In ΔUVW, the measure of ∠W=90°, WV = 65, VU = 97, and UW = 72. What ratio represents the sine of ∠V?

Answer:

x = 3

Step-by-step explanation:

4 ( x - 7 ) = -6x + 12

→ Expand brackets

4x - 28 = -6x + 12

→ Add 6x to both sides

10x - 28 = 12

→ Add 28 to both sides

10x = 30

→ Divide both sides by 10

x = 3

The measure of angle ABP is 90° and the measure of angle APB is 48°.

In the given figure, the measure of arc AB is 108° and the measure of angle ACB is (x+3)°.

Tangent and radius of a circle meet at 90°. If we draw a radius that meets the circumference at the same point, the angle between the radius and the tangent will always be exactly 90°.

Question 6:

Here, The measure of arc AB = 2×The measure of angle ACB

108 = 2(x+3)

⇒ x+3=54

⇒ x =51°

Question 7:

Given that, ∠PAB=42° and line PB is tangent to circle A

Now, ∠ABP =90° (Angle formed by tangent and radius is 90°)

Here, ∠ABP+∠PAB+∠APB=180°

⇒ 90°+42°+∠APB=180°

⇒ 132°+∠APB=180°

⇒ ∠APB=180°-132°

⇒ ∠APB=48°

Therefore, the measure of angle ABP is 90° and the measure of angle APB is 48°.

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Answer:

  x ≈ -8.402, 8.502

Step-by-step explanation:

The usual methods of solving quadratic equations apply to this one. Any of them can be used: graphing, factoring, completing the square, quadratic formula.

Often, when the coefficients are non-integers and have no obvious relationship to each other, the most convenient method of solution is the quadratic formula. It tells you the solution to ax²+bx+c=0 is ...

  \(x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\)

Your equation has the coefficients, a = -0.07, b = 0.007, c = 5, so the solutions are ...

  \(x=\dfrac{-0.007\pm\sqrt{0.007^2-4(-0.07)(5)}}{2(-0.07)}=\dfrac{-0.007\pm\sqrt{1.400049}}{-0.14}\\\\x=0.05\pm\sqrt{\dfrac{200007}{2800}}=0.05\pm\sqrt{71.4310\overline{714285}}\\\\\boxed{x\approx\{-8.40169,\,8.50169\}}\)

Answer:

\(t=8.50, -8.40\:\: \sf (2 \:d.p.)\)

Step-by-step explanation:

Quadratic equations are in the form \(ax^2+bx+c=0\),  where \(a\neq 0\).

There are three basic methods to solve quadratic equations algebraically:

Given quadratic equation:

\(h(t)=-0.07t^2+0.007t+5\)

Method 1 - Factoring

If the trinomial is able to be easily factored, set the equation equal to zero and factor.  Set each factor equal to zero and solve.

As the given example is not easily factored, factoring is not the best method to use on this occasion.

Method 2 - Completing the Square

If the quadratic expression is not able to be easily factored, try completing the square.

Divide all terms by \(a\) (-0.07):

\(\implies t^2-\dfrac{1}{10}t-\dfrac{500}{7}=0\)

Move the constant to the right side:

\(\implies t^2-\dfrac{1}{10}t=\dfrac{500}{7}\)

Add the square of half the coefficient of t to both sides:

\(\implies t^2-\dfrac{1}{10}t+\left(-\dfrac{1}{20}\right)^2=\dfrac{500}{7}+\left(-\dfrac{1}{20}\right)^2\)

\(\implies t^2-\dfrac{1}{10}t+\dfrac{1}{400}=\dfrac{200007}{2800}\)

Factor the perfect trinomial:

\(\implies \left(t-\dfrac{1}{20}\right)^2=\dfrac{200007}{2800}\)

Square root both sides:

\(\implies t-\dfrac{1}{20}=\pm\sqrt{\dfrac{200007}{2800}\)

Add 1/20 to both sides:

\(\implies t=\dfrac{1}{20}\pm\sqrt{\dfrac{200007}{2800}\)

As decimals to 2 decimal places:

\(\implies t=8.50, -8.40\:\:\sf(2 \:d.p.)\)

Method 3 - Quadratic Formula

\(x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\)

This can be used to find both real and imaginary or complex solutions.

Identity the variables:

\(a=-0.07, \quad b=0.007, \quad c=5\)

Substitute the values into the quadratic formula and solve for t:

\(\implies t=\dfrac{-0.007 \pm \sqrt{0.007^2-4(-0.07)(5)} }{2(-0.07)}\)

\(\implies t=\dfrac{-0.007 \pm \sqrt{1.400049}}{-0.14}\)

\(\implies t=\dfrac{0.007 \pm \sqrt{1.400049}}{0.14}\)

\(\implies t=8.50, -8.40\:\: \sf (2 \:d.p.)\)

Finally, a non-algebraic method of solving a quadratic equation is by graphing using a graphical calculator (see attached).  The solutions are the points at which the curve intercepts the x-axis.

Answer:

The answer would be 6 because it is going into minutes meaning 60 would be way too high even though its the next lowest.

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

The other options are equal to and way over 1 hour. 6 is the best answer.

Answer

\(g^-1(x)=\frac{8}{3}x-\frac{128}{3}\)

Step-by-step explanation:

The cost of the tabletop is $251.10. Option C

The formula for calculating the area of a rectangle is expressed as;

Area = lw

Such that the parameters are;

From the diagram shown, we have;

The width = 6 3/4 feet = 27/4 feet

The length = 3 feet

Substitute the values

Area = 27/4 × 3

Multiply

Area = 20. 25 square feet

But;

1 square foot = $12.40

Then  20. 25 square feet = x

x = $251. 10

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a) The amount of water in the pool after 2 hours can be calculated using the equation.

Water in pool = 10L/hour × 2 hours = 20L.

b) The pool will be 80L when the equation is satisfied: 80L = 10L/hour × Time.

Solving for Time, we find Time = 8 hours.

c) Part b) is linear.

a) To calculate the amount of water in the pool after 2 hours, we can use the equation:

Water in pool = Water filling rate × Time

Since the pool gets filled up with 10L of water per hour, we can substitute the values:

Water in pool = 10 L/hour × 2 hours = 20L

Therefore, after 2 hours, there will be 20 liters of water in the pool.

b) To determine the number of hours it takes for the pool to reach 80 liters, we can set up the equation:

Water in pool = Water filling rate × Time

We want the water in the pool to be 80 liters, so the equation becomes:

80L = 10 L/hour × Time

Dividing both sides by 10 L/hour, we get:

Time = 80L / 10 L/hour = 8 hours

Therefore, it will take 8 hours for the pool to contain 80 liters of water.

c) Part b) is linear.

The equation Water in pool = Water filling rate × Time represents a linear relationship because the amount of water in the pool increases linearly with respect to time.

Each hour, the pool fills up with a constant rate of 10 liters, leading to a proportional increase in the total volume of water in the pool.

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Answer:

3 1/5 inches

Step by Step Explanation:

4/5 * 4 = 16/5

16/5 as a mixed number is 3 1/5.

The answer is 3 1/5 inches hope this helps!!

Answer:

i would say 3  1/5

Step-by-step explanation

The correlation in error terms that arises when the error terms at successive points in time are related is termed autocorrelation

The correct answer is an option (a).

Correlation is the mutual connection between two or more variables. These variables can be dependent or independent but there should be random variables.

Autocorrelation is the degree of correlation between the values of the same variables across different data.

Instead of correlation between two different variables, the correlation is between two values of the same variable at times i and i + k.

It is used for the following two purposes:

- To detect non-randomness in data.

- To identify an appropriate time series model if the data are not random.

Therefore, The correlation in error terms that arises when the error terms at successive points in time are related is termed autocorrelation

The correct answer is an option (a).

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92+3.5=95.5

i dont know if that's what you want or is there a variable missing.

Interval notation is (−∞, −4) U (−4, ∞)

The given inequality is ∣x + 4∣ > − 9. Step-by-step explanation: Absolute value inequalities: Inequalities that contain absolute values are known as absolute value inequalities. The absolute value inequality ∣x + 4∣ > − 9 is given.Inequality means that x can take any value except the value that makes the inequality false. If x satisfies the inequality, we write x ∈ (A, B) or x ∈ [A, B), where A and B are any two values that satisfy the inequality.The inequality ∣x + 4∣ > − 9 implies that the absolute value of x + 4 is greater than −9. The absolute value of x + 4 is always greater than or equal to zero.Therefore, the inequality can be written as∣x + 4∣ > 0This inequality implies that x is not equal to −4.The interval of x satisfying the given inequality is x ∈ (−∞, −4) U (−4, ∞), where U represents the union of two intervals. Therefore, the answer in interval notation is (−∞, −4) U (−4, ∞).Thus, the solution to the inequality |x + 4| > -9 in interval notation is (−∞, −4) U (−4, ∞).

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Answer:

400 words in 10 minutes

Step-by-step explanation:

If you divide 280 by 7, you get 40. That means she can type 40 words per minute. 40 times 10 equals 400.

Answer:

there is no equation

plz edit the question

The value of x for the expression 3x² = 12 are 2 and -2.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 = 9 is an equation

We have,

3x² = 12

Divide both sides by 3.

x² = 4

x = √4

x = ±2

Thus,

The value of x is 2 or -2.

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The complete question is:

Solve the following equation algebraically 3x² = 12.​

Answer:

x = 15

Step-by-step explanation:

24/(x+5) = 6/5

By doing cross products we acquire

120 = 6x + 30

Subtract 30 from both sides

90 = 6x

Divide both sides by 6

x = 15

Notes:

( Cross products is when you multiply the top number of the first fraction by the bottom number of the second fraction and the bottom number of the first fraction by the top of the second fraction )

Top number of first fraction is 24 and bottom number of second fraction is 5 so we multiply 24 by 5 to get 120

Bottom number of first fraction is x + 5 and top number of second fraction is 6 so we multiply "x + 5" by 6 to get 6x + 30

We're left with 6x + 30 = 120

We then solve for x algebraically

Answer:

y = 12

Step-by-step explanation:

proportions can be solved by cross-multiplying

to work with smaller numbers, you can simplify \(\frac{14}{10}\) to be \(\frac{7}{5}\)

\(\frac{7}{5}\) = \(\frac{y+9}{15}\)

7(15) = 5(y + 9)

105 = 5y + 45

60 = 5y

y = 12

Answer:

p = - 2

Step-by-step explanation:

Given

n = 2 + 6m ← substitute m = - \(\frac{1}{2}\) into the expression

n = 2 + 6(- \(\frac{1}{2}\) ) = 2 - 3 = - 1

Thus

p = \(\frac{2}{n}\) = \(\frac{2}{-1}\) = - 2

The height h will be equal to 13 cm for the parallelogram.

The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the parallelogram in a two-dimensional plane is called the area of the parallelogram.

Given that a right-angled triangle and a parallelogram are shown b

13 cm and 6 cm. The area of the parallelogram is 4 times the area of the right angle.

The height h will be calculated as,

A= 1/2 x6 x 13 = 3 x 13 =39 square

Area of the parallelogram is,

39=156cm square

156 divided by 12

h=13 cm

Therefore, the height h will be equal to 13 cm for the parallelogram.

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Answer:

x=-3,5

Step-by-step explanation:

When choosing values of x between each intercept and values of x on either side of the vertical asymptotes, it is

important to consider the behavior of the function in those regions.  Choosing values of x close to the intercepts can

give you an idea of the shape of the function in that region.

Choosing values of x close to the vertical asymptotes can help you determine the behavior of the function as x

approaches that value.

Choosing values of x between each intercept and values of x on either side of the vertical asymptotes.

To choose values of x between each intercept and values of x on either side of the vertical asymptotes,

1. Identify the intercepts: Find the points where the function intersects the x-axis and the y-axis. These are the points where the function's value is zero.

2. Identify the vertical asymptotes: Determine the values of x where the function is undefined or has a vertical asymptote.

3. Choose values of x between each intercept: Select a value between each pair of intercepts that you found in step 1. These values will help you understand the function's behavior between the intercepts.

4. Choose values of x on either side of the vertical asymptotes: Select a value slightly less than and slightly greater than each vertical asymptote you found in step 2. These values will help you understand the function's behavior around the vertical asymptotes.

By following these steps, you can analyze the function's behavior around its intercepts and vertical asymptotes.

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6 number of stickers diana given to her sister.

A division is a process of splitting a specific amount into equal parts.

Diana had 41 stickers and she put them in 7 equal groups. To find out how many stickers she put in each group, we can divide 41 by 7:

41 ÷ 7 = 5 with a remainder of 6

This means that Diana put 5 stickers in each of the 7 groups, and she had 6 stickers leftover.

She gave the leftover stickers to her sister, so she gave her sister 6 stickers.

Hence, 6 number of stickers  diana given to her sister.

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No, the statement "In spherical geometry, the sum of the angles in a triangle equals 180 degrees." is not true.

The term triangle in geometry refers the polygon with three vertices, sides and angle.

Here we have given the statement "in Euclidean geometry the sum of the angles in a triangle equals 180 degrees"

And we need to find whether this is this also true in spherical geometry.

Basically, the sum of the angles of a spherical triangle is not equal to 180°. Because, we know that the sphere is a curved surface, where locally the laws of the flat Euclidean geometry are good approximations.

Therefore, here in a small triangle on the face of the earth, then the sum of the angles is only slightly more than 180 degrees.

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Substitution method - the points are (-6, -11/2),(-4,-3), (-8/5,0), (0,2) and (4,7)

what is the substitution method?

To solve many simultaneous linear equations, use the substitution method in algebra. The value of a variable from one equation is substituted in the second equation in this procedure, as the name implies.

we are given the equation,

5x - 4y = -8

case I

when x = -6

5(-6) - 4y  = -8

-30 - 4y = -8

-4y = -8 + 30

-4y = 22

y = -(22/4)

y = -11/2

(x,y) = (-6, -11/2)

case II

when y = -3

5x - 4(-3) = -8

5x + 12 = -8

5x = -8 -12

5x = -20

x = -20/5

x = -4

(x,y) = (-4,-3)

case III

when y = 0

5x - 4y = -8

5x - 4(0) = -8

5x = -8

x = -8/5

(x,y) = (-8/5,0)

case III

when x = 0

5(0) - 4y = -8

0 - 4y = - 8

y= 8/4

y = 2

(x,y) = (0,2)

case IV

when x = 4

5(4) - 4y = -8

20 - 4y = -8

-4y = -8-20

-4y = -28

y = 28/4

y = 7

(x,y) = (4,7)

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Answer:

Now, to make a profit of 12%. Therefore, Selling price of calculator must have Rs. 1400 to make a profit of 12%.

please follow me for more answers please.

The formula to convert liters (L) to nanoliters (nL) is: nL = L x 1,000,000

A liter is a unit of volume used to measure liquids or gases. It is part of the metric system of measurement and is abbreviated as "L". One liter is equal to 1000 cubic centimeters (cc) or milliliters (ml).

To give you a better idea of how much volume a liter represents, think about a typical water bottle that you might buy at a store. A standard water bottle typically contains around 0.5 liters of water, while a larger water bottle may contain 1-2 liters.

In addition to measuring liquids, liters can also be used to measure the volume of gases. For example, the capacity of a car engine might be given in liters, indicating the total volume of air and fuel that the engine can hold.

The liter is a widely used unit of volume around the world, and it is part of the International System of Units (SI).

One liter is equal to 1,000,000 nanoliters. Therefore, to convert liters to nanoliters, you can multiply the value in liters by 1,000,000.

The formula to convert liters (L) to nanoliters (nL) is:

nL = L x 1,000,000

For example, if you have 0.5 liters, the conversion to nanoliters would be:

nL = 0.5 L x 1,000,000

nL = 500,000,000 nL

Therefore, 0.5 liters is equal to 500,000,000 nanoliters.

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Answer:

A: 6

Step-by-step explanation:

The line of best fit of the traffic study is a line through a scatterplot of data points which shows the relationship between the points.

Your information is incomplete as the table isn't given. Therefore, an overview will be given.

The least square methods is used by statisticians to arrive at the geometric equation for the line. A straight line will simply result from a simple regression of two or more independent variables.

A regression that has to do with multiple related variables lead to a curved line. The line of best fit is an important output of regression analysis.

A regression that has two independent variables will have a formula with:

y = c + b1x1 + b2x2

where,

c = constant

b1 = first regression coefficient

x1 = first independent variable

b2 = second regression coefficient

x2 = second independent variable.

In conclusion, the line of best fit expresses the relationship in a scatterplot of the data points.

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Answer:

144

Step-by-step explanation:

The shape is a trapezoid.

Add 6 and 112, which is eighteen

divide eighteen by 2, which is 9

Finally, multiply 9 and sixteen which is 144

Answer:

total cost is £244.4

Step-by-step explanation:

( 37 * 4 ) + ( 15 * 4 ) = 208

208 * .175 = 36.4

208 + 36.4 = 244.4

HOPE THIS HELPS

The number of subs in the order is 8 or 9

Let's call the number of subs in the order "x".

Since the cost of 3 subs is $20, the cost per sub is $20 / 3 = $6.67.

And since the cost of 4 subs is $26, the cost per sub is $26 / 4 = $6.50.

So the cost per sub is between $6.50 and $6.67.

If the total cost is $56, then the cost per sub must be $56 / x.

So:

x = 56/6.5 or x = 56/6.67

Evalutate

x = 8.6 or x = 8.4

Approximate

x = 9 or 8

Hence, the subs is 8 to 9

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