Which equation has solution x = -3?


A) 2x - 7 = -1
B) 3x + 8 = 1
C) 1/2x+8=10
D) 1/2(2x-6)=-6

Since minutes are 1/60 of a degree, we can simplify this to cos (79 + 15/60) = cos (78.25). We can use a calculator to find the exact value, which is 0.268954236.

cos 79 15' = cos (79 + 15/60)

= cos (78 + 45/60)

= cos (78 + 0.75)

= cos (78.75)

= cos (78 + 45/60 + 0.25)

= cos (78.25)

= 0.268954236

The cosine of 79 degrees and 15 minutes is 0.268954236. To calculate this, we convert the minutes to 1/60 of a degree and add it to the angle of 79 degrees. Then, we plug 78.25 into the cosine equation and get the result.

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Answer:

Supplementary, adjacent, linear pair

Step-by-step explanation:

Answer:

The answer is x = \(\frac{-5}{3}\).

Step-by-step explanation:

First, we expand the brackets. Therefore:

\(2x+6 = -4x+(-4)\)

\(2x+6 = -4x -4\)

Then, we separate the like terms:

\(2x+4x = -4-6\)

Then we add the like terms up and solve for x:

\(6x = -10\)

Therefore:

\(x = \frac{-10}{6}\)

which, simplified, is:

\(x = \frac{-5}{3}\).

The new equation with a vertical stretch by 3 is g(x) = 3|x + 1| - 3.

A mathematical equation is a formula that uses the equals sign to connect two expressions in order to express their equality.

When a base graph is multiplied by a particular number greater than 1, it causes a vertical stretch. As a result, the graph is stretched outward while keeping the input values (or x). We anticipate that the y values in a function's graph will be further away from the x-axis when it is vertically extended.

Consider the function,

f(x) = | x + 1 | - 1

Now the new equation for the function with a vertical stretch by 3.

g(x) = 3 × ( | x + 1 | - 1 )

g(x) = 3|x + 1| - 3

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The probability that between 36 and 39 questions are answered correctly, 36 should be changed to 35.5, and 39 should be changed to 39.5. Therefore, the new probability statement accounting for this correction is p(35.5<=x<=39.5).

In this case, a success (x) represents a student getting a C on the exam by answering 36 to 39 questions correctly. You need to find the probability of this event occurring, which can be represented as P(36 ≤ X ≤ 39). Since you'll be using the normal approximation, which is a continuous probability distribution, to approximate this discrete binomial event, you need to apply a continuity correction factor.

The probability statement for the event that a student gets a c on this exam by answering 36 to 39 questions correctly is p(36<=x<=39). The normal approximation, which is continuous, will be used to find the probability of this discrete binomial event. When using a continuous probability distribution to approximate a discrete distribution, a continuity correction factor needs to be applied.
To account for the continuity correction, you should adjust the lower limit of 36 to 35.5 and the upper limit of 39 to 39.5. This adjustment ensures that the probability of answering between 36 and 39 questions correctly is properly accounted for in the continuous approximation.

Therefore, the new probability statement with the continuity correction is P(35.5 ≤ X ≤ 39.5).

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Answer:

the number of tickets remaining is inversely proportional to the time in minutes:

number of tickets remaining  = total amount of tickets - (25 tickets sold per minute x time in minutes) = 350 - 25T

Step-by-step explanation:

for example:

after 5 minutes, the number of tickets remaining = 350 - (25 x 5) = 225 tickets

after 10 minutes, the number of tickets remaining = 350 - (25 x 10) = 100 tickets

after 14 minutes, the number of tickets remaining = 350 - (25 x 145) = 0 tickets

The amount of sand James would need is 113 cm³

Amount is the quantity of a substance.

Since for a science project, James needs to fill a tennis ball with sand but he doesn't know how much he will need. He measured the diameter of the tennis ball and found it to be 6 cm.

The amount of sand he would need is the volume of the tennis ball. The volume of the tennis ball is the volume of a sphere.

Since the tennis ball is a sphere, its volume is V = 4πr³/3 where r = radius = d/2 where d = diameter of tennis ball.

Since d = 6 cm, we have have that its radius r = d/2 = 6 cm/2 = 3cm

To find the amount of sand James would need, we compute the volume of the tennis ball.

So, V = 4πr³/3

= 4π(3 cm)³/3

= 4π × 27 cm³/3

=  4π × 9 cm³

= 36π cm³

= 113.1 cm³

≅ 113 cm³

So, the amount of sand is 113 cm³

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Answer:

Corral 4

Step-by-step explanation:

we need to divide  the area of the corral by the Number of animals In order To know the dedicated  space for each animal

Corral 1 :

(50×40)÷110 = 18.181818181818 < 20

Then it doesn’t meet the requirements.

Corral 2 :

(60×35)÷115 = 18.260869565217 < 20

Then it doesn’t meet the requirements

Corral 3 :

(55×45)÷125 = 19.8 < 20

Then it doesn’t meet the requirements

Corral 4 :

(65×40)÷130 = 20

Then It meets the requirements

Answer:

The missing fraction is 6/12

(you can further simplify this but the question requires that you don't do that)

Step-by-step explanation:

To add fractions easily, their denominators should have the same value, so the denominator should be 12,

Then, to get 16 in the numerator, we need to find a number that on adding to 10, gives 16, or,

10 + x = 16

x = 16 - 10

x = 6

So, the numerator should be 6

so we get the fraction, 6/12

We can also solve it in an alternate way,

\(10/12 + x = 16/12\\x = 16/12 - 10/12\\x = (16-10)/12\\x = 6/12\)

translating phrases and sentences into expressions, equations, and inequalities is an important skill in mathematics. It involves identifying key words and phrases that indicate mathematical operations and relationships. By understanding these key words, we can represent real-world problems using mathematical language and symbols, making it easier to solve and analyze them.

translating phrases and sentences into expressions, equations, and inequalities

When solving mathematical problems, it is often necessary to translate phrases and sentences into mathematical expressions, equations, and inequalities. This process involves identifying key words and phrases that indicate mathematical operations and relationships.

For example, let's consider the following sentence:

'The sum of a number and 5 is equal to 12.'

In this sentence, the key words 'sum,' 'number,' 'equal to,' and '12' indicate that we need to perform addition and find the value of the unknown number. We can represent this sentence as the following equation:

x + 5 = 12

Here, 'x' represents the unknown number.

Similarly, let's consider the following sentence:

'Twice a number decreased by 7 is greater than 15.'

In this sentence, the key words 'twice,' 'decreased by,' 'greater than,' and '15' indicate that we need to perform multiplication, subtraction, and comparison. We can represent this sentence as the following inequality:

2x - 7 > 15

Here, 'x' represents the unknown number.

By understanding key words and phrases, we can effectively translate real-world problems into mathematical language and solve them using expressions, equations, and inequalities.

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1) An inequality to represent the given phrase is 5q>30.

2) An equation to represent the given phrase is 2b²=8.

1) The given phrase is "The product of 5 and q is greater than 30."

Here, the product of 5 and q = 5×q

= 5q

Now, the product is greater than 30.

Thus, 5q>30

q>30/5

q>6

2) The given phrase is "Twice the square of b is equal to 8."

Here, the square of b = b×b

= b²

Twice the square of b = 2b²

So, the product is equal to 8.

That is. 2b²=8

b²=4

b=±2

Therefore,

1) An inequality to represent the given phrase is 5q>30.

2) An equation to represent the given phrase is 2b²=8.

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"Your question is incomplete, probably the complete question/missing part is:"

Translate phrases and sentences into expressions, equations and inequalities.

1) The product of 5 and q is greater than 30.

2) Twice the square of b is equal to 8.

We need to determine whether an 8x8 matrix A exists that satisfies three conditions:

(i) having zeros below the main diagonal,

(ii) having a non-zero entry in the first row and eighth column, denoted as a18

(iii) being diagonalizable. In the second paragraph.

we will either provide an example of such a matrix and prove that it satisfies the conditions, or prove that no such matrix exists.

To provide an example of an 8x8 matrix A that satisfies the given conditions, we need to construct a matrix that satisfies each condition individually.

Condition (i) requires that all entries below the main diagonal of A are zero. This condition can easily be satisfied by constructing a matrix with zeros in the appropriate positions.

Condition (ii) states that a18, the entry in the first row and eighth column, must be non-zero. By assigning a non-zero value to this entry, we can fulfill this condition.

Condition (iii) requires that the matrix A is diagonalizable. This condition means that A must have a complete set of linearly independent eigenvectors. If we can find eigenvectors corresponding to distinct eigenvalues that span the entire 8-dimensional space, then A is diagonalizable.

If we are able to construct such a matrix that satisfies all three conditions, we can provide it as an example and prove that it fulfills the given conditions. However, if it is not possible to construct such a matrix, we can prove that no such matrix exists by showing that the conditions are mutually exclusive and cannot be satisfied simultaneously.

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The fixed trucking cost accounts for approximately 2.8% of the total annual cost.

To compute the optimal order quantities, order intervals, and annual cost for bar stock and sheet stock, we can use the Economic Order Quantity (EOQ) formula:

EOQ = √(2SD/H)

where S is the annual demand, D is the fixed order cost, and H is the holding cost per unit.

For bar stock:

S = 1000 units per year

D = $50 (fixed order cost)

H = 20% of $200 = $40 (holding cost per unit)

Plugging in these values, we get:  

EOQ = √(2 × 1000 × 50 / 40) = 50 units

The optimal order interval is the annual demand divided by the EOQ:

Order interval = S / EOQ = 1000 / 50 = 20 orders per year

The total annual cost of bar stock is:  

Annual cost = (S × D / EOQ) + (EOQ / 2 × H) + (S × H / 2)

Annual cost = (1000 × 50 / 50) + (50 / 2 × 40) + (1000 × 40 / 2) = $2,500

For sheet stock:

S = 500 units per year

D = $50 (fixed order cost)

H = 20% of $150 = $30 (holding cost per unit)

Plugging in these values, we get:

EOQ = √(2 × 500 × 50 / 30) = 29 units (approx.)

The optimal order interval is the annual demand divided by the EOQ:

Order interval = S / EOQ = 500 / 29 = 17.24 orders per year (approx.)

The total annual cost of sheet stock is:

Annual cost = (S × D / EOQ) + (EOQ / 2 × H) + (S × H / 2)

Annual cost = (500 × 50 / 29) + (29 / 2 × 30) + (500 × 30 / 2) = $1,829.31 (approx.)

The fixed trucking cost is $40 per order, which is 80% of the total fixed cost of $50. Therefore, the fraction of the total annual cost consisting of fixed trucking cost is:

Fixed trucking cost / Total annual cost = ($40 × 20) / ($40 × 20 + $10 × 20 + $2,500 + $1,829.31) ≈ 0.028

So, the fixed trucking cost accounts for approximately 2.8% of the total annual cost.

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Answer:

From quadratic formula:

Q=1+168=169

X1,2=1±13/28=>

X1=14/28=1/2

X2=12/28=3/7

(X-X1) (X-X2) =0=>

(X-1/2)(X-3/7)=0

Answer:

hope this helps

Step-by-step explanation :https://youtu.be/mxvAH2KJJig

Order data = 12, 15.2, 15.7, 17, 18.1, 18.8, 21.

Median = 12, 15.2, 15.7, 17, 18.1, 18.8, 21.

Median is the midpoint = 17

Answer:

x^2-2x+5

Step-by-step explanation:

5x^2 -4x +8 + -4x^2 +2x -3

Combine like terms

5x^2-4x^2-4x+2x+8-3

x^2-2x+5

Answer:

Because 43.3 > 40, it is possible that the picture fits in the frame.

Step-by-step explanation:

The correct explanation will be;

''Because 43.3 > 40, it is NOT possible that the picture fits in the frame.''

What is Pythagoras theorem?

The Pythagoras theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the square of the other two sides.

Given that;

A picture frame is 24 in. wide and 36 in. high.

And, A picture with a 40 in. diagonal fit in it.

Now,

Since, A picture frame is 24 in. wide and 36 in. high.

Hence, The length of diagonal is;

⇒ d² = 24² + 36²

⇒ d² = 1,872

⇒ d = 43.26

But, Here a picture with a 40 in. diagonal fit in it.

Hence, The correct explanation will be;

''Because 43.3 > 40, it is NOT possible that the picture fits in the frame.''

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Answer:

Step-by-step explanation:

So sin is defined as \(\frac{opposite}{hypotenuse}\). and cosine is defined as \(\frac{adjacent}{hypoteunse}\). So we need the adjacent side. Since we already have the opposite, and hypotenuse, you can use the Pythagorean identity to solve for the missing side: \(a^2+b^2 = c^2\)

\(15^2 + b^2 = 19^2\)

\(225 + b^2 = 361\)

\(b^2 = 136\)

\(b = \sqrt{136}\)

\(b = \sqrt{4} * \sqrt{34}\)

\(b = 2\sqrt{34}\)

This is the adjacent side, so now plug this into the cosine equation and you get: \(\frac{2\sqrt{34}}{19}\)

There does not exist a scalar function p[x] that satisfies the relationship ∇p[x] = f[x]. Hence, the vector field f[x] is not a gradient vector field.

To show that the vector field f[x] = (-y/(x^2 y^2)^2, x/(x^2 y^2)^2) is not a gradient vector field, we need to demonstrate that there does not exist a scalar function p[x] such that the gradient of p[x] is equal to f[x].

Let's assume that there exists a scalar function p[x] such that the gradient of p[x] is equal to f[x]. In other words, ∇p[x] = f[x]. We can write the components of these vector fields as follows:

∂p/∂x = -y/(x^2 y^2)^2     (1)

∂p/∂y = x/(x^2 y^2)^2     (2)

To check if these partial derivatives satisfy the relationship, we differentiate Equation (1) with respect to y and Equation (2) with respect to x:

∂^2p/∂y∂x = ∂^2p/∂x∂y

Differentiating Equation (1) with respect to y, we get:

∂^2p/∂y∂x = ∂/∂y(-y/(x^2 y^2)^2) = -1/(x^2 y^3)

Differentiating Equation (2) with respect to x, we get:

∂^2p/∂x∂y = ∂/∂x(x/(x^2 y^2)^2) = -2/(x^3 y^2)

Comparing these two results, we can see that -1/(x^2 y^3) is not equal to -2/(x^3 y^2). Therefore, there does not exist a scalar function p[x] that satisfies the relationship ∇p[x] = f[x]. Hence, the vector field f[x] is not a gradient vector field.

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Answer:

It's an irrational number

Step-by-step explanation:

Yes, 8.141141114 is not a rational number . it is a irrational number .generally we can find out a number is rational or irrational by seeing the number. If mentioned number were 8.141141141 then It would be a rational number because after point number 141 is repeated. Hence,Mentioned number is not look like that. so, it is a irrational number

Answer: x=-1 and y=0 .

Step-by-step explanation:

The given linear equations:

\(10y + 9x = -9\ ...(i)\\\\10y + 5x= -5\ ...(ii)\)

Subtract (ii) from (i) , we get

\(10y+9x-(10y+5x)=-9-(-5)\\\\\Rightarrow\ 10y+9x-10y-5x=-9+5\\\\\Rightarrow\ 4x=-4\\\\\Rightarrow\ x=-1\)

Put value of x in (i), we get

\(10y+9(-1)=-9\\\\\Rightarrow\ 10y-9=-9\\\\\Rightarrow\ 10y=-9+9=0\\\\\Rightarrow\ y=0\)

Hence, x=-1 and y=0 .

The 15th term of the geometric progression is a₁₅ = 25/2048

A geometric progression is a sequence in which each term is derived by multiplying or dividing the preceding term by a fixed number called the common ratio.

The nth term of a GP is aₙ = arⁿ⁻¹

The general form of a GP is a, ar, ar2, ar3 and so on

Sum of first n terms of a GP is Sₙ = a(rⁿ-1) / ( r - 1 )

Given data ,

Let the 15th term of the geometric progression be a₁₅

Now , the 4th term of the GP is a₄ = -25

The 9th term of the GP is a₉ = 25/32

Now , nth term of a GP is aₙ = arⁿ⁻¹

Substituting the values in the equation , we get

a₄ = ar³ = -25   be equation (1)

a₉ = ar⁸ = 25/32   be equation (2)

Divide equation (2) by equation (1) , we get

r⁵ = -( 1/32 )

r⁵ = - ( 1/2 )⁵

So , the common ratio r = -1/2

Now , the first term of the GP a is calculated by

ar³ = -25

when r = -1/2

a ( -1/2 )³ = -25

a/8 = 25

a = 200

Now , the 15th term of the geometric progression a₁₅ = ar¹⁴

Substituting the values in the equation , we get

a₁₅ = 200 ( -1/2 )¹⁴

a₁₅ = 200/16,384

a₁₅ = 25/2048

Hence , the 15th term of the GP is 25/2048

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Answer:

i think 3p-p it might not be but maybe

Step-by-step explanation:

Answer:

3=0

Step-by-step explanation:

Answer:

  1/8

Step-by-step explanation:

1 of the 8 branches of the tree is TTH in that order. If all branches are equally likely, the probability is 1/8, or 0.125, or 12.5%.

Answer:

20cm²

Step-by-step explanation:

\( \frac{1}{2} \times x \times y = \frac{1}{2} \times 5 \times 8 = 5 \times 4 = 20\)

Answer:

D:20cm2

Step-by-step explanation:

To calculate the area of a triangle, multiply the height by the width (this is also known as the 'base') then divide by 2.

Answer:

40

Step-by-step explanation:

If a = 2

4 ( 2a + 3a )

4 ( 2 ( 2 ) + 3 ( 2 ) )

= 4 ( 4 + 6 )

= 4 ( 10 )

= 40

The most effective method to find local minimum and maximum values of a function is by using the derivative and the second derivative test. The derivative helps identify critical points, and the second derivative test determines if they are local minimum or maximum values.

To find the local minimum and maximum values of a function, you can use several methods:

a. Derivative: One way to find local minimum and maximum values is by taking the derivative of the function and finding the critical points. Critical points occur where the derivative is equal to zero or undefined. To determine if a critical point is a local minimum or maximum, you can use the second derivative test. If the second derivative is positive at the critical point, it is a local minimum. If the second derivative is negative, it is a local maximum.

b. Integral: The integral of a function can give you information about the behavior of the function. However, it does not directly provide the local minimum and maximum values.

c. Limit: Taking the limit of a function can provide information about its behavior at certain points. However, it does not directly give the local minimum and maximum values.

d. Inflection point: An inflection point is a point on the graph of a function where the concavity changes. It is not directly related to finding local minimum and maximum values.

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Answer:

(0.5, 8.5)

Step-by-step explanation:

use this formula ((x1+x2/2), (y1+y2/2)) if you use desmos graphing calculator and you type this formula in, all you have to do it put in the correct numbers and you get your midpoint.

Hope this helped :)

The midpoint of the segment between the points (−5,13) and (6,4) are (0.5 and 8.5)

We have given that, the points (−5,13) and (6,4)

We have to determine the midpoints

((x1+x2/2), (y1+y2/2))

x1=-5,x2=6,y1=13 and y2=4

-5+6/2=1/2=0.5

and next is,

13+4/2=17/2=8.5

The midpoint of the segment between the points (−5,13) and (6,4) are (0.5 and 8.5)

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