help me plz with algebra!!!
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The difference between the polynomials 9x² + 8x and 2x² + 3x is 7x² + 5x.

A polynomial is formed mathematically by combining one or more algebraic terms (monomials). The roots of "polynomial" are poly- (many) and -nomial (terms). A polynomial can have exponents (powers), constants (numbers), and variables (letters), but not negative exponents or variable division.

Polynomials are typically expressed in standard form. Furthermore, because there are no similar terms among the exponents, they are arranged in descending order (largest to smallest).

To find the difference between

(9x² + 8x) - (2x² + 3x)

We do calculation

= 9x² + 8x - 2x² - 3x

= 9x² - 2x² + 8x - 3x

= 7x² + 5x

Thus, the difference between the polynomials is 7x² + 5x.

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The actual distance between Beitbridge and Musina is 3,900,000 kilometers.

To calculate the actual distance between Beitbridge and Musina, given the scale of the map and the measured distance on the map, we can use the concept of scale.

The scale of the map is given as 1:3,000,000, which means that 1 cm on the map represents 3,000,000 cm in real life.

The measured distance on the map between Beitbridge and Musina is 1.3 cm.

To find the actual distance, we can set up a proportion using the scale:

1 cm on the map / 3,000,000 cm in real life = 1.3 cm on the map / x km in real life.

Simplifying the proportion, we have:

1 / 3,000,000 = 1.3 / x.

Cross-multiplying, we get:

x = (1.3 * 3,000,000) / 1.

x = 3,900,000 / 1.

x = 3,900,000 km.

The actual distance between Beitbridge and Musina is 3,900,000 kilometers.

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Answer:

Step-by-step explanation:

$2,500 x 4% =  it will be $100 yearly interest. so = 8.33 monthly interest

so 8.33 x 18 months = $150 yearly interest

$2,500 x 5% = $125 yearly interest. So = $10.42 monthly interest

$10.42 x 18 months= $187.50

Answer $37.50 more with 5.55%

Amount more ear with high interest rate is $56.25

Amount invested = $2,500

High interest rate = 5.5%
Low interest rate = 4%

Number of month = 18 month = 1.5 year

Amount more ear with high interest rate

Amount more ear with high interest rate = 2500[5.5% - 4%]1.5

Amount more ear with high interest rate = 2500[0.015]1.5

Amount more ear with high interest rate = $56.25

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Answer:

B

Step-by-step explanation:

the range is about 45

Answer:

5 liters

Step-by-step explanation:

Let x represent the number of liters of the 17% solution, and represent the percentages as decimal values:

0.1(2) + (0.17)(x) = 0.15(x + 2)

Simplify:

0.2 + 0.17x = 0.15x + 0.3

Solve for x:

0.17x = 0.15x + 0.1

0.02x = 0.1

x = 5

So, you would need 5 liters of a 17% solution to get a 15% solution

Answer:

3.78%

Step-by-step explanation:

The formula for compound interest is given by:

A(t) = P(1 + r/n)^(nt), where

Thus, we can plug in 8500 for P, 11022 for A(t), 1 for n, and 7 for t to find r:

Step 1:  Plug in the values and simplify:

11022 = 8500 * ( 1 + r/1)^(7 * 1)

11022 = 8500 * (1 + r)^(7)

Step 2:  Divide both sides by 8500:

(11022 = 8500 * (1 + r)^(7)) / 8500

11022/8500 = (1 + r)^(7)

5511/4250 = (1 + r)^(7)

Step 3:  Raise both sides to the 1/7 power (this is the same as taking the 7th root of both sides):

(5511/4250 = (1 + r)^(7))^(1/7)

1.037815641 = 1 + r

Step 4:  Subtract 1 from both sides to find r:

(1.037815641 = 1 + r) - 1

0.0378154607 = r

Step 5:  Multiply 0.0378154607 by 100 to find the interest rate as a percentage:

0.0378154607 * 100

3.78156407 = %

Step 6:  Round to the nearest two decimal places:

3.78

Thus, the interest rate is about 3.78%

Answer: what do you mean? I need more info-

Step-by-step explanation:

I can answer it with more info :)

Answer:

4 pages

Step-by-step explanation:

Answer:

thanks for free points :3

Step-by-step explanation:

The unknown angles of the right angle triangle is 45 degrees.  

A right angle triangle is a triangle with one angle equals to 90 degrees. The sum of angles in a triangle is 180 degrees.

Therefore, the right triangle has two angle measurements that are equal to each other. The third angle is 90 degrees.

Therefore, let's find the angles measure x, the two other equal angles.

Hence,

x + x + 90 = 180

2x + 90 = 180

subtract 90 from both sides of the equation

2x + 90 = 180

2x + 90 - 90 = 180 - 90

2x = 90

divide both sides by 2

x = 90 / 2

x = 45 degrees

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We would reject the null hypothesis h0: p1 – p2 = 0 if our sample results provide strong evidence that the true difference in proportions between the two populations is less than zero.

This means that if our test statistic (calculated using the sample proportions and sample sizes) falls in the rejection region of the null hypothesis, we would reject it in favor of the alternative hypothesis h1: p1 – p2 < 0. Additionally, we would need to determine the level of significance (alpha) and calculate the corresponding critical value or p-value to make a decision on rejecting the null hypothesis.

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Answer:320

Step-by-step explanation:PEMDAS. So first you would do the exponent 2^5= 32 (2x2=4 4x2=8 8x2=16 16x2=32)

Then you multiply 10x32 which equals 320

Answer:

\(y= 500(1+0.15)^x\)

Step-by-step explanation:

This problem can be solved using concept of compound interest

In compound interest

if p is the principal amount

and r is the interest rate

then value of principal amount(A) after n years time is given by

A = p(1+r)^n

=>\(A = p(1+r)^n\)

__________________________________

in the problem

in place of n we have x years

y is the amount which is the total amount after n years

p is the principal money deposited = $500

r = 15%

substituting these value in the formula for amount after n years we have

\(y= 500(1+15/100)^x\\y= 500(1+0.15)^x\)

Thus, function modeling the situation is \(y= 500(1+0.15)^x\)

Answer:

1 and 1/2 multiplied by 2

1 and 1/2 doubled

Answer=3

Since 1 and 1/2 are equal to 1.5, you can add 1.5 to 1.5 to successfully multiply it, getting 3.

Step-by-step explanation:

By permutation and combination, Maximum 171 number of different  2 - person teams are possible.

Provide an example of permutation and combination?

An arrangement of things in a specific order is referred to as a permutation. In this arrangement, the components or components of sets are organized in a linear or sequential order.

                       As an illustration, set A=1,6 has the permutation 2, which is 1,6,1. Permutations include the arrangement of individuals, digits, numbers, alphabets, letters, and colors. Combinations include things like choosing a menu, cuisine, clothing, a subject, and a team.

Total number of ways to choose different 2 person out of 19 person.

                     = ¹⁹C₂

              = 19!/2! (19 - 2)!

              =  19!/2!   17!

             = 19 * 18 * 17!/2 * 1 * 17!

            = 19 * 7

              = 171

Hence, maximum 171 number of different  2 - person teams are possible.

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Answer:

It would help the rabbit by blending in with the environment and avoiding predators.

Step-by-step explanation:

I got the question right ap3x

Answer:

Step-by-step explanation:

It would help the rabbit by blending in with the environment and avoiding predators.

Answer:

Triangle WRD's angles are all 60 degrees, angle W and angle R and angle D.

Triangle WRD is an equiangular, equilateral triangle. It is also an acute triangle, as all angles are less than 90 degrees.

Step-by-step explanation:

You are told that WRD has all equal sides, each 3 inches long.

In a triangle, if sides are equal, then the opposite angles are also equal. So if ALL the sides are equal, then ALL the angles are equal.

The sum of the interior angles in a triangle is always 180 degrees. Since the trhee angles are all equal and they must add up to 180 degrees, 180/3 =60, so the angles must all be 60 degrees.

Triangle are classified by sides as

*** scalene = no equal sides

*** isosceles = two equal sides

*** equilateral = all equal sides

Triangles are classified by angles as

*** right triangle = one 90 degree angle

*** obtuse triangle = one angle larger than 90 degrees

*** acute triangle  = all angles less than 90 degrees

*** equiangular = all angles equal

There can be overlap in the categories, like an acute triangle also being equiangular.

The proof of the identity cos²x(1 + tan²x) = 1 is complete using the mentioned rules.

Hi! I'd be happy to help you complete the proof of the identity cos²x(1 + tan²x) = 1 using the given terms.

1. Statement: cos²x(1 + tan²x) = cosx (sec²x)
  Rule: Identity (using the identity tan²x = sec²x - 1)

2. Statement: cosx (sec²x) = cosx (1 + cos²x)
  Rule: Identity (using the identity sec²x = 1/cos²x)

3. Statement: cosx (1 + cos²x) = cos²x + cos⁴x
  Rule: Distributive Property (cosx * 1 + cosx * cos²x)

4. Statement: cos²x + cos⁴x = 1
  Rule: Pythagorean Identity (since cos²x + sin²x = 1, we substitute sin²x with 1 - cos²x and simplify)

So, the proof of the identity cos²x(1 + tan²x) = 1 is complete using the mentioned rules.

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The surface area of the rectangular prism figure is S = 838 cm²

Given data ,

The formula for the surface area of a prism is SA=2B+ph, where B, is the area of the base, p represents the perimeter of the base, and h stands for the height of the prism

Surface Area of the prism = 2B + ph

So, the value of S is given by

The heights of the prism is represented as 7cm.

S = ( 11 x 20 ) + ( 7 x 20 ) + ( 4 x 20 ) + 2( 5 x 7 ) + 2( 6 x 4 ) + ( 6 x 20 ) + ( 5 x 20 ) + ( 3 x 20 )

On simplifying the equation , we get

S = 220 + 140 + 80 + 70 + 48 + 120 + 100 + 60

S = 838 cm²

Therefore , the value of S is 838 cm²

Hence , the surface area is S = 838 cm²

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When more than 25 shirts are ordered, the price is $15 per shirt, plus $15 shipping and handling.  If $720 was spent on shirts,  the student council ordered 47 shirts.

Let x be the number of shirts ordered. We can set up an equation based on the given information:

If x ≤ 25, then the cost of the shirts is 20x + 20.

If x > 25, then the cost of the shirts is 15x + 15.

We know that the total cost of the shirts is $720. So, we can write:

20x + 20 if x ≤ 25

15x + 15 if x > 25

Setting these equal to each other, we get:

20x + 20 = 15x + 15

5x = 5

x = 1

This doesn't make sense, because the number of shirts ordered must be greater than 1. Therefore, we know that the student council ordered more than 25 shirts.

Using the equation 15x + 15 = 720, we can solve for x:

15x + 15 = 720

15x = 705

x = 47

To check, we can calculate the cost of the shirts:

If 47 shirts are ordered, then the cost is 15(47) + 15 = $720.

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Answer:

39200000

Step by step explanation is in the photo

Answer:

C.

Step-by-step explanation:

5 divided by 2 is the same as 5 times 1/2

\(\frac{5}{1} * \frac{1}{2} =\frac{5}{2} =5/2\)

Answer:

Graph A

Step-by-step explanation:

The y-intercept is -3, which is the y-value when the graph hits the y-axis.

Graph A and B both hit the y-intercept of -3.

The slope is 3/4, which means the line rises 3 units as it runs 4.

This time, only Graph A has the correct slope.

The correct answer is \(\boxed{\text{Graph A}}\)

-Chetan K

Answer:

Graph A

Step-by-step explanation:

The formula is in the form y=mx+c, where m is the gradient and m is the y-intercept, this means that the y-intercept is (0,-3) which rules out Graph B.

To find the gradient we use \(\frac{rise}{run}\), this means that the vertical value has to be 3 and the horizontal distance 4 and this rules out Graph C as its gradient is 3/2. That means that graph A matches the equation the best.

Answer:

1307199.57

Step-by-step explanation:

Follow BEDMAS (brackets first, then exponents, then multiplication and division, then addition and subtraction)

587x6543÷285(32+65)

32+65=97

587 x 6543 ÷ 285 x 97

= 3840741 ÷ 285 x 97

= 13476.2842 x 97

= 1307199.57

The percentage of the population in decimal is p=0.42

The mean of the sample of the binomial distribution=75.6

The standard deviation of the sample of the binomial distribution=6.622

How to convert a decimal to a percentage?

To convert a decimal number into a percentage value, multiply the decimal by 100.

What is binomial distribution?

The binomial distribution gives out either success or failure as two possible results in an experiment, is the discrete probability distribution used in probability theory and statistics.

Given that,

p = 42% = 0.42

q = 1 - p = 1 - 0.42 = 0.58

n = 180

Using the binomial distribution,

mean = \(n \times p\) = \(180 \times 0.42\) = 75.6

standard deviation = \(\sqrt{n \times p \times q}\) = \(\sqrt{180 \times 0.42 \times 0.58}\) = 6.622

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The percentage of the population in decimal is p=0.42

The mean of the sample of the binomial distribution=75.6

The standard deviation of the sample of the binomial distribution=6.622

How to convert a decimal to a percentage?

To convert a decimal number into a percentage value, multiply the decimal by 100.

What is binomial distribution?

The binomial distribution gives out either success or failure as two possible results in an experiment, is the discrete probability distribution used in probability theory and statistics.

Given that,

p = 42% = 0.42

q = 1 - p = 1 - 0.42 = 0.58

n = 180

Using the binomial distribution,

mean =   75.6

standard deviation =  6.622

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Answer: 5 chairs and 2 extra chairs

Step-by-step explanation:

Note that \(\frac{27}{5}=5.4\). This means we can place up to 5 chairs at each table.

However, this means that there will be \(27-5(5)=2\) chairs left over.

The argument that the American criminal justice system evolved as racial control is supported by evidence of racial disparities and discriminatory practices within the system.

The argument that the criminal justice system in America serves as a mechanism for racial control finds support in various instances. Firstly, statistical data consistently reveals significant racial disparities in arrests, convictions, and sentencing. Studies have shown that Black individuals are disproportionately targeted and face harsher penalties compared to their White counterparts for similar offenses.

Secondly, historical evidence such as the War on Drugs and its impact on minority communities further underscores the racialized nature of the criminal justice system. The disproportionate targeting and imprisonment of Black and Brown individuals in connection with drug offenses highlight systemic biases. These examples contribute to the validity of the argument that the criminal justice system in America evolved as a means of racial control.

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Answer:

I got you!

a ≤ 11

For more info, look at the steps in the attached image!

Step-by-step explanation:

Answer:

a ≥11

Step-by-step explanation:

\(21 \geqslant 3a - 21 + 9 \\ 21 \geqslant 3a - 12 \\ 21 + 12 \geqslant 3a - 12 + 12 \\ 33 \geqslant 3a \\ 3a \leqslant 33 \\ a \geqslant 11\)

The answer to the given question is option B, which is (-1.74 and 1.74).

Step-by-step explanation:

Now, we need to find the z values that will enable us to fail to reject the null hypothesis. The p-value for the given level of significance is:

p = 0.0819.

As it is a two-tailed test, the significance level is divided into two equal parts.

The equal parts would be 0.0819/2 = 0.04095.

The z-score corresponding to the probability 0.04095 is -1.74, and the z-score corresponding to the probability 0.95905 (1 - 0.04095) is 1.74.

Therefore, the z-values that will enable us to fail to reject the null hypothesis at the 0.0819 significance level in a two-tailed test is option B, which is (-1.74 and 1.74).

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a) This Parallelogram law essentially relates the lengths of the individual vectors and the lengths of the diagonals of the parallelogram formed by vectors.

b) The Parallelogram Law is proven using the Triangle Inequality and the properties of vectors.

a) Geometric interpretation of the Parallelogram Law,

the Parallelogram Law states that for any two vectors and the sum of the squares of the lengths of the diagonals of a parallelogram formed by these vectors is equal to twice the sum of the squares of the lengths of the individual vectors. Geometrically,this law can be interpreted as follows,

Consider two vectors a and b in a vector space.

When these vectors are added together (a + b) and they form a parallelogram with a and b as adjacent sides.

The diagonal vectors of this parallelogram are a + b and a - b.

The Parallelogram Law states that if you square the lengths of both diagonal vectors (||a + b||² and ||a - b||²) and add them together then we will get the result is equal to twice the sum of the squares of the lengths of the individual vectors (2||a||²+ 2||b||²).

This law essentially relates the lengths of the individual vectors and the lengths of the diagonals of the parallelogram formed by these vectors.

b) Proof of the Parallelogram Law using the Triangle Inequality:

To prove the Parallelogram Law, we'll start with the following steps and utilizing the properties of vectors and the Triangle Inequality:

Start with the left-hand side of the Parallelogram Law:

||a + b||² + ||a - b||²

Expand the squared terms:

(a + b)·(a + b) + (a - b)·(a - b)

Expand the dot products:

(a·a + 2a·b + b·b) + (a·a - 2a·b + b·b)

Simplify by combining like terms:

2(a·a + b·b)

Rewrite in terms of the magnitudes of vectors using the dot product definition:

2(||a||² + ||b||²)

Distribute the 2:

2||a||² + 2||b||²

This matches the right-hand side of the Parallelogram Law, which completes the proof.

Therefore, the Parallelogram Law is proven using the Triangle Inequality and the properties of vectors.

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