Answer:
a. x = 7
b. x = 36/5
Step-by-step explanation:
<u>Points to remember</u>
The ratio of of corresponding sides of similar triangles are equal.
<u>a). To find the value of x</u>
From the figure 1 we get two similar triangles, ΔABC and ADE
We can write,
AB/AD = AC/AE
3/6 = x/(x + 7)
3(x + 7) = 6 * x
3x + 21 = 6x
6x - 3x = 21
3x = 21
x = 21/3 = 7
<u>b). To find the value of x</u>
From the figure b we get
ΔABC ~ ΔEDF
AB/DE = BC/DF
4/5 = x/9
x = (4 * 9)/5 = 36/5
9514 1404 393
Answer:
3. $6000 at 8%; $5000 at 5%
4. 66 2/3 gallons of 9%; 133 1/3 gallons of 6%
Step-by-step explanation:
For many mixture problems, it works well to let a variable represent the amount of the largest contributor used in the mix.
3. Let x represent the amount invested at 8%. Then the total interest is ...
8%x +5%(11000-x) = 730
3%x = 730 -550
x = 180/0.03 = 6000
$6000 was invested at 8%; $5000 was invested at 5%.
__
4. Let x represent the number of gallons of 9% content. Then the alcohol content of the mix is ...
9%x +6%(200 -x) = 7%(200)
3%x = 1%(200) . . . . . subtract 6%(200)
x = 200/3 = 66 2/3 . . . . . divide by 3%
200 -x = 133 1/3
66 2/3 gallons of 9% wine and 133 1/3 gallons of 6% wine should be used.
Answer:
90 square feet
Step-by-step explanation:
36 square feet divided by 4 square yards equals to 9 square feet for 1 square yard.
9 square feet times 10 square yards equals to 90 square feet.
Answer:
We have the functions,
and 
.
After plotting both the functions, we see that,
The graph of F(x) is given below, which has the y-intercept at (0,-1.5) and its horizontal asymptote is x-axis.
Also, the graph of f(x) is a straight line passing through (-4,0) and (0,2).
Further, we can see that the two graphs have intersection points as (-4.873,-0.436) and (2.873,3.436).
