Graph the line with slope -3 passing through the point (4, - 1)

The shortest altitude is 60m when the base of the triangle is 169m.

Altitude, height, or depth are terms used to describe the distance between a point or object and a reference datum. This phrase is also occasionally used to describe depth.

Different reference points and definitions are employed depending on the context (e.g., aviation, geometry, geographical survey, sport, or atmospheric pressure). Altitude can also be used to describe a location's height above sea level, though elevation is more frequently preferred in geography.

Let,  a = 65cm , b = 156cm , and c = 169cm

The Area of a triangle = A = √s(s−a)(s−b)(s−c) s ( s − a ) ( s − b ) ( s − c )

s = (65cm + 156cm + 169cm)/2

s = 195cm

A = √195(195−65)(195−156)(195−169)

A = 5070 m²

Now we find the height of each case

[tex]$ \text h = 2\frac{\text A}{\text {base}}[/tex]

Substitute each base a, b and c

[tex]$ \text h = 2\frac{5070}{ 65}[/tex]

h = 156

height of triangle when base is 65m = 156m

[tex]$ \text h = 2\frac{5070}{ 156}[/tex]

h = 65

height of triangle when base is 156m = 65m

[tex]$ \text h = 2\frac{5070}{ 169}[/tex]

h = 60

height of triangle when base is 169m= 60m

Thus, the shortest altitude is 60m when the base of the triangle is 169m.

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Answer: 29/18 or 1  11/18  

Step-by-step explanation:  When adding fractions, you need the fractions to have a common denominator. In order to get the common denominator, find the lowest common number between 9 and 6. That number is 18.

7/9 times 18 = 14/18         5/6 times 18 = 15/18     14/18 + 15/18 = 29/18

Improper fraction: 29/18        Mixed number:  1   11/18

Answer:

C

Step-by-step explanation:

There are 3 pairs of corresponding sides with proportional lengths.

Answer:

$37.50

Step-by-step explanation:

[tex]P+Prt=39.75 \\ \\ P+P(2)(0.03)=39.75 \\ \\ 1.06P=39.75 \\ \\ P=\$37.50[/tex]

Answer:

A'(2,1) => A(1,-2)

B'(-4,-2) => B(-2,4)

C'(-4,-6) => C(-6,4)

D'(-1,-3) => D(-3,1)

Step-by-step explanation:

:)

Answer:

Step-by-step explanation:

what 1\3 of a full rotation?

so

360° x 1/3 =

360° : 3 =

120°

It took 19 minutes for each to read 115 pages.

What is Algebraic expression ?

Algebraic expression can be defined as the combination of variables , constants and exponents.

Let x be the number of minutes

And y be the number of pages.

y = 96 + x  --equation1 (for danielle )

y=39+4x --equation2 (for lorenzo)

By substituting equation 1 in equation 2.

we get,

96+x = 39 + 4x

96-39+x = 39-39+4x

57+x = 4x

4x-x = 57

3x = 57

x = 57/3

x = 19 .

Substitute x = 19 in equation 1 we get y = 96 + 19 and y=115

in equation 2 we get , y = 39 + 4*19

y = 39+76

y = 115

Hence , it took 19 minutes for each to read 115 pages.

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The amount that Victoria will have in one year if she invests $20 at 7.2% simple interest is $21.44.

The simple interest system does not compound the interest.

This statement implies that interest is not computed on the accumulated interest.  Periodically, the interest is computed on the principal, using the following simple interest formula:

Simple interest = Principal x Rate x Time

Simple interest rate = 7.2% per year

Investment = $20

Investment period = 1 year

Amount in account after 1 year = P + (P x R x T)

= $20 + ($20 x 7.2% x 1)

= $20 + $1.44

= $21.44

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The number of times we will pick an orange or blue marbles = 1/768

The term probability refers to the possibility of happening an event. It is the ratio of favorable outcome to the total possible outcome.

Available marbles = 8

purple marbles = 5

orange marble = 2

blue marble = 1

probability of picking an orange marble = 2/48 = 1/16

as the marble is put back each time after picking up so

the probability of picking a blue marble = 1/48

Now we multiply the probabilities of each individual events = 1/16 × 1/48

                                  the proportion = 1/768            

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The steps for using a compass and straightedge to construct a square are as follows :-

1. Use a straightedge to draw line a and label a point on the line as point P.

2. Construct a line perpendicular to line a through point P.

3. Label a point on this line as point R.

4. With the compass open to the desired side length of the square, place the compass point on point P and draw an arc on line a and an arc on PR←→.

5. Label the points of intersection as points S and T.

6. Keeping the same compass width, place the compass on point T and draw an arc in the interior of∠SPT to intersect the previously drawn arc.

7. Label the point of intersection as point Q.

8. Without changing the compass width, place the compass point on point S and draw an arc in the interior of∠SPT .

9. Use the straightedge to draw QS ,QT,SR and RT.

In geometry, a square is a plane figure with four equal sides and four right angles (90°). A square is a special kind of parallelogram as well as an equilateral rectangle.

A square is a regular quadrilateral in Euclidean geometry, which means that it has four equal sides and four equal angles. It can also be explained as a rectangle with two adjacent sides that are of equal length.

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Real numbers and imaginary numbers are distinguished because real numbers have real square roots whereas imaginary numbers do not.

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Answer:

1The degree and the leading coefficient of a polynomial function determine the end behavior of the graph. The leading coefficient is significant compared to the other coefficients in the function for the very large or very small numbers.

2An asymptote is a line that a graph approaches but never touches. That line can be vertical, horizontal, or even slanted, and graphs can have multiple types of asymptotes.

3constant of variation (k) is a ratio that represents the relationship between the independent variable (x) and the dependent variable (y). It can be found by dividing y by x, if both of those variables have known values.

An absolute value inequality for 35 degrees C with the temperature able to vary as much as 1% is 34.65 ≤ x ≤ 35.35

The term inequality is defined as a relationship between two expressions or values that are not equal to each other

Here we have given that in your chemistry experiment, you are trying to keep the water temperature at 35°C.

And in the experiment to work properly, here the actual temperature can vary as much as 1%.

Here let us consider that x refers the actual temperature

Then it can be written as,

=> 1% of 35

When we simplify this one then we get,

=> 0.01(35) = 0.35

Here let us consider that the value is less that the simplified version, then it can be written as,

=> l x - 35 l ≤ 0.35    

Therefore, it can be rewritten as,

=> -0.35 ≤ x - 35 ≤ 0.35

When we simplify this by add the value 35, then we get the resulting inequality as,

=> 34.65 ≤ x ≤ 35.35

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Answer: Yes and no?

Step-by-step explanation: Yes, because since it is one single number, it would be considered a "linear" polynomial. But no, because since there is only one term, it wouldn't be considered a polynomial.

I only just learned about linear polynomials, so I think the safe answer would just be no, since there is only one term.

The distance between the graph of the equations x =- 4 and x =- 1 is 3 units.

The equations x =- 4 and x =- 1 can be solved to be -4 and -1 respectively. The difference between these two numbers is 3, so the distance between the graphs of the equations is 3 units.

The distance between the graph of two equations can be found by subtracting the solutions of the two equations. For example, when subtracting the solution of x =- 4 and x =- 1, the difference between -4 and -1 is 3. Therefore, the distance between the graphs of the equations x =- 4 and x =- 1 is 3 units.

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Answer:5.3%

Step-by-step explanation:

we say 150/1 multiplied by 0.74/1=$111

then when we convert it back to pounds, we say 111/1 multiplied by 1.28/1 =142.08

150.00-142.08=7.92

7.92/150.00 multiplied by 100=5.28 to 1 decimal place is 5.3%

hope you understand

Yes, there is possibility to construct a triangle whose sides are 2 cm, 3 cm and 5 cm.

According to the SSS or side-side-side rule of triangle, the sum of any two sides of triangle should be greater than third side of triangle. Assuming the side a to be 2 cm, side b to be 3 cm and side c to be 5 cm.

Side a + side b > side c

2 + 3 > 5

Performing addition on Left Hand Side of the equation

5 = 5

Side b + side c > side a

3 + 5 > 2

Performing addition on Left Hand Side of the equation

8 > 2

side c + side a > side b

5 + 2 > 3

Performing addition on Left Hand Side of the equation

7 > 3

Thus, we see the sum to be greater in two situations. Hence, the triangle is possible.

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Answer: 7.29

Step-by-step explanation: you divide the total cost which is 21.87 by 3 to get how much one pair of socks would be and that would be the unit price hope this helps

Answer:

english

Step-by-step explanation:

because by guessing he could only get 1 right on english quiz

Joel should study for science, because the probability of getting all questions correct is 0.004 which is less than 0.016.

It is a branch of mathematics that deals with the occurrence of a random event.

Given that Joe has to take two quizzes tomorrow.

He has only enough time to study for one of them, such that the science quiz has 7 true-or-false questions and

The English quiz has 4 multiple-choice questions.

We have to find the probability that he will get each question correct by guessing.

P(sciene)=0.5⁸

=0.0039

=0.004

P(English)= 0.25³

=0.0156

=0.016

As we know that 0.0156>0.0039

Hence, Joel should study for science, because the probability of getting all questions correct is 0.004 which is less than 0.016.

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Exterior angle of a regular n-sided polygon = 360°/n

Interior angle = 180° - 360°/n

So, with 360/n = (1/8)(180 - 360/n)

360/n = 180/8 - 360/(8n)

(360/n)*(9/8) = 180/8

2*9/n = 1

n = 18

The function y = 0.4(1.06)^t represents exponential growth function and rate of change is 6%.

A function called exponential growth depicts population growth that happens consistently over time. You can assume that data increases exponentially when populations double or triple in size.

Exponential decay, which occurs when data contracts rather than expands, is the opposite of exponential growth.

A function of the form [tex]y=a(1 - r)^t[/tex], where a > 0and 0 < r < 1, is an exponential decay function.

A function of the form [tex]y=a(1 +r)^t[/tex], where a > 0 and r > 0, is an exponential growth function.

As 1.06 > 1,

y = 0.4(1.06)^t is an exponential growth function and the

growth factor = 1 + r

                       = 1 + 0.06

Percent rate of change = 0.06

                                        = 6/100 × 100%

                                         = 6%

Thus, the function y = 0.4(1.06)^t represents exponential growth function and rate of change is 6%.

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Answer: 3/4 is the simplest form

Step-by-step explanation:

your welcome <3

Answer: A = P(1 + r/n)^(nt)

Where

A is the future value of the account

P is the initial principal amount, which is $9,100

r is the annual interest rate, which is 3%

n is the number of times the interest is compounded per year, which is 4 (quarters)

t is the number of years

So the function for the value of the account after t years is:

A = 9100(1 + 0.03/4)^(4t)

To determine the percentage of growth per year (APY), we can use the formula:

APY = ( (A/P)^(1/t) - 1) * n

In this case,

APY = ( (A/9100)^(1/t) - 1) * 4

APY represents the annual percentage yield, which is the interest rate taking compounding into account.

Please note that in the above expression the coefficient 0.03 is rounded to four decimal places as instructed.

Step-by-step explanation:

The range:{-8, 4, 10} and the function as set of ordered pair is {(-2, -8),(2, 4),(4, 10)}

A pair of numbers in a certain order is called an ordered pair. Ordered pairs include, for instance, (1, 2) and (-4, 12). The two numbers' relative placement is crucial: (2) is not equal to (1, 1) (2, 1) — (1, 2)≠(2, 1). (2, 1).

When displaying two variables, ordered pairs are frequently used. By writing (x, y) = (7, - 2), we indicate that x = 7 and y = -2. The terms "x-coordinate" and "y-coordinate" refer to the number that relates to the value of x and the value of y, respectively.

The, function is given as y = 3x - 2

Lets put this in graph

Domain: {-2, 2, 4}

put the x values in function

y = 3(-2) - 2

y = −8

y = 3(2) - 2

y = 4

y = 3(4) - 2

y = 10

Range: {-8, 4, 10}

The function as set of ordered pair is {(-2, -8),(2, 4),(4, 10)}

Thus, the range:{-8, 4, 10} and the function as set of ordered pair is {(-2, -8),(2, 4),(4, 10)}

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On solving the provided question, we can say that in this equation, we can solve by , 13/6=y/3 = > y = 39/6 = 6.5

A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.

in this equation,

we can solve by

13/6=y/3

y = 39/6 = 6.5

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Answer:

100

Step-by-step explanation:

If we add 100 to 8000, get 8100 which is a perfect square: 90^2=8100

The measurement of V can be calculated by adding the two equations: 10x-27 + 2x+29 = V. This simplifies to 12x+2 = V, so V = 12x+2.

Y=(10x-27)

W=(2x+29)

V=Y+W

V= 10x-27 + 2x+29

V= 12x+2.

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So, the correct simplification for the expression (3x^3 y^4 z^4) (2x^3 y^4 z^2) is option d: 6x^6 y^8 z^6.

What is simplification?

To simplify simply means to make anything easier. In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler. Calculations and problem-solving techniques simplify the issue.

The given equation is -

(3x^3 y^4 z^4) (2x^3 y^4 z^2)

On simplification -

=[3·2(x^3+3)(y^4+4)(z^4+2)]

=6x^6y^8z^6

Therefore, the value obtained is 6x^6y^8z^6.

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Answer: 1. Given

2. Combine like terms

3. Division

Answer:

2.83 cm

Step-by-step explanation:

The other leg is also 2cm

Pythagorean Theorem

  hypot ^2 = 2^2 + 2^2

  Hypot = sqrt 8 =~ 2.83 cm

Answer:

Step-by-step explanation:

an isosceles triangle where the two legs form a 90-degree angle is an isosceles right triangle. So, the hypotenuse of the triangle is 2√2