Answer:
x=2
HPT 3x+5y=6 (1) và 2x+y=4 (2)
Nhân phương trình (2) với 5 để hệ số y của 2 phương trình bằng nhau. Ta có:
(2)⇔ 10x+5y=20(3)
Trừ (3) cho (1), có: 7x+0y=14⇒x=2
Answer:
3x+5y=6.....eqn 1
2x+y=4.......eqn 2
y=4-2x.....eqn 3
Step-by-step explanation:
substitute eqn 3 into eqn 1
3x+5(4-2x)=6
3x+20-10x=6
-7x = -14
x=2
a rectangle and Square have equal perimeter .If the rectangle has width 8 and length 12 what the area of a square?
Someone found 100! And added up all its digits. Then, this person added up the digits of this sum. The process was continued until the sum was a one-digit number. What was that number?
Help ASAP
Jack lives 210 miles from Cleveland, where he wants to visit. He has already traveled 125 miles on the bus and then took the train the rest of the way. How many miles were traveled on the train?
Answer:
85 miles
Step-by-step explanation:
He needed to travel a total of 210 miles
He had already traveled 125 miles on bus
And he traveled the rest of the length on the train
If we want to find the distance he traveled on train we simply subtract total distance by distance traveled on bus
So distance traveled on train = 210 - 125 = 85
So he traveled a total of 85 miles on train
Find the value of x.
42°
(5x + 2)
Answer:
x=8
Step-by-step explanation:
assuming this is what you mean:
(5x+2)=42
try to
isolate the variable by subtracting 2 from both sides
5x=40
continue to isolate the variable
divide by 5 on both sides
5x/5=40/5
x=8
The sides of a triangle are 4, 7, and 10. The triangle is dilated by a scale factor of 3 to create a
new triangle. Find the perimeter of the new triangle.
A
21 units
B
63 units
30 units
D
25 units
Answer:
B 63 units
Step-by-step explanation:
Dilatation is an increase of shape , a larger imagine , the dilatation is 3 so times each side by three and add them all up
Sam had $42 to spend on 12 raffle tickets. After buying them he had $6 left. How much did each raffle ticket cost?
Answer:
Each raffle ticket cost $3.
In parallelogram RSTU if RT=36 find RV.
Answer:
rv = 18
Step-by-step explanation:
if rt is 36, rv is half of that so you take 36 and divide by 2 and get 18,
have a great day!!
Answer:
18
Step-by-step explanation:
Because i have parallegram RSTU
=> RT = 2*RV = 2*VT
SU = 2* SV = 2*VU
How much would $600 be worth after 10 years, if it were invested at 4% interest compounded continuously? (Use the formula below and round your answer to the nearest cent.) A(t) = P▪︎e^rt
Answer:
600[tex]e^{10*.04}[/tex]
$895.09
Step-by-step explanation:
A rectangular cube of volume 8000cm3 has
length= 4x
width = 2x
Height= 1x
Find it's length, width and height.
Answer:
volumn= l*b*h
4x*2x*1x= 8000 cm3
8x= 8000 cm3
x= 1000cm3
length = 4000
breadth= 2000
height = 1000
Which choice is equivalent to the product below? √2 x √5 x √8
A. 16√5
B. 4√20
C. 4√5. <-- correct answer
D. 8√10
[tex]\longrightarrow{\green{ C. \:4 \sqrt{5} }}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\orange{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]
[tex] = \sqrt{2} \times \sqrt{5} \times \sqrt{8} [/tex]
[tex] = \sqrt{2 \times 5 \times 8} [/tex]
[tex] = \sqrt{2 \times 5 \times 2 \times 2 \times 2} [/tex]
[tex] = \sqrt{(2 \times 2) \times (2 \times 2) \times 5} [/tex]
[tex] = \sqrt{ {2}^{2} \times {2}^{2} \times 5} [/tex]
[tex] = \sqrt{ {2}^{2} } \times \sqrt{ {2 }^{2} } \times \sqrt{5} [/tex]
[tex] = 2 \times 2 \sqrt{5} [/tex]
[tex] = 4 \sqrt{5} [/tex]
[tex]\red{\large\qquad \qquad \underline{ \pmb{{ \mathbb{ \maltese \: \: Mystique35ヅ}}}}}[/tex]
[tex]\sf Q) \sqrt{2} \times \sqrt{5} \times \sqrt{8}[/tex]
[tex]\sf\implies \sqrt{2 \times 5 \times 8}[/tex]
[tex]\sf\implies \sqrt{2 \times 5 \times 2 \times 2 \times 2}[/tex]
[tex]\sf\implies \sqrt{(2 \times 2) \times (2 \times 2) \times 5}[/tex]
[tex]\sf\implies \sqrt{ {2}^{2} \times {2}^{2} \times 5}[/tex]
[tex]\sf\implies \sqrt{ {2}^{2} } \times \sqrt{ {2 }^{2} } \times \sqrt{5}[/tex]
[tex]\sf\implies 2 \times 2 \sqrt{5}[/tex]
[tex]\sf\implies 4 \sqrt{5}[/tex]
b) Show that the points (1,1), (-1,-1) and ( -root3, root 3 ) are the vertices of an equilateral triangle.
Given:
The vertices of a triangle are [tex](1,1),(-1,-1),(-\sqrt{3},\sqrt{3})[/tex].
To prove:
The given vertices are the vertices of an equilateral triangle.
Solution:
Distance formula:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Let the vertices of the triangle are [tex]A(1,1),B(-1,-1),C(-\sqrt{3},\sqrt{3})[/tex]. Then, by using the distance formula, we get
[tex]AB=\sqrt{(-1-1)^2+(-1-1)^2}[/tex]
[tex]AB=\sqrt{(-2)^2+(-2)^2}[/tex]
[tex]AB=\sqrt{4+4}[/tex]
[tex]AB=\sqrt{8}[/tex]
Similarly,
[tex]BC=\sqrt{(-\sqrt{3}-(-1))^2+(\sqrt{3}-(-1))^2}[/tex]
[tex]BC=\sqrt{(1-\sqrt{3})^2+(1+\sqrt{3})^2}[/tex]
[tex]BC=\sqrt{(1)^2+(\sqrt{3})^2-2\sqrt{3}+(1)^2+(\sqrt{3})^2+2\sqrt{3}}[/tex]
[tex]BC=\sqrt{1+3+1+3}[/tex]
[tex]BC=\sqrt{8}[/tex]
And,
[tex]CA=\sqrt{(1-(-\sqrt{3}))^2+(1-\sqrt{3})^2}[/tex]
[tex]CA=\sqrt{(1+\sqrt{3}))^2+(1-\sqrt{3})^2}[/tex]
[tex]CA=\sqrt{(1)^2+(\sqrt{3})^2+2\sqrt{3}+(1)^2+(\sqrt{3})^2-2\sqrt{3}}[/tex]
[tex]CA=\sqrt{1+3+1+3}[/tex]
[tex]CA=\sqrt{8}[/tex]
Clearly, [tex]AB=BC=CA[/tex].
Since all sides of the given triangle are equal, therefore the given vertices are the vertices of an equilateral triangle.
Hence proved.
Please help!!
The slope of a line that passes through the points (-6, w) and (-10, 4) ls 1/8. What is the
value of w?
Answer:
[tex]\displaystyle w=\frac{9}{2}=4.5[/tex]
Step-by-step explanation:
We can use slope formula:
[tex]\displaystyle m=\frac{y_2-y_1}{x_2-x_1}[/tex]
So:
[tex]\displaystyle m=\frac{4-w}{-10-(-6)}=\frac{4-w}{-10+6}=\frac{4-w}{-4}[/tex]
We are given that this equals 1/8. Therefore:
[tex]\displaystyle \frac{4-w}{-4}=\frac{1}{8}[/tex]
Solve for w. Cross-multiply:
[tex]-4(1)=8(4-w)[/tex]
Distribute:
[tex]-4=32-8w[/tex]
Isolate:
[tex]-8w=-36[/tex]
So:
[tex]\displaystyle w=\frac{-36}{-8}=\frac{9}{2}=4.5[/tex]
How would you solve this problem??
Answer:
x = 14000
Step-by-step explanation:
Function representing the cost to the company,
C(x) = -27x² + 51000x + 20433
Function defining the revenue generated,
R(x) = -36x²+ 303000x
Since, Profit to the company = Revenue - Cost
= R(x) - C(x)
P(x) = -36x² + 303000x - (-27x² + 51000x + 20433)
= -36x² + 27x² + 303000x - 51000x - 20433
P(x) = -9x² + 252000x - 20433
To maximize the profit,
P'(x) = -18x + 252000 [Derivative of the function P(x)]
P'(x) = 0
-18x + 252000 = 0
18x = 252000
x = 14000
Therefore, for the maximum profit company has to produce and sell 14000 phones.
A helicopter is 665 feet above the ground. A girl is looking up at the helicopter to form a line. Her line of sight is 5 feet off the ground. The distance between the girl and the helicopter is 280 feet.
Answer:
67
Step-by-step explanation:
we are given adjacent and opposite sides. thus tan^-1 would be used to determine the angle
opposite side = 665 - 5 = 660
adjacent side = 280
tan = opposite / adjacent
[tex]tan^{-1}[/tex] (660/280) = 67
Answer:
67
Step-by-step explanation:
I took it on EDG
How many cups of chocolate would Linda need for 2 cups of cream
How to do long division
Answer:
if you wanna do long division you have to simply just follow a procedure that is nice and easy so long division method is mainly need to find the square of a number with out using the prime factorization method the procedure is consisting of these of two steps
Obtain the number whose square root is to be computedplace bars every pair of digits starting with the unit digits .Also place a bar on one digit if any not forming a on the extreme left. each pair and the remaining one digit (if any) on the extreme left is called a period think of the largest number whose square is less than or equal to the first period . if this number as the divisor and the quotient put the question above the period and write the product of divisor and question just below the first period.subtract the product of divisor and quotient from the first period and bring down the next point to the right of the remainder this becomes the next dividend.double the question as it appears and enter It to the blank on the right for the next digits, as the next possible divisor.think of a digit to fill the blank in step 6 in such a way that the product of new divisor and its digit is equal to or just less than the new dividend obtained in the step 5 .subtract the product of the digits chosen in steps 7 and the new division from the dividend obtained in step 5 and bring down the next period to the right of the remainder of this becomes new dividend .repeat the steps 5 6 and 7 till all the periods have been taken up .obtain the quotient as a square root of the given number .Hope it helps
If you have 36 ft of fencing, what are the bases and side lengths of the different parallelograms you could enclose with the fencing? Consider only whole-number dimensions.
Answer:
[tex](l,w) = (1,17)[/tex]
[tex](l,w) = (2,16)[/tex]
[tex](l,w) = (3,15)[/tex]
---
---
-
[tex](l,w) = (9,9)[/tex]
Step-by-step explanation:
Given
[tex]P = 36ft[/tex] --- perimeter
[tex]l \to length[/tex]
[tex]w \to width[/tex]
Required
Possible dimension of different parallelogram
The perimeter is calculated as:
[tex]P=2(l+w)\\\\\\[/tex]
So,we have:
[tex]2(l+w)=36[/tex]
Divide by 2
[tex]l + w = 18[/tex]
Since l and w must be positive integers, the possible dimensions are:
[tex](l,w) = (1,17)[/tex]
[tex](l,w) = (2,16)[/tex]
[tex](l,w) = (3,15)[/tex]
---
---
-
[tex](l,w) = (9,9)[/tex]
Put these numbers in order from least to greatest.
0.48,0.73, and 3/10
Answer:
[tex]\frac{3}{10} , 0.48 , 0.73[/tex]
Step-by-step explanation:
In order to put this number in order from least to greatest, we have to turn them into fractions with the same denominator, so firstly we write down all of the decimals as fractions, and we will get...
[tex]0.48 = \frac{48}{100} \\\\0.73 = \frac{73}{100}[/tex]
Now, we need to find the smallest number that is divisible by 100 and by 10, and this number will be the least common denominator. The smallest number that is divisible by 100 and by 10 is 100, therefore 100 is the least common denominator. Now we have to make all of the fractions have the denominator of 100 and we do that in the following way...
[tex]\frac{48}{100}= \frac{48}{100}\\\\\frac{73}{100} = \frac{73}{100}\\\\\frac{3}{10} = \frac{(3)(10)}{(10)(10)} = \frac{30}{100}[/tex]
By looking at this we need to understand that...
[tex]\frac{30}{100}<\frac{48}{100}<\frac{73}{100}[/tex]
Therefore...
[tex]\frac{3}{10} < 0.48 < 0.73[/tex]
simplify the following
(2p+1)(2p-1)
Which linear inequality is represented by the graph? I’m timed hurry plz
Answer:
a
Step-by-step explanation:
first one i believe
Which statement shows how two polynomials 3x + 6 and 5x2 - 4x demonstrate the closure property when multiplied?
O 15x3 + 18x? - 24x may or may not be a polynomial
O 15x3 + 18x2 - 24x is a polynomial
O 15x + 42x2 – 24x may or may not be a polynomial
15x3 + 42x2 - 24x is a polynomial
Here you go, rockstar
B) 15x3 + 18x2 − 24x is a polynomial
✨keep going!✨
For EASY BRAINLIEST!!!
Answer 6. 7. 8. 9. !!
Please help I’m going to fail!
Answer:
Step-by-step explanation: 6 29 7 42
6) a number x increased by -18
x + (-18)
or x - 18
7) x subtracted from its reciprocal
1/x - x
8) two numbers have the sum of 11, one number is q find the other
x + q = 11
x + q - q = 11 - q q - q = 0
x + 0 = 11 - q
x = 11 - q
9) six is added to 4 times a number equals 42, find the number
( I don't know the six steps discussed in class. This is how I would do it)
6 + 4x = 42
6 - 6 + 4x = 42 - 6 isolate the variable, - 6 from both sides
0 + 4x = 36 6 - 6 = 0, 43 - 6 = 36, solve for x
4x/4 = 36/4 divide both sides by 4
1x = 36 /4 4/4 = 1
x = 9
Sam took a total of 12 tests over the course of 6 weeeks if the continued to take tests at the same rate how many tests will Sam have taken after 28 weeks of school
Answer:
56 tests
Step-by-step explanation:
first find the amount of test he took each week. if we divide 12 by 6 (12 ÷ 6 = 2) we find out that he took 2 tests per week.
So if he continues with the same rate for the next 28 weeks of school, in order to find out how many tests he would have taken, we just need to multiply 28 by 2 (28 × 2 = 56), which will be equal to 56
hope this helps! if you have any questions, let me know!
The focus is the point inside a _____________ that helps determine the shape of the curve.
1.vertix
2.parabola
3.directrix
4.quadratic
The focus is the point inside a parabola that helps determine the shape of the curve.
What is a parabola?A parabola is an equation of a curve, such that any point on the curve is equidistant from a fixed point called the focus and a fixed line called the directrix of the parabola.
The equation of a parabola:
y = a(x - h)² + k
We have,
A parabola is a type of curve that is formed when a plane intersects a cone at an angle that is parallel to one of the cone's sides.
One of the key defining features of a parabola is that all points on the curve are equidistant from a fixed point, known as the focus, and a fixed line, known as the directrix.
The focus is located inside the parabola, and its distance from the directrix is equal to the distance from any point on the parabola to the directrix.
This property allows us to use the focus and directrix to determine the shape and location of the parabola.
Thus,
The focus is the point inside a parabola that helps determine the shape of the curve.
Learn more about parabola here:
https://brainly.com/question/21685473
#SPJ2
Which is greater, 2 miles or 1,000 yards? How much greater? Explain. Of 2 miles and 1,000 yards, _____ is greater. Since 2 miles is the same as _____ yards, _____ is __ yards greater than _____ .
Answer:
yards
Step-by-step explanation:
Answer:
Which is greater, 2 miles
1 mile = 1760 yards
2 miles = 2 * 1760
2 miles = 3,520 yards
How much greater?
3,520 - 1000 = 2520 yards
X=
4
7
9
Does anyone know this please help quick !
Answer:
9
Step-by-step explanation:
Intersecting Chords Formula:
a • b = c • d
where a and b are the segments on one chord and c and d are the segments on the other chord
3*6 = 2*x
18 = 2x
Divide by 2
18/2 =2x/2
9 =x
Which description matches the expression 13 minus StartFraction 5 Over y EndFraction? the difference of thirteen and the product of five and a number the quotient of five and a number minus thirteen the difference of thirteen and the quotient of five and a number the sum of thirteen and the quotient of five and a number
Given:
The expression is:
[tex]13-\dfrac{5}{y}[/tex]
To find:
The description that matches the given expression.
Solution:
We have,
[tex]13-\dfrac{5}{y}[/tex]
Here, [tex]\dfrac{5}{y}[/tex] is describes as the quotient of five and a number and the minus sign describes the difference between 13 and the quotient.
So, the description that matches the given expression is "difference of thirteen and the quotient of five and a number".
Therefore, the correct option is C.
Answer:
the difference of thirteen and the quotient of five and a number
Step-by-step explanation:
\frac{(\sqrt{x} +1)^{2} +(\sqrt{x} -1)^{2} )}{(\sqrt{x} +1)(\sqrt{x} -1)} -\frac{3\sqrt{x} +1}{x-1}
Answer:
[tex]= \frac{2x-3\sqrt{x} }{x-1}[/tex]
Step-by-step explanation:
Given the expression
[tex]\frac{(\sqrt{x} +1)^{2} +(\sqrt{x} -1)^{2} )}{(\sqrt{x} +1)(\sqrt{x} -1)} -\frac{3\sqrt{x} +1}{x-1}[/tex]
Expand
[tex]\frac{(\sqrt{x} +1)^{2} +(\sqrt{x} -1)^{2} )}{(\sqrt{x} +1)(\sqrt{x} -1)} -\frac{3\sqrt{x} +1}{x-1}\\= \frac{x+2\sqrt{x}+1+(x-2\sqrt{x} +1) }{x-1}- \frac{3\sqrt{x} +1}{x-1}\\= \frac{2x+1}{x-1} - \frac{3\sqrt{x} +1}{x-1}\\= \frac{2x+1-(3\sqrt{x} +1)}{x-1}\\= \frac{2x-3\sqrt{x} +1-1}{x-1}\\= \frac{2x-3\sqrt{x} }{x-1}[/tex]
This gives the simplified form
A radius of a circle is 8 centimeters long.
One centimeter is about 0.4 inches. About
how long is the radius of the circle in
inches?
Answer:
1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
Step-by-step explanation:
Determine the equation of the line perpendicular to y = 1/5x – 7 and passes through the point (-3,6).
Answer:
y = -5x - 9
Step-by-step explanation:
y = -5x + b
6 = -5(-3) + b
6 = 15 + b
b = -9
