From the observation deck of a skyscraper, Dominic measures a 45^{\circ} ∘ angle of depression to a ship in the harbor below. If the observation deck is 984 feet high, what is the horizontal distance from the base of the skyscraper out to the ship? Round your answer to the nearest tenth of a foot if necessary.

The key features that f(x) and g(x) have in common are; A: Both f(x) and g(x) have the same domain of (∞, -∞).

We are given the functions as;

Polynomial function; f(x) = 2x² - 3x + 5

Exponential function; g(x) = 2ˣ - 5

In this question we must analyze the domain, range, x-intercepts and changing intervals:

The domain of both functions are a set of all real numbers with both functions continuous.

The range of both functions from the graph attached is;

Range of f(x) = (3.875, +∞)

Range of g(x) = (-5, +∞)

The x-intercepts of both functions are;

x-intercept for f(x) is non existent

x-intercept for g(x) is (2.322, 0)

From the attached graph;

f(x) increases over interval of (3.875, ∞)

g(x) increases over the interval of a set of real numbers

Looking at the given options, we can say that option A is the correct one

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Answer:

The blue dot is -19

Step-by-step explanation:

Since every 2 ticks are worth 6 (|-10|-|-4|=6), then one tick is worth 3.

We are going backward, so we can count backward.

We have to go down 3 ticks, so -10-3=-13; -13-3=-16; -16-3=-19.

The blue dot is -19

Answer: The blue dot equals to -19.

Step-by-step explanation:

On the number line, there are the numbers -10 & -4.

-7 would fit in the middle of them. That means the number line goes by minus 3.

Count -10 , -13, -16, then you get on the the blue dot which is -19.

Therefore, -19 is the answer.

The inequality equation given on number line shows as.

What is number line?

In elementary arithmetic, number line could be a image of a graduated line that is visual illustration of the important numbers. each purpose of range|variety} line is assumed to correspond to a true number, and each complex number to a degree.

Main body:

The given inequality is :

y≥ -8

to represent it on the number line we need to select number which are greater than -8 .

Hence the graph on number line looks line as represented in figure.

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The parametric equations for an object moving clockwise along the ellipse are x =  3 cos((2π/3) t) and y = 5 sin((2π/3) t)

Given: the equation of an ellipse x²/9 + y²/25 = 1

Beginning at (0,5) and requiring 3 seconds

The parametric equations representing an ellipse x²/a² + y²/b² = 1  are

x = a cos(t) and y = b sin(t)

where t is the parameter with values between [0, 2π]

If t represents time. Then, if a lap around the ellipse is completed in T seconds we have,

x = a cos((2π/T) t)

y = b sin((2π/T) t)

where 2π/T is the period of the motion.

Combining these results, therefore, we have the parametric equations:

x =  3 cos((2π/3) t)

y = 5 sin((2π/3) t)

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Answer:

the III quadrate the x line (horizontal line) the number there is -4 on the y line (vertical line) -6 from the right side of the III quadrate

The the smallest positive solution to the Trigonometry sin(5x)cos(9x) - cos(5x)sin(9x) = - 0.25 is x = 3.617degree

Trigonometry is a branch of mathematics that studies relationships between the sides and angles of triangles

sin(5x)cos(9x) - cos(5x)sin(9x) = -0.25

sin(5x)cos(5x + 4x) - cos(5x)sin(5x + 4x) = -0.25

-sin( 5x - 9x) = -0.25

-sin (9x -5x) = -0.25

sin ( 4x) = 0.25

Using the sine inverse

arcsin(0.25) = x = 0.25268 rad ≅ 14.47 degree

so dividing this angle by 4

x = 3.617degree

Therefore, the smallest positive solution to the Trigonometry is x = 3.617degree

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Answer:

-3x -12

Step-by-step explanation:

-6x +3x = -3x

-3-9 = -12

The value of the x angle is 107 °

What is the sum of triangle angles?

In Euclidean space, the sum of a triangle's angles equals the straight angle. A triangle has three angles, one at each vertex, and is bounded by two adjacent sides. For a long time, it was unknown whether other geometries existed with different sums.

The angle in the triangle next to 123° is

= 180° - 123°

= 57°

The sum angles in a triangle are 180°

x = 180 - 57 - 16

x = 107 °

Hence, the value of the x angle is 107°.

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(a) The mean of the data item from the group data is 161.

(b) The deviation from the mean for each data is -6,-5,1,3 and 7. respectively.

(c) The sum of the deviation is 0

Grouped data are data formed by aggregating individual observations of a variable into groups, so that a frequency distribution of these groups serves as a convenient means of summarizing or analyzing the data.

(a) To find the mean of the data, we use the formula below.

Formula:

Where:

Substitute these values into equation 1

(b) To calculate the deviation from the mean (M') for each of the data item we use the formula below.

M' = x-M

For data 115,

For data 156,

For data 162,

For data 164,

For data 168,

(c) The sum of the deviation is

Hence, the mean, the diaviation from the mean is -6,-5,1,3 and 7  and the sum of the deviation of the data is 161 and 0 respectively,

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The number of pinto beans in the jar is 24

Ratio, in math, is a term that is used to compare two or more numbers. It is used to indicate how big or small a quantity is when compared to another. In a ratio, two quantities are compared using division. Here the dividend is called the 'antecedent' and the divisor is called the 'consequent

let x be the number of pinto beans

white beans = x + 36

Total beans = 2x + 36

Total share = 2 + 5, which is 7

number of pinto beans(x) = 2/7 * (2x + 36)

x = 2/7 * (2x + 36)

By cross multiplying,

7x =2(2x + 36)

7x = 4x + 72

collect like terms

7x - 4x = 72

3x = 72

x = 72/3

x = 24

In conclusion, 24 pinto beans are in the jar.

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Answer: 45

Step-by-step explanation:

The total profit in all was [tex]1040-900=\$ 140[/tex].

The total profit per pizza was [tex](0.50)(8)=\$4[/tex].

This means they sold [tex]\frac{140}{4}=35[/tex] pizzas.

Adding this to the 10 pizzas held back, there were [tex]35+10=45[/tex] pizzas in the original order.

Answer:

so sometimes this happens to me and I get a parent or a teachers to help me and I’m sometime doing the math wrong when my answer is right so maybe double check work

Step-by-step explanation:

Answer:

y=4x+14

Answer choice 4

Step-by-step explanation:

What is the slope-intercept form of the line that passes through the points (-4,-2) and (-2, 6)?

m=(6+2)/(-2+4)

m=4

Slope-point form: (y+2)=4(x+4)

Simplify to slope-intercept form:

y+2=4x+16

y=4x+14

Answer:  Choice A

Step-by-step explanation:

1/8 = 0.125

That is a decimal that terminates after 3 decimal places (choice A)

The given equation, y = -4(x-3)² + 6, rewritten in standard form is y = -4x² + 24x - 30

From the question, we are to rewrite the given equation in standard form.

The given equation is

y = -4(x-3)² + 6

The standard form of a quadratic equation is

y = ax² + bx + c  

Now, we will express the given equation in the standard form of a quadratic equation.

y = -4(x - 3)² + 6

y = -4(x - 3)(x - 3) + 6

y = -4(x(x -3) -3(x - 3)) + 6

y = -4(x² - 3x - 3x + 9) + 6

y = -4x² + 12x + 12x - 36 + 6

y = -4x² + 24x - 30

Hence, the equation is y = -4x² + 24x - 30

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Answer:

1250 teenagers

Step-by-step explanation:

= 5000 * (1/4)

= 5000 * 0.25

= 1250

Answer:

[tex]\huge\boxed{\sf 1250 \ teenagers}[/tex]

Step-by-step explanation:

Total people = 5,000

= 25% of total people

Key: "of" means "to multiply" and total people = 5000

= 25% × 5000

Key: % means "out of 100"

[tex]\displaystyle =\frac{25}{100} \times 5000\\\\= 25 \times 50\\\\= 1250 \ teenagers\\\\\rule[225]{225}{2}[/tex]

Answer: To make it very simple for ourselves, we can just divide 8 by 4.29. Our answer will then be 1.8648018648 or rounded to 1.86 servings per dollar.

Hope this helps.

Answer:

0,76 x 10^3

Step-by-step explanation:

0,4 x 1,9 = 0,76

10^7 x 10^-4 = 10^(7-4) = 10^3

The probability that the weight will be between 3183 and 4022 grams is; 0.9323

The formula for z-score is;

z-score = (x – μ) / σ

where;

x is sample mean

μ is population mean

σ is standard deviation

Now, we want to find the probability that the weight will be between 3183 and 4022 grams. This is;

P(3183 < X < 4022)

When X = 3183

z = (3183 - 3637)/227

z = -2

When X = 4022

z = (4022 - 3637)/227

z = 1.696

Using online probability between two z-scores calculator, we have;

P(-2 < x < 1.696) = 0.9323

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He is best known in the modern day for the Pythagorean Theorem, a mathematical formula which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares on the other two sides.

Pythagoras was a Greek philosopher who made important developments in mathematics, astronomy, and the theory of music. The theorem now known as Pythagoras's theorem was known to the Babylonians 1000 years earlier but he may have been the first to prove it.

The most famous contribution for which Pythagoras is popular worldwide is the discovery of the Pythagoras Theorem which applies to all Right Angled Triangle. In the theorem, he stated that the sum of the square of both Base and Height will be equal to the square of Hypotenuse of a Right Angle Triangle.

Answer:

a. False

b. True

c. False

d. False

Step-by-step explanation:

(a) is False, the reason is: 39 is odd number and Set A contains only even numbers.

(b) is true  Set A contains even natural numbers and set B contains odd natural numbers. There is nothing common between the two set. This implies that intersection of the two set is empty.

(c) is False, the reason is: 48 is even natural number and Set B contains only odd natural numbers.

(b) is False  Set A contains even natural numbers and set B contains odd natural numbers. The union of two sets is set of natural numbers not the set A.

The quadratic function is y = 2x^2+3x-4.

Given:

The quadratic function y = ax² + bx + c whose graph passes through the given points.(-1,-5), (1,1),(-2,-2)

(-1,-5) passes.

y = ax^2+bx+c

-5 = a(-1)^2+b*-1+c

-5 = a-b+c

(1,1) passes.

1 = a*1^2+b*1+c

1 = a+b+c

(-2,-2) passes.

-2 = a(-2)^2+b*-2+c

-2 = 4a-2b+c

on solving three equations

a = 2 , b = 3 and c = -4

The quadratic equation is y = 2x^2+3x-4.

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Answer:

[tex]\huge\boxed{\sf x = 128\°}[/tex]

Step-by-step explanation:

x + 52° = 180 (Angles on a straight line add up to 180°)

Subtract 52 to both sides

x = 180 - 52

x = 128°

[tex]\rule[225]{225}{2}[/tex]

Answer:

X= 128°

Step-by-step explanation:

The angels on a straighlije add up to 180°

hence <DCA+ <BCA= <BCD

X+ 52°=180°

X=180°-53°

X=128°

Here is the completed table:

                         Tuna     Cheese   Ham   Total

Brown                  21          11             8        40

White                  21           15           24       60

Total                     42        26           32           100

Number of tuna sandwiches that were on white bread : 1/2 x 42 = 21

Number of tuna sandwiches that were on brown bread : total number of tuna sandwiches - total number of tuna sandwiches on white bread: 42 - 21 = 21

Number of ham sandwiches on brown bread : 20% x 32

= 0.25 x 32 = 8

Number of ham sandwiches on white bread : number of ham sandwiches - number of ham sandwiches on brown bread

32 - 8 = 24

Number of white bread sandwiches - number of brown bread sandwiches = 20

number of white bread sandwiches = x + 20

number of brown bread sandwiches = x

x + x + 20 = 100

x + x = 100 - 20

2x = 80

x = 40

number of white bread sandwiches = 40 + 20  = 60

Number of white bread cheese sandwiches = total number of white bread sandwiches - total number of tuna and ham white bread sandwiches

Number of white bread cheese sandwiches = 60 - (21 + 24)

= 60 - 45

= 15

Number of brown bread cheese sandwiches = total number of brown bread sandwiches - total number of tuna and ham brown bread sandwiches

40 - (21 + 8)

40 - 29 = 11

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Answer: its answer b

Step-by-step explanation:

The gross wage of Jose for the week is $422.125.

Given that, during a certain week Jose worked 9 ½ hours Monday to Friday each day, together with 6 hours on Saturday and 4 ½ hours on Sunday.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Let the wage for the normal working week be x

Now, number of hours Jose worked from Monday to Friday

= [tex]9\frac{1}{2}[/tex]

= 19/2 ×5

= 47.5 hours

The normal working day was 8 hours

So, 8×5=40 hours

Over time = 7.5 hours

a) Jose normal wage is

x = 40×5.50

= $220

b) Anytime worked in excess of this was paid for at time-and-a-half

That is, 5.5+5.5/2

= $8.25

Overtime wage =7.5×8.25

= $61.875

c) Saturday work being paid at double-time

That is 5.5×2=$11

Overtime wage for Saturday

= 6×11

= $66

d) Sunday working being paid at triple-time

That is, 5.5×3 =$16.5

Overtime wage for Sunday

= 4.5×16.5

= $74.25

e) His gross wage for the week =220+61.875+66+74.25

=$422.125

Therefore, the gross wage of Jose for the week is $422.125.

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The equation of each line that is perpendicular to the given lines and passes through the stated points are:

20. y = -x + 2

21. y = -7/2x - 35/2

22. y = -8/3x - 7

23. y = 1/4x + 1

In slope-intercept form, y = mx + b, the slope of the equation is m, while the y-intercept of the equation is b.

If two lines are perpendicular to each other, the values of m, which is their slope, are negative reciprocals.

20. The slope of y = 3/3x - 2 is 1, the slope (m) of the line that is perpendicular to it is -1.

Substitute (x, y) = (-2, 4) and m = -1 into y = mx + b, to find the value of b:

4 = -1(-2) + b

4 = 2 + b

4 - 2 = b

2 = b

b = 2

Write the equation of the perpendicular line by substituting m = -1 and b = 2 into y = mx + b:

y = -x + 2

21. The slope of -2x + 7y = 14 is 2/7. Therefore, the slope (m) of the line that is perpendicular to it is -7/2.

Substitute (x, y) = (-3, -7) and m = -7/2 into y = mx + b, to find the value of b:

-7 = -7/2(-3) + b

-7 = 21/2 + b

-7 - 21/2 = b

-35/2 = b

b = -35/2

Write the equation of the perpendicular line by substituting m = -7/2 and b = -35/2 into y = mx + b:

y = -7/2x - 35/2

22. The slope of 3x - 8y = 16 is 3/8. Therefore, the slope (m) of the line that is perpendicular to it is -8/3.

Substitute (x, y) = (-3, 1) and m = -8/3 into y = mx + b, to find the value of b:

1 = -8/3(-3) + b

1 = 8 + b

1 - 8 = b

b = -7

Write the equation of the perpendicular line by substituting m = -8/3 and b = -7 into y = mx + b:

y = -8/3x - 7

23. The slope of 4x + y = 7 is -4. Therefore, the slope (m) of the line that is perpendicular to it is 1/4.

Substitute (x, y) = (4, 2) and m = 1/4 into y = mx + b, to find the value of b:

2 = 1/4(4) + b

2 = 1 + b

2 - 1 = b

1 = b

b = 1

Write the equation of the perpendicular line by substituting m = 1/4 and b = 1 into y = mx + b:

y = 1/4x + 1

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The solution of the absolute value equation is x=1/6.

What is the solution to an equation?

In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.

When |3x-1|- | 2x+5-(5-x)| = 0

When 3x-1 < 0 and 2x+5-(5-x) < 0

-(3x-1) - ( - ( 2x+5-(5-x) ) ) =0

on simplifying, variable cancels out, so no solution

When 3x-1 < 0 and 2x+5-(5-x) > 0

-(3x-1) - (  ( 2x+5-(5-x) ) ) =0

on simplifying, x=1/6

When 3x-1 >0 and 2x+5-(5-x) < 0

(3x-1) - ( - ( 2x+5-(5-x) ) ) =0

on simplifying, x=1/6

When 3x-1 >0 and 2x+5-(5-x) >0

(3x-1) - (  ( 2x+5-(5-x) ) ) =0

on simplifying, variable cancels out, so no solution

So, the solution is x=1/6

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Answer:

3x+4=34

x=10

Step-by-step explanation:

Since it’s in the median it is a number in between the 2 on the shape and the number right between 28 and 40 is 34 so we can set 3x+4 equal to that to find x

3x+4=34

   -4. -4

3x=30

/3.  /3

x=10

Hopes this helps please mark brainliest

Answer:

Step-by-step explanation:

EF is the median, therefore the mean between 28 and 40

(28 + 40) : 2 =

34

3x + 4 = 34

3x = 30

x = 10