[tex]\left \{ {{x+4y=2} \atop {2x+5y=7}} \right.[/tex]

[tex]\begin{cases} 4x+3y=-8\\\\ -8x-6y=16 \end{cases}~\hspace{10em} \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]

[tex]4x+3y=-8\implies 3y=-4x-8\implies y=\cfrac{-4x-8}{3}\implies y=\stackrel{\stackrel{m}{\downarrow }}{-\cfrac{4}{3}} x-\cfrac{8}{3} \\\\[-0.35em] ~\dotfill\\\\ -8x-6y=16\implies -6y=8x+16\implies y=\cfrac{8x+16}{-6} \\\\\\ y=\cfrac{8}{-6}x+\cfrac{16}{-6}\implies y=\stackrel{\stackrel{m}{\downarrow }}{-\cfrac{4}{3}} x-\cfrac{8}{3}[/tex]

one simple way to tell if both equations do ever meet or have a solution is by checking their slope, notice in this case the slopes are the same for both, meaning the lines are parallel lines, however, notice both equations are really the same, namely the 2nd equation is really the 1st one in disguise.

since both equations are equal, their graph will be of one line pancaked on top of the other, and the solutions is where they meet, hell, they meet everywhere since one is on top of the other, so infinitely many solutions.

A function is a relation where there is only one output for every input. In other words for every x value, there is only one y value.

Example : Multiply by 3 is a very simple function.

Input : 0 Output : 0

Input : 1 Output : 3

Input : 2 Output : 6

Input : 3 Output :9

And so on!

Hope this helps!

The image of the triangle is missing, so i have attached it.

Also, the options are;

A) The apothem can be found using the Pythagorean theorem.

B) The apothem can be found using the tangent ratio.

C) The perimeter of the equilateral triangle is 15 cm.

D) The length of the apothem is approximately 2.5 cm.

E) The area of the equilateral triangle is approximately 65 cm².

Answer:

Options A, B & D are true

Step-by-step explanation:

A) We are told that the triangle is an equilateral triangle.

Thus, the 3 sides equal 8.7 cm.

Now from the image, b is half of one of the sides.

Thus, b = 8.7/2 = 4.35 cm

Now, we want to find the apothem "a".

Using Pythagoras theorem, we have;

a² + 4.35² = 5²

a² = 25 - 18.9225

a² = 6.0775

a = √6.0775

a ≈ 2.5 cm.

Thus, option A is true as Pythagoras theorem was able to calculate the apothem "a"

B) since the main triangle is equilateral, it means each angle is 60°.

Now, the radius line from one corner point to the center will divide the 60° angle into 2 equal parts.

Thus, the angle made by the radius line with the base of the triangle is 60/2 = 30°

Now, from tangent ratios, we know that;

Opposite/Adjacent = tan θ

In the small triangle, opposite is apothem "a" while adjacent is b = 4.35 cm

Thus;

a/4.35 = tan 30

a = 4.35 tan 30

a ≈ 2.5 cm.

Thus, option B is correct as Tangent ratio can be used to find the apothem

C) The perimeter of equilateral triangle = 3x

Where x is length of one side.

One side is 8.7 cm

Thus, perimeter = 3 × 8.7 = 26.1 cm

Thus option C is not correct.

D) From calculations above, we saw that in both options A & B, the apothem is approximately 2.5 cm.

Thus, option D is true.

E) Area of triangle is;

A = ½ × base × height

Base = 8.7 cm

To get height, we will use trigonometric ratio. Thus;

h/8.7 = sin 60°

h = 8.7 sin 60°

Thus;

A = ½ × 8.7 × 8.7 sin 60°

A = 32.77 cm²

Thus is not equal to 65 cm². Thus, option E is not correct.

The statements that are true for the considered equilateral triangle are:

For a regular polygon, the apothem is the line segment from the center of the polygon to the mid of one of the sides of the considered polygon.

For this case, referring to the figure attached below, we have:

Since the triangle is equilateral, there can be 6 congruent triangles like BOD.

Thus, Area of triangle ABC = 6 × Area of triangle BOD

Area of BOD = [tex]\dfrac{1}{2} \times x \times 4.35 = 2.175x \: \rm cm^2[/tex]

Area of ABC = [tex]6 \times 2.175x = 13.05x \: \rm cm^2[/tex]

The length of the apothem is x cm, and can be obtained by using Pythagoras theorem.

We can also use the tangent ratio as the line segment BO is bisecting the internal angle B (each internal angle is of 60 degrees in an equilateral triangle), so angle OBD is of 60/2 = 30 degrees. So using angle and the fact that tangent ratio is ratio of side opposite to angle and the remaining adjacent side(not hypotenuse).

[tex]tan(30^\circ) = x/4.35 \implies x = 4.35 \times \tan(30^\circ) \approx 2.5 \: \rm cm[/tex]

Using Pythagoras theorem too, we can get the value of x as:

[tex]5^2 = 4.35^2 + x^2\\x = \sqrt{25 - 18.9225} \approx 2.465 \: \rm cm \approx 2.5 cm[/tex]

Thus, area of the equilateral triangle ≈ [tex]13.05 \times x \approx 13.05 \times 2.5 = 32.575 \: \rm cm^2[/tex]

This isn't 65 sq. cm.

Thus, the statements that are true for the considered equilateral triangle are:

Learn more about tangent ratio here:

https://brainly.com/question/14169279

Answer:

$177.41

Step-by-step explanation:

when it says 32% OF , of always means multiply in word problems so we multiple 132% (1.32) times 134.40

$177.41

Answer:

420

Step-by-step explanation:

32% of its original price

32%=134.40

100%=?

cross multiply

100/100 x 134.40 × 100/32

1×134.40×3.125

=420

Answer:

$6

Step-by-step explanation:

System of equations

x+y = 18

0.03x+0.06y = 5% of 18 = 0.9

(0.03x+0.06y=0.9)*100 = 3x+6y=90

(3x+6y=90)÷3 = x+2y=30

Substract (1)-(2)

x+2y=30 ... (1)

x+y=18 ... (2)

y=12

x+12=18

x=6

Thanks.

The random selection of a blue marble is an illustration of probability

You should expected to pull a blue marble 10 times

The given parameters are:

Blue = 16

Red = 12

Green = 12

The total number of marbles is:

Total = 16 + 12 + 12

So we have:

Total = 40

The probability of selecting a blue marble is:

[tex]P(Blue) = \frac{16}{40}[/tex]

When 25 marbles are selected, the expected number of blue is:

[tex]Blue = n * P(Blue)[/tex]

So, we have:

[tex]Blue = 25 * 16/40[/tex]

[tex]Blue = 10[/tex]

Hence, the expected number of blue marbles is 10

Read more about expected values at:

https://brainly.com/question/15858152

Answer:

1st question

Sry if its wrong xx

Answer:

6:35.

Step-by-step explanation:

I start by adding the hours spent to the time leaving me with 5:50, I then add the 40 which brings it to 6:30 and the additional 5 minutes bringing the final answer to 6:35.

Answer:

6:35 PM

Step-by-step explanation:

When Harold got home, it was already 3:50 PM. Then he played games for an hour and five minutes. Adding on an hour, it made the time 4:50 PM, and then adding on the five minutes, made the time 4:55 PM. When he finished playing games, he took an hour and forty minutes to do his homework. 4:55 PM, adding on the hour makes it 5:55 PM, then adding the 40 minutes, makes it 6:45 PM.

- Educationist

Answer:

Step-by-step explanation:

Given

Total number of marbles is

Probability of getting 2 of the same color is

Probability of 2 reds is:

Probability of 2 blues is:

Required probability is

Answer:

A conversion calculator gave me 8800

Step-by-step explanation:

x + y = 24

2x - y=21

I'm guessing the question was find both numbers.

3x = 35

x=15

3y = 27

y=9

[tex]\qquad\qquad\huge\underline{\boxed{\sf Answer☂}}[/tex]

The y - coordinate of a point lying on that function is represented by f(x) for each value of x, so let's find the corresponding value of x, when f(x) = 0

In the given case, y - coordinate of two points is equal to zero. hence we will get two distinct values of x

that is :

[tex]\qquad \sf  \dashrightarrow \: x = - 2 \: \: and \: \: x = 4[/tex]

Answer:

16 x 4.

Step-by-step explanation:

What multiplies into 64?

could be 16 and 4?

16 x 2 = 32

4 x 2 = 8

32 + 8 = 40, therefore, this is correct.

Using the relation between velocity, distance and time, it is found that:

Velocity is distance divided by time, that is:

[tex]v = \frac{d}{t}[/tex]

A plane traveling with the wind travels 900 miles in 5 hours, hence:

[tex]v_a + v_w = \frac{900}{5}[/tex]

[tex]v_a + v_w = 180[/tex]

The return trip is against the wind and takes 9 hours, hence:

[tex]v_a - v_w = \frac{900}{9}[/tex]

[tex]v_a - v_w = 100[/tex]

From the first equation, we have that:

[tex]v_w = 180 - v_a{/tex]

Replacing on the second:

[tex]v_a - v_w = 100[/tex]

[tex]v_a - 180 + v_a = 100[/tex]

[tex]2v_a = 280[/tex]

[tex]v_a = 140[/tex]

[tex]v_w = 180 - 140 = 40{/tex]

Hence:

More can be learned about the relation between velocity, distance and time at https://brainly.com/question/24316569

Answer: look at the image

Step-by-step explanation:

Answer:

Q = mCpΔT where Q is the energy in heat (joules), m is the mass (grams), Cp is the specific heat capacity (J/g/°C), and ΔT is the change in temperature (T2 - T1) in °C.

Step-by-step explanation:

So, since Q = mCpΔT then m = Q/(CpΔT) or (45.0)/(0.780•2.00) = 45/1.56 = 28.846 grams. Since there are 3 sig figs, we round to:

m = 28.8 g

Answer:

P=141,300(1+0.05)^6

Step-by-step explanation:

r = rate = 5/100 = 0.05

a = starting amount = 141,300

t = time = 6 years

% growth formula:

a(1+r)^t

141,300(1.05)^6

Answer:

P=141,300(1+0.05)^6

Step-by-step explanation:

r = rate = 5/100 = 0.05

a = starting amount = 141,300

t = time = 6 years

% growth formula:

a(1+r)^t

141,300(1.05)^6

The minimum possible area of each square cardboard piece which is used to produce circular drink coasters is 72.25 in².

The equation of the circle is the equation which is used to represent the circle in the algebraic equation form with the value of center point in the coordinate plane and measure of radius.

The standard form of the equation of the circle can be given as,

[tex](x-h)^2+(y-k)^2=r^2[/tex]

Here (h,k) is the center of the circle and (r) is the radius of the circle.

A company produces circular drink coasters. the equation which represents the size of a coaster is,

[tex]x^2+ y^2 = 18.0625[/tex]

The units are in the inches. This equation can be written as,

[tex]x^2+ y^2 = \dfrac{289}{16}\\x^2+ y^2 =\left( \dfrac{17}{4}\right)^2[/tex]

Compare it with the equation of the circle, we get,

[tex]h=0\\k=0\\r=\dfrac{17}{4}\rm\; in[/tex]

The radius of the circular coaster is 17/4. The diameter of it is,

[tex]d=2\times\dfrac{17}{4}\\d=\dfrac{17}{2}\rm \; in[/tex]

Now, each coaster is cut from a square piece of cardboard. The diameter of the circular coaster will be equal to the side of the square piece of cardboard.

[tex]a=d=\dfrac{17}{2}\rm\; in[/tex]

The area of the square is the square of its side. Thus, the area of a square piece of cardboard is,

[tex]A=a^2\\A=\left(\dfrac{17}{2}\right)^2\\A=72.25\rm\; in^2[/tex]

Thus, the minimum possible area of each square cardboard piece which is used to produce circular drink coasters is 72.25 in².

Learn more about the equation of circle here;

https://brainly.com/question/1506955

Answer:

77

Step-by-step explanation:

The area of a rectangle is A = lw. 'A', the area, is 3927, and 'w', the width, is 51. By substituting the values in, we get that 3927 = 51L. Dividing both sides by 51, we get that L, the length, is 77.

Answer:

y = 1/2x - 1

Step-by-step explanation:

The x value is divided by 2 and then has 1 subtracted from it.

also for future posts, put the question in the title that way people know what you need and can click if they know the answer.

Answer:

algebraic expression for 180 degree clockwise rotation about the origin (x,y) → (-y, x) algebraic expression for 270 degree clockwise rotation about the origin equals a 270 degree counterclockwise rotation 90 degree clockwise rotation equals a 90 degree counterclockwise rotation

Step-by-step explanation:

hope this helps

have an awesome day -TJ

Answer:

approximately 14

Step-by-step explanation:

first find out how many sets of 60 there are

200/60=3.3

3.3 sets of 4 apples

but you can't have 2/3 of a rotten apple

so 3.5 sets of 4 rotten apples

4x3.5=14

The value of n will the terminal side fall on the y-axis at n=3

The terminal side of an angle fall along the positive portion of the y-axis,

If it can written in the form of [tex](90^0)a[/tex]

Where a = positive odd integer,

We hyave given the given angle is,

[tex](870n)^0,[/tex]

The terminal side of an angle theta drawn in angle standard position is the side which isn't the initial side

Now for n=3

[tex](870(3))^0=2610^0[/tex]

The  angle will be 2610°

Its terminal side fall along the positive portion of the y-axis,

[tex]2610^0 = (90^0)a \implies a = 29[/tex]......( Positive odd integer )

Therefore  for n = 3,  the terminal side of the angle (870n)° falls along the positive portion of the y-axis,

For n = 4,

Our angle will be 3480°

Its terminal side fall along the positive portion of the y-axis,

[tex]3480^0 = (90^0)a \implies a = 38.6667 ( Not possible )[/tex]

Therefore for n = 4, the terminal side of the angle (870n)° does not fall along the positive portion of the y-axis

Next is for n = 5,

Our angle will be 4350°

Its terminal side fall along the positive portion of the y-axis,

[tex]4350^0 = (90^0)a \implies a = 48.333.. ( Not possible )[/tex]

Thus, for n = 5,  the terminal side of the angle (870n)° does not fall along the positive portion of the y-axis,

For n = 6,

Our angle will be 5220°

Its terminal side fall along the positive portion of the y-axis,

[tex]5220^0 = (90^0)a \implies a = 58..... ( Not possible )[/tex]

Thus, for n = 6,  the terminal side of the angle (870n)° does not fall along the positive portion of the y-axis.

Therefore,the value of n will the terminal side fall on the y-axis at n=3.

To learn more about the terminal side visit:

https://brainly.com/question/24680641

Answer:

a

Step-by-step explanation:

x=3 on edge

Answer:

Step-by-step explanation:

Step-by-step explanation:

Age of dave = y

Age of Julia = x

y = 4x - 8

if y = 16

then

4x - 8 = 16

4x = 16 + 8

4x = 24

x = 24/4

x = 6

Julia is 6 years old

Answer:

Julia is 6 years old.

Step-by-step explanation:

Dave + 8 = 4 Julia

16 + 8 = 4 Julia

24 = 4 Julia

6 = Julia

Julia is 6 years old

Answer:

9 contestants

Step-by-step explanation:

Out of the 16 contestants, 12 of them qualified for the bonus round.

This means, that 12/16, or 75% of the contestants qualified for the bonus round.

Out of the remaining 12 contestants, I would expect (75%)(12), or 9 contestants to qualify for the next bonus round.

Let me know if this helps!

Answer:The answer is 9

Step-by-step explanation:

12 of the 16 contestants on the game show qualified. That is 75% of the contestants. Applying this to the next 12, 12 contestants x 75% is 9 qualifying contestants.

Answer:

40ft

Step-by-step explanation:

What you need to know is the formula for the air of a rectangle:

the long side * the short side.

First calculate the area of the rectangle in the middle: 3*8=24ft

Then we are left with two right-angled triangles, one on the left and one on the right. If we juxtapose them, we realize that it forms a rectangle whose large side measures 8 and the small 2 so 2*8=16ft.

Finally, just add the area of the middle rectangle with the area of our rectangle formed by the two triangles on the right and on the left. So 16+24=40ft

Answer:

I would say 30

Reasoning:

Because that thing your looking at is 180% degree angle and the other side is 90%. x is small it seems to be acute and I think 2x is about 60%.

If im incorrect im terribly sorry but at least my answer wasnt bad like the 1st guys