Find the shaded area

Answer:

[tex]TD \cong GS[/tex]

Step-by-step explanation:

See comment for complete question

Given:

[tex]TM \cong GL[/tex]

[tex]MD \cong LS[/tex]

Required

The information that shows [tex]\triangle MTD \cong \triangle LGS[/tex] by SSS

By SSS implies that, the three sides of both triangles are congruent

Already, we have:

[tex]TM \cong GL[/tex]

[tex]MD \cong LS[/tex]

The third side of [tex]\triangle MTD[/tex] is [tex]TD[/tex]

The third side of [tex]\triangle LGS[/tex] is [tex]GS[/tex]

So, for both to be congruent by SSS, the third sides must be congruent

i.e.

[tex]TD \cong GS[/tex]

Answer: The median is 29

Step-by-step explanation:

I started by arranging the data points from smallest to largest to get 20, 25, 27, 29, 37, 38, 39. Then I found the middle number in the data set and got 29.

Answer: [tex]864\ m^2,\ 24\ m[/tex]

Step-by-step explanation:

Given

Perimeter of the rhombus is [tex]120\ m[/tex]

Length of one of the diagonal is [tex]d_1=36\ m[/tex]

All the sides of the rhombus are equal

[tex]\Rightarrow 4a=120\\\Rightarrow a=30\ m[/tex]

Area of the rhombus with side and one diagonal is

[tex]\Rightarrow \text{Area=}\dfrac{1}{2}d\sqrt{4a^2-d^2}[/tex]

Insert the values

[tex]\Rightarrow \text{Area=}\dfrac{1}{2}\times 36\times \sqrt{4\cdot 30^2-36^2}\\\\\Rightarrow \text{Area= }18\sqrt{3600-1296}\\\Rightarrow \text{Area= }18\times 48\\\Rightarrow \text{Area= }864\ m^2[/tex]

Area with two diagonals length can be given by

[tex]\Rightarrow \text{Area =}0.5\times d_1\times d_2 \\\text{Insert the values}\\\Rightarrow 864=36\times d_2\\\Rightarrow d_2=24\ m[/tex]

Thus, the area of the rhombus is [tex]864\ m^2[/tex] and the length of the other diagonal is [tex]24\ m[/tex]

Answer:

x>4

Step-by-step explanation:

3/(x-4) >0

Divide each side by 3

3/(x-4) * 1/3 >0*1/3

1/(x-4) >0

We know if 1/(x-4) >0 then x-4 > 0

x-4>0

Add 4 to each side

x-4+4 >0+4

x>4

[tex]\boxed{\large{\bold{\textbf{\textsf{{\color{blue}{Answer}}}}}}:)}[/tex]

[tex]:\implies{\dfrac{3}{x-4}>0}\\\\:\hookrightarrow{\dfrac{3}{x-4}×\dfrac{1}{3}>0×\dfrac{1}{3}}\\\\:\longrightarrow{x-4>0}\\\\:\implies{x-4+4>0+4}\\\\ :\dashrightarrow{\sf{x>4}}[/tex]

Answer:

2, 3, 5, 7, 11, 13.

Step-by-step explanation:

A prime number is a number that you don't get a whole number when divided by 2 but you do get a whole number when divided by prime numbers such as 3,5,7,11... Basically a number with two factors, it can only be divided by 1 or themselves. for example:

9/2 = 4.5 (this is not a whole number so it might be a prime.

9/3 = 3 (it works when divided by a prime number.

another:

8/2 = 4 (it gives a whole number when divided by 2 therefor, it can't be a prime number.

Answering:

There are 6 prime numbers at the top^^^^.

One possible answer is  2, 3, 5, 41, 67, 89

Another possible answer is  2, 3, 5, 47, 61, 89

Other answers may be possible.

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

Explanation:

This is a trial and error type of problem. Though with practice it's not as blind of randomly guessing.

We have 9 values here. If we paired them up, then we can form at most 4 pairs (since 9/2 = 4.5 rounds down to 4). That means we won't be able to form six two-digit primes. Some of the primes must be single digits.

We can have 3 single digit primes and 3 two-digit primes since 3+2*3 = 9.

The single digit primes are: 2, 3, 5, 7

Let's say 2 and 5 are definitely locked down to be the single digit group. I'm doing this since we can't have 2 or 5 as the units digit. If the units digit is 2, then 2 is a factor and it's not prime. Similarly, if 5 is the units digit, then 5 is a factor and that two digit value is not prime.

For good measure, we'll throw 3 in there as well and see what happens.

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

The digits we have left are: 1, 4, 6, 7, 8, 9

The number 14 isn't prime, but 41 is prime

67 is prime so that's another two values off the list

lastly, 89 is prime so that works as well.

So one possible sequence is 2, 3, 5, 41, 67, 89

Notice how we can swap the 1 and 7 to go from 41,67 to 47,61; this gets us two other primes. So another possible answer is 2, 3, 5, 47, 61, 89

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

Side note: having the list of primes on a reference sheet is a handy recommendation. You only need to go up as high as 97 which is the largest two digit prime.

Answer: Is this a question? Or statement Yes they can be angles

Step-by-step explanation:

Answer:

Step-by-step explanation:

Relation 1 is a function

Relation 2 is not a function

Relation 3 is a function

Realation 4 is not a function

Answer:

Step-by-step explanation:

15. = 2.39

and jus use mathaway lma

Answer:

x = 60.6 units

Step-by-step explanation:

Hi there!

In this right triangle, we're given the measure of an angle, the side opposite that angle and another side adjacent to that angle (that is not the hypotenuse). In this circumstance, we can use the tangent ratio to help us solve for the missing side:

[tex]tan\theta=\frac{opp}{adj}[/tex]

Plug in the given information:

opp = 27, adj = x, θ = 24

[tex]tan(24)=\frac{27}{x}\\x=\frac{27}{tan(24)} \\x=60.6[/tex]

Therefore, the length of the missing side is 60.6 units when rounded to the nearest tenth.

I hope this helps!

Answer:

Step-by-step explanation:

In order to write the equation of this line, we need to pick 2 points on the graph where the line goes right through the intersection of the grids. Actually, you only need 1 of these, because the line goes through at (0, 15). Another point then can be (6, 6). Locate this point so you know what I means when I say that the line goes right through where the grids intersect at x = 6 and y = 6 (as opposed to somewhere in the middle of one of these grids). Find the slope between these 2 points:

[tex]m=\frac{6-15}{6-0}=-\frac{9}{6}=-\frac{3}{2}[/tex]

Since there's only one choice with that slope, that is the choice you want.

Answer:

70 cents or 0.70 dollars

Step-by-step explanation:

one dime is 10 cents so if you have 7 than you have 70 cents

Answer:

Step-by-step explanation:

This is quite a doozy, my friend. We will set up a d = rt table, fill it in...and pray.

The table will look like this before we even fill anything in:

            d        =        r        *        t

SUV

sedan

Ok now we start to pick apart the problem. Motion problems are the hardest of all story problems ever. This is because there are about 100 ways a motion problem can be presented. So far what we KNOW for an indisputable fact is that the distance from Georgetown to Greenville is 120 km. So we fill that in, making the table:

             d      =      r      *      t

SUV     120

sedan  120

The next part is derived from the sentence "After an hour, the SUV was 24 km ahead of the sedan." This tells us the rate of the SUV in terms of the sedan. If the SUV is 24 km ahead of the sedan in 1 hour, that tells us that the rate of the sedan is r and the rate of the SUV is r + 24 km/hr. BUT we have other times in this problem, one of them being 25 minutes. We have a problem here because the times either have to be in hours or minutes, but not both. So we will change that rate to km/min. Doing that:

24 [tex]\frac{km}{hr}[/tex] × [tex]\frac{1hr}{60min}=.4\frac{km}{min}[/tex] So now we can fill in the rates in the table:

            d      =      r      *      t

SUV    120    =   r + .4

sedan 120    =     r

They left at the same time, so now the table looks like this:

             d      =      r      *      t

SUV    120     =   r + .4  *      t

sedan  120    =      r      *      t

We will put in the time difference of 25 minutes in just a sec.

If d = rt, then the equation for each row is as follows:

SUV:   120 = (r + .4)t

sedan:   120 = rt

Since the times are the same (because they left at the same time, we will set the equations each equal to t. The distances are the same, too, I know that, but if we set the distances equal to each other and then solve the equations for a variable, the distances cancel each other out, leaving us with nowhere to go. Trust me, I tried that first! Didn't work.

Solving the first equation for time:

sedan:  [tex]\frac{120}{r}=t[/tex]  That's the easy one. Now the SUV. This is where that time difference of 25 minutes comes in from the last sentence. Let's think about what that sentence means in terms of the times of each of these vehicles. If the sedan arrived 25 minutes after the SUV, then the sedan was driving 25 minutes longer; conversely, if the sedan arrived 25 minutes after the SUV, then the SUV was driving 25 minutes less than the sedan. The latter explanation is the one I used in the equation. Again, if the SUV was driving 25 minutes less than the sedan, and the equations are solved for time, then the equation for the SUV in terms of time is

[tex]\frac{120}{r+.4}=t-25[/tex] and we solve that for t:

[tex]\frac{120}{r+.4}+25=t[/tex]

Again, going off the fact that times they both leave are the same, we set the equations equal to one another and solve for r:

[tex]\frac{120}{r+.4}+25=\frac{120}{r}[/tex]

I began by first multiplying everything through by (r + .4) to get rid of it in the denominator. Doing that:

[tex][r+.4](\frac{120}{r+.4}) +[r+.4](25)=[r+.4](\frac{120}{r})[/tex] which simplifies very nicely to

[tex]120+25(r+.4)=\frac{120}{r}(r+.4)[/tex]  So maybe it's not so nice. Let's keep going:

[tex]120+25r+10=\frac{120r}{r}+\frac{48}{r}[/tex] and keep going some more:

[tex]130+25r=120+\frac{48}{r}[/tex] and now we multiply everything through by r to get rid of THAT denominator:

[tex]r(130)+r(25r)=r(120)+r(\frac{48}{r})[/tex] giving us:

[tex]130r+25r^2=120r+48[/tex] Now we have a second degree polynomial we have to solve by factoring. Get everything on one side and factor using the quadratic formula.

[tex]25r^2+10r-48=0[/tex]

That factors to

r = 1.2 and r = -1.6 and both of those rates are in km/minute. First of all, we cannot have a negative rate (this is not physics where we are dealing with velocity which CAN be negative) so we throw out the -1.6 and convert the rate of 1.2 km/minute back to km/hr:

[tex]1.2\frac{km}{min}[/tex] × [tex]\frac{60min}{1hr}[/tex] and we get

r = 72 km/h, choice B.

Wow...what a pain THAT was, right?!

The ratio 2:3 means for every 2 inches on the original, the photocopy would be 3 inches.

3/2 = 1.5

The photocopied image is 1.5 times larger than the original.

Side BG on the original is side FG on the copy:

14 x 1.5 = 21 meters

FG = 21 meters

Answer:

FG = 21

Step-by-step explanation:

The ratio is 2:3

2               BC

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

3                FG

2              14

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

3                FG

Using cross products

2FG = 3*14

2FG = 42

Divide by 2

FG = 21

Answer:

OAmalOHopeO

Answer:

I tried out part a) not so sure though. I also think that for part b) u have to convert the m to cm then divide the answers by 50

The real length and width of the dinning room is 7 m and 6.2 m.

The length and width of the lounge in centimeters is 800 cm and 680 cm.

To convert the meter to cm, multiply the given meter value by 100 cm.

To convert the measurement from centimeters to meters, divide the number of centimeters by 100 or multiply the number of centimeters by 0.01.

According to the question

A plan of a house is drawn to a scale of 1:50

On the plan, the dining room is 14 cm long and 12.4 cm wide.

1 m = 100 cm

a. Length of the dinning room = 14 cm  = [tex]\frac{14}{100}[/tex] = 0.14 m

Width of the dinning room = 12.4 cm = [tex]\frac{12.4}{100}[/tex] = 0.124 m

Actual length = 0.14 × 50 = 7 m

Actual width = 0.124 × 50 = 6.2 m

Hence, the real length and width of the dinning room is 7 m and 6.2 m

b. Length of lounge = 8 m

Width of lounge = 6.8 m

1 m = 100 cm

Length of lounge (cm) = 8 × 100 = 800 cm

Width of lounge (cm) = 6.8 × 100 = 680 cm

Hence, the length and width of the lounge is 800 cm and 680 cm.

Find out ore information about meters to centimeter here

https://brainly.com/question/15195034

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[tex]\boxed{\large{\bold{\blue{ANSWER~:) }}}}[/tex]

Answer:

x = -12

Step-by-step explanation:

5x + 2(2x - 23) = -154

Distribute;

5x + 4x - 46 = -154

Collect like terms

9x - 46 = -154

Add 46 to both sides;

9x = -108

Divide both sides by 9

x = -12

Answer:

See explanation

Step-by-step explanation:

Given

[tex]Flat = 20[/tex]

[tex]Visit = 5[/tex]

Required

The function to represent x visits

This is calculated as:

[tex]f(x) = Flat + Visit * x[/tex]

So, we have:

[tex]f(x) = 20 + 5 * x[/tex]

[tex]f(x) = 20 + 5x[/tex]

The second question is incomplete; however, I will explain how to calculate the horizontal asymptote of a rational function.

For polynomials with the same degree (i.e. m = n), the horizontal asymptote is calculated by dividing the coefficients of the highest degrees.

e.g.

[tex]f(x) = \frac{6x^2 + 1}{3x^2 + 4}[/tex] ---the degrees of both is 2

So, the horizontal asymptote is:

[tex]y = 6/3[/tex]

[tex]y =2[/tex]

If the numerator has a higher degree, then there is no horizontal asymptote.

If the denominator has a higher degree, then the horizontal asymptote is:

[tex]y = 0[/tex]

Answer:

First one is B, Second is 5

Step-by-step explanation:

got it right on edge

Step-by-step explanation:

it still remains 125 it doesn't change

Answer:

A(-2,1)》A1(-8, 4)

B(-3,3)》B1(-12,12)

C(-1,3)》C1(-4,12)

HOPE IT HELPS....

The triangle QPR having inscribed triangle STU will allow the artisan to divided his glass piece into four equal triangular pieces.

In order to divide an equilateral triangle into four equal triangular glass pieces, the artisan must;

Since the triangle is equilateral,

PQ = QR = RP

Mid-point divides the lines into equal parts. So,

PS = SQ = QU = UR = RT = TP

Thus, it is proved that

ΔPST = ΔSTU = ΔTUR = ΔQSU

Learn more about 'Equilateral Triangle' here:

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AB= 9 UNITS

hope it helps you...

Answer:

by Pythagoras theorem

in first

a²+ b² = c²

6² + 9² = c²

36 + 81 = 117

AD = 117

and in second

a² + b² = c²

a² + 6² = 117

a² = 117 - 36

AB² = 81

AB = 9

Answer:

The post office charges $0.7cents to send one letter, and the fee is $1.5

Step-by-step explanation:

Answer:

the correct answer is option 1.

The correct explanation is: All equilateral triangles are congruent and therefore similar, with side lengths in a 1:1 ratio.

Those triangles look the same but are different in size.

And in similar triangles,

the corresponding sides are in proportion to each other and the corresponding angles are equal to each other.

In an equilateral triangle, all three sides are congruent, and all three angles are congruent.

Therefore, any equilateral triangle can be transformed into any other equilateral triangle through a combination of translations, rotations, and reflections, without changing the size or shape of the triangle.

Thus, all equilateral triangles are similar, with side lengths in a 1:1 ratio, since they have the same shape but may differ in size.

To learn more about similar triangles;

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Answer:

Step-by-step explanation:

Answer:

siis  corretoed

Step-by-step explanation:

Answer:

x < -51/10

General Formulas and Concepts:

Pre-Algebra

Equality Properties

Step-by-step explanation:

Step 1: Define

Identify

-2(5x + 1) > 49

Step 2: Solve for x

Answer:

x < -51/10

Step-by-step explanation:

-10x -2 > 49

-10x > 51

x < -51/10

Answer:

23 hoiurs

Step-by-step explanation:

Given data

a. The two variables are

1. Number of hours worked

2. The amount earned

b. The rate is given as

=120/8

=$15 per hour

c. The equation is given as

rate=Amount earned/ number of hours worked

15= 345/hours

make hours subject of the formula we have

hours= 345/15

hours= 23 hours

Hence he must work for 23 hours

Answer:

Hello,

Answer 8a²c(a+3c) =8a³c+24a²c

Step-by-step explanation:

2a²+6ac=2a(a+3c)

4a²c+12ac²=4ac(a+3c)

H.C.F=2a(a+3c)*4ac=8a²c(a+3c)

Answer:

1st expression:2a×a+2×3×a×c

2nd expression:2×2×a×a+2×2×3×a×c×c

here,

2×a×a+2×3×a×c

2a^a+6ac

Answer:

Para responder esta pregunta, necesitamos utilizar el gráfico que se ve en la imagen de abajo.

En dicho gráfico, se presenta el porcentaje que gana, en promedio, una mujer comparado con lo que ganaría un hombre en el mismo puesto.

a)  Si una mujer en Suiza gana 1300 francos, ¿cuánto gana un hombre en el mismo puesto y con la misma categoría profesional?

Viendo el gráfico, podemos ver que en Suiza una mujer gana el 68% de lo que gana un hombre.

Entonces, si un hombre gana una cantidad X, tendremos:

X = 100%

y la mujer gana 1300 francos, que es el 68%, entonces podemos escribir:

X = 100%

1300 francos = 68%

Ahora podemos tomar el cociente entre esas dos ecuaciones, para así obtener:

X/(1300 francos) = (100%/68%)

Ahora podemos resolver esto para X:

X = (100%/68%)*(1300 francos) = 1911.76 francos.

Un hombre en la misma posición ganaría 1911.76 francos.

b) Un hombre, por término medio, gana en España un sueldo mensual de 1102 euros netos. ¿Cuánto ganaría si fuese mujer?

Viendo el gráfico, podemos ver que una mujer en España gana el 67% de lo que ganaría un hombre en la misma posición.

El sueldo del hombre es 1102 euros, y en este caso, esto es el 100%, entonces:

1102 euros = 100%

Y sea X el sueldo de la mujer, el cual sabemos que representa el 67%, entonces escribimos:

X = 67%

Así, tenemos dos ecuaciones:

X = 67%

1102 euros = 100%

Tomando el cociente, obtenemos:

X/(1102 euros) = (67%/100%)

Resolviendo para X obtenemos:

X =  (67%/100%)*(1102 euros) = 738.34 euros

Una mujer en la misma posición ganaría 738.34 euros.

Answer:

I'm sorry but i only know a) so yeah

anyway a) is 20 in.

Step-by-step explanation:

Hope it helps!