[tex]\bold{\huge{\blue{\underline{ Solution }}}}[/tex]
Given :-Here, We have,
[tex]\sf{\dfrac{a}{b}}{\sf{=}}{\sf{\dfrac{b}{c}}}{\sf{=}}{\sf{\dfrac{c}{d}}}[/tex]To Prove :-We have to prove that √(a - b - c)(b-c-d) = √ab-√bc-√cdLet's Begin :-[tex]\sf{√(a-b-c)(b-c-d)=√ab-√bc-√cd}[/tex]
Let [tex]\sf{\dfrac{a}{b}}{\sf{=}}{\sf{\dfrac{b}{c}}}{\sf{=}}{\sf{\dfrac{c}{d}}}{\sf{ = k}} [/tex]Therefore,From above, We can conclude that,
a = bk, b = ck, c = dk
a = dk³ , b = dk² , c = dk
By solving RHS :-
[tex]\sf{√(a - b - c)(b-c-d) }[/tex]
[tex]\sf{√(dk³ - dk² - dk) (dk² - dk - d) }[/tex]
[tex]\sf{√d(k³- k² - k) d(k² - k - 1)}[/tex]
[tex]\sf{d√(k³- k² - k) d(k² - k - 1)}[/tex]
[tex]\sf{d√k(k²- k - 1)(k² - k - 1)}[/tex]
[tex]\sf{d(k²- k - 1)√k ...eq(1)}[/tex]
By solving LHS :-
[tex]\sf{√ab - √bc - √cd}[/tex]
[tex]\sf{√dk³(dk²) - √dk²(dk)-√dk(d)}[/tex]
[tex]\sf{√d²k^5 - √ d²k³ - √d²k}[/tex]
[tex]\sf{dk²√k - dk√k - d√k}[/tex]
[tex]\sf{(dk² - dk - d)√k}[/tex]
[tex]\sf{d(k²- k - 1)√k...eq(2)}[/tex]
From eq(1) and eq(2)
[tex]\bold{\red{ LHS = RHS }}[/tex]
That is,
[tex]\sf{√(a-b-c)(b-c-d)=√ab-√bc-√cd}[/tex]
Hence proved .Yes, the RHS and the LHS are equal/
Calculations and Parameters:Given:
[tex]a/b= b/c = c/d[/tex]
We have to prove that √(a - b - c)(b-c-d) = √ab-√bc-√cd
Hence, after we expand the brackets and evaluate, we see that:
a = bk, b = ck, c = dka = dk³ , b = dk² , c = dkAfter the evaluation of the RHS and LHS, we can see that
RHS= LHS .
Read more about maths expressions here:
https://brainly.com/question/2164351
What is the quotient of 840 divided by 70 with a remainder?
Answer:
the quotient is 12 and there is no remainder
Step-by-step explanation:
An unknown number is twelve less than
four
Answer:
-8
Step-by-step explanation:
4 - 12 = -8 hope I'm right lol
what is 13,300 divisble by
Answer:
the answer is 133×100 is 13,300........
I WILL REPORT IF ANY LINKS
Answer:
15$ a day would be the estimate for 1 day
Step-by-step explanation:
Part a)
The diagonal line goes through (0,15) and (2,20)
Find the slope based on those points
[tex](x_1,y_1) = (0,15) \text{ and } (x_2,y_2) = (2,20)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{20 - 15}{2 - 0}\\\\m = \frac{5}{2}\\\\m = 2.5\\\\[/tex]
The y intercept is b = 15 because this is where the line crosses the y axis.
We go from y = mx+b to y = 2.5x+15.
Now plug in x = 1 to find the cost of renting for one day.
y = 2.5x+15
y = 2.5*1+15
y = 17.5
Another way to get the answer is to start at 1 on the x axis number line. Draw a vertical line upward until you reach the curve. From there, draw a horizontal line toward the y axis (refer to the diagram below). You should land somewhere between 15 and 20. The midpoint of which is 17.50
Answer: $17.50=====================================================
Part b)
We can do the reverse idea of the previous part.
Start at y = 25 on the y axis. Draw a horizontal line toward the curve. After reaching the curve, draw a vertical line down until you hit the x axis. You should arrive at x = 4.
Or you can use the algebraic approach since we know the cost equation
y = 2.5x+15
25 = 2.5x+15 ... plug in y = 25
25-15 = 2.5x
10 = 2.5x
2.5x = 10
x = 10/(2.5)
x = 4
Answer: 4 daysA realtor uses a lock box to store the keys to a house that is for sale. The access code for the lock box consists of six
digits. The first digit cannot be 4 and the last digit must be even. How many different codes are available? (Note that 0
is considered an even number.)
Answer:
450,000
Step-by-step explanation:
The first digit has 9 choices
Digits 2 through 5 each have 10 choices
Digit 6 has 5 choices.
9 * 10 * 10 * 10 * 10 * 5 = 450,000
Please help FAST!!!!!
Answer:
Step-by-step explanation:
Pretty obvious this is an exponential decay graph, so it's either 'divide' or 'multiply'.
what is the slope of y−4=−7(x−6)
Answer:
slope = - 7
Step-by-step explanation:
The equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b ) a point on the line
y - 4 = - 7(x - 6) ← is in point- slope form
with slope m = - 7
Answer:
M= -7
Step-by-step explanation:
y - b = m(x - a)
where m is the slope and (a, b ) a point on the line
y - 4 = - 7(x - 6) ← is in point- slope form
with slope m = - 7
pls branliest
-3÷3(a+c(b+5)-(-6+a)) use a=1 b= -6 and c= -4
Answer:
2
Step-by-step explanation:
-3÷3 (1 + (-4) (-6 + 5) - (-6 + 1)
-3 ÷ 3 (-3)(-1) - (-5)
-3 ÷ 3(3) + 5
-3 ÷ 3 = -1
-1(3) + 5
-3 + 5 = 2
I hope this helps!
Drag each number to show whether it is a prime number or a composite number.
Three of the numbers are prime, and three are composite.
Prime:
Composite:
26,3,33,85,61,41
pls help me
PRIMES: 3, 61, 41
COMPOSITES: 26,33,85
how can i solve it formula y= mx + b
Answer:
y = 4/3x - 4
Step-by-step explanation:
you are given b
so y = mx -4
you can look at the graph and see the slope from there. like the y-intercept and the x-intercept
(0,-4) and (3,0)
slope formula is y2-y1/x2-x1
and so you do -4-0/0-3
-4/-3.
so your slope formula would be
y = 4/3x - 4
round 691 513 to the nearest thousand
[tex]691 \: 513 \: = > nearest \: to \: thousands \\ = > \: \: \: \: \: \: \: \: 692 \: 000[/tex]
Two trains leave the station at the same time, one heading east and the other west. The eastbound train travels 18 miles per hour slower than the westbound train. If the two trains are 570 miles apart after 3 hours, what is the rate of the eastbound train?
Formula: Distance = rate * time
570 = (R+(R-18))*3
570 = (2R - 18)*3
190 = 2R-16
208 = 2R
R = 104
Eastbound Train: 86mph
Westbound Train: 104mph
i really need some help on this math problem?can you help me
Answer:
7 units
Step-by-step explanation:
Forming an equation:
There is a one-time signup fee. Let that be represented by "a".
Then, there's also a weekly fee. Let that be represented by "b", i.e., the fee for one week is "b" units.
==> If she goes to the gym for x weeks, then her total weekly fee will be "b" times "x" units.
If we represent her total cost after membership by "y", our equation becomes:
[tex] \boxed{ \sf{y = a + bx}}[/tex]
We're provided with three values of x and y.
When x = 6, y = 133When x = 12, y = 175When x = 24, y = 259The solution to the equation:
Substitute the respective values of x and y into the equation.
#1
133 = a + 6b
==> a = 133 - 6b
#2
175 = a + 12b
Since we only need the values of two variables we'll use only two equations.
Substituting from #1 for a:
175 = (133 - 6b) + 12b
==> 175 = 133 + 6b
==> 175 - 133 = 6b
==> 42 = 6b
==> b = 7
And b is the amount she pays each week.
So, the answer is 7 units.
round to the nearest hundredths
Answer:
AC = 2.96
Step-by-step explanation:
Use the trigonometric ratio cosine:
cosine = adjacent ÷ hypotenuse
cos(65°) = AC ÷ 7
[tex]cos(65) = \frac{AC}{7}[/tex]
Multiply both sides by 7:
7(cos(65)) = AC
(Note: Set your calculator to degrees!)
And plug 7(cos(65)) into your calculator to get:
AC ≈ 2.96
PLEASE HELP ME WITH THIS I NEED HELP
Answer:
a. y = -x
b. Area = xy
c. x = -y
Step-by-step explanation:
a. The perimeter of the garden is the distance all the way around, in this would be x+y+x+y, or 2x + 2y. To solve for y, we’re trying to isolate it on one side. We need to subtract 2x to get 2y = -2x. Divide by 2 to get y = -x.
b. Area is length times width, so x • y, or xy.
c. To express in terms of x, we can take the equation y = -x and multiply it by -1 to get x = -y
what is 3/8 x(1 -1/3)
Answer:
1/4x
Step-by-step explanation:
3/8x(1-1/3)
3/8x - 1/8x = 1/4x
I hope that's right.
Montrer que le cube d’un nombre pair est un multiple de 8
Answer:
so the answer is 16? I dont know , need a better explanation on the question. ill answer until then.
Step-by-step explanation:
Answer:
56
Step-by-step explanation:
the answer might be 56
1/4 + -3/4 fractions
c. help please i need asap
Can someone please help me? I will mark as brainliest. Thank you!!
Answer:
a = 6.5 mperimeter = 52 mStep-by-step explanation:
The shape is a trapezoid on top of a parallelogram. The areas of each of the figures can be found separately, then added together.
Trapezoid areaThe area formula is ...
A = 1/2(b1 +b2)h . . . . where b1, b2 are the base lengths and h is the height
A = 1/2(12 +a)(7) = 3.5(12 +a) = 42 +3.5a
__
Parallelogram areaThe area formula is ...
A = bh
A = (12)(9) = 108
__
The area of the figure is then ...
total area = trapezoid area + parallelogram area
172.75 = 42 +3.5a + 108
22.75 = 3.5a . . . . . . . . . . . . subtract 150
6.5 = a . . . . . . . . . . divide by 3.5
The length 'a' is 6.5 meters.
__
PerimeterThe perimeter is the sum of the side lengths. Opposite sides of the parallelogram are the same length. Clockwise from the bottom left, the sum of side lengths is ...
P = 9.2 +7.8 +6.5 +7.3 +9.2 +12 . . . meters
P = 52 . . . meters
The perimeter is 52 meters.
9) What is the area of the triangle?
A) 66 yd?
B) 132 yd?
C) 136 yd
D) 272 yd
Answer:
C) 136 yd²
Step-by-step explanation:
[tex]\textsf{\large Area of a triangle:}\ \dfrac{1}{2}\cdot b \cdot h[/tex]
Given:
Base: 16 yd.Height: 17 yd.Substitute the given values into the formula.
[tex]\begin{aligned}A\triangle&=\dfrac{1}{2}(16)(17)\\ &=8(17)\\&=\boxed{136}\end{aligned}[/tex]
The area of the triangle is 136 yd².
Compare the decimal numbers 0.447 and 0.474
Answer:
0.027
Step-by-step explanation:
0.474 - 0.447
= 0.027
Answer:
0.027 or 0.447 is greater than 0.474
Step-by-step explanation:
PLEASE HELP DUE TODAY PLEASE HELP DO THE WHOLE PAGE PLEASE SHOW YOUR WORK PLEASE
Answer:
1. Circle A: 1 right angle
Circle B: 2 pairs of parallel sides, 2 pairs of sides with equal length
2. 2 pairs of parallel sides
2 pairs of sides with equal length
3. 2 sides of equal length
Step-by-step explanation:
1. Circle A: 1 right angle
Circle B: 2 pairs of parallel sides, 2 pairs of sides with equal length
2. 2 pairs of parallel sides
2 pairs of sides with equal length
3. 2 sides of equal length
In right triangle ABC, C is the right angle. What does sinB equal? options: sinB, cosB, cosA, not enough information
Answer:
Answer: cos(A)
Step-by-step explanation:
» From trigonometry,
[tex]{ \tt{ \sin( \theta) = \frac{opposite}{hypotenuse} }} \\ [/tex]
[tex]{ \tt{ \red{ \sin(B) = \frac{AC}{AB} }}} \\ [/tex]
» For cosine:
[tex]{ \tt{ \cos( \theta) = \frac{adjacent}{hypotenuse} }} \\ \\ { \red{ \tt{ \cos(A) = \frac{AC}{AB} }}}[/tex]
» Therefore, sinB = cosA
Answer:
Not enough information
explanation:
Taking sin here:
∠A + ∠B + ∠C = 180°
∠A + ∠B + 90 = 180°
∠A + ∠B = 90°
sin(A) + sin(B) = sin(90)
sin(B) = 1 - sin(A)
Taking cos here:
∠A + ∠B + ∠C = 180°
∠A + ∠B + 90 = 180°
∠A + ∠B = 90°
cos(A) + cos(B) = cos(90)
cos(A) + cos(B) = 0
cos(B) = -cos(A)
Milo needs $225 for a new jaket. He already has $54. He earns $9 an hour working for his dad. The equation shows this relationship. How many hours does Milo
need to work for his dad in order to have enough money to purchase the jaket
[tex] \\ \\ [/tex]
To find:-Total hours Milo need to work for his dad[tex] \\ \\ [/tex]
Let :Total hours Milo need to work for his dad be x[tex] \\ \\ [/tex]
Solution:So as we know he already has $54
Actual Money needed = Money needed to buy new jacket – Money he already hasActual Money needed =$225 - $54Actual Money needed = $171Equation formed to find value of x :-
[tex] \leadsto \sf9x = 171[/tex]
[tex] \\ [/tex]
[tex] \leadsto \sf x = \dfrac{171}{9} [/tex]
[tex] \\ \\ [/tex]
[tex] \leadsto \sf x = \dfrac{3 \times 3 \times 19}{9} [/tex]
[tex] \\ \\ [/tex]
[tex] \leadsto \sf x = \dfrac{ \cancel3 \times 3 \times 19}{ \cancel9} [/tex]
[tex] \\ \\ [/tex]
[tex] \leadsto \sf x = \dfrac{ \cancel3 \times 19}{ \cancel3} [/tex]
[tex] \\ \\ [/tex]
[tex] \leadsto \bf x = 19[/tex]
[tex] \\ \\ [/tex]
[tex]\therefore \underline {\textsf{\textbf{No. of hours required is equal to\red{ 19 hours}}}}[/tex]
i literally have a test tomorrow and dont know what to do please help
Answer:
(-6, 1)
Step-by-step explanation:
y = 1 is the equation of a horizontal straight line that passes through (x, 1), where x can be any number. Four points are given. y = 1 for only one of them: (-6, 1). Answer "Yes" for this one point (the one in the second row).
Solve the inequality. Then, graph the solution 15x ≥ −60
Answer:
A closed circle on -4, going to the right.
Step-by-step explanation:
15x ≥ −60
/15 /15
x ≥ -4
This is a closed circle on -4, going to the right.
Hope that helps!
Work out the sum of the first 60 terms of the following arithmetic series:
100 + 94 + 88 +...
Answer:
[tex]S_{60}=-4620[/tex]
Step-by-step explanation:
[tex]S_n=\frac{n}{2}[2a_1+(n-1)d]\\ \\S_{60}=\frac{60}{2}[2(100)+(60-1)(-6)] \\\\S_{60}=30[200+(59)(-6)]\\ \\S_{60}=30[200-354]\\ \\S_{60}=30[-154]\\\\S_{60}=-4620[/tex]
sam knows that 1 inch is about 2.54 centimeters. about how many centimers is 3 inches
Which pair of angles are alternate exterior angles of parallel lines v and w?
b° and d°
a° and b°
a° and d°
a° and c°
Answer:
a and d
Step-by-step explanation:
v and w are parallel lines
R is the transversal
Alternate exterior means on the opposite sides of the transversal and outside of the parallel linea
a and d are alternate exterior angles