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Radda [10]
3 years ago
14

Simplify the following surd expressions-

Mathematics
1 answer:
galben [10]3 years ago
8 0

Answer:

\sqrt{2} and 4\sqrt{11}

Step-by-step explanation:

To simplify like surds, add/ subtract the coefficients.

(a)

\sqrt{2} (6 - 5)

= \sqrt{2} (1)

= \sqrt{2}

(b)

\sqrt{11} ( 1 + 3)

= \sqrt{11} (4)

= 4\sqrt{11}

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3 0
3 years ago
: Find the approximate perimeter of the isosceles triangle A OPD.
AleksAgata [21]

Answer:

24.98 units

Step-by-step explanation:

The picture of the question in the attached figure

we have the coordinates

P(1,-6),D(4,3),O(7,-6)

The perimeter of triangle OPD is equal to

P=OP+PD+OD

the formula to calculate the distance between two points is equal to

d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}

step 1

Find the distance OP

we have

O(7,-6),P(1,-6)

substitute in the formula

d=\sqrt{(-6+6)^{2}+(1-7)^{2}}

d=\sqrt{(0)^{2}+(-6)^{2}}

d_O_P=6\ units

step 2

Find the distance PD

we have

P(1,-6),D(4,3)

substitute in the formula

d=\sqrt{(3+6)^{2}+(4-1)^{2}}

d=\sqrt{(9)^{2}+(3)^{2}}

d_P_D=\sqrt{90}\ units

step 3

Find the distance OD

we have

O(7,-6),D(4,3)

substitute in the formula

d=\sqrt{(3+6)^{2}+(4-7)^{2}}

d=\sqrt{(9)^{2}+(-3)^{2}}

d_O_D=\sqrt{90}\ units

step 4

Find the perimeter

P=6+\sqrt{90}+\sqrt{90}

P=6+9.49+9.49=24.98\ units

4 0
3 years ago
Can someone help with this challenging graph ​
-BARSIC- [3]

Answer:

(a) (-∞, -8) (-6, -4) (-2, ∞)

(b) -6, -2

(c) negative

(d) 5

Step-by-step explanation:

(a)  A function is "decreasing" when the y-value decreases as the x-value increases.

⇒ the function is decreasing over these intervals : (-∞, -8) (-6, -4) (-2, ∞)

(b) Local maxima are the points on the function where it reaches a maximum.

⇒ maxima at x = -6 and x = -2

(c) negative

(d) 5

5 0
2 years ago
Escape park owner was 30% of each order to include long boards he wants to know how many long boards to order out of a total of
Nataliya [291]

Answer:

He should order 15 long boards

Question:

Escape park owner want 30% of each order to include long boards he wants to know how many long boards to order out of a total of 50 skateboards

Step-by-step explanation:

Let x and y represent the number of long board and the total number of skateboard to order.

Given that 30% of each order to include long boards;

x = 30% of y

x = 0.3y .....1

But, the total number of skateboard is given as 50

y = 50

From equation 1

x = 0.3y = 0.3(50)

x = 15

He should order 15 long boards

7 0
3 years ago
What is the measure of the ​hypotenuse​ of a right triangle if the ​legs measure 6in and 8 in
nata0808 [166]

Answer:

10 in

Step-by-step explanation:

6² + 8² = c²

36 + 64 = c²

100 = c²

√100 = c

10 = c

5 0
3 years ago
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