Answer:
49 = (3 + 4)²
Step-by-step explanation:
note that 49 = 7² , then
49 = (3 + 4)²
3p-1=5(p-1)-2(-7-2p)
multiply the first bracket by 5
(5)(p)=5p
(5)(-1)=-5
multiply the second bracket by -2
(-2)(7)=-14
(-2)(-2p)=4p
3p-1=5p-5-14+4p
3p-1=5p+4p-5-14 ( combine like terms)
3p-1=9p-19
move 9p to the other side
sign changes from +9p to -9p
3p-9p-1=9p-9p-19
-6p-1=-19
move -1 to the other side
-6p-1+1=-19+1
-6p=-18
divide both sides by -6 to get p by itself
to get +p
-6p/-6=-18/-6
Answer:
p=3
Answer:
x = 4
Step-by-step explanation:
If you do not want to read the explanation go the the next part in bold
Ok so the shorter leg of the triangle is a radius of the circle. ( This is indicated by the point in the middle of the circle.) for the hypotenuse we are given one part of the length (2) The other part also happens to be a radius ( remember that a radius is a line that starts from the center of the triangle to any point of the circumference. ) Also remember that the radius is equal to 3. That being said the hypotenuse = 2+3 which equals 5.
This triangle then happens to be a right triangle. ( A triangle formed by a tangent line and a radius is a right triangle.) This means that we can use the Pythagorean theorem to solve for x.
Below here is where the work is shown
a² + b² = c². where a and b = legs and c = hypotenuse. We are given the hypotenuse (5) and a leg (3) So we plug in what we are given and solve for the missing information. 5² = 3² + b²
5² = 25
3² = 9
we would then have 25 = 9 + b²
Next we subtract 9 from each side
25 - 9 = 16
9 - 9 cancels out
Now we have 16 = b²
finally we want to get rid of the ²
To do so we take the square root of each side
![\sqrt{16}=4\\\sqrt{b^2}=b\\b = 4](https://tex.z-dn.net/?f=%5Csqrt%7B16%7D%3D4%5C%5C%5Csqrt%7Bb%5E2%7D%3Db%5C%5Cb%20%3D%204)
we're left with b = 4 which means that x = 4
11-
![\frac{1}{2} y=3+6x](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B2%7D%20y%3D3%2B6x)
Taking y to the other side;
11-3-6x=
![\frac{1}{2} y](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B2%7D%20y)
8-6x=
![\frac{1}{2}y](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B2%7Dy%20)
Multiply each side by 2
16-12x=y
y=16-12x
Answer: 0.5
Step-by-step explanation:
Given: Rectangle A′B′C′D′ is the image of rectangle ABCD after a dilation.
Since dilation always produces similar images.
To find a scale factor between two similar figures, find two corresponding sides and write the ratio of the two sides.
AB=|-5-(-8)|=|-5+8|=3 units
A'B'=|-2.5-(-4)=|-2.5+4|=1.5 units
The ratio of the corresponding sides A'B' to AB is given by :-
![\frac{1.5}{3}=\frac{1}{2}=0.5](https://tex.z-dn.net/?f=%5Cfrac%7B1.5%7D%7B3%7D%3D%5Cfrac%7B1%7D%7B2%7D%3D0.5)
hence, the scale factor of the dilation = 0.5