Solve the equation 2x²-x=0

Answer:

x: 8.75

y: 8.5

Step-by-step explanation:

Since the two triangles are similar, you can find the scale of LJK relevant to TRS by dividing 7/4 = 1.75

This means each side of LJK is 1.75 times greater than the respective side of TRS

Now you can plug this in to the other two sides by doing 5*1.75=8.75 and 6*1.75=10.5

This solves x, but since side LK is y+2, y is 10.5-2=8.5

x=8.75

y=8.5

The logarithm of a number raised to a power is  the product of the power. The logarithm of a quotient of two numbers is the difference of the logarithms. The logarithm of a product of two numbers is the sum.

In the given statements, logarithms are used to express relationships between exponentiation, division, and multiplication.

For the first statement, log(4) = 6 implies that 4 raised to the power of 6 is equal to 4. This demonstrates the property that the logarithm of a number raised to a power is equivalent to the power multiplied by the logarithm of the number.

In the second statement, log(2) = log(4) - 8 indicates that the logarithm of 2 is equal to the difference between the logarithms of 4 and 8. This illustrates the property that the logarithm of a quotient of two numbers is equal to the difference of their logarithms.

Lastly, in the third statement, log(4.8) = log(4) + 3 shows that the logarithm of the product 4.8 is equal to the sum of the logarithms of 4 and 3. This property signifies that the logarithm of a product of two numbers is equal to the sum of their logarithms.

These properties of logarithms are fundamental in simplifying calculations involving exponentiation, division, and multiplication.

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The ratio of the perimeters is 4/7.

The ratio of the areas is​ 16/49.

In Mathematics, two (2) geometric figures are considered to be similar when the ratio of their corresponding side lengths are equal and the magnitude of their corresponding angles are congruent.

Since the two (2) geometric figures are similar, we can calculate the scale factor that maps them onto each other as follows:

Ratio of the perimeter of red figure to blue figure = side length of red fig./side length of blue fig.

Ratio of the perimeter of red to blue figure = 4/7

For the ratio of their areas, we have:

​Ratio of the area of red to blue figure = 4²/7²

Ratio of the area of red to blue figure = 16/49

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a) The probability that the third card will be the two of clubs is 1/50 since there are 50 cards left in the deck after the first two cards have been drawn, and only one of them is the two of clubs.
b) Your odds are the same for choosing the two of clubs on each draw since the probability of drawing the two of clubs does not change with each draw.
c) This example illustrates the difference between independent and dependent events. In the case of drawing cards without replacement, the events are dependent since the outcome of one draw affects the probability of the next draw.
d) If we drew the cards with replacement, the marginal probabilities would not change since the probability of drawing any particular card is always 1/52. However, the joint probabilities would change since each draw is now independent.

a) To find the probability that the third card will be the two of clubs, we need to calculate the joint probability of not drawing the two of clubs in the first two draws and drawing it in the third. The probability of not drawing the two of clubs in the first draw is 51/52, and in the second draw, it is 50/51. The probability of drawing the two of clubs in the third draw is 1/50. So, the joint probability is (51/52) * (50/51) * (1/50) = 1/52.

b) The odds of choosing the two of clubs are the same for each draw: 1/52 for the first, second, or third draw. This is because the probability is based on the number of favorable outcomes (one card) over the total possible outcomes (52 cards) in a standard deck.

c) This example illustrates the difference between independent and dependent events. In this scenario, the events are dependent because each card drawn affects the remaining cards in the deck. If the events were independent, the probability of drawing the two of clubs would not change after drawing the first or second card.

d) If we draw cards with replacement, the marginal, joint, and conditional probabilities change because the events become independent. With replacement, the probability of drawing the two of clubs remains constant at 1/52 for each draw. The joint probability of not drawing the two of clubs in the first two draws and drawing it in the third becomes (51/52) * (51/52) * (1/52), and conditional probabilities will not be affected by the previous draws.

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Answer:

x = 4

Step-by-step explanation:

WX = WY

9x - 11 = 7x - 3..........Then subtract 7x to the other side such that  

2x - 11 = -3..........Then add 11 to both sides such that  

2x = 8...........Then divide 2 such that  

x = 4

this is

the equation on the math

The angle between the diagonal AC and the side AB is 90 degrees.

a. To find angle ZA, we need to calculate the vector AB and the vector AD. Then, we can use the dot product formula to find the angle between the two vectors.

Vector AB = B - A = (1, -2, 3) - (0, 1, 2) = (1, -3, 1)

Vector AD = D - A = (2, 1, 0) - (0, 1, 2) = (2, 0, -2)

The dot product of two vectors is given by the formula:

AB · AD = ||AB|| ||AD|| cos(Ф)

The magnitudes of AB and AD can be calculated as follows:

||AB|| = \(\sqrt(1^2 + (-3)^2 + 1^2) = \sqrt(11)\)

||AD|| = \(\sqrt(2^2 + 0^2 + (-2)^2) = \sqrt(8)\)

Substituting the values into the dot product formula:

(1, -3, 1) · (2, 0, -2) = \(\sqrt(11) \sqrt(8)\) cos(Ф)

Using the dot product formula:

(1)(2) + (-3)(0) + (1)(-2) =  \(\sqrt(11) \sqrt(8)\)cos(Ф)

2 - 2 =  \(\sqrt(11) \sqrt(8)\) cos(Ф)

0 =  \(\sqrt(11) \sqrt(8)\) cos(Ф)

Since the dot product is zero, the angle theta is 90 degrees. Therefore, angle ZA is 90 degrees.

b. To find the area of triangle AABD, we can calculate half the magnitude of the cross product of vectors AB and AD.

The cross product of two vectors is given by the formula:

AB x AD = (\(AB_y * AD_z - AB_z * AD_y, AB_z * AD_x - AB_x * AD_z, AB_x * AD_y - AB_y * AD_x\))

Calculating the cross-product:

AB x AD = ((-3)(-2) - (1)(0), (1)(2) - (1)(-2), (1)(0) - (-3)(2))

      = (-6, 4, 6)

The magnitude of the cross-product can be calculated as follows:

||AB x AD|| = \(\sqrt((-6)^2 + 4^2 + 6^2) = \sqrt(112)\)= 4√7

Since the area of a triangle is half the magnitude of the cross product, the area of triangle AABD is (1/2) * 4√7 = 2√7 square units.

c. To find the angle between the diagonal AC and the side AB, we need to calculate the vectors AC and AB, and then use the dot product formula.

Vector AC = C - A = (2, 1, 0) - (0, 1, 2) = (2, 0, -2)

The dot product of AC and AB is given by the formula:

AC · AB = ||AC|| ||AB|| cos(Ф)

The magnitudes of AC and AB are:

||AC|| = √(2² + 0² + (-2)²) = sqrt(8)

||AB|| = √(1² + (-3)² + 1²) = sqrt(11)

Substituting the values into the dot product formula:

(2, 0, -2) · (1, -3, 1) = \(\sqrt(8) \sqrt(11)\) cos(Ф)

Using the dot product formula:

(2)(1) + (0)(-3) + (-2)(1) = \(\sqrt(8) \sqrt(11)\) cos(Ф)

2 - 2 = \(\sqrt(8) \sqrt(11)\)cos(Ф)

0 = \(\sqrt(8) \sqrt(11)\)cos(Ф)

Since the dot product is zero, the angle theta is 90 degrees. Therefore, the angle between the diagonal AC and the side AB is 90 degrees.

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Answer: A. It is a straight line that passes through the origin.

Answer:

7) Linear Pair

8) Linear Pair

9) Vertical Angles

Answer:

Linear Pair

Linear Pair

Vertical Angles

enjoy. - pandamathhelper

Answer:  =-1/2x+-1/2y

Step-by-step explanation:

For 1.) The surface area for the given cylinder =220π

2.) The surface area of the triangular prism = 4,848 in.

To calculate the surface area of the cylinder, Tue formula that should be used is given below;

That is;

surface area of cylinder= 2πrh + 2πr²

where;

radius = 10 mi

height = 9mi

surface area = 2×π×10+2×π×10×10

= 20π+200π

= 220π

For question 2.)

To calculate the surface area of the triangular prism given, the formula that should be used is given below;

Surface area = BH + (B1+B2+B3)L

where;

B = 8 in

H = 6 in

B1 = 8 in

B2 = 6 in

B3 = 10 in

L = 10 in

Surface area = 8×6 + (8+6+10)×10

= 48+4800 = 4,848 in

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Answer:

-5

Step-by-step explanation:

if u graph it, you can see where the y-intercept is.

Answer:

\(\displaystyle \frac{1}{10}(x+9)\)

Step-by-step explanation:

\(\displaystyle \frac{1}{10}x+\frac{9}{10}=\frac{1}{10}(x+9)\) because \(\displaystyle \frac{1}{10}(x+9)=\frac{1}{10}(x)+\frac{1}{10}(9)\) by the Distributive Property

Answer:

Step-by-step explanation:

Answer:

m=(-5y-3y)

Step-by-step explanation:

5m+5y=4m-3y

5m-4m=-5y-3y

m(5-4)=-5y-3y

m=(-5y-3y)/1

The odds against the ball being orange are :

2:1.

To find the odds against the ball being orange, we need to compare the number of non-orange balls to the number of orange balls.

First, let's find the total number of balls in the bag:
10 red + 6 green + 15 orange + 14 blue = 45 balls

Next, we need to find the number of non-orange balls:
10 red + 6 green + 14 blue = 30 balls

Now, we can calculate the odds against the ball being orange as a ratio using a colon to separate the two numbers:
Odds against = number of non-orange balls : number of orange balls
Odds against = 30 : 15

Odds against = 2 : 1

Thus, the odds against the ball being orange are 2 : 1.

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Answer:

Not completely sure, and I know its late but for the other people that look at this, 11.80$

Step-by-step explanation:

I found how many more letters Alexander had over Lucia, then when I got 4 divided it in-between 12.60 - 9.40 (3.20)  I got 0.8. knowing the letter cost i got the initial fee for the mug (5.40) and added 8x0.8 to it, resulting in my answer 11.80$

Penelope has to pay $11.8 for a mug with her own name on it.

Number of letters in Alexander's name = 9

Number of letters in Lucia's name =5

The Difference in the number of letters in both the names

= 9-5

=4 letters

Alexander pays =  $12.60

Lucia pays = $9.40

Difference in payments = 12.60-9.40 = $3.20

It means charge for 4 letters = $3.20

So, charge for 1 letter = $0.80

Number of letters in Penelope's name = 8

So, Penelope will pay = 8*0.80 +fixed fee for the mug

= $6.4 +fixed fee for the mug

The Fixed fee for the mug will be the payment done by Penelope for either Alexander or Lucia minus the charge for each word in the word Alexander or Lucia respectively.

The Fixed fee for the mug = $9.40 - charge for each word in the word "Lucia"

The Fixed fee for the mug = 9.40 - 5*0.80 = $5.40

So, Penelope will pay = 6.4 +5.4 =$11.8

Therefore, Penelope has to pay $11.8 for a mug with her own name on it.

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The 8.22 mL of perchloric acid the pH of the solution is approximately 0.75.

To determine the \(PH\) after adding 8.22 mL of perchloric acid,  to calculate the moles of triethylamine and perchloric acid that have reacted.

First, let's calculate the moles of triethylamine (\(C2H2\))₃\(N\) in the 27.4 mL sample:

Moles of (\(C2H3\))₃\(N\) = Volume (in liters) × Concentration

= 27.4 mL × (1 L / 1000 mL) × 0.230 M

= 0.00630 moles

To calculate the moles of perchloric acid (\(HCIO2\) that have reacted. Since the stoichiometric ratio between triethylamine and perchloric acid is 1:1, the moles of perchloric acid  the same as the moles of triethylamine:

Moles of\(HCIO4\) = 0.00630 moles

After adding 8.22 mL of perchloric acid, the total volume of the solution becomes:

Total volume = Initial volume + Volume of added acid

= 27.4 mL + 8.22 mL

= 35.62 mL

Now we can calculate the concentration of the solution after the titration:

Concentration = Moles / Volume (in liters)

= 0.00630 moles / (35.62 mL × (1 L / 1000 mL))

= 0.177 M

Since we have the concentration of the solution,  calculate the pH using the equation for a strong acid:

pH = -log[acid concentration]

= -log(0.177)

≈ 0.75

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This takes into account the fact that each of the angles has an opposite ray on its other side in addition to the common side they share.

When two rays are linked at their ends, they create an angle in geometry. The sides or arms of the angle are what are known as these rays.

When two lines meet at a point, an angle is created.

An "angle" is the measurement of the "pening" between these two rays. It is symbolized by the character. The circularity or rotation of an angle is often measured in degrees and radians.

Angles are a common occurrence in daily life.

Angles are used by engineers and architects to create highways, structures, and sports venues.

Hence, This takes into account the fact that each of the angles has an opposite ray on its other side in addition to the common side they share.

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The Method of Undetermined Coefficients is a technique used to find a particular solution to a homogeneous linear differential equation.

yp(x) = 3e 8x + c1e 4x + c2e 11x

We are attempting to find a particular solution, yp(x), to the given equation using the Method of Undetermined Coefficients. This method is used when we have a homogeneous linear differential equation with constant coefficients. The first step is to identify the complementary function, which is found by solving the homogeneous part of the equation (in this case, y'' + 17y = 0). The particular solution is then found by making an educated guess for the form of the solution and adjusting the constants of the solution until the equation is satisfied. In this example, we guessed that the particular solution is a linear combination of three exponentials: 3e 8x + c1e 4x + c2e 11x. We then adjusted the constants c1 and c2 until the equation was satisfied.

y'' + 17y = 3e 8x

y'' + 17y - 3e 8x = 0

Homogeneous equation: y'' + 17y = 0

Characteristic equation: r2 + 17 = 0

r = ± 4i

Complementary function: yc(x) = c1e 4x + c2e -4x

Particular solution: yp(x) = 3e 8x + c1e 4x + c2e 11x

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Answer:

x = 25

Step-by-step explanation:

1/5x = 11 - 6

1/5x = 5

x = 5 / (1/5)

x = 5 x 5

x = 25

Hope that helps!

Answer: x=25

Step-by-step explanation:

Answer:

x=-2/3

y=4/5

Step-by-step explanation:

solve for the first variable in one of the equations and then substitute the result into the other equation

Recursive Formula

\(\begin{cases}a_1 = 8\\a_n = a_{n-1}-7\end{cases}\)

The top row says the first term is 8

The bottom row says that to get the nth term, we subtract 7 from the (n-1)th term. So basically we subtract 7 from each term to get the next term.

Note the subscripts tell us which term we're working with.

======================================================

Arithmetic Formula

We have a = 8 as the first term and d = -7 as the common difference.

a(n) = a + d(n-1)

a(n) = 8 + (-7)(n-1)

a(n) = 8 - 7n + 7

a(n) = -7n+15

The nth term arithmetic formula is a(n) = -7n+15

If you plug in n = 1, you should get a(n) = 8

If you plug in n = 2, you should get a(n) = 1

and so on.

=======================================================

Finding the 10th term

Plug in n = 10 to get

a(n) = -7n+15

a(10) = -7(10)+15

a(10) = -70+15

a(10) = -55

The 10th term is -55

The values of t and s that make the equality true are t = -1 and s = -1/3.At these values, the resulting vector is ⟨t−3,3s+3t⟩ = ⟨-1 - 3, 3(-1/3) + 3(-1)⟩ = ⟨-4, -1 - 3⟩ = ⟨-4, -4⟩.

To find the values of t and s that make the equality ⟨t−3,3s+3t⟩=(3s+3t,2+5t⟩ true, we need to equate the corresponding components of the vectors.

Comparing the first components:

t - 3 = 3s + 3t

Simplifying this equation:

-2t - 3 = 3s

Comparing the second components:

3s + 3t = 3s + 5t + 2

Simplifying this equation:

-2t = 2

Dividing both sides by -2, we get:

t = -1

Substituting the value of t into the first equation:

-2(-1) - 3 = 3s

2 - 3 = 3s

-1 = 3s

Dividing both sides by 3, we get:

s = -1/3

Therefore, the values of t and s that make the equality true are t = -1 and s = -1/3.

At these values, the resulting vector is ⟨t−3,3s+3t⟩ = ⟨-1 - 3, 3(-1/3) + 3(-1)⟩ = ⟨-4, -1 - 3⟩ = ⟨-4, -4⟩.

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Answer:

\(y=-x^{2}+2\)

Step-by-step explanation:

The equation for a parabola that opens down and has a vertex of (0,2) is \(y=-x^{2}+2\). Attached is an image of the parabola graphed.

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Note that the complete proof that ∠A ≅ ∠D is given as follows:

Note that the Alternate Interior Angles Theorem states that when two parallel lines are crossed by a transversal, the alternate interior angles are congruent.

The Basic Proportionality Theorem states that in a triangle, a line parallel to one side divides the other sides proportionally.

The Vertical Angles Theorem states that vertical angles are congruent.

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