21. What is the perimeter of the triangle?
18.2 units
18.3 units
9 units
15.5 units
(1,6)
(3, 1)
(6, 1)

Answer:

36

Step-by-step explanation:

when solving for two variables, we need to find one variable in terms of the other.

so, we can turn:

x - y = 5

into

x - y = 5

  + y    + y

x = y + 5

Then, we can substitute "x" in the given equation with "y + 5"

  x² - y² = 30

 (y+5)² - y² = 30

(y + 5)(y + 5)

F: y²    O:  +5y    I:   +5y  L:  25   {foil}

y² + 10y + 25 - y² = 30          {cancel y² - y²}

10y + 25 = 30

      -25      -25

10y  = 5

÷10    ÷10

y = 0.5

x = y + 5

x = 0.5 + 5

x = 5.5

check:

(5.5)² - (0.5)²

30.25  - 0.25 = 30

30 = 30

(TRUE)

now, we must find the value of:

(5.5 + 0.5)²

= (6)²

= 36

So, the value of (x + y)² is found to be 36

hope this helps!!

Answer:

(x + y)² = 36

Step-by-step explanation:

x² - y² ← is a difference of squares and factors as

(x - y)(x + y) , then

5(x + y) = x² - y² = 30 ( divide both sides by 5 )

(x + y) = 6 , then

(x + y)² = 6² = 36

Answer:

Prob Online

Step-by-step explanation:

Can't really think of one

Using the t-distribution, the 95% confidence interval of the population mean rating for Miami is (4.97, 6.51).

The confidence interval is:

[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]

In which:

The parameters for this problem are given as follows:

[tex]\overline{x} = 5.74, s = 2.7, n = 50[/tex]

The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 50 - 1 = 49 df, is t = 2.0096.

Hence the bounds of the interval are given as follows:

[tex]\overline{x} - t\frac{s}{\sqrt{n}} = 5.74 - 2.0096\frac{2.7}{\sqrt{50}} = 4.97[/tex]

[tex]\overline{x} + t\frac{s}{\sqrt{n}} = 5.74 + 2.0096\frac{2.7}{\sqrt{50}} = 6.51[/tex]

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The change is decay and the percentage rate of decrease will be 95%.

An exponential function is a function where a number is raised to the variable i.e. base is raised to the exponent times.

Here given the exponential function is y= 4300(0.042)ˣ

Now we have to identify if the change in exponential function represents growth or decay, and have to determine the percentage rate of increase or decrease.

Here in the exponential function, the base is less than 1 so the change is decay.

The equation represents exponential decay because the decay factor is lesser than 1.

The general form of the exponential equation is:

y(x)= a(1-r)ˣ such that r is the decay.

equating with the equation

y= 4300(0.042)ˣ

a= 4300

and 1-r=0.042

⇒r= 1-0.042

⇒r= 0.958

the perecentage of decay will be r*100= 0.958*100= 95%

Therefore the change is decay and the percentage rate of decrease will be 95%.

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Step-by-step explanation:

please mark me as brainlest

Answer: A. 10.8 km

Step-by-step explanation:

add up all the days:

1.3 + 1.75 + 2.25 + 2.5 + 3 = 10.8 km

Answer:

59°

Step-by-step explanation:

Difference=54-(-5)

=54+5=59

Answer:

RSP, ZXY

SRP, XZY

RPS, ZYX

Step-by-step explanation:

Obviously, the numbers match each other.

ex. R = 41, Z = 41

Those two have the ability to pair in the same order

The value of expression is 7.

An expression is a combination of numbers, variables, functions (such as addition, subtraction, multiplication or division etc.)

Given:

[tex]log 10^{7}[/tex]

Now, using property of log

[tex]log b^{a} =[/tex] a log b

So,

[tex]log 10^{7}[/tex]= 7 log 10

As log 10 = 1

[tex]log 10^{7}[/tex]= 7 (1)

[tex]log 10^{7}[/tex]= 7

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The probability she chooses a number greater than 5 will be 1/2 or 0.5.

Its simple notion is that something will most likely occur. The favorable event's proportion to the overall number of occurrences.

Probability = (Favorable event) / (Total event)

Eleanor randomly decides a number from 1 to 10.

Then the probability she chooses a number greater than 5 will be

Total event = 10

Favorable event = 5 {6, 7, 8, 9, 10}

Then we have

P = 5/10

P = 1/2

P = 0.5

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Answer:

no solutions

Step-by-step explanation:

we use the quadratic formula.

for an equation ax²+bx+c=0, the solutions for x are:

x = (-b±sqrt(b²-4ac))/2a

in our case, a=2, b=-6 and c=5, so:

x= (6±sqrt(36-40))/4

we see that we get a negative number inside the sqrt, so we have no real solutions

Answer:

No solution

Step-by-step explanation:

1) Use the quadratic formula

[tex]x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]

Once in standard form, identify a, b, and c from the original equation and plug them into the quadratic formula.

[tex]2x^2-6x+5=0[/tex]

[tex]a=2\\b=-6\\c=5[/tex]

[tex]x=\frac{-(-6)\pm\sqrt{(-6)^2-4*2*5} }{2*2}[/tex]

2) Simplify

Evaluate the exponent:

[tex]x=\frac{6\pm\sqrt{(-6)^2-4*2*5} }{2*2}[/tex]

[tex]x=\frac{6\pm\sqrt{36-4*2*5} }{2*2}[/tex]

Multiply the numbers:

[tex]x=\frac{6\pm\sqrt{36-4*2*5} }{2*2}[/tex]

[tex]x=\frac{6\pm\sqrt{36-40} }{2*2}[/tex]

Subtract the numbers:

[tex]x=\frac{6\pm\sqrt{36-40} }{2*2}[/tex]

[tex]x=\frac{6\pm\sqrt{-4} }{2*2}[/tex]

Multiply the numbers

[tex]x=\frac{6\pm\sqrt{-4} }{2*2}[/tex]

[tex]x=\frac{6\pm\sqrt{-4} }{4}[/tex]

3) No real solutions because the discriminant is negative

The square root of a negative number is not a real number

[tex]d=-4[/tex]

Result

No solution

The indicated function values are f(0) = 2 and x = -1

The attached figure represents the missing piece in the question

From the attached figure, the function values to calculate are:

f(x) when x = 0 and x when f(x) = 0

From the figure, the graph crosses the y-axis at y = 2 and the x-axis at x = -1

This means that:

f(0) = 2 and f(-1) = 0

Hence, the indicated function values are f(0) = 2 and x = -1

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Answer:

(a) 2.5

Step-by-step explanation:

(a) Since y is directly proportional to x we can write y and x in terms of the following equation:

y = cx where c is a constant
and c = y/x ...(1)
or,

x = y/c ...(2)

For (a)
y = 8 when x = 2 ==> c = y/x = 8/2 =4 from (1)

From (2) we get x = 10/4 = 2.5

The other questions can be solved in a similar fashion

Answer:

(5,-5)

x=5

y=-5

Step-by-step explanation:

How to solve using elimination method.

First, add the two equations.

   2x - 3y = 25

+  5x + 3y = 10

7x=35

The y values got eliminated.

Next, divide 7 from both sides.

7x/7=35/7

x=5

Next, plug-in x=5 into one of the equations.

2(5) - 3y = 25

10-3y=25

Subtract 10 from both sides.

-3y=15

Divide -3 from both sides.

y=-5

Remember a positive divided by a negative is a negative.

Hope this helps!

If not, I am sorry.

Step-by-step explanation:

4.500 mm³ → cm³

1 cm³ = 1.000 mm³

= 4.500 ÷ 1.000

= 4,5 cm³ IS THE ANSWER

It is clear that T lies on the perpendicular bisector of NP. See the explanation below.

Given that M (X,Y) is the midpoint of NP

X thus = (5+1)/2

= 3

Y = (7+1)/2

= 4

Hence, we have M (3,4)

Consequent on the above:

Slope TM (m') = (4-2) / (3-6) = - 2/3

Slope of NP (m) =  (7-1) / (5-1) = 6/4 = 3/2
M' = -1/m

Hence

TM ⊥ NP; and NP ⊥ TM

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Answer:

C) 10320-0.961 = 7,507 Mt

that is my answer please have a great day

The regular price of the camera is $227.

Given that, the total amount paid=$201.75 and the cost of the memory card=$12.35.

Cost of camera=201.75-12.35=$189.4

A discount is a deduction from the usual price of something. To discount means to deduct an amount from the price.

Discount is given to the camera=20%.

The regular price of the camera=189.4+20% of 189.4

=189.4+0.2×189.4=189.4+37.88=$227.28

The estimation to the nearest the whole number is $227.

Therefore, the regular price of the camera is $227.

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answer

yes do it your self

Answer:

m= –4

So, you only need to of the points to find the slope, why not choosing the first two:

[tex]m = \frac{y2 - y1}{x2 - x1} = = = > \\ m = \frac{12 - 8}{ - 3 - ( - 2)} = = = > \\ m = \frac{4}{ - 1} = - 4[/tex]

so basically, this is the slope your looking for

Answer:

C

Step-by-step explanation:

A quadratic has to have an exponent of 2 somewhere. The only one of these functions that does is C

The quadratic parent function is f ( x ) = x²

A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.

The roots of the quadratic equations are

x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )

where ( b² - 4ac ) is the discriminant

when ( b² - 4ac ) is positive, we get two real solutions

when discriminant is zero we get just one real solution (both answers are the same)

when discriminant is negative we get a pair of complex solutions

Given data ,

Let the quadratic equation be represented as A

Now , the value of A is

f ( x ) = x²

The graph of the function f(x) = x² is a parabola that opens upward, symmetric with respect to the y-axis, and its vertex is at the origin (0, 0)

Now , the value of y is the square of x

Hence , the parent function is f ( x ) = x² and graph is plotted

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Answer:

17x

Step-by-step explanation:

3x+4+4x+4+3x-4+3x-4+4x

Collect liketerms

In order to make point D as the vertex in the construction as triangle ABC, the third arc should cross the second arc.

In Geometry, an arc can be defined as a trajectory that is generally formed when the distance from a given point has a fixed numerical value.

In order to make point D as the vertex in the construction as triangle ABC, you must ensure that the third arc crosses the second arc as illustrated in image attached below.

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Answer: The third arc should cross the second arc.

Step-by-step explanation: The guy above me clearly stated it, just wanted to clear up that he is correct :)

Answer:

the answer is B

Step-by-step explanation:

5th root of 32 = 2

5 / 5 = cancels

10 / 5 = 2

15 / 5 = 3

2xy²z³

Answer:

2xy^2z^3

Step-by-step explanation:

Answer:

x≥20

Step-by-step explanation:

-3(6-2x)≥4x+12

or, -18+6x≥4x+12

or, -18-12≥4x-6x

or, -40≥-2x

or, -40/2≥-x

or, -20≥-x

or, 20≥x

= x≥20

The number of pieces that Marco places is given as follows:

30 pieces.

The number of pieces that Marco places is obtained applying the proportions in the context of the problem.

The fractions of each person are given as follows:

Hence the fraction composed by these three people is given as follows:

1/2 + 1/5 = (5 + 2)/10 = 7/10 = 0.7.

Hence Michele's fraction is given as follows:

1 - 0.7 = 0.3.

As Michele arranges 90 pieces, the total number of pieces is given as follows:

0.3x = 90

x = 90/0.3

x = 300.

Marco arranged one tenth, hence the number is:

0.1 x 300 = 30.

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The number of  students like physics more than mathematics is 15 , Option B is the correct answer.

A mathematical way of expressing quantity of a substance is called a Number.

Number of students in a school who like mathematics = 20

Number of students in a school who like physics = 35

number of students in a school who like only physics is 20

number of students who like only Mathematics is 5

the number of  students like physics more than mathematics is 20-5 = 15

Therefore Option B is the correct answer.

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The value of a₄₃ is 3.

Matrices is a plural form of a matrix, which is a rectangular array or a table where numbers or elements are arranged in rows and columns.

Here,  aₓₙ is the element of matrix in which x represents the number of row and n represents the number of column of element.

So, a₄₃ means element from 4th row and 3rd column.

4th row  =  [2  9   3   7]

3rd column = [tex]\left[\begin{array}{ccc}8\\6\\1\\3\end{array}\right][/tex]

the common value between them is 3.

Thus, the value of a₄₃ is 3.

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