Simplify: 45÷3+2×8-12+42


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(-2,-4)

x=-2, y= -4

Have a good day

Answer:

(-2,-4)

Step-by-step explanation:

3x-2y=2

5x-5y=10

--

Multiply 3x-2y=2 by -5 to turn it into -15x+10y=-10

Mutiplu 5x-5y=10 by 2 to turn it into 10x-10y=20

--

Eliminate y

-15x+10y=-10

10x-10y=20

= -5x=10

Divide by -5

x=-2

--

Plug -2 to the first equation

3(-2)-2y=2

-6-2y=2

Move -6 to the other side by adding 6 to both sides

-2y=8

Divide by -2

y=-4

(x,y) = (-2,-4)

The matrix A' for the linear transformation T relative to the basis B' is:

A' = \(\left[\begin{array}{ccc}2&-3\\4&0\\\end{array}\right]\)

To find the matrix A' for the linear transformation T relative to the basis B', we need to determine how the transformation T maps the basis vectors of B' onto the standard basis of \(R^2\).

The basis B' = {(-2, 1), (-1, 1)} consists of two vectors.

We apply the transformation T to each basis vector and express the results as linear combinations of the standard basis vectors (1, 0) and (0, 1).

Applying T to the first basis vector, we have:

T(-2, 1) = 2*(-2) - 3*(1), 4*(-2) = (-4, -2)

Similarly, applying T to the second basis vector, we have:

T(-1, 1) = 2*(-1) - 3*(1), 4*(-1) = (-5, -4)

Now, we express these transformed vectors in terms of the standard basis:

(-4, -2) = -4*(1, 0) - 2*(0, 1)

(-5, -4) = -5*(1, 0) - 4*(0, 1)

The coefficients of the standard basis vectors in these expressions form the columns of the matrix A':

A' = \(\left[\begin{array}{ccc}-4&-5\\-2&-4\\\end{array}\right]\)

Therefore, the matrix A' for the linear transformation T relative to the basis B' is:

A' = \(\left[\begin{array}{ccc}2&-3\\4&0\\\end{array}\right]\)

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Answer:

\(a = \frac{b}{4x} + \frac{7}{4} - \frac{2}{x}\)

b = 7x + 4ax + 8

Step-by-step explanation:

Hope this helps! :D

Also, if possible, can I have brainliest?

The value of the equation is 35 = 15 + 2y , where y is the number of years and the y = 10 years

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

Let the initial height of the weeping willow be = 15 feet

Let the final height of the weeping willow be = 35 feet

The height in feet the weeping willow grows each year = 24 inches = 2 feet

Let the number of years be = y

On simplifying the equation , we get

35 = 15 + 2y

Subtracting 15 on both sides of the equation , we get

2y = 20

Divide by 2 on both sides of the equation , we get

y = 10 years

Hence , the equation is y = 10 years

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A normal distribution has a mean of 120 and a standard deviation of 10 then P(x > 110) is 0.84

Given that mean is 120 and a standard deviation of 10

The z-score for x=110 can be calculated as:

z = (x - μ) / σ = (110 - 120) / 10 = -1

Using a standard normal distribution table

we can find that the probability of a z-score being greater than -1 is 0.8413.

Therefore, P(x > 110) = 1 - P(x ≤ 110)

= 1 - P(z ≤ -1)

= 1 - 0.1587

= 0.8413.

Hence,  a normal distribution has a mean of 120 and a standard deviation of 10 then P(x > 110) is 0.84

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Answer:

SSS

Step-by-step explanation:

ST = YA, SY = TA Given

AS = SA Reflexive property

ΔSTA ≅ ΔAYS SSS

Answer:

b

Step-by-step explanation:

The equation for the transformed logarithm that passes through the points (3,0) and (0,2) can be written as f(x) = -b * log(base a)(x - h) + k, where a, b, h, and k are constants to be determined.

To find the equation for the transformed logarithm, we need to use the given points (3,0) and (0,2) to determine the values of a, b, h, and k. Let's start with the point (3,0). Plugging the x-coordinate (3) into the equation, we have:

0 = -b * log(base a)(3 - h) + k

Next, we'll use the point (0,2) to obtain another equation. Plugging the x-coordinate (0) into the equation, we get:

2 = -b * log(base a)(0 - h) + k

Simplifying these equations, we have a system of equations to solve for a, b, h, and k. However, since the equation involves a logarithm, we need more information to determine the specific values of a, b, h, and k.The transformed logarithm function includes transformations such as vertical stretches/compressions (b), horizontal shifts (h), and vertical shifts (k). Without more specific information about these transformations or the base of the logarithm, it is not possible to determine the equation uniquely.

In general, the equation for a transformed logarithm can be written as f(x) = -b * log(base a)(x - h) + k, where a, b, h, and k are constants determined by the specific transformations applied to the logarithm function. It's important to have additional information or instructions to determine the values of a, b, h, and k and provide an equation that accurately represents the given transformed logarithm.

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Answer:

Sorry,didn't understand your question..

btw thanks for free points

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Answer:

b

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let M(x,y) be the median of ΔABC through A to BC.M will be the midpoint of BC.x1​=5,y1​=3x2​=3,y2​=−1By midpoint formula, x=(x1​+x2​)/2∴x=(5+3)/2=8/2=4By midpoint formula, y=(y1​+y2​)/2∴y=(3+(−2))/2=2/2=1Hence the co-ordinates of M are (4,1).By diatnce formula, d(AM)=[(x2​−x1​)2+(y2​−y1​)2]​x1​=7,y1​=−3x2​=4,y2​=1

The given initial value problem involves solving a second-order linear homogeneous differential equation. The complementary equation is satisfied by the function y₁ = (x+1)eˣ. We need to find a particular solution to the non-homogeneous equation using the method of variation of parameters.

To solve the non-homogeneous equation, we start by finding the Wronskian W(x) = det(y₁, y₂), where y₂ is a second linearly independent solution of the homogeneous equation. Using the Wronskian, we can determine the particular solution yp(x) as follows:

yp(x) = -y₁(x) ∫[(y₂(x)f(x)) / W(x)] dx + y₂(x) ∫[(y₁(x)f(x)) / W(x)] dx,

where f(x) is the non-homogeneous term of the equation.

Next, we need to find the second linearly independent solution y₂(x). Since y₁ = (x+1)eˣ satisfies the complementary equation, we can use the reduction of order method to find y₂. We assume y₂(x) = v(x)(x+1)eˣ, where v(x) is a function to be determined. Substituting this into the homogeneous equation and solving for v(x), we can find y₂(x).

Finally, substituting the values of y₁(x), y₂(x), and f(x) into the formula for yp(x), we can compute the particular solution yp(x). Adding the particular solution and the complementary solution yh(x) = c₁y₁(x) + c₂y₂(x), where c₁ and c₂ are arbitrary constants, gives us the general solution y(x). By applying the initial conditions y(0) = 2 and y'(0) = 7, we can determine the specific values of the constants and obtain the solution y(x) to the initial value problem.

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Answer:

59.04°

58.31 inches

Step-by-step explanation:

The solution triangle is attached below :

Since we have a right angled triangle, we can apply trigonometry to obtain the angle ladder makes with the ground;

Let the angle = θ

Tanθ = opposite / Adjacent

Tanθ = 50/30

θ = tan^-1(50/30)

θ = 59.036°

θ = 59.04°

The length of ladder can be obtained using Pythagoras :

Length of ladder is the hypotenus :

Hence,

Hypotenus = √(adjacent² + opposite²)

Hypotenus = √(50² + 30²)

Hypotenus = √(2500 + 900)

Hypotenus = 58.309

Length of ladder = 58.31 inches

Answer:

59°

58.3 inches

Step-by-step explanation:

Here is the full question :

A ladder is placed 30 inches from a wall. It touches the wall at a height of 50 inches from the ground. The angle made by the ladder with the ground is degrees, and the length of the ladder is inches.

Please check the attached image for a diagram explaining this question

The angle the ladder makes with the ground is labelled x in the diagram

To find the value of x given the opposite and adjacent lengths, use tan

tan⁻¹ (opposite / adjacent)

tan⁻¹  (50 / 30)

tan⁻¹ 1.667

= 59°

the length of the ladder can be determined using Pythagoras theorem

The Pythagoras theorem : a² + b² = c²

where a = length

b = base

c =  hypotenuse

√(50² + 30²)

√(2500 + 900)

√3400

= 58.3 inches

a function is a rule that assigns each value of the variable to exactly one value of the dependent variable

The stemplot may not be the most effective way to represent this data set since it can become cumbersome and difficult to interpret, especially for larger data sets.

A better way to represent this data set would be to use a histogram or a frequency table. These methods provide a clearer visualization of the distribution of the data and allow for easier analysis and comparison.

A histogram divides the range of the data into intervals or bins and represents the frequency or count of observations within each bin using bars. This allows for a visual representation of the distribution and helps identify patterns, central tendencies, and potential outliers.

Alternatively, a frequency table can be created by grouping the data into intervals and recording the number of observations falling into each interval. This table provides a concise summary of the data distribution and can be used to calculate various statistical measures.

Both the histogram and the frequency table provide a clearer and more concise representation of the data set, making it easier to analyze and draw insights from the information.

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One ream of paper refers to a standardized quantity of paper that typically consists of 500 sheets of paper of a specific size and weight.

A ream of paper is a commonly used quantity in the paper industry and refers to a standardized amount of paper. A ream usually consists of 500 sheets of paper of a specific size and weight. The size and weight of the paper may vary depending on the intended use, but the most common size for a ream of printer paper is 8.5 x 11 inches, also known as "letter size." One ream of paper is often used as a baseline for pricing and ordering paper products. For example, if you were to order "10 reams of paper," you would receive 5,000 sheets of paper.

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Answer:

The answer is A.

Step-by-step explanation:

This is because the Triangle is being rotated counter clockwise 90 degrees, then reflected over the Y axis.

So, point (-6, 8) would become (-8, -6), and so forth.

1287 different combinations of 9 movies can he rent if he wants all 4 children's movies as "Marlon is picking out some movies to rent, and he has narrowed down his selections to 4 documentaries, 4 mysteries, 5 comedies, and 4 children's movies. She want all 4 children's movie".

Combinations are ways to choose items from a collection in mathematics where the order of the selection is irrelevant. Let's say we have a trio of numbers: P, Q, and R. Then, combination determines how many ways we can choose two numbers from each set. The definition of the combination is "An arrangement of objects where the order of the objects is irrelevant." Combining these two words means "Selection of things," where the order of the items is irrelevant. If n>k, nCk = n!/k!(n-k)!

Here,

4C4=1

4+4+5+4=17-4=13

9-4=5

13C5

1287*1=1287

1287 different combinations of 9 movies can he rent if he wants all 4 children's movies. If he wants to rent all 4 children's movies, there are 1287 different combinations of 9 movies "Marlon has chosen four documentaries, four mysteries, five comedies, and four children's movies from his list of potential rentals. She desires all 4 of the kid's movies ".

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A part of a line that has 1 endpoint and extends indefinitely in only one direction is called a ray.

A ray is named using its endpoint first, and then any other point on the ray

Properties of ray:

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Answer:

Hello,

Step-by-step explanation:

P(x)=x^3-5x^2-7x+51

Since the coefficients are all reals,

4+i (conjugate of 4-i) is also a root.

The polynomial est divisible by (x-4-i)(x-4+i)=(x-4)²+1=x²-8x+17

If we divide P(x) by x²-8x+17 we find the quotient (x+3) and the remainder 0

P(x)=(x+4)(x-4-i(x-4+i)

Roots are -4,4+i and 4-i

Answer:

All the roots are -3, 4-i and 4+i.

Step-by-step explanation:

If oine root is 4 - i then another one is 4 + i as complex roots occur as conjugate pairs.

(4 - i)(4 + i)

= 16 - i^2

= 17.

As the last term = 51 = 3 * 17

looks like the other root is 3 or -3.

By the Factor theorem

If x = 3 then f(3) = 0

f(3) = 27 - 5(3)^2 - 7(3) + 51

     = 27 - 45 - 21 + 51 = 12 so 3 is not a root.

If x = -3:

f(-3) = -27 - 45 _ 21 + 51

      = 0

So,  x = -3 is a root.

Answer:

9x^2 -1

Step-by-step explanation:

(3x-1) (3x+1)

FOIL

first: 3x*3x = 9x^2

outer:3x*1 =3x

inner: -1 *3x = -3x

last: -1*1 = -1

Add them together

9x^2 +3x-3x-1

Combine like terms

9x^2 -1

Answer:

9x²-1

Step-by-step explanation:

1) (3x-1)(3x+1)

transfer difference of squares using this rule:

(a-b) (a+b) = a²-b²

2) (3x)²-1²

expand (3x)²

3) 3²x²-1²

calculate 3 to the power of 2 and 9

4) 9x²-1²

calculate 1 to the power of 2 and get 1

5) 9x²-1

you recieve your answer, B.

The converse statement of the conditional statement is  "If the shoes are new, then the shoes are clean"

The conditional statement is given as:

"If the shoes are clean, then the shoes are new."

The converse of the conditional statement is such that:

The hypothesis and the conclusion are switched

So, we have the converse statement to be:

"If the shoes are new, then the shoes are clean"

Hence, the converse statement of the conditional statement is

"If the shoes are new, then the shoes are clean"

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Here are the options for this question.

If the shoes are not clean, then the shoes are not new.

If the shoes are clean, then the shoes are not new.

If the shoes are not new, then the shoes are not clean.

If the shoes are new, then the shoes are clean.

Your answer is D, If the shoes are new, then the shoes are clean.
A converse to a statement is swapping the hypothesis and conclusion.

Hope that helps!

Answer:

5+6 +(3*3)

Step-by-step explanation:

If you are allowed to mix the numbers then

5 + 6 + (3*3)

5+6 = 11

3*3 = 9

11+9 = 20

Hope this helps

The answer is (D) A scatter plοt, because it wοuld shοw the assοciatiοn οr relatiοnship between each data pοint given

Yοu want tο determine if a scatter plοt οr line graph is a mοre apprοpriate way tο represent the relatiοnship between a manatee's weight and height.

Variables

The variables οf cοncern in the data are weight and height. Time is nοt invοlved. (Eliminates chοices B and D.)

Functiοnal relatiοnship

It seems likely there may nοt be a functiοnal relatiοnship between weight and height. That is, manatees οf the same weight may have different height, and vice versa. This suggests a line graph wοuld nοt be a useful way tο represent the relatiοnship

A scatter plοt in this case wοuld be used tο relate weight οn οne axis tο height οn the οther axis. Any relatiοnship between them wοuld shοw up as grοuped data pοints, οr data pοints that generally fall οn a line οr curve.

Since the "marine biοlοgist is interested in seeing the relatiοnship between a manatee's weight and height", ...

A scatter plοt [is mοre apprοpriate] because it wοuld shοw the assοciatiοn οr relatiοnship between the twο variables.

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Answer:

area = 38.47 cm²

Step-by-step explanation:

area = 1/4(3.14)(7²) = 38.47 cm²

The speed you used is 24 miles per hour.

You cover 36 miles for 1 hour 30 minutes. The speed used by you can be calculated as follows:

Speed is measured as the ratio of distance to the time in which the distance was covered.

Hence,

speed = distance / time

Where

distance = 36 miles

time  = 1 hours 30 minutes

Therefore,

Speed = 36 / 1.5

speed = 24 miles per hour

Therefore, your a fast by 24 miles per hour.

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Answer:

\(\frac{15}{10}\)  and \(\frac{3}{10}\)

 \(\frac{15}{10} -\frac{12}{10} = \frac{3}{10}\)

Step-by-step explanation:

Given

       \(\frac{3}{2} - \frac{6}{5}\)

Now the L.C.M = 10

 =  \(\frac{15-12}{10}\)

 =  \(\frac{15}{10} -\frac{12}{10} = \frac{3}{10}\)

Answer:

7,750 ways

Step-by-step explanation:

To determine the number of ways that 2 people can be chosen to receive the free tickets, we need to use combinations because the order of the selection does not matter.

The number of ways to choose 2 people out of 125 can be calculated using the combination formula:

n C r = n! / (r! * (n-r)!)

where n is the total number of people, and r is the number of people we want to choose.

In this case, n = 125 and r = 2, so we have:

125 C 2 = 125! / (2! * (125-2)!)

= 125! / (2! * 123!)

= (125 * 124) / 2

= 7750

Therefore, there are 7,750 ways that 2 people can be chosen to receive the free tickets.

The correct coordinates are (2,6)

Take x1 plus x2 then divide by 2

Take y1 plus y2 then divide by 2

So, -2+6=4 and 4+8=12.

So, 4/2=2 and 12/2=6 therefore, we have (2,6)

:)

Over 7 years, there would be 49% increase, so 600 (1.49) = 894

$894

Answer:

Rishi spent 3/4 of an hour for 2 days working on his science project . kyle spent 1/4 of an hour for 6 days working on his science project. who spent more time working on his science project.

Step-by-step explanation:

rishi and kyle spent the same amount of time.

6/4 and 6/4 hours