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The difference of number p and 2 is at least 5

hichkok12 [17]

Step-by-step explanation:

The difference of number p and 2 is at least 5

means

p - 2 ≥ 5

then

p ≥ 7

6 0

3 years ago

Quadrilateral ABCD is translated to get quadrilateral A'B'C'D'. vertex A is at (-5,2) , and vertex A' is ay (2,-2), quadrilatera

belka [17]

Answer:

(-1,3)

Step-by-step explanation:

Given that the quadrilateral ABCD is translated to get quadrilateral A'B'C'D'. The vertex A is at (-5,2) is translated to vertex A' is at (2,-2).

The translation is x-direction, a, is the difference of x-coordinates of both the points, a=2-(-5)=2+5=7.

The translation is y-direction, b, is the difference of y-coordinates of both the points, b = -2-2 = -4.

As all the points are translated by the same magnitude as well as in the same direction, so by adding a to x and b to y coordinate of any points, the translated point can be determined.

The vertex of point B is (-6,5), so, the vertex of the point B' would be (-6+a, 5+b)=(-6+7, 5+(-4))=(-1,3).

Hence, the vertex of point B' is (-1,3).

5 0

3 years ago

Isosceles right triangle ABC has a hypotenuse, AB, with a length of 18 feet.

kiruha [24]

we know that

if ABC is an isosceles right triangle

then

side AC=side BC

angle A=angle B=45 degrees

cos B=adjacent side angle B/hypotenuse

adjacent side angle B=BC

hypotenuse=AB------> 18 ft

angle B=45 degrees

cos 45°=(√2)/2

so

cos 45°=BC/AB-------> solve for BC

BC=AB*cos 45-------> BC=18*(√2)/2------> BC=9√2 ft

AC=BC--------> AC=9√2 ft

the answer part 1) is

the exact lengths of the two sides, AC and BC is

AC=9√2 ft

BC=9√2 ft

Part b) Find the Area of triangle ABC

Area=b*h/2-------> AC*BC/2-----> (9√2)*(9√2)/2--------> 81 ft²

the answer part b) is

the area of triangle ABC is equal to 81 ft²

7 0

3 years ago

A 26 ft long ramp is used to reach 10 ft up a wall. The ramp covers a horizontal distance of 24 ft. To make the ramp less steep,

Anika [276]

Answer:

The length of new ramp is 49.03 ft.

Step-by-step explanation:

It is given that 26 ft long ramp is used to reach 10 ft up a wall. The ramp covers a horizontal distance of 24 ft.

If the horizontal distance is doubled, then the horizontal distance is 48 ft. The height remains same. Therefore the height of ram is 10 ft.

Use pythagoras in new right angle triangle.

$hypotenuse^2=base^2+perpendicular^2$

$(AE)^2=(AD)^2+(ED)^2$

$(AE)^2=(48)^2+(10)^2$

$(AE)^2=2304+100$

$AE=\sqrt{2404}$

$AE=49.0306027\approx 49.03$

Therefore the length of new ramp is 49.03 ft.

7 0

3 years ago

3 pounds of bananas cost $7. At this rate, how much does 1 pound of bananas cost?

Furkat [3]

Answer:

Step-by-step explanation:

To find the cost of 1 pound of bananas we use ratio and proportion

From the question

3 pounds of bananas costs $7

Then 1 pound will cost

$\frac{7 \times 1}{3} = \frac{7}{3 } \\ = 2.33333...$

We have the final answer as

Hope this helps you

7 0

3 years ago