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maw [93]
2 years ago
13

What is 922/21 as a mixed number?

Mathematics
1 answer:
Fed [463]2 years ago
4 0

Answer:

The answer is 43 and 19 over 21

Step-by-step explanation:

21 goes into 922 43 times. This giving you 903. 43 Will then be your Whole number. You the subtract 922 by 903, this giving you 19. 19 is going to be your numerator. Then you always keep the denomonator which is 21. This giving you 43 and 19 over 21

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Solve the system of equations.<br> ​ <br> −5x−3y−9=0<br> 4x−18y−54=0<br> y=? x=?<br> ​
Darina [25.2K]

Answer:

Step-by-step explanation:

Eq. 1 )   −5x−3y−9=0

Eq. 2)   4x−18y−54=0

there are two routes to solve this,   Substitution or  elimination,  I'll go for the 2nd one because I can see that the y values are a multiple of each other :)

    6 *( −5x−3y−9=0 )

Eq. 3) -30x -18y =54

subtract Eq. 2 from Eq. 3  :)

-30x -18y =54

<u>-( 4x−18y=54)</u>

-34x = 0

so according to the equations then x =0 but,  that's not really a full answer, so now we should go back and try the other method, substitution,

then:

-5x = 9 +3y

x = - 9/5 + (-3/5)y

now plug that into Eq. 2

4( - 9/5 + (-3/5)y ) - 18y = 54

-36/5 + (-12/5)y -18y = 54

(-12/5)y - (90/5)y = 54+36/5

-(102/5)*y =270/5+36/5

-(102/5)y = 306/5

y = (-5/102)*(306/5)

y = -306/102

y = -3

then plug in for either equation

-5x-3( -3) = 9

-5x + 9 = 9

-5x = 0

x = 0

now we have the full answer

check it by plugging in both x and y into the 2nd equation

4(0) - 18(-3) = 54

54= 54

this seems good  

3 0
3 years ago
Two sides of a triangle have length 6 and 8. Which of the following are possible areas of the triangle?
Svet_ta [14]

Answer:

I, II and III

Step-by-step explanation:

Two sides of a triangle have length 6 and 8.

the maximum possible area occurs in the right angle .

To find maximum area we use the area of the triangle formula

area of triangle = \frac{6 \cdot 8}{2} = 24

So maximum possible area is 24 units^2

all the given possible values are less than and equal to 24

so all the three options are correct

I, II and III

4 0
2 years ago
Dierdre’s work to solve a math problem is shown below.
kramer

Step-by-step explanation:

step 1

6 0
3 years ago
Read 2 more answers
Triangle KML and triangle PRQ are shown in the figure belowK404008 cms4 cms10 cmsOL3 cms6 cmsRM17) Are these triangles similar?1
s2008m [1.1K]

Two triangles are similar if the only difference between them is the size, this means that their internal angles must be the same. If we look at the picture the first triangle has one angle equal to 40 degrees, one equal to 80 degrees and the third one is unkown (x). The second triangle has one angle equal to 40 degrees, one equal to 60 degrees and the third one is unkown (y). The sum of the internal angles of a triangle must be equal to 180 degrees, with this information we can find the values of the missing angles. We have:

\begin{gathered} 40+80+x=180 \\ 120+x\text{ = 180} \\ x\text{ = 180-120=60} \end{gathered}\begin{gathered} 40+60+y=180 \\ 100+y=180 \\ y=180-100=80 \end{gathered}

Therefore the internal angles of the first triangle are (40,80,60) and the angles of the second triangle are (40,80,60) as well, therefore they are similar.

Two triangles are congruent if they have sides with the same length. Which is not the case, because the sides of one triangle is (8, 10, 6) while the other is (4,3 and unkown). Therefore they are not congruent.

8 0
1 year ago
Find the limit of the function algebraically. limit as x approaches negative nine of quantity x squared minus eighty one divided
scoray [572]
Let me express the equation clearly:

lim x→-9  (x²-81)/(x+9)

Initially, we solve this by substituting x=-9 to the equation. 

((-9)²-81)/(-9+9) = 0/0

The term 0/0 is undefined. This means that the solution is not see on the number line because it is imaginary. Other undefined terms are N/0 (where N is any number), 0⁰, 0×∞, ∞-∞, 1^∞ and ∞/∞. One way to solve this is by applying L'Hopitals Rule. This can be done by differentiating the numerator and denominator of the fraction independently. Then, you can already substitute the x=-9.

(2x-0)/(1+0) = 2x = 2(-9) = -18

The other easy way is to substitute x=-8.999 to the original equation. Note that the term x→-9 means that x only approaches to -9. Thus, you substitute a number that is very close to -9. Substituting x=-8.999

((-8.999)²-81)/(-8.999+9) = -18

7 0
3 years ago
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