Write the system of equations as a matrix equation AX=B, with A as the coefficient matrix of the system.x+2y=−112x+6y=−30

When $428 doubles, it means that the

Answer:

what is the problem ???

Step-by-step explanation:

Answer:

7500$

Step-by-step explanation:

The value of the expression given as 3 - √x⁵ is 3 - x^2√x

Expressions are mathematical statements that are represented by variables, coefficients and operators

The expression is given as

3 - √x⁵

Express 5 as the sum of 4 and 1

So, we have the following equation

3 - √x⁵ = 3 - √x^(4 + 1)

Apply the law of indices to expand the equation

So, we have the following equation

3 - √x⁵ = 3 - √(x^4 * x)

Next, we expand the equation

So, we have the following equation

3 - √x⁵ = 3 - √x^4 * √x

Evaluate the square root of x^4

So, we have the following equation

3 - √x⁵ = 3 - x^2 * √x

Evaluate the product

So, we have the following equation

3 - √x⁵ = 3 - x^2√x

Hence, the value of the expression is 3 - x^2√x

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The score required for the exam so that the score is higher than 30.85% is 412 for certain standardized test.

The formula for finding the z-score is;

z = (x - μ)/σ

x = sample size

μ = mean of the population

σ = standard deviation of the population.

The given values are-

μ = 421

σ = 18

Probability = 30.85% = 0.3085

Check the z-score from the negative z table for 0.3085

z score = -0.5

Put the values in z formula and find x.

z = (x - μ)/σ

-0.5 = (x - 421)/18

Simplifying;

x = -9 + 421

x = 412

Thus, the score required for the standardized test is found as 412.

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If a ball is thrown directly upward with a velocity of 88 ft/s, its height (in feet) after t seconds is given by y = 88t - 16t².The ball will reach its maximum height at 121 feet.

Given equation:

y = 88t - 16t²

Maximum height dy/dt = 0

88-32t = 0

32t = 88

t = 88/32sec

t = 2.75sec

Hence,

Maximum height attained by the ball :

Maximum height attained by the ball = 88(2.75)-16(2.75)²

Maximum height attained by the ball = 242 - 121

Maximum height attained by the ball = 121 feet

Therefore the maximum height is 121 feet.

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Answer:

d) given

Step-by-step explanation:

nothing has been done yet, the statement is given as stated above the statement

The real and complex zeros for the function given as .f(x) = x³ - x² + 3x - 3 are x = 1 and x = ±i√3, respectively

The equation of the function is given as

f(x) = x³ - x² + 3x - 3

Group the terms of the function in two's

So, we have the equation

f(x) = (x³ - x²) + (3x - 3)

Factor each group in the function

f(x) = x²(x - 1) + 3(x - 1)

Factor out x - 1

f(x) = (x² + 3)(x - 1)

Set to 0

(x² + 3)(x - 1) = 0

This gives

x² = - 3 and x = 1

Evaluate the roots

x = ±i√3 and x = 1

Hence, the zeros of the equation are x = ±i√3 and x = 1

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In order to determine which person is the first to win both prizes, you have to find the least common multiple to both numbers 14 and 10.

To determine what is the least common multiple number you proceed as follow:

You list different multiples of each number 14 and 10.

For 14: 14 28 42 56 70 84 98 112

For 10: 10 20 30 40 50 60 70 80

The least common multiple is 70, becasue is the first common number in each list.

Hence the 70th person in the line will win both prizes.

Answer:

Question A: They should add product B because it has a 69% rate of approval. They can be 69% confident that the addition of product B will be successful.

  Question B: 31% of people would prefer cookie A over cookie B

Step-by-step explanation:

The mean increases by 23 and the median stays the same.

A data set's mean (average) is calculated by summing all of the numbers in the set, then dividing by the total number of values in the set. When a data collection is ranked from least to greatest, the median is the middle value.

Given the data set: 352, 409, 424, 471, 497, 503, 515, 525, 561

(a) Mean = [tex]\frac{352+409+424+471+497+503+515+525+561}{9}[/tex]

Mean = [tex]\frac{4257}{9}[/tex]

= 473

The number 561 from this list changes to 768.

New mean = [tex]\frac{352+409+424+471+497+503+515+525+768}{9}[/tex]

= [tex]\frac{4464}{9}[/tex]

= 496

Thus, the mean increases by 496 - 473 = 23.

(b) Median = mid value

= 497

When the number 561 changes to 768, still the mid value will remain the same i.e. the median remains the same.

Therefore, the mean increases by 23 and the median stays the same.

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Answer:

The new price of the article is $270

Step-by-step explanation:

270-240/240

x 100% = 12.5%

12.5x240/100

= 30

It is known that any exponential function with the form f(x)=a^x is an increasing function while a function of the form g(x)=a^(-x) is a decreasing function.

Furthermore, it a function h(x) is increasing, then the function -h(x) is decreasing. By analogy, if a function k(x) is decreasing, then -k(x) is increasing.

Now let's analyze the functions from the problem.

Since (6/7)^x is increasing and the multiplying factor of 10 is positive, then the function f(x) is also increasing.

Use these rules to find whether each function is increasing or decreasing.

Remember that increasing functions are used to represent growth while decreasing functions are used to represent decay.

Using the highest common factor, the greatest number of identical binders that the teacher can make is 18.

The highest common factor or multiple of the given numbers is the highest number that can divide them without a remainder.

We know that 2, 9, and 18 can divide 54, 36, and 72 without leaving a remainder.

We can see that the highest common factor is 18.

When we divide 54 by 18, the quotient is 3. If you divide 36 by 18, the quotient is 2.  When you divide 72 by 18, the result is 4.

The number of lined paper = 54 pieces

The number of grid paper = 36 pieces

The number of dividers = 72 dividers

The common factors of 54, 36, and 72 are 2, 9, and 18.

The highest common factor of 54, 36, and 72 is 18.

Thus, 18 binders containing 3 pieces of lined paper, 2 pieces of grid paper, and 4 dividers can be made from the collection, using their HCF.

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Answer:

B

Step-by-step explanation:

it is simple.

because AB > AD, their size representations must have the same relationship.

therefore,

9x - 16 > 1.5x + 42

that could be simplified to

7.5x > 58

The inequality that represents AB > AD is B: 9x - 16 > 1.5x + 42.

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

Given, In Rectangle ABCD the length of AB is greater than the length of AD.

∴ The inequality that represents this is AB > AD which is,

9x - 16 > 1.5x + 42.

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The value of x is 4.

The perimeter of any shape is the sum of lengths of all its sides.

We are provided with the sides of triangle i.e., 5x-1, 5x-1 and 2.2x +10.

So, The perimeter of a triangle = sum of length of all three sides = (5x-1) + (5x-1) + (2.2x +10)

The perimeter of a triangle = 12.2x + 8                            equation 1

Also, we are provided with the side of square i.e.,  6.5x -11.8.

The perimeter of a square = 4 (side) = 4 (6.5x - 11.8)

The perimeter of a square = 26x - 47.2                            equation 2

As per question,

Perimeter of a triangle =  Perimeter of a square

12.2x + 8  = 26x - 47.2    

13.8x = 55.2

x = 4

So we can write,  the value of x is 4.

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Answer:

1 1/2 = 3/2

3/2 x 14

= 42/2

=21

Step-by-step explanation:

As you can see in the given figure the minute hand of a clock rotate from 12:40 to 1:10 formig a straigth angle.

A straight angle in radians is π radians.

The BEST strategy for this proof is (A) Use the Midpoint Formula to find the coordinates of M, then use the Distance Formula to verify that AC= BD

The theorem is given as

Theorem: The diagonals of a parallelogram bisect one another.

Also, we have the following given parameters

AD//BC; AB//CD;

AC and BD intersect at M.

The above means that:

Lines AD and BC are parallel lines, and AB and CD are parallel lines

The statement AC and BD intersect at M implies that

AM = MC and BM = MD.

The above means that we need to calculate the lengths of the above segments, and then make comparison

The lengths of the segments can be calculated using the distance formula

Other than that, the coordinate of the point M needs to be calculated

The option that satisfies the above conditions is (a)

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Answer:

600

Step-by-step explanation:

[tex]R(1)=400 \\ \\ R(2)=1000 \\ \\ R(2)-R(1)=600[/tex]

The first unit is kilograms because the bus is really heavy.

The second is kilometers because meters are too small.

The third one is milliliters because liters are too much for ice cream.

Answer: 72 i think

Step-by-step explanation:

Hello! So...

We are given the following to solve:

Solve for x.

[tex]6(x+3)-8=4x+2(4+x)[/tex]

_______________________________________________________

1. Expand both sides of the equation.

[tex]6(x+3)-8=6x+10[/tex]

[tex]4x+2(4+x)=6x+8[/tex]

[tex]6x+10=6x+8[/tex]

______________________________

2. Subtract 10 from both sides.

[tex]6x+10-10=6x+8-10[/tex]

_______________________________

3. Simplify.

[tex]6x=6x - 2[/tex]

_______________________________

4. Subtract 6x from both sides.

[tex]6x-6x=6x-2-6x[/tex]

_______________________________

5. Simplify.

[tex]0=-2[/tex]

^Notice, the sides are not equal in the solution. This being said, there would be no solution.

___________________________________________________

Hope this helps! If you need anything else, feel free to comment below. Thanks and good luck!

Answer: [tex]\Large\boxed{A. -\dfrac{1}{ 5}}[/tex]

Step-by-step explanation:

Given expression

[tex]-\dfrac{3}{8} \times \dfrac{8}{15}[/tex]

Combine the fractions

[tex]=\dfrac{-3\times 8}{8 \times 15}[/tex]

Cancel out the 8 on both the numerator and denominator

[tex]=\dfrac{-3}{ 15}[/tex]

Divide 3 on both the numerator and denominator

[tex]=\dfrac{-3\div 3}{ 15\div 3}[/tex]

[tex]=\Large\boxed{-\dfrac{1}{ 5}}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Ivan will catch up to Horatio in 3 hours .

In the question ,

it is given that

speed of Horatio is 1 miles per hour

speed of Ivan is 2 miles per hour .

and Ivan leaves 3 hours late than Horatio .

Let "t" be the time ( in hours ) taken for  Ivan to meet Horatio ,

So, the distance covered by Ivan will be 2*t .

Since Horatio left 3 hours before so the time taken for Horatio to meet Ivan is (t+3).

So, the distance covered by Horatio will be 1*(t+3) .

The distance covered for Horatio and Ivan will be equal ,

which means

2*t = 1*(t+3)

2t = t + 3

2t - t = 3

t = 3

Therefore , Ivan will catch up to Horatio in 3 hours .

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First of all, we have to find the mean of x values.

According to the given graph, the x values are: 0, 1, 2, 2, 3, 3, 4, 5, 6, 7.

So, the mean is

The mean of x values is 3.3.

The y values are: 2, 2, 3, 4, 4, 4, 5, 6, 8, 9.

The mean would be

The mean of y values is 4.4.

Now, we find the standard deviation for x values and y values.

The equation of the circle in standard form whose center is at (h, k) = (4, 0) is (x - 4)² + y² = 26.

In this question we find the coordinates of the endpoints of the diameter of the circle, then, the center of the circle is the midpoint of the line segment. The center of the circle is found by midpoint formula:

(h, k) = 0.5 · (5, 5) + 0.5 · (3, - 5)

(h, k) = (4, 0)

And the radius of the circle is determined by Pythagorean theorem:

r = √[(4 - 5)² + (0 - 5)²]

r = √[(- 1)² + (- 5)²]

r = √26

Then, the equation of the circle in standard form is describe below:

(x - h)² + (y - k)² = r²

If we know that (h, k) = (4, 0) and r = √26, then the equation of the circle is:

(x - 4)² + y² = 26

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