Answer:
a = 15
Step-by-step explanation:
Given
3a + b = 54 ← substitute b = 9
3a + 9 = 54 ( subtract 9 from both sides )
3a = 45 ( divide both sides by 3 )
a = 15
The value of x in the equation 4x + 8y = 40 is 8.4. and the value of a in the equation 3a + b = 54 is 15.
What is a system of equations?A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
Given;
A) 4x + 8y = 40
Now substitute y = 0.8
4x + 8(0.8) = 40
4x = 40 - 6.4
x = 8.4
B) 3a + b = 54
Now substitute b = 9
3a + 9 = 54 ( subtract 9 from both sides )
3a = 45 ( divide both sides by 3 )
a = 15
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Jeremy is trying to explain why a triangle with side lengths 35, 30, 60 is not a right triangle. His explanation is shown below. Step 1: 35 squared + 30 squared question mark equals 60 squared Step 2: (35 + 30) squared question mark equals 60 squared Step 3: 65 squared question mark equals 60 squared Step 4: 4,225 not-equals 3,600 Which best describes Jeremy's explanation? Jeremy's explanation is accurate. Jeremy's explanation is inaccurate. He wrote the leg lengths in the incorrect order in step 1. Jeremy's explanation is inaccurate. He incorrectly combined terms in step 2. Jeremy's explanation is inaccurate. He multiplied incorrectly in step 4.
Answer:
He incorrectly combined terms in step 2
Step-by-step explanation:
In Step 2, you can't combine 30² + 35² into (30 + 35)² so the answer is "He incorrectly combined terms in step 2".
Answer:
The answer is C
Step-by-step explanation:
Jeremy’s explanation is inaccurate. He incorrectly combined terms in step 2.
PLEASE PLEASE PLEASE HELP ASAP *grade 9 work* best answer gets brainliest :)
Which of the following are solutions to the equation below?
Check all that apply.
x2 - 8x+ 16 = 5
A. *= V11+ 4
)
B. x= -15+4
O C. x= -15-4
D. x= V5 + 4
E. x= -111-4
OF. x= V5 - 4
Answer:
x² - 8x+ 16 = 5
x² - 8x + 16 - 5 = 0
x² - 8x + 11 = 0
Using the quadratic formula
x = -b±√b² - 4ac / 2a
a = 1 , b = - 8 c = 11
x = --8±√(-8)² - 4(1)(11) / 2(1)
x = 8 ± √ 64 - 44 / 2
x = 8±√20 / 2
x = 8 - √ 20 / 2 or x = 8 + √ 20 / 2
x = - √ 5 + 4 or x = √5 + 4
Hope this helps
Rain trees are planted every 15 metres apart along a road pavement, Bougainvillea
bushes are planted every 1.6 metres apart along the same pavement,
A rain tree and bougainvillea bush are planted at a common point A along the
pavement. Find the distance from A to the next point where a rain tree and
bougainvillea bush are planted together.
Please help with this question.
Answer:
120 m
Step-by-step explanation:
LCM of 1.6 and 15 will give us the distance
Put 1,6 and 15 in same format:
16/10= 2*2*2*2/10150/10= 2*3*5*5/10LCM= 2*2*2*2*3*5*5/10= 120 m
So the next point is 120 m apart
the area of a sector of a circle of radius 15cm is 110cm², calculate the angle of subtended at yhe center of the circle by the arc?
Answer:
44/45 radians
Step-by-step explanation:
The area is given by the formula ...
A = (1/2)r²θ
where θ is the central angle in radians.
Filling in the given numbers, we have ...
110 cm² = (1/2)(15 cm)²θ
θ = (220 cm²)/(225 cm²) = 44/45 radians
The subtended angle is 44/45 radians, about 56.02°.
cos^4a=1/8(3+4cos2a+cos4a)
Answer:
Below.
Step-by-step explanation:
cos2a = 2 cos^2 a - 1
cos^4a = 8cos^4 a - 8cos^2 a + 1
Right side of the identity =
1 /8(3 + 4cos2a + cos4a)
= 1/8( 3 + 4(2 cos^2 a - 1) + 8cos^4 a - 8cos^2 a+1)
= 1/8 (3 + 8 cos^2 a - 4 + 8 cos^4 a - 8cos^2 a + 1)
= 1/8 (8cos^4 a)
= cos^4 a = the left side.
I realised that I should have derived the identity for cos 4a as well , which i have done in the picture.
The given identity, cos⁴a = 1/8(3 + 4cos2a + cos4a) is proved.
How is proving identities done?To prove a given identity, say f(a) = f(b), we proceed to simplify any of the expressions among the L.H.S. f(a) and the R.H.S. f(b), to get the other term. If we get the simplified form as the other term, our identity holds and is proved.
How do we solve the given question?We know cos2A = 2cos²A - 1.
Going by the same formula, we derive the value of cos4A.
cos4A = 2cos²2A - 1
or, cos4A = 2(2cos²A - 1)² - 1, putting value of cos2A
or, cos4A = 2(4cos⁴A - 4cos²A + 1) - 1, (expanding (2cos²A - 1)² using the formula of (a-b)² = a² -2ab + b²)
or, cos4A = 8cos⁴A - 8cos²A + 2 - 1, (expanding)
or, cos4A = 8cos⁴A - 8cos²A + 1, (simplifying)
∴ cos4A = 8cos⁴A - 8cos²A + 1.
Given identity to us is, cos⁴a = 1/8(3 + 4cos2a + cos4a).
To prove the identity, we proceed with the R.H.S.:
= 1/8(3 + 4cos2a + cos4a)
We put values of cos2A and cos4A in this expression, to get
= 1/8(3 + 4(2cos²a - 1) + (8cos⁴a - 8cos²a + 1))
Expanding the equation, we get
= 1/8(3 + 8cos²a - 4 + 8cos⁴a - 8cos²a + 1)
Simplifying, we get
= 1/8(8cos⁴a) = cos⁴a = L.H.S.
Hence, the given identity is proved.
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Can somebody plz help me
Answer: A
Step-by-step explanation:
2x²-2x-9=0
this is a quadratic equation so we will use the quadratic formula .
Δ= b²-4*a*c
b= -2a= 2c= -9let's calculate Δ to khow how many solutions this equations have .
Δ= (-2)²-4*2*(-9)
= 76
we notice that 76>0
so this equation has two solutions : (-b-√76)/4 and (-b+√76)/4
let's calculte the values : (-b-√76)/4= [tex]\frac{-2-\sqrt{76} }{4}[/tex] (-b+√76)/4=[tex]\frac{-2+\sqrt{76} }{4}[/tex]the trick here is to notice that :
[tex]\sqrt{76}[/tex] = [tex]\sqrt{19*4}[/tex]
= [tex]\sqrt{19} *\sqrt{4}[/tex]
= 2[tex]\sqrt{19}[/tex]
Now we will simplify Δ by factoring by 2
[tex]\frac{2*(-1(+/-)\sqrt{19} }{2*2}[/tex] = [tex]\frac{-1(+/-)\sqrt{19} }{2}[/tex]so the answer is a .
1
11 Kenzie monitors her investment on a technology
stock. She uses the expression 2013e2+, where t
is the time in years, to estimate the future value
of the stock. What is the meaning of 2013 in this
context?
A. beginning year
B. invested amount
C. future value
D. annual growth rate
Answer:
B
Step-by-step explanation:
The term 2013 in this context refers to the amount invested.
Mathematically, in finance, we can express the amount to be recouped on an investment, having a particular rate of return over a couple of years using the general formula;
V = P(1+r)^t
Such as in the case of amount obtained in a compound interest formula
Where P is the present value or principal or amount invested
V is the future value
r is the rate of investment
with t being the time taken
what is the solution to the system of equations? A. (7,4) B. (7,13/3) C. (8,14/3) D. (9,7)
Answer:
B. (7, 13/3)
Step-by-step explanation:
Since the graph doesn't show the intersecting point, we must use algebra to solve this (Substitution or elimination).
Step 1: Substitute y
1/3x + 2 = 4/3x - 5
Step 2: Isolate x
-x + 2 = -5
-x = -7
x = 7
Step 2: Find y using x
y = 1/3(7) + 2
y = 7/3 + 2
y = 13/3
F(x)=x^2. What is g(x)?
Answer:
g(x)= 5x
Step-by-step explanation:
You should go back to the graph and notice that the abscissa 1 goes with the ordinate 5.
Now ask yourself how do I get 5 using 1. There many ways but notice that the function is growing and both functions f and g geow the same way. Wich mean that g(x)= 5x is a valid option.
notice that 0 is going with o at the ordinate.
some little calculations . m=(5-0)/(1-0)= 5
so the function is g(x)=5x+p
p is 0 since it is the first ordinate
so g(x)= 5x
Pls help it is urgent .A trader bought a plate for 120 naira and sold it for 168 naira.What is his percentage profit.
Answer:
Percentage profit=40%
Step-by-step explanation:
Cost price=120 Naira
Sold price=168 Naira
Profit=Sold price- cost price
=168-120
=48 Naira
Percentage profit=profit/cost price×100
=48/120×100
=0.4×100
=40%
Percentage profit=40%
Factor completely.
a 2 + 28 a + 27
Hey there! :)
Answer:
(x + 27)(x + 1)
Step-by-step explanation:
Given:
a² + 28a + 27
Find numbers that add up to 28 and multiply to 27:
We can find that the numbers 27 and 1 add up to 28 and multiply to form 27. Therefore, the equation in factored form is:
(x + 27)(x + 1)
Answer:
(a+27)(a+1)Solution,
[tex] {a}^{2} + 28a + 27 \\ = {a}^{2} + (27 + 1)a + 27 \\ = {a}^{2} + 27a + a + 27 \\ = a(a + 27) + 1(a + 27) \\ = (a + 27)(a + 1)[/tex]
Hope this helps..
Good luck on your assignment..
what day of the week will be 2019 days from monday?
Answer:
Thursday
Step-by-step explanation:
Since one week is equivalent to 7 days, lets find how to write 2019 days as a combination of full weeks (which will land one again on Monday), plus days:
Notice that 2019 = 2016 + 3 = 288 * 7 + 3
Then 2019 days is the same as 288 weeks plus 3 days.
The 288 weeks from Monday will take us to another Monday, and the added 3 days to a Thursday.
A tree casts a 25 m shadow when the angle of elevation to the sun is
40°. Approximately how tall is the tree?
25 m
A 25 m
B 19 m
C 21 m
D 16 m
Answer:
C. 21 m
Step-by-step explanation:
As shown in the picture, we need to use tan∅ (opposite over adjacent) to solve for the height of the tree:
tan40° = h/25
25tan40° = h
h = 20.9775
h ≈ 21 m
17.
Rewrite y =
16X - 32
- 3 to make it easy to graph using a translation. Describe the graph.
Answer:
y=16x - 35
graph is in the pic
Answer:
Parent Function:
y=√x
Horizontal Shift: Right 2 Units
Vertical Shift: Down 3
Units
Reflection about the x-axis: None
Vertical Stretch: Stretched
Step-by-step explanation:
4.- En una pastelería han preparado 30 pasteles. Los van a colocar en bandejas de forma que en cada bandeja haya el mismo número de pasteles y no sobre ninguno. ¿De cuántas formas los puede colocar?
Answer:
7 formas
Step-by-step explanation:
En la pastelería, se han preparado 30 pasteles.
Cada bandeja contendrá la misma cantidad de pasteles.
Para encontrar de cuántas maneras puedes ponerlos, tenemos que encontrar los factores de 30. Ellos son:
1, 2, 3, 5, 6, 10, 15, 30
Esto significa que podemos tener:
30 bandejas que contienen 1 bandeja cada una
15 bandejas con 2 tortas cada una
10 bandejas con 3 tortas cada una
6 bandejas con 5 tortas cada una
5 pasteles que contienen 6 pasteles cada uno
3 bandejas con 10 pasteles cada una
2 bandejas con 15 tortas cada una
Esto significa que hay 7 formas de colocar los pasteles.
To make a specific hair dye, a hair stylist uses a ratio of 1 1/8 oz of red tone, 3/4 oz of gray
tone, and 5/8 oz of brown tone. If the stylist needs to make 20 oz of dye, how much of
each dye color is needed
Answer:
We can call the amounts of red, gray, and brown dye 1 1/8x, 3/4x and 5/8 x respectively and we can write the equation:
1 1/8x + 3/4x + 5/8x = 20
2 1/2x = 20
x = 8 which means that the stylist needs 1 1/8 * 8 = 9 oz red, 3/4 * 8 = 6 oz gray and 5/8 * 8 = 5 oz brown.
oi tu bem com voces eu sou novo oiiiiii
Answer:
Please post useful questions thanks!
Step-by-step explanation:
Horatio is solving the equation Negative three-fourths + two-fifths x = StartFraction 7 Over 20 EndFraction x minus one-half. Which equations represent possible ways to begin solving for x? Check all that apply. Two-fifths x = StartFraction 7 Over 20 EndFraction x + one-fourth Two-fifths x = StartFraction 7 Over 20 EndFraction x + five-fourths Negative three-fourths = negative StartFraction 1 Over 20 EndFraction x minus one-half Negative three-fourths = three-fourths x minus one-half Negative three-fourths + StartFraction 1 Over 20 EndFraction x = negative one-half
Answer:
x = 5
Step-by-step explanation:
Step 1: Write equation
-3/4 + 2/5x = 7/20x - 1/2
Step 2: Subtract 7/20x on both sides
-3/4 + 1/20x = -1/2
Step 3: Add 3/4 to both sides
1/20x = 1/4
Step 4: Divide 1/20 on both sides
x = 5
Answer: Answer: The answer is A,C,E
A: 2/5x = 7/20 x+ 1/4
C: -3/4 = -1/20 x -1/2
E: -3/4 + 1/20 x= -1/2
Which statement is true about centimeters and kilometers?
Answer:
Centimeters are smaller than kilometers
Step-by-step explanation:
Remember:
Which is equal to a rotation of 90°ccw?
A. 180°cw rotation about the origin
В. 270°cw rotation about the origin
C. 180ºccw rotation about the origin
D. 270ºccw rotation about the origin
Answer:
В. 270°cw rotation about the origin
Step-by-step explanation:
We can rotate a total of 360 degrees in a circular pattern.
If we rotate x degrees in one direction, this rotation is equivalent to rotating (360 - x) in the other direction, because we would arrive in the same place.
So if we rotate 90 degrees in the counter clockwise direction, this is equivalent to rotating (360 - 90) = 270 degrees in the opposite direction, that is, in the clockwise direction.
So the correct option is B. -> 270°cw rotation about the origin.
if f(x)=5x-7 what is f(3)
Answer:
f(3) = 8
Step-by-step explanation:
f(x) = 5x - 7
Put x as 3 and evaluate.
f(3) = 5(3) - 7
f(3) = 15 - 7
f(3) = 8
Answer: 8
Step-by-step explanation:
Determine the measure of each missing angle
Answer:
w=y=86
Step-by-step explanation:
A triangle has a total angle of 180 degrees
w=y because the triangle is isoceles meaning that two sides are the same length (they are marked with a line through them)
180-94=86 degrees=w+y
w+y so 86/2=43 degrees
w=y=86
is that all the missing angles?
Use algebraic rules of equations to predict the solution type to the system of equations. Include all of your work for full credit.
Answer:
Systems of linear equations
Infinite amount of solutions
Step-by-step explanation:
Step 1: Rearrange 1st equation
2y = -x + 10
6y = -3x + 30
Step 2: Multiply top equation by 3
6y = -3x + 30
6y = -3x + 30
Since they have the same slope and same y-intercept, they are both the same line. That means that the systems of linear equations has infinite amount of solutions.
Dale is 4 years older than sue. Five years ago the sum of their ages was 64. How old are they now?
Answer:
39 and 35
Step-by-step explanation:
On August 1, Ira’s bank balance was $300. During the month, he wrote three checks for $115.25 and made it be deposit of $165. Which of the following best represents his checking account balance at the end of the month?
A. 119.25
B. -119.25
C. -$45.75
D.349.75
Of a certain road 7.264km are down hill, 3.873km are up hill and 6.89 are level.what is the length of the road pls urgent tnx
Answer:
18.027
Step-by-step explanation:
7.264+3.873+6.89
18.027
Which two consecutive whole numbers does 39 lie between? Why?
5 and 6 because 39 falls between 52 = 25 and 62 = 36.
4 and 6 because 39 falls between 42 = 16 and 62 = 36.
6 and 7 because 39 falls between 62 = 36 and 72 = 49.
5 and 7 because 39 falls between 52 = 25 and 72 = 49
Answer:
Step-by-step explanation:
6 and 7
Lara's living room is 9 meters wide and 9 meters long. She wants to install purple carpet that costs $8.00 per square meter. How much will it cost to buy enough carpet for the living room?
Answer:
$648.00
Step-by-step explanation:
==>Given:
Squared living room of 9m by 9m
Cost of purple carpet per m² = $8.00
==>Required:
Cost of buying carpet to cover the squared living room
==>Solution:
Find the area of the room:
Area of squared room = 9m × 9m = 81m²
Find cost of purple carpet that would cover 81m²:
Let x be the cost of carpet required to cover the room.
Thus,
1m² = $8.00
81m² = x
cross multiply
1*x = 8.00*81
x = 648
Cost of purple carpet to cover the living room = x = $648.00
Pls ppl answer dis question PLS PLS PLS No scaming pls
4√3 x^2+5x-2√3
Answer:
\the zeroes are (2√3)/ 3, (√3)/4,
or -1.15, 0.43 to the nearest hundredth.
Step-by-step explanation:
I am assuming you want to find the zeroes of this function:
4√3 x^2+5x-2√3 = 0
Using the quadratic formula:
x = [ -5 +/- √((5)^2 - 4 * 4√3 * -2√3) ] / (2 * 4√3 )
= ( - 5 +/- √(25 - (-32*3)) / 8√3
= (-5 +/- √ 121) / 8√3
= (-5 - 11) / 8√3 or (-5 + 11) / 8√3
= -16/8√3 or 6/8√3
= -16√3/ 24 or 6√3 / 24
= -2√3/ 3 or √3/4.
