Which quadrilaterals always have diagonals that are perpendicular?​

Answer:

ABCD and EFGH

ABCD and PQRS (or EFGH and PQRS)

Dilate by a scale factor of 3

Step-by-step explanation:

Congruent means they have the same shape and size.

Similar means they have the same shape, but not necessarily the same size.

The orientation (rotation angle) or position do not matter.

EFGH is reflected and rotated, so it maintains the same shape and size as ABCD.  Therefore, they are congruent.

PQRS is scaled and translated, so it has the same shape, but different size than ABCD.  Therefore, they are similar but not congruent.

Also, PQRS is similar to EFGH, but not congruent.

To make EFGH congruent to PQRS, we need to make it the same size.  So we need to scale EFGH by a factor of 3.

25 scholars × 3 candies = 75 candies

5 candies for himself = 80

Answer: 80 candies

An inequality statement to represent the least number of candies that Mr.Rogers can buy is 80≥x.

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

Given that, Mr.Rogers distribute the candy equally among his 25 scholars.

Let the total number of candies be x.

Here, inequality is 25×3+5≥x

80≥x

Therefore, an inequality statement to represent the least number of candies that Mr.Rogers can buy is 80≥x.

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Answer:

Jamie: His inequality would look like this:  25x >= 600

Stella: Her inequality would look like this: 15y >= 600

Her limitations would be listed as: y=40

Yep. Stella has plenty of money by baking 40 pies; $600.

We can back that up by breaking this down. So. We know that it cost $600 to pay upfront and Jamie makes $25 per car he washes. Stella would make $15 for every pie she baked. So simply, let x represent the number of cars Jamie washes. Let y represent the number of pies Stella makes. Easy.

Since the cost for washing one car is $25

Now, in order to sign up for the trip, money obtained from car washing must be greater than or equal to $600. We know that. Now, lets see their profit margins.

Since the cost for making one pie is $15

Therefore, the cost of making y pies is 15y.

Now, in order to sign up for the trip, money obtained from pie making must be greater than or equal to $600 so with that being the case... 15y>=600

We all know the maximum number of pies that Stella can make is 40. So, the value of can't exceed 40 and must be less than or equal to 40. So.... y<=40

Bam.

In order to sign up for the trip, Stella's total earning must be at least $600. So, is the minimum condition for signing up for the trip. Now, let us solve the above equation for . So our end project looks like this: 15y = 600 y = 600/15 = 40

The minimum number of pies required for signing up for the trip is 40 and luckily that's the maximum supply Stella has for pies. Therefore, she can sign up for the trip by making all the 40 pies and earning a total of 600 dollars.

Step-by-step explanation:

Answer:

Step-by-step explanation:

The correct answer is x = 3

The value of x in the equilateral triangle is 3 units.

A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.

We know the perimeter of any planer figure except a circle is the sum of the lengths of all the sides and we also know that an equilateral triangle has equal sides and equal angles.

∴ We can equate any of the two sides of the given equilateral triangle.

So, 5x = 6x - 3.

5x - 6x = - 3.

- x = - 3.

x = 3.

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Answer: 45

Step-by-step explanation: To divide this start with finding how many times 585 goes into 13 which is 0. I put a picture for you to look at.

Answer:

Rs 2163.20.

Step-by-step explanation:

The formula for this is

A = P(1 + r)^t     where P is the amount invested, r = the rate (as a decimal) and t = the number of years.

So for rs 2000 we have:

A = 2000(1 + 0.04)^2 = Rs 2163.20

Answer:

70 people

Step-by-step explanation:

Final answer:

The total number of employees at the company is calculated using the given ratio of men to women, 2 to 3, along with the information that there are 42 women. By converting the ratio into actual numbers, we find that there are 28 men and 42 women, totaling 70 employees.

Explanation:

The question asks about the total number of employees in a company given the ratio of men to women and the number of women. To find the answer, we will use the ratio of men to women, which is 2 to 3, and the information that there are 42 women working for the company.

Answer:

1 ¹/₉ hours

Step-by-step explanation:

Let's say L is Larry's speed, C is Curly's speed, and M is Moe's speed.

1 = 2 (L + C)

1 = 1 ⅔ (C + M)

1 = 1 (L + C + M)

Solve the system of equations.  First, simplify the equations:

1 = 2L + 2C

3 = 5C + 5M

1 = L + C + M

Double the third equation and subtract the first equation from it:

2 = 2L + 2C + 2M

1 = 2L + 2C

1 = 2M

M = 1/2

Plugging into the second and third equations, we get:

C = 1/10

L = 2/5

Therefore, the time it takes Larry and Moe together is:

1 = t (L + M)

t = 1 / (L + M)

t = 1 / (2/5 + 1/2)

t = 1 / (4/10 + 5/10)

t = 1 / (9/10)

t = 10/9

t = 1 ¹/₉ hours

It takes them 1 ¹/₉ hours, or 1 hour 6 minutes 40 seconds.

Larry and Moe would take 5/3 hours, or 1 hour and 40 minutes, to build a bookcase together, based on the rates of building individually and in different pairs.

Larry and Curly together build a bookcase in 2 hours. This means that together they have a rate of 0.5 bookcases per hour, since 1 divided by 2 is 0.5. Similarly, Curly and Moe together can build one in 1 2/3 hours, which is the same as 5/3 hours. Therefore, their collective rate is 3/5 bookcases per hour. Larry, Curly, and Moe together can build a bookcase in 1 hour, which means their combined rate is 1 bookcase per hour.

Let's denote the rates of work for Larry, Curly, and Moe as L, C, and M respectively. When working together the sum of their rates equates to the rate at which they finish the job together. Hence:

L + C = 0.5 (Larry and Curly's rate)

C + M = 3/5 (Curly and Moe's rate)

L + C + M = 1 (Larry, Curly, and Moe's rate)

Using the first two equations, we can solve for L and M by substituting the values into the third equation:

L + 3/5 = 1

L = 1 - 3/5 = 2/5

C + 0.5 = 1

C = 1 - 0.5 = 0.5

Now we know that Larry's rate is 2/5 bookcase per hour, and Curly's rate is 0.5 bookcase per hour. We can use Curly's rate to find Moe's rate:

C + M = 3/5

0.5 + M = 3/5

M = 3/5 - 0.5 = 1/5

Larry and Moe's combined rate is L + M = 2/5 + 1/5 = 3/5 bookcases per hour.

To find the time it takes for Larry and Moe to build one bookcase together, we take the reciprocal of their combined rate:

Time = 1 / (L + M) = 1 / (3/5) = 5/3 hours, which is equal to 1 hour and 40 minutes.

Answer:

About 34

Step-by-step explanation:

There are 168 chocolate chips in 5 ounces. That means you want to know how many chips there are per ounce. Divide 168 by 5 and you get approximately 34 chocolate chips per ounce (33.6 if you need this)

Answer:

34

Step-by-step explanation:

All you have to do is divide

168 / 5 = 33.6

so about 34 chocolate chips in an ounce

[tex]f = 30000 - (2000 \times m)[/tex] is an equation to represent the height of the airplane in feet above the ground f(x) in relationship to time in minutes x

Step-by-step explanation:

As given that the plane is at 30000 feet above the grounds. And starts descending at the rate of 2000 feet/ min  

So, let us consider the below,

H= height in feet above ground

r = rate of descent

m = minutes

So, now frame the required equation format with the given data as follows,

                           [tex]H = 30000 - (2000 \times m)[/tex]

Answer: 6 columns.

Step-by-step explanation:

24 ÷ 4 = 6

Answer:

6

Step-by-step explanation:

24 divided by 4 = 6

Answer:

3/4 cup milk

Step-by-step explanation:

I order to be able to compare quantities that come in fraction form, the best is to write all of them as equivalent fractions with the same denominator. That way just looking at the magnitude of the numerators will allow us to give the answer.

the fractions to consider are: [tex]\frac{3}{4} \,,\, \frac{2}{6} \,, \, and\, \frac{8}{12}[/tex]

so the denominators in question are: 4, 6, and 12.

We see that 12 is the Least Common Denominator (LCD) of these three, since 4 divides perfectly 12, 6 divides 12 perfectly, and 12 divides itself perfectly as well.

Now, the initial fractions can be re-written with equivalent fractions showing denominator 12.We do such by multiplying numerator and denominator of the first fraction by "3" in order to get a "12" in the denominator. By multiplying the second fraction by 2 in numerator and denominator to get a "12" in the denominator. Notice that we don't need to modify the third fraction since it is already expressed with denominator 12:

[tex]\frac{3}{4} \,,\, \frac{2}{6} \,, \, and\, \frac{8}{12}=\\=\,\frac{9}{12} \,,\, \frac{4}{12} \,, \, and\, \frac{8}{12}[/tex]

Therefore, the greatest of these is the first fraction, that shows a "9" in the numerator (the largest of the three numerators)

The equivalent expression using associative property is [tex]5 \times(3 \times 12)[/tex]

Given expression is [(5.3). 12]

We are asked to write a equivalent expression using associative property

The associative property states that you can add or multiply regardless of how the numbers are grouped. By 'grouped' we mean 'how you use parenthesis'. In other words, if you are adding or multiplying it does not matter where you put the parenthesis

Associative property is as follow:-

a + (b + c) = (a + b) + c   { for Addition}

(a x b) x c = a x (b x c)  { for multiplication}

The given expression is [(5.3). 12], which can be written as

[tex](5 \times 3) \times 12=5 \times(3 \times 12)[/tex]

Answer:

8.76/24.3= 0.36

16.95/32.6= 0.519 round up to make 0.52

Step-by-step explanation:

8.76/24.3= 0.36

16.95/32.6= 0.519

Answer:

∠5 = 27°

Step-by-step explanation:

CDB = ABD (alternate angle)

∠2 = ∠5

∠5 = 27°

(Correct me if i am wrong)

Answer:

∠5 = 27°

Step-by-step explanation:

CDB = ABD (alternate angle)

∠2 = ∠5

∠5 = 27°

Answer:

3:59 PM

Step-by-step explanation:

When the plane arrives in Fargo, the time is 13:59 or 1:59 PM in pacific time. From the pacific to central, you add 2 hours. 1:59 + 2 hours is 3:59 PM.

The price of car is $18000

Step-by-step explanation:

Given

Sales tax on car = $1080

Rate = 6%

Let x be the price of the car

We know that as the rate of sale tax is 6%, 6% of x is 1080

Using mathematical notation

0.06x = 1080

Dividing both sides by 0.06

[tex]\frac{0.06x}{0.06} = \frac{1080}{0.06}\\\\x = 18000[/tex]

Hence,

The price of car is $18000

Keywords: Rate of tax, Percentage

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Answer: 19

Step-by-step explanation:

j+2j-3 = 30

3j = 33

j = 11

and

b = 2j-3

b = 2(11)-3

b = 19

Answer:19

Step-by-step explanation:

it's 94.20967742 if you simplify it you will get 94.21

5,841 divided by 62 equals 94 with a remainder of 13. You can find this using long division, where 62 goes into 584 (from 5,841) nine times and then into 261 (the remainder with the next digit) four times.

To find the result of 5,841 divided by 62, we can use long division. Let's break down the problem step by step:

To express this as a decimal, we could continue the division process by adding a decimal point and zeros to the dividend, but that is not requested in this problem.

Final answer:

To double the area of the rectangular garden, the dimensions should increase by 5 meters.

Explanation:

To double the area of the rectangular garden, we need to find the increase in dimensions that will result in double the original area. The original dimensions are 5m by 7m, so the original area is 5m x 7m = 35 square meters. To double this area, the new area should be 35 square meters x 2 = 70 square meters. Let's assume the increase in dimensions is 'x'. The new dimensions will be (5m + x) by (7m + x). We can set up the equation:

(5m + x)(7m + x) = 70 square meters

Expanding and simplifying the equation, we get:

35m + 5x + 7x + x^2 = 70 square meters

Combining like terms, we have:

x^2 + 12x + 35 = 70 square meters

Next, we rearrange the equation into standard form:

x^2 + 12x + 35 - 70 = 0

Simplifying further, we get:

x^2 + 12x - 35 = 0

Now we can solve this quadratic equation by factoring or using the quadratic formula. Factoring the equation gives us:

(x + 7)(x - 5) = 0

Setting each factor equal to zero, we have:

x + 7 = 0 or x - 5 = 0

Solving for 'x', we get:

x = -7 or x = 5

Since a negative value doesn't make sense in this context, we can conclude that the dimensions should increase by 5 meters.

Answer:

$717336

Step-by-step explanation:

The total of monthly payments for a 3-year loan is $22317.12.

So, the total amount has to pay back in 3 years is $(22317.12 × 12 × 3) = $803416.32.

Let the amount of money that was originally borrowed is $x and the given APR is 4%.

Then we can write, [tex]x(1 + \frac{4 \times 3}{100}) = 803416.32[/tex]

⇒ 1.12x = 803416.32

⇒ x = $717336 (answer)

25x+35y=405 and y= x+3 can be used to determine the number of bottles of soda and number of bottles of juice purchased where, x represents the number of soda bottles and y represents the number of juice bottles.

Step-by-step explanation:

Given,

Sugar contained by each soda bottle = 25 grams

Sugar contained by each juice bottle = 35 grams

Let,

x be the number of soda bottles.

y be the number of juice bottles.

According to given statement;

25x+35y=405   Eqn 1

y= x+3   Eqn 2

25x+35y=405 and y= x+3 can be used to determine the number of bottles of soda and number of bottles of juice purchased where, x represents the number of soda bottles and y represents the number of juice bottles.

Keywords: Linear equation, substitution method

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Answer:

3 friends

Step-by-step explanation:

The mean age is 27 so 3 friends are above that age.

The average age of the friends is 27. Only two of the friends, both aged 31, are older than the average age.

To find out how many of the friends are older than the average age, we need to first find the arithmetic mean of the ages. We do this by adding up all the ages and dividing by the number of ages. So, (20+31+28+31+25)/5 = 27. Once we have the average, we can see that the ages of 31 and 31 are larger than the average of 27. Therefore, there are 2 friends whose ages are older than the average.

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Answer:

C) 6 inches

Step-by-step explanation:

Given function:

[tex]Y=1.3x-0.8[/tex]

The function compares plant height in inches to the age of plant in weeks.

So, we can say

[tex]Y[/tex] represents height of plant in inches.

[tex]x[/tex] represents age of the plant in weeks.

In order to predict the height of the plant in 5 weeks, we will plugin [tex]x=5[/tex] in the given function and evaluate [tex]Y[/tex]

⇒ [tex]Y=1.3(5)-0.8[/tex]

⇒ [tex]Y=6.5-0.8[/tex]

⇒ [tex]Y=5.7[/tex] inches

Thus the approximate height of plant in 5 weeks would be [tex]\approx 6[/tex] inches

Answer:

C: 6

Step-by-step explanation:

Answer:

36 hours - 6,300

24 hours - 4,200

In 36 hours, 6300 quarts of ice cream could be made. The rate per day would be 6300 quarts per day.

350 quarts of ice cream are made in 2 hours. To find out how many quarts could be made in 36 hours, we can set up a proportion: 350 quarts / 2 hours = x quarts / 36 hours. Solving for x gives us 6300 quarts in 36 hours. To find the rate per day, we divide the total quarts made in 36 hours by the number of days: 6300 quarts / 1 day = 6300 quarts per day.

How to distribute  2.5(-y + 2)

= (2.5 * -y) + (2.5 * 2)

= -2.5y + 5

Distributive Property is when you multiply different addends from a sum then add them.

______

Best Regards,

Wolfyy :)

Answer:30

Step-by-step explanation:

it’s division. there’s some left over but they wouldn’t make a complete page.

493/16=30.8....

Answer: -8 - (3 x N) = 19

n = number

Step-by-step explanation: i think thats how u write it

Answer:

[tex](-8)-3n=19[/tex]

Step-by-step explanation:

In the equation, the difference of -8 and the product of 3 and n (refering to "the number" in the question) equals 19.

Hope this helps

Answer: ABC is isosceles

Step-by-step explanation:

The coordinate of points given are:

A(1,-4)

B(-1, -2 )

C ( -2 , -5 )

For ABC to be isosceles , then AB must be equal to BC or AB = AC

The next thing to do  is to find the value of AB , BC and AC using the formula for finding distance between two points which is given by:

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

Calculating AB first , we have

[tex]\sqrt{(-1-1)^{2}+(-2+4)^{2}  }[/tex]

= [tex]\sqrt{4+4}[/tex]

=[tex]\sqrt{8}[/tex]

Therefore:

AB = [tex]\sqrt{8}[/tex]

Calculating BC , we have :

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

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

D = [tex]\sqrt{10}[/tex]

Therefore:

BC = [tex]\sqrt{10}[/tex]

Calculating AC , we have :

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

D = [tex]\sqrt{(-2-1)^{2}+(-5+4)^{2}  }[/tex]

D = [tex]\sqrt{10}[/tex]

Therefore:

AC = [tex]\sqrt{10}[/tex]

Since AC = BC then triangle ABC is isosceles

Practice Analytic Geometry

1. Find the midpoint of the line segment defined by the points: (sqrt 2, 0) and (0, -sqrt 2)

Answer is ((sqrt 2)/2, (-sqrt2)/2)

2. Find the distance of the line segment joining the two points: (5,4) and (-2,1)

Answer is sqrt 58

3. Find the distance of the line segment joining the two points: (1/2, -5/2) and (-4/3, -1/6)

Answer is (sqrt 317)/6

4. Given triangle ABC with vertices at A (1,-4), B (-1, -2), and C (-2,-5), prove or disprove that triangle ABC is an isosceles

Answer triangle ABC is isosceles since AB = sqrt 8, BC = sqrt 10, and AC = sqrt 10

Answer:

x-intercept = (1, 0)

y-intercept = (0, −3)

Step-by-step explanation:

These is the only answer that make the most sense:

x-intercept: [tex]\displaystyle 0 = y[/tex]

y-intercept: [tex]\displaystyle 0 = x[/tex]

I am joyous to assist you anytime.

The intercepts of the graph function are:

The x-intercept is (-1, 0).

The y-intercept is (0, 3).

A function has an input and an output.

A function can be one-to-one or onto one.

It simply indicated the relationships between the input and the output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

From the graph,

The x-intercept is the point when y = 0.

The y-intercept is the point when x = 0.

So,

The x-intercept is (-1, 0).

The y-intercept is (0, 3).

Thus,

The intercepts of the graph function is:

The x-intercept is (-1, 0).

The y-intercept is (0, 3).

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