Calculate the value of a in the triangle below.
15 cm
12 cm
a cm

The first table represents a linear function.

A linear function is one that changes at a constant rate. Any linear function has an increase or decrease that is constant. The slope of the line, denoted by the letter m in the equation y = mx + b, is this constant rate of change.

Given are the tables with values of x and y.

In a table of linear functions, the ratio of the difference in y values to the difference in x values is consistently constant.

The first table is given as:

x y

1 3

2 7

3 11

4 15

Only table 1 in the provided tables represents a linear function.

This is because the equivalent values of y change by 4 when the value of x changes by 1.

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For this case

P = 10 000

i=0.055

t=120

After you compute the formula you would get

A = 6 170 141

The quotient and remainder when −34 is divided by 6 is -6 and 2 respectively.

Dividend = Divisor x Quotient + Remainder

For the given question,

The number -34 is to be divided by 6.

In this, dividend is -34 and divisor is 6.

Now while dividing the number comes should be less than -34.

Thus, -34 divided by 6 gives quotient as -36 and remainder as 2.

Where,  the remainder r has to satisfy 0≤r<6, and in particular cannot be negative.

Therefore, the quotient and remainder when −34 is divided by 6 is -6 and 2 respectively.

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Answer:

1.7^28/1.6^21 the second option.

Step-by-step explanation:

Answer:

3rd option

Step-by-step explanation:

In the 3rd option, two sides from each triangle in the large triangle are compared.

A linear function with the same y-intercept as the one that is represented by the graph is: table 1.

In Mathematics, the slope of any linear function can be calculated by using this formula;

Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope, m = (y₂ - y₁)/(x₂ - x₁)

At points (-3, -4) and (-1, 2) from table 1, the slope of the line would be calculated as follows:

Slope, m = (2 + 4)/(-1 + 3)

Slope, m = 6/2

Slope, m = 3.

Note: The y-intercept of the line shown on the graph is equal to 5 because the x-value is zero (0) at this point.

By using point (-3, -4), the y-intercept of this line would be calculated by using the slope-intercept form:

y = mx + b

Where:

Making y-intercept (b) the subject of formula, we have:

y-intercept, b = y - mx

y-intercept, b = -4 - 3(-3)

y-intercept, b = -4 - (-9)

y-intercept, b = -4 + 9

y-intercept, b = 5.

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Complete Question:

Which linear function has the same y-intercept as the one that is represented by the graph?

The equation in function notation is: f(x) = 3x + 9.

Slope of the line = 3

Y-intercept = 9

X-intercept is: -3.

In function notation, the equation can be written as .f(x) = mx + b, where:

Given the equation, -3x + y = 9, rewrite in function notation as:

-3x + y + 3x = 3x + 9

y = 3x + 9

f(x) = 3x + 9

Slope of the line is, m = 3.

The y-intercept of the equation is, b = 9.

To find the x-intercept, substitute y = 0 into y = 3x + 9:

0 = 3x + 9

-3x = 9 [subtraction property of equality]

-3x/-3 = 9/-3 [division property of equality]

x = -3

The x-intercept is: -3.

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The function is -|x+3|. The range is (-∞,0].

Given that,

The function is -|x+3|

We must determine the function's range.

A function's domain and range are its constituent parts. The domain of a function is the set of all possible input values, whereas the range of a function is its potential output. Range, Domain, and Function. A is the domain and B is the co-domain if a function f: A → B exists that maps every element of A to an element in B.

The function is -|x+3|

The domain is (-∞,∞)

The range is (-∞,0]

Therefore, the range is (-∞,0].

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Answer:

see image

Step-by-step explanation:

See attached image

Length: 18 in.

Width: 6 in.

We can use “x” as the width in this scenario. If the width is x, then the length is 3x, since length is three times the width. The perimeter would be length + length + width + width. Since the perimeter is 48, we could say that:

x + x + 3x + 3x = 48

Which simplifies to 8x=48

If you divide by 8 on both sides, you get

X=6. Then you Can plug 6 back into your x width and 3x length.

(See attached image) hope this helped!

Hello!

Let's set up some variables:

Let's consider the relationship between the length and the width:

              [tex]\hookrightarrow L=3W[/tex]

The perimeter of the rectangle is equal to 48 and 2W + 2L

  [tex]\hookrightarrow 2L + 2W = 48[/tex]

Let's replace the 'L' in terms of 'W' and solve:

    [tex]2(3W) + 2W = 48\\6W + 2W=48\\8W = 48\\W = 6[/tex]

Since L = 3W

  [tex]\hookrightarrow L = 3W = 3*6 = 18[/tex]

Answer:

Hope that helps!

By evaluating the given linear equation, we will see that the missing values in the table are:

Here we have a table that relates the inputs, x, with the outputs, y, of the linear equation:

y = 2x + 1

To find the missing values we need to evaluate the linear equation in the given inputs, a is the value that we get when x = -2, evaluating in that we get:

a = 2*(-2) + 1

a = -4 + 1

a = -3

The value of b is what we get when x = 0.

b = 2*0 + 1

b = 1

The value of c is what we get when x = 1.

c = 2*1 + 1

c = 3

The value of d is what we get when x = 2.

d = 2*2 + 1

d = 4 + 1

d = 5

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To answer this question, we need to remember the next theorem:The

We have that the hypotenuse is the largest side of a right triangle. In this case, it is equal to (5 + 20) = 25 units.

The leg of the right triangle we need to find is m, and we know that the projection of m on the hypotenuse is 5 units.

Theref

ANSWER

194 grams

EXPLANATION

We have that the half life of the uranium is 2 years.

This means that it will take 2 years for the uranium to decay to half of its original value.

The formula for exponential decay is:

where y = the value after the decay

a = initial value

b = rate of decay.

t = number of years

First, we have to find b.

We have that 776 grams of uranium will decay to half its amount (388 grams) in 2 years. This means that:

Therefore, after 4 years (t = 4), the amount of uranium left will be:

That is the amount of uranium that will be left after 4 years.

Answer:

Step-by-step explanation:

Remember that for a given terminal point of an angle, we define those trigonometric functions as following:

This way, we'll have that:

Answer:

answer to question 1: 24

Explanation: (btw sorry i couldn't answer question 2) multiply 8 times 3 and you get the answer

The required group of number is 24 of 1/8 in 3.

Algebra is a study of mathematical expressions, in which numbers and quantities are represented in formulas and equations by letters and other universal symbols.

The given numbers are 1/8 and 3.

Let there are n number of groups of 1/8 in 3.

To find the value of number of groups n,

Use equation form,

1/8 n = 3

n = 3 x 8

n = 24.

There are 24 groups of 1/8 in 3.

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The amount of money that will be in the account after 4 years is $3,583.16

How many times is interest compounded annually?

The fact that the interest rate of 9% in this scenario is compounded daily means that the interest is compounded every day of the year, 365 days in a year, hence, our future value formula needs an adjustment for daily compounding as shown below:

FV=PV*(1+r/m)^(n*m)

FV=the accumulated balance in the account after 4 years=unknown

PV=amount invested or deposited initially=$2500

r=annual interest=9%

m=number of times in a year that interest is compounded=365

n=number of years=4

FV=$2500*(1+9%/365)^(4*365)

FV=$3,583.16

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Answer:

x > 56

Step-by-step explanation:

x/8 - 13 > -6

x/8 > 7

x > 56

The function has no minimum or maximum

The function is given as

f(x) = -2/3x + 5 if x < 0

f(x) = -x^2 + 4x + 5 if x > 4

The above function is a piecewise function

And the type of functions in the piecewise function are

A linear function does not have a minimum or a maximum

This means that the function would have no minimum or maximum

Hence, the minimum or the maximum value of the function does not exist

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Answer:

BC ≈ 9.0

Step-by-step explanation:

using the tangent ratio in the right triangle

tan42° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{BC}{AC}[/tex] = [tex]\frac{BC}{10}[/tex] ( multiply both sides by 10 )

10 × tan42° = BC , then

BC ≈ 9.0 ( to 1 dec. place )

The values are given as:

(a) Approximate the value of e^6 to 4 decimal places:

The value of

The approximate value to 4 decimal places is 403.4288.

(b) Approximate the value of e^(-0.66) to 4 decimal places:

Approximated value to 4 decimal places is 0.5168..

Answer:

See below

Step-by-step explanation:

1   note the other angle at d = 62   ( isosceles triangle)

2  x = 180 - 62 - 62 -25

Answer:

x = 31°

Step-by-step explanation:

since AB = BD then Δ ABD is isosceles with base angles congruent, so

∠ ADB = ∠ BAD = 62°

the sum of the 3 angle in Δ ABD = 180° , so

∠ ABD = 180° - 62° - 62° = 180° - 124° = 56°

∠ ABD and ∠ CBD are a linear pair and sum to 180° , so

56° + ∠ CBD = 180° ( subtract 56° from both sides )

∠ CBD = 124°

the 3 angles in Δ CBD sum to 180° , then

x + 124° + 25° = 180°

x + 149° = 180° ( subtract 149° from both sides )

x = 31°

The equation y = –117.5 x + 31,379.9 gives the population y of a city in x years after 1975 , in real world ,

Rate of Change means The city’s population decreases by about 118 people each year , and Y-intercept means  In 1975, the city’s population was about 31,380 people.

In the question ,

the equation that gives the population y of a city in x years is

y = –117.5 x + 31,379.9

let us find the population for 1976

So , x = 1 ,

we get , y = –117.5(1) + 31,379.9

y = –117.5 + 31,379.9

y = 31262.4

So, the population in the year 1976 is 31262.4

change in population = population in 1976 - population in 1975

= 31262.4 - 31,379.9

= -117.5

≈ -118

to find the population in the year 1977

x = 2 ,

we get , y = –117.5(2) + 31,379.9

= –235 + 31,379.9

= 31144.9

change in population = population in 1977 - population in 1976

= 31144.9 - 31262.4

= -117.5

≈ -118

From above , we can see that the population is decreasing in the year 1976 and 1977 , by  118 people,

hence , we can say that , the city’s population decreases by about 118 people each year

For population in 1975 , we put x=0 ,

So , y = –117.5(0) + 31,379.9

= 31379.9

≈ 31380

Therefore , the equation y = –117.5 x + 31,379.9 gives the population y of a city in x years after 1975 , in real world ,

Rate of Change means The city’s population decreases by about 118 people each year , and Y-intercept means  In 1975, the city’s population was about 31,380 people .

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Answer:

1575

Step-by-step explanation:

Comment

You are just asked to figure out the commission. The rule is to place 100 underneath what is given as the %. In effect, % = x / 100 in decimal form. In this case x = 2.5

So the % is 2.5/100 = 0.025 as a decimal

So commission is 63000 * 0.025 = $1575 commission

The value of [x] in the figure given is 54.

Alternate interior angles are the angles formed when a transversal intersects two coplanar lines. They lie on the inner side of the parallel lines but on the opposite sides of the transversal.

Given are two parallel lines.

The two lines are parallel and are intersected by a transversal. Assume

that  -

∠1 = (x +3)°

∠2 = (2x - 61)°

Now, the angle at the vertically opposite position with respect to ∠2 will have same measurements. Let's call this ∠3 = (2x - 61)°.

Now, ∠3 and ∠1 are alternate interior angles and their measures will be equal. So, we can write -

∠1 = ∠3

x + 3 = 2x - 61

3 + 61 = 2x - x

x = 64

The value of [x] is 54

Therefore, the value of [x] in the figure given is 54.

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In figure one the value of   ∠2 = 65 °  ∠1 = 115° .

In figure two the value of   ∠2 = 74°  ∠1 = 106°.

In the case of parallel lines, corresponding angles are congruent. Corresponding pairs are all angles that are situated in the same location with respect to the parallel and transversal lines. According to the definition of corresponding angles, when three parallel lines intersect two of them, the angles that are present at each intersection and are in the same relative position are said to be corresponding angles. Alternate angles, co-Interior angles, and matching angles are three facts regarding angles in parallel lines that we use to do this. When a transversal crosses two parallel lines, alternate and matching angle pairs coincide. Only when a transversal crosses two parallel lines perpendicularly are consecutive angles congruent. When a transversal intersects two parallel lines, however, subsequent angles are not necessary.

Figure 1

Given angle = 65°

=  ∠2

Cause they are corresponding angles.

∠1  + ∠2 = 180°

∠1   = 115

Figure 2

Given angle = 74 °

= ∠ 2

Cause they are corresponding angles.

∠1  + ∠2 = 180°

∠1   = 106°

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Answer:

Equations:
Cost equation C(x) = 100 + 5x
Sales equation S(x) = 15x

Graph provided

Solution at breakeven point i.e. where sales = costs is at x = 10 lbs

Step-by-step explanation:

Total cost = $100 capital cost of equipment + production cost of $5 per pound of soap

Cost equation C(x) = 100 + 5x  where x is the number of pounds of soaps produced

Sales Equation S(x) = 15x where x is the number of pounds of soap sold

The break-even quantity (in lbs) of soap to be sold to pay for equipment is when both equations are equal to each other

100 + 5x = 15x
==> 15x = 100 + 5x
==> 15x - 5x = 100   (subtract 5x on both sides)

==> 10x = 100

==> x = 10 lbs of soap

At this quantity, Sales and Costs are evened out

Answer:

Step-by-step explanation:

We need to find the volume of the cone with:

First, find the height, using Pythagorean, where hypotenuse of the triangle is 8 cm and base is the radius = 5 cm/2 = 2.5 cm:

Find the volume of the cone: