Answers
In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way. The relationships between two or more items are frequently represented by the points on a graph.
Explain the graph of the solution?We graph both equations in the same coordinate system in order to visually solve a system of linear equations. The intersection of the two lines is where the system's answer will be found.
Any two ordered pairs can be used to create a solution set on a graph by connecting them with a straight line. Thus, any point along this graphed line would be included in the solution set.
There is only one solution that holds true for both equations if the equations' graphs cross. There are no solutions that hold for both equations if the equations' graphs do not meet (for instance, if they are parallel).
The answer for this graph is -4.
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Related Questions
Prove that,if one root of the equation ax^2+bx+c=0 is twice the other,then 2b^2=9ac
Answers
The proof of the quadratic equation is represented by the equation 18(m₂)² = 18(m₂)²
What are quadratic equations?Quadratic equations are second-order polynomial equations and they have the form y = ax² + bx + c or y = a(x - h)² + k
How to prove the roots of the quadratic equation?The quadratic equation is given as
ax² + bx + c = 0
From the question, we understand that
One of the roots is twice the other
This means that
m₁ = 2m₂
Where m₁ and m₂ are the roots of the quadratic equation
The quadratic equation is then represented as
(x - m₁) * (x - m₂) = 0
Substitute m₁ = 2m₂ in the equation (x - x₁) * (x - x₂) = 0
So, we have
(x - 2m₂) * (x - m₂) = 0
Expand the brackets
So, we have
x² - 2xm₂ - xm₂ + 2(m₂)² = 0
Evaluate the sum and the difference.
So, we have
x² - 3xm₂ + 2(m2)² = 0
In the above equation, we have
a = 1
b = -3m2
c = 2(m₂)²
Recall that
2b² = 9ac
So, we have
2 * (-3m₂)² = 9 * 1 * 2(m₂)²
Evaluate
18(m₂)² = 18(m₂)²
The above equation is true
Hence, it is true that if one root of the equation ax² + bx + c = 0 is twice the other, then 2b² = 9ac
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Which statement is true regarding the graphed functions?
On a coordinate plane, a straight red line with a positive slope, labeled g of x, crosses the x-axis at (negative 6, 0) and the y-axis at (0, 6). A straight blue line with a negative slope, labeled f of x, crosses the x-axis at (negative 0.75, 0) and the y-axis at (0, negative 2).
Answers
The following statement is true about the functions f(x) and g(x):
f(–2) = g(–2)
What are linear equations?Linear equations are equations that have constant average rates of change.
Note that the constant average rates of change can also be regarded as the slope or the gradient
How to determine the true statement about the functions?A system of linear equations is a collection of at least two linear equations.
In this case, the system of functions is given as
Functions f(x) and g(x)
From the attached graph, we can see that:
The values of the function f(x) at f(2), or f(4) do not have a match to the function g(x) at g(2) or g(4).
However, the functions intersect at x = -2
This means that f(-2) = g(-2)
Hence, the true statement about the functions is f(–2) = g(–2)
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Complete question
Which statement is true regarding the graphed functions?
See attachment
f(4) = g(4) f(4) = g(–2) f(2) = g(–2) f(–2) = g(–2)
I need help because i can’t seem to understand it
Answers
sinA = 0.37
cosA = 0.93
tanA = 0.40
secA = 1.08
cscA = 2.69
cot A = 2.50
Explanation:Given that a = 4, b = 10. To obtain c, we use the Pythagorean theorem:
[tex]\begin{gathered} c^2=a^2+b^2 \\ =4^2+10^2 \\ =116 \\ c=\sqrt{116}=10.77 \end{gathered}[/tex]Now
[tex]\begin{gathered} \sin A=\frac{Opposite}{hypotenuse}=\frac{a}{c} \\ \\ =\frac{4}{10.77}=0.37 \end{gathered}[/tex][tex]\begin{gathered} \cos A=\frac{adj}{hyp}=\frac{b}{c} \\ \\ =\frac{10}{10.77}=0.93 \end{gathered}[/tex][tex]\begin{gathered} \tan A=\frac{opp}{adj}=\frac{a}{b} \\ \\ =\frac{4}{10}=0.40 \end{gathered}[/tex][tex]secA=\frac{1}{cosA}=\frac{10.77}{10}=1.08[/tex][tex]cscA=\frac{1}{sinA}=\frac{10.77}{4}=2.69[/tex][tex]cotA=\frac{1}{tanA}=\frac{10}{4}=2.50[/tex]I need help finding an answer, please.
Answers
From the given actual height of tower 1083 feet and width 410 feet, the
scale model is equal to 1.98 feet tall.
As given,
Eiffel Tower's actual height = 1083 feet
Eiffel Tower's actual width at base = 410 feet
Scale model's width at base = 0.75 feet
To find: how much tall is the scale model of the Eiffel Tower
Let us assume the height of the scale model of the Eiffel Tower to be x feet
Then by the property of similarity of scale models, ratio of the height of actual Eiffel Tower to its scale model will be equal to the ratio of the width of their base.
=> [tex]\frac{x}{1083} = \frac{0.75}{410}[/tex]
=> x = 1.98 feet
Therefore, the width of the base of the scale model of the Eiffel Tower is 1.98 feet with given actual height and width 1083feet and 410 feet respectively.
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What is the solution for 2(4x-11)+9 =19
Answers
Answer:
x=4
Step-by-step explanation:
Answer:
(2×4x-2×11)+9=198x-22+9=198x=22+19-98x=32x=32÷8x=4
Step-by-step explanation:
(2-√3)²=7-4√3
How we solve this question ?
Hurry answer please
Answers
Proved using the formulae
Refer to pic
Slope intercept form for points through (0,-5) and (4,0)
Answers
Answer:
y = (5/4)x - 5
Step-by-step explanation:
(0, -5) and (4, 0)
(x₁, y₁) (x₂, y₂)
y₂ - y₁ 0 -(-5) 5
m = ------------- = ------------ = ---------
x₂ - x₁ 4 - 0 4
y - y₁ = m(x - x₁)
y -(-5) = (5/4)(x - 0)
y + 5 = (5/4)x - 0
-5 -5
----------------------------
y = (5/4)x - 5
I hope this helps!
Solve F(x) for the given domain. Include all of your work in your final answer. Submit your solution.
F(x) = x2 + 2
F(x - h) =
Answers
Based on the domain, the equation of the function f(x) is F(x - h) = x^2 - 2xh + h^2 + 2
What is the domain of a function?The domain of the function is the set of input values of the graph
How to determine the solution of the function f(x)?The equation of the function is given as
F(x) = x^2 + 2
The required function is given as
F(x - h)
The above means that the value of x in the function F(x) = x^2 + 2 is x - h
i.e.
x = x - h
So, we substitute x - h for x in the equation F(x) = x^2 + 2
This gives
F(x - h) = (x - h)^2 + 2
Evaluate the exponent
So, we have
F(x - h) = x^2 - 2xh + h^2 + 2
The above equation cannot be further simplified
Hence, the solution of the function f(x) at the given domain is F(x - h) = x^2 - 2xh + h^2 + 2
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A linear relationship is shown in the graph.
Which equation best represents the relationship between x and y?
Answers
(A) The equation y = ( 1/4 )x + 2 best represents the relationship between x and y.
From the graph, we can see that the line is passing through points ( - 8, 0 ) and ( 0, 2 ).
So, to obtain the equation that represents the best relationship we will substitute the points in the equation to check whether they satisfy or not.
Consider option (a),
y = ( 1/4 )x + 2
For ( - 8, 0) :
0 = ( 1/4 ) × - 8 + 2
0 = - 2 + 2
0 = 0
For ( 0, 2 ):
y = ( 1/4 )x + 2
2 = (1/4) × 0 + 2
2 = 2
Hence, the equation y = ( 1/4 )x + 2 passes through both points.
Consider option (b),
y = 4x - 8
For point ( - 8, 0 )
y = 4(-8) - 8
y = - 32 - 8 = - 40 ≠ 0
For point ( 0, 2)
y = 4(0) - 8 = - 8 ≠ 2
Hence, the equation y = 4x - 8 does not pass through the points.
Consider option (c),
y = ( 1/4 )x - 8
For ( - 8, 0 )
y = ( 1/4 ) × - 8 - 8
y = - 2 - 8 = - 10 ≠ 0
For ( 0, 2)
y = ( 1/4 ) × 0 - 8 = - 8 ≠ 2
Hence, the equation y = ( 1/4 )x - 8 does not pass through points.
Consider option (d),
y = 4x + 2
For point ( - 8, 0 )
y = 4( - 8) + 2
y = - 32 + 2 = - 30 ≠ 0
For point ( 0, 2)
y = 4( 0 ) + 2 = 2
2 = 2
Hence, the equation passes through ( 0, 2) but does not pass through the point ( - 8, 0 ).
Therefore, the equation that represents the relationship between x and y is y = ( 1/4 )x + 2
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PLEASE HELP QUICK!!!!
A candy store sells caramels and milk chocolate by the pound. The table below shows the total cost, in dollars, for a pound of each type of candy the store sells.
Answers
Answer:
Conversion of Dollars to Pounds is $1=0.90£
Step-by-step explanation:
b) when you calculate the amount you paid in total for 5 caramels and 4 milk chocolates, the total comes to $97,6 which is close to $100
Hope this helps !!
What is the reason for each step in the solution of the equation?
4x−1=−2(x+1)
Answers
the waiters at a restaurant have agreed to give one third of their tips to the kitchen staff if a waiter collects 72$ how much does he end up keeping
Answers
Answer:
48
Since they are giving one third of it to the staff, they are keeping 2 thirds of it for themselves. Two thirds of 72 is 48.
Answer:
He keeps $48.
Step-by-step explanation:
If he gives away 1/3, he keeps 2/3 so that's what we need to calculate.
First find 1/3 of 72 by dividing by 3: 72/3=24
Now to find 2/3, multiply by 2: 24*2=48
(72/3)*2= $48
Which expression represents the distance between 14.6 and −5.2 on the number line?
A. |-5.2 + 14.6|
B. |5.2 - 14.6|
C. |14.6 - {-5.2}
Answers
Answer:
The correct expression is
C. |14.6 - (-5.2)|
The table shows the information about the heights, in cm, of a group of yr11 girls
Answers
# 13 i
MODELING REAL LIFE The post office and the grocery store are both on the same straight road between the
school and your house. The distance from the school to the post office is 376 yards, the distance from the post office
to your house is 929 yards, and the distance from the grocery store to your house is 513 yards.
a. What is the distance from the post office to the grocery store?
yards
b. What is the distance from the school to your house?
yards
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Answer:
What is the role of ethnocentrism in defining the concept of “progress”
Step-by-step explanation:
11 of 25 students in class own a dog.What is the ratio of students who own a dog to students in the class?What is the ratio of students who own a dog to students who DON'T own a dog?
Answers
Answer:
(a)11:25
(b)11:14
Explanation:
he total number of students in the class = 25
The number of students that own a dog = 11
do not 25-11=14
(a)The ratio of students who own a dog to students in the class will be:
[tex]=11\colon25[/tex](b)The ratio of students who own a dog to students who DON'T own a dog will be:
[tex]=11\colon14[/tex]Question 1 (1 point)
write an equation (slope-intercept form) of the line
passing through the point (-20, 4)
that is perpendicular to the line
2x + 5y = 10.
y =
Blank 1:
Answers
The an equation (slope-intercept form) of the line is 2y = 5x + 108.
What is described as the slope-intercept form?A line's equation can be written in a variety of ways, each of which is valid. The slope-intercept form of such a line is a way of writing a line's equation so that the slope and y-intercept are easily recognizable. The slope of the line is its steepness, and the y-intercept is the point where line intersects the y-axis.For the given question;
The equation of the perpendicular line is given as 2x + 5y = 10.
The passing points of the line (-20, 4)
(x₁, y₁) = (-20, 4)
The equation of line in slope-intercept form is given as; y = mx + c.
Where, c is the y intercept and m is the slope.
The relation of the slope of two perpendicular lines are-
m₁ x m₂ = -1
The equation of line is-
2x + 5y = 10; find m₁
5y = -2x + 10
y = (-2/5)x + 10
Comparing with standard form.
m₁ = (-2/5)
Then, m₁ x m₂ = -1
(-2/5) x m₂ = -1
m₂ = 5/2
Put in the equation of line;
y - y₁ = m(x - x₁)
Put the values;
y - 4 = (5/2) (x + 20)
Solving;
2y - 8 = 5x + 100
2y = 5x + 108
Thus, the an equation (slope-intercept form) of the line is 2y = 5x + 108.
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Find the output, d, when the input, t, is 4 for d (t)- 13-4t. d(-2) -
Answers
The output of the given equation d (t)- 13-4t. d(-2) when the input is t=4 will be - will be -323
Give an illustration of what is a differential equation?Equations with General Differential. Consider the differential equation y′=3x2, which has a derivative and is an illustration of a differential equation. The variables x and y are related because y is an unidentified function of x. The derivative of y is also on the equation's left-hand side.
What are differential equations used for?The sciences, from which the equations originated and where the solutions found application, were the first to influence the mathematical theory of differential equations.
As the equation says: d(t)=13-4t.d(-2)
First we will calculate d(-2)
d(-2)=13-(4*-2)
d(-2)=21
d(4)=13-4*4*21
d(4)=-323
By this, the Final answer that is output for d would be -323.
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You make an investment of $2250.00 with an absolute change of ―$350.00. What is your investment now
worth and what was the percent change?
Answers
1. The investment of $2,250 with an absolute change of -$350 is now worth $1,900.
2. The percentage change in the worth of the investment is -15.56%.
What is a percentage change?A percentage change refers to the percentage difference between the initial value and the current value.
To compute the percentage change, use the absolute change and divide by the initial value, then multiply by 100.
For this investment of $2,250 which is now worth $1,900, there was a percentage change of -15.56%, implying that it has drastically reduced in value.
Initial Investment Cost = $2,250.00
Absolute change in investment value = $350
Current value of investment = $1,900 ($2,250 + $350)
The percentage change = -15.56% (-$350/$2,250 x 100)
Thus, the investment is currently valued at $1,900, having lost $350 in value, which in percentage terms, is -15.56%.
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provide the correct reason for the statement in line 3. (please help)
Answers
The property that completes the proof is the segment addition postulate
How to determine the statement that represents the reason in the proof?The given parameters in the question are:
The point C is the midpoint of AE
BC = CD
The above implies that
AC = CE
And it also means that:
The line segment BC and the line segment CD have equal lengths
Using the above as a guide, we have the following equations
AB + BC = AC
CD + DE = CE
The above equations are true because of the segment addition postulate
This postulate states that:
For any two points (A and C) located on a line segment and a third point (b) between the initial points. The lengths between the points can be represented as AB + BC = AC
Hence, the statement that represents the reason 3 in the proof is (b) segment addition postulate
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The softball team is selling hats. John bought 3 for $24.00. Stacey bought 5 for $40.00. Jim bought 2 for $16.00.
Why does this verbal description represent a proportional relationship?
Answers
The value of the hats bought by John, Stacey, and Jim are $8 per hat. This shows a proportional relationship.
What is a proportional relationship?It should be noted that a proportional relationship is one where it van be expressed as y = kx.
In this case, John bought 3 for $24.00. This will be:
= $24 / 3
= $8 per hat
Stacey bought 5 for $40.00. This will be:
= $40 / 5
= $8 per hat
Jim bought 2 for $16.00. This will be:
= $16/2
= $8 per hat
Therefore, it's a proportional relationship.
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What is the area, in square inches, of a square whose perimeter is 44 inches?
Answers
The area is 121 square inches
Explanation:The perimeter of a square is given as:
P = 4l
where l is the length of its sides
Given that the perimeter is 44 inches, we have:
44 = 4l
l = 44/4 = 11
The length of it's sides is 11 inches.
The area is given as:
[tex]\begin{gathered} A=l^2 \\ \\ =11^2 \\ =121 \end{gathered}[/tex]The area is 121 square inches.
Answer:121 square inches.
Step-by-step explanation:
Question
Two sides of a right triangle have lengths of 5 inches and 12 inches. Which of the following could be the
length, in inches, of the third side of the triangle?
A 3
B 8
C 13
D 17
Answers
a^2+b^2=c^2
5^2+12^2=c^2
25+144=c^2
169=c^2
Square root 169=c
13=c
13*13=169
7. STEM The male Cuban tree frog is about the size of the
female Cuban tree frog. The average size of the female Cuban
tree frog is shown at the right. What is the size of the male
Cuban tree frog? (Example 4)
Answers
Answer:
Step-by-step explanation:
The male Cuban tree frog is about 2/5 the size of the female Cuban tree frog. The average size of the female Cuban tree frog is 6 inches. What is the size
Let f (x) = 3x+4 and g(x) = 4x^2+4x.
After simplifying,
(f∘g)(x) = _____ <---- answer
PLEASE HELP!
Answers
It should be noted that the value of (f.g)(x) will be
12x³ + 28x² + 16x.
How to illustrate the information?It should be noted that a function is simply used.to illustrate the relationship between the expressions that's given in the data.
From the information, the following can be illustrated:
f(x) = 3x + 4
g(x) = 4x² + 4x
Therefore, (f.g)(x) will be the multiplication of the variables. This will be illustrated as:
= (3x + 4) × (4x² + 4x)
= 12x³ + 12x² + 16x² + 16x
= 12x³ + 28x² + 16x
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Please help me im begging
Answers
Let's say x is the number of ounces. Since the cost for each ounce is $0.85 then we can find the cost for the total amount of ounces by multiplying it by the cost of each one:
$0.85 · x
This is not the total cost, since the total cost has an additional of $5.50. Then the total cost is given by
c = $5.50 + $0.85x
Answer: C: c = 0.85x + 5.50What is the value of x?
Answers
Answer: Value of x is 16
Step-by-step explanation:
Triangle ABC and ADE are Similar Triangles using Angle-Angle-Angle similarity,
therefore,
[tex]\frac{AB}{BC}=\frac{AD}{DE}[/tex]
AB=x
BC=8
AD=x+6
DE=11
on substituting value,
[tex]\frac{x}{8}=\frac{x+6}{11}[/tex]
on cross multiplying,
11x = 8x+48,
subtracting 8x on both sides,
3x = 48,
dividing both sides by 3,
x=16
Therefore, value of x is 16
Deluxe coffee is to be mixed with regular coffee to make at
least 43 pounds of a blended coffee. The mixture must
contain at least 12 pounds of deluxe coffee. Deluxe coffee
costs $6 per pound and regular coffee $5 per pound. How
many pounds of each kind of coffee should be used to
minimize costs?
Answers
Answer:
12 pounds of deluxe and 31 pounds of regular.
Step-by-step explanation:
$227 is the minimum cost.
Answer:
We have to minimize the cost of 51 pounds of blended coffee.
The mixture must contain 13 pounds of deluxe coffee.
Deluxe coffee costs $4 per pound while regular coffee costs $3 for the same amount.
So, we need to maximize the concentration of regular coffee in the blended coffee to minimize our costs, but we must mix 13 pounds of deluxe coffee in order to make the blended coffee as it is the condition given to us in the problem.
Hence, apart from this 13 pounds, all the rest weight in blended coffee should come from the regular one.
Hence, the amount of regular coffee we have to use = (51 - 13) = 38 pounds.
Now, the cost of the 51 pounds of blended coffee
38×3+13×4 = ₹166.
Find the length and width of a rectangle sandbox, where the length is 3 feet longer than it’s width if you are building it with 22 feet of lumber
Answers
Let the length be represented by l and the width, w.
The question says that the length is 3 feet longer than the width. This means that
[tex]l=w+3[/tex]The perimeter of a rectangle is given as
[tex]2(w+l)=P[/tex]The perimeter of the sandbox is given as 22 feet.
Substituting the values for the perimeter and the length (w + 3) into the perimeter formula, we have
[tex]2(w+w+3)=22[/tex]Solving, we have
[tex]\begin{gathered} 2(2w+3)=22 \\ 2w+3=\frac{22}{2} \\ 2w=11-3 \\ 2w=8 \\ w=\frac{8}{2} \\ w=4 \end{gathered}[/tex]Now that we have the value for the width, we can calculate the length as
[tex]\begin{gathered} l=w+3 \\ l=4+3 \\ l=7 \end{gathered}[/tex]The length is 7 feet and the width is 4 feet.
if RS equals 59 and ST equals 10x - 31 find x
Answers
The chord RS and chord ST subtends equal angles the center. So length of chord ST is equal to length of chord RS.
Determine the value of x.
[tex]\begin{gathered} RS=ST \\ 59=10x-31 \\ 10x=59+31 \\ x=\frac{90}{10} \\ =9 \end{gathered}[/tex]So value of x is 9.