ABC is an equilateral triangle, solve y

Answer:

11.21157846 =x

Step-by-step explanation:

We know log b (a) = c  can be written as b^c =a

log 3 (x) = 2.2

3^2.2 = x

11.21157846 =x

Answer:

[tex]\large \boxed{\sf \bold{A.} \ x=11.21}[/tex]

Step-by-step explanation:

[tex]\large \sf log_3 (x)=2.2[/tex]

Solve this by converting the logarithmic statement into its equivalent exponential form, using the relationship:

[tex]\large \sf log_b(y)=x[/tex]

[tex]\large{\sf y=b^x}[/tex]

Apply the relationship.

[tex]\large \sf log_3 (x)=2.2[/tex]

[tex]\large \sf x=3^{2.2}[/tex]

[tex]\large \sf x=11.21157845...[/tex]

[tex]\large \sf x \approx 11.21[/tex]

Answer:

The answer is (3×7) + (12×2) .

[tex](3 \times 7) + (12 \times 2)[/tex]

[tex] = 21 + 24[/tex]

[tex] = 45[/tex]

Answer: 1880 pounds

Step-by-step explanation: when you take the average adult weight, around 160 lbs. you multiply that by eight. you get 1280. then you estimate that each of the children weigh around 100 lbs, then you add 600 to 1280 and get 1,880 lbs

Answer:

18

Step-by-step explanation:

3⋅6−2+2​

Use PEMDAS = Parentheses, Exponent, Multiplication, Division, Addition, Subtraction

First we multiply, then add or subtract so,

18 - 2 + 2

Now we subtract,

16 + 2

Now we add,

18

Answer:

(A) [tex]y = x+3[/tex]

Step-by-step explanation:

Using the values of (-6, -3), (3,6), and (5,8) we can substitute the values into each equation and see if the equation meets the requirements for all 3.

Let's test A first.

[tex]-3 = -6+3[/tex]

Correct, let's try the second pair.

[tex]6 = 3+3[/tex]

Correct, let's try the third pair.

[tex]8 = 5+3[/tex]

So yes, this equation works.

For fun, let's try the other equations.

Let's test B.

[tex]-3 = -6-3[/tex]

This is not true as -6 -3 = -9. So this equation is immediately ruled out.

Let's test C.

[tex]-3 = 2\cdot-6[/tex]

Again this doesn't work, as -6 times 2 is -12. So this equation is also ruled out.

Let's try D.

[tex]-3 = \frac{1}{2}\cdot-6[/tex]

This works, as half of -6 is -3 - however the equation will only work if all 3 pairs work for it.

Let's try the second pair.

[tex]6 = \frac{1}{2}\cdot3[/tex]

This doesn't work, as half of 3 is 1.5. This equation is also ruled out.

Therefore, A is the only equation that works with these pairs.

Hope this helped!

Answer:

-3=x <13

Step-by-step explanation:

[tex] - 9 = \frac{2x}{3} - 7 < 5[/tex]

Multiply through by 3

[tex] - 27 = 2x - 21 < 15[/tex]

Add 21 to all sides

[tex] - 6 = 2x < 36[/tex]

Divide through by 2

[tex] - 3 = x < 18[/tex]

The solutin set is

[tex]{- 3 = x < 18}[/tex]

Answer:

Step-by-step explanation:

We first need to find h. Since h is the x coordinate of Q, and Q is on the line 3x + 4y = 6, we will plug in the x value of h and the y value of 3 and solve for h:

3h + 4(3) = 6 and

3h + 12 = 6 and

3h = -6 so

h = -2

The coordinates for Q are (-2, 3). Now we can use that to find the slope of the line QR:

[tex]m=\frac{8-3}{3-(-2)}=\frac{5}{5}=1[/tex]

So the slope of QR is 1. Now we will choose one of the coordinates on line QR as our x and y coordinates to write the equation for the line in point slope form then in standard form:

y - 8 = 1(x - 3) and

y - 8 = x - 3 and

y - x = 5 or

-x + y = 5. If your teacher does not want you to lead with a negative:

x - y = -5 would be your equation in standard form.

Answer:

When x = -4 and y = -6, p = 37.75

Step-by-step explanation:

Given that p = x² - y²/x² + x·y, we have;

p = (x² × x² -y² + x·y×x²)/x²

p = (x²⁺² - y² + x¹⁺² × y)/x²

p = (x⁴ - y² + x³·y)/x²

Therefore, p in the simplest form is given as follows;

[tex]p = \dfrac{x^4 - y^2 + x^3 \cdot y }{x^2}[/tex]

To find the value of p when x = -4 and y = -6, we plug in the value of x and y into the above equation to get the following equation;

[tex]p = \dfrac{(-4)^4 - (-6)^2 + (-4)^3 \cdot (-6) }{(-4)^2} = 37.75[/tex]

Therefore, the value of p when x = -4 and y = -6 is equal to 37.75.

Answer: terminating

Step-by-step explanation:

Answer:

7.2 is a terminating decimal.

Step-by-step explanation:

Terminating decimals are decimals that have an end point. The decimal does not continue to go on and on with numbers but, it stops at one number which makes it terminating.

Repeating decimals are decimals that go on and on with the same number or same patterns of numbers.

So, since 7.2 has an endpoint, then it is a terminating decimal.

Answer:

reflection across y = x

Step-by-step explanation:

Transformation is the movement of a point from its initial position to a new position. If a shape is transformed, all its point are also transformed. Types of transformation is reflection, rotation, transformation and dilation.

If a point is reflected across the x axis, the x coordinate is the same but the y coordinates is negated. If X(x, y) is reflected across the x axis the new point is X'(x, -y)

If a point is reflected across the y axis, the y coordinate is the same but the x coordinates is negated. If X(x, y) is reflected across the y axis the new point is X'(-x, y)

If a point is reflected across y = x, the x coordinate and y coordinates are interchanged. If X(x, y) is reflected across the y=x axis the new point is X'(y, x)

If a point is reflected across y = -x, the x coordinate and y coordinates are interchanged and both negated. If X(x, y) is reflected across the y=ix axis the new point is X'(-y, -x)

The vertices of △ABC are A(-1, 3), B(2, 4), and C(-5, 6). The vertices of △A′B′C′ are A′(3, −1), B′(4, 2), and C′(6, −5). The reflection of △ABC to form​​ ​△A′B′C′ shows a reflection across x axis since the x and y coordinates are interchanged

Answer:

reflection across y = x

Step-by-step explanation:

Let x = weight and y = height. It is possible to have a certain weight correspond to multiple heights. This means the input x has multiple output y values. Therefore, we cannot have a function here. A function is only possible if for any x input, there is exactly one y output. The x value must be in the domain.

Answer:

11.8%

Step-by-step explanation:

Here in this question, we want to find the probability of no success in the binomial experiment for 6 trials.

Let p = probability of success = 30% = 30/100 = 0.3

q = probability of failure = 1-p = 1-0.3 = 0.7

Now to calculate the probability, we shall need to use the Bernoulli approximation of the binomial theorem.

That would be;

P(X = 0) = 6C0 p^0 q^6

6C0 is pronounced six combination zero

= 6 * 0.3^0 * 0.7^6 = 1 * 1 * 0.117649 = 0.117649

This is approximately 0.1176

If we convert this to percentage we have 11.76%

But we want our answer rounded to the nearest tenth of a percent and that is 11.8%

Hi there! :)

Answer:

[tex]\huge\boxed{m\leq 2}[/tex]

Equation:

8m - 6 ≤ 10

Add 6 to both sides:

8m ≤ 16

Divide both sides by 8:

8m/8 ≤ 16/8

m ≤ 2

Answer:

8m - 6≤ 10

m≤2

Step-by-step explanation:

8m - 6≤ 10

Add 6 to each side

8m - 6+6≤ 10+6

8m ≤ 16

Divide each side by 8

8m/8 ≤16/8

m≤2

Answer:

about 11.03 million

Step-by-step explanation:

Use the equation I = P(1+r/100)^n - P (I is the compound interest, P is the principle, r is the rate percent, and n is the number of years):

Substitute the values given:

I = 70,000,000(1 + 5/100)^3 - 70,000,000

Use a calculator to solve and you will get ~11.03 million.

The formula for the amount earned with compound interest after n years is given as:

A = P [tex](1 + r/n)^{nt}[/tex]

P = principal

R = rate

t = time in years

n = number of times compounded in a year.

The interest the company paid is $11 million.

It is the interest we earned on the interest.

The formula for the amount earned with compound interest after n years is given as:

A = P [tex](1 + r/n)^{nt}[/tex]

P = principal

R = rate

t = time in years

n = number of times compounded in a year.

We have,

P = $70 million

r = 5%

t = 3 years

n = 1

A = 70 ( 1 + 0.05)³

A = 70 ( 1.05)³

A = 70 x 1.05 x 1.05 x 1.05

A = $81 million

The amount of interest.

= A - P

= 81 - 70

= $11 million

Thus,.

The interest the company paid is $11 million.

Learn more about compound interest here:

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Answer:

Step-by-step explanation:

Since we are finding cos A we have

From the question

AC = √96

AB = 14

Substitute the values into the above formula

That's

We have the final answer as

Hope this helps you

Answer:

(7, 5)

Step-by-step explanation:

(x+5)/2, ( y-3)/2)=(6,1)

(x+5)/2=6, x= 7

( y-3)/2=1, y=5

Answer:

Area : 14+10+40=64 square unit

Step-by-step explanation:

the area of the top rectangle with sides  2 and 7

A=2*7=14 square unit

the area of the middle rectangle with sides : (7-5)=2 and side (7-2)=5

Area=5*2=10 square unit

the bottom rectangle : sides 10 and 4

Area=10*4=40

add the areas : 14+10+40=64 square unit

Answer:

10800

Step-by-step explanation:

1 trimesters cost = 1450 + 350  $

2 year -> 6 trimester

1800$ x 6 = 10800 $

Answer:

The answer is

Step-by-step explanation:

The distance between two points can be found by

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

where

( x1 , y1) and ( x2 , y2) are the points

So the distance between (-4,4) and (1,0) is

We have the final answer as

Hope this helps you

Answer:

4 2^(1/3) or 5.0396841995794926590688424291129134022810058588060319203279004486... decimal

Step-by-step explanation:

Simplify the following:

(2^(1/3))^7

Hint: | For all a>=0, (a^(1/3))^m = a^(m/3). Apply this to (2^(1/3))^7.

Multiply exponents. (2^(1/3))^7 = 2^(7/3):

2^(7/3)

Hint: | Separate the exponent of 2^(7/3) into integer and fractional parts.

2^(7/3) = 2^(6/3 + 1/3) = 2^(6/3)×2^(1/3):

2^(6/3) 2^(1/3)

Hint: | Divide 6 by 3.

6/3 = (3×2)/3 = 2:

2^2 2^(1/3)

Hint: | Evaluate 2^2.

2^2 = 4:

Answer:  4 2^(1/3) or 5.0396841995794926590688424291129134022810058588060319203279004486... decimal

Answer:

--1-- (of set 23456)

2   4

5 3

 6

--2-- (of set 23456)

2   3

5 4

 6

--3-- (of set 23456)

2   5

6 3

 4

--4-- (of set 23456)

2   3

6 5

 4

--5-- (of set 23456)

3   5

4 2

 6

--6-- (of set 23456)

3   2

4 5

 6

--7-- (of set 23456)

3   6

5 2

 4

--8-- (of set 23456)

3   2

5 6

 4

--9-- (of set 23456)

3   5

6 4

 2

--10-- (of set 23456)

3   4

6 5

 2

--11-- (of set 23456)

4   5

3 2

 6

--12-- (of set 23456)

4   2

3 5

 6

--13-- (of set 23456)

4   6

5 3

 2

--14-- (of set 23456)

4   3

5 6

 2

--15-- (of set 23456)

5   4

2 3

 6

--16-- (of set 23456)

5   3

2 4

 6

--17-- (of set 23456)

5   6

3 2

 4

--18-- (of set 23456)

5   2

3 6

 4

--19-- (of set 23456)

5   6

4 3

 2

--20-- (of set 23456)

5   3

4 6

 2

--21-- (of set 23456)

6   5

2 3

 4

--22-- (of set 23456)

6   3

2 5

 4

--23-- (of set 23456)

6   5

3 4

 2

--24-- (of set 23456)

6   4

3 5

 2

--1-- (of set 34567)

3   5

6 4

 7

--2-- (of set 34567)

3   4

6 5

 7

--3-- (of set 34567)

3   6

7 4

 5

--4-- (of set 34567)

3   4

7 6

 5

--5-- (of set 34567)

4   6

5 3

 7

--6-- (of set 34567)

4   3

5 6

 7

--7-- (of set 34567)

4   7

6 3

 5

--8-- (of set 34567)

4   3

6 7

 5

--9-- (of set 34567)

4   6

7 5

 3

--10-- (of set 34567)

4   5

7 6

 3

--11-- (of set 34567)

5   6

4 3

 7

--12-- (of set 34567)

5   3

4 6

 7

--13-- (of set 34567)

5   7

6 4

 3

--14-- (of set 34567)

5   4

6 7

 3

--15-- (of set 34567)

6   5

3 4

 7

--16-- (of set 34567)

6   4

3 5

 7

--17-- (of set 34567)

6   7

4 3

 5

--18-- (of set 34567)

6   3

4 7

 5

--19-- (of set 34567)

6   7

5 4

 3

--20-- (of set 34567)

6   4

5 7

 3

--21-- (of set 34567)

7   6

3 4

 5

--22-- (of set 34567)

7   4

3 6

 5

--23-- (of set 34567)

7   6

4 5

 3

--24-- (of set 34567)

7   5

4 6

 3

Step-by-step explanation:

This javascript code is extremely brute-force, but it does the job:

function checkIfInSet(i, set) {

   return i.toString().split('').sort().join('') === set;

}

function checkIfMagic(s) {

   return (parseInt(s[0]) + parseInt(s[1]) == parseInt(s[3]) + parseInt(s[4]))

}

function printMagic(s) {

   console.log(`${s[0]}   ${s[4]}`);

   console.log(` ${s[1]} ${s[3]}`);

   console.log(`  ${s[2]}\n`);

}

function checkSet(set) {

   let counter = 1;

   for(let i=1; i<99999; i++) {

       if (checkIfInSet(i, set) && checkIfMagic(i.toString())) {

           console.log(`--${counter++}-- (of set ${set})`);

           printMagic(i.toString());

       }

   }

}

checkSet('23456');

checkSet('34567');

Answer:Conversion units

Step-by-step explanation: 1 ft^3= 0.028m^3 .: 1440ft^3=40.776m^3, so $1.75x40.776=$71.358~ $71.36.:

Answer:

$71.36

Step-by-step explanation:

1 foot = 0.3048 metros

1 cubic feet = (0.3048metros)³ = 0.02932 cubic meters   (aprox.)

1440 cubic feet = 1440*0.02932 = 40.7763 m

$1.75 por cubic meter:

1.75*40.7763 = $71.36

Answer:

One thousand two hundred and forty five.

Hope this helps! （づ￣3￣）づ╭❤～

Step-by-step explanation:

verifying, by putting [tex] \theta=60^{\circ}[/tex]

LHS≠RHS

hence the question is FALSE

Answer:

21.4 m²

Step-by-step explanation:

To find the surface area of this whole triangular prism, we have to look at the bases (the triangles), find their surface area, then look at the sides (the rectangles) and find theirs.

Let's start with the triangles. The area of any triangle is [tex]\frac{bh}{2}[/tex]. The base of this triangle is 2m (because there are 2 one meters) and the height is 1.7m.

[tex]\frac{2\cdot1.7}{2} = \frac{3.4}{2} = 1.7[/tex]

So the area of one of these triangles is 1.7m. Multiplying this by two, because there are two triangles in this prism:

[tex]1.7\cdot2=3.4[/tex]

Now let's find the area of the sides.

The side lengths are 2 and 3, so

[tex]2\cdot3=6[/tex], and there are 3 sides (including the bottom/floor) so [tex]6\cdot3=18[/tex].

Now we add.

[tex]18+3.4=21.4[/tex] m².

Hope this helped!

Answer: 21.4 square meters^2

Step-by-step explanation:

The product of (4z² + 7z – 8) and (–z + 3) is -4z³ + 5z² + 29z - 24

(4z² + 7z – 8) and (–z + 3)

= -4z³+ 12z² - 7z² + 21z + 8z - 24

= -4z³ + 5z² + 29z - 24

Therefore, the product of (4z² + 7z – 8) and (–z + 3) is -4z³ + 5z² + 29z - 24

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Answer:

-6xy - 16x -24y -64

Step-by-step explanation:

(2x+8)(-3y-8) =

To find the answer,

First multiply, the first number on both sides,

2x * -3y = -6xy

Then the first number on the left side and the second number on the right side,

2x * -8 = -16x

Then the second number on the left side and the first number on the right side,

8 * -3y = -24y

Then the second number on the left side and the second number on the right side,

8 * -8 = -64

Now add all the answers,

-6xy -16x -24y -64

Answer:

-6xy-16x-24y-64

Step-by-step explanation:

(2x+8)(-3y-8)​

Foil

First 2x*-3y = -6xy

outer -8*2x = -16x

inner -3y *8 = -24y

last -8*8 = -64

Add them together

-6xy-16x-24y-64

For a given initial quantity A, a decrease of x% can be written as:

A - A*(x%/100%) = A*(1 - x%/100%)

With this, we need to construct an exponential decrease equation for the given situation, and we will find that the equation is:

P(t) = 300*(0.77)^t

Now let's see how we found that.

In this case, we know that:

The initial number of animals is 300.

They decrease at an anual rate of 23%.

This means that after the first year, the population will be:

P(1) = 300 - 300*(23%/100$) = 300*( 1 - 0.23) = 300*(0.77)

After another year, the population decreases again, so we get:

P(2) = 300*(0.77) - 300*(0.77)*(23%/100$) = 300*(0.77)^2

Here we already can see the pattern, the population in the year t, we will get:

P(t) = 300*(0.77)^t

Then we can see that the correct option is C.

If you want to learn more, you can read:

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Answer:

80 feet

Step-by-step explanation:

1 inch represents 10 feet

Then 8 inches represent = 8 × 10

= 80 feet