The upper-left coordinates on a rectangle are (-8,8), and the upper-right coordinates are (-3,8). The
rectangle has an area of 15 square units
Draw the rectangle on the coordinate plane below.
y
dan
Hub
2
6
W
AN
1
S
Do 5 problems
Lesson 16: Common factors​

Answer:

Centre: [tex](\frac{1}{2} ,2)[/tex]

Radius = [tex]2[/tex]

Step-by-step explanation:

General formula for a circle: [tex](x-a)^2+(y-b)^2=r^2[/tex], where [tex]r=[/tex] the radius of the circle and [tex](a,b)[/tex] is the centre of the circle.

To find the centre and radius of the circle we should re-write the given equation in the form of the general formula.

So, put the terms with the same variables together:

[tex]4x^2-4x+4y^2+16y+1=0[/tex]

We can see that there is a common factor of [tex]4[/tex], so let's simplify by dividing by [tex]4[/tex]:

[tex]x^2-x+y^2+4y+\frac{1}{4} =0[/tex]

Here we can get it into the general formula by completing the square.

We do this by turning a quadratic with form [tex]ax^2+bx+c=0[/tex] into the form [tex](x-d)^2-e+c=0[/tex], where d is half of the coefficient of [tex]x[/tex], e is [tex]d^2[/tex] and c is the constant of the quadratic.

So let's re-write the equation of the circle:

[tex](x-\frac{1}{2} )^2-\frac{1}{4} +(y-2)^2-4+\frac{1}{4} =0[/tex]

Simplify: [tex](x-\frac{1}{2} )^2 +(y-2)^2-4} =0[/tex]

Now we can see that it's very similar to the general equation and all we have to do is bring the [tex]4[/tex] over to the right side.

[tex](x-\frac{1}{2} )^2 +(y-2)^2} =4[/tex]

So, now we can find the radius and centre.

[tex](a,b) = (\frac{1}{2} ,2)[/tex]

[tex]r^2=4, r=2[/tex]

Answer:

i think its b

Step-by-step explanation:

that was on my test and i do not remember what anwer i put

Answer:

Step-by-step explanation:

circle A is

x²+y²+6x-4y-12=0

x²+6x +y²-4y =12

think (a+b)² = a²+2ab+b² we have a=x, b= 3

and (a-b)² = a²-2ab+b² so we have a=y, b=2

x²+6x +9 +y²-4y+4 = 12-9-4

(x+3)² +(y-2)²= -1

compare to the general equation of a circle (x-h)²+(y-k)² =r²

the center is at (-3,2) and the radius is √-1 =i

Circle B has center (0, -4) and radius 3 so the equation is

(x-0)²+(y-(-4))² =3²

x² +(y+4)² = 9

point (√8, -3) is on the circle if it verifies the equation

√8² +(-3+4)² = 9

8+1 =9 true so the point is on the circle

Circle A and circle B are not similar because they do not have the same center and radius

Answer:

Hello! answer: 7

Step-by-step explanation:

80 + 80 = 160 360 - 160 = 200 200 ÷ 2 = 100 and 14 × 7 = 98 and 98 + 2 = 100 therefore x = 7 HOPE THAT HELPS!

Answer:

[tex]A) ~7[/tex]

Step-by-step explanation:

[tex]80+14x+2=180[/tex]

[tex]14x+82=180[/tex]

[tex]14x=98[/tex]

[tex]x=7[/tex]

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

hope it helps..

have a great day!!

Answer:

B, 600

I've attached a graph to help ya!

Hope this helps!

Answer:

3, 5, 6

Step-by-step explanation:

Angles that will be congruent to the given angle, 94° would be any angle that is corresponding to 94°, any angle that is vertical to 94°, any angle that is the alternate interior angle to 94°.

Thus.

Angle 3 = 94° (vertical angles)

Angle 5 = 94° (corresponding angles)

Angle 6 = 94° (alternate interior angles)

Answer:

The answer is B It is located on the Quadrant ll

Step-by-step explanation:

have a good day :)

Answer:

Step-by-step explanation:

[tex] {x}^{2} + 7x + 3 = 0[/tex]

Answer:

2.1

-2.2

-2.3

…

-2.9

-2.01

Answer:

[tex]241\frac{5}{16}[/tex]

Step-by-step explanation:

Answer:

[tex]x = 14[/tex]

Step-by-step explanation:

[tex](5x - 3) + 63 + (3x + 8) = 180 \\ 8x + 68 = 180 \\ 8x = 112 \\ x = 112 \div 8 \\ x = 14 \\ so \\ (5 \times (14) - 3) = 67 \\ (3 \times (14) + 8) = 50[/tex]

Answer:

The slope is undefined.

Step-by-step explanation:

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

m=(-3-2)/(6-6)

m=-5/0

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Answer:

29 Mbps

Step-by-step explanation:

the scan rate of Dave's antivirus =

203 Mb / 7 s = 29 Mb/s or 29Mbps

Answer:

x^2-12x+37

Step-by-step explanation:

Let's start by putting this into vertex form which will be (x-6)^2+1

Now lets solve our equation to get parabola standard form

x^2-12x+37

Answer:

Step-by-step explanation:

[tex]\sf\purple{The\:radius\:of\:the\:cylinder\:is\:approximately \:28 \:ft.}[/tex]

[tex]\sf\blue{Height\:of\:the\:cylinder\:(h) }[/tex] = 10 ft.

[tex]\sf\pink{Volume\:of\:the\:cylinder}[/tex] = 25,456 ft³.

[tex]\sf\purple{The\:radius\:of\:the\:cylinder.}[/tex]

We know that,

[tex]\sf\red{Volume\:of\:a\:cylinder}[/tex] =[tex]\pi {r}^{2} h \\ ✒ \: 25456 \: {ft}^{3} = \pi {r}^{2} \times 10 \: ft \\ \: ✒ \: {r}^{2} = \frac{25456 \times 7 \: {ft}^{3} }{22 \times 10 \: ft} \\ ✒ \: {r}^{2} \: = \frac{178192 \: {ft}^{2} }{220} \\ \: ✒ \: {r}^{2} = 809.9636 \: {ft}^{2} \\ \: ✒\: r \: = \sqrt{809.9636 \: {ft}^{2} } \\ ✒ \: r \: = 28.45 \: ft[/tex]

Hence, the radius of the cylinder is 28.45 feet.

[tex]\circ \: \: { \underline{ \boxed{ \sf{ \color{green}{Happy\:learning.}}}}}∘[/tex]

Answer: first one: false second one: true

Step-by-step explanation:

Answer:

$48 deposited

Step-by-step explanation:

84 times 1/3 = 28

80 times 1/4 = 20

28 + 20 = 48

Answer:

B.  (3, ∞)

Step-by-step explanation:

Look at the graph of function f(x) = e^x.

The range is from 0, 0 not included, to infinity, or, in interval notation, (0, ∞).

The function g(x) = f(x) + 3 is the same as g(x) = e^x + 3.

g(x) is the the function f(x) shifted 3 units up.

That makes the range of g(x) from 3, 3 not included, to infinity.

Range: (3, ∞)

Answer:

see photo

Step-by-step explanation:

Plato/Edmentum

Answer:

87 minutes

Step-by-step explanation:

Assuming 1 1/2 is 112, take 25 away from 112

Answer:

Option (4)

Step-by-step explanation:

Proportional relationship means,

y ∝ x

y = kx

[tex]k=\frac{y}{x}[/tex]

Here, k = proportionality constant

Therefore, if the graph of a line passes through the origin (0, 0) table will represent the proportional relationship.

From table 1,

For a point (1, 2)

[tex]k=\frac{2}{1}=2[/tex]

For another point (3, 2)

[tex]k=\frac{3}{2}=1.5[/tex]

In both the cases 'k' is not same of constant.

Therefore, table (1) is not proportional.

For table (2),

Line passes through (2, 0).

That means there is a x-intercept → (2, 0)

Therefore, table doesn't represent a proportional relationship.

For table (3),

Line passes through a point (0, 1)

It means given line has a y-intercept → y = 1

Therefore, table doesn't represent a proportional relationship.

For table (4),

Line of this table passes through two points (1, 3) and (2, 6)

[tex]k=\frac{3}{1}=3[/tex]

[tex]k=\frac{6}{2}=3[/tex]

Therefore, proportionality constant for the given table is 3.

Now we can graph table (4).

Answer:

2[tex]\sqrt{5}[/tex]

Step-by-step explanation:

8/4 = 2

[tex]\sqrt{20} / \sqrt{4}[/tex] = [tex]\sqrt{5}[/tex]

Therefore: 2[tex]\sqrt{5}[/tex]

Hope this helps!

Answer:

[tex]2\sqrt{5}[/tex]

Step-by-step explanation:

[tex]\frac{8\sqrt{20}}{4\sqrt{4}} = \frac{2 \cdot 4 \cdot \sqrt{4} \cdot \sqrt{5}}{4 \cdot \sqrt {4}} = 2\sqrt{5}[/tex]

Answer:

7+√5/4

Step-by-step explanation:

if that is = a, find the value of a + 1 over a

​Given that a = 3 - √5

a+1/1 = (3-√5)+1/3 - √5

4-√5/3 - √5

Rationalize

4-√5/3 - √5 * 3+√5/3 + √5

= 12 +4√5-3√5-√25/9-5

= 12+√5-5/4

= 7+√5/4

Hence the requred answer is  7+√5/4

Answer:

Solution given:

100( x + 5 ) = 200 ( 6 - x)

distributing

100x+500=1200-200x

100x+200x=1200-500

300x=700

x=[tex] \frac{700}{300} [/tex]

x=[tex] \frac{7}{3} [/tex]

:.x=[tex] \frac{7}{3} [/tex] or[tex] 2\frac{1}{3} [/tex]