In a quadrilateral ABCD , AB = BC and CD = DA . Then , the quadrilateral is a :

a) Parallelogram

b) Rhombus

c) Kite

d) Trapezium​

Answer:

AC = 70

BG = 38

GC = 28

AE = 63

Step-by-step explanation:

The given parameters are;

The centroid of ΔABC = G

The length of FC = 35

The length of AG = 42

The length of BF = 57

The length of DG = 14

Given that the centroid is the intersection of the medians, we have;

FA = FC = 35 Definition of median line FB, (point F is the midpoint of AC)

AC = FA + FC = 35 + 35 = 70 by segment addition postulate

AC = 70

BG = 2/3 × BF = 2/3 × 57 = 38 Definition of median line BF

BG = 38

DG = 14 = 1/3 × DC Definition of median line

∴ DC = 3 × DG = 3 × 14 = 42

GC = 2/3 × DC = 2/3 × 42 = 28 Definition of median line DC

GC = 28

AG = 42 = 2/3 × AE Definition of median line AE

∴ AE = 3/2 × 42 = 63

AE = 63.

Answer:

D.The distance you drive

Step-by-step explanation:

If you describe this situation as function, then it will look as:

The range of the function is the set of output values

In this case the range is the distance you drive

Correct option is D.

Answer:

The distance you drive

Step-by-step explanation:

i just took the test

Answer:

If I read the question right, then the answer is -36.5.

Step-by-step explanation:

Like I said, only if I read the question right. I read it as

(-35) - 1.5.

If I'm wrong, then I'm sorry.

The product of (−35)∙(−1). (5) will be 105. It is obtained by multiplying the term one by one.

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.

We can utilize multiplication for a number of common tasks, such as figuring out how much it will cost to buy several identical things, calculating sales tax, and figuring out area and other geometric measurements.

It is given that,

=(−35)∙(−1).5

Multiply the term step by step as

=(−35)∙(−1).5

The multiplication of two negative terms gives a positive value.

=(35)5

=105

Thus, the product of (−35)∙(−1). (5) will be 105. It is obtained by multiplying the term one by one.

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Answer:

yes the both have all the same angles

Step-by-step explanation:

180-90=90

90-35=55

Answer:

Equation of line is given as y = mx + c, where m is the gradient and c is the y-intercept.

First, rearrange x + 7y = 21 into y = mx + c form.

x + 7y = 21

7y = - x + 21

y = -1/7x + 3

Parallel lines have the same gradient so gradient of line is -1/7.

Equation of line is now y = -1/7x + c.

Substitute (-14,4) into the equation to find c.

4 = -1/7(-14) + c

4 = 2 + c

c = 2

Hence, equation of line is y = -1/7x + 2.

The given double integral is ∫ ∫ (x² + y²)dx dy, and we need to evaluate it over the region in the positive quadrant where x+y≤1.

To evaluate this double integral, we can first determine the limits of integration for both x and y based on the given region. In the positive quadrant, x and y both range from 0 to 1.

Now, integrating the inner integral with respect to x, we get:

∫ (x² + y²)dx = (1/3)x³ + y²x + C1,

where C1 is the constant of integration.

Next, we integrate the resulting expression with respect to y:

∫ [(1/3)x³ + y²x + C1] dy = (1/3)x³y + (1/3)y³x + C1y + C2,

where C2 is another constant of integration.

Finally, we evaluate this double integral over the given region by substituting the limits of integration:

∫∫ (x² + y²)dx dy = ∫[0 to 1] ∫[0 to 1-x] (x² + y²)dy dx.

Performing the integration, we can find the numerical value of the double integral within the given region.

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Answer:

x=16

Step-by-step explanation:

Starting equation:

2x-10+2x-5=3x+1

First combine all like terms on the left side

4x-15=3x+1

Now subtract 3x from both sides so that x is only on the left

x-15=1

Finally add 15 to both sides to isolate your variable

x=16

Answer:

Step-by-step explanation:

2x-10+2x-5=3x+1

Find X

2x - 10 + 2x - 5 = 3x + 1  combine similar terms

2x + 2x - 3x = 10 + 5 + 1  simplify

x = 16  

Answer:

C

Step-by-step explanation:

in order of containment it goes

Quadrilaterals

Parallelograms and trapezoids

kites rhombuses and rectangles

squares

Answer:

Hey there!

All parallelograms are four sided shapes, also called quadrilaterals.

Hope this helps :)

Answer: 9x²-6x+5

Step-by-step explanation:

To find (gοf)(x), you want to plug f(x) into g(x). It is the same as g(f(x)).

g(f(x))=(3x-1)²+4                  [distribute by FOIL]

g(f(x))=9x²-6x+1+4              [combine like terms]

g(f(x))=9x²-6x+5  

Now, we know that (gοf)(x)=9x²-6x+5.

Answer: 11a2b+ab+ab2

Step-by-step explanation:

Answer:

hey! you can use it!!

Step-by-step explanation:

thanks

can see picture but i tried sorry

Answer:

? =8.77

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

sin theta = opposite side/ hypotenuse

sin 20 = 3 / ?

? = 3/ sin 20

? = 8.7714132

To the nearest hundredth

? =8.77

The radius of the beryllium atom is two times larger than the radius of the nitrogen atom. In other words, the beryllium atom is twice as large as the nitrogen atom.

To determine which atom has the larger radius and the difference in size between them, we compare the given radii of a nitrogen atom and a beryllium atom.

The radius of a nitrogen atom is5.6 * 10^(-11) meters.

The radius of a beryllium atom is 1.12 *10^(-10) meters.

Comparing the two radii, we find that the radius of the beryllium atom is larger than that of the nitrogen atom.

To calculate the difference in size between the two atoms, we can divide the radius of the beryllium atom by the radius of the nitrogen atom:

(1.12 * 10^(-10)) / (5.6 * 10^(-11)) = 2

Therefore, the radius of the beryllium atom is two times larger than the radius of the nitrogen atom. In other words, the beryllium atom is twice as large as the nitrogen atom.

This difference in size can be attributed to the number of protons, neutrons, and electrons in each atom. Beryllium has a larger atomic number and more protons and neutrons in its nucleus, which leads to a larger overall size compared to nitrogen.

It's important to note that atomic radii can vary depending on the measurement technique and the specific context, but based on the given values, we can conclude that the beryllium atom has a larger radius and is twice as large as the nitrogen atom.

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Answer:

Step-by-step explanation:

If the regular price of a T-shirt is 10 USD and the store sells off its wares at 80% of its regular price, then the price at which the store would still the aforementioned T-shirt would be 80% of its 10 USD price.

80% of $10 =

0.8 * 10 = $8

This means that the price at which the T-shirt will go for, due to the ongoing sales will be $8.

Also, being asked to find the 10% and 20% of $10 is just as simple

10% of $10 =

0.1 * 10 = $1

20% of $10 =

0.2 * 10 = $2

Therefore, the 10% and 20% of $10 is $1 and $2 respectively.

The amount of money to be deducted from the vehicle's SunPass account is $2.65

To obtain the total toll fee charged; we take the product of the toll fee at the Orlando (1 - 4) mile post and the Number of times the car passes through the toll post.

The discounted toll fee at Orlando(1 - 4) mile post is $0.53

Number of times vehicle passes = 5

Hence, The total fee charged will be :

($0.53 × 5) = $2.65

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Speed is the rate of distance over time.

The speed of the boat is 13mph south-west

Given

\(v_1 = 12mph\) --- west

\(v_2 = 5mph\) -- south

The speed is illustrated with the attached image

Because both speeds act at a diagonal, the speed (v) of the boat is calculated using Pythagoras theorem as follows:

\(v^2 = 12^2 + 5^2\)

\(v^2 = 144 + 25\)

\(v^2 = 169\)

Take square root

\(v = \sqrt{169\)

\(v = 13\)

Hence, the speed of the boat is 13mph south-west

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Answer:

x=2

Step-by-step explanation:

Answer:

y is less than or equal to 2

Step-by-step explanation:

the shading area is under Y=2

The probability of rain tomorrow is the same regardless of whether it has rained in the past two days or not. Therefore, we cannot use the given information to make a prediction about the weather tomorrow.

In example 4.4, we are given a situation where it has not rained in the past two days. The question asks for the probability of rain tomorrow. This type of question falls under the category of conditional probability. In conditional probability, we find the probability of an event given that another event has already occurred.
To solve this problem, we can use Bayes' theorem. Bayes' theorem states that the probability of an event A given that event B has occurred is equal to the probability of event B given that event A has occurred multiplied by the probability of event A divided by the probability of event B.
Let us define the events in this problem as follows:
A = It will rain tomorrow
B = It has not rained in the past two days
Using the given information, we know that P(B) = 0.75 (since there are four possible outcomes: rain yesterday, rain day before yesterday, rain both days, no rain both days, and we are given that the latter has occurred). We need to find P(A|B).
To find P(A|B), we need to find P(B|A), which is the probability that it has not rained in the past two days given that it will rain tomorrow. Since we do not have any information about the relationship between these two events, we can assume that they are independent.
Therefore, P(B|A) = P(B) = 0.75
Now, we can use Bayes' theorem to find P(A|B):
P(A|B) = P(B|A) * P(A) / P(B)
P(A|B) = 0.75 * P(A) / 0.75
P(A|B) = P(A)
This means that the probability of rain tomorrow is the same regardless of whether it has rained in the past two days or not. Therefore, we cannot use the given information to make a prediction about the weather tomorrow.

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Answer:

Step-by-step explanation:

the answer is 152

Answer:

3 and 1/4

Step-by-step explanation:

To create a table of values for the equation 2x - 6y = 12, we can choose different values of x and solve for y. We will start with x = 0 and then choose other values of x to generate more points.

When x = 0, the equation becomes:

2(0) - 6y = 12

-6y = 12

y = -2

So the first point on the table is (0, -2).

When x = 2, the equation becomes:

2(2) - 6y = 12

4 - 6y = 12

-6y = 8

y = -4/3

So the second point on the table is (2, -4/3).

When x = 4, the equation becomes:

2(4) - 6y = 12

8 - 6y = 12

-6y = 4

y = -2/3

So the third point on the table is (4, -2/3).

When x = 6, the equation becomes:

2(6) - 6y = 12

12 - 6y = 12

-6y = 0

y = 0

So the fourth point on the table is (6, 0).

Therefore, the table of values for the equation 2x - 6y = 12 is:

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By solving a quadratic equation we can see that the width of the path measures 20 meters.

We know that the pool measures 18 meters by 20 meters, then the area of the pool alone is:

A = 18m*20m = 360 m^2

Now, if the path has a width x, then the rectangle that includes the path and the pool has dimensions:

(18m + 2x) and (20m + 2x)

And its area is given by:

(18m + 2x)*(20m + 2x)

And we know it is equal to 1520 m^2, then (i'm not writting the units in the computation):

(18 + 2x)*(20 + 2x) = 1520

360 + 4x^2 + 76x = 1520

Now we just need to solve that quadratic equation:

4x^2 + 76x - 1520 + 360 = 0

4x^2 + 76x - 1160 = 0

The solutions are:

x = (-76 ± √(76^2 - 4*4*(-1160))/(2*4)

x = (-76 ± 156)/4

We only care for the positive solution, which gives:

x = (-76 + 156)/4 = 20

We conclude that the width of the path measures 20 meters.

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Answer:

The correct option is;

∠MKL

Step-by-step explanation:

From the construction of the line LKJ to form the exterior  angle ∠JKM, we have that the segment MK of triangle KML forms two adjacent angles on JKL which are ∠JKM and ∠MKL, therefore, the adjacent interior angle to angle ∠JKM is angle ∠MKL

PLease find attach The drawing of triangle KML showing the extended point J

Answer:

B) ∠MKL

Step-by-step explanation:

Took the quiz on edge

Answer:

13/-9

Step-by-step explanation:

Answer:

Step-by-step explanation:

The expresion is 3(5 + 6). The expression is represented