Answer:
x = 7.535 and y = 0.307
Step-by-step explanation:
Given that,
Two equations,
2x + 3y = 8 ...(1)
x – 5y = 6....(2)
Multiply equation (2) by -2.
-2x + 10y = -12....(3)
Now, adding equations (1) and (2),
2x + 3y -2x + 10y = 8-12
13y = 4
y = 0.307
Put the value of y in equation (2).
x – 5(0.307) = 6
x = 6 + 1.535
x = 7.535
So, the solutions of the given equation are x = 7.535 and y = 0.307.
Oscar bought 15 gallons of water at $1.98 per gallon. He wants to divide this water in bottles of 1/8 gallon each. What is the cost of a bottle of water?
Answer:
Step-by-step explanation:
True or False?
k = 3 over 4 is a solution to the inequality 12k + 2 < 12.
True
False
Answer:
False.
Step-by-step explanation:
...................
Explain why y +1 = 1.2(x + 2) and y- 5 = 1.2(x – 3) represent the same line, despite having
different equations.
Answer:
They have the same slope
Step-by-step explanation:
The standard equation of a line in point-slope form is expressed as;
y-y0 = m(x-x0)
We can see that both equations given are written in this form with a slope of 1.2. For two lines to be equal, they must have the same slope no matter the point on the lines. Hence the two equations are equal since they have different slopes.
Which of the following is true of the discriminant for the graph below?
Considering that the quadratic equation has no solutions, the discriminant is classified as:
C. Negative.
What is the discriminant of a quadratic equation and how does it influence the solutions?A quadratic equation is modeled by:
[tex]y = ax^2 + bx + c[/tex]
The discriminant is:
[tex]\Delta = b^2 - 4ac[/tex]
The solutions are as follows:
If [tex]\mathbf{\Delta > 0}[/tex], it has 2 real solutions.If [tex]\mathbf{\Delta = 0}[/tex], it has 1 real solutions.If [tex]\mathbf{\Delta < 0}[/tex], it has 2 complex solutions.Looking at the graph, the equation has no solutions, hence [tex]\Delta < 0[/tex] and option C is correct.
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James' truck uses 8 gallons of gas per day. He filled his tank up with 36 gallons of gas. How many days will James be able to drive using 36 gallons of gas?
Answer:
4.5
Step-by-step explanation:
36 ÷ 8 = 4.5
James will be able to drive for 4.5 days.
Mark me as brainliest please
James will be able to drive [tex]=4\frac{1}{2}[/tex] days.
What is arithmetic maths ?Arithmetic is the fundamental of mathematics that includes the operations of numbers like addition, subtraction, multiplication and division.
We have,
James' truck uses gas per day [tex]=8[/tex] gallons
Tank has gas [tex]=36[/tex] gallons
Now,
According to the question,
Number of days James will drive [tex]= \frac{Total\ gas}{Gas\ used\ per\ day}[/tex]
[tex]=\frac{36}{8}[/tex]
Number of days James will drive[tex]=4\frac{1}{2}[/tex] days
Hence, we can say that James will be able to drive [tex]=4\frac{1}{2}[/tex] days.
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Please need help explanation need it
Answer:
308 m^3
Step-by-step explanation:
The volume is given by
V = l*w*h where l is the length , w is the width and h is the height
V = 7*4*11
V = 308 m^3
Can I know the answer for the above questions
Answer:
Step-by-step explanation:
Show Workings.
Question is in attached image.
Answer:
A.]A chord of a circle of diameter 40 cm subtends an angle of 70° at the centre of the circle.
Solution given;
diameter [d]=40cm
centre angle [C]=70°
(a) Find the perpendicular distance be tween the chord and the centre of the circle.
Answer:
we have
the perpendicular distance be tween the chord and the centre of the circle=[P]let
we have
P=d Sin (C/2)
=40*sin (70/2)
=22.9cm
the perpendicular distance be tween the chord and the centre of the circle is 22.9cm.
(b) Using = 3.142, find the length of the minor arc.
Solution given;
minor arc=[tex]\frac{70}{360}*πd=\frac{7}{36}*3.142*40[/tex]
=24.44cm
the length of the minor arc. is 24.44cm.
B.]In the diagram, XZ is a diameter of the cir cle XYZW, with centre O and radius 15/2 cm.
If XY = 12 cm, find the area of triangle XYZ.
Solution given:
XY=12cm
XO=15/2cm
XZ=2*15/2=15cm
Now
In right angled triangle XOY [inscribed angle on a diameter is 90°]
By using Pythagoras law
h²=p²+b²
XZ²=XY²+YZ²
15²=12²+YZ²
YZ²=15²-12²
YZ=[tex]\sqrt{81}=9cm[/tex]
:.
base=9cm
perpendicular=12cm
Now
Area of triangle XYZ=½*perpendicular*base
=½*12*9=54cm²
the area of triangle XYZ is 54cm².
Answer:
Question 1a)
d = 40 cm ⇒ r = 20 cm
Let the perpendicular distance is x.
Connecting the center with the chord we obtain a right triangle with hypotenuse of r and leg x with adjacent angle of 70/2 = 35°.
From the given we get:
x/20 = cos 35°x = 20 cos 35°x = 16.383 cm (rounded)b)
The minor arc is 70° and r = 20
The length of the arc is:
s = 2πr*70/360° = 2*3.142*20*7/36 = 24.437 cm (rounded)Question 2Since XZ is diameter, the opposite angle is the right angle, so the triangle XYZ is a right triangle.
r = 15/2 cm ⇒ XZ = d = 2r = 2*15/2 = 15 cmFind the missing side, using Pythagorean:
[tex]YZ = \sqrt{XZ^2 - XY^2} = \sqrt{15^2-12^2} = \sqrt{81} = 9[/tex]The area of the triangle:
A = 1/2*XY*YZ = 1/2*12*9 = 54 cm²what is 8/9 divide 2/3?
Answer:
4/3
Step-by-step explanation:
8/9 ÷ 2/3
Simplify the complex fraction.
4/3
Step-by-step explanation:
8/9 ÷ 2/3
Simplify
4/3 is the correct answer
for each relation, decide whether or not it is a function
Answer:
Relation 1,2,and 4 are functions, but relation 3 not is a function.
Step-by-step explanation:
function 1 input, no function with the same input like m in relation 3.
which of the following equations are perpendicular
which statement must be true about line TU?
Answer:
line TU has no slope in the diagram above
convert 4 seconds to hour
Answer:
0.00111111 hrs
Step-by-step explanation:
Have a nice day
Answer:
4/3600 = .001111 hr
Step-by-step explanation:
4 seconds * 1 hour * 1 minute = 4/3600 = .001111 hr
60 minutes 60 seconds
What is the solution to this equation?
7x - 2(x - 10) = 40
O A. x = 4
O B. x = 12
O C. x = 6
D. X = 10
Answer:
A. x = 4
Step-by-step explanation:
[tex]7x-2(x-10)=40\\7x-2x+20=40\\5x+20=40\\5x=20\\x=4[/tex]
Ashish deposite rs 1000 every month is a recurring deposit account for period of 12 months. If the bank pays interest at a certain rate p.A. And ashish gets 12715 as the maturity value of this account at what rate of interest did he pay every month
Solution :
Given :
Principal amount, P = Rs. 1000
Time period = 12 months
The maturity value = Rs. 12,715
We know that,
[tex]$ SI = \frac{PTR}{100}$[/tex]
[tex]$SI = 1000 \times \frac{n(n+1)}{2 \times 12} \times \frac{R}{100}$[/tex]
[tex]$SI = 1000 \times \frac{12(12+1)}{2 \times 12} \times \frac{R}{100}$[/tex]
SI = 65 R
So we know,
maturity value = principal amount + SI
12715 = 1000 + 65 R
65 R = 12715 - 1000
65 R = 11715
R = 18%
So the rate is 18%
Answer:
[tex]R=11\%[/tex] p.a.
Step-by-step explanation:
Given:
the principal amount deposited each month, [tex]P=Rs. 1000[/tex]
amount after maturity of one year, [tex]A=Rs. 12715[/tex]
We have the formula as:
[tex]I=\frac{PR}{100}\times\frac{T(T+1)}{2\times 12}[/tex]
where:
R = rate of interest per annum
T = time in months
[tex]A-12P=\frac{PR}{100}\times\frac{T(T+1)}{2\times 12}[/tex] [since the principal is deposited each month]
[tex]715=\frac{1000\times R}{100}\times \frac{12\times 13}{24}[/tex]
[tex]R=11\%[/tex] p.a.
Let f(x) = 2x - 7 and g(x) = -6x - 3. Find f(x) + g(x) and state its domain.
HELP PLSSSSS!!!!!!!!!!!!!!!!!!!!!!!!!!!
A : 12x2 - 48x + 21; all real numbers
B: -14x2 + 36x - 18; all real numbers except x = 7
C: 12x2 - 48x + 21; all real numbers except x = 1
D: -14x2 + 36x - 18; all real numbers
Answer:
Step-by-step explanation:
f(x) + g(x) = 2x - 7 - 6x - 3
f(x) + g(x) = -4x - 10
The domain is any real number.
I think you have mixed up the question. None of the choices are correct. They look like they belong to another choice.
It could be f(x)*g(x)
(2x - 7) (-6x - 3)
-12x^2 - 42x - 6x + 32
-12x^2 - 48x + 21
Well it could be either A or C since they are identical.
What is the period 3 pi and 4 pi
Answer:
i think i know the answer sorry if im wrong but i would say B
Step-by-step explanation:
- CA Geometry A Illuminate Credit 4 FF.pdf
Answer:
hii
Step-by-step explanation:
What is the recursive formula for this geometric sequence?
-4, -24, -144, -864, ...
= -4
O A.
an =
2n-1 • 30
OB.
la = -4
ar = 2n-16
fa
= -6
C.
= 2n-1 • 30
= -6
O D.
lan
ar = 2n-1.4
Answer:
a1 = -4
an = an-1 * 6
Step-by-step explanation:
-4, -24, -144, -864, ...
First find the common ratio
Take the second term and divide by the first term
-24/-4 = 6
The common ratio is 6
The recursive formula is
a1 = -4
an = an-1 * 6
N is the centriod of triangle. Find XN if XG = 33
Answer:
22
Step-by-step explanation:
The centroid divides a median in two parts that have this ratio = 1/3 and 2/3
In particular the part between the vertex and the centroid is 2/3 of the median.
So we have:
XN = (33 * 2)/3 = 22
What is the measure of ∠
A. 6°
B. 42°
C. 60°
D. 49°
Answer:
<XYZ is equal to 49°
Step-by-step explanation:
Set the two expressions equal to each other so 7x+7=5x+19. Subtract 5x from 7x and 7 from 19 which is equal to 2x=12 that means x is 6. then plug 6 into (7x+7) which is equal to 49.
Choose the one that is FALSE. *
A. 1/4 = 2/8
B. 3/4 = 10/12
C. 5/10 = 1/2
D. 10/12 = 5/6
Answer:
B. 3/4 = 10/12
Step-by-step explanation:
A. 1/4*2/2 = 2/8
B. 3/4*3/3 = 9/12 not10/12
C. 5/10*5/5 = 1/2
D. 10/12 divided by 2/2 = 5/6
Thank you so much for your help
Answer:
1.1x
Step-by-step explanation:
that is the procedure above
Evaluate the expression 3(5 + 2)(7 - 2) using order of operations.
Answer:
105
Step-by-step explanation:
The order of operations is written as PEMDAS. These letters stand for:
-Parentheses
-Exponents
-Multiplication
-Division
-Addition
-Subtraction
We follow these steps in order to solve expressions efficiently. Now, we are going to use PEMDAS to evaluate the expression 3(5+2)(7-2) step by step.
3(7)(5) The first step is to simplify the numbers in the parentheses.
There are no exponents, so we skip to the next step, multiplication.
(3*7)(5)
21(5)
105
PEMDAS is no longer needed because 105 has come out to be our answer.
I hope this helps you out! Have an an awesome day :3
Calculate the answer to the correct number of significant figures: (1.705 + 0.5067) / (0.2 * 1.243) = ______.
8.897
8.8966
8.9
9
8.90
Answer:
8.9
Step-by-step explanation:
they said to the sig. figure so since it's 8.8966, so the answer will be 8.9
The answer to the correct number of significant figures is 8.897, the correct option is A.
What are Significant Figures?Significant figures is a positional notation, these are the digits that are required to understand the quantity of something.
The expression is
⇒(1.705 + 0.5067) / (0.2 * 1.243)
=2.2117/0.2486
=8.89662
≈ 8.897
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If a 750 ml bottle of juice costs £1.90 and a 1 litre bottle of the same juice costs £2.50 then the 750 ml bottle is better value.
Answer:
The 1 liter bottle is better value
Step-by-step explanation:
Cost of 750 ml = £1.90
Cost of 1 liter = £2.50
1000 ml = 1 liter
Cost per 250 ml
750 ml / 3 = £1.90 / 3
250 ml = £0.6333333333333
Approximately,
£ 0.633
Cost per 250 ml
1 liter / 4 = £2.50 / 4
250 ml = £0.625
The 750 ml bottle is not a better value
The 1 liter bottle is better value
Select the correct answer.
What is the value of x in the triangle?
Answer:
The answer is A. 21
Hope it helps.
Step-by-step explanation:
• • •
the hypotenuse of a right angled triangular field is 50ft and the legs are in the ratio 7:24, find the area of the right angled triangular field triangular field also find the cost of paving the field with brick at the rate of rs.20per square ft
Answer:
Step-by-step explanation:
If one leg is 7x than other leg is 24x
Using Pythagoras
50² = (7x)² + (24x)²
2500 = 49x² + 576x²
2500 = 625x²
x² = 2500/625 = 4
x = +2 or -2 ; x is positive
Means 7 x = 14 and 24x = 48
The two sides are 14cm and 48cm
Test: 14² + 48² = 196 + 2304 = 2500= 50²
Solve. -7x+1-10x^2=0
Answer:
[tex]-7x+1-10x^2=0[/tex]
[tex]-10x^2-7x+1=0[/tex]
[tex]quadratic\:equation:-[/tex] [tex]ax^2+bx+c=0[/tex]
[tex]solutions:-\\\\x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
[tex]For \\A=-10\\B=-7\\C=1[/tex]
[tex]x_{1,\:2}=\frac{-\left(-7\right)\pm \sqrt{\left(-7\right)^2-4\left(-10\right)\cdot \:1}}{2\left(-10\right)}[/tex]
[tex]\sqrt{\left(-7\right)^2-4\left(-10\right)\cdot \:1}=\sqrt{89}[/tex]
[tex]x_{1,\:2}=\frac{-\left(-7\right)\pm \sqrt{89}}{2\left(-10\right)}[/tex]
[tex]x_1=\frac{-\left(-7\right)+\sqrt{89}}{2\left(-10\right)},\:x_2=\frac{-\left(-7\right)-\sqrt{89}}{2\left(-10\right)}[/tex]
[tex]\frac{-\left(-7\right)+\sqrt{89}}{2\left(-10\right)}=-\frac{7+\sqrt{89}}{20}[/tex]
[tex]\frac{-\left(-7\right)-\sqrt{89}}{2\left(-10\right)}=\frac{\sqrt{89}-7}{20}[/tex]
[tex]x=\frac{\sqrt{89}-7}{20}[/tex]
OAmalOHopeO
Determine the period
Answer:
3 units
Step-by-step explanation:
The period of a wave is the time taken to complete a cycle of motion of the wave
In the given figure, the graduations of the x-axis, which is the usually time axis = 1 unit
At the origin, (0, 0), the vertical displacement of the wave = 0
The maximum value of the wave function is between x = 0 and x = 1
The minimum value of the wave function is between x = 2 and x = 3
At the point (3, 0) the value of the wave function is again 0, and a cycle of the wave is completed
Therefore, the period of the wave = 3 units of the x-variable
