a right triangular prism has a triangular base with legs of 5 centimeters and 12 centimeters and a hypotenuse of 13 centimeters. what is the surface area in square centimeters if the height is 2 centimeters?

Answer:

y=-3/2+3

Step-by-step explanation:

so you have to solve for y

Answer:

32cm

Step-by-step explanation:

Let x represent the width

if the width = x

therefore the length = x+8

The perimeter = 72cm

[tex]x + x + 8 = 72[/tex]

[tex]x + x + 8 - 8 = 72 - 8[/tex]

[tex]x + x = 64[/tex]

[tex]x + x = 2x[/tex]

[tex]2x = 64[/tex]

[tex] \frac{2x}{2} = \frac{64}{2} [/tex]

[tex]x = 32[/tex]

Answer:

18cm

Step-by-step explanation:

wide = 8cm + length

perimeter = 2(L + B)

Answer:

18 Kg

Step-by-step explanation:

We can use algebra to solve for the mass, m, given the delivery price, $70.

Starting with the formula:

price ($) = 7 + 3.5m

We can substitute $70 for price ($) and solve for m:

$70 = 7 + 3.5m

Subtracting 7 from both sides:

$63 = 3.5m

Dividing both sides by 3.5:

m = 18

Therefore, the mass of the parcel is 18 kg.

Answer:

4

Step-by-step explanation:

3*9=9(x-1)

x-1=3

x=4

Answer:

Step-by-step explanation:

6 km = 6000 m

5 min = 300 s

6000m / 300s  = 20 m/s

Answer:

20 m/s

Step-by-step explanation:

The average speed of the fish can be calculated by dividing the distance traveled by the time taken.

First, we need to convert the distance from km to meters:

6 km = 6,000 meters

Next, we need to convert the time from minutes to seconds:

5 minutes = 5 × 60 = 300 seconds

Finally, we divide the distance traveled by the time taken:

Average speed = 6000 meters / 300 seconds = 20 m/s

So, the average speed of the fish is 20 m/s.

The distance between the star from the Sun in astronomical units

is 28.6 AU.

We know a right-angled triangle has three sides they are -: Hypotenuse,

Opposite and Adjacent.

We can remember SOH CAH TOA which is,

sin = opposite/hypotenuse, cos = adjecent/hypotenuse and

tan = opposite/adjacent.

From the reference angle of 2 degrees, d can be thought of as the adjacent side and the distance from the Sun and the Earth can be thought of as the opposite side.

Now, We know tan = opposite/adjacent.

tan2° = 1/d.

d = 1/0.035.

d = 28.6 AU.

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The expanded form of the expression [tex]\frac{a^2 - (b + c)^2}{c^2 - (a - b)^2}[/tex] is [tex]\frac{a^2 - b^2 - 2bc - c^2}{c^2 - a^2 + 2ab - b^2}[/tex].

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, An expression [tex]\frac{a^2 - (b + c)^2}{c^2 - (a - b)^2}[/tex].

We know, (a ± b)² = a² ± 2ab + b².

Therefore, [tex]\frac{a^2 - (b + c)^2}{c^2 - (a - b)^2}[/tex]

[tex]= \frac {a^2 - (b^2 + 2bc + c^2)}{c^2 - (a^2 - 2ab + b^2)}[/tex]

[tex]= \frac{a^2 - b^2 - 2bc - c^2}{c^2 - a^2 + 2ab - b^2}[/tex]

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Answer:

All the answers are bolded in the step-by-step explanation.

Hope it helps :)

Step-by-step explanation:

The radius of the top of a cylinder is always the same length as the radius of the base of a cylinder.

Radius of the base of can A: 10 cm

Radius of the base of can B: 18 cm

To find the area of the bases, use the area formula that you put as your first answer.

Area of the base of can A:

[tex]A=\pi (10^{2} )[/tex]

[tex]A=100\pi[/tex]

[tex]A=314[/tex] cm (Assuming we're only using 3.14 and not any other decimals)

Area of the base of can B:

[tex]A=\pi (18^{2} )[/tex]

[tex]A=324\pi[/tex]

[tex]A=1017.36[/tex] cm (Again, assuming we're only using 3.14 and not any other decimals)

The base of can B has a greater Area

To find the height, look at the diagram

Height of can A: 28cm

Height of can B: 9cm

Can A has a greater height

To find the volume, use the equation that you put as your answer for question 2 or just multiply the area of the base times the height.

Volume of can A:

[tex]314*28=V[/tex]

[tex]V=8792[/tex]

Volume of can B:

[tex]1017.36*9=V[/tex]

[tex]V=9156.24[/tex]

Can B holds more paint

Answer:

d = 3

Step-by-step explanation:

4d+9=21

4d = 12

d = 3

Let's check

4(3) + 9 = 21

12 + 9 = 21

21 = 21

So, d = 3 is the correct answer.

Answer: 3 = d

Step-by-step explanation:

4d + 9 = 21

     - 9   - 9

4d = 12

—     —

4       4

d = 3

From the graph, the range in the viewing window is [-3,3]

What are domain and range of a function ?

The range of values that we are permitted to enter into our function is known as the domain of a function. In a function like f, this set represents the x values (x). The collection of values that a function can take on is known as its range. The values that the function outputs when we enter an x value are in this set.

f(x)= -100|x| + 75

Take few values for x and find corresponding f(x) values

The graph will be symmetrical in nature

It is absolute value function

Example:

when x=0.75

f(x) = -100(0.75)+75

     = -75+75

     = 0

Range is the y values

From the graph, the range in the viewing window  is [-3,3]

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Using the formula of Interest I = PRT and given values the value of P is $5250.

Interest is the sum over and above the original amount (the amount borrowed) that is paid to a lender or depositor by a borrower or deposit-taking financial institution at a set rate. Interest differs from profit, in that interest is received by a lender, whereas profit is received by the owner of an asset, investment or enterprise.

Given that, the formula is I = PRT

I = $7140, R = 0.17, T = 8

To find the value of P, from the formula

7140 = P * 0.17 * 8

⇒ 7140 = P * 1.36

divide both sides with 1.36 we get

⇒ 7140/1.36 = P

⇒ P = $5,250

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The lowest value of the equation is at x = -2 when (x + 2) = 0.

A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. It is also known as the polynomial of degree 2 since the greatest degree term in a quadratic function is of the second degree.

Given the function,

x² + 4x + 2

to find the lowest value,

factorize the function,

x² + 4x + 2

add and subtract 4 from the function,

x² + 4x + 2 + 4 - 4

x² + 4x + 4 - 2

(x + 2)² - 2

here (x + 2)² is always positive,

and lower value will be x = -2 when (x  + 2)  = 0

Hence lowest value will be at x = -2.

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The correct question is,

Lowest value of  x² + 4x + 2.

The interquartile range is least affected by an outlying value in the data set of the range, interquartile range, and variance is True.

Max to min value is the range. Range can substantially change if there are any outliers.

Since the threshold values for Q3 and Q1 are not outliers, the IQR won't change.

Outliers cause variance to be misinterpreted since they vastly increase variance.

Interquartile range:

You may determine the spread of the midpoint of your distribution using the interquartile range.

The interquartile range contains half of the values for any distribution that is ordered from low to high. The first 25% of values are found in the first quartile (Q1), while the last 25% are found in the fourth quartile (Q4).

The third quartile (Q3) less the first quartile (Q1) is the interquartile range (Q1). This provides us with the data set's middle half's range.

The interquartile range is calculated using only 2 values, much like the range. The IQR, however, is less impacted by outliers because the two values are more likely to be average scores because they are drawn from the middle of the data set.

The IQR provides a reliable indicator of variability for both skewed and normal distributions.

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The wave amplitude was A =  15849 Ao times stronger the wave amplitude of the earthquake was than Ao.

The formula to solve this is given as

K = log (A / Ao)

Where we have k to be the constant that is measured on the richter scale as 4.2

Then when we put this in the formula, we would have:

4.2 = log (A / Ao)

take the log of both sides of the equation

[tex]10^4^.^2 = \frac{A}{Ao}[/tex]

15848.9 approximately 15849

15849 = A / Ao

cross multiply to get the value of A

A =  15849 Ao

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The evaluation of expression is 5/4.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Given;

The expression; ( 6^2 - 4^2 ) x ( 1/4 )^2

=( 6^2 - 4^2 ) x ( 1/4 )^2

=(36-16)*(1/16)

=20*1/16

=5/4

Therefore, the algebraic expression answer will be 5/4.

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The equation of the horizontal asymptote will be y = -2.

An asymptote is a line that constantly reaches a given curve but does not touch at any infinite distance.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

From the graph, the horizontal asymptote is parallel to the x-axis and the equation of the horizontal asymptote is given as,

y = - 2

The equation of the horizontal asymptote will be y = -2.

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The probability that we get the same faces when we roll 3 fair six-faced dice is 44.44%.

Simply put, the probability is the likelihood that something will occur.

We can discuss the likelihood of several outcomes or the potential of one outcome when we are unsure of how something will turn out.

Statistics is the study of events that fall into a probability distribution.

Therefore, there is a chance that each one is unique:

6/6 * 5/6 * 4/6 = 120/216

Therefore, the likelihood that at least two of them will display the same face is:

1 - 120/216 = 96 / 216 =44.44%

Therefore, the probability that we get the same faces when we roll 3 fair six-faced dice is 44.44%.

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The juice is 27 and the tornadoes are 21.

An equation is a mathematical statement that shows that two expressions are equal by using an equal sign (=). Equations are used to find the value of an unknown variable or to show the relationship between variables.

We know that the number of the juice and the tornadoes can be x and y

We then have that;

5x + 3y = 24 ----- (1)

4x + 2y = 30 ----- (2)

Multiply equation 1 by 4 and equation 2 by 5 we have that;

20x + 12y = 96 ---- (3)

20x + 10y = 150 ----- (4)

Subtract (3) from (4)

-2y =54

y = -27

Then;

5x + 3(-27) = 24

x = 21

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Answer:

  See attached

Step-by-step explanation:

You want the numbers for quotient, dividend, and remainder in the area model of 49÷3.

The number in each rectangle is its area, which is the product of the divisor on the left and the quotient at the top. These can be considered the length and width of the rectangle. The rectangle area is their product.

The remainder is put in the box at upper right. It is a value that is smaller than the divisor on the left.

The line at the bottom summarizes the division. The quotient is the sum of the quotient values at the top of the model, and the remainder is what's left over: the number that is too small to divide further.

The simplified expression of 1+sin^2-cos^x / 2sin^2x  issin^2(x) / 2(1 + cos(x)) + 1 / 2(1 - cos(x))

To simplify this expression, we can first simplify the numerator by combining the terms inside the parentheses:

1 + sin^2(x) - cos(x) = sin^2(x) + 1 - cos(x)

Next, we can factor the denominator trigonometric identity sin^2(x) + cos^2(x) = 1:

2 sin^2(x) = 2(1 - cos^2(x)) = 2 - 2cos^2(x)

Now we can substitute these simplified expressions into the original expression:

(1 + sin^2(x) - cos(x)) / (2 sin^2(x))

= (sin^2(x) + 1 - cos(x)) / (2 - 2cos^2(x))

= [(1 - cos(x)) + sin^2(x)] / [2(1 - cos(x))(1 + cos(x))]

1+sin^2-cos^x / 2sin^2x = [sin^2(x) / 2(1 + cos(x))] + [1 / 2(1 - cos(x))]

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Answer:

  (d)  6.3

Step-by-step explanation:

You want the measure of side CD in ∆CDE ~ ∆CFG with CG=6, GE=2.4, and FD=1.8.

The corresponding sides of the two triangles are proportional:

  CD/CE = FD/GE

  CD = CE×FD/GE = (6+2.4)×1.8/2.4

  CD = 6.3

__

Additional comment

Lengths on segment CD are 3/4 of those on segment CE, so CF = 4.5. CD is the sum of CF and FD: 4.5 +1.8 = 6.3.

[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \pounds 400\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ t=years\dotfill &2 \end{cases} \\\\\\ I = (400)(0.05)(2) \implies I = 40[/tex]

The system of linear equations that has an unique solution has this feature:

Different slopes.

Then we must replace into the equations the variables x = 2 and y = -1, and verify if the equations are satisfied.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

The number of solutions for a system of two linear functions is defined as follows:

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Answer:

Step-by-step explanation:

Use SOH CAH TOA.

Using TOA or tangent = tan0 = opp/adj.

tan0 = 1500m/800m  ->  tan0 = 1.875

Use inverse tan or tan^-1.

0 = tan^-1(1.875)

0 = 61.93 degrees.

Answer:

A. 12 TT

B. 6 TT

C. 9 TT

D. 18 TT

The correct answer is D. 18 TT. The formula for circumference is C = 2TT x radius, so with TT equal to 3.14, the circumference of the circle is 18.28 TT which is approximately equal to 18 TT.

the ordered pair will be (3,-1) lies in the inverse function.

What is inverse function?

A function that returns the initial value for which a function has produced output is called an inverse function. If f(x) is a function that produces the value y, then f-1(y), which is the inverse function of y, will produce the value x. Inverse and reciprocal functions should not be confused. The output's original value is returned by the function's inverse, which is represented by the symbol f-1 (x). While the reciprocal of a function is represented by 1/f(x) or f(x)-1

Those that do are referred to as invertible. For a function f: X Y to have an inverse, it must possess the characteristic that there is exactly one x in X such that f(x) = y for every y in Y. This characteristic guarantees the existence of a function g: Y X that has the required connection to f.

function g(x)=∛(x−4)

So the inverse of the function

g ¬(x) = x³+4

So the ordered pair will be (3,-1)

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The Length of wheel chair ramp should be 54.94 feet.  as we calculated this by given height of ramp is 5 feet and angle of elevation is 5.22 degree.

Here it is given that the height of ramp from ground is 5 feet and angle of elevation is 5.22 degree .Now we can see that this is a height and distance question. For that we have to use trigonometric ratio. And all trigonometric ratio are the angle of right angle triangle so here we have to find tangent of angle

so tanФ = perpendicular /base

and in this question the perpendicular is 5 feet and and the base we have to find and angle 5.22 degree.

let the length of ramp is  = y and then put the value on formula we have

tan 5.22 = 5/y

y = 5/(tan5.22) = 5/0.091 =54.94

The length of wheel chair ramp is  54.94 feet .

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