Write the function in standard form.
Y=(3x-2)(3x+6)

Answer:

Option (A).

Step-by-step explanation:

[tex]8\frac{4}{5}[/tex] is a mixed fraction and can be written as,

[tex]8\frac{4}{5}=8+\frac{4}{5}[/tex] [Combination of a whole number and a fraction]

When we multiply this mixed fraction by 7,

[tex]7\times 8\frac{4}{5}=7\times (8+\frac{4}{5})[/tex]

          [tex]=(7\times 8)+(7\times \frac{4}{5})[/tex] [Distributive property → a(b + c) = a×b + a×c]

          [tex]=56+\frac{28}{5}[/tex]

          [tex]=56+5\frac{3}{5}[/tex]

          [tex]=56+5+\frac{3}{5}[/tex]

          [tex]=61+\frac{3}{5}[/tex]

          [tex]=61\frac{3}{5}[/tex]

Therefore, [tex]7\times 8\frac{4}{5}=61\frac{3}{5}[/tex] will be the answer.

Option (A) will be the correct option.

Answer:

Step-by-step explanation:

If EG is parallel to the side of the rectangle then lenght of EG is equal to width of rectangle.

If F and H are midpoints of sides of rectangle then FH is parallel to the side of rectangle {wich is perpendicular to the side parallel to EG}. That means the lenght of FH is equal to lenght of rectangle, and FH is perpendicular to EG.

Then FH is sum of hights of triangles EFG and EHG [tex](FH=H_{_{\Delta EFG}}+H_{_{\Delta EHG}})[/tex], and the area of EFGH is sum of areas of triangles EFG and EHG [tex](A_{kite}=P_{_{\Delta EFG}}+P_{_{\Delta EHG}})[/tex].

So the area of the rectangle:  [tex]\bold{A_{rectangle}=EG\cdot FH}[/tex]

The area of the kite:

                                  [tex]A_{kite}=P_{_{\Delta EFG}}+P_{_{\Delta EHG}}\\\\A_{kite}=\frac12 EG\cdot H_{_{\Delta EFG}}+\frac12 EG\cdot H_{_{\Delta EHG}}\\\\ A_{kite}=\frac12 EG\cdot (H_{_{\Delta EFG}}+H_{_{\Delta EHG}})\\\\A_{kite}=\frac12 EG\cdot FH\\\\A_{kite}=\frac12 A_{rectangle}[/tex]

No matter the height of the triangles, so no matter the location of the EG

Answer:

AAS

Step-by-step explanation:

Δwzy=Δwzv

to prove the equality:

1- wz is a common side

angle:  wzv=wzy=90 degrees ( height of triangle)

angle v= angle y

Since WZ bisects W, it's good  to say that vwz and zwy

prove one side is equal and two angles

so ASA or AAS is the answer

The solution is where the two red lines cross. This is the point (3,-4)

If you knew the equation of each red line, you can plug (x,y) = (3,-4) into each equation. You should find the two equations lead to true statements.

Answer:

im pretty sure its the third one

Step-by-step explanation:

i guessed but it might be right

Answer:

(1.5,-3) and (4.5,-3)

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

In order to make the equation undefined, you should make the denominator 0. Remember that dividing anything by 0 will become undefined.

[tex]2x-4=0\\\frac{2x=4}{2} \\x=2[/tex]

Answer:

[tex]\boxed{x = 2}[/tex]

Step-by-step explanation:

A rational expression is undefined when Denominator = 0

Here Denominator = 2x-4

So,

=> 2x - 4 = 0

Adding 4 to both sides

=> 2x = 4

Dividing both sides by 2

=> x = 2

Answer:

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

Step-by-step explanation:

Given y is inversely proportional to x then the equation relating them is

y = [tex]\frac{k}{x}[/tex] ← k is the constant of variation

To find k use the condition y = 5 when x = 7, then

5 = [tex]\frac{k}{7}[/tex] ( multiply both sides by 7 )

35 = k

y = [tex]\frac{35}{x}[/tex] ← equation of variation

When x = 70, then

y = [tex]\frac{35}{70}[/tex] = [tex]\frac{1}{2}[/tex]

Answer:

D.

Step-by-step explanation:

A function is when each x-value has only 1 y-value.

A: When x = 5, there are two values for y.

B: When x = -3, there are two values for y.

C: When x = -4, there are two y-values.

D: Each x-value has exactly one y-value.

So, your answer should be D.

Hope this helps!

Option (D) is accurate since the fourth option's x value has exactly one y value.

D. {(₋7,9), (₋4,₋9), (5,15), (7,19)}

What are functions?

Each element of X receives exactly one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and co-domain, respectively.

When we say that a variable quantity y is a function of a variable quantity x, we indicate that y depends on x and that x's value determines what y's value will be. This reliance can be expressed as follows: y = f (x)

Given,

In the first case, y has two different values of 13 and 17, which is not permitted in a function, with the same value of x = 5. The first case is not a function as a result.

For the same value of x = 3 in the second case, y has two different values of 1 and 1, which is not permitted in a function. The second example is therefore not a function.

In the third case, for the same value of x = ₋4, y has two different values of 52 and 16 which is not allowed in a function. Therefore, third case is not a function.

Here, in the fourth situation, no x value is identical and there is only one possible y value.

Hence we get the answer as {(₋7,9), (₋4,₋9), (5,15), (7,19)} which represents the function.

Learn more about "functions" here-

brainly.com/question/10439235

#SPJ2

Answer:  A) 1       B) [tex]\sqrt5[/tex]

Step-by-step explanation:

[tex]A)\quad \dfrac{2\sqrt3}{\sqrt{12}}=\dfrac{2\sqrt3}{2\sqrt3}=1\\\\\\\\B)\quad \dfrac{5\sqrt7}{\sqrt{35}}=\dfrac{5\sqrt7}{\sqrt5\cdot \sqrt7}=\dfrac{5}{\sqrt5}\bigg(\dfrac{\sqrt5}{\sqrt5}\bigg)=\dfrac{5\sqrt5}{5}=\sqrt5[/tex]

Answer:

Step-by-step explanation:

[tex]10 + {(2 \times 3)}^{2} \div 4 \times {( \frac{1}{2}) }^{3} [/tex]

To raise a product to a power, raise each factor to that power

[tex] = 10 + 4 \times 9 \div 4 \times {( \frac{1}{2} )}^{3} [/tex]

To raise a fraction to a power, raise the numerator and denominator to that power

[tex] = 10 + 4 \times 9 \div 4 \times \frac{1}{8} [/tex]

Any expression divided by itself equals 1

[tex] = 10 + 1 \times 9 \times \frac{1}{8} [/tex]

Any expression multiplied by 1 remains the same

[tex] = 10 + 9 \times \frac{1}{8} [/tex]

Calculate the product

[tex] = 10 + \frac{9}{8} [/tex]

Write all numerators above the common denominator

[tex] = \frac{80 + 9}{8} [/tex]

Add the numbers

[tex] = \frac{89}{8} [/tex]

Divide

[tex] = 11.125[/tex]

Hope this helps..

Best regards!!

Answer:

11 1/8

Step-by-step explanation:

Okay so I messed up big time. So I had to edit this! I am really sorry if you read mine before. I fixed mine. So this is the right answer. Sorry!

Answer:

The correct answer is D because we proved that the triangles ΔDBE and ΔADF are congruent so that means that DE = segment A F because of CPCTC.

Answer:

The correct answer is D because we proved that the triangles ΔDBE and ΔADF are congruent so that means that DE = segment A F because of CPCTC.

Step-by-step explanation:

Answer:

[tex]\frac{3n^2-7n+15}{(n+3)(n-4)}[/tex] will be the answer.

Step-by-step explanation:

The given expression is,

[tex]\frac{3n}{(n+3)}+\frac{5}{(n-4)}[/tex]

By solving this expression,

[tex]\frac{3n}{(n+3)}+\frac{5}{(n-4)}[/tex]

= [tex]\frac{3n(n-4)}{(n+3)(n-4)}+\frac{5(n+3)}{(n+3)(n-4)}[/tex]

= [tex]\frac{3n(n-4)+5(n+3)}{(n+3)(n-4)}[/tex]

= [tex]\frac{3n^2-12n+5n+15}{(n+3)(n-4)}[/tex]

= [tex]\frac{3n^2-7n+15}{(n+3)(n-4)}[/tex]

Therefore, fraction given in option (2) will be the answer.

Answer:

  -0.0062 and 27.5

Step-by-step explanation:

You can write the equation of the line using the 2-point form:

  y = (y2 -y1)/(x2 -x1)(x -x1) +y1

The given values of the variables are ...

  (h, T) = (10000, -34.5) and (15000, -65.5)

Putting these into the formula, we have ...

  T = (-65.5 -(-34.5))/(15000 -10000)(h -10000) +(-34.5)

  T = -31/5000(h -10000) -34.5

  T = -0.0062h +62 -34.5

  T = -0.0062h +27.5

The appropriate choice is ...

  -0.0062 and 27.5

Answer:

cos C

Step-by-step explanation:

Using the cosine ratio in the right triangle

cos C = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{BC}{AC}[/tex] = [tex]\frac{12}{13}[/tex]

Answer:

x = 0

Step-by-step explanation:

i) x - 11 + 1 < 15

x - 10 < 15

x < 10 + 15

x < 25

ii) x - 11 + 1 > 15

x - 10 > 15

x > 25

Therefore to compare (i) and (ii)

25 < x < 25

In any case, x = 0

Answer:

$1.935

Step-by-step explanation:

As the store is offering a 15% discount, you have to calculate the 15% of the price of the game app to find the amount of the discount:

Price of the game app= 12.90

12.90*15%=1.935

According to this, the answer is that the amount of the discount if you buy the game app during the sale is $1.935 and you would have to pay: 12.90-1.935= $10.965.

Answer:

[tex]a^2+3\,a\,b-5\,a\,b-15\,b^2=(a-5\,b)\,(a+3\,b)[/tex]

Step-by-step explanation:

Work via factoring by groups:

!) re arrange the terms as follows:

[tex]a^2-5ab+3ab-15b^2[/tex]

then extract the common factor for the first two terms (a), and separately the common factors for the last two terms (3 b):

[tex]a^2-5ab+3ab-15b^2\\a\,(a-5\,b)+3\,b\,(a-5\,b)[/tex]

Now notice that the binomial factor (a-5 b) is in both expressions, so extract it:

[tex]a\,(a-5\,b)+3\,b\,(a-5\,b)\\(a-5\,b)\,(a+3\,b)[/tex]

which is the final factorization.

Answer:

[tex] \boxed{\sf (a + 3b)(a - 5b)} [/tex]

Step-by-step explanation:

[tex] \sf Factor \: the \: following: \\ \sf \implies {a}^{2} + 3ab - 5ab - 15 {b}^{2} \\ \\ \sf Grouping \: like \: terms, \\ \sf {a}^{2} + 3ab - 5ab - 15 {b}^{2} = {a}^{2} + (3ab - 5ab) - 15 {b}^{2} : \\ \sf \implies {a}^{2} + (3ab - 5ab) - 15 {b}^{2} \\ \\ \sf 3ab - 5ab = - 2ab : \\ \sf \implies {a}^{2} - 2ab - 15 {b}^{2} \\ \\ \sf The \: factors \: of \: - 15 \: that \: sum \: to \: - 2 \: are \: 3 \: and \: - 5. \\ \\ \sf So, \\ \sf \implies {a}^{2} + (3 - 5)ab - 15 {b}^{2} \\ \\ \sf \implies {a}^{2} + 3ab - 5ab - 15 {b}^{2} \\ \\ \sf \implies a(a + 3b) - 5b(a + 3b) \\ \\ \sf \implies (a + 3b)(a - 5b)[/tex]

Answer:

Scale 1: 1 centimeter = 3 meters.

Scale 2: 1 centimeters = 4 meters.

Step-by-step explanation:

your answer should be A

15*3=45

15*4=60

Answer:

A.)Scale 1: 45 m; Scale 2: 60 m

Step-by-step explanation:

bcuz......uhhhhhhh, ummmmmm:/

Answer:

9 = k :)

Step-by-step explanation:

1. distribute 3 to the -1/4 k and to the 3 and get -3/4 k + 9 = 1/4 k

2. add 3/4 k to both sides and get 9 = k

Answer:

x=10 y=12

Step-by-step explanation:

just multiply 15 and 18 by 1/3 because both triangle are similar.

Answer:

x = 10; y = 12

Step-by-step explanation:

find the scale factor ratio using corresponding sides: 9 / 6 = 3/2 so the ratio is 3:2

from large triangle to small triangle you will get:

1. 15 / x

2. 18 / y

to implement the ratio, set the side length ratio equal to the scale factor:

1. [tex]\frac{15}{x}[/tex] = [tex]\frac{3}{2}[/tex]

2. [tex]\frac{18}{y}[/tex] = [tex]\frac{3}{2}[/tex]

cross multiply:

1. 30 = 3x

2. 36 = 3y

divide:

1. x = 10

2. y = 12

Answer:

ADB and ADC

Step-by-step explanation:

SAS is side angle side. so, which 2 triangles have same side, then angle, then side. We have to have it in that specific order.

Answer:

ABD and ECD

Step-by-step explanation:

EDC and ADB are vertical angles, so that is the angle we need for the SAS postulate. The markings on each of the corresponding sides is the same, which means we have 2 congruent sides, as well as an angle.

Answer: [tex]-50a^{11}b^{9}[/tex]

Step-by-step explanation:

Any negative exponent can be moved to the other side of the fraction as a positive exponent.[tex]\frac{1}{x^{-3}}=x^3\\ \frac{x^{-3}}{1}=\frac{1}{x^3}[/tex]

Thus, simply move the negative exponents from the bottom into the numerator to get. -10a^2*b^4*5a^9*b^5.  Then, use the exponent rule to get [tex]-50a^{11}b^{9}[/tex]

Hope it helps <3

Answer:

  57°

Step-by-step explanation:

There is a right angle at the point of tangency, so the angle of interest is the complement of the one given:

  m∠K = 90° -m∠J = 90° -33°

  m∠K = 57°

Answer:

11

Step-by-step explanation:

Prime factor: 43659 = 3*3*3*3*7*7*11

Pair: √43659 = √3²×3²×7²×11

11 is odd therefore 11 must be divided by 43659

Answer:

125

Step-by-step explanation:

1 x 1  x 1 = 1

5 x 5 x 5 = 125

125 / 1 = 125

125 is your answer

Step-by-step explanation:

c^2( c^2-10c+25)

=c^4 - 10c^3 + 25c^2

S - a randomly chosen pregnancy result in a successful delivery

C - a randomly chosen pregnancy ending in a C section

Answer:

Sum of interior angles of 12 sided object = 1800°

Step-by-step explanation:

Formula to calculate the sum of interior angles of a polygon is,

Sum of the interior angles of a polygon = (n - 2) × 180°

Where n = number of sides of the polygon.

If number of sides of a polygon are 12,

For n = 12,

Sum of interior angles = (12 - 2) × 180°

                                     = 10 × 180°

                                     = 1800°

Therefore, sum of interior angles of a 12 sided polygon will be 1800°.

Answer:

3,500 tons

Step-by-step explanation:

We know that 1,400 tons is 2/5 of the Consolidated Brick Company's output.

This means that 1/5 must be equal to 700 tons if 2/5 is 1,400.

So, we can find the total output by multiplying 700 by 5, since 700 is 1/5 of the total.

700(5) = 3,500 tons