15÷(3+13)2 i need help

Answer:

23 and 24

Step-by-step explanation:

let the 2 consecutive numbers be n and n + 1 , then

n² + (n + 1)² = 1105

n² + n² + 2n + 1 = 1105 ( subtract 1105 from both sides )

2n² + 2n - 1104 = 0 ( divide through by 2 )

n² + n - 552 = 0 ← in standard form

(n + 24)(n - 23) = 0 ← in factored form

equate each factor to zero and solve for n

n + 24 = 0 ⇒ n = - 24

n - 23 = 0 ⇒ n = 23

However, n > 0 , then n = 23 and n+ 1 = 23 + 1 = 24

the numbers are 23 and 24

The distance from the Sun to Mars is 3. 9 times farther

Ratio can be described as a mathematical comparison between two or more numbers or elements in relation to each other on the basis of their sizes or magnitudes.

It is however known to show how many times one number or elements contains another.

Based on the information given, we have;

To determine the ratio of their distances from the Sun, we have;

Distance from the Sun to Mars /Distance from the Sun to Mercury

Substitute the values

2.28×10^8/5.79×10^7

Divide through

3. 9 times

Hence, the distance is 3. 9 times farther.

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Answer:

-30  I don't see -30 as an answer option.  Please check the problem.

Step-by-step explanation:

c²a + 2a÷b

c²a + 2a/b   Enter values for a, b and c for a = -3, b= 2 and c = 3.

(3)²(-3) + 2(-3)/(2)

(9)*(-3) + (-6)/(2)

-27 + (-3)

-27 - 3 = - 30

The slope-Intercept form of the given line is y=x-1.

A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of line is given by,

y =mx + c

where,

x is the coordinate of the x-axis,

y is the coordinate of the y-axis,

m is the slope of the line, and

c is y-intercept.

The given line passes through (0,-1) and (1,0). Therefore, the slope of the given line can be written as,

Slope of the line, m = [0 - (-1)]/(1 - 0)

                                 = 1 / 1

                                 = 1

Now, the equation of the line passing through (0,-1) can be written as,

y = mx + c

(-1) = 1(0) + C

-1 = 0 + C

C = -1

Substitute all the value in the equation of the line,

y = m(x) + c

y = 1(x) + -1

y = x - 1

Hence, the equation of the given line is y=x-1.

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The equation of the line from the given graph can be written as  y = x + 1.

A straight line can be written in the form of equation as, y = mx + c.

Two straight lines intersect each other only at one point.

When two straight lines are parallel to each other the angle between them is zero.

From the given graph the points on the straight line can be determined as (1, 0) and (2, 1).

The slope of the line passing through points (x₁, y₁) and (x₂, y₂) is given as slope = (y₂ - y₁) / (x₂ - x₁).

Then, the slope of the line is (2 - 1) / (1 - 0) = 1

Now, the equation of the line can be written as,

(y - 1) / (x - 0) = 1

⇒ y - 1 = x

⇒ y = x + 1

Hence, the equation of the line in slope-intercept form is given as y = x + 1.

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Answer:

Step-by-step explanation:

3p. = 2m - 5q

-2m. = -3p - 5q

Divide through by -2

m. = (3p + 5q) \2

The equation can be rearranged and expressed in terms of p and q is m = (3p+5q)/2.

Given equation 3p = 2m - 5q

3p + 5q = 2m

(3p + 5q) / 2 =m

Hence, m = (3p+5q) / 2  

To express the equation in terms of p and q we need to put all the p and q terms to one side of the equation and m terms to another side of the equation. It can be easily seen that 3p is already on one side and we just need to bring a q term to this side which can be done by shifting 5q from the right-hand side to left-hand side. The equation is now 3p+5q. Now to get the equation in terms of m we need to divide the whole equation by 2 which will give m = (3p+5q) / 2.

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1) Simple interest is $41600, 2) compound interest is $ 43264, 3) Amount at the end of Simple interest is $301600, 4) Amount at the end of Compound interest is $303264, 5) Difference in the amount of simple and compound interest is $ 1664.

Here it is given:

Principle (P) =$ 260000

Time(t) = 2 years

Rate (R) = 8%

1) We have to find the simple interest:

Simple interest(SI) = P× t × R/ 100

                               = 260000× 2× 8/ 100

                               = $41600

2) We have to find Compound Interest

Compound interest(CI) =P( 1 + R/100[tex])^{t}[/tex]- P

                                     = 260000( 1 + 8/100[tex])^{2}[/tex]- 260000

                                     = 260000( 27/25[tex])^{2}[/tex] - 260000

                                     = 303264 - 260000

                                     = $43264

3) Amount at the end of simple interest

Amount = P + SI

             = 260000 + 41600

             =$301600

4) Amount at the end of compound interest

Amount = P + CI

             = 260000+ 43264

             = $303264

5) Difference between the amount at simple interest and compound interest

Difference = 303264 - 301600

                  = $1664

Therefore the simple interest is $41600, the compound interest is $43264, the Amount at the end of simple interest is $ 301600, the amount at the end of the compound interest is $303264, and the difference in the amount of simple interest and compound interest is $1664.

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The equation of the line is y=3x+1 when the line is on the graph of the given picture.

Given that,

In the picture we have a graph.

We have to find the equation of the line.

We know that,

From the graph we can see the points,

(1,4) and (0,1)

We know that the equation of the line is y=mx +b

The y and x value are from the points and the m is the slope that is rise by run and b is the y intercept.

m is rise/run

m= 1-4/0-1

m=-3/-1

m=3

b is 4=3(1)+b

4=3+b

b=4-3

b=1

The equation of the line is y=3x+1

Therefore, The equation of the line is y=3x+1 when the line is on the graph of the given picture.

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Answer: 27/31 is the answer

Step-by-step explanation:

31/27 x 27/31 = 1 because 27/31 is the recprical

Answer:x = 31/27 = 1.148 

Step-by-step explanation:

The mean and standard deviation of this sampling distribution is 1 cm and 0.033 cm, respectively.

The sample mean is the arithmetic mean of all the samples of processor chips. The mean of the sample group is known as the sample mean.

Let X denote the multiple random samples of 35 processor chips and each of which represents the size of the processor chips.

Let 'x' be the sample mean of all the random samples X which represents the size of the processor chips.

The mean of the size of processor chips= μ =1 cm

The mean of the sampling distribution x of sample means is equal to the mean of the sizes of the processor chips μ

Mean of sampling distribution x  = mean of the size of the processor chips μ

⇒ x = μ

   x = 1 cm

The mean of this sampling distribution is 1 cm.

The standard deviation is the amount of variation among the set of values. It is the measure of the dispersion of values in the data set.

The size of the processor chips has a standard deviation of 0.2 cm so σ = 0.2 cm

Let 'x' be the standard deviation of random samples X of the size of processor chips.

Number of random multiple samples of processor chips, n =35

The standard deviation of this sampling distribution can be calculated by using the below formula;

x = σ/[tex]\sqrt{n}[/tex]

Substituting the value of \sigma as "0.2" cm and the value of "n" as 35 in the above formula, we get;

x = 0.2/√35

x = 0.033 cm

The standard deviation of this sampling distribution is 0.033 cm.

The mean of this sampling distribution is 1cm and the standard deviation of this sampling distribution is 0.033 cm.

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Answer: [tex]g(2n)=4n^2 -8n[/tex]

Step-by-step explanation:

Substituting [tex]2n[/tex] for [tex]x[/tex],

[tex]g(2n)=(2n)^2 -4(2n)\\\\g(2n)=4n^2 -8n[/tex]

Answer:

-7

Step-by-step explanation:

6/2=3

3+1= 4

2-5= -3

-3-4= -7

6/2+1= 4

2-5-4= -7

*Do what is in the parenthesis first!!*

1. Translation; y= f(x) + 2

2. Reflection; y= -f(x)

3. Stretch; y= 2f(x)

4. Shrink; y= 1/2 f(x)

Each point in a figure is moved the same distance in the same direction using a type of transformation known as translation.

A reflection is the shape's mirror image. A line, called the line of reflection, will allow an image to reflect through it. Every point in a figure is said to reflect the other figure when they are all equally spaced apart from one another.

Given:

When f(x) shifts 2 units up, we have

y= f(x) + 2; Translation

When the graph of f(x) to a symmetric position on the opposite side of the x-axis

y= -f(x); Reflection

When it stretches f(x) by a factor of 2

y= 2f(x); Stretch

When it reduces f(x) by a factor of 1/2

y=  1/2f(x); Shrink

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The probability of the next flip result in a trail is 0.5.

Given that,

If you flip a coin 100 times and receive 80 heads and 20 tails.

We have to find what is the probability that the upcoming flip will result in a tail based on these findings.

Probability refers to potential. This branch of mathematics deals with the occurrence of a random event. The value's range is 0 to 1. Probability has been applied into mathematics to predict the likelihood of different events.

Gonna determine how likely something is to occur, use probability. Many things are hard to predict with 100% certainty.

One is the probability of every event in a sample space.

Next flip result is independent of the past results.

P(Next flip result is tail) = 1/2 = 0.5

Therefore, The probability of the next flip result in a trail is 0.5.

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Answer:

No

Step-by-step explanation:

The sum of the squares of the lengths of the two shorter sides is [tex]10^2+12^2=244[/tex].

The square of the length of the largest side is [tex]14^2=196[/tex].

Because these two values are not equal, the side lengths do not satisfy the Pythagorean theorem. Therefore, the triangle is not a right triangle.

The subtraction between the functions f(x) = 4 · x - 8 and g(x) = - 3 · x + 1 is equal to (f - g) (x) = 7 · x - 9.

Herein we find f(x) and g(x) defined as linear functions and we are asked to find the subtraction between two functions, which is defined below:

(f - g)(x) = f(x) - g(x)

If we know that f(x) = 4 · x - 8 and g(x) = - 3 · x + 1, then the result of the subtraction of the two functions is:

(f - g) (x) = f(x) - g(x)

(f - g) (x) = (4 · x - 8) - (- 3 · x + 1)

(f - g) (x) = 7 · x - 9

The subtraction between the two functions is (f - g) (x) = 7 · x - 9.

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Step-by-step explanation:

In a candy box, there are 3 times as many candies with nuts as candies without nuts. There are 12 candies in the box. How many candies with nuts are in the box?

let:

without nuts = x

with nuts = 3x

so:

x + 3x = 12

4x = 12

x = 3, so there are 3 candies without nuts.

Because there are three times more candies with nuts than without:

3 * 3 = 9 candies with nuts

Answer:

9 candies with nuts

Step-by-step explanation:

Suppose the number of candies is x

there three times as many candies with nuts as candies without nuts, so 3x

there are 12 candies in total

3x+x=12

4x=12

x=3

3x=9

The length of the road in the simplest radial form is 10[tex]\sqrt{29}[/tex].

Here a rectangle of dimensions is 20m by 50m. So the length of 50m and the breadth is 20m

As the road is diagonal of the rectangle.

So we have to find the length of the diagonal of the rectangle.

Formula to find the diagonal of rectangle:

Diagonal = [tex]\sqrt{l^{2} + b^{2} }[/tex]

length (l) = 50m

Breadth(b) = 20m

Diagonal = [tex]\sqrt{50^{2} + 20^{2} }[/tex]

               = [tex]\sqrt{2500 + 400}[/tex]

               = √2900

              = 10√29

Therefore the length of the road is 10√29.

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Answer:

Step-by-step explanation:

Isabella,  do you know how to do the "elementary row operations"?

Also, when did they begin teaching  linear algebra in H.S.  :DDD  nice work getting there.

Gauss Jordan, just mean get your matrix in RREF  (Reduced Row Echelon Form)

I suggest using Matlab to do this.  it's got the  "RREF(x)  function to do this exact thing.  

Your teacher probably wants you to do this by hand.  thou, huh.  :/  

here is my Matlab code and the answer

clc

close all

clear

format compact

A=[3 -4 2;0 -1 7]

mymatx=rref(A)

A =

    3    -4     2

    0    -1     7

mymatx =

   1.0000         0   -8.6667

        0    1.0000   -7.0000

Yes, maybe it's totally cheating, but it seems fair nowadays to use technology that is commonly available.    :)

So answer A) looks right

The coordinates of point N are (8.66, 21)

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.

The coordinates of a point dividing a straight line joining two coordinates in the ratio m : n is given by -

x =  [tex]$\frac{mx_2+nx_1}{m+n}[/tex]

y = [tex]$\frac{my_2+ny_1}{m+n}[/tex]

We have LMN as a straight line such that the coordinates of L are (-3,1) , coordinates of M are (4,9) and LM : MN is 2 : 3.

Assume the coordinates of point N are (a, b).

We can write -

9 =  (2b + 3)/5

4 = (-6 + 3a)/5

2b + 3 = 45

b = 21

3a - 6 = 20

3a = 26

a = 8.66

Therefore, the coordinates of point N are (8.66, 21)

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The factors of the number 100 are: 1, 2, 4, 5, 10, 20, 25, 50, 100. If you add them up, you will get the total of 217

The blanks are -2 and 0.5 respectively, by solving the expression (8 - 2x) *(-0.25x)

What does the term Algebraic Expression means?

In mathematics, an algebraic expression is an expression composed of variables and constants as well as algebraic operations (addition, subtraction, etc.). Terms combine to form expressions.

Solution:

Given the expression, we need to solve it by using the properties of basic multiplication.

= (8 - 2x)*(-0.25x)

= (8*(-0.25x)) + (-2x * (-0.25x))

= -2x + 0.5[tex]x^{2}[/tex]

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The annual percentage rate of depreciation of the number of rhinos represented by the statistics is approximately 6.41 %

The rate of depreciation is the rate at which the number or value of an item reduces within each specified period.

The initial number of black rhinos in 1970 = 60,500

The number of black rhinos remaining in 2011 = 4,000

The annual rate of depreciation can be found using the formula;

Where;

FV = The future value = 4,000

PV = The present value = 60,500

r = The annual depreciation rate

n = The number of years

[tex]4,000 = 60,500 \times \left(1+\dfrac{r}{100} \right)^{(2011-1970)}=60,500 \times \left(1+\dfrac{r}{100} \right)^{41}[/tex]

[tex]\left(1+\dfrac{r}{100} \right)^{41} = \dfrac{4000}{60500} = \dfrac{8}{121}[/tex]

[tex]r = 100\times \left(\sqrt[41]{ \dfrac{8}{121}} - 1\right) \approx -6.41[/tex]

The annual rate of depreciation is approximately 6.41%

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We're given :
Patricia originally has $3425.82 in her account.

After that, she deposits $9120.75, meaning her amount in her account goes up by $9120.75

Lastly, she withdraws $185.90, meaning her amount in her account goes down by $185.90.

Therefore, after the transactions, she has a total of : 3425.82 + 9120.75 - 185.90 = $12360.67

5. Based on arc and central angle relationship, m∠BCD is: B. 108°.

6. The length of arc PQ is: H. 3.14 m

7. Length of CF is: A. 6 cm.

To find the length of an arc, the formula to use is:

Arc length = ∅/360 × 2πr

5. Measure of arc AB = 72°

Measure of arc BD = 180 - measure of arc AB

Measure of arc BD = 180 - 72

Measure of arc BD = 108°

Measure of angle BCD = measure of arc BD [central angle theorem]

Measure of angle BCD = 108°

The answer is: B. 108°

6. ∅ = 60°

r = 3 m

Arc length = 60/360 × 2 × π × 3

Arc length = 3.14 m

The answer is: H. 3.14 m

7. Since the distance between the two chords, AB and CD are equal, therefore, AB = CD.

AB = CD = 12 cm

CF = 1/2(CD)

CF = 1/2(12)

CF = 6 cm.

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Answer:

yes, you did it right!

Step-by-step explanation:

You firsth calculate how much 15% of £600 are.
You did it exactly right. It's £90.
And to work out rhe value of the shares one week later, you add the £90 to the £600.

The solution for k in the equation given as 20+ 7k = 8k+ 16 is 4

From the question, the algebraic expression is given as

20+ 7k = 8k+ 16

There is no constant to multiply or divide in the expression

So, the equation remains the same

20+ 7k = 8k+ 16

Collect the like term in the above equation

This gives

8k - 7k = 20 - 16

Evaluate the like term in the above equation

So, we have the following representation

k = 4

The above equation cannot be solved further

Hence, the solution is k = 4

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