Identify the slope and y-intercept of the following equation:

y = 4x + 1​

The ramp will rise 16.8 inches from the ground at its highest end, when the angle of elevation is 19 degrees and the length of the fiberboard is 27 inches.

To calculate the height of the ramp at its highest end:

1. First, calculate the length of the hypotenuse of the triangle formed by the ramp, using the Pythagorean Theorem. This can be done by squaring the length of the ramp (27 inches) and the angle of elevation (19 degrees) and adding them together. The result is 750.41 inches.

2. Next, take the square root of the result from step 1. This gives us 27.45 inches, which is the length of the hypotenuse.

3. Then, subtract the length of the ramp from the length of the hypotenuse. This gives us 8.45 inches.

4. Finally, divide the result from step 3 by 2. This gives us the height of the ramp at its highest end, which is 16.8 inches.

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In set-builder nοtatiοn, we can write:

Dοmain οf h(x): { x ∈ R | x ≤ 1/3 οr x ≥ 2/3 }

Range οf h(x): { y ∈ R | y ≥ 0 }

In mathematics, a functiοn is a rule that maps each element in οne set, called the dοmain, tο a unique element in anοther set, called the range. It is a relatiοn between a set οf inputs and a set οf pοssible οutputs with the prοperty that each input is related tο exactly οne οutput.

The dοmain οf h(x) is the set οf all values οf x that make the functiοn well-defined, i.e., there shοuld be nο negative number inside the square rοοt.

Tο find the dοmain οf h(x), we set the expressiοn inside the square rοοt tο be nοn-negative and sοlve fοr x:

3x² - 5x + 2 ≥ 0

Factοrizing the quadratic expressiοn, we get:

(3x - 2)(x - 1) ≥ 0

The sοlutiοn set fοr this inequality is given by the interval:

x ≤ 1/3 οr x ≥ 2/3

Therefοre, the dοmain οf h(x) is:

{ x ∈ R | x ≤ 1/3 οr x ≥ 2/3 }

The range οf h(x) is the set οf all pοssible values that the functiοn can take. Since the square rοοt is always nοn-negative, the range οf h(x) is:

{ y ∈ R | y ≥ 0 }

In set-builder nοtatiοn, we can write:

Dοmain οf h(x): { x ∈ R | x ≤ 1/3 οr x ≥ 2/3 }

Range οf h(x): { y ∈ R | y ≥ 0 }

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Answer: i don't know what type of answer ur looking for but

the answer for substitution is x=-4, y=7

Step-by-step explanation:

y = 3x + 19

8x + 2y = - 18   ====>   y = -4x - 9

Equate the two expressions of 'y'

3x + 19 = - 4x- 9

7x = -28

x = -4       then y = 3x + 19 = 3(-4) + 19 = 7

(-4, 7)

Answer:

hey kid the answer is twice

the diameter of a circle is twice the length of its radius

Step-by-step explanation:

Answer: (2 times) the length of the radius

Step-by-step explanation:

r= 2D

see attachment

Answer:

Let's assume that the width of the rectangle is 'w' meters.

According to the problem, the length of the rectangle is three times its width, so the length is:

l = 3w

The area of the rectangle is given as 300 m², so we have:

lw = 300

Substituting the value of 'l' in terms of 'w', we get:

(3w)w = 300

Simplifying the above equation, we get:

3w^2 = 300

Dividing both sides by 3, we get:

w^2 = 100

Taking the square root on both sides, we get:

w = 10

So the width of the rectangle is 10 meters.

Using the value of 'w', we can find the length of the rectangle:

l = 3w = 3(10) = 30

So the length of the rectangle is 30 meters.

The perimeter of the rectangle is given by:

P = 2(l + w)

Substituting the values of 'l' and 'w', we get:

P = 2(30 + 10) = 2(40) = 80

Therefore, the perimeter of the rectangle is 80 meters.

Step-by-step explanation:

Brody bought 2 drinks and 10 pretzels.  Let's use algebra to solve this problem. Let d be the number of drinks that Brody bought, and let p be the number of pretzels that he bought. We know that he bought a total of 12 drinks and pretzels, so:

d + p = 12

We also know that each drink costs $6 and each pretzel costs $3.25, and he spent a total of $44.10 on drinks and pretzels. So:

6d + 3.25p = 44.10

We can use the first equation to solve for one of the variables in terms of the other. For example, we can solve for p:

p = 12 - d

Substituting this into the second equation, we get:

6d + 3.25(12 - d) = 44.10

Simplifying:

6d + 39 - 3.25d = 44.10

2.75d = 5.10

d = 1.85 (rounded to two decimal places)

Since d represents the number of drinks, we can't have a fractional value for it. However, we can round it to the nearest whole number and use that to solve for p:

d ≈ 2

p = 12 - d = 12 - 2 = 10

Therefore, Brody bought 2 drinks and 10 pretzels. We can check that this solution satisfies both equations:

2 + 10 = 12 (first equation)

6(2) + 3.25(10) = 44.10 (second equation)

Therefore, our solution is correct

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Brody and his children went into a movie theater and he bought $44.50 worth

of drinks and pretzels. Each drink costs $6 and each pretzel costs $3.25. He

bought a total of 12 drinks and pretzels altogether. Determine the number of

drinks and the number of pretzels that Brody bought

The surface area of the figure in item 14 is given as follows:

1112.8 mm².

The surface area of a rectangular prism of height h, width w and length l is given by:

S = 2(hw + lw + lh).

This means that the area of each rectangular face of the prism is calculated, and then the surface area is given by the sum of all these areas.

The figure in item 14 is composed as follows:

Hence the surface area of the figure is given as follows:

S = 5 x 13 x 13 + 4 x 0.5 x 10.3 x 13

S = 1112.8 mm².

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Answer:

Quadratic

Step-by-step explanation:

I have no idea how to explain it except that it follows the standard               ax² + bx + c format

Quadratic is the answer to your question! :)

Answer:

The x-intercept is (1, 0).

The correct numerical expression for "9 times 4 added to the difference of 3 and 2" is:

9 x 4 + (3 − 2)

First, we need to calculate the difference of 3 and 2, which is 1. Then, we add it to the product of 9 and 4, which is 36. So the final expression is:

36 + 1 = 37

Therefore, the correct numerical expression is 9 x 4 + (3 − 2) = 37.

Answer:

1. =2.5759 ; 2. =0.8290 ;  3. =2  ; 4. =1.7959 ; 5. = 3.9138

Step-by-step explanation:

1. Taking logarithm with base 3 on both sides, we get:

b = log₃(17)

b ≈ 2.5759

2. Taking logarithm with base 12 on both sides, we get:

r = log₁₂(13)

r ≈ 0.8290

3. Taking logarithm with base 9 on both sides, we get:

n = log₉(49)

n = 2

4.Taking logarithm with base 16 on both sides, we get:

v = log₁₆(67)

v ≈ 1.7959

5.Taking logarithm with base 3 on both sides, we get:

a = log₃(69)

a ≈ 3.9138

Answer:

Proofs attached to answer

Step-by-step explanation:

Proofs attached to answer

A parabola is a U-shaped curve that can open upwards or downwards. Its equation is typically in the form y = ax^2 + bx + c, where a, b, and c are constants. The properties of a parabola are determined by these constants.

Description about vertex,max/min,axis of

Description about vertex,max/min,axis ofsymmetry,zero(s),direction of opening,y-intercept of parabola:

Vertex: The vertex is the point where the parabola changes direction. It is the highest or lowest point on the curve, depending on whether the parabola opens upwards or downwards. The vertex is located at the point (-b/2a, f(-b/2a)), where f(x) is the

function that defines the parabola.

Max/min: The maximum or minimum value of the parabola is the y-coordinate of the vertex. If the parabola opens downwards, the maximum value occurs at the vertex. If the parabola opens upwards, the minimum value occurs at the vertex.

Axis of Symmetry: The axis of symmetry is a vertical line that passes through the vertex and divides the parabola into two mirror-image halves. The equation of the axis of symmetry is x = -b/2a.

Zero(s): The zero(s) of the parabola are the x-values where the parabola intersects the x-axis. These are also called roots or solutions of the quadratic equation. If the discriminant (b² - 4ac) is positive, the parabola intersects the x-axis at two points. If the discriminant is zero, the parabola intersects the x-axis at one point (which is also the vertex). If the discriminant is negative, the parabola does not intersect the x-axis and has no real roots.

Direction of Opening: The direction of opening of the parabola is determined by the sign of the coefficient a. If a is positive, the parabola opens upwards, and if a is negative, the parabola opens downwards.

y-intercept: The y-intercept is the point where the parabola intersects the y-axis. It is located at the point (0, c), where c is the constant term in the quadratic equation.

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Correct question is "For each parabolas, describe the following properties:

Vertex

Max/min

Axis of

Symmetry

Zero(s)

Direction of

Opening

y-intercept."

Option D : The equation that demonstrates the inverse property is D. 3/4 x 4/3= 1, which shows that the multiplication of the reciprocal of a number equals 1.

According to the multiplicative property known as the inverse property, the result of multiplying any non-zero number by its inverse or reciprocal will equal the multiplicative identity, which is 1.

The inverse property of multiplication states that for any non-zero number a, its inverse or reciprocal, when multiplied by a, will result in 1. The reciprocal of a number is the number that when multiplied by the original number results in 1.

For example, the reciprocal of 3 is 1/3 because 3 x 1/3 = 1.

Similarly, the reciprocal of 4/3 is 3/4 because (4/3) x (3/4) = 1.

So, if we multiply 3/4 by its reciprocal 4/3, we get:

(3/4) x (4/3) = (3 x 4) / (4 x 3) = 12 / 12 = 1

This shows that the product of 3/4 and 4/3 is 1, which is the multiplicative identity. Hence, this equation demonstrates the inverse property of multiplication.

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Which equation would demonstrate the inverse property?

A. (3x4) + (3x5) = 3(4+5)

B. 3x5 = 5x3

C. 3x4x5= (3x4)x5

D. 3/4 x 4/3= 1

So, there are 18 possible outcomes in the sample space.

In probability theory, the sample space of an experiment is the set of all possible outcomes that can occur. It is denoted by the symbol S and represents the total set of possible results that can be obtained from a given experiment.

For example, when rolling a standard six-sided die, the sample space is {1, 2, 3, 4, 5, 6}, because those are the only possible outcomes of the experiment. Similarly, when flipping a coin, the sample space is {heads, tails}.

The sample space is an essential concept in probability theory because it helps to determine the likelihood or probability of various outcomes occurring in a given experiment.

Here's the tree diagram for the given problem:

markdown

Copy code

        Lunch

           /     |      \

    Soup Salad Sandwich

    /              |         |    

Tortellini Lentil     Caesar

                          /          |      \

               Roast Beef Ham   Turkey

The possible outcomes in the sample space are all the combinations of soup, salad, and sandwich.

There are 2 options for soup (Tortellini, Lentil), 3 options for salad (Caesar, Macaroni, Garden), and 3 options for sandwich (Roast Beef, Ham, Turkey). Therefore, the total number of possible outcomes in the sample space is:

2 x 3 x 3 = 18

So, there are 18 possible outcomes in the sample space.

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[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ P(\stackrel{x_1}{3}~,~\stackrel{y_1}{4})\qquad R(\stackrel{x_2}{7}~,~\stackrel{y_2}{4}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ 7 +3}{2}~~~ ,~~~ \cfrac{ 4 +4}{2} \right) \implies \left(\cfrac{ 10 }{2}~~~ ,~~~ \cfrac{ 8 }{2} \right)\implies \stackrel{ \textit{\LARGE S} }{(5~~,~~4)}[/tex]

The life insurance policy will pay $2,256,150 to Jeff's beneficiaries per year. The solution has been obtained by using the simple interest.

What is simple interest?

A way to figure out how much interest will be charged on a sum of money at a specific rate and for a specific duration of time is by using simple interest. The principal amount in a basic interest calculation is constant.

We are given that Jeff has to put $2,225,000 into a bank account if it ever had to make payments on the policy and the company also expects interest rates to be at 1.4% at that time.

So, from this we get,

⇒ Total Interest = $2225000 × 1.4% × 1

⇒ Total Interest = $31,150

Amount payable by company = $2225000 + $31,150

Amount payable by company = $2,256,150

Hence, the life insurance policy will pay $2,256,150 to Jeff's beneficiaries per year.

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The missing length w of the given trapezium with the area of  128.885 cm² is found to be: w = 14.9 cm.

A closed-form, two-dimensional quadrilateral with two parallel, opposite sides is called a trapezium. The bases and legs of a trapezium are referred to as parallel and non-parallel, respectively. Four sides as well as four corners make up the trapezium.

The term "isosceles trapezium" refers to a trapezium with equal-length legs, meaning that the 2 non parallel sides are equal.

Area of Trapezium =  ½ (Sum of parallel sides) × (Height between parallel sides)

128.885  =  ½(5.3 + 12) × w

128.885 * 2  =  17.3 w

w = 128.885 * 2 / 17.3

w = 14.9

Thus, the missing length w of the given trapezium with the area of  128.885 cm² is found to be: w = 14.9 cm.

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Answer:

put 5 units up

Answer:

1. is the distance from the center of the circle to any point on it's circumference

The number of expected double crossover progeny when multiply by the total number of progeny is 47.

When chromosomal pieces are swapped out twice, it is known as a double crossover. In the case of a double crossing, the two ends of the chromosome are still parental, but another sister chromatid sequence has "swapped" into the space between the crossovers;

When homologous chromosomes are combined, crossovers happen.

Chromatids from various chromosomes can be aligned. Exchange chromatids from, for example, segments a collision between two identical chromosomes occurs at an similar spot along their respective lengths. they are After swapping the segments, the chromatids have split between the point of contact and the chromatids' tips.

We have,

number of double crossovers is 0.305 x 0.155 x 1000

so 0.305 x 0.155 x 1000 = 47

So number of expected double crossover progeny is 47.

Test cross:

Progeny whithered wing smooth body and speck body

Genetic distance between sm and sp is 15.5

15.5 = 2x + 33 /1000 x 100

155 = 2x + 33

2x = 155-33

x = 122/2

x = 61.

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The expressions -4(3e+4) is equivalent to  -7+3(-4e-3)

Given expression:

[tex]-7+3(-4e-3)[/tex]

Expand expression:

[tex]-7-12e-9[/tex]

Regroup like terms:

[tex]-12e-9-7[/tex]

= [tex]-12e-16[/tex]

Factor -4 to get:

[tex]-4(3e+4)[/tex]

A mathematical expression is a combination of numbers, symbols, and/or variables that represent a mathematical statement. It can be a simple expression like "2 + 3," or a more complex one like "sin(x) + 3y^2 - 7."

Expressions can be used to perform calculations, represent relationships between different quantities, or describe geometric shapes and structures. They are an essential tool in mathematics and are used in a wide range of fields, including science, engineering, finance, and economics.

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Complete question:

Which expressions are equivalent to -7+3(-4e-3)?

Choose all answers that apply:

(Choice A)

-4(3e+4)

(Choice B)

12e

(Choice C)

None of the above

The formula for the volume of the shaded region is given as follows:

V = π/3[(R² - r²)(H - h)]

The volume of a cone of radius r and height h is given by the equation presented as follows, which the square of the radius is multiplied by π and the height, and then divided by 3.

V = πr²h/3.

Hence, for the large cone, the volume is given as follows:

Vl = πR²H/3.

For the smaller cone, the volume is given as follows:

Vs = πr²h/3.

Hence the volume of the shaded region is given as follows:

V = Vl - Vs

V = πR²H/3 - πr²h/3

V = π/3[(R² - r²)(H - h)]

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Answer:

a) The circumference of a circle is the perimeter of the circle. The circumference of the circle is the distance around a circle, that is the arc length of the circle. The circumference of a circle is given by:

Circumference = 2π × radius; but diameter = 2 × radius. Hence:

Circumference = π * diameter.

Given that diameter of the tire = 2.5 ft:

Circumference of the tire = π * diameter = 2.5 * π = 7.85 ft

b) since the circumference of the tire is 7.85 ft, it means that 1 revolution of the tire covers a distance of 7.85 ft.

1 mile = 5280 ft

The number of rotation required to cover 1 mile (5280 ft) is:

number of rotation =

Step-by-step explanation:

Thats the best i can find.

Answer:

Your answer is correct and you showed all the necessary steps to find the circumference and the number of times the tire would have to rotate to travel one mile. Well done!

In system equation method,

a) Amount of red portion = 240 ml.

b) There are 300 mL of blue potion used and 100 mL of red potion used.

c)  There is a ratio of 2 (blue potion):1 (red potion), there will be a 35% amount of magical syrup.

What is equation?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

(a)  We can use a system equation here to solve this.

Let x=amount of red potion used

Let y=total amount of potion in solution

Then,

=>200 + x =  y

=> 0.15(200) + 0.75x = 0.25y

0.15(200) because 15% of the blue potion=.15 and there is 200mL.

0.75x because 75% of the red potion=.75 and there is x amount of it

0.25y because we want 25% of the total potion=.25 and there is y amount of it.

We can substitute for y in the second equation:

=>0.15(200) + 0.75x = 0.25(200 + x)

=> 30 + 0.75x = 50 + 0.25x

=> -20 = -0.5x

=> x = 40

Knowing that x=40, we know that y=240, meaning our answer is 240.

b.) We can again use a system for this problem

Let x=Amount of red potion

Let y=Amount of blue potion

=> x + y = 400

=> 0.3(400) = 0.15y + 0.75x

0.3(400)=30% of the 400 mL

0.15y=15% of the magic syrup

0.75x=75% of the magic syrup

We can substitute for x in this equation:

=>120 = 0.15y + 0.75(400 - y)

120 = 0.15y + 300 - 0.75y

-180 = -0.6y

y = 300, x = 100

There are 300 mL of blue potion used and 100 mL of red potion used.

c.) Let x=amount of red potion

Let y=amount of blue potion

=> 0.15x + 0.75y = 0.35(x + y)

0.35(x+y) because the total amount of the potion is x+y

=>0.15x + 0.75y = 0.35x + 0.35y

0.4y = 0.2x

2y = x

Whenever there is a ratio of 2 (blue potion):1 (red potion), there will be a 35% amount of magical syrup.

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Answer:

[tex]90 { \: cm}^{2} [/tex]

Step-by-step explanation:

First, we can find one triangle's area (they are all the same and isosceles):

h = XY = 6 cm, a = BC = 5 cm

[tex]s(triangle) = \frac{1}{2} \times h \times a = \frac{1}{2} \times 6 \times 5 = 15[/tex]

And now, multiply this number by 6 (since there are 6 of these identical triangles):

S(hexagon) = 15 × 6 = 90 cm^2

Step-by-step explanation:

1)  x^2 - 4x + 1

   re-arrange into   vertex form  y = a ( x-h)^2 + k    where h, k is the vertex

y =    (x^2 -4x) +1     'complete the square'  

                 ( take 1/2 of x coeff square it and add and subtract it )

       (x^2 - 4x +4)  - 4    + 1     reduce it

y=      (x-2)^2  -3         shows vertex is  2, -3

    Back to original equation  

   x^2 -4x + 1        using Quadratic Formula   x = 2 ± sqrt (3)  = 3.73 and .268

   line of symmetry = x value of vertex    x = 2

Range  is     -3 ≤ y ≤ + ∞

  domain is   - ∞  ≤  x  ≤ + ∞

2)   Similar to above....try it yourself

The probability of getting a red king card from the deck of cards is 1/26.

The probability formula can be used to determine the likelihood of an event by only dividing the favourable number of possibilities by the entire number of possible outcomes.

As there can never be more favourable outcomes than there are possible outcomes, the probability of an event happening can range from 0 to 1. As a result, 0 cannot represent the percentage of successful outcomes.

Given,

We have a deck of cards.

So, total no of cards = 52

Now, no of red cards = 26.

Now total no. of kings = 4.

Total no. of red kings = 2

Probability of picking a red king from the deck =

2/52

=1/26

Therefore, the probability of getting a red king card from the deck of cards is 1/26.

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Answer:

1: 9

2: 16

3: 225

4: 196

5: 25

6: 256

Step-by-step explanation:

Math :)

Using the sine's function in the given triangle, the value of x is 75.7 respectively.

What is the triangle?

A triangle is a 3-sided polygon that is occasionally (though not frequently) referred to as the trigon.

There are three sides and three angles in every triangle, some of which may be the same.

The angle total of a triangle will always be equal to 180°.

A quadrilateral can be divided in half from corner to corner to form a triangle because the angle total of a quadrilateral is equal to 360°.

A triangle is effectively half of a quadrilateral, therefore it makes sense that its angle measurements are also half. 180° is one-half of 360°.

So, right triangles are used to depict figures like this one, which has a hypotenuse of 85, a base of x, and a top angle of 63°.

The hypotenuse and the side that faces the angle are both present.

The sine function's opposite/hypotenuse ratio is as follows:

sin 63° = x/85

Now, solve as follows:

sin 63° = x/85

85(sin 63°) = x

75.7 = x

Therefore, using the sine's function in the given triangle, the value of x is 75.7 respectively.

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Complete question:

In this triangle, what is the value of x? Enter your answer, rounded to the nearest tenth, in the box.