Figure ABCD is a rectangle with point A (−2, 5). What rule would rotate the figure 90° clockwise?

Answer:

Step-by-step explanation:

Give the equation 5x² + 27x = 14 − 13x, we are to write the steps needed to solve for x using the completing the square method.

Step 1: Rewrite the equation in a quadratic form by first adding 13x to both sides of the equation.

5x² + 27x +13x= 14 − 13x+13x

5x² + 40x = 14

Step 2: factor out the common constant in the left hand side of the equation.

5(x²+8x) = 14

Step3: The next step to take is to divide through by the the value of 5 to have;

5(x²+8x)/5 = 14/5

x²+8x = 14/5

Step 4: complete the square of the equation at the left hand side by adding the square of half of the coefficient of x to both sides i.e {1/2(8)}² which is 4²

x²+8x +4² = 14/5+4²

x²+8x +16 = 14/5+16

(x+4)² = 94/5

Step 5: Taking the square root of both sides

√(x+4)² = ±√94/5

x+4 = ±√94/5

Step 6: subtract 4 from both sides

x+4-4 = ±√94/5 - 4

x = ±√94/5 - 4

Hence the solution to the equation using completing the square method is x = -4±√94/5

Answer:

5(x2 + 8x + 16) = 94

Step-by-step explanation:

Answer:

[tex]x = 15[/tex]

Step-by-step explanation:

Since lines f and g are parallel, that means that the top angles will be the same, while the bottom angles will also be the same.

The angles of any quadrilaterals all add up to 360°, so we can create the equation like this:

[tex]3x + 3x + (6x + 45) + (6x+45) = 360[/tex]

Combine like terms so we can get a simpler equation:

[tex]6x + 12x + 90 = 360\\18x + 90 = 360[/tex]

Now let's solve for x!

[tex]18x + 90 - 90 = 360 - 90\\18x = 270\\18x\div18 = 270\div18\\x = 15[/tex]

So [tex]x = 15[/tex].

Hope this helped!

Answer:

15

Step-by-step explanation:

3x + 6x + 45 = 180

9x = 135

x = 15

Answer:

x-intercept(s):  

( 4/ 3 , 0 )

y-intercept(s):  

( 0 ,  − 4 /5 )

Step-by-step explanation:

Answer:

vertical intercept: (0 , (-4/5))

Step-by-step explanation:

substitute x=0

-3 * 0 - 4 = -5y - 8

y= -4/5

alternative form

y= 0.8

Answer:

Step-by-step explanation:

4x^5 + 7x^3

x^3(4x^2 + 7)

The GCF is x^3

Explanation : As you can see, [tex]\sqrt{-16}[/tex] is not a real number, and hence should be expressed as 4[tex]i[/tex], [tex]i[/tex] being an imaginary number. Respectively [tex]\sqrt{-64}[/tex] will be 8[tex]i[/tex]. Therefore this expression boils down to [tex]\left(3+4i\right)\left(6-8i\right)[/tex]. All we have to do from now on is expand this expression.

Apply the rule [tex]\left(a+bi\right)\left(c+di\right)=\left(ac-bd\right)+\left(ad+bc\right)i[/tex], in this case where [tex]a=3,\:b=4,\:c=6,\:d=-8[/tex],

[tex]\left(3\cdot \:6-4\left(-8\right)\right)+\left(3\left(-8\right)+4\cdot \:6\right)i[/tex]

Let's simplify each part, [tex]3\cdot \:6-4\left(-8\right)[/tex] and [tex]3\left(-8\right)+4\cdot \:6[/tex]. Afterwards we can add [tex]i[/tex], and refine.

[tex]3\cdot \:6-4\left(-8\right) = 50[/tex] ; [tex]3\left(-8\right)+4\cdot \:6 = 0[/tex]

Therefore our simplified expression will be [tex]50+0i[/tex], otherwise known as just 50. That is our solution.

Answer:

Step-by-step explanation:

The equation that represents Jacob's age is  x = y + z + 2

From the question, the following information was provided :

Jacob's age is two years more than the sum of the ages of his siblings Becky and Micah.

This above information can be represented with the equation below

Jacob = 2 + ( Becky + Micah) (equation 1)

If :

x represents Jacob's age

y represents Micah's age

z represents Becky's age

Equation 1, can be rewritten as x = y + z + 2

Micah's age can be determined by making Micah the subject of the formula in the above equation

Micah = Jacob - Becky - 2   (equation 2)

If :

x represents Micah's age

y represents Becky's age

z represents Jacob's age

Micah's age can be rewritten as :

x = z - y - 2

Becky's age  age can be determined by making Becky the subject of the formula in the first equation.

Becky = Jacob - Micah - 2 (equation 3)

If:

x represents Becky's age

y represents Jacob's age

z represents Micah's age

Equation 3 can be rewritten as :

x = y - z - 2

Check here for a related question : https://brainly.com/question/21843246?referrer=searchResults

Using a system of equations, it is found that the correct equation is given by:

[tex]x = y + z + 2[/tex], which is option B.

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

[tex]x = y + z + 2[/tex]

Which is given by option B.

A similar problem is given at https://brainly.com/question/24233433

Answer:

x + 2(2x-4) = 10

Step-by-step explanation:

Here in this question, we want to select which is the correct answer if we substitute for the value of y in the second equation, using the first.

In the first, we have;

y = 2x -4

Now, let’s input this value of y into the second equation.

By direct substitution, what we have is the following;

x + 2y = 10

—-> x + 2(2x -4) = 10

Answer:  [tex]-3\sqrt{5}[/tex]

-3 times the square root of 5

=============================================

Explanation:

Let [tex]x = \sqrt{5}[/tex]

Replace all the root 5 terms with x and we go from

[tex]3\sqrt{5}-8\sqrt{5}+2\sqrt{5}[/tex]

to

[tex]3x-8x+2x[/tex]

From here, combine like terms to get

[tex]3x-8x+2x = -5x+2x = -3x[/tex]

and the last thing to do is replace the x with sqrt(5)

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

Meaning that,

[tex]3x-8x+2x = -3x[/tex]

[tex]3\sqrt{5}-8\sqrt{5}+2\sqrt{5} = -3\sqrt{5}[/tex]

Answer:

-25, -5

Step-by-step explanation:

Let's write a system of equations. Lets call x and y the numbers, where x is 5 times y.

x + y = -30

x = 5y

Plugging this in, we get:

5y + y = -30

y = -5

Since y = -5, we can plug this in, and see that x = -25.

Answer:

-5 & -25

Step-by-step explanation:

1st number=x

2nd number=5x

x+5x=-30

6x=-30

x=-5

5x=-25

So the numbers are -5 & -25

Answer:

c.

Step-by-step explanation:

From the last row in the matrix z = 1.

From the second row:

y + 5z = -4

y = -4 -5(1) = -9.

From the first row:

x + -1 = -3

x = - 3 + 1

x = -2.

Answer:

8

Step-by-step explanation:

Calculate the distance d using the distance formula

d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]

with (x₁, y₁ ) = z₁(6, 2) and (x₂, y₂ ) = z₂(6, 10)

d = [tex]\sqrt{(6-6)^2+(10-2)^2}[/tex]

   = [tex]\sqrt{0^2+8^2}[/tex]

   = [tex]\sqrt{64}[/tex] = 8

hope this helps you alot

x - 3 = 27

add three to both sides

then x= 30

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         Hi my lil bunny!

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Let's solve your equation step-by-step.

[tex]x-3=27[/tex]

Step 1: Add 3 to both sides.

[tex]x -3 + 3 = 27 +3[/tex]

[tex]x = 30[/tex]

So the answer is : [tex]x = 30[/tex]

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Hope this helped you.

Could you maybe give brainliest..?

❀*May*❀

Answer:

48°

Step-by-step explanation:

arc BC = 136(2) -145 = 127

arc DC = 83(2) - 127 = 39

arc AD = 360 - 145- 127 - 39 = 48

Answer:

49 degrees

Step-by-step explanation:

Measure of arc ABC = 116*2 = 232 degrees.

Measure of arc BC = 232-145 = 87 degrees.

Measure of arc BCD = 83*2 = 166 degrees.

Measure of arc DC = 166-87 = 79 degrees.

Measure of arc AD = 360 - (145+87+79) = 360 - 311 = 49 degrees

Answer:

Explained below.

Step-by-step explanation:

The question is:

Please answer me these questions or one: v please. My math class room is 700 m2, how much is 1/4 of the room? How long is 3/4 of the room? . How many minutes is 3/5 of a half hour? . It takes 4/7 of a liter of paint to paint a square meter of wall, if we want to paint 2/5 of a square meter of wall, how much paint will we need? . If it takes 2/5 of an orange to make a glass of orange juice, how many oranges do you need to make 2 and a half glasses?

(1)

Compute 1/4th of the math class room as follows:

[tex]=700\times\frac{1}{4}\\=175[/tex]

Thus, 1/4th of the math class room is 175 m².

(2)

Compute 3/4th of the math class room as follows:

[tex]=700\times\frac{3}{4}\\=525[/tex]

Thus, 3/4th of the math class room is 525 m².

(3)

Compute 3/5th of half an hour as follows:

[tex]=30\times \frac{3}[5}\\=18[/tex]

Thus, 3/5th of half an hour is 18 minutes.

(4)

A square meter of wall required 4/7 liter of paint.

Then 2/5 of a square meter will require,

[tex]=\frac{4}{7}\times \frac{2}{5}\\\\=\frac{8}{35}[/tex]

Thus, 8/35 liter of paint will be used to pain /5 of a square meter of the wall.

(5)

1 glass of orange juice can be made using 2/5 of an orange.

Then 2 and half glass will require,

[tex]=\frac{2}{5}\times 2\frac{1}{2}\\\\=\frac{2}{5}\times \frac{5}{2}\\\\=1[/tex]

Thus, 1 orange will be required to make 2 and half glass of orange juice.

Answer:

Step-by-step explanation:

8: 8, 16, 24, 32, 40, 48, 56

x^5y^3z^2

14: 14, 28, 42, 56

x^3y^2z

the LCM is 56x^5y^3z^2

Answer:

Below

Step-by-step explanation:

5)

The sequence includes the terms 3,6,9,12,15.. and so on

Notice that each time we add 3.

The first term is 3.

We can see it in a different way

● 3 = 3×1

● 6 = 3×2

● 9 = 3×3

● 12 = 3×4

Let 1 be n. Notice what happens

● 3 = 3n

● 6 = 3 × (n+1)

● 9 = 3 × (n+2)

● 12 = 3 × (n+3)

So we can express it as.

● a1 = 3 × 1 =3

● a2 = 3×2 =6

● a3 = 3×3 = 9

So the third term is a3 wich is 9

● a6 = 3×6 = 18

So the sixth term is 18 .

■■■■■■■■■■■■■■■■■■■■■■■■■■

6)

the sequence is defined by:

● f(n-1) = -0.5 f(n)

Repalce n-1 with n and n with n+1

● f(n) = -0.5 f(n+1)

So to get a term you must multiply the next one by -0.5

The first term in the sequence is 120.

● 120 = -0.5 f(n+1)

● f(n+1) = 120/-0.5

● f(n+1) = -60

So the second term is -60

Answer:

[tex]\huge \boxed{9}[/tex]

Step-by-step explanation:

3 raised to 2 is 3 to the power of 2.

[tex]3^2 =3 \times 3 = 9[/tex]

3 is multiplied by itself.

Answer:

(-8,2)

Step-by-step explanation:

This is because when you reflect a point across the x-axis, the x-coordinate fo the point remains the same and the y-coordinate's sign gets switched.

(x,y) --> (x,-y)

(-8,-2) --> (-8,2)

Answer:

= 49

Step-by-step explanation:

[tex]\frac{-7^{7} }{-7^{5} }[/tex]

= -7⁷⁻⁵

= -7²

= -7*-7

= 49

Answer:

B) Associative Property of Multiplication

Step-by-step explanation:

*if it's wrong idk how, but I apologise*

Answer:

x = 80

Step-by-step explanation:

Tangent Chord Angle  =1/2 Intercepted Arc

40 = 1/2 x

80 = x

Answer:

y = [tex]\sqrt{x+5}[/tex] + 7

Step-by-step explanation:

Given the graph of f(x) then f(x + k) is a horizontal translation of f(x)

• If k > 0 then a shift to the left of k units

• If k < 0 then a shift to the right of k units

Thus a translation of 5 units to the left

y = [tex]\sqrt{x+5}[/tex]

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

• If c > 0 then shift up by c units

• If c < 0 then shift down by c units

Thus

y = [tex]\sqrt{x+5}[/tex] + 7 ← translated equation

Answer:

We conclude that the proportion of families with children under the age of 18 who eat dinner together seven nights a week has​ decreased.

Step-by-step explanation:

The complete question is: In a previous​ poll, ​46% of adults with children under the age of 18 reported that their family ate dinner together seven nights a week. Suppose​ that, in a more recent​ poll, 480 of 1081 adults with children under the age of 18 reported that their family ate dinner together seven nights a week. Is there sufficient evidence that the proportion of families with children under the age of 18 who eat dinner together seven nights a week has​ decreased? Use the [tex]\alpha[/tex] = 0.10 significance level.

Let p = population proportion of families with children under the age of 18 who eat dinner together seven nights a week.

So, Null Hypothesis, : p 46%      {means that the proportion of families with children under the age of 18 who eat dinner together seven nights a week has increased or remains same}

Alternate Hypothesis, : p < 46%      {means that the proportion of families with children under the age of 18 who eat dinner together seven nights a week has​ decreased}

The test statistics that will be used here is One-sample z-test for proportions;

                             T.S.  =    ~  N(0,1)

where, [tex]\hat p[/tex] = sample proportion of families = [tex]\frac{480}{1081}[/tex] = 0.44

           n = sample of adults with children under the age of 18 = 1081

So, the test statistics =    

                                   =  -1.32

The value of z-statistics is -1.32.

Also, the P-value of the test statistics is given by;

                    P-value = P(Z < -1.32) = 1 - P(Z [tex]\leq[/tex] 1.32)

                                  = 1 - 0.9066 = 0.0934

Since the P-value of our test statistics is less than the level of significance as 0.0934 < 0.10, so we have sufficient evidence to reject our null hypothesis as the test statistics will fall in the rejection region.

Therefore, we conclude that the proportion of families with children under the age of 18 who eat dinner together seven nights a week has​ decreased.

Answer:

The balloon contains 456.3 kg of helium

Step-by-step explanation:

Density=mass / volume

Volume=2600 cubic meters of helium

Density=0.1755 kilograms per cubic meters

Mass=x

Find mass, x

Density=mass / volume

Mass=Density × volume

=0.1755 * 2600

=456.3 kg

The balloon contains 456.3 kg of helium

Answer:

The answer to your question is given below.

Step-by-step explanation:

To divide 2635 by 17 using long division method, we simply do the following:

2635 ÷ 17

17 can not go into 2. Therefore, we try 17 into 26, keeping 35 constant.

26 ÷ 17 = 1

Put the 1 on top.

Multiply 17 by 1

17 x 1 = 17

Subtract 17 from 26

26 – 17 = 9

Put the 9 in from of 35 to become 935

Next:

935 ÷ 17

17 can not go into 9. Therefore, we try 17 inot 93 keeping 5 constant.

93 ÷ 17 = 5

Put the 5 on top together with the 1 to become 15.

Multiply 17 by 5

17 x 5 = 85

Subtract 85 from 93

93 – 85 = 8

Put the 8 in front of 5 to become 85

Next:

85 ÷ 17

17 can not go into 8. Therefore, we try 85

85 ÷ 17 = 5

Put the 5 on top together with 15 to become 155

Multiply 17 by 5

17 x 5 = 85

Subtract 85 from 85

85 – 85 = 0

Since no number is remaining, we shall stop here.

Therefore,

2635 ÷ 17 = 155

Please attached photo for further details.

Answer:

411,600.000× 10^3 OR 4.11600000×10^8

Step-by-step explanation:

The expontent seems to be 3 so you move the decimal point over <this way 3

if it is 8 you move it over this way < 8

Answer:

411,600.000× 10^3 OR 4.11600000×10^8

Step-by-step explanation:

The expontent seems to be 3 so you move the decimal point over <this way 3

if it is 8 you move it over this way < 8

Answer:

The expression that could help calculate the price of the TV is;

$P - 20% of $P

Step-by-step explanation:

Here, we want to write an expression that corresponds to the price of a television set that is on sale at a price which is 20% off the regular price.

From the question, we can see that the regular price is $P

So now we are having 20% off;

This corresponds to;

20/100 * p = p/5 = 0.2p

So in the expression form, we can have;

$P - 20% of $P

Answer:

After 6 years = 87120 people.

Before 6 years = 5808 people.

Step-by-step explanation:

To calculate how many populations that are added in every 10% in 3 years:

72600 × 10/100 = 7260

After 6 years = 72600 + 7260 × 2 = 87120 people.

Before 6 years = 72600 - 7260 × 2 = 5808 people.