Evaluate when a=1/2 and b=7 b*2 - 16a + 5

Answer:

168 cm^2

Step-by-step explanation:

This rhombus is made up of two triangles. To find triangle area, base x height/2 (but bc there are two triangles we don’t need to divide by 2). To do this, 14 x 12 to get 168cm^2

Answer:

Put the point a tiny bit more than half way between 14 and 15.

Step-by-step explanation:

If you are allowed to use a calculator, put in sqrt215 and you get out 14.66, that goes a little bit more than halfway between 14 and 15.

If you are not allowed to use a calculator, think of the numbers on the numberline in terms of answers to *perfect square* questions.

So 12 is sqrt 144.

13 is sqrt 169.

14 is sqrt 196.

15 is sqrt 225.

So the 215 in your question is in between 196 and 225.

215 is closer to 225 (than to 196) so put the point closer to sqrt 225. That is, in between 14 and 15 and just a tad bit closer to 15.

The skater's total score would be 58 points (7.25 x 8 = 58).

Just dividing the total number of values in a data set by the sum of all of the values yields it. A frequency table of data or raw data can both be used for the calculation.

The following equation can be used to determine each skater's overall score, s, assuming that they each receive evaluations from eight judges and have a mean score of 7.25 points:

s = 7.25 x 8

The total score is determined by multiplying the average score by the quantity of judges in this equation. In this instance, the skater would have earned 58 points overall (7.25 x 8 = 58).

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In a skating competition each skater receives scores from eight judges a skater has a mean (average) of 7.25 points. Write an equation to find the skaters total score?

a. 7.25 × 8

b. 7.25⁸

c. 7.25 - 8

d. 7.25/8

The values of x that could make the triangle into different types of triangles are:

For a triangle to be valid, the sum of the lengths of any two sides must be greater than the length of the third side.

Right Triangle:

A triangle is a right triangle if it satisfies the Pythagorean theorem: a² + b² = c², where c is the longest side (hypotenuse).

6² + 8² = x²

36 + 64 = x²

100 = x²

x = 10

Acute Triangle:

A triangle is acute if the sum of the squares of the two shorter sides is greater than the square of the longest side. Since we already know that the right triangle has x = 10, we can choose a value for x that is less than 10 to form an acute triangle.

Let's take x = 9:

6² + 8² > 9²

36 + 64 > 81

100 > 81

Obtuse Triangle:

A triangle is obtuse if the sum of the squares of the two shorter sides is less than the square of the longest side. We can choose a value for x that is greater than 10 to form an obtuse triangle.

Let's take x = 11:

6² + 8² < 11²

36 + 64 < 121

100 < 121

The possible values of x for each triangle type are:

Right Triangle: x = 10

Acute Triangle: x = 9

Obtuse Triangle: x = 11

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The value of n (S) is 5, n (T) is 7, n (∪) is 11 and n (∩) is 1. The solution has been obtained by using the given sets.

What is a set?

Sets are represented as a collection of well-defined objects or elements and it does not change from person to person. A set is symbolised by a capital letter. The number of items in the finite set is known as the cardinal number of a set.

We are given two sets as S = {r, e, l, a, x} and T = {i, t, s, o, k, a, y}.

Now,

n (S) = 5

This is because there are 5 elements in this set.

n (T) = 7

This is because there are 7 elements in this set.

S ∪ T = {r, e, l, a, x, i, t, s, o, k, y}

n (∪) = 11

This is because there are 11 distinct elements in the sets.

S ∩ T = {a}

n (∩) = 1

This is because there is only 1 element common in the sets.

Hence, the required solution has been obtained.

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The probability based on the information will be;

a. Likely, probability is 25%

b. Likely, probability is 25%

c. Impossible, probability is 0%

d. Unlikely, probability is 33.3%

The probability of rolling a 5 on a 6 sided die is 1/6 or approximately 16.67%.

The probability of not rolling a 5 on a 6 sided die is 5/6 or approximately 83.33%. This can also be:

= 100 - 16.67

= 83.33%

The probability of spinning an even number on a spinner with numbers 1-8 is 4/8 or 1/2 or 50%.

The probability that a white horse is George is 1/5 or 20%.

An event that has probability of 0% is something that is impossible, such as rolling a 7 on a 6-sided die. An event that has a probability of 100% is something that is certain, such as flipping a coin and getting either heads or tails.

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b equal for the top of the bookcase to have the correct area= 5 cm2

A solid object's surface area is a measurement of the total area that the surface of the object takes up.

The definition of arc length for one-dimensional curves and the definition of surface area for polyhedra (i.e., objects with flat polygonal faces), where the surface area is the sum of the areas of its faces, are both much simpler mathematical concepts than the definition of surface area when there are curved surfaces.

A smooth surface's surface area is determined using its representation as a parametric surface, such as a sphere.

This definition of surface area uses partial derivatives and double integration and is based on techniques used in infinitesimal calculus.

Henri Lebesgue and Hermann Minkowski at the turn of the century sought a general definition of surface area.

L × b = 300

b = 300 / L

b = 300 / 60 = 5

Hence, b equal for the top of the bookcase to have the correct area= 5 cm2.

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Answer:

μ (∠1) = 82°

μ (∠2) = 98°

μ (∠3) = 82°

μ (∠4) = 98°

Step-by-step explanation:

As the vertically opposite angles are equal to each other,

μ (∠2) = μ (∠4)

   98° = 98°

As the angles in a straight line are added up to 180°,

μ (∠2) + μ (∠3) = 180

98 + μ (∠3) = 180

μ (∠3) = 180 - 98

μ (∠3) = 82°

As the vertically opposite angles are equal to each other,

μ (∠3) = μ (∠1)

   82° = 82°

Answer:

2 real zeros at x = - 2 , x = 1

Step-by-step explanation:

f(x) = x² + x - 2

to find the zeros let f(x) = 0 , that is

x² + x - 2 = 0 ← in standard form

(x + 2)(x - 1) = 0 ← in factored form

equate each factor to zero and solve for x

x + 2 = 0 ⇒ x = - 2

x + 1 = 0 ⇒ x = - 1

there are 2 real zeros , x = - 2 and x = 1

Answer:

Matt's typing speed increased by 18.75%.

Step-by-step explanation:

To find the percent increase, we can use the following formula:

percent increase = (new value - old value) / old value x 100%

Using this formula, we can calculate the percent increase in Matt's typing speed as follows:

percent increase = (38 - 32) / 32 x 100%

percent increase = 6 / 32 x 100%

percent increase = 0.1875 x 100%

percent increase = 18.75%

Answer:

B.......................

Because the x2 term's coefficient is positive, the function will rise without  equation bound as x approaches infinity or negative infinity. As a result, no horizontal asymptote exists.

An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x + 3" equals the number "9".

The y-intercept of the equation y = (0,0) is the point on the line where it meets the y-axis and corresponds to the value of y when x equals 0. As a result, the equation y = 0's y-intercept is (0,0).

An equation's domain is the set of all possible values of x for which the equation is defined.

a) Because there are no constraints on the potential values of x, the domain of the equation y = x2 - 4x is all real integers.

b) The domain of the equation y = 1/(x-4) includes all real numbers except x = 4, which is undefined since division by zero is undefined.

c) Because the term within the square root must be non-negative, the domain of the equation y = sqrt(x-3)(x-4) is x >= 3.

As x approaches a specific value, the graph of the function approaches but never reaches vertical asymptotes. As the denominator of a rational function hits 0, they arise.

Because y = (x-3)(x-4) is not a rational function, it lacks vertical asymptotes.

A function's horizontal asymptote is a horizontal line that it approaches when x approaches infinity or negative infinity.

The dominant term in the formula as x gets extremely large or very tiny is x2, thus we can rewrite the equation as [tex]y = x2 - 7x + 12[/tex]  .

Therefore, Because the x2 term's coefficient is positive, the function will rise without bound as x approaches infinity or negative infinity. As a result, no horizontal asymptote exists.

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Step-by-step explanation:

y = x^2 / z      now triple x and z

y = (3x)^2 / 3z = 9x^2 / 3z = 3 * x^2 / z  <==== this is 3 times the original

    y is tripled

In the equation y = 10 - 0.1x, the coefficient 0.1 represents the slope of the line.

it represents the rate of change of y with respect to x, which is the amount by which y changes for every unit increase in x.

In this case, the slope is negative (-0.1), which means that as the number of minutes on hold (x) increases by 1 unit, the level of satisfaction (y) decreases by 0.1 units.

In other words, the longer a customer spends on hold, the lower their level of satisfaction is likely to be. The slope is a key parameter in the equation and provides valuable information about the relationship between the two variables.

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Answer:The leading term in a polynomial is the term with the highest degree.

Step-by-step explanation:

Step-by-step explanation:

y = 3 x^2 - 4 x - 1

leading coefficient is 3  and its sign is ' + '   or positive

The blanks of the number pyramid puzzle can be filled with numbers calculated below.

A number pyramid puzzle is a type of mathematical puzzle where a pyramid-shaped grid of numbers is given, with some of the numbers missing.

Check the attached image for labeling. Since each number is the product of the two numbers directly beneath it. We can say:

m = -4 * 0.5 = -2

k = 0.5 * 1/8 = 1/16

x * (-1/8) = 8

x = 8/(-1/8)

x = -64  

y = x * 1/8

y = -64 * 1/8

y = -8

j = m * k

j =  -2 * 1/16 = -1/8

p = -48 * m

p = -48 * (-2) = 96

n = y * 8

n = -8 * 8 = -64

t = p * j

t = 96 * (-1/8) = -12

w = -1/2 * n

w = -1/2 * (-64) = 32

c = t * 1/16

c = -12 * 1/16 = -3/4

u = 1/16 * w

u = 1/16 * 32 = 2

d = c * u

d = -3/4 * 2 = -3/2

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The graph is increasing from 0 minutes to 40 minutes, decreasing from 40 minutes to 80 minutes, and constant from 80 minutes to 200 minutes.

The rate of global warming is increasing. Every year, average global temperatures continue to rise, leading to more extreme weather events and disruptions to the environment. This has been caused by human activities, such as burning fossil fuels, which release carbon dioxide and other greenhouse gases into the atmosphere. These gases trap heat, leading to a rise in temperatures.

The domain of the relation is the set of all time values, ranging from 0 minutes to 200 minutes. The range of the relation is the set of all depth values, ranging from 0 feet to 8 feet.

The graph represents a function because for every value of time, there is exactly one corresponding value of depth.

The graph shows the depth of water in a horse trough over a certain amount of time. The graph starts at 0 feet and increases to a maximum of 8 feet over the first 40 minutes. After 40 minutes, the depth of the water starts to decrease until it reaches a minimum of 2 feet at 80 minutes. After 80 minutes, the depth of the water remains constant at 2 feet until the end of the graph at 200 minutes.

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Answer:2.04

Step-by-step explanation:

Answer:

5683200

Step-by-step explanation:

Move the decimal 4 places to the right because [tex]10^4[/tex] has 4 zeros.

Answer:

There is 5% of the juice left.

Step-by-step explanation:

We know that originally, the container had 80 oz of orange juice, this is 100% in our case.

Then we can write a relation:

80 oz = 100%

Now there are 4 ounces left, in the same way as before, we can write this as:

4 oz = X%

We want to find X%

First, let's write our equations:

4 oz = X%

80 oz = 100%

We can take the quotient between these two equations to get:

(4oz/80oz) = (X%/100%)

We need to solve this for X%, then we get:

(4oz/80oz)*100% = X% = 5%

This means that 4 oz is 5% of the initial volume of the juice container.

Then we can conclude that there is 5% of the juice left.

All corresponding side lengths have a ratio of [tex]\frac{1}{3}$[/tex] or less, we can conclude that the scale factor of the dilation is less than or equal to [tex]\frac{1}{3}$[/tex]

We can use the distance formula to find the length of the sides of both quadrilaterals, and then find the ratio of corresponding side lengths to determine the scale factor of the dilation.

Let's start with the original quadrilateral ABCD. The length of AB is:

[tex]$\sqrt{(9 - (-3))^2 + (3 - 0)^2} = \sqrt{12^2 + 3^2} = \sqrt{153}$[/tex]

Similarly, the lengths of BC, CD, and DA are:

[tex]BC: $\sqrt{(9 - 9)^2 + (9 - 3)^2} = 6$[/tex]

[tex]CD: $\sqrt{(-3 - 9)^2 + (3 - 9)^2} = \sqrt{144 + 36} = \sqrt{180} = 6\sqrt{5}$[/tex]

[tex]DA: $\sqrt{(-3 - (-3))^2 + (3 - 0)^2} = 3$[/tex]

Now, let's find the corresponding side lengths of the dilated quadrilateral A'B'C'D'. The length of A'B' is:

[tex]$\sqrt{(3 - (-1))^2 + (1 - 0)^2} = \sqrt{16 + 1} = \sqrt{17}$[/tex]

Similarly, the lengths of B'C', C'D', and D'A' are:

[tex]B'C': $\sqrt{(3 - 3)^2 + (3 - 1)^2} = 2$[/tex]

[tex]C'D': $\sqrt{(-1 - 3)^2 + (1 - 3)^2} = \sqrt{16 + 4} = \sqrt{20} = 2\sqrt{5}$[/tex]

[tex]D'A': $\sqrt{(-1 - (-3))^2 + (1 - 0)^2} = \sqrt{4 + 1} = \sqrt{5}$[/tex]

Now we can find the ratio of corresponding side lengths:

[tex]$\frac{\text{length of A'B'}}{\text{length of AB}} = \frac{\sqrt{17}}{\sqrt{153}} = \frac{\sqrt{17} \cdot \sqrt{153}}{153} \approx 0.821$[/tex]

[tex]$\frac{\text{length of B'C'}}{\text{length of BC}} = \frac{2}{6} = \frac{1}{3}$[/tex]

[tex]$\frac{\text{length of C'D'}}{\text{length of CD}} = \frac{2\sqrt{5}}{6\sqrt{5}} = \frac{1}{3}$[/tex]

[tex]$\frac{\text{length of D'A'}}{\text{length of DA}} = \frac{\sqrt{5}}{3}$[/tex]

Since all corresponding side lengths have a ratio of [tex]\frac{1}{3}$[/tex] or less, we can conclude that the scale factor of the dilation is less than or equal to [tex]\frac{1}{3}$[/tex]. To find the exact scale factor, we can choose any two corresponding side lengths and take their ratio.

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Answer: what shape?

Step-by-step explanation:

More info please

Answer:

Both data sets represent multiplicative relationships. In Table A, y is 3.5 times x, and in Table B, y is 9.2 times x.

The correct statement is: Both data sets represent multiplicative relationships. In Table A, y is 3.5 times x, and in Table B, y is 9.2 times x.

The value of x that makes A parallel to B is 15.

Alternate exterior angles are a pair of angles that lie outside of two parallel lines and are on opposite sides of the transversal. In other words, they are a pair of non-adjacent angles that are formed when a transversal intersects two parallel lines. The angles are congruent, meaning that they have the same measure.

The term "alternate" refers to the fact that they are on opposite sides of the transversal and "exterior" indicates that they are outside of the parallel lines. Alternate exterior angles are important in geometry because they can be used to prove that two lines are parallel. If the alternate exterior angles are congruent, then the lines are parallel.

Since the alternate exterior angles are equal, we can set them equal to each other:

8x + 30 = 10x

Subtracting 8x from both sides, we get:

30 = 2x

Dividing both sides by 2, we get:

15 = x

So the value of x that makes A||B is 15.

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Answer:

The cone takes up one-third of the volume of the cylinder. (the cylinder is 3x bigger than the cone)

Step-by-step explanation:

Answer:

B. is right.

Step-by-step explanation:

Volume of cone = volume of cylinder/3

Therefore the volume of the cylinder is 3 x that of cone

The demand equation for commodity A is Xa = (4/10)Xb.

A demand equation is a mathematical representation of the relationship between the quantity of a good or service that consumers are willing to buy and the various factors that influence that demand, such as price, income, and preferences.

In the given question,

To find the consumer's demand equation for A, we need to use the utility maximization rule, which states that a consumer will allocate their budget in such a way as to maximize their total utility subject to their budget constraint.

Let Xa be the quantity of commodity A and Xb be the quantity of commodity B. We know that the consumer has $30 to spend, so the budget constraint is:

3Xb + pXa = 30

where p is the price of commodity A. We also know the utility function:

U = 4XgXb

To maximize U subject to the budget constraint, we can use the Lagrangian method:

L = 4XgXb + λ(30 - 3Xb - pXa)

where λ is the Lagrange multiplier.

To find the demand equation for A, we need to take the partial derivative of L with respect to Xa and set it equal to zero:

∂L/∂Xa = -λp = 0

This gives us λ = 0, which we can substitute back into the Lagrangian equation to get:

L = 4XgXb + 0(30 - 3Xb - pXa)

L = 4XgXb

To find the demand equation for A, we need to take the partial derivative of L with respect to p and solve for Xa:

∂L/∂p = -4XgXb/Xa = -30/3

Xa = (4/10)Xb

So the demand equation for commodity A is Xa = (4/10)Xb.

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The demand equation for commodity A is Xa = (4/10)Xb.

What is demand equation?

A demand equation is a mathematical formula that expresses the relationship between the quantity of a good or service that consumers are willing and able to purchase and various factors that affect that quantity, such as price, income, and the prices of other goods.

To find the consumer's demand equation for A, we need to use the utility maximization rule, which states that a consumer will allocate their budget in such a way as to maximize their total utility subject to their budget constraint.

Let Xa be the quantity of commodity A and Xb be the quantity of commodity B. We know that the consumer has $30 to spend, so the budget constraint is:

3Xb + pXa = 30

where p is the price of commodity A. We also know the utility function:

U = 4XgXb

To maximize U subject to the budget constraint, we can use the Lagrangian method:

L = 4XgXb + λ(30 - 3Xb - pXa)

where λ is the Lagrange multiplier.

To find the demand equation for A, we need to take the partial derivative of L with respect to Xa and set it equal to zero:

∂L/∂Xa = -λp = 0

This gives us λ = 0, which we can substitute back into the Lagrangian equation to get:

L = 4XgXb + 0(30 - 3Xb - pXa)

L = 4XgXb

To find the demand equation for A, we need to take the partial derivative of L with respect to p and solve for Xa:

∂L/∂p = -4XgXb/Xa = -30/3

Xa = (4/10)Xb

So the demand equation for commodity A is Xa = (4/10)Xb.

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Answer:

Step-by-step explanation:

To find the LCM of the given expressions, we need to factor each expression completely and then find the product of the highest powers of all the factors.

ax² - (a² + ab)x + a²b can be factored as:

ax² - (a² + ab)x + a²b = a(x - b)(x - a)

bx² - (b² + bc)x + b²c can be factored as:

bx² - (b² + bc)x + b²c = b(x - c)(x - b)

cx² - (c² + ac)x + c²a can be factored as:

cx² - (c² + ac)x + c²a = c(x - a)(x - c)

Now, the LCM is the product of the highest powers of all the factors.

The highest power of a is a², the highest power of b is b², and the highest power of c is c². So, the LCM is:

LCM = a²b²c²(x - a)(x - b)(x - c)

Therefore, the LCM of ax² - (a² + ab)x + a²b, bx² - (b² + bc)x + b²c and cx² - (c² + ac)x + c²a is a²b²c²(x - a)(x - b)(x - c).

Answer:x=23

Step-by-step explanation:

x+1+7x-5=180

8x-4=180

8x=184

x=184/8

x=23