PLEASE HELP ILL GIVE YOU 25 POINTS

Answer: 49.5

Step-by-step explanation:

Let Thomas' age be [tex]T[/tex]. Then, Hulian's age is [tex]T+14[/tex].

[tex]T+T+14=113\\\\2T+14=113\\\\2T=99\\\\T=49.5[/tex]

a) The perimeter of a rectangle is the sum of all four sides. So to find the perimeter we can add these two sides together, and then double the result.

The simplified expression for the perimeter of the rectangle would be:

2(2n - 3 + 4)

This can also be written as:

2(2n + 1)

This expression represents the mathematical operation where the sum of 2n - 3 and 4 is calculated, then multiplied by 2 to find the perimeter of the rectangle.

b) If the perimeter of the rectangle is 26, we can use the expression for the perimeter that we found earlier to solve for the value of n.

The perimeter of the rectangle is:

2(2n + 1) = 26

So if we divide both sides of the equation by 2, we get:

2n + 1 = 13

then if we subtract 1 from both sides

2n = 12

then if we divide by 2

n = 6

So the value of n is 6.

I hope this helps :)

Answer:

a. [tex]P = 4n + 2[/tex]

b. [tex]n = 6[/tex]

Step-by-step explanation:

a. The formula for the perimeter of a rectangle was:

[tex]P = 2L + 2W[/tex]

Given that the length was 2n-3 and the width was 4, substitute the values its formula:

[tex]P = 2L + 2W\\P = 2(2n-3) + 2(4)\\P = 4n - 6 + 8\\P = 4n + 2[/tex]

b. Since the perimeter of the rectangle was already indicated, we will just sunstitute it to the expression that we get from a.

[tex]P = 4n + 2\\26 = 4n + 2\\26 - 2 = 4n\\24 = 4n\\6 = n[/tex]

Answer:

Step-by-step explanation:

Love these kinda problems.

Alr,

d/dx of lnx = 1/x

let 3x³ + 12x = t

dt/dx = 9x² + 12 ( d/dx of xⁿ = n[tex]x^{n-1}[/tex])

then, d/dx of ln t= 1/t x dt/dx  = 1/(3x³+12x) x (9x² + 12) = (3x² + 4)/(x³ + 4x)

Pls mark as brainliest if possible. Cheers

The values are;

1. 35/3 days - Direct proportion

2. 4254 - Direct proportion

3. 120 teachers - Indirect proportion

Proportion can be described as an equation that has two ratios set equal to each other.

It is also seen as a mathematical comparison of numbers, terms, or variables.

The different types of proportion are;

From the information given, we have;

1. If 3 men completes the project in 7 days

Then 5 men would finish it in x days

cross multiply

x = 5(7)/3

x = 35/3 days

2. If 25kg of rice cost 1130

Then 100kg would cost x

cross mutiply

x = 1130(100)/25

x =  4,254

3. If there are 90 teachers = 1500 students

Then x teachers = 2000 students

x = 2000(90)/1500

x = 120 teachers

Hence, the values are 35/3 days, 4, 254 and 120 teachers.

Learn more about proportion here:

https://brainly.com/question/1781657

#SPJ1

The alternate interior angles are the angles that are formed inside the two parallel lines, when it is intersected by a transversal, and are equal to its alternate pairs.

Alternate interior angles are the angles formed when a transversal intersects two coplanar lines. They lie on the inner side of the parallel lines but on the opposite sides of the transversal. The transversal crosses through the two lines which are Coplanar at separate points.

Alternate angles are shaped by the two parallel lines crossed by a transversal. Consider the given figure, EF and GH are the two parallel lines. If two parallel lines are cut by a transversal, then the alternate angles are equal.

In order to understand alternate interior angles, one must first picture a set of parallel lines, and then a line intersecting them. The intersecting line is called a transversal, and all the angles formed between the parallel lines are the interior angles.

At the point of intersection of transversal and two lines we have:

∠3 + ∠4 = 180 .........(1)

∠6 + ∠8 = 180 ...........(2)

We know that angle 4 and angle 8 are equal:

Thus, using 1 and 2 we have:

∠3 = ∠6

Hence, ∠3 and ∠6 are congruent.

Now, using the alternate interior angle we know that:

∠3 = ∠6

Also, we have:

∠5 + ∠6 = 180 (Straight line)

Substituting the value of ∠6 = ∠3 we have:

∠5 + ∠3 = 180

Thus, the two angles are supplementary.

Learn more about alternate interior angles here:

https://brainly.com/question/28971625

#SPJ1

The expression for the given word phrase is

46M + M² + 2 + 1/M²

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Number = M

Reciprocal of M = 1/M

Now,

46 x (M + 1/M)²

Step 1:

46M + M² + 2 + 1/M²

Thus,

The expression is 46M + M² + 2 + 1/M²

Learn more about expressions here:

https://brainly.com/question/3118662

#SPJ1

The observed time cycles of five given elements are 2.1, 1.01, 3.4, 4.1, 1.5 respectively

To determine the observed time (OT),

The observed time (OT) of each cycles will be added together for each element. and divided by total number of cycles for each element.

This is done in the following ways

1) (1.2+2.0+2.2+2.1+2.1)/5 = 10.5/5 = 2.1

2) (1.1+1.0+1.2) = 3.3/3 = 1.1

3) (3.4+3.5+3.3+3.5+3.4+3.3)/6 = 20.1/6 = 3.4

4) 4.0+4.2)/2 = 8.2/2 = 4.1

5) (1.4+1.4+1.5+1.5+1.5+1.4)/6 = 8.7/6 = 1.5

therefore each elements total cycle OT is added and then it is divided with each elements relevant number of cycles and this as a result provides the answer to the question

Learn more about number of observed time on https://brainly.com/question/28549017

#SPJ1

Answer:

Question 4:

Question 5:

Question 6:

Step-by-step explanation:

Given vertices of the pre-image:

If the pre-image is reflected in the line x = -1, the transformation rule is:

Therefore the vertices of the image are:

Given vertices of the pre-image:

If the pre-image is rotated 180° about the origin, the transformation rule is:

Therefore the vertices of the image are:

Given vertices of the pre-image:

If the pre-image is rotated 270° about the origin, the transformation rule is:

If the direction of a rotation is not specified, then it is counterclockwise.

Therefore the vertices of the image are:

Plot the given coordinates of the polygon in the coordinate plane and connect it with a smooth curve.

A two-dimensional geometric shape with a finite number of sides is called a polygon. A polygon's sides are constructed from segments of straight lines joined end to end.

A coordinate plane is a two-dimensional plane created by the intersection of two number lines. The x-axis, a horizontal number line, and the y-axis, a vertical number line, are two of these number lines.

Plot the points on the graph according to the given coordinates. Connect all the points. The polygon is triangle.

Learn more about polygon here:

https://brainly.com/question/24464711

#SPJ1

The daily cost to heat a building at 10 degrees celsius is  $82.72

From the question, we have the following parameters that can be used in our computation:

f(x)=6(1.3)^-x

Then, we have

x = 10

This implies that

f(-10) = 6(1.3)^-(-10)

Evaluate the expression

f(-10) = 82.72

This means that the cost to heat is $82.72

Also, the domain is all set of real numbers and the range is y > 0

Read more about exponential functions at

https://brainly.com/question/2456547

#SPJ1

Complete question

During the winter if the low temperature outside is x Celsius,the daily cost to heat a building can be determined using the function f(x)=6(1.3)^-x.find and interpret the given function values and determine an appropriate domain for the function

f(10)

Answer:

2 miles

Step-by-step explanation:

Distance = speed x time

= 10mph x 1/5

= 2 miles

Side AC in the triangle is 3.6 and side BC in the triangle is 1.7

The sine rule states that if a, b and c are the lengths of the sides of a triangle, and A, B and C are the angles in the triangle; with A opposite a, etc., then a/sinA=b/sinB=c/sinC.

To find side AC :

4/sin90 = AC / sin64.3

AC × sin90 = sin 64.3 × 4

AC = 0.9 ×4

AC = 3.6 ( nearest tenth)

To find side BC:

using Pythagoras theorem

4² = 3.6² + (BC)²

16 = 12.96 +(BC)²

(BC)² = 16 - 12.96

(BC)² = 3.04

BC = √ 3.04

BC = 1.7( nearest tenth)

learn more about sine rule from

https://brainly.com/question/20839703

#SPJ1

Answer:

B)  x + y ≤ 30,000

     x ≥ 8,000

     x ≥ 3y

Step-by-step explanation:

Definition of the variables:

If Tamara has $30,000 and part or all of which she wants to invest into a combination of corporate bonds and municipal bonds, then the sum of the investments in the two bonds will be less than or equal to $30,000:

If Tamara wants to invest no less than $8,000 into corporate bonds, then the amount invested in corporate bonds (x) will be greater than or equal to $8,000:

If Tamara wants to invest at least three times as much into corporate bonds than into municipal bonds, then the amount invested in corporate bonds (x) will be greater than or equal to 3 times the amount invested in municipal bonds (y):

The graph of the given piecewise function is as attached below.

Piecewise function is a function consisted of pieces of different functions over different intervals.

From the case we have:

f(x) = 3x - 5 if x ≤ -1

f(x) = -2x + 3 if -1 < x < 4

f(x) = 2 if x ≥4

To construct the piecewise function, we can try to find the base points of each functions.

f(x) = 3x - 5; if x ≤ -1

We will take x = -1 to approximate the line position

f(-1) = 3(-1) - 5

f(-1) = -3 - 5 = -8

f(x) = -2x + 3; if -1 < x < 4

(x = -1)

f(-1) = -2 (-1) + 3

f(-1) = 2 + 3 = 5

(x = 4)

f(4) = -2 (4) + 3

f(4) = -8 + 3 = -5

f(x) = 2; if x ≥ 4

(x = 4)

f(4) = 2

We can put each points on the graph and try to construct the piecewise function.

Please refer to the attached graph below for the piecewise function graph

Learn more about Piecewise Function here: brainly.com/question/17919672

#SPJ1

The graph that represents a geometric sequence is Graph A.

A geometric sequence is a sequence of numbers in which each term after the first is found by multiplying the preceding one by a fixed, non-zero number called the common ratio.

Examples of geometric sequences include:

2, 4, 8, 16, 32, ... (common ratio of 2)

1/3, 2/3, 4/3, 8/3, ... (common ratio of 2/3)

5, -25, 125, -625, ... (common ratio of -5)

Geometric sequences have the property that the ratio of any two consecutive terms is always the same, and the quotient of any two consecutive terms is the common ratio.

This is shown only in the first graph so Graph A shows the geometric sequence.

Find out more on geometric sequence at https://brainly.com/question/1509142

#SPJ1

Answer:

10

Step-by-step explanation:

The given series is a geometric series with the first term a = 8, and the common ratio r = 1/5. To find the sum of the series, we can use the formula for the sum of an infinite geometric series:

S = a / (1 - r)

So, in this case, the sum of the series is:

S = 8 / (1 - 1/5) = 8 / (4/5) = 8 * (5/4) = 40/4 = 10.

Therefore, the sum of the series is 10.

Answer:

10

Step-by-step explanation:

A geometric series is the sum of the terms of a geometric sequence.

[tex]\boxed{\begin{minipage}{5.5 cm}\underline{Sum of an infinite geometric series}\\\\$S_{\infty}=\dfrac{a}{1-r}$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\ \phantom{ww}$\bullet$ $r$ is the common ratio.\\\end{minipage}}[/tex]

Given geometric series:

The ellipsis means to "continue in this pattern".  Therefore, find the sum to infinity of the given geometric series.

From inspection of the sequence, the first term is 8:

[tex]\implies a=8[/tex]

To find the common ratio, divide consecutive terms:

[tex]\implies r=\dfrac{a_2}{a_1}=\dfrac{1.6}{8}=0.2[/tex]

Substitute the found values of a and r into the geometric series formula:

[tex]\implies S_{\infty}=\dfrac{8}{1-0.2}=\dfrac{8}{0.8}=10[/tex]

Therefore, the sum of the given geometric series is 10.

The midpoint of f(x) over the interval [1, 2] is 4.8655

Generally, The point that represents the precise midway point between an interval's beginning and ending points is known as the midpoint of the interval. It may be determined by calculating the average of the two values that serve as endpoints.

For instance, the value 5 would represent the point that is exactly in the middle of the interval [3,7].

The midpoint of the interval [1, 2] is

(1 + 2) / 2

= 1.5.

To calculate the value of f(x) at x = 1.5, we need to substitute 1.5 for x in the function:

f(1.5) = 6 * ln(1.5^2)

= 6 * ln(2.25)

= 6 * 0.83

= 4.8655

Read more about interval

https://brainly.com/question/13708942

#SPJ1

The relationship between a young person's height and the recommended wheel diameter is a function, as each input is associated to a single output.

To verify whether a relation represents a function, we need to observe if each input is mapped to only one output.

The input and output variables for this problem are given as follows:

As for each height, there is only one recommended wheel diameter, we have that each input is mapped to a single output, and thus the relationship between a young person's height and the recommended wheel diameter is a function.

More can be learned about relationships and functions at https://brainly.com/question/29701528

#SPJ1

a. The explanatory variable is the new blood clot medication, and the confounding variable is the time period of 12 hours after the stroke begins.

b. The explanatory variable is the new software program, and the confounding variable is the 1-hour period after school

The confounding variable may invalidate the conclusions of the study because it is possible that the higher rate of total recovery is not due to the new medication, but rather due to the fact that the patients are being treated within the crucial 12-hour period after the stroke begins. To eliminate the effect of the confounding variable, the study could be conducted as a randomized controlled trial, where patients are randomly assigned to receive either the new medication or a placebo, and both groups are treated within the 12-hour period after the stroke begins.

In (b) the explanatory variable is the new software program, and the confounding variable is the 1-hour period after school. The confounding variable may invalidate the conclusions of the study because it is possible that the higher scores are not due to the software, but rather due to the fact that the students using the software were given more time to study and practice. To eliminate the effect of the confounding variable, the study could be conducted as a randomized controlled trial, where students are randomly assigned to use the software or not, and both groups are given the same amount of time to study and practice.

Learn more about variables on:

https://brainly.com/question/82796

#SPJ1

The time it takes until the deposit amounts to $6,000 is 2.6 years

From the question, we are to calculate how long it takes until the deposit amounts to $6000

From the compound interest formula, we have that

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

Where A is the amount

P is the principal

r is the interest rate

n is the number of times compounded per year

and t is the time.

From the given information,

P = $5,000

r = 7%= 0.07

n = 12

t = ?

A = $6,000

Putting the parameters into the formula

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

6000 = 5000(1 + 0.07/12)^(12×t)

6000/5000 = (1 + 0.0058333)^12t

1.2 = (1.0058333)^12t

Take log1.0058333 of both sides

31.346375 = 12t

31.346375/12 = t

t = 2.6 years

Hence, the time it takes is 2.6 years

Learn more on Compound interest here: https://brainly.com/question/25545513

#SPJ1

Answer: 844000

Step-by-step explanation:

843857 = 844000 because you round up

The solution for the expression 112 ÷ 0.16 is 700.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

112 ÷ 0.16

This can be written as,

= 112/0.16

= 700

Thus,

The solution is 700

Learn more about expressions here:

https://brainly.com/question/3118662

#SPJ1

Step-by-step explanation:

as always with % calculations :

first find what is 100% or 1%. everything else can be calculated from that.

in our case, we got 100% = 18.

therefore, 1% = 100%/100 = 18/100 = 0.18

how many % are 4 students ?

as many as the times 1% (0.18) fits into 4 :

4 / 0.18 = 22.22222222... %

so,

22.22222222... %

of the students passed.

therefore,

100 - 22.22222222... = 77.77777777... %

of the students did not pass.

Answer:

>4

Step-by-step explanation:

the answer of the question is >4

Answer:

[tex] - 2 \sqrt{5} [/tex]

Step-by-step explanation:

[tex] \sqrt{20} - \sqrt{80} [/tex]

[tex]2 \sqrt{5} - 4 \sqrt{5} [/tex]

[tex](2 - 4) \sqrt{5} [/tex]

[tex] - 2 \sqrt{5} [/tex]

Answer:

0.65 and 13/20

Step-by-step explanation:

Answer:

Step-by-step explanation:

You want to know the amounts invested at each rate if twice as much is invested at 4.5% as at 3.5%, and the total earnings are $1875.

Let x represent the amount invested at 3.5%. Then 2x is the amount invested at 4.5%, and the total earnings are ...

  0.035x +0.045(2x) = 1875

  0.125x = 1875 . . . . . . . . . collect terms

  x = 15000 . . . . . . . . . divide by 0.125

  2x = 30000 . . . . . . . find the other value invested

The amount deposited at 3.5% is $15,000; the amount deposited at 4.5% is $30,000.

The two column proof showing that  ΔWXZ ≅ ΔYXZ is as shown below

From the given triangle, we see that;

Given: WX ≅ XY, XZ bisects WXY

Prove: ΔWXZ ≅ ΔYXZ

The two column proof for the above is as follows;

Statement 1;  WX ≅ XY, XZ bisects 2

Reason 1; Given

Statement 2: ∠WXZ ≅ YXZ

Reason 2; Angle bisector

Statement 3; XZ ≅ XZ

Reason 3: Reflexive property of congruence

Statement 4:  ΔWXZ  ≅ ΔYXZ

Reason 4:  SAS Congruence Postulate

Read more about two column proof at; https://brainly.com/question/1788884

#SPJ1

√25  is the greatest value of the expressions .

What is an expression in maths ?

A number, a variable, or a mix of both plus certain operation symbols make up an expression. Two expressions are combined to form an equation, which is joined by the equal sign.

                         The combination of 8 and 3 is an example of a word. Example sentence: The result of adding 8 and 3 is 11. An expression in mathematics is made up of a mixture of variables, numbers, and functions (such as addition, subtraction, multiplication or division etc.) In some ways, phrases and expressions are comparable.

√25   = 5

√5  =   2.2360

√8  =   2.8284

√10 =    3.1622

Learn more about Expressions

brainly.com/question/14083225

#SPJ1