Subtract -2a+7b=-5 from the other equation so the b-terms become opposites

If you know two angles and one side of a triangle, you can use the Law of Cosines to find the length of the other two sides.

The Law of Cosines states that for a triangle with sides a, b, and c, and angles A, B, and C opposite to those sides, the following formula holds:

c² = a² + b² - 2ab cos(C)

Where C is the angle opposite to side c.

So, if you know the measures of two angles (A and B) and the length of one side (c), you can use the Law of Cosines to find the lengths of the other two sides (a and b) by using the following formulas:

a = √(c² + b² - 2bc cos(A))

b = √(c² + a² - 2ac cos(B))

You can use the above equations to find the sides of the triangle, if you have the measures of two angles and one side.

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Answer:

[tex](a)\ \sqrt{20}=2\sqrt{5}[/tex]

[tex](b)\ \sqrt{300} = 10 \sqrt{3}[/tex]

[tex](c)\ \sqrt{128} = 8 \sqrt{2}[/tex]

Step-by-step explanation:

Required

Simplify

[tex](a)\ \sqrt{20}[/tex]

Express 20 as 4 * 5

[tex]\sqrt{20}=\sqrt{4 * 5}[/tex]

Split

[tex]\sqrt{20}=\sqrt{4} * \sqrt{5}[/tex]

This gives:

[tex]\sqrt{20}=2 * \sqrt{5}[/tex]

[tex]\sqrt{20}=2\sqrt{5}[/tex]

[tex](b)\ \sqrt{300[/tex]

Express as 100 * 3

[tex]\sqrt{300} = \sqrt{100} * \sqrt{3}[/tex]

This gives:

[tex]\sqrt{300} = 10 * \sqrt{3}[/tex]

[tex]\sqrt{300} = 10 \sqrt{3}[/tex]

[tex](c)\ \sqrt{128}[/tex]

Express as 64 * 2

[tex]\sqrt{128} = \sqrt{64*2}[/tex]

Split

[tex]\sqrt{128} = \sqrt{64} * \sqrt{2}[/tex]

[tex]\sqrt{128} = 8 * \sqrt{2}[/tex]

[tex]\sqrt{128} = 8 \sqrt{2}[/tex]

Questions 4 and 5 are not clear

Follow the steps in 1 - 3 to solve 4 and 5

The portion left to mow is 3x+3.5 /4

Linear equations help in representing the relationship between variables such as x, y, and z, and are expressed in exponents of one degree. In these linear equations, we use algebra, starting from the basics such as the addition and subtraction of algebraic expressions.

Given here:Nick mowed about 3.5 of the school lawn yesterday. He mowed another 1/4 of the lawn this morning. Let the whole lawn be x then on the first day portion left to be mowed is x-3.5 and on the second day he moved 1/4 of this quantity thus portion of lawn left to be mowed is

x-x-3.5/4

=3x+3.5 /4

Hence, The portion left to mow is 3x+3.5 /4

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The area of the cross-section of the sphere in square inches in terms of pi will be 169π inch^2.

The area of a two-dimensional shape created when a three-dimensional object, like a cylinder, is cut perpendicular to a predetermined axis at a point is known as the cross-sectional area.

An area is projected onto the plane when a plane slices through a solid object. The axis of symmetry is then perpendicular to that plane. The cross-sectional area refers to its projection.

The cross-section of a sphere is a circle. Hence the area of the cross-section is the area of a circle with a radius of 13, which is given by π*r^2

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Answer:

[tex]\displaystyle \frac{d}{dx}[\sin(9x)] = 9 \cos(9x)[/tex]

General Formulas and Concepts:

Calculus

Differentiation

Derivative Property [Multiplied Constant]:                                                           [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]

Basic Power Rule:

Derivative Rule [Chain Rule]:                                                                                 [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle y = \sin(9x)[/tex]

Step 2: Differentiate

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation

Answer:

It would be y = 2x+4

Step-by-step explanation:

This is because Isabella has started with 4 baked pies and is gaining additional pies with in amounts of 2 pies.

With this, 4 would be by itself and 2 would be attached to the variable x for the unknown amount of additional pies.

Lastly, you would have this all equaling y, as y is the total amount of pies.

Answer:

8 is the answer

Therefore , the solution of standard deviation is  because the value of 1452.2 cm3 does not fall between the range of 917.4 cm3 and 1422.2 cm3.

Standard deviation, often known as variance in a set of data, is a statistical measure of variation. A low standard deviation indicates that the values are more likely to be near the mean of the collection, whereas a high standard deviation indicates that the values are widely distributed. How far the data depart from the mean is expressed by the standard deviation, abbreviated as.

Here,

Considering the details here,

The average brain volume is 1169.8 cm3, while the standard deviation is 126.2 cm3.

The much lower results are u-2 = 11169.8-2(126.2) => 917.4.

Reason: According to the range rule of thumb, the required incredibly low values are 91.7 cm3 or less.

Hint: Use the algorithm to identify values that are at least considerably high.

Step: 2

Considering the data supplied,

The average brain volume is 1169.8 cm3, while the standard deviation is 126.2 cm3.

Significantly higher values include,

u-2α = 11169.8+ 2(126.2)

=> 1422.2

Justification: According to the range rule of thumb, the necessary significantly high values must be 1422.2 cm3 or higher.

Hint: To determine whether the value 1452.2 cm3 is very high, use the findings of steps (1) and (2).

Step: 3

Using step 1 and step (4),

917.4 is among the significantly low numbers or less.

The significantly high values are 1422.2 or higher.

Yes, 1452.2 cm3 is a noticeably high value.

The apt response is choice (B).

Reason: The value is much higher than expected based on the range rule of thumb because the value of 1452.2 cm3 does not fall between the range of 917.4 cm3 and 1422.2 cm3.

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Answer:

x = 90

Step-by-step explanation:

If x = 3 and y = 4 then when y = 120 just find out what times 4 = 120

which is 30.

so just multiply 30 for x = 3, then the answer will be 90

x = 90

Answer:

x=90

Step-by-step explanation:

x is directly proportional to y

Therefore, if the initial y value was 4 and the final y value is 120. This means that y initial had been multiplied 120/4 times, which is 30.

Same goes for x. If x initial is 3, then the final x value would be x/3=30. This means that x=3×30, which is equal to 90.

Answer:

12.4

Step-by-step explanation:

First you need to find the hypotenuse of the other triangle, because it makes up a necessary side for finding AD. Pythagorean theorem states that

a^2 + b^2 = c^2 where a and b are leg lengths and c is the hypotenuse. For the triangle on the left, you're given 2 legs. So you can substitute those into that formula:

a^2 + b^2 = c^2

(10)^2 + (6)^2 = c^2

100 + 36 = c^2

136 = c^2.

Now take the square root of both sides to isolate c.

11.6619038 = c.

11.6619038 rounds to 11.7 so c = 11.7

Now that you have the second leg length for the triangle on the right, you can find its hypotenuse.

Follow the same process. Substitute your values into the equation and then solve for c:

a^2 + b^2 = c^2

(11.7)^2 + (4)^2 = c^2

136.89 + 16 = c^2

152.89 = c^2

Now find the square root of both sides to isolate c

12.3648696 = c.

12.3648696 rounds to 12.4 so c = 12.4

So the distance of AD is 12.4

Answer:

1428

Step-by-step explanation:

I did 16 times 8.5 times 10.5. Good Luck!

Answer:

5940

number of sides = 15

Step-by-step explanation:

Sum of the interior angles = (n-2)×180

(35-2)×180

=33×180

= 5940

Sum of the interior angles = (n-2)×180

(n-2)×180 = 2340

(n-2) = 2340/180

n-2 = 13

n = 13 + 2 = 15

so total sides are 15

The complate table is,

Statement                                                 Reasons

1) K is the midpoint of segments                      Given

  RM and JL.

2) RJ ≅ ML                                                  SSS Congruence Postulate

3) RK ≅ MK ,  JK ≅ LK                                 Definition of Midpoint

4) RK = MK , JK = KL                                    Definition of Congruence

                                                                   Segments

5) Δ EGF ≅ Δ EGH                                      CPCTC

A line segment is a part of line having two endpoints and it is bounded by two distinct end points and contain every point on the line that is between its endpoint.

Given that;

K is the midpoint of segments RM and JL.

Now,

Since, K is the midpoint of segments RM and JL.

Hence, We get;

   Statement                                                 Reasons

1) K is the midpoint of segments                      Given

  RM and JL.

2) RJ ≅ ML                                                  SSS Congruence Postulate

3) RK ≅ MK ,  JK ≅ LK                                 Definition of Midpoint

4) RK = MK , JK = KL                                    Definition of Congruence

                                                                   Segments

5) Δ EGF ≅ Δ EGH                                       CPCTC

Thus, The complete table is shown above.

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Answer:

121

Step-by-step explanation:

180 - (56 + 65) = 59

180 - 59 = 121

Answer:

Step-by-step explanation:

3x=24

x=8

Answer:

B. √50

Step-by-step explanation:

[tex]7^{2}[/tex] is 49 so √49 is 7

So,

since the closest number to 49 is 50, that is the answer.

[tex]\sqrt{51}[/tex] is the closest square root to 7.

The square root of a number is defined as the value, which gives the number when it is multiplied by itself. The radical symbol √ is used to indicate the square root. If a number is a perfect square, we can easily find the square root of the number. If the given number is not a perfect square number, the square root can be found using the long division method.

[tex]\sqrt{51} = 7.141\\\sqrt{50} = 7.071\\ \sqrt{46} = 6.782\\ \sqrt{47} =6.855[/tex]

(using calculator)

Absolute distance from 7 :

|7.141 - 7| = 0.141

|7.071 - 7| = 0.71

|6.782 - 7| = 0.218

|6.855 - 7| = 0.145

(The absolute value of a number refers to the distance of a number from the origin of a number line. It is represented as |a|, which defines the magnitude of any integer ‘a’. The absolute value of any integer, whether positive or negative, will be the real numbers, regardless of which sign it has.  It is represented by two vertical lines |a|, which is known as the modulus of a.)

Since, 0.141 is the least distance. [tex]\sqrt{51}[/tex] is the closest square root to 7.

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Answer:

10^11

Step-by-step explanation:

This question helps you practice some exponent rules. To "fix" a negative exponent you push it across the fraction bar. The 10^-3 on the bottom becomes a 10^3 on the top. See image.

Then, when you have 10^8 • 10^3, that is when you are multiplying, you add the exponents.

10 ^ (8+3)

= 10^11

see image

Answer:

b) BC = 30

Step-by-step explanation:

triangle ACD is equal to ABC so BC = 2xBD = 30

Answer:

U can find it using Cos 60 degree

A = 1, y = -2/3, The value of a for which the system of equations has a unique solution is a = -3.

1. Set the first equation equal to 0:

2x + ay = 2

2. Subtract 2x from both sides of the equation to get:

ay = -2

3. Divide both sides of the equation by a to get:

y = -2/a

4. Substitute this value of y into the second equation to get:

6x + 3(-2/a) = 3

5. Multiply both sides of the equation by a and simplify to get:

6ax - 6 = 3a

6. Add 6 to both sides of the equation to get:

6ax = 3a + 6

7. Divide both sides of the equation by 6 to get:

x = (3a + 6)/6

8. The value of a for which the system of equations has a unique solution is a = -3.

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Answer:

7.29%

Step-by-step explanation:

Given data

Principal=  $1,000

Final amount= $2,400

TIme= 12 years

The expression for the compound interest is given as

A= P(1+r)^t

Make r subject of fomula

r = ln(A/P) / t

r= ln(2400/1000)/12

r= ln(2.4)/12

r= 0.875/12

r= 0.0729

Hence the rate is 7.29%

[tex]x^2[/tex] - (b+c)x +bc=0  is the quadratic equation whose roots are b,c.

If the roots of a quadratic equation are given, the equation can be written by factoring the equation using the roots.

Given the roots, let's say r1 and r2, the quadratic equation can be written as (x - r1)(x - r2) = 0.

Expanding the above equation x^2 - (r1 + r2)x + r1r2 = 0

Therefore, if the roots of a quadratic equation are given as r1 and r2, the quadratic equation can be written as:

x^2 - (r1 + r2)x + r1r2 = 0

since we are given that the root of the equation are b,c;

so r1=b,r2=c;

putting the value in the above equation we get the equation with b and c as root:

[tex]x^2[/tex] - (b+c)x +bc=0

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Complete question :

The coefficient b and c in the equation [tex]x^2+bx+c[/tex] is also root of another equation where c≠0 .

please write the equation

Answer:

C) 32

Explanation:

it's adding by 4, 6, 8, and then 10; 22 + 10 = 32, so C will be the answer.

Hope this helps!

The length of OP to the nearest tenth of a foot is 16.9 ft

What is a right-angle triangle?

It is a triangle in which one of the angles is 90 degrees and the other two are sharp angles. The sides of a right-angled triangle are known as the hypotenuse, perpendicular, and base.

ΔOPQ is right triangle

 Tan (p) = opposite/adjacent = OQ/PQ

Tan (76) =  OQ/4.1

4.010 = OQ/4.1

OQ = 4.010 * 4.1 = 16.441

OP² = OQ² + PQ² = 16.441 ² + 4.1² = 287.116

=> OP = √ 287.116 = 16.944

OP≅ 16.9 ft

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Answer:

65%

Step-by-step explanation:

100%-> 10

1%->0.1

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

10 - 3 1/2 = 6 1/2

6 1/2 ÷ 0.1 = 65

Equation that will determine the amount of last year’s budget

Two or more expressions with an Equal sign is called as Equation.

Given that a school plans to spend twice the amount it did last year on its winter dance , less the cost of the disco ball which was $150 since they have it from last year

A total of $1,500 is being spent this year.

We need to find the equation which determine the amount of last year’s budget

2a-150=1500

When a is the amount of last year’s budget

Hence, 2a-150=1500 is the equation that will determine the amount of last year’s budget

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Answer:

28

Step-by-step explanation:

2x + 3x + 40 =180

5x= 180 - 140

5x=140

x= 28

Answer:

Step-by-step explanation:

We know that the sum of interior angles of a triangle is 180° so we can say:

40 + 2x + 3x = 180°

40 + 5x = 180°

5x = 140°

x = 28°

Now substitute in 28 for the value of x in Angle A:

=> 2x would become 2(28)

=> 56° = ∠A

Hope this helps!

Answer:

$13

Step-by-step explanation:

The expected payoff for the winner would be the ticket cost, $3, plus the prize money, $10, which totals $13. This is the expected value of playing the game. However, it's important to note that this does not guarantee that the winner will receive exactly $13, as the outcome of the game is dependent on chance and the player's skill. There is always a chance that the player could win more or less than the expected value.