2
What is the solution of the equation 6x - 3 = -51?
A. -9
B. -8
c. 8.
D. 9​

Answer:

(x + 1)/4x² + 4(x + 1)/4x²

Step-by-step explanation:

x+1/4x² + x+1/x²

The above can be simply as follow:

Find the least common multiple (LCM) of 4x² and x². The result is 4x²

Now Divide the LCM by the denominator of each term and multiply the result with the numerator as show below:

(4x² ÷ 4x²) × (x + 1) = x + 1

(4x² ÷ x²) × (x + 1) = 4(x + 1)

x+1/4x² + x+1/x² = [(x + 1) + 4(x + 1)]/ 4x²

= (x + 1)/4x² + 4(x + 1)/4x²

Therefore,

x+1/4x² + x+1/x² = (x + 1)/4x² + 4(x + 1)/4x²

Answer: A

Step-by-step explanation:

Answer:

Step-by-step explanation:

1. Given

2. Given

3. Reflective Property

4. SAA

Answer:

(c) the supplements of congruent angles are congruent.

Step-by-step explanation:

Since JKL and JLK are respectively the supplements of angles 3 and 4, we can use the justification

(c) the supplements of congruent angles are congruent.

Answer:

The answer will be C

Step-by-step explanation:

It will not be HL theorem nor SAS postulate so that gives you with C and D. Now D is incorrect because those angles arent complementary

Hi king,

Write [tex]4x^{2} + 16x - 9[/tex] in vertex form:

f(x)=[tex]4x^{2} + 16x - 9[/tex]

f(x)=[tex]4(x+2)^{2} -25[/tex]

Write [tex]5x^{2} - 10x + 4[/tex] in vertex form:

g(x)=[tex]5x^{2} - 10x + 4[/tex]

g(x)=[tex]5(x-1)^{2} -1[/tex]

Have a great day.

Confidence interval for mean, when population standard deviation is unknown:

[tex]\overline{x}\pm t_{\alpha/2}\dfrac{s}{\sqrt{n}}[/tex]

, where [tex]\overline{x}[/tex] = sample mean

n= sample size

s= sample standard deviation

[tex]t_{\alpha/2}[/tex] = Critical t-value for n-1 degrees of freedom

We assume the population has a normal distribution.

Given, n= 19 , s= 3.8 , [tex]\overline{x}=22.4[/tex]

[tex]\alpha=1-0.99=0.01[/tex]

A) Critical t value for [tex]\alpha/2=0.005[/tex] and degree of 18 freedom

[tex]t_{\alpha/2}[/tex] = 2.8784

B) Required confidence interval:

[tex]22.4\pm ( 2.8744)\dfrac{3.8}{\sqrt{19}}\\\\=22.4\pm2.5058\\\\=(22.4-2.5058,\ 22.4+2.5058)=(19.8942,\ 24.9058)\approx(19.9,\ 24.9)[/tex]

Lower bound = 19.9 years

Uppen bound = 24.9 years

C) Interpretation: We are 99% confident that the true population mean of lies in (19.9, 24.9) .

Answer:

The ratios are;

[tex]\dfrac{BC}{AB} = \dfrac{3}{5}[/tex]

[tex]\dfrac{AC}{AB} = \dfrac{4}{5}[/tex]

[tex]\dfrac{BC}{AC} = \dfrac{3}{4}[/tex]

[tex]\dfrac{DE}{AD} = \dfrac{3}{5}[/tex]

[tex]\dfrac{AE}{AD} = \dfrac{4}{5}[/tex]

[tex]\dfrac{DE}{AE} =\dfrac{3}{4}[/tex]

Step-by-step explanation:

Given that the lengths of the sides are;

[tex]\overline {AB}[/tex]  = 20

[tex]\overline {BC}[/tex]  = 12

[tex]\overline {AC}[/tex]  = 16

[tex]\overline {AD}[/tex]  = 10

[tex]\overline {DE}[/tex]  = 6

[tex]\overline {AE}[/tex]  = 8

The ratios are;

[tex]\dfrac{Length \ opposite \ \angle A}{Hypothenus} = \dfrac{BC}{AB} = \dfrac{12}{20} = \dfrac{3}{5}[/tex]

[tex]\dfrac{Length \ adjacent\ \angle A}{Hypothenus} = \dfrac{AC}{AB} = \dfrac{16}{20} = \dfrac{4}{5}[/tex]

[tex]\dfrac{Length \ opposite \ \angle A}{Length \ adjacent \ \angle A} = \dfrac{BC}{AC} = \dfrac{12}{16} = \dfrac{3}{4}[/tex]

[tex]\dfrac{Length \ opposite \ \angle A}{Hypothenus} = \dfrac{DE}{AD} = \dfrac{6}{10} = \dfrac{3}{5}[/tex]

[tex]\dfrac{Length \ adjacent\ \angle A}{Hypothenus} = \dfrac{AE}{AD} = \dfrac{8}{10} = \dfrac{4}{5}[/tex]

[tex]\dfrac{Length \ opposite \ \angle A}{Length \ adjacent \ \angle A} = \dfrac{DE}{AE} = \dfrac{6}{8} = \dfrac{3}{4}[/tex]

Answer:

Step-by-step explanation:

Answer: C. graph that contains the points (-3,0) and (-5,4).

Step-by-step explanation:

Given equation of line: [tex]y=-2x-6[/tex]

Now, Let's check each option

A. Put (x,y)=(0,-3), i.e. x=0 and y=-3 in given equation

[tex]-3=-2(0)-6\\\\\Rightarrow\ -3=-6[/tex]

which is not true.

So, option A. is not correct.

B. Put (x,y) = (3,0), i.e. x=3 and y=0

[tex]0=-2(3)-6\\\\\Rightarrow\ 0=-6-6\\\\\Rightarrow\ 0=-12[/tex]

which is not true.

So option B. is not correct.

C. Put (x,y) = (-3,0), i.e. x=-3 and y=0

[tex]0=-2(-3)-6\\\\\Rightarrow\ 0=0[/tex] , which is true.

Put (x,y) = (-5,4) ,

[tex]4=-2(-5)-6\\\\\Rightarrow\ 4=10-6\\\\\Rightarrow\ 4=4[/tex], which is true.

So both points in option C satisfy the given equation.

That means, option C is correct.

D. Put (x,y) = (-6,0)

[tex]0=-2(-6)-6\Rightarrow\ 0=6[/tex] , which is not true.

So option D. is not correct.

Answer:

4.5 cm

Step-by-step explanation:

apothem=R/2=9/2=4.5 cm

Answer:

14.42 units

Step-by-step explanation:

Assuming that this is a right triangle (i.e ∠ACB = 90°), we can use the Pythagorean formula to solve this:

AB² = AC² + BC²

AB² = 12² + 8²

AB = √(12² + 8²)

AB = 14.42 units

Answer:

Hi, there!!!!

See explanation in pictures.

I hope it helps you...

Answer:

x = 10 units, y = 5 units

Step-by-step explanation:

Given triangle ABC is a 30-60-90 triangle,

m∠C = 60°

By applying Sine rule in the given triangle,

Sin(60)°= [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]

Sin(60)° [tex]=\frac{\text{AB}}{\text{AC}}[/tex]

[tex]\frac{\sqrt{3}}{2}=\frac{\text{AB}}{\text{AC}}[/tex]

[tex]\frac{\sqrt{3}}{2}=\frac{5\sqrt{3}}{x}[/tex]

x = 10 units

Similarly, by applying Cosine rule in the given triangle,

Cos(60)° = [tex]\frac{\text{Adjacent side}}{\text{Hypotenuse}}[/tex]

Cos(60)° = [tex]=\frac{\text{BC}}{\text{AC}}[/tex]

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

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

y = 5 units

Therefore, x = 10 units and y = 5 units will be the answer.

Answer:

[tex]f(0)=g(0)[/tex] and [tex]f(2) = g(2)[/tex]

Step-by-step explanation:

According to the question, the curved red line represents [tex]g(x)[/tex] and the straight blue line represents [tex]f(x)[/tex].

The important thing here is that the equality of functions [tex]f(x)=g(x)[/tex] is represented as a common function between their curves. So, we just need to find such a common point for both.

[tex]f(x)[/tex] has points (0, 4) and (2, 0).

[tex]g(x)[/tex] has points (0,4) and (2,0).

Notice that both functions have the same y-value for x=0 and x=2, that means

[tex]f(0)=g(0)[/tex] and [tex]f(2) = g(2)[/tex].

Therefore, the right answer is the first choice.

The correct answer is option A which is f(2) = g(2) and f(0) = g(0)

A function in mathematics set up a relationship between the dependent variable and independent variable. on changing the value of the independent variable the value of the dependent variable also changes.

According to the question, the curved red line represents g(x) while the straight blue line represents f(x).

The important thing here is that the equality of functions f(x) = g(x)  is represented as a common function between their curves. So, we just need to find a common point for both.

f(x) has points (0, 4) and (2, 0).

g(x) has points (0,4) and (2,0).

Notice that both functions have the same y-value for x=0 and x=2, which means

f(2) = g(2) and f(0) = g(0)

Therefore correct answer is option A which is f(2) = g(2) and f(0) = g(0)

To know more about function follow

https://brainly.com/question/2833285

#SPJ5

Answer:

explanation

Step-by-step explanation:

the reason for your statement is just your explanation of why you think that.

Answer:

1133.54 in.^2

Step-by-step explanation:

The answer is the area of the circle which is in white inside the square. We are not looking for the shaded area.

A = (pi)r^2

r = d/2 = 38 in./2 = 19 in.

A = (3.14)(19 in.)^2

A = (3.14)(19 in.)(19 in.)

A = 1133.54 in.^2

Answer:

Step-by-step explanation:

Given,

Diameter ( d ) = 38

Radius ( r ) = 38/2 = 19

π = 3.14

Now, let's find the area :

[tex]\pi \: {r}^{2} [/tex]

Plug the values

[tex]3.14 \times {(19)}^{2} [/tex]

Evaluate the power

[tex]3.14 \times 361[/tex]

Calculate the product

[tex]1133.54 \: {in}^{2} [/tex]

Hope this helps..

Best regards!!

Answer:

D. Batch 5.

Step-by-step explanation:

The batch should have the same proportion of blue to white to yellow.

In Batch 1, there are two parts of blue, 1.5 parts of white, and 1 part of yellow.

In Batch 5, there are four parts of blue, 3 parts of white, and 2 parts of yellow.

4 / 2 = 2

3 / 2 = 1.5

2 / 2 = 1

Since the proportions are equal to those found in Batch 1, D. Batch 5 will create the same colors as the first batch.

Hope this helps!

Answer:

A

Step-by-step explanation:

Answer - 1) -6/3

2)3/20

3)3/4

Hope this may helps you

Answer:

A.-2

B.its 3/20=0.15

C.3/4=0.75

Answer:

x=70

Step-by-step explanation:

the angles opposite 3.5 equal 55 degrees

180-55-55=70

Answer:

70°

Step-by-step explanation:

since the both size are equal which is 3.5,it is equal length, so the other angle should be 55 also. Just use the triangle =180° ，180-55-55=70°

Answer:

Oh man! I totally understand why you are struggling!

Step-by-step explanation:

You want the textbook or the cheat sheet?

Lets go with the cheat sheet.

So, notice the line segments, correct?

The way to find those is Pythagorean Theorem.

The squares of the legs of the triangle add up to the length of the hypotenuse squared. Imagine that the lengths of the sides ARE Hypotenuses. Then, form a triangle, with the legs (Other sides of the triangle except the hypotenuse) either vertically or horizontally(I explain it better below).

In other words, we need to create a right triangle with AB as the hypotenuse to use Pythagorean Theorem. How do we do that?

Count the number of units both vertically and horizontally from point A to B. Essentially, make a horizontal line segment starting at A, and stop it over B. Then, make a vertical line that goes down to B from that ending point (Remember to count the number of units along the way).

Those are your legs. Then, use those measurements in the Pythagorean Theorem:

[tex]12^{2} + 8^{2}=AB[/tex]

I'm confident you can solve this! If you know mathematics...

Then, repeat for either AD or BC.

Then, use the formula for area of the Rectangle. How do we know that it is a rectangle? Well, I'm skipping this part because it will take too long to do, but I can explain it later if you want!

Oh, well.

Hope this helps! Stay Safe!  

Answer:

A Yes, because every x value corresponds to exactly one y value

Step-by-step explanation:

A function has a one to one correspondence, or every x goes to only one y value

Since each x goes to only 1 y value this is a function

Answer: It is a function

Step-by-step explanation:

One way to tell if it is a function or not, is to look at the X and Y. While 2 different X values can get the same Y value, one X value should not have 2 different Y values. In the table you can see, there are no repeating X values that have different Y values.

EXAMPLES:

(14, 15)

(13,15)

If these two showed up in a table, it could still be a function

(14, 15)

(14, 16)

If these pairs showed up in a table, than it would not be considered a function

Answer:

Step-by-step explanation:

REcall that f(x) is a polynomial whose one of its roots is -3+i. The fundamental algebra theorem states that any polynomial of degree n has n complex roots. In the real case, it can be also interpreted as any polynomial can be factored in factors of degree at most 2.

Consider that given a polynomial of degree 2 of the form [tex]ax^2+bx+c[/tex] the solutions are given by

[tex] x = \frac{-b \pm \sqrt[]{b^2-4ac}}{2a}[/tex]

In this case, the fact that x is real or complex depends on the number [tex]b^2-4ac[/tex] which is called the discriminant. When this number is negative, we have that x is a complex root. Let say that [tex]b^4-4ac<0[/tex] and that [tex]\sqrt[]{b^4-4ac}=di[/tex], so the roots are given by

[tex] x_1 = \frac{-b + di}{2a}, x_2 = x_1 = \frac{-b - di}{2a}[/tex]

this means that, whenever we have a complex root, the other root is the complex conjugate. Recall that the complex conjugate of a complex number of the form a+bi is obtained by changing the sign of the imaginary part, that is a-bi.

So, in our case since -3+i is a root, then -3-i necessarily is another root.

If -3 + i is a root then -3 - i is too.

Therefore, the answer is -3 - i

Answer:

15

Step-by-step explanation:

Use the Pythagorean Thereom:

[tex]r^{2}[/tex] = [tex]9^{2}[/tex]+[tex]12^{2}[/tex]

[tex]r^{2}[/tex] = 81+144

[tex]r^{2}[/tex] = 225

[tex]r[/tex]= 15

Please mark me as Brainliest!

Answer:

100= Initial Amount

1/4= decay factor for each week

w= number of weeks

1/4w= decay factor after w weeks

1 - 0.4= decay factor for each week

w= number of weeks

0.4= percent decrease

Step-by-step explanation:

Answer:

  14

Step-by-step explanation:

The rectangle has side lengths of 3 and 4. There are two of each length, so the total length of all the sides is ...

  P = 2(l +w) = 2(4 +3) = 2(7)

  P = 14 . . . . units

━━━━━━━☆☆━━━━━━━

▹ Answer

111

▹ Step-by-Step Explanation

[tex]3(8 - 4)^{2} + 7 * 9\\\\3 * 4^{2} + 7 * 9\\\\3 * 16 + 63\\\\48 + 63\\\\= 111[/tex]

Hope this helps!

CloutAnswers ❁

Brainliest is greatly appreciated!

━━━━━━━☆☆━━━━━━━

Answer:

(identity has been verified)

Step-by-step explanation:

Verify the following identity:

(sec(A) + tan(A)) (1 - sin(A)) = cos(A)

Write secant as 1/cosine and tangent as sine/cosine:

(1 - sin(A)) (1/cos(A) + sin(A)/cos(A)) = ^?cos(A)

Put 1/cos(A) + sin(A)/cos(A) over the common denominator cos(A): 1/cos(A) + sin(A)/cos(A) = (sin(A) + 1)/cos(A):

(sin(A) + 1)/cos(A) (1 - sin(A)) = ^?cos(A)

Multiply both sides by cos(A):

(1 - sin(A)) (sin(A) + 1) = ^?cos(A)^2

(1 - sin(A)) (sin(A) + 1) = 1 - sin(A)^2:

1 - sin(A)^2 = ^?cos(A)^2

cos(A)^2 = 1 - sin(A)^2:

1 - sin(A)^2 = ^?1 - sin(A)^2

The left hand side and right hand side are identical:

Answer: (identity has been verified)

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           Hi my lil bunny!

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Let's do this step by step.

Prove that sec A ( 1 - sin A) ( sec A + tan A) = 1

Solving L.H.S

sec A ( 1 - sin A) ( sec A + tan A)

[tex]= \frac{1}{cos A} ( 1 - sin A ) ( \frac{1}{cos A} + \frac{sin A }{cos A})[/tex]

[tex]= \frac{(1 - sin A)}{cos A} ( \frac{1 + sin A }{cos A })[/tex][tex]= \frac{( 1 - sin A)( 1 + sin A)}{cos A X cos A}[/tex]

We know that [tex]( a - b) ( a + b) = a^2 - b^2[/tex]

[tex]= \frac{( 1^2 - sin^2 A)}{cos^2 A}[/tex]

[tex]= \frac{( 1 - sin^2 A)}{cos^2 A}[/tex]

[tex]= \frac{cos^2 A}{cos^2 A}[/tex]                         [tex]| cos^2 A + sin^2 A = 1 | cos^2 A = 1 - sin^2 A |[/tex][tex]1 - sin^2 A = cos^2 A[/tex]

[tex]= 1[/tex]

[tex]= R . H. S[/tex]

Thus, L.H.S = R.H.S

Hence proved.

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Hope this helped you.

Could you maybe give brainliest..?

❀*May*❀

B

C

=

16.17

(

2

d

p

)

c

m

Explanation:

In triangle ABC, side

A

C

=

15

, Angles are

∠

B

=

68

0

;

∠

C

=

24

0

and

∠

A

=

180

−

(

68

+

24

)

=

88

0

We know by sine law

A

C

sin

B

=

B

C

sin

A

or

15

sin

68

=

B

C

sin

88

or

B

C

=

15

⋅

sin

88

sin

68

=

16.17

(

2

d

p

)

c

m

Step-by-step explanation:

Answer:

Step-by-step explanation:

m∠B = 68°,      m∠C = 24°,       AC = 15 cm

m∠A = 180° - 68° - 24 = 88°

by sine law:

                  [tex]\dfrac{BC}{\sin(A)}=\dfrac{AC}{\sin(B)}\\\\\\BC=\dfrac{15}{\sin\left(6\big8^o\right)}\cdot \sin\left(8\big8^o\right)\\\\\\BC\approx\dfrac{15}{0.9272}\cdot 0.9994=16.168032....\\\\\\BC\approx16.17[/tex]

Answer:

60

Step-by-step explanation:

8640/60 is 144. 144 is a perfect square. 12*12 is 144

Hey there! I'm happy to help!

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

INTRO TO PERFECT CUBES

A perfect cube is any number whose cube root is an integer. In English, that means that if you take any number without a fraction (this is called an integer, such as -7, 8, 100, none have fractions) and multiply it by itself three times, you get a perfect cube.

If you cube the number 4, you get 64, which is (4×4×4). 64 is an example of a perfect cube.

You can use the cube root button on your calculator to see if a number is a perfect cube. If you do the cube root of 64, you get 4, telling you that 64 is a perfect cube. The cube root of 10 is 2.154434...... so 10 is not a perfect square because it does not give you an integer (number that does not have a fraction) as the answer.

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

SOLVING THE PROBLEM

So, we want to find the smallest numbers we can divide 8640 to equal a perfect cube.

I will assume that we will not be dividing by fractions but only whole numbers (positive integers).

We could try dividing by 1, but we see that 8640 is not a perfect cube because it's cube root is 20.519711....

Let's just keep counting up! The first divisor we run into that gives a quotient that it is a perfect cube is the smallest whole number possible that will give us that result.

8640÷2=4320

∛4320≈16.2865....... Not a perfect cube

8640÷3=2880

∛2880≈14.22757..... Not a perfect cube

8640÷4=2160

∛2160≈12.92660..... Not a perfect cube

8640÷5=1728

∛1728=12, a perfect cube!

Since 12 cubed is equal to 1728, this means that 1728 is a perfect square, so 5 is the smallest number we can divide 8640 by to get a perfect square.

The answer is 5.

I hope that this helps! Have a wonderful day! :D

Answer:

6 ft and 8 ft

Step-by-step explanation:

let x be the length of one leg then (x + 2) is the other leg.

Using Pythagoras' identity in the right triangle, that is

x² + (x + 2)² = 10² ← expand left side and simplify

x² + x² + 4x + 4 = 100 ( subtract 100 from both sides )

2x² + 4x - 96 = 0 ( divide all terms by 2 )

x² + 2x - 48 = 0 ← in standard form

(x + 8)(x - 6) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 8 = 0 ⇒ x = - 8

x - 6 = 0 ⇒ x = 6

But x > 0 ⇒ x = 6

Thus the 2 sides are 6 ft and x + 2 = 6 + 2 = 8 ft