We have the following equation:
h (t) = - 16t ^ 2 + 161t + 128
We substitute the value of h (t) = 170:
170 = -16t ^ 2 + 161t + 128
We rewrite the equation:
-16t ^ 2 + 161t + 128 - 170 = 0
-16t ^ 2 + 161t - 42 = 0
We look for the roots of the equation:
t1 = (161/32) + root (23233) / 32
t2 = (161/32) - root (23233) / 32
Answer:
The object is 170 feet off the ground at the following times:
t1 = (161/32) + root (23233) / 32
t2 = (161/32) - root (23233) / 32
Answer:
x=35
Angle measurements of the triangle from least to greatest:
35,40,105
Step-by-step explanation:
The sum of the angles of a triangle is 180 degrees.
So we know that 40+3x+x=180.
First step is to combine the like terms on the left hand side:
40+4x=180
Second step is to subtract 40 on both sides.
4x=140
Third step is to divide both sides by 4:
x=35
The angle that is given is the one that is 40 degrees.
So the angle whose measurement is x is really 35 degrees.
The angle whose measurement is 3x is real 3(35)=105 degrees.
In order from least to greatest we have:
35,40,105
Answer:
The ratio that exist between this three elements are 25 : 19 : 13.
Step-by-step explanation:
Ratio compares one thing to another. Ratios indicate the comparison of the size of a number to another . One trick about ratio is that you can multiply or divide the ratios by same number. For example the ratio of boy to girls can be represented as 3 : 4. If you multiply the ratios by 2 you will get the ratio 6 : 8 and it still represent the same ratios of boys to girls. Ratios can be written as a fraction for example 3/4 for our example.
The cost of the unit is made up of $6.25 , $4.75 and $3.25.
$6.25 $4.75 $3.25 . Let us multiply by 100 to remove the decimals.
625 : 475 : 325 . Now let simplify the ratios by dividing through by 25.
625/25 : 475/25 : 325/25 . The simplest ratios can be written as follows
The ratios are 25 : 19 : 13.
The perimeter of a rectangle is given by the formula,
We substitute,
and
into the above formula to obtain the expression,
We now group the x and y terms on the Left Hand Side of the equation to get.
We now divide through by 2 to get,
Therefore the width of the rectangle is
