Rút gọn các biểu thức sau:

Write the phrase as a numerical expression.

mariarad [96]

3. 8+5

4. 2x - 8

Step-by-step explanation:

3. for example : 5 more than the number means

x+5 so that's how we get the answer as 8+5

4. This can be explained in two folds firstly, for example: 2 less than the number means x-2.

secondly;7 times the number means 7x so therefore we get our final answer as 2x - 8

7 0

3 years ago

Find the vertex : f(x)=3x^2-18x+10

Vlad [161]

f(x)=3x^2-18x+10

a = 3, b = -18 and c = 10

The vertex of a parabola is in form a(x+d)^2 + e

d = b/2a = -18/2(3) = -18/6 = -3

e = c-b^2/4a = 10 - -18^2/4(3) = 10-27 = -17

Now the vertex form of the parabola becomes 3(x-3)^2 -17

Use the vertex form of the parabola in the vertex form of y = a(x-h)^2 +k

Where a = 3, h = -3 and k = -17

Now you have y = 3(x-(-3))^2 +(-17)

Simplify: y = 3(x+3)^2 -17

The vertex becomes the h and k values of (3,-17)

3 0

3 years ago

A helicopter is flying at an elevation of 575 feet directly above a horizontal highway. Two motorists are driving cars on the hi

Ket [755]

Answer:

Distance between cars rounded to the nearest foot is : 1903 ft

Step-by-step explanation:

Notice that two right triangles can be used to represent the diagram of this situation. One between the car whose angle of depression is $28^o$ , and the other with the car with angle of depression $35^o$ (see attached image)

Each triangle in the attached image is depicted with a different color. and as one can see, the distance between both cars is the addition of the side "x" in one triangle, to the side "y" in the other.

Notice as well that the information known for both right-angle triangles is one acute angle, and the side opposite to it. And what one needs to find is the side adjacent to this acute angle. Then, the function to use in both triangles, is the tangent:

a) For the $28^o$ [orange] triangle :

$tan(28^o)=\frac{575}{y} \\y=\frac{575}{tan(28^o)} \\y=1081.42\,\,ft$