The perimeter of the rectangle below is 76
units. Find the length of side BC.
.
Write your answer without variables.

Answer:

(x - 3)² + (y - 2)² = 8

Step-by-step explanation:

the equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

The radius is the distance from the centre to a point on the circle

To find r use the distance formula

r = √(x₂ - x₁)² + (y₂ - y₁)²

with (x₁, y₁ ) = (3, 2) and (x₂, y₂ ) = (5, 4)

r = [tex]\sqrt{(5-3)^2+(4-2)^2}[/tex] = [tex]\sqrt{4+4}[/tex] = [tex]\sqrt{8}[/tex]

(x - 3)² + (y - 2)² = ([tex]\sqrt{8}[/tex])²

(x - 3)² + (y - 2)² = 8 ← equation of circle

Answer:

Ricky = 1201

Pedro = 1476

Step-by-step explanation:

Assign variables

let p be the number of Pedro's base hits

let r be the number of Ricky's base hits

Create a system of equations

p + r = 2677            <= Pedro and Ricky got 2677 base hits

p = r + 275              <= Pedro had 275 more hits than Ricky

Solve using the substitution method (replace a variable with an expression)

p + r = 2677

Substitute "p" with "r + 275"

r + 275 + r = 2677

Combine like terms to simplify

2r + 275 = 2677

Isolate "r" by moving everything else to the right side.

2r = 2677 - 275                  Subtract 275 from both sides

2r = 2402

2r/2 = 2402/2                     Divide both sides by 2

r = 1201                              Ricky's base hits

To find Pedro's hits, substitute "r" into any equation.

p = r + 275

p = 1201 + 275                    Substitute r = 1201, then add

p = 1476                             Pedro's base hits

∴ Ricky had 1201 base hits and Pedro had 1476 base hits.

Final answer:

By setting up an equation where R represents Ricky's hits, and calculating R + 275 for Pedro's hits, we can solve for R and then find the number of hits for each player. Ricky had 1201 hits, while Pedro had 1476 hits.

Explanation:

To solve the problem of determining how many base hits Pedro and Ricky each had last season, we can use algebra. Let's let the variable R represent the number of hits Ricky had. Since Pedro had 275 more hits than Ricky, we can express Pedro's number of hits as R + 275. According to the question, the sum of their hits is 2677, so the equation will be R + (R + 275) = 2677.

Now, let's solve the equation:

R + R + 275 = 2677

2R + 275 = 2677

2R = 2677 - 275

2R = 2402

R = 2402 / 2

R = 1201

So, Ricky had 1201 hits. To find Pedro's hits, we substitute R into the expression R + 275:

Pedro's hits = R + 275 = 1201 + 275 = 1476

Therefore, Ricky had 1201 hits and Pedro had 1476 hits.

The formula of a distance between two points:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

We have the points (1, 3) and (3, 1). Substitute:

[tex]d=\sqrt{(3-1)^2+(1-3)^2}=\sqrt{2^2+(-2)^2}=\sqrt{4+4}=\sqrt8\approx2.8[/tex]

Answer:

Step-by-step explanation:

You just add and subtract

Answer:2x−3y=6

Step-by-step explanation:Standard form: Ax + By = C

Just take 2/3x to the other side.

So the answer would be

−23x+y=−2

In standard form

x

can't be negative and A, B and C need to be an integers (whole numbers)

(I multiplied the whole equation by -3)

2x−3y=6

So the final answer would be: 2x−3y=6

Answer:

The domain is {3,4,5,6}

Step-by-step explanation:

Because all your x - values is ur domain and ur y - values is ur range

The concept of solving a problem by elimination is to solve for one variable, by getting rid of the other.

Let's solve [2y = x + 2, x - 3y = -5] in terms of y.

Start by transforming the second equation into one of the same form as the first (y = x + c).

x-3y = -5

x = -5 + 3y

3y = x+5

Now we have two equations that are in the same form:

3y = x+5

2y = x+2

To solve in terms of y, we need to get rid of x -- so subtract the first equation from the second equation - this will yield the following:

y = 3 [[ 3y - 2y = y, x - x = 0, 5 - 2 = 3 ]]

Now take this information and solve for x:

2(3) = x+2

6 = x+2

x = 4

Now we have the solution, just make it a coordinate point:

(4, 3)

Answer:

Apex Answer (4,3)

Step-by-step explanation:

Just did the apex quiz yall add me julius_rob

Answer:

AAS(Angle-Angle-Side) postulate states that if two angles and the non-included side one triangle are congruent to two angles and the non-included side of another triangle, then the two triangles are congruent

In triangle RAS and triangle QAT

[tex]\angle R =\angle Q[/tex]   [Angle]

[tex]AS =AT[/tex]    [Side]                                       [Given]

By Base Angle Theorem states that in an isosceles triangle(i.e, AST), the angles opposite the congruent sides(AS =AT) are congruent.

⇒ [tex]\angle 5= \angle 6[/tex]      [By base ∠'s of isosceles triangle are equal]

By definition of supplementary angles, if two Angles are Supplementary when they add up to 180 degrees.

[tex]\angle 4[/tex], [tex]\angle 5[/tex] are supplementary and [tex]\angle 6[/tex], [tex]\angle 7[/tex] are supplementary.

⇒[tex]\angle 4+ \angle 5 =180^{\circ}[/tex] and

[tex]\angle 6+ \angle 7 =180^{\circ}[/tex]  

Two [tex]\angle 's[/tex] supplementary to equal [tex]\angle 's[/tex]

[tex]\angle 4+ \angle 5 =\angle 6+ \angle 7[/tex]

Since,  [tex]\angle 5 =\angle 6[/tex]  

then, we get;

[tex]\angle 4 =\angle 7[/tex]  [Angle]

then, by AAS postulates,

[tex]\triangle RAS \cong \triangle QAT[/tex]

By CPCT[Corresponding Part of Congruent Triangles are equal]

[tex]RS = QT[/tex]              Hence Proved!

The number you are looking for is 89.

The number you are looking for is 89.

Here is how we can find it:

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[tex]\sqrt{a}=b\iff b^2=a\ for\ a\geq0\ and\ b\geq0\\\\\dfrac{4}{-3\sqrt{64}}=\dfrac{\not4^1}{-3(\not8_2)}=-\dfrac{1}{6}[/tex]

Answer:

The system of linear equations are

y = 15 + 2x  

y = 3x

Step-by-step explanation:

Let us assume that the number of new release movies be x.

Let us assume that the total cost  be y.

As given

Members of a movie rental club pays a minimum of $15 annual membership fee and $2 for new release movies.

Than the equation becomes

y = 15 + 2x

As given

Nonmembers pay $3 for new release movies.

y = 3x

Therefore the system of linear equations are

y = 15 + 2x  

y = 3x

Answer:

SA = 201 in^2

Step-by-step explanation:

The formula for surface area of a sphere is

SA = 4pi r^2

We know that the diameter is 8

To find the radius we cut the diameter in half.

r = d/2

r = 8/2 =4

Substitute in what we know.

SA = 4 *pi *4^2

    = 4*pi*16

   = 64*pi

Letting pi = 3.14

  = 200.96 in^2

We want to round to the nearest whole number

SA = 201 in^2

Answer:

4 heads

Step-by-step explanation:

Assuming the coins are properly weighted such that each side is equally likely, this means that getting heads is the same probability as getting tails. We're told that getting 2 heads and 4 tails is a 23.4% chance. If we somehow fool our brains into thinking heads and tails swap, then it would be 4 heads and 2 tails. The swap is simply changing the labels for each coin. It really doesn't matter. This symmetry is useful to help simplify larger problems.

If the coins were altered so that the chances of getting heads on any single coin toss was something like 60%, then swapping the labels wouldn't work because the two sides would be different.

Answer:

4617 yd

Step-by-step explanation:

30.5 ft make 1 roll of tape

Length of tape = 454 × 30.5/1

Length of tape = 13 847 ft

1 ft = 3 yd

Length of tape = 13 847 × 1/3

Length of tape = 4617 yd

The coefficient of q in the sum of (23q - 34) and (-16q - r) is 7.

In mathematics, a coefficient is a numerical factor or constant that multiplies a variable or term in an algebraic expression. It determines the scale or magnitude of the term and is often used in equations, polynomials, and linear expressions.

The sum of the two expressions is (23q - 34) + (-16q - r).

To find the coefficient of q in this sum, we need to combine the like terms.

Combining the q terms, we have 23q - 16q = 7q.

Therefore, the coefficient of q in the sum of the two expressions is 7.

Answer:

y = 3(x + 3)² - 31

Step-by-step explanation:

the equation of a parabola in vertex form is

y = a(x - h)² + k

where (h. k) are the coordinates of the vertex and a is a multiplier

To obtain this form use the method of completing the square

take out a common factor of 3 from the first 2 terms

y = 3(x² + 6x) - 4

add/subtract ( half the coefficient of the x-term)² to x² + 6x

y = 3(x² + 2(3)x + 9 - 9 ) - 4

y = 3(x + 3)² - 27 - 4

y = 3(x + 3)² - 31 ← in vertex form

Answer:

9R30  

Step-by-step explanation:

         9

36)354

    324

      30

Answer:

angle A and angle D equals 100 degrees, angle B and angle E equals 30 degrees, and angle C and angle F equal 50 degrees.

Step-by-step explanation:

a triangle has to equal 180 degrees, and since they are similar, it should equal the same. Hope this helped you. :))

The angles of triangles △ABC and △DEF, which are similar, are 100°, 30°, and 50°. This is calculated using the properties of similar geometry and the fact that the sum of all angles in a triangle equals 180°.

In Triangle Similarity, the corresponding angles are equal due to the property of similarity in geometry.

Since we know that △ABC and △DEF are similar and we have m∠A=100° and m∠B=30°, we can determine that angles A and B in triangle △DEF are also 100° and 30°, respectively.

The third angle in both triangles can be calculated using the property that the sum of all angles in a triangle equals 180°.

Hence, in △DEF and △ABC we can calculate the measure of the third angle by 180° - (100°+30°) = 50°.

So for triangles △ABC and △DEF, the angles are 100°, 30° and 50° respectively.

Learn more about Triangle Similarity here:

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Answer:

First one is wrong. x should be 16.

Second one is not completely visible, so cannot say.

Step-by-step explanation:

In the last step, the divison by 4 yields:

x/16 = 1, so x = 16

Answer:

A) (1/9)^8

Step-by-step explanation:

9^-5 × 9^-3 =

Rule: a^m * a^n = a^(m + n)

= 9^-8

Rule: (a^m)^n = a^(mn)

= (9^-1)^8

Rule: a^-m = 1/a^m

= (1/9)^8

Answer: A) (1/9)^8

Answer:

Total charge per month = $ 16 + (0.08) * x

equation for having same charge

0.08 x - 0.12 y = 8

Step-by-step explanation:

Part 1:

Monthly fee = $ 16

Per check fee = $ 0.08

Checks signed in month = x

Total Charge monthly = Monthly fee + Checks fee

Putting the values

Total charge per month = 16 + (0.08) * x             ...........(i)

Part 2: Let she signs y checks for account B

Monthly fee of B = $ 14

per check fee = @ 0.12

Total Charge = monthly fee + checks fee

                     =  $ 14 + y *(0.12)                         ..................(ii)

For having same value in the bank then equation (i) and  (ii) shuld be equal to each other

i.e.

16 + 0.08x = 24 + 0.12y

0.08 x - 0.12 y = 24-16

0.08 x - 0.12 y = 8

this will be the equation

Answer:

$60

Step-by-step explanation:

Each payment was 10% of $600.

You need to find what 10% of $600 is.

To find a percent of a number, multiply the percent by the number. Change the percent to a decimal by moving the decimal point of the percent two places to the left.

10% of $600 =

= 10% * $600

= 0.10 * $600

= $60

Answer:

60

Step-by-step explanation:

600 * .10= 60

Answer:

System has only one solution. x= 4 and y = 2.

Step-by-step explanation:

We have given two equations :

2x + y = 10    ----------(1)

x - 3y = -2   ----------(2)

From equation (2), we can write:

x - 3y = -2

or x = -2 + 3y  , substitute this in equation (1).

We get,  2x + y = 10

2*(-2 + 3y) + y = 10

-4 + 6y + y = 10

7y = 10 + 4

y = 14/7 = 2

And x = -2 + 3*2 = -2 + 6 = 4

Hence we get x= 4 and y = 2. System has only one solution

The system of equations 2x+y=10 and x-3y=-2 has one solution, which is found by solving for y in terms of x using the first equation, substituting into the second equation, and solving for x, then solving for y. The solution is (4, 2).

To solve the system by substitution, we can express one variable in terms of the other using one of the equations and then substitute this into the second equation. Starting with the system:

2x + y = 10

x - 3y = -2

We can solve the first equation for y:

y = 10 - 2x

Next, we substitute this expression for y into the second equation:

x - 3(10 - 2x) = -2

Solving this equation for x:

x - 30 + 6x = -2

7x = 28

x = 4

Now we substitute x = 4 back into the equation y = 10 - 2x to find y:

y = 10 - 2(4)

y = 2

So the one solution to the system is (4, 2).

Since we found a unique solution, the system of equations has exactly one solution and is therefore consistent and independent.

Answer:

-3

Step-by-step explanation:

6-4 (x+3)

2(x+3)

2x+6=0

2x=-6

2x/2= -6/2

x=-3

Answer:

7 buses are needed.

Step-by-step explanation:

There are 325 students and adults.

Each bus holds 48 people.

The number of buses needed = [tex]\frac{325}{48}[/tex] = 6.770833333

Since we cant have 0.770833333 buses, we accept that only 7 buses are needed here and that;

325 - (48 × 6) = 37 people will not fill the last bus.

Answer:

$.43 per pen

Step-by-step explanation:

To find the unit rate, we take the price of the pens and divide by the number of pens

$1.29/3

$.43 per pen

Answer: $0.43

Step-by-step explanation:

Unit rate is how much each pen costs.

If the total amount is $1.29 for all three pens, then the price for one pen should be calculated by 1.29/3, therefore, the answer is $0.43

Answer:

slope = 2.5 and the y intercept is 3

Step-by-step explanation:

To find the slope we can use the formula

m = (y2-y1)/(x2-x1)

I will use the point (2,8) (6,18)  We can pick any 2 point we want.

 = (18-8)/(6-2)

  = (10/4)

  = 2.5

To find the y intercept we need to find the equation of the line.

We will use the point slope form

y-y1= m(x-x1)

y-8 = 2.5(x-2)

Distribute the 2.5

y-8 = 2.5x-5

Add 8 to each side

y-8+8 = 2.5x-5+8

y = 2.5x+3

This equation is in slope intercept form  y = mx+b

where the slope is 2.5 and the y intercept is 3

Hi There!

-----------------------------------

Find The Slope:

[tex]m = \frac{13 - 8}{4 - 2} = \frac{5}{2} or 2.5[/tex]

-----------------------------------

Find The Y-Intercept:

Substitute using x = 2 and y = 8

Use y = mx + b

Substitute: 8 = 2.5(2) + b

Simplify: 8 = 5 + b

Subtract 5 too both sides: 8 - 5 = 5 + b - 5

Simplify: 3 = b

Y-Intercept = 3

-----------------------------------

Point Slope Form: y - 8 = 2.5(x - 2)

Slope Intercept Form: y = 2.5x + 3

-----------------------------------

Hope This Helps :)

Answer:   The answer is C

Step-by-step explanation:  15 - 2 = 13     13+5=18

Hope this helps :)

Answer:

[tex]\frac{2}{81}[/tex]

Step-by-step explanation:

Step 1

List the experimental probabilities of each color using the first letter of that color. The spinner is spun 18 times The probabilities are listed below. P(blue)=3/18, P(red=4/18), P(white) =3/18, P(yellow)=2/18, P(black)=5/18, P(purple)=1/18

Step 2

The second step is to calculate the required probability given the information in step 1. The probability that George will spin a red and then a yellow is obtained by multiplying the probability that he spins a red and the probability that he spins a yellow. This calculation is shown below,

[tex]P=P(red)\times P(yellow)=\frac{4}{18} \times \frac{2}{18} =\frac{8}{324} =\frac{2}{81}.[/tex]

The correct answer is  [tex]\frac{2}{81}[/tex]

Answer: 2.50

Step-by-step explanation: your answer is 2.50