore, as p > 0, the parabola opens upwards.

[tex]\boxed{\begin{minipage}{5.8 cm}\underline{Standard form of a parabola}\\(with a vertical axis of symmetry)\\\\$(x-h)^2=4p(y-k)$\\\\where:\\ \phantom{ww}$\bullet$ $p\neq 0$\\ \phantom{ww}$\bullet$ Vertex: \;$(h,k)$\\ \phantom{ww}$\bullet$ Focus:\; $(h,k+p)$\\ \phantom{ww}$\bullet$ Directrix: \; $y=(k-p)$\\ \phantom{ww}$\bullet$ Axis of symmetry: \; $x=h$\\\end{minipage}}[/tex]

Therefore:

Substitute the values into the formula:

[tex]\implies (x-h)^2=4p(y-k)[/tex]

[tex]\implies (x-1)^2=4\cdot 3(y-(-2))[/tex]

[tex]\implies (x-1)^2=12(y+2)[/tex]

See attachment 1 for the graph of the parabola.

Given equation of a parabola:

[tex](y-4)^2=8(x+2)[/tex]

As the y-variable is contained within the squared part of the equation, the parabola has a horizontal axis of symmetry.

[tex]\boxed{\begin{minipage}{5.8 cm}\underline{Standard form of a parabola}\\(with a horizontal axis of symmetry)\\\\$(y-k)^2=4p(x-h)$\\\\where:\\ \phantom{ww}$\bullet$ $p\neq 0$\\ \phantom{ww}$\bullet$ Vertex: \;$(h,k)$\\ \phantom{ww}$\bullet$ Focus:\; $(h+p,k)$\\ \phantom{ww}$\bullet$ Directrix: \; $x=(h-p)$\\ \phantom{ww}$\bullet$ Axis of symmetry: \; $y=k$\\\end{minipage}}[/tex]

Therefore:

If p > 0, the parabola opens to the right, and if p < 0, the parabola opens to the left.   Therefore, as p > 0, the parabola opens to the right.

Find the y-intercepts of the graph by substituting x = 0 into the equation:

[tex]\implies (y-4)^2=8(0+2)[/tex]

[tex]\implies (y-4)^2=16[/tex]

[tex]\implies y-4=\pm4[/tex]

[tex]\implies y=4\pm4[/tex]

[tex]\implies y=0, y=8[/tex]

To sketch the graph of the parabola, plot:

Draw a curve through the vertex and y-intercepts, opening to the right.

Use the axis of symmetry to ensure the curve is symmetric.

See attachment 2 for the graph of the parabola.

Answer: 745.31 cm²

Total area of the figure can be obtained by adding area of the semi circle and rectangle.

The radius of the semi circle is given as 12.5cm and it's area is equal to (πr²)/2

I hope you understand It's simple!

The probability percentage the year will have an annual rainfall less than 43 inches is 61.41%.

How to calculate the probability?

Given

μ = 41.4

σ = 5.5

First, we need to find the z score when the rainfall 43 inches. So:

z = (x - μ) / σ

z = (43 - 41.4) / 5.5

z = 0.2909

Then, to find out the probability we need to find P(z < 0.2909) in the z score table. So, we get 0.6141 or in percentage is 61.41%.

Thus, the probability percentage the year will have an annual rainfall less than 43 inches is 61.41%.

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Answer:

if you don't mind is there a starting number or a chart so i can calculate and solve this for you!

Answer:

$325

Step-by-step explanation:

t +b = 582

t = b - 68

b - 68 + b = 582

2b = 582 + 68

2b = 650

2/2 b = 650 / 2

b = 325

The linear function or equation represents the height of the bamboo h with respect to time t is y = 3x + 12 and the time taken to reach 66 inches is 3 months.

A straight line on the coordinate plane is represented by a linear function.

A linear function always has the same and constant slope.

A linear function is a function that varies linearly with respect to the changing variable.

4.1)

The linear equation is given as y = mx + c

Here, m is the slope while c is the y-intercept.

Given line has a y-intercept of 12.

Slope m = (12 - 24)/(0 - 4) = 3

Thus, h = 3t + 12

4.2)

Time is taken to bamboo to 66 inches tall,

66 = 3t + 12

3t = 54

t = 3 months.

Hence "The linear function or equation represents the height of the bamboo h with respect to time t is y = 3x + 12 and the time taken to reach 66 inches is 3 months".

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Answer: -2

Step-by-step explanation:

since g(x) is a function, x needs to be 0 in order to find the y-intercept. so we plug in 0 to the function. -|0+6|+4=-2 so the y-intercept is -2

Answer:

Step-by-step explanation:

reciprocal of 51/3 is 3/16

Hi you need to change 5 1/3 from mixed number to improper fraction 51/3=(5x3)+1  /3 =16/3

The  reciprocal   of 16/3 is 3/16

The G.P. of a term is 256/243.

To find out the G.P. for the 3rd term:

Let us consider the 1st term to be 'a'.

So, [tex]ar^{2}=18[/tex] ....... Equation (1)

Also [tex]ar^{6} = \frac{32}{9}[/tex] .....  Equation (2)

Dividing (2) by (1), we get,

[tex]\frac{ar^{6}}{ar^{2}} = \frac{32}{162}[/tex]

[tex]r^{4}[/tex] = 16/81.

r = 2/3.

Putting r in equation (1) than we will get

a = 81/2.

So, 10th term = [tex]ar^{9}[/tex]

= (81/2) ×(512/19683)

= 256/243.

Hence the answer is the G.P. of a term is 256/243.

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The possible outcomes in the sample space of this experiment are

{(h,1),,(h,2),(h,3),(h,4),(h,5),(h,6),(t,1),(t,2),(t,3),(t,4),(t,5),(t,6)}

Jo flips a coin sample space for a coin = {h, t}

and rolls a 6-sided die sample space for a die = {1,2,3,4,5,6}

at a time coin is tossed and the die is rolled

the possible outcomes in the sample space of this experiment are

{(h,1),,(h,2),(h,3),(h,4),(h,5),(h,6),(t,1),(t,2),(t,3),(t,4),(t,5),(t,6)}

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Answer: __________________________________________

3x + 9

Answer: 3x + 9

Step-by-step explanation:

Ther right option is that there is not enough evidence to conclude that there is enough association between vaccine location and severe reaction.

Given that,

Children who received the vaccine in the thigh received the first random sample. Children who received the immunization in the arm provided the second random sample.

The chi-square test yields a chi square is 2.0609 with a P value of 0.1511 meaning, the chi square test is not statistically significant.

A,B is therefore out.

C is not also right.

D is what we get when we cannot reject null hypothesis.

Therefore, We cannot conclude that there is dependence.

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The statement can you use to conclude that quadrilateral xyzw is a parallelogram

The statement to conclude that quadrilateral XYZW is a parallelogram is

XY = WZ and XW = YZ

Quadrilateral :

A quadrilateral is a closed shape and a type of polygon that has four sides, four vertices and four angles. It is formed by joining four non-collinear points.

Parallelogram :

A parallelogram is a two-dimensional geometrical shape, whose sides are parallel to each other , where the pair of parallel sides are equal in length.

So we can conclude that :

XY is parallel to WZ  and XW is parallel to YZ .

so ,

XY = WZ and XW = YZ is the conclusion .

Hence , the answer is XW = YZ and XY = WZ

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(a) Hamburgers sells faster than Wraps ,

(b) The graph of the equations that represents the Hamburgers and Wraps sold are shown below .

In the question ,

it is given that

the rate at which the hamburgers are selling = 160 hamburgers per hour ,

we need to find the rate at which the wraps are selling

From the table ,

we can see that the wraps are sold in an Arithmetic Progression ,

So , at 60 minutes the wraps sold = 2.5 + (n-1)d

= 2.5 + 59×2.5

= 2.5 + 147.5

= 150

So , after one hour , number of wraps sold is 150 and the number of hamburgers sold is 160 .

Similarly , after 2 hours , the number of wraps sold will be 300 and number of hamburgers sold will be 320 .

So, the hamburgers sells faster than wraps .

the slope(steepness)  of the hamburgers = (number of hamburgers sold)/60

= 160/60

= 2.667

the slope(steepness) of the wraps = (number of wraps sold)/60

= 150/60

= 2.5

from the above data , we can see that the steepness of hamburgers is more ,

which means that the hamburgers sells faster than wraps .

the equation that denotes the number of hamburgers sold is y = 2.667x

the equation that denotes the number of wraps sold is y = 2.5x

where x is time in minutes .

The graph that represents the growth rate of hamburger and wraps is shown below .

Therefore , (a) Hamburgers sells faster than Wraps ,

(b) The graph of the equations that represents the Hamburgers and Wraps sold are shown below .

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The larger bottle will be able to hold a volume of 1372ml

If two solids are similar, then the ratio of their volumes is equal to the cube of the ratio of their corresponding linear measures.

This shows that the ratio of the cube of length of the bottle is equal to the the ratio of their volumes

the length of the smaller bottle = 15, the cube of the length= 15^3= 3375

the length of the larger volume = 21, the cube of the length is 21^3=9261

therefore 3375/9261= 500/x

x is the volume of the larger bottle

therefore x= 500×9261/3375

x= 1372ml.

therefore the volume of the larger bottle is 1372ml

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Answer:

B. 700+200

Step-by-step explanation:

691+208=899

A. 600+200=700

B.700+200=900

C.700+300=1000

D.900+200=1100

B is closest to 899

Answer:

700+200

Step-by-step explanation:

we round these numbers to the closest hundreds by looking at the tenth place

5 or more we round up

4 or less we let it rest and round down

691 since it is 9 in the tenths place we round up to 700

208 since the tenths place is 0 we round down to get 200

700+200 is the answer hopes this helps please mark brainliest

Answer:

a) x=5

b) x=4

Step-by-step explanation:

4x-3=2x+7

-2x.  -2x

2x-3=7

   +3. +3

2x=10

x=5

2x+6=7x-14

-2x.   -2x

6=5x-14

+14. +14

20=5x

/5. /5

4=x

Hopes this helps please mark brainliest

The equation of the parabola is y = -x² - 2x + 5

What is a Parabola?

A Parabola, open curve, a conic section produced by the intersection of a right circular cone and a plane parallel to an element of the cone. A parabola is a plane curve generated by a point moving so that its distance from a fixed point is equal to its distance from a fixed line

The equation of the parabola is given by

( x - h )² = 4p ( y - k )

where ( h , k ) is the vertex and ( h , k + p ) is the focus

y is the directrix and y = k - p

The equation of the parabola is also given by the equation

y = ax² + bx + c

where a , b , and c are the three coefficients and the parabola is uniquely identified

Given data ,

The equation of the parabola with the points

A ( -5 , -10 ) , B ( -3 , 2 ) and C ( 2 , -3 )

So , from the equation of parabola ,we get

y = ax² + bx + c

Substituting the values of x and y , in the equation of point A , we get

-10 = a ( -5 )² - 5b + c

-10 = 25a - 5b + c   be equation (1)

Substituting the values of x and y , in the equation of point B , we get

2 = a ( -3 )² - 3b + c

2 = 9a - 3b + c   be equation (2)

Substituting the values of x and y , in the equation of point C , we get

-3 = a ( 2 )² + 2b + c

-3 = 4a + 2b + c   be equation (3)

By the method of brute force , we can solve the equations and derive the equation for the parabola

So , the equation for the parabola will be

y = -x² - 2x + 5

Now , substituting the values of x and y from the points , we get

For point A ( -5, -10 )

-10 = - 25 + 10 + 5

-10 = -10

Therefore , the equation is TRUE

Now , substituting the values of x and y from the points , we get

For point B ( -3, 2 )

2 = -9 + 6 + 5

2 = 2

Therefore , the equation is TRUE

Now , substituting the values of x and y from the points , we get

For point C ( 2 , -3 )

-3 = -4 - 4 + 5

-3 = -3

Therefore , the equation is TRUE

Hence , the equation of the parabola is y = -x² - 2x + 5

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The equation  that can be used to find the number of hotdogs

and sodas sold at the swim meet.

a)x+0.50y=150

b)  y=-2x+300

c)Number of soda sold y =220 if hot dog is 40.

d)  x intercept=150. It is related to the total earnings of soda and hot dogs sold.

f) y intercept = 300 . It is related to the 2 times of the total earnings of soda and hot dogs sold.

What is x-intercept and y-intercept?

An equation's or a function's graph that contacts the x axis is said to have a "X intercept." This is comparable to a point having a value of zero. Given that it is located on the horizontal axis, this is sometimes referred to as the horizontal intercept. The y value at the point where the line meets the y axis is known as the y intercept. By examining the graph and identifying the point that crosses the y axis, we may determine the y intercept. This point's x coordinate will always be 0. It will be recorded as (0,y). Given that it is on the vertical axis, this is also referred to as a vertical intercept.

Let us take number of hot dogs sold as x and number of soda sold as y.

Cost of one hot dog = $1.00

Cost of one soda = $0.50

Then , cost of x number of hot dogs sold = 1x

cost of y number of soda sold = 0.50y

Then, . At the end of the day you made $150.

=> 1x+0.50y= 150

a) standard form of the equation is ,

=> x+0.50y=150 ------->1

b) x+0.50y=150

=> x+[tex]\frac{1}{2}[/tex]y=150

=>2x+y=150*2

=>2x+y=300

Then slope intercept form is  y=-2x+300------->2

c) Number of hot dogs sold x=40 and put into 2 ,

then ,  y=-2(40)+300

=> y=-80+300

=>y=220

Number of soda sold y =220

d) To find x intercept put y=0 into 1 , then

=> x+0=150

=>x=150

Here x intercept=150. It is related to the total earnings of soda and hot dogs sold.

e)To find y intercept put x=0 into 1,

=> 0+0.50y=150

=> y = 150/0.50

=> y =300

Here y intercept = 300 . It is related to the 2 times of the total earnings of soda and hot dogs sold.

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The length of side x is 6cm

We need to find the scale factor of the shapes below are mathematically similar.

it can be found using the two bases given.

The base of the smaller triangle is 9  and that of large triangle is 12

9/12 = 3/4

The smaller triangle is 3/4 of the larger one.

Multiply the known side by 3/4

X = 8 x 3/4 = 6

X= 6

Therefore, the length of side x is 6cm

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Miguel's sister's red gumdrops weigh 0.5 pounds.

Formulate based on the conditions stated: [tex]\frac{3}{8} + x = \frac{7}{8}[/tex]

Unknown terms should be moved to the left side of the equation: [tex]x = \frac{7}{8} - \frac{3}{8}[/tex]

Numerators written over common denominator: [tex]x = \frac{7-3}{8}[/tex]

Determine the total or difference: [tex]x = \frac{4}{8}[/tex]

Remove the connecting element: [tex]x = \frac{1}{2}[/tex]

get the outcome: or x = 0.5 or 50%

A fraction is a mathematical symbol representing any quantity of equal parts, and it also represents a portion of a whole. In common English, the word "fraction" is used to describe the quantity of parts of a particular size. Fractions speed up and simplify calculations by making it easier to divide and evaluate numbers.

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Answer:20

Step-by-step explanation: my man

Answer:

20

Step-by-step explanation:

1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 10

+ 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 10

= 20