A piece of cloth costs 200$.if the piece was 5m longer, and the cost of each metre of clth was 2$ less, the cost of the piece would have remained unchanged. How long is the piece and what is its original number of persons.

Answer:

1. 79°

2. 54°

3. 107.5°

4. 44°, 35 cm

5. 76°, 3.5 cm

6. m∠U=36°, m∠M=m∠D=72°,  MD=8.6 cm

7. 78°, 93 cm

8. 81°, 75 cm

Step-by-step explanation:

1. The diagram shows an isosceles triangle because TH = OT. Angles adjacent to the base OH of isosceles triangle are congruent, so

[tex]m\angle H=m\angle O[/tex]

The sum of the measures of all interior angles is always 180°, thus

[tex]m\angle H+m\angle O+m\angle T=180^{\circ}\\ \\2m\angle H+22^{\circ}=180^{\circ}\\ \\2m\angle H=180^{\circ}-22^{\circ}\\ \\2m\angle H=158^{\circ}\\ \\m\angle H=79^{\circ}[/tex]

2. The diagram shows an isosceles triangle DGO because DG = GO. Angles adjacent to the base DO of isosceles triangle are congruent, so

[tex]m\angle D=m\angle O=63^{\circ}[/tex]

The sum of the measures of all interior angles is always 180°, thus

[tex]m\angle D+m\angle O+m\angle G=180^{\circ}\\ \\63^{\circ}+63^{\circ}+m\angle G=180^{\circ}\\ \\m\angle G=180^{\circ}-63^{\circ}-63^{\circ}\\ \\m\angle G=54^{\circ}[/tex]

3. The diagram shows an isosceles triangle SLO because LO = SO. Angles adjacent to the base SL of isosceles triangle are congruent, so

[tex]m\angle S=m\angle L[/tex]

The sum of the measures of all interior angles is always 180°, thus

[tex]m\angle S+m\angle L+m\angle O=180^{\circ}\\ \\2m\angle L+35^{\circ}=180^{\circ}\\ \\2m\angle L=180^{\circ}-35^{\circ}\\ \\2m\angle L=145^{\circ}\\ \\m\angle L=72.5^{\circ}[/tex]

Angles OLE and L (SLO) are supplementary (add up to 180°), so

[tex]m\angle OLE=180^{\circ}-m\angle L\\ \\m\angle OLE=180^{\circ}-72.5^{\circ}\\ \\m\angle OLE=107.5^{\circ}[/tex]

4. The diagram shows an isosceles triangle AMR because [tex]m\angle A=m\angle M=68^{\circ}[/tex] (angles adjacent to the side AM are congruent, so triangle AMR is isoseceles).

The sum of the measures of all interior angles is always 180°, thus

[tex]m\angle A+m\angle M+m\angle R=180^{\circ}\\ \\m\angle R+2\cdot 68^{\circ}=180^{\circ}\\ \\m\angle R=180^{\circ}-2\cdot 68^{\circ}\\ \\m\angle R=44^{\circ}[/tex]

To legs in isosceles triangle are always congruent, so

[tex]RM=AR=35\ cm[/tex]

5. The diagram shows isosceles triangle RYD because YD = RD. Angles adjacent to the base RY are congruent, so

[tex]m\angle R=m\angle Y[/tex]

The sum of the measures of all interior angles is always 180°, thus

[tex]m\angle R+m\angle Y+m\angle D=180^{\circ}\\ \\2m\angle Y+28^{\circ}=180^{\circ}\\ \\2m\angle Y=180^{\circ}-28^{\circ}\\ \\2m\angle Y=152^{\circ}\\ \\m\angle Y=76^{\circ}[/tex]

To legs in isosceles triangle are always congruent, so

[tex]YD=RD=3.5\ cm[/tex]

6. The diagram shows an isosceles triangle UMD because UM = UD. Angles adjacent to the base MD of isosceles triangle are congruent, so

[tex]m\angle D=m\angle M=72^{\circ}[/tex]

The sum of the measures of all interior angles is always 180°, thus

[tex]m\angle D+m\angle M+m\angle U=180^{\circ}\\ \\72^{\circ}+72^{\circ}+m\angle U=180^{\circ}\\ \\m\angle U=180^{\circ}-72^{\circ}-72^{\circ}\\ \\m\angle U=36^{\circ}[/tex]

To legs in isosceles triangle are always congruent, so

[tex]UM=UD=14\ cm[/tex]

The perimeter of isosceles triangle MUD is 36.6 cm, so

[tex]UM+MD+UD=36.6\\ \\MD=36.6-14-14\\ \\MD=8.6\ cm[/tex]

7. The sum of the measures of all interior angles is always 180°, thus

[tex]m\angle T+m\angle S+m\angle B=180^{\circ}\\ \\m\angle T+78^{\circ}+24^{\circ}=180^{\circ}\\ \\m\angle T=180^{\circ}-78^{\circ}-24^{\circ}\\ \\m\angle T=78^{\circ}[/tex]

Triangle STB is isosceles triangle because [tex]m\angle S=m\angle T=78^{\circ}[/tex] (angles adjacent to the side ST are congruent, so triangle STB is isoseceles).

To legs in isosceles triangle are always congruent, so

[tex]SB=TB\\ \\y+22.5=38.5\\ \\y=38.5-22.5\\ \\y=16[/tex]

Hence,

[tex]ST=16\ cm\\ \\TB=SB=38.5\ cm[/tex]

and the perimeter of triangle STB is

[tex]P_{STB}=16+38.5+38.5=93\ cm[/tex]

8. The diagram shows isosceles triangle CNB because CN = CB. Angles adjacent to the base RY are congruent, so

[tex]m\angle N=m\angle B[/tex]

The sum of the measures of all interior angles is always 180°, thus

[tex]m\angle N+m\angle B+m\angle C=180^{\circ}\\ \\2m\angle N+18^{\circ}=180^{\circ}\\ \\2m\angle N=180^{\circ}-18^{\circ}\\ \\2m\angle N=162^{\circ}\\ \\m\angle N=81^{\circ}[/tex]

To legs in isosceles triangle are always congruent, so

[tex]CB=CN=2x+90\ m[/tex]

The perimeter of the triangle CNB is

[tex]2x+90+2x+90+x=555\\ \\5x+180=555\\ \\x+36=111\\ \\x=111-36\\ \\x=75\ m[/tex]

So, [tex]NB=75 \ m[/tex]

Answer:

[tex] \sqrt{x^2} = |x| [/tex]

Step-by-step explanation:

[tex] \sqrt{x^2} = |x| [/tex]

The radical symbol when used for a square root means the non-negative  square root. You cannot state that sqrt(x^2) = x because x may be negative. That is why you need use the absolute value symbol.

Answer:

The number is -4.

Step-by-step explanation:

Let the number be n.

Given:

Max adds 7 to a number.

hence it is given as n+7

Multiply's the sum by -4 the result is 3 times the same number.

Hence the equation can be written as;

[tex]-4(n+7)=3n[/tex]

Now Solving the above equation to find value of n we get;

[tex]-4(n+7)=3n\\-4n-28=3n\\-4n-3n=28\\-7n=28\\n=\frac{28}{7}=-4[/tex]

The value of n is -4.

Now when we add 7 to number -4 we get answer as 3.

And when the sum is multiplied by -4 we get answer -12.

Also 3 times of number is equal to 3 multiplied by -4 we get answer as -12.

Hence when the sum is multiplied by -4  it is equal to 3 times of same number.

Hence from above we can say that the number is -4.

Final answer:

The number that satisfies Max's operation of adding 7 to a number and then multiplying by -4 to get 3 times the same number is -4.

Explanation:

Max adds 7 to a number n, then multiplies the sum by -4, and the result is 3 times the same number n. To find the number n, we first write down the equation that represents this situation:

-4(n + 7) = 3n

Next, we solve for n:

Distribute -4 inside the parenthesis: -4n - 28 = 3n

Move all n terms to one side: -4n - 3n = 28

Combine like terms: -7n = 28

Divide both sides by -7 to isolate n: n = -4

The number n that satisfies this equation is -4.

Answer:

I believe the answer is A.

Step-by-step explanation:

Multiply each nunber by .10

Afterwards subtract what you get from the number (ex-20,000)

You get the next number after it.

Do the same for each number

The statement that is true about the given table is "The situation can be modelled by an exponential decay function with a percent change of -10%".

Consider the function:

y= a(1 ± r)ˣ

where m is the number of times this growth/decay occurs, a = initial amount, and r = fraction by which this growth/decay occurs.

Given that An event management company purchases a new van. The value of the van, x years after the purchase, is shown in the table.

Now, if the rate of decay and the initial price of the van can be found by substituting the value of x and y in the equation as shown below.

For the first column from the table, when the value of x and y is 0 and 20,000, respectively.

y= a(1 + r)ˣ

20,000 = a(1 + r)⁰

20,000 = a (1)

a = 20,000

For the second column from the table, when the value of x and y is 1 and 18,000, respectively. Also, the value of a=20,000.

y= a(1 + r)ˣ

18,000 = 20,000(1 + r)¹

18,000/ 20,000 = 1 + r

0.9 = 1 + r

0.9 - 1 = r

-0.1 = r

r = -0.1 = -10%

Hence, the statement that is true about the given table is "The situation can be modelled by an exponential decay function with a percent change of -10%".

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Answer:

-24*sqrt(35)

Step-by-step explanation:

Answer:

700 dollars,

Step-by-step explanation:

what you do is divide 511 by 73 then multiply the number by 100

Proportion which can be used to represent equivalency of 3 feet in 1 yard and 12 feet in 4 yard is 3 : 1 : : 12 : 4

Given that

There are 3 feet in one yard  

And there are 12 feet in 4 yard  

Number of feet in one yard = 3 that is feet  : yard = 3 : 1  

Number of feet in 4 yards = 12 that is feet : yard = 12 : 4  

And 3 feet in 1 yard is equivalent to 12 feet in 4 yards means

[tex]\frac{3}{1}=\frac{12}{4}[/tex]

That is 3 : 1 : : 12 : 4

A proportion is statement that two ratios are equal. It can be written in two ways: as two equal fractions a/b = c/d; or using a colon, a : b = c : d

Hence proportion which can be used to represent equivalency of 3 feet in 1 yard and 12 feet in 4 yard is 3 : 1 :: 12 : 4

Answer: Proportion which can be used to represent equivalency of 3 feet in 1 yard and 12 feet in 4 yard is 3 : 1 : : 12 : 4

Step-by-step explanation: D

Answer:

$116 for four months

Step-by-step explanation:

$29 • 4 = 116

Answer:

Perimeter = (20 + 2x) mm.

Step-by-step explanation:

The octopus pupil has length 20 mm and the expression for its area is given by (20x - 200) square mm.

If the width of the octopus pupil is w, then 20w = 20x - 200

⇒ w = (x - 10) mm.

Therefore, the expression for its perimeter is 2(Length  + Width) = 2 ( 20 + x - 10) = 2( 10 + x) = (20 + 2x) mm. (Answer)

The expression that represents the perimeter of the octopus pupil is 20 millimeters.

To find the expression that represents the perimeter of the octopus pupil, you need to know the length and area of the pupil. The length is given as 20 millimeters, and the area is represented by the expression (20x-200) square millimeters. The perimeter of a shape is the sum of all its side lengths.

So, for the octopus pupil, the perimeter can be found by adding up the lengths of all its sides. Since the shape is not specified, we'll assume it's a regular shape with all sides equal in length.

To find the expression for the perimeter, we need to know the number of sides. If we assume it has n sides, then each side has a length of 20/n millimeters. Therefore, the perimeter expression would be 20/n multiplied by n, which simplifies to 20 millimeters.

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Answer:

-0.5

Step-by-step explanation:

It looks like it's increasing by 0.5

Answer:-0.5

Step-by-step explanation:Say you were doing it in postive form half of 1 is 0.50 meaning you just add a negative sign

Answer:

0

Step-by-step explanation:

1/3(4+8)-2^2

1/3(12)-2^2

1/3(12)-4

4-4

0

The conclusion about the relationship between the number of cars sold and the high temperature is "The high temperature and the number of cars sold may have a negative correlation, but one may not cause the other". Option D.

What can you conclude about the relationship between the number of cars sold and the high temperature?

Correlation in scatter plot indicates the strength and direction of a relationship between two variables. A positive correlation means that as one variable increases, the other also increases, while a negative correlation means that as one variable increases, the other decreases.

Therefore, from the scatter plot, it can be concluded that high temperature and the number of cars sold may have a negative correlation, but one may not cause the other.

Complete question:

A salesperson uses a scatter plot to compare the number of cars sold on a particular day to the high temperature that day. What can you conclude about the relationship between the number of cars sold and the high temperature?

A) Lower temperatures mean more cars are sold.

B) There is no correlation between the number of cars sold and the high temperature.

C) The more cars are sold, the more the temperature drops.

D) The high temperature and the number of cars sold may have a negative correlation, but one may not cause the other.

Answer:

464 students

Step-by-step explanation:

So in all he has 29 liters of punch

11L blackberry punch

18L Lemon line punch

29L collectively

so if 1 liter is enough for 16 students we would multiply 16 students by 29 liters of punch giving you 464.

Answer:

There is no solution for x.

Step-by-step explanation:

We are given that [tex]\sin (\cos x) = 1[/tex] and we have to solve for x.

Let us assume that [tex]\cos x = \theta[/tex] then [tex]\sin \theta = 1[/tex] ........ (1)

Now, we know that for any value of x the value of cos x lies between 1 to - 1.

Hence, [tex]1 \geq  \cos x \geq  - 1[/tex]  for all x.

⇒ [tex]1 \geq  \theta \geq  - 1[/tex]

Now, for [tex]1 \geq  \theta \geq  - 1[/tex], the value of [tex]\sin \theta[/tex] can never be equal to 1.

Hence, there is no solution for x. (Answer)

Answer:

OPTION A and OPTION C

Step-by-step explanation:

OPTION A:

[tex]$ \frac{1}{5}x - 10 $[/tex] and [tex]$ \frac{1}{5}(x - 50) $[/tex]

Consider [tex]$ \frac{1}{5}(x - 50) = \frac{x}{5} - \frac{50}{5} $[/tex]

This is equal to [tex]$ \frac{1}{5}x - 10 $[/tex].

This is exactly the first expression. So, we say both expressions are equivalent.

OPTION B:

[tex]$ \frac{1}{3} x - 6 $[/tex] and [tex]$ - \frac{1}{3}(3x  + 18) $[/tex]

Distributing [tex]$ -\frac{1}{3} $[/tex] to [tex]$ (3x + 18) $[/tex] we get:

[tex]$ \frac{-x}{3} + \frac{-18}{3} $[/tex]

⇒ [tex]$ -x - 6[/tex]

This is not equivalent to the first expression.

OPTION C:

[tex]$ \frac{1}{2}x + 8 $[/tex] and [tex]$ \frac{1}{2}(x + 16) $[/tex]

[tex]$ \frac{1}{2}(x + 16) = \frac{x}{2} + \frac{16}{2} $[/tex]

[tex]$ \implies \frac{1}{2}x + 8 $[/tex]

This is exactly the first expression. So, we say the expressions are equal.

We apply similar techniques to OPTION D and OPTION E. Note that the expressions are not equal in both the options.

Answer:

40

Step-by-step explanation:

-1.6(-25)=40

Answer:

40

Why didn't you just use a calculator      

Answer:

The number is        x=2.5      x=5/2

Step-by-step explanation:

x = number

2(1/x) = 32/40

2/x = 32/40

cross multipli cation

2*40 = 32x

80=32x

2.5 = x or  5/2 or 2(1/2)

Answer:Tueyndi

Step-by-step explanation:

Answer:1.6,9,14

Step-by-step explanation:

so x+6 input is x so you put the number in the input where the x is so 0+6=6,and 3+6=9 and so on.....

Answer:

42 TOTAL

Step-by-step explanation:

Answer:

The solution in the attached figure

Step-by-step explanation:

we have

[tex]y > \frac{2}{3}x+3[/tex] ----> inequality A

The solution of the inequality A is the shaded area above the dashed line [tex]y=\frac{2}{3}x+3[/tex]

The slope of the dashed line is positive

The y-intercept of the dashed line A is (0,3)

The x-intercept of the dashed line A is (-4.5,0)

[tex]y\leq -\frac{1}{3}x+2[/tex] ----> inequality B

The solution of the inequality B is the shaded area below the solid line [tex]y=-\frac{1}{3}x+2[/tex]

The slope of the solid line is negative

The y-intercept of the solid line B is (0,2)

The x-intercept of the solid line B is (6,0)

The solution of the system of inequalities is the shaded area between the shaded line and the solid line

using a graphing tool

see the attached figure

Answer:

B

Step-by-step explanation:

On edge 2021

Answer:

Step-by-step explanation:

5*m+t=4

Answer:

[tex]5(m+t)=4r[/tex]

Step-by-step explanation:

The given statement is

"Five times the sum of m and t is as much as four times r".

To find the equivalent expression to the given sentence, we just need to transform each part in mathematical expressions. Just remember, times is product, "as much as" indicates equality.

So, the part five times the sum of m and t, represents the product between the number five and the binomial expression, as follows

[tex]5(m+t)[/tex]

As much as four times r, expresses that the first part is equivalent to the product between 4 and r,

[tex]5(m+t)=4r[/tex]

Therefore, the expression is [tex]5(m+t)=4r[/tex]

Answer:

21 feet

Step-by-step explanation:

multiple 13 by two which should give you 26 subtract 26 from 68 which them gives you 42.

then divide 42 by 2 which gives you 21 for your final answer.

Answer:

The given function[tex]R(x) = x - x + x^2  - x[/tex] has 2 x -intercepts.

Step-by-step explanation:

Here, the given polynomial function is :

[tex]R(x) = x - x + x^2  - x\\\implies R(x) = x^2 - x[/tex]

or,  [tex]y  = x^2 - x[/tex] ............  (1)

X- intercept is the point in the graph of R(x), where the coordinate y = 0.

Now, substituting the value of y  =  0 in (1) find all x - intercepts:

[tex]y  =  0   \implies x^2 - x = 0\\x(x-1)  =0\\\implies(x-0)(x-1) = 0[/tex]

⇒ Either x = 0 ,         or x - 1 = 0 ⇒  x = 1

⇒The given function has two x intercepts at x  = 0 and x = +1

Hence, the given function[tex]R(x) = x - x + x^2  - x[/tex] has 2 x -intercepts.

Answer:

2 x-intercepts on edge2020

Step-by-step explanation:

Answer:

Angle a+ Angle b= 90 degrees

Step-by-step explanation:

a=180-124

a=56

b=180-90-56

b=34

a+b

34+56= 90

The solution is, the value is, Angle a+ Angle b= 90 degrees.

In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle. The two rays are called the sides of an angle, and the common endpoint is called the vertex.

here, we have,

from the given figure we get,

we have,

a=180-124

a=56

and,

b=180-90-56

b=34

now,

a+b

putting the values , we get,

34+56= 90

Hence, The solution is, the value is, Angle a+ Angle b= 90 degrees.

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This answer explains how to calculate the difference in the amount of nuts eaten by Paco and Levi.

To find out how much more Paco ate than Levi:

Calculate how much each person ate: Paco ate 3/4 cup, Levi ate 1/2 cup.

Subtract Levi's amount from Paco's: 3/4 - 1/2 = 1/4 cup.

Therefore, Paco ate 1/4 cup more than Levi.

Answer:

length =11m

width =6m

Step-by-step explanation:

let the w = x

L = 3x-7

area =L*w

66 = (3x-7)*x

66 = [tex]3x^{2} -7x[/tex]

[tex]3x^{2} -7x-66=0[/tex]

[tex]3x^{2} -18x+11x-66=0[/tex]

3x(x-6)+11(x-6)=0

(3x+11)(x-6)=0

x-6=0

x=6

recall,

L = 3x-7 =3*6-7=11

Answer:

The answer is 3.

Step-by-step explanation:

If you divide by the middle on all corners in the end you will get 3 lines of symmetry because you eventually used all three line.

Hope this helped!

Answer:

the answer is A. 3

Step-by-step explanation:

i just took the test

Answer:

The number of math problems Annabelle solved = 5 problems

The number of pages Annabelle read=  20 pages

Step-by-step explanation:

Given:

Time taken for Annabelle to solve one problem =3 minutes

Time taken for Annabelle to read one page =2 minutes

Total time taken by Annabelle to complete her homework= 55 minutes

To find:

Total Number of problems solved by Annabelle=?

Total Number of pages read by Annabelle=?

Solution:

Let the number of problem solved be x

Let the number of pages read be y

It is given that the number pages read is 4 times the number of problem solved

So number of pages read y= 4x

Now time taken to solve x problems =  time taken to solve one problem X total number of problem

=>[tex]3\times x[/tex]

=>[tex]3x[/tex]

Similarly,

Time taken to read 4x pages= total number of pages read X  time taken to read one problem

=>[tex](4x)\times 2[/tex]

=>[tex]2(4x)[/tex]  

Now we know that

Time taken to solve x problems + Time taken to read 4x pages= 55  minutes

3x + (4x)2=55

3x+8x=55

11x=55 [tex]x=\frac{55}{11}[/tex]

x=5

So number of problem solved is x=5

Number of pages read  y=4(x)=4(5)=20

Answer:

C. I can’t really enter square roots

Step-by-step explanation:

a^2/3 = a^2*a^1/3

Which is the cube root of a squared