I'll do the first problem to get you started.
Triangle SRT is a right triangle with the 90 degree angle located at angle RST. This is because segment SR is an altitude of the triangle. Altitudes of a triangle go from a vertex to the opposite side, and they are perpendicular to the opposite side.
The acute angles of right triangle SRT add up to 90 degrees. They are complementary angles.
(angle SRT) + (angle STR) = 90
(4x-8) + (6x+13) = 90 .... substitution
10x + 5 = 90
10x + 5 - 5 = 90 - 5 .... subtract 5 from both sides
10x = 85
10x/10 = 85/10 .... divide both sides by 10
x = 8.5
Therefore the answer is choice A) x = 8.5
Answer:
Step-by-step explanation:
Yes it is a quadratic equation
5x^2 + 40x = -7
5x^2 + 40x + 7 = 0
a = 5
b = 40
c = 7
-40/10 <u>+</u> (sqrt(1600 - 4(5)(7)))/10
-4 <u>+</u> (sqrt(1600-160))/10
-4 <u>+</u> (sqrt(1440))/10
-4 <u>+</u> 12(sqrt(10))/10
-4 <u>+</u> 6/5(sqrt(10))
By solving a system of equations, we will see that you must use 6.67 pounds of chocolate-covered almonds.
<h3>
How to solve the system of equations?</h3>
First, we need to define the two variables:
- x = number of pounds of the $9.99 chocolate-covered almonds used.
- y = number of pounds of the $5.99 chocolate-covered raisins used.
If we mix that, we will get:
x*$9.99 + y*$5.99 = (x + y)*C
That equation means that the cost of the individual elements of the mixture, must be equal to the total cost of the mixture. Where C is the cost of each pound of the mixture, and we know that:
C = $8.75
y = 3
Replacing that, we get:
x*$9.99 + 3*$5.99 = (x + 3)*$8.75
Now we can solve that for x:
x*$9.99 - x*$8.75 = 3*$8.75 - 3*$5.99
x*$1.24 = $8.28
x = $8.28/$1.24 = 6.67
Then you must use 6.67 pounds of the chocolate-covered almonds.
If you want to learn more about systems of equations:
brainly.com/question/13729904
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14.49272 es el resultado pues tienes que poner millares o solo dejarlo en 14.492
Answer:
58 ft squared.
Step-by-step explanation:
The formula for area of a trapezoid is (h/2)(b1 + b2). Let's plug in the values:
(4/2) * (12+17) = 2 * 29 = 58ft^2.
