help plsss ! 10 points !

Answer:

M = -3

4(10m + 30)/5 = -3(m+3)

4x10(m+3)/5 = -3(m+3)

40(m+3)

​​ =−3(m+3)

8(m+3)=−3(m+3)

8m+24=−3m−9

8m+24+3m=−9

11m+24=−9

11m=−9−24

11m=−33

m=−

​11

​

​33

​​

m=−3

Hope I helped

Answer:

x < 6/7

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Step-by-step explanation:

Step 1: Define

7x/3 < 2

Step 2: Solve for x

Here we see that any value x smaller than 6/7 would work as a solution to the inequality.

Answer:

Sara could list the factors of 18 and 30 and then find the greatest value that the lists have in common. The length of the longest equal-sized pieces that she can cut from both boards with no wood left over, is 3 inches. She will be able to cut 6 pieces from the 18-inch board and 10 pieces from the 30-inch board. She will have enough wood to cut 10 equal-sized pieces for her club project.

Hope this helps you Merry Christmas!!!!

Answer:

1/12 of a gallon per day

Step-by-step explanation:

1/2 or 0.5 divided by 6 is .083333333 or 1/12

Answer:

1/12

Hope it helps ;)

Answer:

(x−2)(x−7)

Step-by-step explanation:

Answer:

Step-by-step explanation:

x^2 - 9x + 14

(x - 7)(x - 2)

Answer 1 -16 3y-2 >16 k-1 >24 -8.8x>24-8.8x<32

Step-by-step explanation:

k>3, x> - 10-11,y>2-3 (128k-127)

Answer:

Step-by-step explanation:

From the triangle KNM, we can see that two of the angles M K N and Angle N M K are the same. If two of the angles are equal this means that two of the sides of the triangles are also equal. This type of triangle is known as an ISOSCELES TRIANGLE.

An isosceles triangle is a triangle that has two of its angles and sides to be equal.

Answer:

km =nm

Step-by-step explanation:

Answer:

3ab(4a + 5b)

Step-by-step explanation:

Given

12a²b + 15ab² ← factor out 3ab from each term

= 3ab(4a + 5b)

Answer:

The first answer is correct, 3ab(4a + 5b)

Step-by-step explanation:

[tex]12a^2b + 15ab^2\\= 3ab(4a + 5b)[/tex]

Answer:

431 and 43

Step-by-step explanation:

Two numbers: y1 and y

Number one: y1 = 10 * y + 1

(10 * y + 1) + y = 474

11y = 473

y = 43

Two numbers: 431 and 43

check: 431 remove 1 (digit) -> 43

431+43=474

Answer:

it should be 7

Step-by-step explanation:

Answer:

you basically divide y/x for tables. on a graph you just try to find the constant k

Step-by-step explanation:

Answer:

c= 3.4

Step-by-step explanation:

Answer:

B. 3:5

Step-by-step explanation:

3+4=7

12-7=5

Pepperoni = 3

Cheese = 5

Answer:

x = 0.76

Step-by-step explanation:

plugged it into calculator

Answer:

y ≥ -3

Step-by-step explanation:

When we talk of the range of a function, we are referring to the y-values which are possible for the function to take

From the diagram, we can see that the y-values starts from -3 which shows it is inclusive and extends from it

So, the possible range values of the function are values of y starting from -3 and above it

In inequality sign, we can have this as

y ≥ -3

Answer:

They cost 3.89 bc 35.01 ÷ 9 is 3.89 and 3.89 × 9 is 35.01

Answer:

13x - 4 + 80 = 180⁰ (Sum of co interiar angles)

13x +76 = 180⁰

13x = 180⁰ - 76⁰

x = 104/13

x = 8

Answer:

(-2)

Step-by-step explanation:

We have to find the determinant of the given matrix,

[tex]A=\begin{bmatrix}(a-1) & (a^2-a+1)\\ (a+1) & (a^2+a+1)\end{bmatrix}[/tex]

det A = (a - 1)(a² + a + 1) - (a + 1)(a² - a + 1)

         = a(a² + a + 1) - 1(a²+ a + 1) - a(a² - a + 1) - 1(a² - a + 1)

         = a³ + a² + a - a² - a - 1 - a³ + a² - a - a² + a - 1

         = (a³ - a³) + (-a² + a² - a² - a²) - 1 - 1

         = -2

Therefore, determinant of the given matrix is (-2).

Answer:

8

Step-by-step explanation:

add 4 plus 4 then omg watch this you get 8 abracadabra....

you're welcome

8

Step-by-step explanation:

Answer:

The interest rate is 5.278%

Step-by-step explanation:

4298.55=1987.22(1+r/100)^15

r=5.278%

The answer.................................. is x=-2

Answer: I guess B

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

trust me

Problem 1

Since point P is the tangent point, this means angle OPT is a right angle

angle OPT = 90 degrees

Let's use the Pythagorean theorem to find the missing side 'a'

a^2 + b^2 = c^2

a^2 + 7^2 = 12^2

a^2 + 49 = 144

a^2 = 144 - 49

a^2 = 95

a = sqrt(95)

a = 9.7467943

a = 9.7

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

Let's use the sine and arcsine rule to find angle y

sin(angle) = opposite/hypotenuse

sin(y) = 7/12

y = arcsin( 7/12 )

y = 35.6853347

y = 35.7

The value of y is approximate. Make sure your calculator is in degree mode. Arcsine is the same as inverse sine or [tex]\sin^{-1}[/tex]

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

Problem 2

Focus on triangle OHP. This may or may not be a right triangle. The goal is to test if it is or not.

We use the converse of the Pythagorean theorem to check.

Recall that the converse of the Pythagorean theorem says: If a^2+b^2 = c^2 is a true equation, then the triangle is a right triangle. The value of c is always the longest side. The order of a and b doesn't matter.

In this case we have

Which leads to

a^2 + b^2 = c^2

7^2 + 13^2 = 16^2

49 + 169 = 256

218 = 256

We get a false equation at the end, since both sides aren't the same number, which means the original equation is false.

We don't get a^2 + b^2 = c^2 to be true, therefore this triangle is not a right triangle.

Consequently, this means angle OPH cannot possible be 90 degrees (if it was then we'd have a right triangle). Therefore, point P is not a tangent point.

You follow the same basic idea for triangle OQH and show that point Q is not a tangent point either. Or you could use a symmetry argument to note that triangle OPH is a mirror reflection of triangle OQH over the line segment OH. This implies that whatever properties triangle OPH has, then triangle OQH has them as well for the corresponding pieces.

y˚ = 36˚

a = 9.7

How to find the value of a

When there is a line that’s tangent of a circle, it’s ALWAYS going to be perpendicular to the line of the centre of the circle. So you can see that line PT is perpendicular to the line that comes out from the centre of the circle (the line that’s labeled as PO, or labeled as a length of 7). This means that it forms a right angle (two lines that are perpendicular to each other).

Like the other problem I solved for you, you can use the Pythagorean Theorem ([tex]a^{2}+b^{2}=c^{2}[/tex]) to find what a is, because you can see that it forms a triangle in the diagram. But here is one main thing to know when using the Pythagorean Theorem: The triangle HAS TO BE a right triangle, meaning that it has to have a right angle. But we already proved that it forms a right angle because line PT is perpendicular/tangent to line PO (labeled as a length of 7). So, we can for sure use the Pythagorean Theorem. The steps are shown below:

Steps (the variables a, b, and c are in italics so it’s not confusing to look at):

-You can rearrange the formula from the Pythagorean Theorem, which is [tex]a^{2}+b^{2}=c^{2}[/tex] to only get a because we want to know what a is.

Rearranged formula: [tex]a=\sqrt{c^{2} -b^{2} }[/tex]  or  [tex]a=-\sqrt{c^{2} -b^{2} }[/tex]  It has to ways/options for a to equal because when finding the square root of a number, it can be either positive or negative. But in this problem, it’s going to be positive because we’re finding the length of something.

-The variable c in the formula means the hypotenuse of the triangle. In the diagram, you can see that 12 is the hypotenuse, which means that b is 7.

-Since we know what c and b are, you can plug them into the new formula:

[tex]a=\sqrt{12^{2}-7^{2} }[/tex]

-Simplify it:

[tex]a=\sqrt{144-49}[/tex]

-Subtract inside the radical:

[tex]a=\sqrt{95}[/tex]  Then simplify it to get: [tex]a= 9.74679434...[/tex]  And it wants us to round to the nearest tenth. So you finally get [tex]a=9.7[/tex].

You can check your answer by putting a back into the original Pythagorean Theorem formula ([tex]a^{2} +b^{2}= c^{2}[/tex]):

Steps

-Plug a, b, and c into the formula (use [tex]\sqrt{95}[/tex] for a because using a rounded decimal won’t give you an exact answer):

[tex](\sqrt{95^{2}})+(7^{2})=(12^{2})[/tex]

-Simplify to get:

[tex]95+49=144[/tex]

-Add:

[tex]144=144[/tex]

This is very true. So our answer is correct.

ANSWER: [tex]a=9.7[/tex]

How to solve for y˚

Since all three angles in a triangle add up to 180˚ and you already know two of them, you should know what the third one is. The two angles that are given are 90˚ (because it’s a right triangle) and 54˚.

You can be written as:

90˚ + 54˚ + y = 180˚

Solve for y:

144˚ + y = 180˚

Subtract 134˚ from both sides to get y by itself:

y = 36˚

ANSWER: y˚ = 36˚

___________________________________________________________

Reminder for you: If you don’t remember from the very beginning on the top of the the page, I said that inorder to know if a line is tangent, it’s ALWAYS going to be perpendicular to the line of the centre of the circle.

So we need to test if line PH is perpendicular to the line that comes out from the centre of the circle (the line that’s labeled as PO, or labeled as a length of 7 cm).

We can do this by using the Pythagorean Theorem ([tex]a^{2}+b^{2}=c^{2}[/tex]) because if you still don’t remember what I said at the very beginning, I said that there is one main thing to know when using the Pythagorean Theorem: The triangle HAS TO BE a right triangle, meaning that it has to have a right angle.

So we can use the Pythagorean Theorem to find if line PH and line PO (labeled as 7 cm) are perpendicular/form a right angle.

Here are your mathematical calculations of the answer:

-Plug the values from the numbers that are from the triangle:

[tex]13^{2} +7^{2} =16^{2}[/tex]  (16 is the hypotenuse, c, because it’s the longest side of the triangle)

-Simplify:

[tex]169+49=256[/tex]

-Add:

[tex]218=256[/tex]

This is false because 218 does not equal 256. Therefore, the triangle does not have a right angle, which means that line PH is not perpendicular/tangent to line PO.

ANSWER: The wire is not a tangent to the circle at P and at Q because when using the Pythagorean Theorem to prove if line PH is perpendicular to line PO, the result is false.

Sorry for the very, very, long explanation. But hopefully you understand and that this helps with your question! :)

Answer:

3x+17=8mVwx+12

Step-by-step explanation:

I used a calculator so... I guess trust the calc?

Answer:

Step-by-step explanation:

he concept of direct variation is summarized by the equation below.

We say that yy varies directly with xx if yy is expressed as the product of some constant number kk and xx.

Cases of Direct Variation

However, the value of kk can’t equal zero, i.e. k \ne 0k  



​  

=0.

Case 1: k > 0k>0 (kk is positive)

If xx increases then the value of yy also increases, or if xx decreases then the value of yy also decreases.

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Case 2: k < 0k<0 (kk is negative)

If xx increases then the value of yy decreases, or if xx decreases then the value of yy increases.

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Arithmetic Sequence Formula Problem #1 Video

If we isolate kk on one side, it reveals that kk is the constant ratio between yy and xx. In other words, dividing yy by xx always yields a constant output.

k=y/x

kk is also known as the constant of variation, or constant of proportionality.

Examples of Direct Variation

Example 1: Tell whether yy varies directly with xx in the table below. If yes, write an equation to represent the direct variation.

Solution:

To show that yy varies directly with xx, we need to verify if dividing yy by xx always gives us the same value.

Since we always arrived at the same value of 22 when dividing yy by xx, we can claim that yy varies directly with xx. This constant number is, in fact, our k = 2k=2.

To write the equation of direct variation, we replace the letter kk by the number 22 in the equation y = kxy=kx.

When an equation that represents direct variation is graphed in the Cartesian Plane, it is always a straight line passing through the origin.

Think of it as the Slope-Intercept Form of a line written as

y = mx + by=mx+b where b = 0b=0

Here is the graph of the equation we found above.

Example 2: Tell whether yy varies directly with xx in the table below. If yes, write an equation to represent direct variation.

Solution:

Divide each value of yy by the corresponding value of xx.

The quotient of yy and xx is always k = - \,0.25k=−0.25. That means yy varies directly with xx. Here is the equation that represents its direct variation.

Here is the graph. By having a negative value of kk implies that the line has a negative slope. As you can see, the line is decreasing from left to right.

In addition, since kk is negative we see that when xx increases the value of yy decreases.

Example 3: Tell whether if yy directly varies with xx in the table. If yes, write the equation that shows direct variation.

Solution:

Find the ratio of yy and xx, and see if we can get a common answer which we will call constant kk.

It looks like the kk-value on the third row is different from the rest. In order for it to be a direct variation, they should all have the same kk-value.

The table does not represent direct variation, therefore, we can’t write the equation for direct variation.

Example 4:  Given that yy varies directly with xx. If x = 12x=12 then y = 8y=8.

Write the equation of direct variation that relates xx and yy.

What is the value of yy when x = - \,9x=−9?

a) Write the equation of direct variation that relates xx and yy.

Since yy directly varies with xx, I would immediately write down the formula so I can see what’s going on.

We are given the information that when x = 12x=12 then y = 8y=8. Substitute the values of xx and yy in the formula and solve kk.

We will use the first point to find the constant of proportionality kk and to set up the equation y = kxy=kx.

Substitute the values of xx and yy  to solve for kk.

The equation of direct proportionality that relates xx and yy is…

We can now solve for xx in (xx, - \,18−18) by plugging in y = - \,18y=−18.

Example 6: The circumference of a circle (CC) varies directly with its diameter. If a circle with the diameter of 31.431.4 inches has a radius of 55 inches,

Write the equation of direct variation that relates the circumference and diameter of a circle.

What is the diameter of the circle with a radius of 77 inches?

a) Write the equation of direct variation that relates the circumference and diameter of a circle.

We don’t have to use the formula y = k\,xy=kx all the time.  But we can use it to come up with a similar set-up depending on what the problem is asking.

The problem tells us that the circumference of a circle varies directly with its diameter, we can write the following equation of direct proportionality instead.

The diameter is not provided but the radius is. Since the radius is given as 55 inches, that means, we can find the diameter because it is equal to twice the length of the radius. This gives us 1010 inches for the diameter.

The equation of direct proportionality that relates circumference and diameter is shown below. Notice, kk is replaced by the numerical value 3.143.14.

Answer:

64z^2

Step-by-step explanation:

Here's why, it's actually very simple we use exponent rule when raising something to a power. In this case we're raising the term to the second power. So we raise both -8, and z. As so: (-8)^2 x (z)^2

Which equals 64z^2.

Answer:

483 9/100

Step-by-step explanation:

I think this is the answer