Answer:
UV=29
Step-by-step explanation:
In right triangles AQB and AVB,
∠AQB = ∠AVB ...(i) {Right angles}
∠QBA = ∠VBA ...(ii) {Given that they are equal}
We know that sum of all three angles in a triangle is equal to 180 degree. So wee can write sum equation for each triangle
∠AQB+∠QBA+∠BAQ=180 ...(iii)
∠AVB+∠VBA+∠BAV=180 ...(iv)
using (iii) and (iv)
∠AQB+∠QBA+∠BAQ=∠AVB+∠VBA+∠BAV
∠AVB+∠VBA+∠BAQ=∠AVB+∠VBA+∠BAV (using (i) and (ii))
∠BAQ=∠BAV...(v)
Now consider triangles AQB and AVB;
∠BAQ=∠BAV {from (v)}
∠QBA = ∠VBA {from (ii)}
AB=AB {common side}
So using ASA, triangles AQB and AVB are congruent.
We know that corresponding sides of congruent triangles are equal.
Hence
AQ=AV
5x+9=7x+1
9-1=7x-5x
8=2x
divide both sides by 2
4=x
Now plug value of x=4 into UV=7x+1
UV=7*4+1=28+1=29
<u>Hence UV=29 is final answer.</u>
Answer:
b. y = -9
Step-by-step explanation:
A line with zero slope has no dependence on x. It is simply ...
... y = constant
The constant must be the same as the y-value of the point you want the line to go through. Since the point is (12, -9), the constant is -9 and the equation is ...
... y = -9
Divide 7% into $240 dollars and hat should get you your answer.
hope this helps!
Distance Formula: 
Point 1: (9,0)
Point 2: (5,-8)
D = sqrt[ (5 - 9)^2 + (-8 - 0)^2 ]
D = sqrt[ (-4)^2 + (-8)^2 ]
D = sqrt[ 16 + 64]
D = sqrt(80)
Hope this helps!
Since it includes 11% sales tax, this means that (purchase)+11% of (purchase)=25.00. Since 11% = 0.11 by multiplying it by 1/100, we have 1*purchase+0.11*purchase=1.11*purchase=25.00. Dividing both sides by 1.11, we get around 22.73 as the original purchase. This means that the difference between the purchase price and the total price is the sales tax, which is around 2.27 dollars.
Feel free to ask further questions!
