The perimeter of an equilateral triangle is 30 cm. Find the length of each side of the triangle.

Answer:

3 dolla

Step-by-step explanation:

Answer:

The awnser is 64

Step-by-step explanation:

It is 64 because you devide the perimiter (32) by 4, to get all sides, and then multiply 1 side by the other to get 64

THIS METHOD ONLY WORKS FOR A SQUARE

Answer:

C. [tex](5-\frac{1}{2})^6[/tex]

Step-by-step explanation:

Given

[tex]15(5)^2(-\frac{1}{2})^4[/tex]

Required

Determine which binomial expansion it came from

The first step is to add the powers of he expression in brackets;

[tex]Sum = 2 + 4[/tex]

[tex]Sum = 6[/tex]

Each term of a binomial expansion are always of the form:

[tex](a+b)^n = ......+ ^nC_ra^{n-r}b^r+.......[/tex]

Where n = the sum above

[tex]n = 6[/tex]

Compare [tex]15(5)^2(-\frac{1}{2})^4[/tex] to the above general form of binomial expansion

[tex](a+b)^n = ......+15(5)^2(-\frac{1}{2})^4+.......[/tex]

Substitute 6 for n

[tex](a+b)^6 = ......+15(5)^2(-\frac{1}{2})^4+.......[/tex]

[Next is to solve for a and b]

From the above expression, the power of (5) is 2

Express 2 as 6 - 4

[tex](a+b)^6 = ......+15(5)^{6-4}(-\frac{1}{2})^4+.......[/tex]

By direct comparison of

[tex](a+b)^n = ......+ ^nC_ra^{n-r}b^r+.......[/tex]

and

[tex](a+b)^6 = ......+15(5)^{6-4}(-\frac{1}{2})^4+.......[/tex]

We have;

[tex]^nC_ra^{n-r}b^r= 15(5)^{6-4}(-\frac{1}{2})^4[/tex]

Further comparison gives

[tex]^nC_r = 15[/tex]

[tex]a^{n-r} =(5)^{6-4}[/tex]

[tex]b^r= (-\frac{1}{2})^4[/tex]

[Solving for a]

By direct comparison of [tex]a^{n-r} =(5)^{6-4}[/tex]

[tex]a = 5[/tex]

[tex]n = 6[/tex]

[tex]r = 4[/tex]

[Solving for b]

By direct comparison of [tex]b^r= (-\frac{1}{2})^4[/tex]

[tex]r = 4[/tex]

[tex]b = \frac{-1}{2}[/tex]

Substitute values for a, b, n and r in

[tex](a+b)^n = ......+ ^nC_ra^{n-r}b^r+.......[/tex]

[tex](5+\frac{-1}{2})^6 = ......+ ^6C_4(5)^{6-4}(\frac{-1}{2})^4+.......[/tex]

[tex](5-\frac{1}{2})^6 = ......+ ^6C_4(5)^{6-4}(\frac{-1}{2})^4+.......[/tex]

Solve for [tex]^6C_4[/tex]

[tex](5-\frac{1}{2})^6 = ......+ \frac{6!}{(6-4)!4!)}*(5)^{6-4}(\frac{-1}{2})^4+.......[/tex]

[tex](5-\frac{1}{2})^6 = ......+ \frac{6!}{2!!4!}*(5)^{6-4}(\frac{-1}{2})^4+.......[/tex]

[tex](5-\frac{1}{2})^6 = ......+ \frac{6*5*4!}{2*1*!4!}*(5)^{6-4}(\frac{-1}{2})^4+.......[/tex]

[tex](5-\frac{1}{2})^6 = ......+ \frac{6*5}{2*1}*(5)^{6-4}(\frac{-1}{2})^4+.......[/tex]

[tex](5-\frac{1}{2})^6 = ......+ \frac{30}{2}*(5)^{6-4}(\frac{-1}{2})^4+.......[/tex]

[tex](5-\frac{1}{2})^6 = ......+15*(5)^{6-4}(\frac{-1}{2})^4+.......[/tex]

[tex](5-\frac{1}{2})^6 = ......+15(5)^{6-4}(\frac{-1}{2})^4+.......[/tex]

[tex](5-\frac{1}{2})^6 = ......+15(5)^2(\frac{-1}{2})^4+.......[/tex]

Check the list of options for the expression on the left hand side

The correct answer is [tex](5-\frac{1}{2})^6[/tex]

[tex]\text{Molly used the addition property of equality}\\\\\text{In the equation shown in the question, you can see that Molly is trying}\\\text{to find the value of "d"}\\\\\text{In order to do this, she must get the "d" variable by itself}\\\\\text{To do this, she adds "3d" to both sides to get the "d" variable on one side}\\\\[/tex]

Answer:

Jordan weighs 120 pounds, Sam weighs 60 pounds

Step-by-step explanation:

We can create an equation 2s=J. Our second equation is S+J=180. We can substitute J for 2s and our new equation will be 3s=180. We can divide 3 from both sides and we get s= 60. And we know that Jordan weighs two times as sam, then Jordan weighs 120 pounds.

Answer: Jordan=120. Sam=60

Step-by-step explanation: Together they weigh 180 pounds Jordan weighs twice as much as sam. We can write their values as Sam=x and Jordan=2x then we can make a equation

2x+x=180

3x=180

x=60

Then we can substitute x in Jordan and sams values to get our final answe;

Jordan=120. Sam=60

Answer:

-3.2 is the opposite of 3.2

2.3 is the opposite of -2.3

1.5 is the opposite of -1.5

-5.1 is the opposite of 5.1

Step-by-step explanation:

If your value is a positive, make it a negative

Ex. 3-->-3

If your answer is a negative, make it a positive

Ex. -3-->3

Answer:

-3.2 is the opposite of 3.2

2.3 is the opposite of -2.3

1.5 is the opposite of -1.5

-5.1 is the opposite of 5.1

Answer:

8mins

Step-by-step explanation:

(2x60)/15=8 I hope this helps, hope it's right

Answer:

8 minutes

Step-by-step explanation:

You will multiply 60 times 2 and then divide by 15 leaving you with 8

Answer:

I would try 10 again but this time put the degree sign in. Sometimes the computer registers in incorrect if it doesn't have a degree sign

Step-by-step explanation:

Also, this is a random note but in geometry, minutes and seconds are classified as smaller units in angles than degrees. 60 minutes is a degree and 60 seconds is a minute so that means 3600 seconds is a degree.

Answer:

y = 3x

Step-by-step explanation:

Assume a slope of 3

The y intercept is 0

The slope intercept form of the equation is

y= mx+b where m is the slope and b is the y intercept

y =3x+0

y = 3x

Answer:

A and C

Step-by-step explanation:

The roots of the quadratic function f(q) = q² - 125 are q = 5 and q = -5.

A function has an input and an output.

A function can be one-to-one or onto one.

It simply indicated the relationships between the input and the output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

The quadratic function f(q) = q² - 125 can be factored as (q - 5)(q + 5).

Now,

To find the roots, we set the function equal to zero and solve for q:

So,

q² - 125 = 0

(q - 5)(q + 5) = 0

q - 5 = 0 or q + 5 = 0

q = 5 or q = -5

Therefore,

The roots of the quadratic function f(q) = q² - 125 are q = 5 and q = -5.

Learn more about functions here:

https://brainly.com/question/28533782

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Answer:

f(x)/g(x) = 4x^2+6x-3  remainder -12

or

f(x)/g(x) = (4x^2+6x-3)/(2x+1) + (-12)/(2x+1)

or

((4x²+6x-3)-12)/(2x+1)

Step-by-step explanation:

f(x)= 8x³ + 16x² -15

g(x) = 2x+1.

Using long division,

f(x)/g(x) = 4x^2+6x-3  remainder -12

Answer:

Tina

Step-by-step explanation:

Since Amy owns the dog, she doesn't have the ferret and we know that Jewel doesn't have the ferret so the answer is Tina.

Answer:

According to the graph, f(−3)=3 and f(9)=-7

-7-3/9-(-3)= −10/12

Therefore the answer is -5/6

From Khan

The average rate of change over the interval [-3,9] will be 63 units per one unit change in y - value.

        [tex]b^x = \underbrace{b \times \dots \times b}_{x \text{ times}}[/tex]

        where : [m] → is slope of line and [c] → is the y - intercept

We have the following function -

f(x) = x³ - 9

The average rate of change would be -

r = {720 - (- 36)}/{9 - (- 3)}

r = 756/12

r = 63

Therefore, the average rate of change over the interval [-3,9] will be 63 units per one unit change in y - value.

To solve more questions on exponents, visit the link below-

https://brainly.com/question/28966438

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[ Complete question -

what is the average rate of change of f(x) = x³ - 9 over the interval [-3,9] ]

Answer:

The second option (see attached image)

Step-by-step explanation:

You are looking for a box diagram that represents 9 units, and from those, clearly marked sections that contain 3/2 = 1.5 units.The idea is to count how many 1.5 units you have in 9 units.

The in the second diagram you see 9 boxes subdivided in half. Then outlined in red other smaller boxes of length 1.5 units. We can clearly see from the diagram that there are exactly 6 of these smaller 1.5 units red boxes to produce the total 9 unit object.

Answer:

62.5°

Hope this helps :)

Answer:

pen: $1.50 notebook: $2.00

Step-by-step explanation:

4×1.50 =6

5×2 = 10

6+10= 16

3×1.50= 4.50

8×2= 16

4.50 + 16 = 20.50

Answer:

Neither

Step-by-step explanation:

This is a linear function as opposed to an exponential function as there are no x terms in higher powers.

Answer:

I graphed the function and its exponential growth

Step-by-step explanation:

Answer:

a + b = 12

Step-by-step explanation:

Given

Quadrilateral;

Vertices of (0,1), (3,4) (4,3) and (3,0)

[tex]Perimeter = a\sqrt{2} + b\sqrt{10}[/tex]

Required

[tex]a + b[/tex]

Let the vertices be represented with A,B,C,D such as

A = (0,1); B = (3,4); C = (4,3) and D = (3,0)

To calculate the actual perimeter, we need to first calculate the distance between the points;

Such that:

AB represents distance between point A and B

BC represents distance between point B and C

CD represents distance between point C and D

DA represents distance between point D and A

Calculating AB

Here, we consider A = (0,1); B = (3,4);

Distance is calculated as;

[tex]Distance = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]

[tex](x_1,y_1) = A(0,1)[/tex]

[tex](x_2,y_2) = B(3,4)[/tex]

Substitute these values in the formula above

[tex]Distance = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]

[tex]AB = \sqrt{(0 - 3)^2 + (1 - 4)^2}[/tex]

[tex]AB = \sqrt{( - 3)^2 + (-3)^2}[/tex]

[tex]AB = \sqrt{9+ 9}[/tex]

[tex]AB = \sqrt{18}[/tex]

[tex]AB = \sqrt{9*2}[/tex]

[tex]AB = \sqrt{9}*\sqrt{2}[/tex]

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

Calculating BC

Here, we consider B = (3,4); C = (4,3)

Here,

[tex](x_1,y_1) = B (3,4)[/tex]

[tex](x_2,y_2) = C(4,3)[/tex]

Substitute these values in the formula above

[tex]Distance = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]

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

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

[tex]BC = \sqrt{1 + 1}[/tex]

[tex]BC = \sqrt{2}[/tex]

Calculating CD

Here, we consider C = (4,3); D = (3,0)

Here,

[tex](x_1,y_1) = C(4,3)[/tex]

[tex](x_2,y_2) = D (3,0)[/tex]

Substitute these values in the formula above

[tex]Distance = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]

[tex]CD = \sqrt{(4 - 3)^2 + (3 - 0)^2}[/tex]

[tex]CD = \sqrt{(1)^2 + (3)^2}[/tex]

[tex]CD = \sqrt{1 + 9}[/tex]

[tex]CD = \sqrt{10}[/tex]

Lastly;

Calculating DA

Here, we consider C = (4,3); D = (3,0)

Here,

[tex](x_1,y_1) = D (3,0)[/tex]

[tex](x_2,y_2) = A (0,1)[/tex]

Substitute these values in the formula above

[tex]Distance = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]

[tex]DA = \sqrt{(3 - 0)^2 + (0 - 1)^2}[/tex]

[tex]DA = \sqrt{(3)^2 + (- 1)^2}[/tex]

[tex]DA = \sqrt{9 + 1}[/tex]

[tex]DA = \sqrt{10}[/tex]

The addition of the values of distances AB, BC, CD and DA gives the perimeter of the quadrilateral

[tex]Perimeter = 3\sqrt{2} + \sqrt{2} + \sqrt{10} + \sqrt{10}[/tex]

[tex]Perimeter = 4\sqrt{2} + 2\sqrt{10}[/tex]

Recall that

[tex]Perimeter = a\sqrt{2} + b\sqrt{10}[/tex]

This implies that

[tex]a\sqrt{2} + b\sqrt{10} = 4\sqrt{2} + 2\sqrt{10}[/tex]

By comparison

[tex]a\sqrt{2} = 4\sqrt{2}[/tex]

Divide both sides by [tex]\sqrt{2}[/tex]

[tex]a = 4[/tex]

By comparison

[tex]b\sqrt{10} = 2\sqrt{10}[/tex]

Divide both sides by [tex]\sqrt{10}[/tex]

[tex]b = 2[/tex]

Hence,

a + b = 2 + 10

a + b = 12

Answer:

a+b=6

Step-by-step explanation:

The tutor verified answer is mostly correct however, if you look under both by comperision sections you will see that it is:

[tex]4\sqrt{2}[/tex] and [tex]2\sqrt{10}[/tex] thus the answer is 4+2=6

Answer:

a) [tex]\boxed{-4}[/tex]

b) [tex]\boxed{26}[/tex]

c) [tex]\boxed{-12}[/tex]

d) [tex]\boxed{-9}[/tex]

e) [tex]\boxed{10}[/tex]

f) [tex]\boxed{-12}[/tex]

Step-by-step explanation:

1) [tex]\frac{41 - 3^2}{\sqrt{36}* 3-26 }[/tex]

=> [tex]\frac{41-9}{6*3-26}[/tex]

=> [tex]\frac{32}{18-26}[/tex]

=> [tex]\frac{32}{-8}[/tex]

=> -4

2) [tex]12+\sqrt[3]{8} * (9-2)[/tex]             ∴ [tex]\sqrt[3]{8} = 2[/tex]

=> [tex]12+2*(7)[/tex]

=> 12 + 14

=> 26

3) [tex]\frac{28-(7^2+3)}{-13+3*5}[/tex]

=> [tex]\frac{28-(49+3)}{-13+15}[/tex]

=> [tex]\frac{28-52}{2}[/tex]

=> [tex]\frac{-24}{2}[/tex]

=> -12

4) [tex]\frac{28}{4} - \sqrt[3]{8} * 2^3[/tex]

=> 7 - 2 * 8

=> 7 - 16

=> -9

5) [tex]7^2-5*8+1[/tex]

=> 49 - 40 + 1

=> 9 + 1

=> 10

6) [tex](2 * \sqrt{16} ) - (\sqrt[3]{27} * \sqrt{81} ) + 7[/tex]

∴  [tex]\sqrt{16} = 4, \sqrt[3]{27} = 3 , \sqrt{81} = 9[/tex]

=> (2 * 4) - (3 * 9) + 7

=> 8 - 27 + 7

=> -19 + 7

=> -12

Answer:

[tex]\boxed{\mathrm{view \: explanation}}[/tex]

Step-by-step explanation:

Apply order of operations to solve each expression.

[tex]\frac{41-9}{6 \times 3-26}[/tex]

[tex]\frac{41-9}{18-26}[/tex]

[tex]\frac{32}{-8}=-4[/tex]

[tex]12+2\times 7[/tex]

[tex]12+14=26[/tex]

[tex]\frac{28-(49+3)}{-13+15}[/tex]

[tex]\frac{28-52}{2}[/tex]

[tex]\frac{-24}{2} =-12[/tex]

[tex]7-2 \times 8[/tex]

[tex]7-16=-9[/tex]

[tex]49-40+1[/tex]

[tex]=10[/tex]

[tex](2 \times 4)-(3 \times 9) +7[/tex]

[tex]8-27+7[/tex]

[tex]=-12[/tex]

Answer: D

Step-by-step explanation:

In every other solution, x gets canceled out, so it has no impact on the equation.  Thus, A, B, and C all have either infinite or no solution, because they have 6x on both sides of the equation.

Further proof:

6x-6=15x+15

Add(6)

6x=15x+21

Subtract(15x)

-9x=21

Divide(-9)

x = -2 3/9

Hope it helps <3

Answer:

d) 6x - 6 = 15x + 15

Step-by-step explanation:

Well let’s solve.

a)

6x - 15 = 6x + 15

Lets use the communicative property which is the moving of numbers.

We can start with -15, so we do +15,

6x = 6x + 30

Then we can do -6x

0 = 30

This is a false statement meaning there is no solution.

b)

6x - 6 = 6x + 15

We can start by doing +6

6x = 6x + 21

-6x

0 = 21

Again, this is a false statement meaning this has no solutions.

c)

6x + 15 = 6x + 15

So we do -15

6x = 6x

If this is the case then there is infinitely many solutions.

d)

6x - 6 = 15x + 15

So we can start by doing +5p6

6x = 15x + 21

Then we can do -15x

-9x = 21

then we can do 21 / -9 which is -2 1/3.

x = -2 1/3

So this has one solution.

Answer:

[tex]y = -2x[/tex]

Step-by-step explanation:

Given

x || 0 || 1 || -2

y || 0 ||  -2 || 4

Required

Determine the function rule

First, we have to determine the slope of the function using;

[tex]m = \frac{y_1 - y_2}{x_1 - x_2}[/tex]

Where x and y represent any two corresponding values of x and y

When x = 0; y = 0  [tex](x_1,y_1)[/tex]

When x = 1; y = -2  [tex](x_2,y_2)[/tex]

Substitute these values in [tex]m = \frac{y_1 - y_2}{x_1 - x_2}[/tex]

[tex]m = \frac{0 - (-2)}{0 - 1}[/tex]

[tex]m = \frac{0 +2}{0 - 1}[/tex]

[tex]m = \frac{2}{- 1}[/tex]

[tex]m = -2[/tex]

Next, is to determine the function rule; using slope intercept form as follows;

[tex]y - y_1 = m(x - x_1)[/tex]

Take any corresponding values of x and y as x1 and x2

When x = -2; y = 4

[tex]y - y_1 = m(x - x_1)[/tex] becomes

[tex]y - 4 = -2(x - (-2))[/tex]

[tex]y - 4 = -2(x + 2)[/tex]

Open the bracket

[tex]y - 4 = -2x -4[/tex]

Add 4 to both sides

[tex]y - 4 + 4 = -2x - 4 + 4[/tex]

[tex]y = -2x[/tex]

Hence, the function rule is [tex]y = -2x[/tex]

Answer:

y = -2 x - 1

Step-by-step explanation:

Answer:

c. (x-3) is not a factor.

Step-by-step explanation:

Answer:

x=25

Step-by-step explanation:

To find x (hypotenuse), it is a^2+b^2=c^2

24^2+7^2=625

[tex]\sqrt{625}[/tex]=25

x=25

Hope this helps!!

3x+4y=12 is Linear.

y-1/2x+6 is Linear.

y=4x^2 is nonlinear.

y+2=|4| is linear.

y+6=4x is linear.

In order to tell whether an equation is linear or not, you have to first see if there is any variable^2 or more than ^1. If that is the case, it isn't linear. For example the equation x^2=4 or y^5=100 isn't linear. It also isn't linear if the equation is divided by X or Y.For example the equation 1/x=1 isn't linear or 1/y^2=5 isn't linear.

A question is also linear if you can write it in the form y=mx+b , 'm' meaning the slope of the equation and 'b' meaning the y-intercept of the equation.

Answer: The answer is the picture shown below

Step-by-step explanation:

To do this you will need to make a coordinate plane about 20 up and 20 down. So there is a formula that is y=mx+b which is called the slope intercept form and as you can see the problem given to you was already given in this formula. The variable m in the equation is the slope and slope is also known as rise (which basically means go up if positive and down if negative) over run (which is right if positive and left if negative) and as you can see in the equation the number 4/5 is the variable m. Since slope is rise over run 4 would be the rise and 5 would be the run, so you would go up 4 and right 5 because they are both positive. Now there is another variable that is b which would be the -1. In slope intercept formula b is the y intercept so -1 is where the line would cross the y axis. Now that you know all the parts to the slope you can put it together giving you the answer.

Answer:

Step-by-step explanation:

[tex]y=\dfrac{4}{5}x-1[/tex]

This is an equation for a line in the slope-intercept form.

For the straight line we only need two points on the coordinate plane.

Choose two x values. Place them in the equation and calculate the y values.

For x = 0:

[tex]y=\dfrac{4}{5}(0)-1=0-1=-1\to(0,\ -1)[/tex]

For x = 5:

[tex]y=\dfrac{4}{5}(5)-1=4-1=3\to(5;\ 3)[/tex]

Mark points on the coordinate plane and draw a line through these points.

Answer:

Total mass of materials = 4.8kg

For gravel

55% of the materials are gravel

So we have

55/100 × 4.8 kg

= 2.64kg

For sand

30% of the materials are sand

We have

30/100 × 4.8

= 1.44kg

For cement

The remaining materials were cement so we add the masses of both the sand and gravel and subtract it from the total mass

That's

4.8 - (2.64 + 1.44)

4.8 - 4.08

= 0.72 kg

She earns £ 800 per week

She receives a raise of 7.5% which is

100 + 7.5 = 107.5%

So we have

107.5 / 100 × £ 800

= £ 860

She now earns £ 860 per week

Hope this helps you

Step-by-step explanation:

1)of 4.8kg concrete 55% is gravel,30% is sand and 15% is cement.

percent=Rate*Base

Pgravel=55%*4.8kg

Pgravel=2.64kg

Psand=30%*4.8kg

Psand=1.44kg

Pcement=15%*4.8kg

Pcement=0.72kg

2)percent=Rate*Base

percent=7.5%*£800

percent=60£

total earn=60£ + £800

total earn=£860

Answer:what!?

Step-by-step explanation:

Answer:

102

Step-by-step explanation:

Since 2 + 8 = 10, then the cube root of 5x+2 = 8

Since 8×8×8=512, then 5x+2=512

5x=510, so x=102

Answer:

C) 102

Step-by-step explanation:

Hello !

2 + ∛(5x + 2) = 10

∛(5x + 2) = 10 - 2

∛(5x + 2) = 8

(∛(5x + 2))³ = 8³

5x + 2 = 512

5x = 512 - 2

5x = 510

x = 510 : 5

x = 102

Good luck !