Answer:
x= -4 and y=2
Step-by-step explanation:
-3x+y=14 ...eqn 1
2x+3y= -2....eqn 2
from eqn 1
-3x+y=14
y=14+3x
substitute y=14+3x into eqn 2
2x+3(14+3x) = -2
2x+ 42+ 9x = -2
11x= -2-42
11x= -44
x = -4
substitute X = -4 into eqn 1 to get y
-3x+y=14
-3(-4) +y =14
12+y= 14
y= 14-12
y =2
Smith has p small balloons and 20 big balloons write the expression that shows how many balloons smith has?
Smith's balloon is an algebraic expression
The expression that represents how many Balloons Smith has is p + 20
How to determine the number of ballons?The given parameters are:
Small = p
Big = 20
Add the number of small and big ballons to get the total number of ballons
Total = Small + Big
This gives
Total = p + 20
Hence, the expression that represents how many Balloons Smith has is p + 20
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What is the name of the line? *
GH is a tangent to the given circle.
What is a Tangent?A line that only touches a circle or an ellipse at one point is said to be tangential in geometry. If a line contacts a curve at point P, that point is referred to as the point of tangency. In other words, it is described as the line that, at that particular location, indicates the slope of a curve.
As per the given diagram:
The line segments AB, AC, DC and EF are drawn in the diagram also a line GH is drawn in the diagram.
A line GH is drawn such that it's extending from both of its end towards infinity, and it touches the circle at only one point, which is G. This satisfies all the conditions for the line GH to be a tangent.
Hence, GH is a tangent to the given circle.
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Please help quick!
Subtracting a number is the same as adding its opposite.
Use this understanding to complete each of the equations below.
Enter numbers to evaluate −5−(−7).
‐5 –(‐7)= ‐5 + _______
= ________
Enter numbers to evaluate −5−7.
‐5− 7 = ‐5 + _______
= ________
Answer:
First space: 7
second space: 2
third space: -7
last space: -12
Step-by-step explanation:
To subtract, use "Add the opposite". In the problem the minus has aready been changed to adding, so you just change the second number (-7 in the first part or 7 in the second part) to their opposite sign. see image.
Which economic system has no government involvement in the market?
a capitalism
.. communism
C. socialism
l. No economic system is free from government involvement.
Please select the best answer from the choices provided
Answer: I.
Step-by-step explanation:
Capitalism is clearly not the answer. Capitalist governments such as America have their fingers into the economic trading.
Socialism and Communism sound plausible, but Communism is giving people money by their work, and Socialism is everything is owned by the public. Both still involve themselves in markets, so the answer is I
Answer:
d.
No economic system is free from government involvement.
Step-by-step explanation:
Please I really need help
Answer:
NM = 17, LY = 5, m<NLY = 53.13 degrees, m<NMY = 28.07 degrees
Step-by-step explanation:
To solve for NM, you just use the Pythagorean theorem,
[tex]8^{2} + 15^{2} = x^{2}[/tex]
64 + 225 = [tex]x^{2}[/tex]
289 = [tex]x^{2}[/tex]
[tex]17 = x[/tex]
To solve for LY, you can use geometric mean,
[tex]\frac{10}{y} = \frac{15+y}{10}\\\\100 = 15y + y^{2} \\y^{2} +15y - 100 = 0\\(y+20)(y-5) = 0\\y= 5[/tex]
To solve for the other angles, use the inverse.
Sin-1, = 8/10
= 53.13
Other angle =
Tan-1 = 8/15
= 28.07
Hope this helps, I put a lot of time into this :)
Which coordinates best represents the vertex of the graph first correct answer gets Brianliest
Answer:
The vertex of the graph is:
the minimum point for a parabola that opens upwardsthe maximum point for a parabola that opens downwardsAs this parabola opens upwards, the vertex is the minimum point.
From inspection of the graph, vertex = (-3, -1)
Equation of the graph
From inspection we can see that the x-intercepts are when
x = -4 and x = -2
[tex]\sf x = -4 \implies x+4=0[/tex]
[tex]\sf x = -2 \implies x+2=0[/tex]
Therefore:
[tex]\sf y=(x+4)(x+2)[/tex]
Expand:
[tex]\sf \implies y=x^2+6x+8[/tex]
Answer:
[tex]B)f(x) = {x}^{2} + 6x + 8[/tex]
Step-by-step explanation:
Let [tex] f(x)=x^2[/tex] be the parent function. With transformation of function, firstly,we know that,
We can move it up or down by adding a constant to the y-valuealgebraically
g(x)=x²+CClearly, The parabola is moved down by 1 unit thus, C is -1. Therefore our function transforms to
f(x)=x²-1secondly, we know that,
We can move it left or right by adding a constant to the x-valuealgebraically,
g(x)=(x+C)²in case,
C is positive, g(x) moves to the left and vise versaSince the parabola is moved left by 3 unit, C is +3, and hence Our function eventually becomes
[tex]f(x) = (x + 3 {)}^{2} - 1[/tex]simplifying it yields:
[tex]\implies \boxed{f(x) = {x}^{2} + 6x + 8}[/tex]
Hence,B is our required answer
Find the value of x. Round your answer to the nearest tenth
Hope you enjoy :)))))))
When do I use the quadratic formula?
Answer:
Step-by-step explanation:
Quadratic equations are commonly used in situations where two things are multiplied together and they both depend on the same variable. For example, when working with area, if both dimensions are written in terms of the same variable, you use a quadratic equation.
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar.
A complex number, (a + bi), multiplied by (2 + 3i) and added to -i gives the product of (-11 + 5i) and (1 – i).
a = and b =
The value of a is equal to 3 and the value of b is equal to 4.
Complex Number
A Complex Number is represented by z=a+bi, where:
a= real part
bi= imaginary number
b= imaginary part
i= [tex]\sqrt{-1}[/tex], therefore i²= -1
For solving this question, you should solve the product (-11 + 5i) * (1 – i). After that, you should compare the previous results with the result for expression ( (a + bi)* (2 + 3i) )-i. From this comparison, using the linear system you will find the variables a and b.
Step 1 - Solve the product (-11 + 5i) * (1 – i)(-11 + 5i) * (1 – i)=
-11 +11i +5i -5i²
-11 +16i -5i², as i²= -1 you can rewrite
-11 +16i -5(-1)
-11 +16i +5
-6+16i
Then,
(-11 + 5i) * (1 – i)= -6+16i
Step 2 - Simplify the expression ( (a + bi)* (2 + 3i) )-i( (a + bi)* (2 + 3i) )-i
(2a+3ai +2bi +3bi²) -i, as i²= -1 you can rewrite
(2a+3ai +2bi +3b(-1)) -i
(2a+3ai +2bi -3b) -i
( (2a-3b) + i(3a +2b) ) -i ,
For adding complex numbers, you must add or subtract the corresponding real and imaginary parts. Thus, you will have:
(2a-3b) + i(3a +2b-1)
Then,
( (a + bi)* (2 + 3i) )-i= (2a-3b) + i(3a +2b-1)
Step 3 - Identify real and imaginary parts for previous results
For (-11 + 5i) * (1 – i)= -6+16i
real part = -6
imaginary part = 16
For ( (a + bi)* (2 + 3i) )-i= (2a-3b) + i(3a +2b-1)
real part = 2a-3b
imaginary part = 3a +2b-1
Step 4 - Construct a linear system from real and imaginary parts2a-3b= -6
3a +2b-1=16, you can rewrite as 3a +2b=17.
Thus the system will be:
[tex]\begin{bmatrix}2a-3b=-6\\ 3a+2b=17\end{bmatrix}[/tex]
Step 5 - Solving the linear system
2a-3b=-6 (1)
3a+2b=17 (2)
Multiplying equation 1 by 2 and equation 2 by 3, you can rewrite as:
4a-6b= -12
9a+6b=51
Sum the equations
4a-6b+9a+6b= -12 +51
13a= 39
a=39/13=3
Replacing the value of a=3 in equation 1, you can find b.
2a-3b=-6 (1)
2*3-3b= -6
6 -3b = -6
-3b = -6 -6
-3b= -12
b= -12/-3 = 4
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Find the value of y for the given value of x.
y=2−9x;x=2/3
Answer:
-4
Step-by-step explanation:
y=2-9×(2/3)=2-6= -4
Solve:
x + 1/x = 4 1/4
Ans: 4,1/4
Answer:
x = 4, 1/4
solving steps
[tex]\sf \rightarrow x + \dfrac{1}{x}=4\dfrac{1}{4}[/tex]
make the denominators same
[tex]\sf \rightarrow \dfrac{x(x)}{x} + \dfrac{1}{x}=4\dfrac{1}{4}[/tex]
simplify the following
[tex]\sf \rightarrow \dfrac{x^2}{x} + \dfrac{1}{x}=\dfrac{17}{4}[/tex]
join both fractions together
[tex]\sf \rightarrow \dfrac{x^2+1}{x}=\dfrac{17}{4}[/tex]
cross multiply
[tex]\sf \rightarrow 4(x^2+1)=17(x)[/tex]
simplify
[tex]\sf \rightarrow 4x^2-17(x)+4=0[/tex]
completing square
[tex]\sf \rightarrow 4x^2-16(x)-x+4=0[/tex]
factor
[tex]\sf \rightarrow 4x(x-4)-1(x-4)=0[/tex]
group the variables
[tex]\sf \rightarrow (4x-1)(x-4)=0[/tex]
simplify
[tex]\sf \rightarrow (x-4)=0, \ (4x-1) =0[/tex]
final answer
[tex]\sf \rightarrow x=4, \ x =\dfrac{1}{4}[/tex]
Answer:
[tex]\boxed{x = \dfrac{1}{4}}[/tex] and [tex]\boxed{x = 4}[/tex]
Step-by-step explanation:
Given equation:
[tex]x + \dfrac{1}{x} = 4\dfrac{1}{4}[/tex]
Step-1: Convert the mixed fraction on the R.H.S into improper fraction
[tex]x + \dfrac{1}{x} = 4\dfrac{1}{4}[/tex]
[tex]x + \dfrac{1}{x} = \dfrac{4 \times4 + 1}{4}[/tex]
[tex]x + \dfrac{1}{x} = \dfrac{16 + 1}{4}[/tex]
[tex]x + \dfrac{1}{x} = \dfrac{17}{4}[/tex]
Step-2: Make common denominators on the L.H.S:
[tex]x + \dfrac{1}{x} = \dfrac{17}{4}[/tex]
[tex]\dfrac{x^{2} }{x} + \dfrac{1}{x} = \dfrac{17}{4}[/tex]
Step-3: Combine the denominators on the L.H.S
[tex]\dfrac{x^{2} }{x} + \dfrac{1}{x} = \dfrac{17}{4}[/tex]
[tex]\dfrac{x^{2} +1}{x} = \dfrac{17}{4}[/tex]
Step-4: Use cross multiplication
[tex]\dfrac{x^{2} +1}{x} = \dfrac{17}{4}[/tex]
[tex]x^{2} +1} = \dfrac{17x}{4}[/tex]
[tex]4(x^{2} +1}) = {17x}[/tex]
Step-5: Simplify the distributive property
[tex]4(x^{2} +1}) = {17x}[/tex]
[tex]4x^{2} +4} = {17x}[/tex]
[tex]-17x + 4x^{2} +4} = 0[/tex]
Step-6: Change "-17x" to "-16x - x" as it is equivalent
[tex]-17x + 4x^{2} +4} = 0[/tex]
[tex](-16x - x) + 4x^{2} +4} = 0[/tex]
Step-7: Factor the common terms
[tex](-16x - x) + 4x^{2} +4} = 0[/tex]
[tex]-16x - x + 4x^{2} +4} = 0[/tex]
[tex]4x(-4 + x) - 1(x - 4) = 0[/tex]
Step-8: Group the terms
[tex]4x(-4 + x) - 1(x - 4) = 0[/tex]
[tex](x - 4)(4x - 1) = 0[/tex]
Step-9i: Use cross multiplication for (x - 4)
[tex](x - 4)(4x - 1) = 0[/tex]
[tex]x - 4 = \dfrac{0}{4x - 1 } = 0[/tex]
Step-9ii: Use cross multiplication for (4x - 1)
[tex](x - 4)(4x - 1) = 0[/tex]
[tex]4x - 1 = \dfrac{0}{x - 4} = 0[/tex]
Thus [tex]x - 4 = 0[/tex] and [tex]4x - 1 = 0[/tex].
Step-10: Simplify both equations
[tex]4x - 1 = 0[/tex] [tex]x - 4 = 0[/tex]
[tex]4x = 0 + 1[/tex] [tex]x = 0 + 4[/tex]
[tex]4x = 1[/tex] [tex]\boxed{x = 4}[/tex]
[tex]\boxed{x = \dfrac{1}{4}}[/tex]
The length of a rectangle is six times its width.
If the perimeter of the rectangle is 126 in, find its area. Answer in inch ^2
Answer:
486 square inches.
Step-by-step explanation:
126 = w + 6w + w + 6w
126 = 14w
width = 9 inches
A = wl
A = (9)(9*6)
A = 486 square inches
How do do this problem
Answer:
42 in
Step-by-step explanation:
The lengths of the tangent segments drawn from an external point to a circle are equal.
AT and RT meet at point T
⇒ AT = RT = 9 in
RE and GE meet at point E
⇒ RE = GE = 5 in
AN and NG meet at point N
⇒ AN = GN = 7 in
Total perimeter = AT + RT + RE + GE + GN + AN
= 9 + 9 + 5 + 5 + 7 + 7
= 42 in
multiplication problem
Answer:
No, that is incorrect.
When doing a multiplication problem, you cannot simply take out a number from a number and expect the same result. This is under some circumstances. Let's solve the equations to see the results.[tex]21 * 34 = 714\\20 * 35 = 700[/tex]
As shown in the expressions, the results differ, proving our theory from earlier.__________________________________________________________
Questions?Ask me in the comments box, please.
Jordan has a part-time job selling candy. He works 3 hours each day. The function p(x) = 12 + 2x models his daily earnings, where x is the number of candies he sells during the day. Jordan sells 10 to 23 candies per day. Which interval contains all of the values in the range of the function?
The interval contains all of the values in the range of the function 32 to 58 dollars.
How to find the ranges of the function?The function is as follows:
p(x) = 12 + 2x
where
x = number of candies sold during the day.He sells 10 to 23 candies per day.
Therefore,
x = 10 and x = 23
Hence,
p(10) = 12 + 2(10) = 12 + 20 = 32
p(23) = 12 + 2(23) = 12 + 46 = 58
Therefore, the interval contains all of the values in the range of the function 32 to 58 dollars.
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1. Oscar and Eli set up a lemonade stand. If they have prepared 2 1/2 gallons of lemonade, how many 1-cup servings can they sell? A) 10 B 20 C
40 D 80
Answer:
40 cups
Step-by-step explanation:
There are 16 cups in one gallon. So 16 * 2 1/2 = 40
if sin = 3/5, than cos =
Answer:
cos θ = 4/5
Explanation given below in the image,
I hope my answer helps you.
1 point
2. Three boards are unloaded into the factory.
А
B
С
Board A is three times the length of board C, plus 5 inches. Board B is two
times the length of board C, plus 3 inches. The total length of all three boards
is 104 inches. How long is each board?
Your answer
??
A researcher is studying the growth of bacteria. He starts with 260 of the bacteria. It grows continuously at a rate of 1% per hour. How many bacteria will there be in 6 hours?
Which of the following is the correct factorization of the polynomial below?
p^3 - 125q^3
A. (p - 5q)(p^2 + 5pq + 25q^2)
B. (p - 25q)(p^2 + 25pq + 25q^2)
C. (p^2 + 10q)(p^3 + 25pq + 5q^2)
D. The polynomial is irreducible.
The correct factored form of the expression p³ - 125q³ is,
(p - 5q)(p² + 5pq + 25q²).
What is a polynomial?A polynomial is an algebraic expression.
A polynomial of degree n in variable x can be written as,
a₀xⁿ + a₁xⁿ⁻¹ + a₂xⁿ⁻² +...+ aₙ.
What is a factor of a polynomial?We know that if x = a is one of the roots of a given polynomial x - a = 0 is a factor of the given polynomial.
To confirm if x - a = 0 is a factor of a polynomial we replace f(x) with f(a) and if the remainder is zero then it is confirmed that x - a = 0 is a factor.
We know, a³ - b³ = (a - b)(a² + ab + b²).
Given, An expression p³ - 125q³.
= p³ - (5q)³.
= (p - 5q)(p² + p.5q + (5q)²).
= (p - 5q)(p² + 5pq + 25q²).
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The Changs updated their bedroom by purchasing a new lamp for $89.95 and a comforter set for $239.99. They paid 6 3/5% sales tax on their purchases. If the Changs paid $351.72 total, determine if they paid the correct amount.
Answer:
Step-by-step explanation:
In order to determine the correct answer, we need to confirm it first by making the solution below:Costs: $89.95 = New Lamp $239.99 = Comforter 6 3/5% = Sales Tax (convert this to decimal and we get 6.6%) $351.72 = Total amount the Chang's paidLet's get the total costs first which is $329.946.6% of 329.94 is $21.78The total cost with the tax would be $351.72.Therefore, the Chang's paid the correct amount. The correct answer would be option D. The Chang's family paid the correct amount for their purchases.
Find SU, TU, and ST.
Answer:
SU=6
TU=6
ST=12
Step-by-step explanation:
SU and TU are equal because their hypotenuses are equal (10).
With this knowledge, you know that 2x+2=3x.
Subtracting 2x from both sides shows that x=2, so you can substitute that into the original line segment values in order to get 6 for both SU and TU. Double this to find the value of ST (12).
The function f is given in three equivalent forms. Which form most quickly reveals the zeros (or "roots") of the function?
A) f(x) = 1/2x^2-5x+21/2
B) f(x) = 1/2(x-3)(x-7)
C) f(x) = 1/2(x-5)^2-2
Write one of the zeroes
pls help im sorry this looks so messy
Solve the system of linear equations. separate the x- and y- values with a coma. -4x+3y=-17 -3x+4y=-11
Answer:
1, 5
Step-by-step explanation:
I may be a little wrong but;
Multiply it by 3 and 4-
-12x+9y=-51
12x-16y=44
-7y=-7
y=1
x=5
The volume of the sphere is 500 - cubic units.
3
What is the value of x?
04 units
O 5 units
----
O 8 units
O 10 units
Answer:
8 po yan po sagot ko .. correct me if I wrong
There was 1/2. Of a cake left over from Hannah’s birthday party when she and her sister came home from school the next day they ate 2/3 of the left over cake for a snak. How much of the whole cake did the girls eat
Answer:
1/3
Step-by-step explanation:
This problem would be 1/2 x 2/3. The answer would be 1x2 over 2x3.
15/2 + 13/8+ 14/4+ 2/1+52/8+36/4=
Answer:
30.125
the answer is 30.125 so that is the answer of this question
Type The Correct Answer,
Answer:
0.72 meters
Step-by-step explanation:
by dividing 6.48 by 9, we get 0.72 meters
Answer:
here
Step-by-step explanation:
[90 POINTS] An air conditioning system needed for a new warehouse is built in the shape of a rectangular prism. The warehouse is 250 feet long, 125 feet wide, and 22 feet high. A one-ton air conditioning unit can cool 12,000 cubic feet.
What is the volume of the warehouse, and what size air conditioner is needed?
Answer:
The warehouse has 31,250 cubic feet of space.
The air conditioner has to be at least 55 tons.
Answer:
687,500 for first blank
60 tons for second blank
Step-by-step explanation:
It is correct on edmentum
What is the area, in square meters, of the shaded part of the rectangle shown below?