4h10 · 6h6

How do I solve this?

Answer:

x = 11

Step-by-step explanation:

Since those two opposite sides are parallel, their values are equal.

17+5 = 22.

22/2 = 11. x is equal to 11. GOOD LUCK!

Answer:

20 ponds

Step-by-step explanation:

1 third us 20 pounds times by 3 is 60 so if its a 1 third sale it will cost 20 pounds

Answer: $2,466.45

Step-by-step explanation:

Hi, to answer this question we have to apply the compounded interest formula:

A = P (1 + r/n) nt

Where:  

A = Future value of investment (principal + interest)  

P = Principal Amount  

r =  Nominal Interest Rate (decimal form, 3.5/100= 0.035)

n=   number of compounding periods in each year (365)

Replacing with the values given

3,500= P (1+ 0.035/365)^365(10)

Solving for P

3,500= P (1.00009589)^3650

3,500/  (1.00009589)^3650 =P

P = $2,466.45

Answer:

98

Step-by-step explanation:

The value of t such that the area to the left of −|t| plus the area to the right of |t| equals 0.01 is: t = −|t1| + 0.005 = −0.245 (approx)

Let’s consider the value of t such that the area to the left of −|t|−|t| plus the area to the right of |t||t| equals 0.01. Now, we know that the area under the standard normal distribution curve between z = 0 and any positive value of z is 0.5. Also, the total area under the standard normal distribution curve is 1.Using this information, we can calculate the value of t such that the area to the left of −|t| is equal to the area to the right of |t|. Let’s call this value of t as t1.So, we have:

Area to the left of −|t1| = 0.5 (since |t1| is positive)
Area to the right of |t1| = 0.5 (since |t1| is positive)

Therefore, the total area between −|t1| and |t1| is 1. We need to find the value of t such that the total area between −|t| and |t| is 0.01. This means that the total area to the left of −|t| is 0.005 and the total area to the right of |t| is also 0.005.

Now, we can calculate the value of t as follows:

Area to the left of −|t1| = 0.5
Area to the left of −|t| = 0.005

Therefore, the area between −|t1| and −|t| is:

Area between −|t1| and −|t| = 0.5 − 0.005 = 0.495

Similarly, the area between |t1| and |t| is:

Area between |t1| and |t| = 1 − 0.495 − 0.005 = 0.5

Area to the right of |t1| = 0.5
Area to the right of |t| = 0.005

Therefore, the value of t such that the area to the left of −|t| plus the area to the right of |t| equals 0.01 is the value of t1 plus the value of t:

−|t1| + |t| = 0.005
2|t1| = 0.5
|t1| = 0.25

Therefore, the value of t such that the area to the left of −|t| plus the area to the right of |t| equals 0.01 is:
t = −|t1| + 0.005 = −0.245 (approx)

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TRUNCATED to one decimal place, it's 50.2

ROUNDED to one decimal place, it's 50.3

The round-off of 50.272 to 1 decimal place using rules of rounding

numbers are 50.3.

Rounding off numbers means making a number simpler by adjusting it to its nearest place according to certain rules.

Rounding a number to one decimal place means keeping only the first digit after the decimal point and neglecting the rest. In this case, the digit in the second decimal place is 7, which is greater than or equal to 5. As per the rounding rules, if the digit is greater than 5, the preceding digit is increased by 1.

So, 50.272 becomes 50.3 when rounded to one decimal place.

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(-2, 5) Minimum

Step-by-step explanation:

y-5=(1/3)(x + 2)²

y-5=(1/3)(x²+4x+4))

y-5=1/3x²+4/3x+4/3

y=1/3x²+4/3x+4/3+5

y=1/3x²+4/3x+4/3+15/3

y=1/3x²+4/3x+19/3

graph is attached

x= -b/2a

x= (-4/3)/2(1/3)

x= (-4/3)/(2/3)

x= (-4/3)*(3/2)

3's cancel

x= (-4/1)*(1/2)

x = -4/2

x = -2

plug -2 back into

y=1/3x²+4/3x+19/3

y=1/3*4+4/3*-2+19/3

y=4/3-8/3+19/3

y=15/3

y=5

(-2,5)

if a is positive

graph looks like a smile

so minimum

if a is negative

graph looks like a frown

so maximum

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Answer:

91 cents per ounce

Step-by-step explanation:

Divide 13.59 by 15

Answer: $0.91

Step-by-step explanation:

Take $13.59 divided by 15 = $0.91 per ounce

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The proportionality is the direct relation of two variables thus the constant of proportionality of the given graph is 1/2.

The ratio is the division of the two numbers.

Proportion is the relation of a variable with another. It could be direct or inverse.

For example x ∝ y

The graph of seconds and ounces has shown.

If we look at the graph it is clear that as the ounces are increasing the seconds are also increasing. Therefore, it is a direct proportion.

Let's suppose the proportion is x ∝ y where x is ounces while y is seconds.

Removing proportionality,

x = ky

k = x/y

Substitute,(x,y) = (1,2)

k = 1/2

Hence "The proportionality is the direct relation of two variables thus the constant of proportionality of the given graph is 1/2".

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Answer:

y - 7 = 6(x - 2)

Step-by-step explanation:

1. Since we're given one point and the slope of a line, we can use the point slope form: \(y-y_1=m(x-x_1)\)

2. (Plugging in values)

Therefore, one equation of the line is y - 7 = 6(x - 2).

Answer:

\(x=18,\:y=6\)

Step-by-step explanation:

Solve by substitution

\(\begin{bmatrix}x+y=24\\ 75x+60y=1710\end{bmatrix}\)

\(\mathrm{Substitute\:}x=24-y\)

\(\begin{bmatrix}75\left(24-y\right)+60y=1710\end{bmatrix}\)

\(\begin{bmatrix}1800-15y=1710\end{bmatrix}\)

\(\mathrm{For\:}x=24-y\)

\(\mathrm{Substitute\:}y=6\)

\(x=24-6\)

\(x=18\)

\(\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}\)

\(x=18,\:y=6\)

The distance between your house and school is 4.1 miles.

According to the given question.

Point c represents your house.

Point d represents post office which is directly west to the point c i.e from house.

And point e represents school which is west of the post office.

Also, it is given that the distance between house and post office, cd is 1.7 miles.

And the distance between the post office and school,de is 2.4 miles.

Now, if we see the attached figure we can say that

cd + de = ce

⇒ 1.7miles  + 2.4miles  = 4.1 miles

Hence, the distance between your house and school is 4.1 miles.

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════════ ∘◦❁◦∘ ════════

════════════════════

x1 = (-9)

y1 = 3

x2 = (-2)

y2 = 7

════════════════════

Mid point = ..?

════════════════════

#note that . in this equation is ,

\(mid \: poimt \: = ( \frac{y2 - y1}{2} ).( \frac{x2 - x1}{2} )\)

\(mid \: poimt \: = ( \frac{7 - 3}{2} ).( \frac{( - 2) - ( - 9) }{2} ) \)

\(mid \: poimt \: = ( \frac{5}{2} ).( \frac{7}{2} ) \)

════════════════════

Answer:

Height of the kite = 86.60 meter (Approx)

Step-by-step explanation:

The angle of elevation to see a kite from a stone lying to the ground is 60 degrees. If a thread is tied with a kite and a stone, then that thread is 100 meters long, find the height of the kite.

Given:

Length of thread = 100 meter

Angle of elevation = 60°

Find:

Height of the kite.

Computation:

Using trigonometry application:

Height of the kite / Length of thread = Sin 60°

Height of the kite / 100 = √3 / 2

Height of the kite = [√3 / 2]100

Height of the kite = 50√3

Height of the kite = 86.60 meter (Approx)

Answer:(−5x3−6x2−5)(−5x2−2x) = 25x5+40x4+12x3+25x2+10x

Step-by-step explanation:

Answer:

2.75

Step-by-step explanation:

Divide 13.75 by five.

Answer:

answer 1

Step-by-step explanation:

x^2+4x+7

=(x^2+4X+4)+3

=(x+2)^2+3

The equation of the circle, obtained by applying the completing the square method to the specified equation indicates that the center and radius of the circle are;

Center (0, 6) and radius 7.5

The general form of the equation of a circle is; (x - h)² + (y - k)² = r², where;

(h, k) = The coordinates of the center of the circle

r = The measure of the length of the radius

The possible equation obtained from a similar question on the internet can be presented as follows;

x² + y² - 12·y - 20.25 = 0

The above equation can be evaluated using the completing the square method and excluding the x² term as follows;

y² - 12·y - 20.25 = 0

y² - 12·y = 20.25

y² - 12·y + (-12/2)² = 20.25 + (-12/2)²

y² - 12·y + (-6)² = 20.25 + (-6)² = 56.25

(y - 6)² = 56.25

Therefore;

y - 6 = √(56.25) = ±7.5

The possible equation of the circle obtained by plugging in the x² term therefore is; (x - 0)² + (y - 6)² = 7.5²

The center of the circle is therefore;

(h, k) = (0, 6)

The radius of the circle, r = 7.5

The possible correction is therefore, option (a), where the 5 is a typing error

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The answer is the system of equations is x = 0.290566 and

y = 40.603774.

To solve this system of equations using a matrix, we have to write it in the form AX = B, where A will be coefficient matrix, X will be variable matrix, and B, constant matrix.

The system of equations is:

                                     y = 650x + 175

                                     y = 25,080 - 120x

To write it in matrix form, arrange coefficients and constants as follows:

| 650 -1 | | x | | 175 |

| -120 1 | * | y | = | 25,080 |

So, coefficient matrix A is:  | 650 -1 |

                                                  | -120 1 |

Variable matrix X is: | x |

                                         | y |

And constant matrix B is: | 175 |

                                                | 25,080 |

The coefficients in the first column of the matrix are coefficient of x in each equation, and coefficients in the second one are the coefficients of y. The constants in the matrix are constants from each equation.

To solve for X, we use matrix algebra to isolate X. First, we have find the inverse of matrix A:

\(A^{-1 }\) = (1 / det(A)) * adj(A)

where, det(A) is determinant of A, and adj(A) represents adjugated of A (the transpose of the co-factor matrix of A).

We can calculate these as follows:

det(A) = (650 * 1) - (-120 *(-1)) = 530

adj(A) = | 1 120 |

          = |-1 650 |

So \(A^{-1 }\)  = (1 / 530) * | 1 120 |

            = | 0.001887 0.226415 |

   \(A^{-1 }\)   = |-1 650 | |-0.001887 1.226415|

Now we can solve for X:

X = \(A^{-1 }\)* B

X = | 0.001887 0.226415 | * | 175 |

  = | 0.290566 |

  = |-0.001887 1.226415 | | 25,080 | | 40.603774|

So, the system of equations is x = 0.290566 and y = 40.603774.

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Final answer:

The given matrix does not match either the first equation 'y = 650x + 175' nor the second equation 'y = 25,080 - 120x'. There's a discrepancy between the coefficients given in the matrix and those in the equations.

Explanation:

The first step is to express both equations in terms of y to match the matrix provided. However, the equations already match this format.

The first equation is y = 650x + 175, so if we place the terms in matrix form, we'll get: Column 1 as -650 (the coefficient of x) and Column 2 as 1 (the coefficient of y) and Column 3 as -175 (the constant).

For the second equation, which is y = 25,080 - 120x, again converting all terms as per the columns in matrix form, the coefficients will be Row 2 - Column 1 as 120 (the coefficient of x), Column 2 as 1 (the coefficient of y), and Column 3 as 25,080 (the constant).

Given that the matrix provided doesn't match either of these equations, there must be a mistake in the matrix or in these equations.

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The centroid of a triangle is the point where the three medians of the triangle intersect. In this case, the triangle has vertices at (0, 0), (5, 0), and (0, 7).

First, let's calculate the average x-coordinate:
¯x = (0 + 5 + 0) / 3 = 5/3 ≈ 1.67

Next, let's calculate the average y-coordinate:
¯y = (0 + 0 + 7) / 3 = 7/3 ≈ 2.33, the centroid of the triangle with vertices at (0, 0), (5, 0), and (0, 7) is approximately (1.67, 2.33).
In summary, the centroid of the triangle with verticesvertices at (0, 0), (5, 0), and (0, 7) is located at approximately (1.67, 2.33). This point represents the average position of the three vertices and is the intersection point of the medians of the triangle.

The centroid coordinates are found by taking the average of the x-coordinates and the average of the y-coordinates of the three vertices. In this case, we add up the x-coordinates (0 + 5 + 0 = 5) and divide by 3 to get an average of 5/3, which is approximately 1.67. Similarly, we add up the y-coordinates (0 + 0 + 7 = 7) and divide by 3 to get an average of 7/3, which is approximately 2.33. These values represent the x-coordinate (¯x) and the y-coordinate (¯y) of the centroid, respectively. Therefore, the centroid of the triangle is located at approximately (1.67, 2.33).

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Answer:

65 apples

Step-by-step explanation:

We Know

John has 8 boxes of apples.

Each box holds 10 apples.

If 5 of the boxes are full, and 3 of the boxes are half full, how many apples does John have?

Let's solve

5 boxes are full: 5 x 10 = 50 apples

3 boxes are half full = 3(1/2 · 10) = 15 apples

50 + 15 = 65 apples

So, John has 65 apples.

To determine the points of intersection we first equate the expressions, then we solve for x. Once we have the values of x for which the functions are equal we plu them on one of the function to find its corresponding value of y.

a)

Let's equate the functions and solve for x:

Now we find the corresponding values of y for each value of x; to do this we use the second equation.

When x=3:

Hence the functions intersect at (3,11)

When x=2:

Hence the functions intersect at (2,6)

Therefore the function intersect at the points (3,11) and (2,6).

b)

Let's equate the functions and solve for x:

Now we find the corresponding values of y for each value of x; to do this we use the second equation.

When x=7:

Hence the functions intersect at (7,-26)

When x=-1:

Hence the functions intersect at (-1,-2)

Therefore the function intersect at the points (7,-26) and (-1,-2).

The required using the corresponding letter to each answer in order, Key, MATZ.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
x² - 4 = 0

x² = 4

x = ±2

The solution is x = 2 or x = -2.

2n² - 32 = 0

2n² = 32

n² = 16

n = ±4

The solution is n = 4 or n = -4.

3y² = 300

y² = 100

y = ±10

The solution is y = 10 or y = -10.

4d² + 4 = 8

4d² = 4

d² = 1

d = ±1

The solution is d = 1 or d = -1.

Using the corresponding letter to each answer in order, we get, Key, MATZ.

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The integral of \(9^2 - 10x + 6\) with respect to x is \((9x^2 - 5x^2 + 6x) + C\). 8. If y = \(x\sqrt{8x^2 - 7}\), then dy/dx = \(\frac {dy}{dx}=(\sqrt{8x^2 - 7} + x * \frac 12) * (8x^2 - 7)^{-1/2} * (16x) - 0\). 9. If\(y = 3^x\), then \(y' = 3^x * \log(3)\). 10. The solution to the differential equation dy/dx = 10xy, with the initial condition y = 70, is \(y = 70 * e^{5x^2}\).

7. The indefinite integral of \((92x^2 - 10x + 6)^3 dx\) is \((1/3) * (92x^3 - 5x^2 + 6x)^3 + C\). To evaluate this integral, we can expand the square and integrate each term separately using the power rule for integration. The constant of integration, represented by 'C', accounts for any possible constant term in the original function.

8. To find the derivative of \(y = x\sqrt{8x^2 - 7}\), we can apply the chain rule. First, we differentiate the outer function (x) as 1. Then, we differentiate the inner function (8x² - 7) using the power rule, resulting in 16x. Multiplying these two differentials together, we get dy/dx = 16x.

9. Given \(y = 3^x\), we can find y' (the derivative of y with respect to x) using the exponential rule. The derivative of a constant base raised to the power of x is equal to the natural logarithm of the base multiplied by the original function. Therefore, \(y' = 3^x * \log(3)\).

10. The differential equation dy/dx = 10xy can be solved by separating variables. Rearranging the equation, we have dy/y = 10x dx. Integrating both sides, we obtain \(\log|y| = 5x^2 + C.\). To find the particular solution, we can substitute the given initial condition y = 70 when x = 0. Solving for C, we find \(C = \log|70|\). Thus, the solution to the differential equation is \(\log|y| = 5x^2 + \log|70|\).

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Answer:

Step-by-step explanation:

-x² + 70x - 600

If we multiply all by -1, we have

x² - 70x + 600

If we factorise this, we have

x² - 10x - 60x + 600

x(x - 10) - 60(x - 10)

(x - 10) (x - 60)

x = 10

x = 60

If the company sells 10, or 60 items, their profit is 0

Answer:

arc IAR

Step-by-step explanation:

major arc mean longer arc of circle connecting two end points