the width of a rectangle is twice as long as the length. if the length is increased by 50% and the width is decreased by 20%, the perimeter becomes 248. find the width and length of the original rectangle.

Answers:

Center = (1, 5)

Radius = 3

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Work Shown:

[tex]x^2+y^2-2x-10y+17 = 0\\\\(x^2-2x)+(y^2-10y)+17 = 0\\\\(x^2-2x+0)+(y^2-10y+0)+17 = 0\\\\(x^2-2x+1-1)+(y^2-10y+25-25)+17 = 0\\\\(x^2-2x+1)+(y^2-10y+25)+(-1-25+17) = 0\\\\(x-1)^2+(y-5)^2-9 = 0\\\\(x-1)^2+(y-5)^2 = 9\\\\(x-1)^2+(y-5)^2 = 3^2[/tex]

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Explanation:

The idea is to complete the square for the x and y terms separately.

Notice the jump from step 3 to step 4 has the first 0 turn into 1-1, and the second 0 turn into 25-25. This is to help complete the square for each part.

The x^2-2x+1 factors to (x-1)^2 and y^2-10y+25 factors to (y-5)^2

Once we reach the last step, we have something in the form [tex](x-h)^2+(y-k)^2 = r^2[/tex]

Center = (h,k) = (1,5)

Radius = r = 3

Answer:  90

Step-by-step explanation:

[tex]\displaystyle\ \Large \boldsymbol{} (\sqrt{0,04}-\sqrt{(-1,2)^2}+\sqrt{121 } ) \cdot \sqrt{81} = \\\\\\(0,2-1,2+11)\cdot 9=(11-1)\cdot 9=90[/tex]

area: 40p² + 24p

wide: 8p

(40p² + 24p)/ 8p

5p + 3

so, length: 5p + 3 -> (a)

perimeter = wide x 2 + length x 2

16p + (10p + 6)

26p + 6 -> (b)

Answer:

y² = (1/16)x³

Step-by-step explanation:

Given that :

y² varies directly as the cube of x

y² α x³

y² = kx³ - - - (1)

Where, k = constant of f proportionality

We can obtain the value of k ; when x= 4 and y = 2

2² = k4³

4 = 64k

k = 4/64

k = 1/16

Putting k = 1/16 in (1)

y² = (1/16)x³

Answer:

C

Step-by-step explanation:

As n → ∞

[tex]\frac{85}{n}[/tex] , [tex]\frac{75}{2n}[/tex] , [tex]\frac{15}{2n^2}[/tex] → 0

Then

15 - 35 - 0 + 55 + 0 + 0

= - 20 + 55

= 35 → C

Answer:

Step-by-step explanation:

Just using pythagorean theorem,

13.2²+16.9²=c²

174.24+285.61=c²

c²=√459.85

c= 21.4441134114

c = 21.4 (nearest tenth)

Answer:

9c^7d^13

Step-by-step explanation:

Look at the attachment

The line bisects the cord which we have to find

Its a right angle triangle

[tex]\boxed{\sf P^2=H^2-B^2}[/tex]

[tex]\\ \Large\sf\longmapsto P=\sqrt{H^2-B^2}[/tex]

[tex]\\ \Large\sf\longmapsto P=\sqrt{10^2-6^2}[/tex]

[tex]\\ \Large\sf\longmapsto P=\sqrt{100-36}[/tex]

[tex]\\ \Large\sf\longmapsto P=\sqrt{64}[/tex]

[tex]\\ \Large\sf\longmapsto P=8cm[/tex]

Distance of the chord from centre is 8cm.

Answer:

[tex]\frac{7}{15}[/tex]

Step-by-step explanation:

To find the reciprocal of a fraction, simply switch the numerator and denominator.

Since [tex]2\frac{1}{7}[/tex] is a mixed number, start by converting it to a common fraction using [tex]a\frac{b}{c}\implies \frac{a \cdot c+ b}{c}[/tex]

Therefore, [tex]2\frac{1}{7}[/tex] as a common fraction is:

[tex]\frac{2\cdot 7+1}{7}=\frac{14+1}{7}=\frac{15}{7}[/tex]

Now switch the numerator and denominator to find the reciprocal:

[tex]\rightarrow \boxed{\frac{7}{15}}[/tex]

Answer:

7/15

Step-by-step explanation:

2 1/7 is 2*7+1/7 = 15/7. The reciprocal of this would happen if you flip it upside down. Thus, the reciprocal is 7/15.

1.

C. 5x + 4 - 2x is an algebraic expression

Answer:

how much protein did he take per day tho?

Answer: A

Step-by-step explanation: A function is when every domain (x value) corresponds to one range (y value) so that it passes the vertical line test

Answer:

4^(-2)

Step-by-step explanation:

4^4(4^-7)(4)

We know that a^b * a^c = a^(b+c)

4^4(4^-7)(4^1)

4^(4+-7+1)

4^(-2)

Answer:

Step-by-step explanation:

If [tex]y=x^2-2x+5-6x[/tex] then

[tex]y=x^2-8x+5[/tex] by combining like terms. (I'm thinking you might have mistyped the problem because this representation is weird).

[tex]\frac{dy}{dx}=2x-8[/tex]

Answer:

10/3 days  or 3 1/3 days

Step-by-step explanation:

Let d = number of days total

75% of the days is 10

.75 d = 10

d = 10/.75

d = 40/3 days

We want to know how man is 25% of d

d * 25%

(40/3) *.25

10/3 days

Answer:

9

Step-by-step explanation:

let the price of one can food be x,

4x=17.20

x=4.3

number of can foods that can be purchased = 38.70/x = 38.7/4.3 = 9

4CANS=$17.20

$38.70

cross multiply

4 multiply by 38.70 =154.8 divide by 17.20

ANSWER = 9

The triangle is missing and so i have attached it.

Answer:

x = 93°

Step-by-step explanation:

From the triangle attached, we can say that;

<SQP + <SQR = 180°

This is because sum of angles on a straight line equals 180°.

Secondly, we know that sum of angles in a triangle also equals 180°.

Thus;

<SQR + <QSR + <SRQ = 180

From the attached triangle, we see that;

<QSR = 35°

<SRQ = 58°

Thus;

<SQR + 35° + 58° = 180°

<SQR + 93° = 180°

<SQR = 180° - 93°

<SQR = 87°

From earlier on, we saw that;

<SQP + <SQR = 180°

Plugging in <SQR = 87°, we have;

<SQP + 87° = 180°

<SQP = 180° - 87°

<SQP = 93°

We are told in the question that <SQP is denoted by x.

Thus;

x = 93°

Answer:

The value of x is answer D: 93

Answer:

I think it is 2, downwards

Answer:

vertical shift of 2 units up

Step-by-step explanation:

Given f(x) then f(x) + c is a vertical translation of f(x)

• If c > 0 then a shift up of c units

• If c < 0 then a shift down of c units

f(x) = 9 | x + 1 | + 2

Represents a vertical shift of 2 units up of the parent function

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Explanation:

It's a bit strange why your teacher has the "26 degree" label pointing at a side length, rather than an actual angle. I'm assuming your teacher meant to aim it at angle C. In other words, I'm assuming they meant to say angle C = 26 degrees.

If that assumption is correct, then,

A+B+C = 180

38+B+26 = 180

B+64 = 180

B = 180-64

B = 116

Then we can use the law of sines like so:

a/sin(A) = b/sin(B)

a/sin(38) = 10/sin(116)

a = sin(38)*10/sin(116)

a = 6.84986152123146

a = 6.8

Side 'a' is approximately 6.8 inches long. So that's why the answer is choice A.

Answer:

x = 23

General Formulas and Concepts:

Pre-Algebra

Equality Properties

Algebra I

Step-by-step explanation:

Step 1: Define

3(2x) = 138

Step 2: Solve for x

Answer:

6

Step-by-step explanation:

Altitude = 3400t +600

21,000 = 3400t +600

21000-600= 3400t

20400/3400 = 3400t/3400

t= 6

Answered by Gauthmath

Answer:

7:16 P.M.

Step-by-step explanation:

24/90=4/15. There are 60 minutes in an hour, so we have 240/15=16.

Answer:

Use pythagoras theorem

Answer:

See below.

Step-by-step explanation:

Call the sum of the first n terms S.

S = a + ar + ar^2 + ar^3 + ... + ar^(n -1)

Multiply both sides by r.

Sr = ar + ar^2 + ar^3 + ar^4 + ... + ar^n

No subtract S - Sr.

      S =  a + ar + ar^2 + ar^3 + ar^4 + ... + ar^(n -1)

(-)    Sr =       ar + ar^2 + ar^3 + ar^4 + ... + ar^(n - 1) + ar^n

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  S - Sr = a - ar^n

S(1 - r) = a(1 - r^n)

S = a(1 - r^n)/(1 - r)

S = a(r^n - 1)/(r - 1)

a + ar + ar^2 + ar^3 + ... + ar^(n -1) = a(r^n - 1)/(r - 1)

Answer:

(b) It is symmetrical about [tex]x = 1[/tex]

Step-by-step explanation:

Given

[tex]y = 2(x - 1)^2 - 5[/tex]

See attachment for options

Required

True statement about the graph

First, we check the line of symmetric

[tex]y = 2(x - 1)^2 - 5[/tex]

Expand

[tex]y = 2(x^2 - 2x + 1) - 5[/tex]

Open bracket

[tex]y = 2x^2 - 4x + 2 - 5[/tex]

[tex]y = 2x^2 - 4x -3[/tex]

A quadratic equation [tex]y = ax^2 + bx + c[/tex] has the following line of symmetry

[tex]x = -\frac{b}{2a}[/tex]

By comparison, the equation becomes:

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

[tex]x = \frac{4}{4}[/tex]

[tex]x = 1[/tex]

Hence, the line of symmetry is at: [tex]x = 1[/tex]

(b) is true.

Answer: It is symmetrical about x=1

Step-by-step explanation: