Answer:
Step-by-step explanation:
Given
Required
Determine CD
Since Point C is on segment BD, then we have
Substitute x + 4 for BC; 5x for CD and 5x + 7 for BD
Collect Like Terms
Multiply both sides by -1
Substitute 3 for x in
Hence, the length of CD is 15 units
Step-by-step explanation:
To find the length of CD, set BC equal to BD and solve for x. Substitute the value of x into CD to find the numerical length.
To determine the length of CD, we need to find the value of x first. We can do this by setting the expressions for BC and BD equal to each other and solving for x. So, x + 4 = 5x + 7. Solving this equation, we find that x = -1. Now we can substitute this value of x into the expression for CD, giving us CD = 5(-1) = -5. However, since lengths cannot be negative, we take the absolute value to find that the numerical length of CD is 5.
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The percentage is the change with respect to the original thus the percentage increase in her pay will be 20%.
The percentage is defined as a given amount in every hundred. It is a fraction with 100 as the denominator percentage is represented by the one symbol %.
The percentage is also called the indicatinghundredths. Thus, 2% is two-hundredth, which means 2%=2/100=0.02.
As per the given,
Originalamount = $10
Increased pay = $12
% increase = (12 - 10)/10 x 100
⇒ 20%
Hence "The percentage is the change with respect to the original thus the percentage increase in her pay will be 20%".
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x = 3; the diver hits the water 3 feet away horizontally from the board
x = 10; the diver jumps in the pool at 10 feet per second
x = 3; the diver jumps in the pool at 3 feet per second
The diver hits the water 3 feet away horizontally from the board.
The correct option is (b)
A quadratic equation is a second-order polynomial equation in a single variable x, ax²+bx+c=0 with a ≠ 0 .
Given function: f(x)= -x² -7x +30
Factorising f(x), we get
-x² -7x +30 =0
x² +7x -30 =0
x² +10x - 3x -30 =0
x(x+10)-3(x+10)=
(x+10)(x-3)=0
The roots of this quadratic equation are x = 3 and -10.
As, the diver is on a diving board we will not use -10.
Hence, the diver hits the water 3 feet away horizontally from the board.
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Answer:
50 boys
Step-by-step explanation:
The number of groups = 24
The average number of children = 16
The new average number of children when one group is added = 18
The ratio of boys to girls in the group that just joined = 5:6
The initial number of boys = 220
Let the initial number of children
The initial total number of children = 24 × 16 = 384
The initial number of girls = 384 - 220 = 164
The final number of children = 25 × 18 = 450
The number of children in the group that joined in the game = 450 - 384 = 66
The ratio of boys to girls in the group = 5:6
Therefore, we get;
The number of boys = 66 × 5/11 = 30
The number of girls = 66 - 30 = 36
The number of boys at the end = 220 + 30 = 250
The number of girls at the end = 164 + 36 = 200
The number of more boys than girls at the end = 250 - 200 = 50
The number of more boys than girls at the end = 50 boys