Answer:
a = 1/42, b = 1/7, c = 1/3 and d = 1/2
Step-by-step explanation:
a = bcd (1)
a + b = cd (2)
a + b + c = d (3)
a + b + c + d = 1 (4)
Substituting equation (3) into equation (4), we have
a + b + c = d (3)
a + b + c + d = 1 (4)
(a + b + c) + d = 1 (4)
d + d = 1 (5)
2d = 1
dividing through by 2, we have
d = 1/2
Taking equation (2) and equation (3), we have
a + b = cd (2)
a + b + c = d (3)
substituting equation (2) into equation (3), we have
a + b = cd (2)
(a + b) + c = d (3)
cd + c = d
Factorizing, we have
c(d + 1) = d
dividing through by d + 1, we have
c = d/(d + 1)
substituting d = 1/2 into the equation, we have
c = d/(d + 1)
c = 1/2 ÷ (1/2 + 1)
c = 1/2 ÷ 3/2
c = 1/2 × 2/3
c = 1/3
Taking equations (1) and (2), we have
a = bcd (1)
a + b = cd (2)
Substituting equation (1) into (2), we have
a = bcd (1)
a + b = cd (2)
bcd + b = cd (2)
Factorizing, we have
b(cd + 1) = cd
dividing through by (cd + 1), we have
b = cd/(cd + 1)
substituting the values of c and d into the equation,, we have
b = cd/(cd + 1)
b = 1/3 × 1/2/(1/3 × 1/2 + 1)
b = 1/6/(1/6 + 1)
b = 1/6 ÷ 7/6
b = 1/6 × 6/7
b = 1/7
Since a = bcd, substituting the values of b,c and d into the equation, we have
a = bcd
a = 1/7 × 1/3 × 1/2
a = 1/42
So, a = 1/42, b = 1/7, c = 1/3 and d = 1/2
Doubling x and adding 3 is the same as tripling x and adding 1
Answer:
2x + 3 = 3x + 1
x = 2
hope that helps ✌
Find the values of x and y that make these triangles congruent by the HL Theorem.
i need alot of help in this
Not the best way to do it, but it should look something like this.
A payday loan store charges $25 for a one-month loan of $600. What annual interest rate is this equivalent to?
Answer:
50%
Step-by-step explanation:
1. determine the monthly interest rate
monthly interest rate = interest / loan amount
monthly interest = 25 / 600 = 4.17%
2, multiply the monthly interest rate by 12 to determine the annual interest rate
Annual interest = 4.17 x 12 = 0.5 = 50%
Find Tan(ß) in the triangle
Answer:
the answer is
tan (B)=p/b
=5/12
Answer: C)5/12
Step-by-step explanation:
The tangent is equal to the ratio of the opposite cathet to the adjacent one.Then [tex]\bf tg \beta = \dfrac{5}{12}[/tex]The graph of the function f(x) = (x + 2)(x - 4) is shown. Which describes all of the values for which the graph is negative and increasing?
all real values of x where x < -2
all real values of x where -2 < x < 4
all real values of x where 1 < x < 4
all real values of x where x < 0
Answer:
C. All real values of x where 1 < x < 4
Step-by-step explanation:
The function is negative below the zeros which would be from -2 to 4.
It would be increasing from the vertex which is 0 to 4.
Therefore, C makes the most sense out of all the choices.
Answer:
C was correct
Step-by-step explanation:
Factor completely, show work.
x² - 49
You want to pull out the square roots of each term since they are both perfect squares.
Factor using the difference of squares formula: a2-b2=(a+b)(a-b)
This formula allows the middle term to cancel out.
=x2 - 49
=(x + 7)(x - 7)
ANSWER: (x + 7)(x - 7)
Hope this helps! :)
how do you expand brackets
Answer:
multiply each term in the bracket by the expression outside the bracket
:)
Step-by-step explanation:
A stationary shop markdown their writing boards by 40%. The markdown is $32. What is the original selling price and selling price after markdown of the writing boards?
A.$50, $25
B.$60, $24
C.$80, $48
D.$70, $28
Answer:
The original price is 80
The new price is 48
Step-by-step explanation:
Let x be the original price
x - .4x = new price
.6x = new price
.4x = markdown
.4x= 32
.4x/.4 = 32/.4
x =80
The original price is 80
.6x = new price
.6(80) = 48
Which linear inequality represents the graph below?
(-2,3)
(0-2)
A. y<-{x-2
O B. y<-x-2
O C. ysx-2
O D. ys-x-2
Answer:
B.
Step-by-step explanation:
1. We can clearly see that the "rise" is 5 and the "run" is 2, which cancels out both A. and D.
2. The line is dashed, which therefore cancels out both C. and D.
3. Just by canceling out those two can help you see that B fits what is seen in this figure because option A. has the wrong amount of "rise" over "run".
The linear inequality can be obtained from the given graph (the nature
of the line and the feasible (shaded) region).
Response:
[tex]B. \ y < -\dfrac{5}{2} \cdot x - 2[/tex]
How can the graph of the inequality be determined?The given points in the graph are;
(-2, 3), and (0, -2)
The slope of the line is therefore;
[tex]Slope = \dfrac{-2 - 3}{0 - (-2)} = \mathbf{-\dfrac{5}{2}}[/tex]
The equation of the line is therefore;
[tex]y - 3 = \mathbf{ -\dfrac{5}{2} \cdot (x - (-2))}[/tex]
[tex]y = -\dfrac{5}{2} \cdot x - 5 + 3 = -\dfrac{5}{2} \cdot x - 2[/tex]
[tex]y = \mathbf{-\dfrac{5}{2} \cdot x - 2}[/tex]
Given that the left side (below the line of the equation of the graph) is
shaded and the line of the graph is a broken line, the correct option is
therefore;
[tex]B. \ y < -\dfrac{5}{2} \cdot x - 2[/tex]
Learn more about the graph of inequalities here:
https://brainly.com/question/19251897
what is the total cost
Answer:
Step-by-step explanation:
We need to first find the perimeter of this oddly-shaped rink. We have a rectangle for which we are enclosing 3 of its sides, and the fourth "side" is a half-circle. Let's find the perimeter (or circumference) of the circle, divide it in half because we have half a circle, then add in the remaining 3 sides from the rectangle, shall we?
C = πd. The diameter of the circle is the same as the shorter length in the rectangle, 26. Therefore,
C = (3.14)(26) so
C = 81.64 m for a whole circle, and for half of that circle, the circumference is
C = 40.82 m
Now we can find the perimeter of the rink:
40.82 + 61 + 26 + 61 = p so
p = 188.82 m
If the fencing costs $6.20 per meter and we have 188.82 m, then the total cost is
[tex]cost=\frac{6.20dollars}{meter}*188.82meters[/tex]. The label "meter" cancels out, leaving us with
cost = $1170.82
What’s the rate of change please help
Answer:
Rate of change, is also another word for slope.
Slope --> y2 - y1 / (x2-x1)
Assuming the table is already in xy, the cords are in xy form too.
1) (8,8)
2) (11,10)
Plug points into slope eq
--> 10 - 8 = 2
----> 11 - 8 = 3
2/3 Is the slope/rate of change.
When solving the system of equations, which expression could be substituted for r in the first equation?
3r + 2t = 15
r = 4 – t
Answer:
4-t
Step-by-step explanation:
We use the second equation and r = 4-t
every time we see r in the first equation replace it with 4-t
find the least number in which when divided by 8 20 and 24 leave remainder 2 in each case.
Answer:
Solution: Factors of
8 = 2x2x2
12 = 2x2x3
18 = 2x3x3
24 = 2x2x2x3
LCM = 2x2x2x3x3 = 72
Add 5 to 72 to get 77 as the answer
Evaluate the expression when x=-6.
x^2-9x+4
Answer:
- 14
Step-by-step explanation:
x = - 6
x^2 - 9x + 4
= ( - 6 )^2 - 9 ( - 6 ) + 4
= 36 + 54 - 4
= 36 - 50
= - 14
Answer:
[tex]94[/tex]
Step-by-step explanation:
[tex]x^2 - 9x + 4[/tex]
[tex](−6 {)}^{2} −9 (−6) + 4[/tex]
[tex]36 − 9 (−6) + 4[/tex]
[tex]36 + 54 + 4[/tex]
[tex]90+4[/tex]
[tex]94[/tex]
Hope it is helpful....Which point bisects the segment ZV?
Bisect means it is in the middle so that the length of each side would be the same.
The bisector is point W
find the shaded area ..
Answer:
39°
Step-by-step explanation:
The angle adjacent to 115° in the lower triangle = 180° - 115° = 65°
angle on circle in lower triangle
= 180° - (65 + 76)° ← angle sum in triangle
= 180° - 141° = 39°
Angles on the circle subtended from the same arc are congruent, then
shaded angle = 39°
Find the product using suitable property: a.46*102 b.55*1004
Answer:
please
Step-by-step explanation:
follow me
please
please
please
which is the total length of both sides of the roof 4x
Answer:
b. 40m
Step-by-step explanation:
[tex]length \: of \: x \\ {x}^{2} = {8}^{2} + {6}^{2} \\ {x}^{2} = 64 + 36 \\ {x}^{2} = 100 \\ \sqrt{ {x}^{2} } = \sqrt{100} \\ x = 10m[/tex]
[tex]x = 10m \\ 4x = 4 \times 10 \\ 4x = 40m[/tex]
Find the area of the regular polygon. Round your answer to the nearest hundredth
Answer:
Step-by-step explanation:
Use the Pythagorean theorem to find the length of the missing side that is 1/2 the side of the missing heptagon. You have to assume that the figure is a regular heptagon, something you should point out to your teacher. Math really requires well qualified diagrams.
c^2 = a^2 + b^2
c = 2.77
a = 2.5
b = 1/2 the side of the heptagon.
2.77^2 = 2.5^2 + b^2
7.6729 =6.25 + b^2
7.5629 - 6.25 = b^2
b^2 = 1.4229
b = sqrt(1.4229)
b = 1.1928
But the side is twice that long
s = 2.3857
Now draw another line from the side you just found. It will be the same length as 2.77. It's a radius of the circumcircle.
Area of the triangle so formed is
Area = 1/2 * b * h
b = 2.3857
h = 2.5
Area = 1/2 * 2.5 * 2.3857
Area = 2.982
There are 7 such triangles.
Answer: 7 * 2.982
Answer: 20.87
Select the correct answer from each drop-down menu.
CD is perpendicular to AB and passes through point 95, 12).
If the coordinates of A and B are (-10, -3) and (7,14), respectively, the x-intercept of CĐ is (blank). The point
(Blank) lies on CD.
Answer:
Hello! the answer is CD is 17,0 (-2,19)
Find the value of x in the triangle shown below.
Answer:
50
Step-by-step explanation:
Solve the following, where 0° < θ < 360°.
If cos θ=2/3 and tan θ<0
Find θ.
Answer:
The angle θ = 312°.
Step-by-step explanation:
0° < θ < 360°
If cos θ = 2/3 and tan θ < 0
As cos θ is positive and tan θ is negative so the angle is in fourth quadrant.
cos θ = 2/3
θ = 312°
Find all solution(s) of the quadratic equation x2 – 100 = 0. Question 9 options: A) x = 10, –10 B) x = –10 C) x = 10 D) x = 100, –100
Answer:
x = - 10, x = 10
Step-by-step explanation:
Given
x² - 100 = 0 ( add 100 to both sides )
x² = 100 ( take the square root of both sides )
x = ± [tex]\sqrt{100}[/tex] = ± 10
solutions are x = - 10, x = 10
Likes s and t are perpendicular if the slope of line s is 5 what is the slope of line t?
Answer:
Gradient of line t is -1/5
Step-by-step explanation:
[tex]{ \sf{m _{s} \times m _{t} = - 1}} \\ { \sf{5 \times m _{t} = - 1 }} \\ { \sf{m _{t} = - \frac{1}{5} }}[/tex]
Someone can help me with this ? I don’t understand
Answer:
-3
Step-by-step explanation:
Can someone help me out
Answer: V=9.4 cm^3
Step-by-step explanation:
[tex]V=\pi r^2h\\V=\pi (1)^2(3)\\V=9.4cm^3[/tex]
a trader is given 15% discount on goods bought from a factory. If the original price of an item in the factory is 45000. Calculate the amount the trader paid for them
Answer:
38,250
Step-by-step explanation:
Its a 15% discount so youre only paying 85% of the original 45,000. You then multiply 45,000 by .85 to find what youre paying because the decimal version of 85% is .85. You can find the decimal version of a percentage by dividing the percentage by 100; 85/100=.85. Once you multiply 45,000 by .85 you get 38,250.
REfer and answer
Pls its urgent
Pls fast
I need help to find the value of x. Round to the nearest tenth
Answer:
17.1
Step-by-step explanation:
tan(35)=12/x, x=17.1
Answer:
x ≈ 17.1
Step-by-step explanation:
The angle is 35 degrees, so we do tan(35)
Which equals the side divided by x.
tan(35) = 12 / x
So x ≈ 17.1