if in a quadrilateral you have a pair of sides congruent and parallel does that make the shape a parallelogram

Complete question is;

Jane is training for a triathlon. After swimming a few laps, she leaves the health club and bikes 16 miles south. She then runs 12 miles west. Her trainer bikes from the health club to meet jane at the end of her run. Use the pythagorean theorem to write an equation for the distance janes trainer bikes

Answer:

x = √(12² + 16²)

Step-by-step explanation:

We are told that;

She bikes from health club to South = 16 miles

From South to West = 12 miles

Her trainer bikes from the health club to meet her at the end which is west.

I have attached a diagram showing this movement in form of a triangle.

From the diagram I attached, I have depicted the distance the trainer bikes as x.

Using pythagoras theorem;

x² = 12² + 16²

x = √(12² + 16²)

The perimeter and area of a rectangle are (5,6) and (6,5).

The perimeter method for a rectangle states that P = (L + W) × 2, where P represents perimeter, L represents length, and W represents width. when you are given the size of a square form, you may simply plug within the values of L and W into the formula that allows you to clear up for the fringe.

A perimeter is a closed course that encompasses, surrounds, or outlines either a two-dimensional shape or a one-dimensional period. The perimeter of a circle or an ellipse is known as its circumference. Calculating the perimeter has several practical programs.

The perimeter P of a rectangle is given by means of the method, P=2l+2w, in which l is the period and w is the width of the rectangle. The place A of a rectangle is given with the aid of the components, A=lw, wherein l is the length and w is the width.

The perimeter of the rectangle:

P=2l+2w=22

divide 2 into both sides

l+w=11 -------------> (1)

w=11-l

Area of the rectangle:

l*w=30

l(11-l)=30

11l-l^2-30=0

l^2-11l+30=0

By factor method,

(l-5)(l-6)=0

l=5,6.

Substitute this value in w,

l=5 implies w=6

l=6 implies w=5

There we have two solutions.

The length and breadth of the rectangle is

(5,6) and (6,5).

Learn more about perimeter here https://brainly.com/question/397857

#SPJ9

The monthly income of the first person is $600.

Given that, the average monthly income of three persons is RS 3,600.

The income of the first is 1/5 of the combined income of the other two.

Here, Let income of the first be A, let income of the second be B and let Income of the third be C.

A+B+C=3600 -----(i)

Income for the first person = 1/5(B+C) -----(ii)

Substitute equation (ii) in equation (i), we get

(B+C)/5 +B+C =3600

B+C+5B+5C=3600×5

6B+6C=18000

6(B+C)=18000

B+C=3000 ------(iii)

Substitute (iii) in equation (i), we get

A=$600

Therefore, the monthly income of the first person is $600.

To learn more about an equation visit:

https://brainly.com/question/14686792.

#SPJ1

\( \huge \: \tt \green{Answer} \)

Olivia and kieran share ratio 2 : 5

\( \texttt{olivia's share \: of \: money = £42 }= \frac{2}{7} \\ \)

Total Amount of Money = Olivia's share of money × Reciprocal of olivia's share

\( \tt \: = > 42 \times \frac{7}{2} \\ \\ = > 147\)

Kieran's share of Money =

\( = > 147 \times \frac{5}{7} \\ \\ = > \sf{ \pink{£105}}\)

It should be noted that Ruby will be able to reach the fish

It should be noted that sea level simply means the sea base level that is used for measuring the elevation and the depth on the Earth.

It should be noted that Ruby looks over the edge of her boat and sees fish 0.4 meter below the surface of the water and Ruby holds a 1-meter long net at 0.5 meter above sea level.

It should be noted that he will be able to each the fish. This will be illustrated as:

=1m - (0.4 + 0.5)

= 1 - 0.9

= 0.1m

Therefore, the long net is enough to reach the fish.

Learn more about sea level on:

brainly.com/question/22136251

#SPJ1

Ruby looks over the edge of her boat and sees fish 0.4 meter below the surface of the water. If Ruby holds a 1-meter long net at 0.5 meter above sea level. Can she reach the fish?

Answer:

width = 3/10 mi

Step-by-step explanation:

area = length * width

width = area/length

width = (3/4 mi^2)/(2 1/2 mi)

width = (3/4 mi^2)/(5/2 mi)

width = 3/4 * 2/5 mi

width = 6/20 mi

width = 3/10 mi

P(8/3) is not equal to zero, we can conclude that 8/3 is not a zero of P(x). Therefore, our suspicion was incorrect.

What is quadratic equation and how to solve it ?

A quadratic equation is a second-degree polynomial equation of the form ax^2 + bx + c = 0, where a, b, and c are constants and x is the variable.

To solve a quadratic equation, there are different methods, such as factoring, completing the square, and using the quadratic formula. The quadratic formula is the most general method and can be used for any quadratic equation.

It states that the solutions to the equation ax^2 + bx + c = 0 are given by the formula

x = (-b ± sqrt(b^2 - 4ac)) / (2a).

We can use this formula to find the roots of the equation by substituting the values of a, b, and c into the formula and simplifying.

To confirm if 8/3 is a zero of the quadratic function P(x) = 3x^2 - 4x - 7, we can substitute 8/3 for x in the equation and check if the resulting expression is equal to zero. If P(8/3) equals zero, then we can confirm that 8/3 is indeed a zero of P(x).

P(8/3) = 3(8/3)^2 - 4(8/3) - 7

= 3(64/9) - 32/3 - 7

= 64/3 - 32/3 - 21/3

= 11/3

Since P(8/3) is not equal to zero, we can conclude that 8/3 is not a zero of P(x). Therefore, our suspicion was incorrect. If we want to find the zeros of P(x), we can use the quadratic formula or factor the equation into (3x + 1)(x - 7) = 0 to get the roots x = -1/3 and x = 7.

To know more about Quadratic equation visit:-

https://brainly.com/question/1214333

#SPJ1

From Mark studies of a parallelogram and discovering that the slope of the diagonals are 5/3 and -3/5 the conjecture that can be made is

The diagonals are perpendicular to each other

The two different lines that cross each other at a 90° angle are called perpendicular lines.

If two lines intersect at a 90 degree angle, we say that the two lines are perpendicular.

Perpendicular lines have a feature which relates with the slope of the line as being a negative reciprocal

In the context of the given problem,

diagonal 1 has slope 5/3, the negative reciprocal is -3/5.

Since the two diagonals posses this relationship they are said to be parallel

Learn more on slope of a perpendicular line  at:

https://brainly.com/question/28804591

#SPJ1

Yes. Both are equal to 0.5 in decimal form.

Answer:

yes

Step-by-step explanation:

2/4=1/2

0.5=0.5

so 2/4=1/2 in decimal form

(a) The  percentage of married couple households that are one native, one foreign is 7.3%

(b) The number of married couple households that are one native, one foreign is 4,051,500

(a) Percentage =100%-(79.5%+13.2%)

Percentage =100%-92.7%

Percentage =7.3%

(b)Number of married couple households =7.3%*55,500,000

(b)Number of married couple households =4,051,500

Inconclusion:

(a) The  percentage of married couple households that are one native, one foreign is 7.3%

(b) The number of married couple households that are one native, one foreign is 4,051,500

Learn more here:

https://brainly.com/question/23598164

Answer:

x = 15

Step-by-step explanation:

4(x - 20) = - 20 ( divide both sides by 4 )

x - 20 = - 5 ( add 20 to both sides )

x = 15

Answer:

150 people entered the comic store.

Step-by-step explanation:

First, divide 45 by 3 to turn the %30 into %10, a better number to get to a %100 easier. You get 15. Then multiply 15 by 10 to get to %100, which is 150.

Answer:

I hope this helps.

Step-by-step explanation:

====================================================

Work Shown:

6^(x-2) = 36^(x+3)

6^(x-2) = ( 6^2 )^(x+3) ... replace 36 with 6^2

6^(x-2) = 6^(2(x+3)) .... use the rule (a^b)^c = a^(b*c)

6^(x-2) = 6^(2x+6) .... distribute

x-2 = 2x+6 .... bases are both 6, so the exponents must be equal

2x+6 = x-2

2x-x = -2-6

x = -8 This is the only solution

Alternatively, you can use logarithms to solve for x. Though in my opinion that is a messier route to take.

------------------------

Checking the answer:

Plug x = -8 into the original equation. Simplify both sides. We should get the same value on both sides. If not, then we made an error in solving for x

6^(x-2) = 36^(x+3)

6^(-8-2) = 36^(-8+3)

6^(-10) = 36^(-5)

0.00000001653818 = 0.00000001653818

We get the same value on both sides. This confirms we have the right answer.

The true inequality from the list of options is (c) -x - 6 > -3.5

To determine which inequality is true when x is -5, we need to substitute -5 for x in each inequality and simplify.

a) -x – 6 < -3.5

Substituting x = -5, we get:

-(-5) - 6 < -3.5

5 - 6 < -3.5

-1 < -3.5

This is false, so option a) is not true.

b) -x – 6 > 3.5

Substituting x = -5, we get:

-(-5) - 6 > 3.5

5 - 6 > 3.5

-1 > 3.5

This is false, so option b) is not true.

c) -x - 6 > -3.5

Substituting x = -5, we get:

-(-5) - 6 > -3.5

5 - 6 > -3.5

-1 > -3.5

This is true, so option c) is true.

Hence, the correct option is (c) -x - 6 > -3.5

Read more about inequality at

https://brainly.com/question/25275758

#SPJ1

Complete question

Which inequality is true when the value of x is -5?

a) -x – 6 < -3.5

b) -x – 6 > 3.5

c) -x - 6 > -3.5

d) x - 6 > -3.5

If we want the two ratios to be equivalent, then we need to use x = 15 and y = 33.

Let's say that we have a simple ratio between two amounts, it is A:B

If we multiply both of these amounts by the same scalar, k, we will get:

k*A and k*B

And the ratio between the new amounts k*A: k*B is equivalent to the first ratio, A:B

So we will use this to solve the problem, here we have two ratios:

5:2:11 = x:6:y

Note that in the first ratio the first value is 2, and in the second case it is 6 so let's find the value of k such that:

2*k = 6

k = 6/2 = 3

Then if we multiply the correspondent values in the first ratio by 3, we will get:

x = 5*3 = 15

y = 11*3 = 33

Then we can see that the ratios:

5:2:11 and 15:6:33 are equivalent.

Learn more about equivalent ratios:

https://brainly.com/question/2328454

#SPJ1

The linear equation we need to solve is:

$27.50*w = $309.99 - $144.99

And the solution is w = 6.

How to write and solve the equation?

We know that the cost of the gaming chair is $309.99.

To buy this, you already have saved $144.99, and save another $27.50 per week, then the amount you have after w weeks is:

f(w) = $144.99 + $27.50*w

So the linear equation we need to solve is:

$144.99 + $27.50*w = $309.99

To solve this we need to isolate w.

$144.99 + $27.50*w = $309.99

$27.50*w = $309.99 - $144.99

w = ($309.99 - $144.99)/$27.50 = 6

So they can buy the chair after 6 weeks.

Learn more about linear equations at:

brainly.com/question/13763238

#SPJ1

Answer:

its actually 16

Step-by-step explanation:

just guess my dood :)

if we notice the tickmarks on the triangle, we can see the all sides are equal, namely is an equilateral triangle, and if all sides are equal, then all interior angles are equal as well.

Let's recall that the sum of all interior angles in a triangle is 180°, now if we divide that by 3, that gives us 60, namely each angle in the equilateral triangle is 60°, that means

\(10x=60\implies x=\cfrac{60}{10}\implies \boxed{x=6} ~\hfill 12y=60\implies y=\cfrac{60}{12}\implies \boxed{y=5}\)

Answer:

Yes, these triangles are congruent by Angle-Side-Angle.

A. The margin of error for a 99% confidence interval is $$2,320.75.

B. The confidence interval for the mean starting salary of college graduates who have taken a statistics course is CI = $42,462.25 to $47,103.75

PART A.

The margin of error (ME) is determined using the formula:

ME= z ∗ σ/√n

where:

z is the z-score for the desired confidence level

σ is the population standard deviation

n is the sample size

For a 99% confidence level, the z-score is 2.576. The population standard deviation is $10,272, and the sample size is 130.

Substituting these values into the formula, we have:

ME =  2.576 ∗ 10272/√130

ME = $2,320.75

PART B

The confidence interval (CI) is determined using the formula:

CI = \(\bar{x}\) ± ME

where:

\(\bar{x}\) is the sample mean

ME is the margin of error

The sample mean is $44,783, and the margin of error is $2,320.75.

Substituting the values into the formula, we get:

CI= 44783 ± 2320.75

CI = $42,462.25 to $47,103.75

Learn more about margin of error on:

https://brainly.com/question/31876031

#SPJ1

Answer:

16 deliveries

Step-by-step explanation:

238 ≤ 10d + 78

160 ≤ 10d

16 ≤ d

Thus, he needs to make at least 16 deliveries to make at least $238 in one day.  Any less than 16 deliveries will cause him to fall short of his goal and any more than 16 deliveries will cause him to exceed his goal.

Answer:

11.5

Explanation and Check part below

Hope this helps :)

Step-by-step explanation:

x stands for an unknown value, so we will put the x next to the 6 to solve the equation.

6x = 69

--- ---- <------ fraction bar/divide

6 6

x = 11.5

Check:

6 (11.5) = 69

69 = 69

True statement.

The value of x in the angles is 19.

When lines intersect, angle relationships are formed such as vertically opposite angles, adjacent angles etc.

Therefore, let's find the value of x in the intersecting lines.

Hence,

7x - 8 = 6x + 11 (vertically opposite angles)

Vertically opposite angles are congruent and they share the same vertex point.

Hence,

7x - 8 = 6x + 11

subtract 6x from both sides of the equation

7x - 8 = 6x + 11

7x - 6x - 8 = 6x - 6x + 11

x - 8 = 11

add 8 to both sides of the equation

x - 8 + 8 = 11 + 8

x = 19

learn more on angles here: https://brainly.com/question/17395336

#SPJ1

The probability of drawing a king from a standard deck of 52 cards is 1/13.

In a standard deck of 52 playing cards, there are four kings: the king of hearts, the king of diamonds, the king of clubs, and the king of spades.

To find the probability of drawing a king, we need to determine the ratio of favorable outcomes (drawing a king) to the total number of possible outcomes (drawing any card from the deck).

The total number of possible outcomes is 52 because there are 52 cards in the deck.

The favorable outcomes, in this case, are the four kings.

Therefore, the probability of drawing a king is given by:

Probability = (Number of favorable outcomes) / (Number of possible outcomes)

= 4 / 52

= 1 / 13

Thus, the probability of drawing a king from a standard deck of 52 cards is 1/13.

This means that out of every 13 cards drawn, on average, one of them will be a king.

It is important to note that the probability of drawing a king remains the same regardless of any previous cards that have been drawn or any other factors.

Each draw is independent, and the probability of drawing a king is constant.

For similar question on probability.

https://brainly.com/question/7965468  

#SPJ8

Answer:

380 seconds

Step-by-step explanation:

Convert 6 minutes to seconds by multiplying 6 times 60, because there are 60 seconds per minute.
6 x 60 = 360

Now add the 20 seconds.
360 + 20 = 380

6 minutes and 20 seconds are equal to 380 seconds.

Answer:

Hello There Again. The correct answer is D.

Explanation: Because it shows that you need to subtract 2.75 - 3.50 which that will be 75. So the correct answer will be D.

Hope It Helps! :)

Sixth graders paid a total of $508.50 for all their meals on Monday.

Answer:

The digit 2 is worth 2 tens (i.e 20)

Step-by-step explanation:

It's in the tens place, thus 2 tens, meaning 20

Answer:

20

Step-by-step explanation:

Answer:b

Step-by-step explanation:

To analyze this data, you would use An ANOVA F test.

An example of a continuous probability distribution is the normal distribution, in which the majority of data points cluster in the middle of the range, while the remaining ones taper off symmetrically toward either extreme. The distribution's mean is another name for the center

The study involves comparing the weight loss of four groups of participants (weight-loss pill alone, weight-loss pill with a low-fat diet, placebo pill alone, or placebo pill with a low-fat diet) after six months of treatment. ANOVA (Analysis of Variance) is a statistical method used to analyze the differences among means of two or more groups.

In this case, ANOVA can be used to determine if there are significant differences in weight loss among the four treatment conditions.

A t-test or z-test would be appropriate if there were only two groups being compared.

A chi-square test is used to analyze categorical data, which is not applicable in this scenario where the data is continuous.

Therefore, an ANOVA F test would be used.

Learn more about normal distribution here:

https://brainly.com/question/29509087

#SPJ2