Simplify (in picture)

Answer:

79

Step-by-step explanation:

91 x 2 is 182. 340-182 is 158 divide by 2 and you get 79

Answer:

The width is 79 yards

Step-by-step explanation

Okay, so the perimeter of a shape is the sum of all the side-lengths of said shape. Because the shape is a rectangle, there are 4 sides (2 sides being the length, 2 sides being the width). This being said, the equation that can be used to find the perimeter is Perimeter = Length + Length + Width + Width or Perimeter = 2Length + 2Width. You would then plug in your given variables and solve for width. I have shown my work in the image below, I hope this is helpful :)

Answer:

[tex]\frac{1}{2} QP = UT[/tex]

Step-by-step explanation:

We are given  a ΔPQR  in which S is the mid point of QP  , T is the mid point of  QR , U is the mid point of PR

i) is true

⇒ [tex]\frac{1}{2} QP = UT[/tex]

Using mid segment theorem which states that In a triangle, the line joining the midpoints of any two sides will be parallel to the third side and that same line joining the midpoints is also half of length of third side .

So, by refering image we can see that UT is the line joining the two mid points . So, by using above theorem    1/2QP=UT and UT is parallel to PQ

Thus, (i) statement is true

⇒[tex]\frac{1}{2} QP = UT[/tex]

Answer:

it's A and D

Step-by-step explanation:

Answer:

1. [tex]x=56^o[/tex]

2. Exterior angle = [tex]116^o[/tex]

Step-by-step explanation:

1.

We can see from our given diagram that (2x+4) degrees is the measure of exterior angle of triangle PQR.

Since the measure of exterior angle of a triangle equals to the sum of the opposite interior angles. So measure of our given triangle's exterior angle will be equal to sum of measure of angle P and angle Q.

We can represent this information as:

[tex](2x+4)^o=60^o+x^o[/tex]

[tex]2x^o+4^o=60^o+x^o[/tex]

Let us subtract [tex]x^o[/tex] from both sides of our equation.

[tex]2x^o+4^o-x^o=60^o+x^o-x^o[/tex]

[tex]x^o+4^o=60^o[/tex]

Let us subtract [tex]4^o[/tex] from both sides of our equation.

[tex]x^o+4^o-4^o=60^o-4^o[/tex]

[tex]x=56^o[/tex]

Therefore, value of x is 56 degrees.

2. Since the measure of exterior angle of our given triangle is 2x+4, let us substitute x=56 in our expression to find the measure of exterior angle.

[tex]\text{Measure of exterior angle}=(2x+4)^o[/tex]

[tex]\text{Measure of exterior angle}=(2*56+4)^o[/tex]

[tex]\text{Measure of exterior angle}=(112+4)^o[/tex]

[tex]\text{Measure of exterior angle}=116^o[/tex]

Therefore, the measure of exterior angle of our given triangle is 116 degrees.

Answer: Choice B

I'm assuming choice B shows the quantity (1-cos(60)) all over the quantity (1+cos(60)), and that is one big fraction under the square root.

The trig identity we'll use is what I'm showing in the attached images below. All we do is replace theta with 60 and that's all there is to it. An identity like that is either memorized or you will have it handy on a notecard or reference sheet.

Answer:

[tex]\pm \sqrt{\frac{1-\cos 60^{\circ}}{1+\cos 60^{\circ}}}[/tex]

Step-by-step explanation:

Tangent function is one of the trigonometric function such that [tex]\tan \theta =\frac{\sin \theta }{\cos \theta }[/tex]

Basically, we can also say that tangent function is ratio of side opposite to the angle and side adjacent to the angle.

Given: [tex]x=60^{\circ}[/tex]

We need to rewrite [tex]\tan \left ( \frac{x}{2} \right )[/tex].

As [tex]\tan \left (x \right )=\pm \sqrt{\frac{1-\cos 2x}{1+\cos 2x}}[/tex]

As we need to express [tex]\tan \left ( \frac{x}{2} \right )[/tex], divide angle by 2, we get,

[tex]\tan \left ( \frac{x}{2} \right )=\pm \sqrt{\frac{1-\cos x}{1+\cos x}}[/tex]

At [tex]x=60^{\circ}[/tex],

[tex]\tan \left ( \frac{60^{\circ}}{2} \right )=\pm \sqrt{\frac{1-\cos 60^{\circ}}{1+\cos 60^{\circ}}}[/tex]

Answer:

(1)

Closed circle graph

(2)

Closed circle graph

Step-by-step explanation:

(1)

we are given

[tex]|x|=1[/tex]

we know that absolute value is always positive

so, we can write as

[tex]-x=1[/tex]

[tex]x=-1[/tex]

[tex]x=1[/tex]

So, value of x are

[tex]x=-1,x=1[/tex]

so, graph will be of closed circle

(2)

we are given

[tex]|x|=2[/tex]

we know that absolute value is always positive

so, we can write as

[tex]-x=2[/tex]

[tex]x=-2[/tex]

[tex]x=2[/tex]

So, value of x are

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

so, graph will be of closed circle

Answer:

|x| = 1

Closed circles on -1 and 1.

|x| = 2

Closed circles on -2 and 2.

(See attachments.)

Answer:

The two numbers are 6 and 19.

Step-by-step explanation:

To find these, we must first set the first number as x. Then we can set the second one in terms of x as 2x + 7.

Now that we have these values, we can add them together and set equal to 25.

x + 2x + 7 = 25

3x + 7 = 25

3x = 18

x = 6

With the first value being 6, we can solve for the second by using the equation built.

2x + 7

2(6) + 7

12 + 7

19

Answer:

The actual distance is 56 km

Step-by-step explanation:

We can use ratio's to solve this problem

1 cm            8cm

---------- = -----------------

7 km           x km

Using cross products

1 * x = 8 * 7

x = 56

x = 56 km

Answer:

4.1 years.  

Step-by-step explanation:

We have been given that The Lisbon’s new heat pump cost $4,500. They bought it to replace their old furnace and air  conditioner which cost about $2,800 a year to  run. The heat pump will save them approximately  39% a year.

Yearly cost was 2800 at first and the pump will save 39% of 2800. So annual saving with new heat pump will be:

[tex]\frac{39}{100}*2800=0.39*2800[/tex]

Let x be the number of years in which heat pump will pay for itself, so saving in x years will be:

[tex]0.39*2800*x[/tex]    

Now let us equate the savings by new heat pump with cost of heat pump to find the number of years (x).

[tex]0.39*2800*x=4500[/tex]

[tex]1092*x=4500[/tex]

[tex]x=\frac{4500}{1092}[/tex]

[tex]x=4.1208791208791209\approx 4.1[/tex]

Therefore, the heat pump will pay for itself in 4.1 years.

The heat pump will pay for itself in approximately 4.1 years.

To determine the number of years it will take for the heat pump to pay for itself, we need to calculate the annual savings from using the heat pump instead of the old furnace and air conditioner, and then divide the initial cost of the heat pump by these annual savings.

First, we calculate the annual savings by applying the 39% savings rate to the old cost of running the furnace and air conditioner:

Annual savings = 39% of $2,800

 = 0.39 * $2,800

 = $1,092

Now, we divide the initial cost of the heat pump by the annual savings to find out how many years it will take to recoup the cost:

Number of years to pay for itself = Initial cost of heat pump / Annual savings

 = $4,500 / $1,092

 = 4.12 years

Rounded to the nearest tenth, the heat pump will pay for itself in approximately 4.1 years.

To find the sales tax on a $60 bill with a 5% rate, convert the percentage to a decimal (0.05) and multiply by the total amount ($60). The sales tax is $3.

The sales tax on a total bill can be calculated by converting the percentage rate of the sales tax into a decimal and then multiplying it by the total amount of the bill.

In this case, the total cost is $60 and the sales tax rate is 5%. First, convert 5% into a decimal by dividing it by 100, which gives us 0.05. Then, multiply this decimal by the total bill amount to find the amount of sales tax. The calculation would be as follows:

$60 × 0.05 = $3

Therefore, the sales tax for a $60 bill at a 5% rate is $3.

Answer:

= 5/3 * pi  inches

  or approximately 5.235987756 inches

Step-by-step explanation:

The formula for arc length = r * theta  where theta is in radians

arc length = 10 * pi/6

                 = 10/6 * pi

                = 5/3 * pi

                or approximately 5.235987756 inches

Answer: 5.23 inches

Step-by-step explanation:

Let the length of the arc intersected by a central angle x be l.

Given:- Central angle[tex]x=\frac{\pi}{6}\text{ radians}[/tex]

Radius r= 10 inches

We know that ,

[tex]l=x\ r\\\\\Rightarrow\ l=\frac{\pi}{6}\times10\\\\\Rightarrow\ l=\frac{3.14\times10}{6}= 5.2333333333\approx5.23\text{ inches}[/tex]

Thus, the length of the arc of a central angle [tex]\frac{\pi}{6}\text{ radians}[/tex] is 5.23 inches.

Answer:

option:B

Step-by-step explanation:

on saturday the number of ice-cream cones sold are 8x+16

on sunday the number of ice cream cones sold are 7x-9

so the total number of ice cream cones sold are=number of ice cream cones sold on saturday+number of ice cream cones sold on sunday

=8x +16+7x-9

=15x+ 7

hence option B is correct.

Answer:

B. 15x + 7

Step-by-step explanation:

We are given that,

The number of ice-creams sold on Saturday = 8x + 16 and

The number of ice-creams sold on Sunday = 7x - 9

Therefore,

The total number of ice-creams sold = Number of ice-creams sold on Saturday + Number of ice-creams sold on Sunday

i.e. Total number of ice-creams = (8x+16)+(7x-9) = (8x+7x)+(16-9) = 15x + 7

Hence, the total number of ice-creams sold is 15x + 7.

Answer:

The zoo's daily supply of leaves is 500 kg leaves at most.

Each giraffe eats 24 kg leaves per day.

Step-by-step explanation:

We have been given an inequality: [tex]47E+24G\leq 500[/tex], where E represents the number of elephants and G represents the number of Giraffes. Every day, each giraffe eats the same amount of leaves, and each elephant eats 47 kg of leaves.

We can see that each elephant eats 47 kg of leaves per day, which is represented by 47E in our given inequality. The amount of leaves eaten by a giraffe is 24 kg, which is represented by 24G in our given inequality, therefore, each giraffe eats 24 kg leaves per day.

We can see that total amount of leaves eaten by E elephants and G giraffes is less than or equal to 500, which means that zoo's daily supply of leaves is at most 500 kg.

Answer:

1. Daily supply of leaves is 500 kg;

2. Each giraffe eats 24 kg of leaves per day.

Step-by-step explanation:

Let E represent the number of elephants and G represent the number of giraffes that the zoo can feed with its daily supply of leaves.

If each elephant eats 47 kg of leaves, then E elephants eat 47E kg of leaves.

Consider inequality

[tex]47E+24G \leq 500.[/tex]

The first term of this inequaliy represents the number of kilograms all elephants in zoo eat per day. The second term 24G represents the number of kilograms all giraffes in zoo eat per day. The sum 47E+24G represents the number of kilograms all elephants and giraffes in zoo eat per day (together). This amount of leaves should be less or equal than 500 kg. This means that all elephants and giraffes cannot eat more than 500 kg of leaves per day.

Given:

Tracy invests $5,000 at 4.5% and the simple interest earned on the investment is moved into a separate account at the end of each year.

To Find:

The total simple interest accumulated in the checking account after 2 years.

Answer:

$450 is the total simple interest accumulated in the checking account after 2 years.

Step-by-step explanation:

The principal sum invested by Tracy is $5000.

The rate of simple interest is given to be 4.5% and the time period given is 2 years.

To calculate the total amount of interest accrued we use the formula

[tex]\frac{P.R.T}{100}[/tex]

where P is the pricipal amount of money, R is the rate of interest and T is the time period.

So, putting the given values into the formula, we have

[tex]\frac{(5000)(4.5)(2)}{100}\\\\=\frac{45000}{100}\\\\=450[/tex]

Thus, $450 is the total simple interest accumulated in the checking account after 2 years.

Answer:

That would be C.

Step-by-step explanation:

7C2 = 7! / (7-2)! * 2!

7C2  = 7*6*5*4*3*2*1 / 5*4*3*2*1 * 2*1

= 7*6 / 2

= 21

Answer: Phillip is correct. The triangles are not congruent.

How do we know this? Because triangle ABC has the 15 inch side between the two angles 50 and 60 degrees. The other triangle must have the same set up (just with different letters XYZ). This isn't the case. The 15 inch side for triangle XYZ is between the 50 and 70 degree angle.

This mismatch means we cannot use the "S" in the ASA or AAS simply because we don't have a proper corresponding pair of sides. If we knew AB, BC, XZ or YZ, then we might be able to use ASA or AAS.

At this point, there isn't enough information. So that means John and Mary are incorrect, leaving Phillip to be correct by default.

Note: Phillip may be wrong and the triangles could be congruent, but again, we don't have enough info. If there was an answer choice simply saying "there isn't enough info to say either if the triangles are congruent or not", then this would be the best answer. Unfortunately, it looks like this answer is missing. So what I bolded above is the next best thing.

Answer:

Phillip states that the triangles are not congruent.

Step-by-step explanation:

Assume for a second the triangles are congruent.

Then the angles are equal

<A =< X

<B= <Y

<C = <Z

Then

Triangle ABC = Triangle XYZ

from this information

AB = XY

and BC = YZ

and CA = ZX

but the only other piece of information we have is CA = 15 and XY = 15

If this is true then CA = ZX = 15  and AB = XY = 15

That would make this an isosceles triangle  (AB = AC)

so angles B  and C would have to be equal,  but they are not.  

So these two triangles cannot be congruent.

The sum of the first ten terms in the geometric series 4 – 12 + 36 – 108 + ... will be the negative 59048.

The series is given below.

4 – 12 + 36 – 108 + …

The complete series wall be

4 – 12 + 36 – 108 + 324 – 972 + 2916 – 8748 + 26244 – 78732

Then the sum of the first ten terms in the geometric series will be

⇒ 29524 – 88572

⇒ – 59048

More about the sum of the geometric series link is given below.

https://brainly.com/question/2771750

#SPJ1

Answer:

Option b is the correct choice.

Step-by-step explanation:

We are asked to find the which of our given expressions has 13y as a term.

Since we know that a term can be a signed number, a variable, or a constant multiplied by a variable or variables as 2a or 5b. In term 2a, 2 is coefficient and a is a variable.

We can see that in 13y, 13 is coefficient and y is variable.

Let us see our given choices one by one.

a. [tex]\frac{13y}{4}-2y[/tex]

Let can write our 1st term as:

[tex]\frac{13}{4}y-2y[/tex]

We can see that both of our terms have y variable, but our 1st term has a coefficient 13/4 and 2nd term has a coefficient of -2. As none of these terms have 13 as a coefficient, therefore, option a is not a correct choice.

b. [tex]8+13y-yz[/tex]

We can see that 8 is a constant, while 13y and -yz are terms. Since our expression has 13y as a term, therefore, option b is the correct choice.

c. [tex]4+13yz[/tex]

We can see that 4 is a constant and 13yz is a term as it has variables yz.  Since our given term has two variables, therefore, option c is not a correct choice as well.

d. [tex]13+y[/tex]

We can see that 13 is a constant and y is term of our given expression. Since our expression don't have 13 as coefficient, therefore, option d is not a correct choice.

b- 8+13y −yz. In the provided options, 13y is a standalone term in expression option b, which is 8+13y−yz. A term is part of an algebraic expression separated by plus or minus signs.

The student is asking to identify in which expression 13y is a term. The correct answer is option b, which is 8+13y−yz. In this expression, 13y is a separate term that is being added to 8 and subtracted by yz.

It's important to recognize that in algebraic expressions a term is a single mathematical expression that can be a number, a variable, or the product of numbers and variables separated by a plus (+) or minus (−) sign. In the case of 13y, it is a term because it is separated by addition or subtraction in the expression. Other options include division or other variables combined with 'y', which do not present '13y' as a standalone term.

Answer:

Each of them need to pay to buy a whole pie together = $1.50

Step-by-step explanation:

Unit rates defined as the rates are expressed as a quantity of 1, such as 7 feet per second or 9 miles per hour, they are called unit rates.

As per the statement: You sell pies at a farmers' market for $7.50 each.

⇒ Cost of each pie = $7.50

Also, five people want to share a pie by splitting the cost equally.

Number of people = 5

then, by definition of unit rate;

unit rate per people = [tex]\frac{Cost of whole pie}{Number of people} = \frac{7.50}{5} = \$1.50[/tex]

Therefore, $1.50 will each of them need to pay to buy a whole pie together.

Each person needs to pay $1.50.

Calculating Individual Payments for a Shared Pie

If five people want to share a pie by splitting the cost of $7.50 equally, we need to divide the total cost by the number of people to find out how much each person will pay. To do this, we take $7.50 and divide it by 5. This calculation gives us:

$7.50 / 5 = $1.50

Therefore, each of the five people will need to pay $1.50 to buy the whole pie together. This allows them to split the cost equally and purchase the pie at the farmers' market.

Solve the equation 3 cot x + √3 = 0 by isolating cot x, and recognizing that tan x = -√3. The equation has solutions x = 120° and x = 300° in the given domain.

To solve the equation 3 cot x + √3 = 0 for the domain 0 ≤ x ≤ 360°, we can follow these steps:

Thus, the solutions to the equation 3 cot x + √3 = 0 in the domain 0 ≤ x ≤ 360° are x = 120° and x = 300°.

Answer:

hey mate..

plzz add more to ur question soo that we can answer it...!

;)

The expression which represents the total number of pencils will be 7x where x is the number of pencils.

An expression is a combination of some mathematical symbol such that an arithmetic operator and variable such that all are constrained and create an equation.

In other meaning, expression is very useful to determine the end or root value of constraint.

As per the given,

Cindy has 2 boxes of pencils. Patrice has 5 boxes of pencils.

Suppose the number of pencils in each box is "x" as it is the same.

Total pencils in Cindy boxes = 2x

Total pencils in Patrice boxes = 5x

Total pencils = 2x + 5x = 7x

Hence "The expression which represents the total number of pencils will be 7x where x is the number of pencils".

To learn more about expression,

https://brainly.com/question/14083225

#SPJ5

The complete question is below,

Answer:

B.4.47

Step-by-step explanation:

The equation to calculate the distance between two points is

D=[tex]\sqrt{(x_{1}-y_{1}  )^{2}+(x_{2}-y_{2}  )^{2 }[/tex]

here

[tex](x_{1},y_{1})=(-1,5)\\(x_{2},y_{2})=(3,7)[/tex]

substituting the values

[tex]\sqrt{(-1-3)^{2}+(5-7)^{2}  }[/tex]

[tex]\sqrt{(-4)^{2}+(-2)^{2}  }[/tex]

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

[tex]\sqrt{20}=4.47[/tex]

Answer:

184.85 square mm

Step-by-step explanation:

The area of a sector of a circle is [tex]\frac{1}{2} r^{2} \theta[/tex], where r is the radius and [tex]\theta[/tex] is the angle in radians subtended by the arc at the centre of the circle.

Since, diameter = 40.6 mm

So, radius(r)=20.3 mm and  [tex]\theta[/tex]=[tex]\frac{2 \pi}{7}[/tex] radians

So, area of sector= [tex]\frac{1}{2} r^{2} \theta[/tex]

=[tex]\frac{1}{2} (20.3)^2 (\frac{2 \times 3.14}{7})[/tex]

=184.85 square mm

The area of the sector using given data is equal to 184.96 mm².

The area of a sector with a central angle of 2π7 radians and a diameter of 40.6 mm.

To solve this, we need to find the radius of the circle, which is half the diameter, and then use the formula for the area of a sector, which is ½ ×r² × θ, where θ is the angle in radians.

First, find the radius: r = ½ × diameter = 0.5 × 40.6 mm = 20.3 mm.

Then, substitute the values into the formula for the area of a sector:

Area = ½ × (20.3 mm)² × (2π7)

        = 1/2 × (20.3)² × (2 × 3.14 /7)

        = 1/2 × 412.09 × 0.89714

        = 184.96 mm²

Rounded to the nearest hundredth, the area of the sector is 184.96 mm².

Answer: D) 93

The red arc that spans from point X to point Z is 186 degrees, half of which is 186/2 = 93 and this is equal to the inscribed angle XYZ. I'm using the inscribed angle theorem which says that the arc measure is two times the inscribed angle that cuts off the arc.

Answer:

Faulty question in my opinion. See below.

Step-by-step explanation:

The central angle = the arc angle in degrees. So the central angle is 186 degrees.

The angle XYZ is 1/2 174 87 because it is 1/2 the measurement of the minor  arc which is 174. That answer is not there unfortunately. The central angle must be on the same side as the arc measurement. The arc angle is on the opposite side of XZ. I would ask your instructor about this one.

This is a pretty simple proof, actually.

A parallelogram's diagonal always bisects each other.

The given proves that both diagonals bisect each other at point N. So if they bisect each other, it is a parallelogram.

Answer:

8x(4+z) and 32x+8z, = Not equivalent

9(g+h) and 9g+9h = Equivalent

Step-by-step explanation:

Answer:

x≥4

Step-by-step explanation

24+4x≥40. Subtract 24 from both sides to get 4x≥16. Divide both sides by 4 to get x≥4.

Answer:

it requires more than or equal to 4 tanks

Step-by-step explanation:

An elephant needs to drink at least 40 gallons of water each day. A drinking tank contains 4 gallons of water. The elephant has already consumed 24 gallons of water. How many more tanks x of water does the elephant need to drink? Write your answer as an inequality.

An elephant drinks 40 gallons of water

a tank contains 4 gallon of water

lets convert the 40 gallons of water to tanks,t

40/4=10t

the elephant has consumed 24 gallons already

it means it has consumed 24/4=6t

x=more tanks need to drink

xt+6t≥10t..................1

xt≥10t-6t

x≥4

it requires more than or equal to 4 tanks