The correct answer is option A. Which is the solution of the given equation will be (15,15).
What is an equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
Given equations are solved as:-
a - 1.2b = -3 or a = -3 + 1.2b
0.2a + 0.6b = 12
Put the value of a from equation 1 to the equation second.
0.2 ( -3 + 1.2 b) + 0.6b = 12
-0.6 + 0.24b + 0.6b = 12
0.84b = 12 + 0.6
0.84 b = 12.06
b = 15
Put the value of b in the first equation to find the value of a.
a = 1.2b - 3
a = (1.2 x 15) - 3
a = 15
Therefore the correct answer is option A. Which is the solution of the given equation will be (15,15).
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What is the perimeter of triangle JKL (same triangle as question #1)?
Answer:
x=30
Step-by-step explanation:
You have to use intercept theorem, also known as Thales's theorem to slvoe this.
A number cube with the numbers 1 through 6 is rolled. What is the theoretical probability, as a decimal, of the number cube showing a 1? Round the decimal to the nearest hundredth
Answer:
0.17 (rounded)
Step-by-step explanation:
There's only one way a 1 can appear on a number cube out of 6 possible sides. Thus, the theoretical probability of the number cube showing a 1 is 1/6, or 0.17 rounded.
What characteristics do all points in Quadrant I share?
A. The x-coordinate is positive and the y-coordinate is positive.
B. The x-coordinate is negative and the y-coordinate is negative.
C. The x-coordinate is positive and y-coordinate is negative.
D. The x-coordinate is negative and y-coordinate is positive.
Answer:
Option A
Step-by-step explanation:
Remember the things.
In Q1
x>0,y>0in Q2
x<0,y>0in Q3
x<0,y<0in Q4
x>0,y<0Answer:
A. The x-coordinate is positive and the y-coordinate is positive.
Step-by-step explanation:
The Cartesian plane is divided into four regions by the x-axis and y-axis.
These regions are called "quadrants".
Quadrant I is the top right region, where x and y coordinates of points are positive.
From here, move in a counterclockwise direction.
Therefore, Quadrant II is the top left region, where the x-coordinate is negative and the y-coordinate is positive.
Quadrant I → (x, y)
Quadrant II → (-x, y)
Quadrant III → (-x, -y)
Quadrant IV → (x, -y)
What is value of x in the equation 6x+7-2x=3+5x-9
Answer: x = 13
Step-by-step explanation: First, we simplify the equation to get 4x + 7 = 5x - 6. Then, from there, we subtract 7 on both sides to get 4x = 5x - 13. Then we subtract 5x from both sides, which would give us -x = -13. Finally, we can divide both sides by -1 (because remember, x = 1) to get that x = 13. Hope this helps!
Help will mark brainliest!
a) The compound interest equation is [tex]C = 4250 \cdot 0.9675^{t}[/tex].
b) There is an approximate loss of $ 987.16.
c) The stock will take approximately 12.979 to decrease by half.
How to find stock losses by compound interest model
Compound interest model represents the gain of a deposit as a function of the number of periods and initial amount. The model is represented below:
[tex]C = C_{o}\cdot (1+r)^{t}[/tex] (1)
Where:
[tex]C_{o}[/tex] - Initial capital, in monetary units.[tex]r[/tex] - Interest rate.[tex]t[/tex] - Period number.[tex]C[/tex] - Current capital, in monetary units.Capital decreases in time when interest rate is a negative number. The equation that models the situation is [tex]C = 4250 \cdot 0.9675^{t}[/tex] and the current capital after eight years is:
C = 4250 · 0.9675⁸
C = 3262.84
That represents an approximate loss of $ 987.16.
And the number of periods required to decrease the capital by half is:
[tex]2125 = 4250 \cdot 0.9675^{t}[/tex]
[tex]0.5 = 0.9675^{t}[/tex]
㏒ 0.5 = t · log 0.9675
t ≈ 20.979
The stock will take approximately 12.979 to decrease by half.
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Pls help! I don't get this!!
Answer:
5; 2n + 5 ≤ 15
6; n/5 ≤ 15
7; 5n ≥ 15
Step-by-step explanation:
"a number" means a variable denoted "n"
"product" means to multiply
"quotient" means to divide
"The sum" means to add
"is at least" means greater than or equal to or ≥
"is no greater than" means less than or equal to or ≤
"Is at most" means less than or equal to or ≤
B Christian installed an electric pump to pump water from a borehole into a 30 000 litre cement dam. If the water is pumped at a rate of 75 litres per minute. How long does it take to fill the dam?
A.4 h
B.6 h 40 min
C.6 h 20 min
D.3h 40 min
Given the amount of water needed to fill the cement dam and the water pump rate, the time needed to fill the dam is 400 minutes or 6hours 40minutes.
Option B)6h 40min is the correct answer.
How long does it take to fill the dam?Given that;
Amount of water needed to fill the dam A = 30000 litresPump rate r = 75 litres per minuteTime needed to fill the dam T = ?To determine how long it take to fill the dam, we say;
Time need = Amount of water needed ÷ Pump rate
T = A ÷ r
T = 30000 litres ÷ 75 litres/minute
T = 400 minutes
Note that; 60min = 1hrs
Hence,
T = 6hours 40minutes
Given the amount of water needed to fill the cement dam and the water pump rate, the time needed to fill the dam is 400 minutes or 6hours 40minutes.
Option B)6h 40min is the correct answer.
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Acellus
Type SSS, SAS, ASA, SAA, or HL to
justify why the two larger triangles are
congruent?
Write an equation for each translation y=sin x, pi/4 units to the right
The equation of the translation is y = sin(x - π/4)
How to determine the translation?The equation is given as:
y = sin(x)
The rule of translation to the right is:
(x,y) => (x - h,y)
This gives
(x,y) => (x - π/4,y)
So, we have:
y = sin(x - π/4)
Hence, the equation of the translation is y = sin(x - π/4)
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Which expression is equivalent to startfraction startroot 10 endroot over rootindex 4 startroot 8 endroot?
The expression that is equivalent to √10 / (4√8) is given as √5 / 8
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Given the equation:
√10 / (4√8)
Simplifying:
= √10 / (4√(4 * 2))
= √10 / (8√2)
= √5 / 8
The expression that is equivalent to √10 / (4√8) is given as √5 / 8
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Ok help me I don’t understand stand this
Answer:
Step-by-step explanation:
Comment
It is not possible to figure out what choices are are given for the first blank. I will say that the probable choice has the word product in it.
The second blank is the actual number of choices. It is 3 page count times color or 3*4 = 12 different choices.
Answer
product
12
5. If the longer side of the rectangle is 25.5 in., what are its width, perimeter, and area?
Step-by-step explanation:
1) The width of the rectangle is 10.2 in.
2) The perimeter of the rectangle is 71.4 in.
3) The area of the rectangle is 260.1 sq.in
It's always a good idea to check your solutions to any equation in the original equation. When solving an absolute value equation, when must you check for extraneous solutions?
A. Sometimes, when u only get one solution
B. Never
C. Always
D. Sometimes, when the variable appears both inside and outside the absolute value expression
You should must check for an extraneous solution when the variable appears both inside and outside the absolute value expression
What is an extraneous solution?
An extraneous solution is a solution that in obtained after completely solving an equation but it does not work in the original given equation.
You should must check for an extraneous solution when the variable appears both inside and outside the absolute value expression (Option D).
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A bag has 4 red marbles,5 blue, 3 green and 1 yellow. what is the probability of pulling a red marble.
Answer as a fraction, decimal and percent
Answer:
4/13 is the answer
total = 4+3+5+1= 13
let a be the event of getting red marbles= total is 4
probability=4/13
Selma's house is 1,450 cm long. How many meters
long is Selma's house?
Answer:
14.5 Meters
Step-by-step explanation:
1 centimeter= 0.01 Meters
1450 cm x 0.01 =14.5
Solve the system by elimination. 8x+3y=4 2x+y=2
Answer:
x = -1
y = 4
Step-by-step explanation:
Solving system of linear equations by elimination method.
8x + 3y = 4 ---------------(I)
2x + y = 2 --------------(II)
Multiply the second equation by (-3) and then add them.Thus y will be eliminated and we will obtain the value of 'x'.
(I) 8x + 3y = 4
(II)*(-3) -6x - 3y = -6 {Now add}
2x = -2
x = -2/2
[tex]\sf \boxed{\bf x = -1}[/tex]
Plugin x = (-1) in any one of the equations. Here I have chosen equation (II)
2*(-1) + y = 2
-2 + y = 2
y = 2 + 2
[tex]\sf \boxed{\bf y = 4}[/tex]
How is 0.136¯¯¯¯ written as a fraction in simplest form?
Enter your answer in the box.
Answer:
[tex]\frac{3}{22}[/tex]
Step-by-step explanation:
the bar above 36 means that the digits 36 are being repeated
we require 2 equations with the repeating digits placed after the decimal point.
let x = 0.13636.. ( multiply both sides by 10 and 1000 )
10x = 1.3636... (1)
1000x = 136.3636... (2)
subtract (1) from (2) thus eliminating the repeating digits
990x = 135 ( divide both sides by 990 )
x = [tex]\frac{135}{990}[/tex] = [tex]\frac{3}{22}[/tex] ← in simplest form
Eliminate the parameter:
x = (3t+ 2)² y = t - 2
Solve for t in terms of y :
[tex]y = t - 2 \implies t = y + 2[/tex]
Substitute this into the parametric equation for x :
[tex]x = (3t + 2)^2 \implies x = (3(y + 2) + 2)^2 \implies \boxed{x = (3y+8)^2}[/tex]
Find the 5th term of the sequence which has a first term of 1 and has a common ratio of 2.3. Round your answer to the nearest hundredth if necessary.
The 5th term of the sequence is 27.98
How to determine the 5th term?The given parameters are:
First term, a = 1Common ratio, r = 2.3The nth term of a geometric sequence is calculated using:
[tex]T_n = ar^{n-1[/tex]
So, we have:
[tex]T_5 = 1 * 2.3^{5-1[/tex]
Evaluate the difference
[tex]T_5 = 1 * 2.3^4[/tex]
Evaluate the product
[tex]T_5 = 27.98[/tex]
Hence, the 5th term of the sequence is 27.98
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Answer the follwing grade 5 questions of HFC and LCM
Answer:
give clear image is next question
Step-by-step explanation:
i will give you the answer
11. 6.2 m B 1.8m Calculate the value of x. NOT TO SCALE
Answer:
24.19
Step-by-step explanation:
[tex] \tan(x) = \frac{6.2}{13.8} \\ x = { \tan}^{1} \frac{6.2}{13.8} \\ x = 24.19320899[/tex]
or the value of x can be 24.20
Quadrilateral RSTU is a rectangle and m/RVU = 72°.
What is m/VRU?
Answer: [tex]18^{\circ}[/tex]
Step-by-step explanation:
In triangle RUV, angle RUV is a right angle (and thus measures 90 degrees), and angle RVU measures 72 degrees.
Since angles in a triangle add to 180 degrees, angle VRU measures
180-90-72=18 degreesI need help with 7 8 and 9 question perimeter and area
The perimeter and area of the equilateral, isosceles and right angled triangle are 16.2mm 12.6mm², 15.2in and 9.61in², 21.47yds and 16.81yds² respectively.
What is the area of the equilateral, isosceles and right angle triangle?Note that:
The perimeter of an Equilateral triangle is expressed as P = 3a
The area of an Equilateral triangle is expressed as A = ((√3)/4)a²
Where a is the dimension of the side.
The perimeter of an Isosceles triangle is expressed as P = 2a + b
The area of an Isosceles triangle is expressed as A = (ah)/2
Where b is the slant height, a is the dimension of the base and h is the height.
The perimeter of a Right angled triangle is expressed as P = a + b + c
The area of a Right angled triangle is expressed as A = (ab)/2
Where a and b is the dimension of the two sides other than the hypotenuse and c is the hypotenuse.
For the Equilateral triangle.
Given that;
a = 5.4mmPerimeter P = ?Area A = ?Perimeter P = 3a
P = 3 × 5.4mm
P = 16.2mm
Area A = ((√3)/4)(5.4mm)²
A = ((√3)/4)( 29.16mm² )
A = 12.6mm²
The Perimeter and Area of the Equilateral triangle are 16.2mm 12.6mm² respectively.
For the Isosceles triangle.
Given that;
Base a = 3.4inSlant height b = 5.9inPerimeter P = ?height h = ?Area A = ?Perimeter P = 2a + b
P = 2(b) + a
P = 2(5.9in) + 3.4in
P = 11.8in + 3.4in
P = 15.2in
The height h is the imaginary line drawn upward from the center of a.
First, we calculate the height using Pythagorean theorem
x² = y² + z²
Where x = b = 5.9in, y = a/2 = 3.4in/2 = 1.7in, and z = h
(5.9in)² = (1.7in)² + h²
34.81in² = 2.89in² + h²
h² = 34.81in² - 2.89in²
h² = 31.92in²
h = √31.92in²
h = 5.65in
Now, the area will be;
A = (ah)/2
A = (3.4in × 5.65in )/2
A = 19.21in²/2
A = 9.61in²
The Perimeter and Area of the Isosceles triangle are 15.2in and 9.61in² respectively.
For the Right angled triangle.
Given that;
a = 8.2ydsb = 4.1ydsc = 9.17ydsPerimeter P = ?Area A = ?Perimeter P = a + b + c
P = 8.2yds + 4.1yds + 9.17yds
P = 21.47yds
Area A = (ab)/2
A = ( 8.2yds × 4.1yds)/2
A = ( 33.62yds²)/2
A = 16.81yds²
The Perimeter and Area of the Right angled triangle are 21.47yds and 16.81yds² respectively.
Therefore, the perimeter and area of the equilateral, isosceles and right angled triangle are 16.2mm 12.6mm², 15.2in and 9.61in², 21.47yds and 16.81yds² respectively.
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What substitution should be used to rewrite 6(x 5)2 5(x 5) – 4 = 0 as a quadratic equation?
A plane has a speed of 840 km/h in still air. It can travel 3120 km with the wind in the same time it would take to travel 1920 km against the wind. Find the speed of the wind.
Answer:
200 KM/H
Step-by-step explanation:
A plane has a speed of 840 km/h in still air. It can travel 3120 km with the wind in the same time it would take to travel 1920 km against the wind. Find the speed of the wind.
let x=speed of wind
(840+x)=speed of plane with wind
(840-x)=speed of plane against wind
Travel time = distance/speed (same with and against the wind)
3120/(840+x)=1920/(840-x)
cross-multiply
3120*840-3120x=1920*840+1920x
3120*840-1920*840=1920x+3120x
5040x=1008000
x=200 km/hr
answer
Speed of wind=200 km/hr
4 people completed their work in one hour how will it take 3 people to finish it give your answer in minutes
it would be 45 minutes
Find the solution to each system please show your work!
Answer:
infinite number of solutions
Step-by-step explanation:
x + y = 1 → (1)
3y = - 3x + 3 ( add 3x to both sides )
3x + 3y = 3 ( divide through by 3 )
x + y = 1 → (2)
since the 2 equations are the same, this indicates the system has an infinite number of solutions
What is this and how do you solve it
b²-4ac is the discriminant (D)!
you use it when you have a second degree function and want to find the x. If:
D<0 -> no x that we can find
D=0 -> 1 answer for x
D>0 -> 2 answers for x
when your D is = or > 0 then you use these formulas to find the x:
x1= (-b-VD)/2a
x2= (-b+VD)/2a
example1:
f(x)=2x²+3x+4=0
D= b²-4ac
= 3²-4×2×4
=9- 32
=-23
-> no answers for x
example2:
f(x)=2x²+5x+2=0
D= 4²-4×2×2
= 25-16
=9
x1= (-b-VD)/2a
= (-5-3)/4
= -8/4
=-2
x2= (-b+VD)/2a
= (-5+3)/4
=-2/4
=-1/2
A timer is started and a few moments later a model airplane is launched from the ground. Its height (in feet) as a function of time (in seconds after the timer was started) is given by the equation h(t)=−(t−12)2+81
. Which of the following statements is true?
The airplane reaches its minimum height of 12 feet in 81 seconds.
The airplane reaches its maximum height of 81 feet in 12 seconds.
The airplane reaches its minimum height of 81 feet in 12 seconds.
The airplane reaches its maximum height of 12 feet in 81 seconds.
The statement which is true is the airplane reaches its maximum height of 81 feet in 12 seconds.
Since the height of the plane is a function given by a parabola, we need to know the equation of a parabola in vertex form
What is the equation of a parabola in vertex form?The equation of a parabola with vertex (h,k) is given by y = a(x - h) + k
Since the height (in feet) of the airplane as a function of time (in seconds after the timer was started) is given by the equation h(t) = −(t − 12) + 81
Since this is the equation of a parabola in vertex form, comparing h with y, we have that a = -1, h = 12 and k = 81Since a = -1 < 0 this implies that the point (h, k) = (12, 81) is a maximum pointSo, the statement which is true is the airplane reaches its maximum height of 81 feet in 12 seconds.
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COSINE LAW: Solve triangle PQR. round angles to the nearest tenth
Answer:
Hi,
Step-by-step explanation:
PR²=PQ²+QR²-2*PQ*QR*cos(51°)
=15²+12²-2*15*12*cos(51°)
=142,444659....
PR=11.9350...
PQ²=QR²+PR²-2*QR*PR*cos(R)
cos(R)=(12²+142.444...-15²)/(2*12*11.9350...)=0,21451112....
angle R=77,61315...°≈77.6°
angle P=180°-51°-77.6°≈51,4°