Answer:
By trigonometric ratio;
XZ/sin(b) = XY/sin(c) = YZ/sin(a)
MN/sin(c) = NZ/sin(f) = MZ/sin(d)
∴ XZ/MZ = XY/MN × (sin(b)/(sin(d))
XY/MN = XZ/MZ × (sin(b)/sin(d))
Where (sin(b)/(sin(d)) = V;
(XZ/MZ)/(XY/MN) = (XY/MN × V)/(XZ/MZ × V)
(XZ/MZ)/(XY/MN) = (XY/MN)/(XZ/MZ)
∴ (XZ/MZ)² = (XY/MN)²
∴ XZ/MZ = XY/MN QED
Step-by-step explanation:
Whereby the shapes in the question are triangles ΔXYZ and ΔMNZ, and given that we have;
XZ/MZ = YZ/NZ, and from the attached drawing, we have;
∠XZY = ∠NZM
By trigonometric ratio, we have;
XZ/sin(b) = XY/sin(c) = YZ/sin(a)
∴ XZ = sin(b)×XY/sin(c)
MN/sin(c) = NZ/sin(f) = MZ/sin(d)
MZ = sin(d)×MN/sin(c)
∴ XZ/MZ = sin(b)×XY/sin(c)/(sin(d)×MN/sin(c)) = XY/MN × (sin(b)/(sin(d))
XY = sin(c) × XZ/sin(b), MN = sin(c) × MZ/sin(d)
XY/MN = sin(c) × XZ/sin(b)/(sin(c) × MZ/sin(d)) = XZ/MZ × (sin(b)/sin(d))
Let 'V' represent (sin(b)/(sin(d)), we have;
XZ/MZ = XY/MN × V...(1)
XY/MN = XZ/MZ × V...(2)
Dividing equation (1) by (2) gives;
(XZ/MZ)/(XY/MN) = (XY/MN × V)/(XZ/MZ × V) = (XY/MN)/(XZ/MZ)
(XZ/MZ)/(XY/MN) = (XY/MN)/(XZ/MZ)
∴ (XZ/MZ)² = (XY/MN)²
∴ XZ/MZ = XY/MN
Select the two values of x that are roots of this equation.
x2 - 5x + 2 = 0
Answer:
C and D
[tex] {x}^{2} - 5x + 2 = 0 \\ x = \frac{5± \sqrt{17} }{2} [/tex]
does this look correct ?
Answer: it looks correct to me!!!
Look at the attached picture above
(just from the top half, then apply this same thing to the rotated/reflected bottom half)
I NEEDDD HELPPPPP PLEASEEE
Answer:
#3
Hope this helped! Please give brainliest to let me know <3
Step-by-step explanation:
Presale tickets (p) are each worth $7: represented in the equation as 7p.
Door tickets (d) are each worth $10: represented in the equation as 10d.
They sold 345 tickets, so p+d=345. They collected $2550, so 7p+10d=2550.
Final answer:
(3) [tex]\left \{ {{7p+10d=2550} \atop {p+d=345}} \right.[/tex]
complete the solution find the value of y when x equals 1 9x+7y=-12
Solve for x. Round to the nearest tenth, if necessary.
Answer:
Step-by-step explanation:
take 60 degree as reference angle
using cos rule
cos 60=adjacent/hypotenuse
1/2=80/x
x=80*2
x=160
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
a triangle with side lengths of 15,30, and 35 is a right triangle. true or false?
Answer:
false
Step-by-step explanation:
15²+30² = 225+900 = 1125
35² = 1225
Since Pythagoras theorem doesn't hold for this triangle, it is not a right triangle.
oanciewuv bwhgubviweucnwelkv helppppppppppp
Answer:
-4 19/20
Step-by-step explanation:
2 1/5 ÷ -4/9
Change to an improper fraction
(5*2+1)/5 =11/5
Copy dot flip
11/5 * -9/4
-99/20
Changing back to mixed number
-4 19/20
Answer:
-99/20 or -4.95
Step-by-step explanation:
make the first fraction a simple fraction by multiplying the denominator by the whole number and adding the numerator.
which equals 11/5. Then you multiple by the reciprocal of 4/-9 which is -9/4
to look like 11/5 * -9/4 = -99/20
You are jumping on a trampoline. For one jump, your height y (in feet) above the trampoline after t seconds can be represented by y= -16t^2+24t. How many seconds are you in the air?
Answer:
[tex]1.5\; \rm s[/tex].
Step-by-step explanation:
The person in this question is in the air whenever the height is greater than [tex]0[/tex].
The graph of [tex]y = -16\, t^{2} + 24\, t[/tex] is a parabola opening downwards. Rearrange and find values of [tex]t[/tex] that would set this expression to [tex]0[/tex].
[tex]\begin{aligned}y &= -16\, t^2 + 24\, t \\ &= t\, (-16\, t + 24) = -8\, t\, (2\, t - 3)\end{aligned}[/tex].
The first factor, [tex]t[/tex], suggests that [tex]t = 0[/tex] would set this expression to [tex]0[/tex]- quite expected, since the person is on the ground right before jumping.
The second factor, [tex](2\, t - 3)[/tex], suggests that [tex]2\, t = 3[/tex] (in other words, [tex]t = 3/2 = 1.5[/tex]) would also set this expression to [tex]0[/tex]. Hence, this person would be once again on the ground [tex]1.5[/tex] seconds after jumping.
Hence, this person is in the air between [tex]t = 0[/tex] and [tex]t= 1.5[/tex] for a total of [tex]1.5\; \rm s[/tex].
You bike 4 miles the first day of your training 4.5 miles a second Day 5.5 miles a day day and 7.5 miles the fourth day if you continue this pattern how many miles do you bike the seventh day
Answer:
rth sdh h trh
Step-by-step explanation:
trh rhgf
How do I do this (With instructions if you could) (Will give brainliest)
A submarine begins its descent from the surface of the water and dives 20 feet for each minute. What would be the depth of the submarine after 2/3 hours?
Answer:
Distance = speed * time
Convert feet to meter (C units) = about 6
Convert hours to second (C units) = about 2399
Distance = 6 * 2399
= 1439 meters
4721 foot
Write the slope-intercept form of the equation for the line
Find the solution set of this inequality. Enter your answer in interval notation using grouping symbols. -2x+5<3
Step-by-step explanation:
-2x+5<3
-2x>3-5
-2x>-2
Divide both sides by -2
x>1
Answer:
-2x+5<3
-2x<-2
x<1
Solve for x:−2(x+9)=−1(x+−1)+2
Answer:
A
Step-by-step explanation:
expanding the bracket, we would have
-2x -18 = -x+1+2
-2x+x= 3 +18
-x=21
x=-21
Answer:
A
Step-by-step explanation:
−2(x+9)=−1(x+−1)+2
Use distributive property
-2x - 18 = -1x + 1 +2
-2x - 18 = -1x + 3
+18 +18
-2x = -1x +21
+1x +1x
___________
-x = 21
we need to have a positive x so multiply x by -1. -x times -1 = x
What we do on the left side has to happen to the right side too
So, 21 times -1 = -21
Therefore, x = -21
Hope this helps :)
A Rice Krispies Treats Recipe calls for 3 cups of
marshmallows and 1/2 box of Rice Krispies
1. How many cups of marshmallows do you need if you are using a box of Rice
Krispies?
A complete answer includes:USE CROSS PRODUCT, All steps for solving the problem
shown, Final answer with correct labels
2. Complete the ratio table based on the Rice Krispies Treats Recipe. Fill out all entries.
3
6
10
18
Cups of
Marshmallows
1/2
8
Boxes of Rice
Krispies
MacBook Pro
Answer:
1 is the answer have a good day
Rachel has two coupons for a bicycle.
Coupon A:
15% off of a $95 bicycle
$18 rebate on a $95 bicycle
Coupon B:
Choose the coupon that gives the lower price.
Then fill in the blank with the correct value.
Coupon A gives the lower price.
Х
The price with coupon A is $(less than the price with coupon B.
Coupon B gives the lower price.
The price with coupon B is $ less than the price with coupon A.
$
Answer: Coupon B gives the lower price
The price of coupon B is 3.75 dollars less than the price of coupon A.
======================================================
Explanation:
15% off means she saves 15% of the original price.
15% of 95 = 0.15*95 = 14.25
Rachel saves $14.25 if she goes with coupon A.
We can see that coupon B gives the lower price because we have more in savings (since 18 is larger than 14.25).
If she goes with option A, then she spends 95-14.25 = 80.75 dollars. If she goes with option B, then she spends 95-18 = 77 dollars. Going with option B means she saves 80.75-77 = 3.75 dollars
Or you could note that 18-14.25 = 3.75 is another way to find out how much is saved when comparing the two coupons.
hey you guys its your favorite gal, hopin in to ask a couple more questions for the better in me (im honestly just asking for points and for answers, thanks for being loyal as always )
Select the correct answer.
Martin runs 100 meters in 15 seconds. What is the equation for d, the distance in meters that Martin covers per second?
A.
15 + d = 100
B.
100 + d = 15
C.
d × 15 = 100
D.
d × 100 = 15
Answer:
c
Step-by-step explanation:
We are dividind how 100 can fit in 15 seconds
which is 100 /15
therefore when C when u tak it to the other side it divides 100 in 15
d×15=100
d=100/15
Use the law of cosines to find the length of side C.
Answer:
[tex]\text{D. 36.64}[/tex]
Step-by-step explanation:
The Law of Sines is given by [tex]\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}[/tex] and works for any triangle.
Therefore, we have the proportion:
[tex]\frac{c}{\sin 41.5^{\circ}}=\frac{37}{\sin 42^{\circ}},\\\\c=\frac{37\sin 41.5^{\circ}}{\sin 42^{\circ}}=36.6399945706\approx \boxed{36.64}[/tex]
Evaluate 32 + (7 − 2) ⋅ 4 − 6 over 3 . (1 point)
Answer:
50
Step-by-step explanation:
Given:
32 + (7 − 2) ⋅ 4 − 6/3
Using the acronym PEMDAS
P = parenthesis
E = Exponential
M = Multiplication
D = Division
A = Addition
S = Subtraction
32 + (7 − 2) ⋅ 4 − 6/3
= 32 + (5) • 4 - 6/3
= 32 + 20 - 6/3
= 32 + 20 - 2
= 52 - 2
= 50
Therefore,
32 + (7 − 2) ⋅ 4 − 6/3 = 50
Suppose f(x) = mx + b. What is the inverse function in terms of m and b?
Answer:
f^(-1)(x) = (x-b)/m or x/m - b/m
Step-by-step explanation:
f(x) = y = mx + b
To find the inverse function, interchange x and y and solve for y, i.e.
x = my + b
my = x-b
y = (x-b)/m = x/m - b/m
press the image to see the whole question
Let x be the hottest temperature.
Equation: x - (-35.67) = 148.98
So,
x - (-35.67) = 148.98
=> x + 35.67 = 148.98
=> x = 148.98 - 35.67
=> x = 113.31
what is the vertex form of the equation y equals 3x squared + 6x - 4
Answer:
y = 3(x + 1)² - 7
Step-by-step explanation:
y = 3x² + 6x - 4
First, factor out the coefficient of the quadratic eq'n:
y = 3(x² + 2x - ⁴/₃)
Use the "complete the square" rule;
The "x² + 2x" should be rewritten as "(x + 1)² - 1", i.e. place into squared brackets x (without the power 2) and add half the coefficient of the x-term, you then need to subtract the square of the constant term in the squared brackets and then simplify:
y = 3((x + 1)² - 1 - ⁴/₃)
y = 3((x + 1)² - ⁷/₃)
Finally, multiply the 2 terms you end up with by the 3, factored out initially:
y = 3(x + 1)² - 7
What point is this?
A milkman pays tk.6.40 per liter of milk.He adds water and sells the mixture at tk.8 per liter.By doing this,he makes 37.5% profit.Find the proportion of water to milk received by the customers?
Answer:
1 : 10
Step-by-step explanation:
Let :
Water = x
Milk = y
Purchase = 6.4 * y = 6.4y
Sales = 8(x + y)
Profit accrued = 37.5%
Sales = profit made from sales
8(x + y) = 6.4x * (100%+37.5%)
8(x + y) = 6.4x * 1.375
8x + 8y = 8.8x
8y = 8.8x - 8x
8y = 0.8x
y/x = 8/0.8
y/x = 10 / 1
y : x = 10 : 1
in math what are 3 ways numbers are related
Answer:Recognise three numbers that are related through the operations of addition and subtraction.
Recognise that there are two related addition and two subtraction equations in a 'family of facts'.
Write and read sets of related addition and subtraction equations.
Step-by-step explanation:that is all
CD is a perpendicular bisector of chord AB and a chord through CD passes through the center of a circle. Find the diameter of the wheel.
Answer:
[tex]12\frac{1}{5}[/tex] in
Step-by-step explanation:
I don't know if you got this pic but this is the answer for this pic
Suppose you are making a deposit into your checking account. You have a check for $350, cash and coins totaling $225 and you want to receive a $100 bill. What is the total deposit amount? (Show your work)
Answer:
The total deposit amount is 225.
Step-by-step explanation:
-350 + 225 + x = 100
-125 + x = 100
x = 225
Hope this helps. :)
Stay safe, happy, and healthy. Have a great day!
What is the slope of the line that passes through the points (0, -2) and (9,-5)?
Answer:
-1/3
Step-by-step explanation:
y2 - y1 / x2 - x1
-5 - (-2) / 9 - 0
-3 / 9
-1/3
Help me really quick pleaseeee
Manny's Mexican Restaurant has a policy of adding
a 17% automated tip if you have a party of 8 or
more.
Write an equation to represent the relationship
between tip(t) and the billib).
Answer:
Use the equation ?/45.20 = 35\100 and what you get is your answer
Hope this helps
Step-by-step explanation:
solve the simultaneous linear algebra quadratic equation 2x-y=8 3x-y=17
Answer:
2x-y=8
(3x-y=17)*_1
2x-y=8
-3x+y=-17
#-x=-9, x=9 & y=-10
Answer:
x = 9 and y = 10
Step-by-step explanation:
Subtract the second equation from 1 as in doing so the y will get cancelled as they are of the opposite sign.
2x - y = 8
-3x + y = -17
-----------------
- x = - 9
Therefore,
x = 9
Now we will add the value of x to any of the equation from the question.
2x - y = 8
2(9) - y = 8
18 - y = 8
Therefore,
y = 10
