find the solution to the equation by completing the square x^2-6x=7. what is the smallest and largest value of x

Answer:

A scale factor of 2  was applied to the first triangle to get the resulting image.

This scale factor is a reduction.

Hope this helps!

Answer:

0.5, reduction

Step-by-step explanation:

The scale is the ratio of the triangle after the transformation to the triangle before the transformation:

1.7 / 3.4 = 0.5

Since this is less than 1, it's a reduction.

Answer:

Option C. [tex]110\°[/tex]

Step-by-step explanation:

step 1

Determine the measure of angle AGC

we know that

The measure of the inner angle is the semi-sum of the arcs comprising it and its opposite.

so

[tex]m<AGC=\frac{1}{2}[81\°+59\°][/tex]

[tex]m<AGC=\frac{1}{2}[140\°][/tex]

[tex]m<AGC=70\°[/tex]

step 2

Determine the measure of angle FGC

we know that

[tex]m<AGC+m<FGC=180\°[/tex] ----> by supplementary angles

so

[tex]70\°+m<FGC=180\°[/tex]

[tex]m<FGC=180\°-70\°=110\°[/tex]

Answer:

First one is a slope between 0 and 1

second one is a slope lower than 0

third one is a slop higher than 1

last one is a slope higher than 1 (technically undefined)

Step-by-step explanation:

Answer:

y=3/2

x=13/6

Step-by-step explanation:

y=3x-5 → -3x +y = -5

3y-x+1 → -x +3y = -1

Multiply the 2nd eq by -3 and add to 1st one and replace it

-3x +y = -5 → -8y =-6

3x -9y = -1     3x -9y = -1  

→ y =3/2=1.5 . Replace this value in any eq -3x + 3/2 = -5  → x =13/6

Answer:

Step-by-step explanation

20=36

1=x

Then cross multiply

20x=36

x=1.8

If it takes her 1.8 minutes to complete 1 item then:

1=1.8

35=x

x=63

It takes her 63 minutes

Answer:

Tracy made $458.64 that day

Answer:

A.

[tex]2xy^2(10x+3)[/tex]

B.

[tex](x+5)^2[/tex]

C.

[tex](x-6)(x+6)[/tex]

Step-by-step explanation:

Part A. The expression [tex]2x^2y^2+6xy^2+18x^2y^2[/tex] consists of three terms: [tex]2x^2y^2,\ \ 6xy^2,\ \ 18x^2y^2[/tex] The first and the last terms are like terms, we can add them:

[tex]2x^2y^2+18x^2y^2=20x^2y^2[/tex]

Now,

[tex]20x^2y^2=2xy^2\cdot 10x\\ \\6xy^2=2xy^2\cdot 3[/tex]

So,

[tex]2x^2y^2+6xy^2+18x^2y^2=2xy^2(10x+3)[/tex]

Part B. The expression [tex]x^2+10x+25[/tex] is a square of [tex]x+5,[/tex] so

[tex]x^2+10x+25=(x+5)^2[/tex]

Part C. Use the difference of squares formula:

[tex]x^2-36=x^2-6^2=(x-6)(x+6)[/tex]

Answer is

Unrelated to AB

Answer:

will be the perpendicular bisector of line segment AB.

Step-by-step explanation:

We know from the construction of a perpendicular bisector of a line segment.  If,we draw two arc of the same radii at the ends of a line segment AB.

These arc intersect with each other at distinct point C and point D (as shown in the figure of the question), then the line passes through the point C and point D must be perpendicular to the given line segment AB and bisect the line segment AB.

Answer:

-3/5

Step-by-step explanation:

Answer:

[tex]-\frac{3}{5}[/tex]

Step-by-step explanation:

Remember that the tangent trigonometric ratio is the opposite side of right triangle divided by the adjacent side:

[tex]tan(\alpha )=\frac{opposite-side}{adjacent-side}[/tex]

[tex]tan(\alpha )=-\frac{4}{3}[/tex]

Comparing the equations we can infer that:

opposite side = 4

adjacent side = 3

Now we can use Pythagoras to find the hypotenuse of our right triangle:

[tex]hypotenuse^2=side^2+side^2[/tex]

[tex]hypotenuse^2=4^2+3^2[/tex]

[tex]hypotenuse^2=25[/tex]

[tex]hypotenuse=\sqrt{25}[/tex]

[tex]hypotenuse=5[/tex]

Remember that the cosine trigonometric ratio is the adjacent side divided by the hypotenuse; in other words:

[tex]cos(\alpha)=\frac{adjacent-side}{hypotenuse}[/tex]

We know that adjacent side = 3 and hypotenuse = 5.

Replacing values:

[tex]cos(\alpha )=\frac{3}{5}[/tex]

Now, remember that cosine means x and sine means y. In Quadrant 2 x is negative, which means that cosine is negative.

So, if [tex]tan(\alpha )=-\frac{4}{3}[/tex] in quadrant 2, then [tex]cos(\alpha )=-\frac{3}{5}[/tex]

Answer:

7)V=16257.74

8)V= 226.19

9)V=12.56

10)V=6283.18

11)r=6.631

12)h=69.05

13)V=35328.78

Step-by-step explanation:

Volume of cylinder is given by formula:

V=πr^2h

where r is radius and h is height of cylinder

7)

r=15

h=23

Putting values in formula:

V= π(15)^2(23)

 =5175π

  =16257.74

8)

diameter=6

r=d/2=3

height =?

Finding height by pythagoras theorem:

h^2= 10^2-6^2

     =100-36

     =64

h=8

Putting values in formula:

V=π(3)^2(8)

  = 72π

   = 226.19

9)

r= 2

h=1

Putting values in formula:

V=π(2)^2(1)

  =4π

  = 12.56

10)

diameter =20

r=d/2=10

h=20

Putting values in formula:

V=π(10)^2(20)

  =2000π

  =6283.18

Now finding the missing measures:

11)

Given V=210π

h = 15

r=?

Putting values in formula:

210π=π(r)^2(15)

r^2= 210π/15

    =14π

r= 6.631

12)

V=197.82

r=3

h=?

Putting values in formula:

197.82=π(3)^2(h)

h= 197.82/9π

 = 69.05

13)

r=21

h=25.5

Putting values in formula:

V= π(21)^2(25.5)

 =11245.5π

  =35328.78 !

The value of the calculated volume and height of the cylinders are

7) 16,259.9 mm³

8) 904.9 yd³

9) 12.6 ft³

10) 25136.0 ft³

11) 6.8 m

12) 7.0 m

13) 35333.4 in³

The volume of a cylinder is given by = πr²h

where

r is the radius

h is the vertical height

7) h = 23 mm, r = 15 mm

V = π(15)²(23)

=5175*π

= 16,259.9 mm³

8) r = 6 yd, slant height = 10 yd

Use Pythagorean theorem to find the height

10² = 6² + h²

h² = 100-36

= 64

h = √64 = 8 yd

V = π(6)²(8)

= 288*π

= 904.9 yd³

9) r = 2 ft, h = 1 ft

V = π(2)²(1)

= 4π

= 12.6 ft³

10) r = 20 ft, h = 20 ft

V = π(20)²(20)

= 8000*π

= 25136.0 ft³

11) V = 210 ft³, h = 15 ft

1 foot = 0.3048 m

15 ft = 0.3048*15

= 4.572 m

210π = πr²(4.572)

r² = 210/4.572

= 45.9317

r = √{45.9317}

= 6.8 m

12) V = 197.82 m³, r = 3 m

197.82 = π(3)²x

197.82 = 3.142*9*x

197.82 = 28.278x

x =197.82/28.278

= 7.0 m

13) r = 21 inches, h = 25.5 inches

V = π(21)²(25.5)

= 11245.5*π

= 35333.4 in³

learn more about cylinder here

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Answer:

D, neither

Step-by-step explanation:

to determine whether a function is even, odd or neither, we need to know what it means

an even function is symmetric with respect to the y-axis

an odd function is symmetric with respect to the origin

to solve an equation to see if its even or odd, we would need to substitute x in the equation for -x.

in an even function when we substitute f(-x), it should be equal to to f(x)

in an odd function when we substitute f(-x), it should be equal to -f(x)

so lets test the function given to see if its even

f(x) = x³ + 4x

f(-x) = (-x)³ + 4(-x)

f(-x) = x³ - 4x

f(-x) = x³ - 4x ≠ f(x) = x³ + 4x

comparing this to the orignal function, we see that f(-x) = x³ - 4x is not even as we did not get the same output as the original function

now we should test to see if its odd. we have already seen what f(-x) is, now lets try -f(x) and compare it to f(-x) and f(x)

-f(x) = -(x³ + 4x) -->

-f(x) = -x³ - 4x ≠ f(-x) = x³ - 4x

f(-x) = x³ - 4x ≠ f(x) = x³ + 4x

comparing this to f(x) and f(-x), we see that it not odd as we did not get the same output

so the answer is D, neither even nor odd

Answer:

(-6,-7)

Step-by-step explanation:

Answer:

Equation: a - 16 = 3

Answer: a = 19

The lcd would be 10x^3y^3

Answer:

The LCM will be: [tex]10x^3y^3[/tex]

and The Solution will be: [tex]\frac{12y^2-5x}{10x^3y^3}[/tex]

Step-by-step explanation:

We need to solve the problem

[tex]\frac{6}{5x^3y}-\frac{1}{2x^2y^3}[/tex]

Since there is minus sign, so we take LCM of 5x^3y and 2x^2y^3

The LCM will be: [tex]10x^3y^3[/tex]

Our equation will become after taking LCM

[tex]=\frac{12y^2}{10x^3y^3}-\frac{5x}{10x^3y^3}\\=\frac{12y^2-5x}{10x^3y^3}[/tex]

Answer:

x = 14

Step-by-step explanation:

Given

- [tex]\frac{1}{5}[/tex](x - 4) = - 2

Multiply both sides by 5 to eliminate the fraction

- (x - 4) = - 10 ← distribute parenthesis by - 1

- x + 4 = - 10 ( subtract 4 from both sides )

- x = - 14 ( multiply both sides by - 1 )

x = 14

Answer:

The answer is B.

Answer:0.81

Step-by-step explanation:

A: Given teenager owns a skateboard. P(A) = 0.48

B:  Given teenager owns roller blades. P(B) = ? - we dont know and dont need

AB: Given teenager owns a skateboard and roller blades. P(AB) = 0.39

P(B/A) = P(AB)/P(A) = 0.39/0.48 = 0.8125

Answer:

0.81

Step-by-step explanation:

Just divide them and write as a decimal.

D.

Because... You have four cousins, that means you're gonna divide 74.92 by 4.

Multiply the three numbers

4•4•3= 48 cm

Final answer:

The missing length of the hypotenuse (c) in the right triangle with legs a=6 and b=8 is found using the Pythagorean theorem. By squaring both a and b, adding those squares together, and then taking the square root, we determine that c equals 10 units.

Explanation:

To find the missing length of the hypotenuse (c) of the right triangle when given the lengths of the other two sides (a and b), we can use the Pythagorean theorem. The theorem states that for a right triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b). In mathematical terms, this is represented as a² + b² = c².

Given that side a is 6 and side b is 8, we can substitute these values into the theorem's formula:

Therefore, the length of the hypotenuse (c) is 10 units.

ANSWER

D. G(x)=(x+1)²

EXPLANATION

The equation of the red graph is

[tex]F(x) = {x}^{2} [/tex]

This function has its vertex at the origin.

The blue graph is obtained by shifting the red graph 1 unit to the left.

The vertex will now be at (-1,0)

The equation of the new function in the vertex form is

[tex]G(x)= {(x + 1)}^{2} [/tex]

The correct choice is D.

Answer:

(8, 4)

Step-by-step explanation:

AD is enlarged to JM

AD² = 2² + 1² = 4 + 1 =5

AD =  √5

then you plug in JM

JM² = 6² + 3² = 36 + 9 = 45

JM = √45 = 3 √5

so if

JM=3 AD

then

ML= 3 DC

then you add

5+3=8

the coordinates for point L are (8, 4)

Answer:

Option B is right.

Step-by-step explanation:

Given that an artist designed a badge for a school club.

ABCD is given in the picture.

AD = [tex]\sqrt{(-7+8)^2 +(7-5)^2} \\=\sqrt{5}[/tex]

If JKLM is enlargement of ABCD, then scale factor would b the ratio of AD to JM

JM = [tex]\sqrt{(5-2)^2+(4+2)^2} \\=\sqrt{45} \\3\sqrt{5}[/tex]

Scale factor = 3

AB = 3 hence JK = 9

DC = 1 and so ML = 3

ML is parallel to x axis with a distance of 3 units.

COordinates of L = (5+3, 4) = (8,4)

Option B is right

What are th choices to pick from? : )

Answer:

a) x ≥ -1 , x ≠ 6

Step-by-step explanation:

To quickly solve this problem, we can use a graphing tool or a calculator to plot the equation.

Please see the attached images below, to find more information about the graph

The correct answer is option

a) x ≥ -1 , x ≠ 6

Answer:

a) [tex]x\geq -1,x\neq 6[/tex]

Step-by-step explanation:

We have been given a function [tex]f(x)=\frac{\sqrt{x+1}}{(x+4)(x-6)}[/tex]. We are asked to find the domain of our given function.

We can see that our given function is a rational function and numerator of our given function is a square root.

To find the domain of our given function, we will find the number that will make our denominator 0 and the domain of square root function will be the values of x that will make our numerator non-negative.

Undefined points for our given function:

[tex](x+4)(x-6)=0[/tex]

[tex]x+4=0\text{ or }x-6=0[/tex]

[tex]x=-4\text{ or }x=6[/tex]  

The domain of denominator is all values of x, where x is not equal to negative 4 and positive 6.

Non negative values for radical:

[tex]x+1\geq 0[/tex]

[tex]x+1-1\geq 0-1[/tex]

[tex]x\geq -1[/tex]

The domain of numerator is all value of x greater than or equal to negative

Upon combining real regions and undefined points for our given function, the domain of our given function will be all values of x greater than or equal to negative 1, where x is not defined for 6.

Therefore, domain of our given function is [tex]x\geq -1,x\neq 6[/tex].

The area of the path is ².

3.14×10×10

= 314m²

3.14×7×7

= 154m²

Area of bigger circle - area of smaller circle

= (314 - 154) m²

= 160m²

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Answer:

V

Step-by-step explanation:

Under a reflection in the x- axis

a point (x, y) → (x, - y)

Under a reflection in the y- axis

a point (x, y) → (- x, y)

Hence

U(- 6.5, 1 ) → W(- 6.5, - 1) ← reflection in x- axis

W(- 6.5, 1) → V(6.5, -1) ← reflection in y- axis

Answer:

i think its v

Step-by-step explanation:

i hope this is right

Answer:

Multiply 30 × 2.

Subtract 10 from 30.

Add the product and the difference.

Add that sum to 30.

Add 30 + 30.

Subtract 10 from 30.

Add the sum and the difference.

Add that sum to 30

Step-by-step explanation:

Since 308 people can visit each day, and there's 8 shows each day, we just multiply 308 by 8.

308*8 = 2464 people.

Answer:

[tex]\sin\left(-180^o+\theta\right)=-\sin\left(\theta\right)[/tex]

Step-by-step explanation:

We need to find the value of [tex]\sin(-180^o+ \theta)[/tex]

So let's apply formula

[tex]\sin\left(A+B\right)=\sin\left(A\right)\cos\left(B\right)+\sin\left(B\right)\cos\left(A\right)[/tex]

[tex]\sin\left(-180^o+\theta\right)=\sin\left(-180^o\right)\cos\left(\theta\right)+\sin\left(\theta\right)\cos\left(-180^o\right)[/tex]

[tex]\sin\left(-180^o+\theta\right)=0\cdot\cos\left(\theta\right)+\sin\left(\theta\right)\cdot\left(-1\right)[/tex]

[tex]\sin\left(-180^o+\theta\right)=0-\sin\left(\theta\right)[/tex]

[tex]\sin\left(-180^o+\theta\right)=-\sin\left(\theta\right)[/tex]

corresponding angles

Answer: Corresponding angles.

Step-by-step explanation:

They cant be supplementary, two angles are supplementary when their addition is equal to 180°, in this case, the supplementary angles are 1 with 3, and 5 with 7, for example.

Vertical angles mean that they are in opposite quadrants, so this option can be discarded. (an example of this are angles 1 and 4)

Alternate interior angles mean that the angles are in a "touching" quadrant. so this option can be discarded (an example of this can be angles 1 and 6)

Corresponding angles mean that both angles are in the same quadrant. In this case, you can see that both angles are in the top left quadrant, so they are corresponding angles.