Put the following equation of a line into slope-intercept form, simplifying all
fractions.
4x + 3y = –21

Given:

The ratio of the measures of the three sides of a triangle is [tex]\dfrac{1}{4}:\dfrac{1}{3}:\dfrac{1}{6}[/tex].

Its perimeter is 31.4 centimeters

To find:

The shortest side of the triangle.

Solution:

Let the measures of the three sides of a triangle are [tex]\dfrac{1}{4}x,\dfrac{1}{3}x,\dfrac{1}{6}x[/tex] respectively (in cm).

Its perimeter is 31.4 centimeters.

[tex]\dfrac{1}{4}x+\dfrac{1}{3}x+\dfrac{1}{6}x=31.4[/tex]

[tex]\dfrac{3x+4x+2x}{12}=31.4[/tex]

[tex]\dfrac{9x}{12}=31.4[/tex]

[tex]\dfrac{3x}{4}=31.4[/tex]

On further simplification, we get

[tex]3x=4\times 31.4[/tex]

[tex]3x=125.6[/tex]

Divide both sides by 3.

[tex]x=\dfrac{125.6}{3}[/tex]

[tex]x=41.867[/tex]

Now, the sides of triangle are

[tex]\dfrac{1}{4}(41.867)=10.467[/tex]

[tex]\dfrac{1}{3}(41.867)=13.956[/tex]

[tex]\dfrac{1}{6}(41.867)=6.978[/tex]

Therefore, the length of the shortest side is 6.978 cm.

Answer:

a

Step-by-step explanation:

Answer:

Step-by-step explanation:

(0, -5) (5, 0)

(0 + 5)/(5 - 0)

5/5= 1

y + 5 = x - 0

y = x - 5

Answer:

400 feet

Step-by-step explanation:

on way up you travel 35 ft in 30 sec or 144 ft in 120 sec (2 min)

on way down you travel 304 ft in 120 sec (2 min)

the distance traveled for 5 minutes at rate from way 'up' is 360 feet

the distance traveled for 5 minutes at rate from way 'down' is 760 feet

difference is 400 feet

Answer:

400

Step-by-step explanation:

Sleepy

Answer:

y =9

Step-by-step explanation:

you know the distance is 10 and some of the x,y points. so start filling what you know into the distance formula

10= √((9-1)^2 + (y-3)^2 )

square both sides to get ride of the square root

100 = 64 + (y-3)^2

36 = (y-3)^2

6 = y-3

y = 9

double check by using 9 for Y and you'll see it works.

Answer:

d = 9

Step-by-step explanation:

solving for d

let's get ride of the fraction first so multiple the whole thing by 3

3= 1d - 6

add 6 to both sides

9 = d

easy peasy.

Answer:

Step-by-step explanation:

Answer:

4/9

Step-by-step explanation:

(2/3)^2 is another way of writing:

2/3*2/3

Which is 4/9

Hope this helps

Answer:

2/3*2/3      4/3

Step-by-step explanation:

Answer:

The number of hours.

Step-by-step explanation:

The dependent variable is what you are mesuaring.

Answer:

y=5 m=3

Step-by-step explanation:

i mean it shows you the y intercept and the slope and the linear function all in that one picture

Answer:

y-intercept = 5  

slope = -1/3

Step-by-step explanation:

Answer:

3/10

Step-by-step explanation:

Answer:

5 yr and 39 yr

Step-by-step explanation:

Let x = the age of the younger

then 7x + 4 = the age of the older

Now x + 7x + 4 = 44

8x + 4 = 44

8x = 40

x = 5

7x + 4 = 7(5) + 4 =  35 + 4 = 39

Check:  5 + 39 = 44

the total sale was neither a profit nor loss , 0%

Step-by-step explanation:

1st table :

100%-> 9900

110%-> 10890

10890-9900=990(earned)

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

2nd table :

100%->9900

90%-> 8910

9900-8910=990(lost)

990-990=0

hence the total sale was neither a profit nor loss , 0%

Answer:

(-4,4)

Step-by-step explanation:

I believe that's it

Let's solve your system by substitution.

−3x+y=−2;y=4x

Rewrite equations:

y=4x;−3x+y=−2

Step: Solvey=4xfor y:

y=4x

Step: Substitute4xforyin−3x+y=−2:

−3x+y=−2

−3x+4x=−2

x=−2(Simplify both sides of the equation)

Step: Substitute−2forxiny=4x:

y=4x

y=(4)(−2)

y=−8(Simplify both sides of the equation)

Answer:

x=−2 and y=−8

Answer:

80%

Step-by-step explanation:

Answer: The answer to this math question about solving for the value of k with the given full of the angles is k = 6.

Step-by-step explanation: As always to remember, all of the forming angles to a straight line with a sum of 180 degrees, so anyways, here are 6 steps in order to solve for the value of k:

Step 1. First, let's find the measures of the value of all 3 angles, the measures of all 3 angles are, 8°, 90°, and 40° that looks in the equation form like this: [tex]7k + 8 + 90 + 40 = 180.[/tex]

Step 2. Next, after finding the measures of the value of all 3 angles, it's time to add all 3 angles up together that looks in the equation form like this: [tex]7k + 138 = 180.[/tex]

Step 3. Then, let's move positive 138 to the right side so you got negative 138, and keep the positive 180 the same when moving to the left side that looks in the equation form like this: [tex]7k = 180 - 138.[/tex]

Step 4. In addition to that, after moving positive 138 to the right side so you got negative 138, and keep the positive 180 the same when moving to the left side, it's time to subtract 138 degrees and 180 degrees that looks in the equation form like this: [tex]7k = 42.[/tex]

Step 5. Now last but not least is finally, after subtracting 138 degrees and 180 degrees, it's time to divide the both sides by 7 that looks in the equation form like this: [tex]\frac{7k}{7}=\frac{42}{7}.[/tex]

Step 6. Hence the value of k is 6.

I hope that my full given answer with my full given step-by-step explanation is very helpful to your own math question about solving for the value of k with the given full of the angles, please mark me as Brainliest, take care, always be safe, and have a great rest of the day and a great weekend! :D

Sincerely,

Jason Ta,

The Ambitious of The Brainly And The Role of The TDSB And WHCI Student of The High School.

Answer:3/

1

Step-by-step explanation: 0 < 2 < 3 = 3

0 is less than 2 is less than 3 is equal to 3

0/

1

< 2/

1

< 3/

1

= 3/1

h o p e      i t      h e l p s O_O

Answer:D

Step-by-step explanation:

Answer:

x= 10 hope it helps have a nice day

Answer:

x=10

Step-by-step explanation:

[tex]\frac{8}{12} =\frac{x}{15}[/tex]

8×15=12x

120=12x

120/12=x

10=x

x=10

Hope this helps! :)

Answer:

D

Step-by-step explanation:

The degree of a polynomial is determined by the largest exponent of a term within the polynomial.

Given

7x³ + 4x - 5 + 8[tex]x^{5}[/tex]

The term with the largest exponent is 8[tex]x^{5}[/tex] with exponent 5

Thus the polynomial is of degree 5 → D

Answer:

4

Step-by-step explanation:

6/(6+6) = 5/(5+5) = (3x+5)/(5x+14) = 1/2

3x+5 = 1/2*(5x+14)

6x+10 = 5x+14

x = 4

Answer:

9 cm

Step-by-step explanation:

1/3x3=1

10-1=9

Answer:

probaly 2

Step-by-step explanation:

you have to figure out the slope.

y1 - y2/x1-x2

Step-by-step explanation:

1pound =0.4536kiligrams=,453.6grams

1square inch =2.54×2.54=6.4516

(32pounds/inch√2square

×453.6g)

(14515.2g/inch √2

÷6.4516)/6.4516

(2,262.34414)1cm√2

2262g/cm2

Step-by-step explanation:

Put the what given of y in equation 2 to equation of 1

So you get

[tex] \frac{4}{5} x + \frac{2}{5} x - 7 = - 4 \\ \frac{6}{5} x = 3 \\ x = \frac{15}{6 } \\ x = \frac{5}{2} [/tex]

Then put the value of x in second equation

You will get

[tex]y = - \frac{2}{5} \times \frac{5 }{2} + 7 \\ \\ y = 6[/tex]

Answer:

she didnt multiply 5 times 12

Answer:

The whole slices of the cakes of Luke, Kira and Ali are 6, 9 and 12 respectively. So it is possible.

Step-by-step explanation:

It's possible because they cut cakes into different number of slices.

You know that Luke, Kira and Ali each served [tex]\frac{2}{3}[/tex] of their own cake and Luke served 4 slices, Kira served 6 slices and Ali served 8 slices.

Being x the whole slices of cake, and if Luke served [tex]\frac{2}{3}[/tex] of his cake, which are 4 slices, the whole slices of cake of Luke is:

[tex]\frac{2}{3}*x=4 slices[/tex]

Solving:

x= 4 ÷[tex]\frac{2}{3}[/tex]

x= 6

Then, whole slices of Luke's cake is 6.

Performing the same approach for Kira you get:

[tex]\frac{2}{3}*x=6 slices[/tex]

x= 6 ÷[tex]\frac{2}{3}[/tex]

x= 9

Then, whole slices of Kira's cake is 9.

Finally, performing the same approach for Ali you get:

[tex]\frac{2}{3}*x=8 slices[/tex]

x= 8 ÷[tex]\frac{2}{3}[/tex]

x= 12

Then, whole slices of Ali's cake is 12.

The whole slices of the cakes of Luke, Kira and Ali are 6, 9 and 12 respectively. So it is possible.

Answer:

y=500x+25000

where y is height in ft

and x is time in minute....