Answers
In order to express y = x² + 4x +9 in graphing form and graphing it we can follow these steps:
1. complete squares to express the equation in the form y = (x - p)² + q
We have to add and subtract (b/2)² on the right, where b is the coefficient of the second term of the equation
y = x² + 4x +9 + (4/2)² - (4/2)²
y = x² + 4x +9 + (2)² - (2)²
We can gorup and factor some terms of the equation by applying the following formula:
(x + a)² = x² + 2ax + a²
then by writing 4x as 2×2x we get:
y = x² + 2×2x + (2)² - (2)² +9
y = (x + 2)² - (2)² + 9
y = (x + 2)² - 4 + 9
y = (x + 2)² + 5
For an equation of the form y = (x - p)² + q, the vertex is (q, p), then, the vertex of the parabola is (-2, 5)
2. Determine the x-intercepts by replacing 0 for y and solving for x, like this:
0 = (x + 2)² + 5
0 - 5 = (x + 2)² + 5 - 5
-5 = (x + 2)²
±√-5 = √(x + 2)²
±√-5 = x + 2
x = -2 ± √-5
As you can see, on the right side the argument of the square root is a negative number, which makes the solution of this equation a complex number, then which means that the parabola won't intercept the x-axis.
3. Find the y-intercept by replacing 0 for x:
y = (0 + 2)² + 5
y = (2)² + 5
y = 4 + 5
y = 9
Then, the y-intercept of this parabola is (0, 9)
By graphing the vertex (-2, 5) and the y-intercept (0, 9) and joining them with the parabola we get the following graph:
Related Questions
The diagonal of a rectangle is 25 inches. The width is 15 inches. What is the area of the rectangle?
Answers
Answer:
300 in²
Step-by-step explanation:
Hello!
Because the diagonal forms right triangles, we can use the Pythagorean Theorem to find the missing length of the rectangle.
a² + b² = c²
a = legb = legc = hypotenuseIn this case, 25 is c, and 15 is a. We can solve for b using the formula.
Solve for ba² + b² = c²15² + b² = 25²225 + b² = 625b² = 400b = 20So the missing length of the rectangle is 20. We can find the area by multiplying 15 and 20
15 * 20 = A300 = AThe area is 300 in².
The amounts of money three students earn at their jobs over time are given in the tablesStudent ETime (hr) Amount Earned2$15.005$37.508$60.00Student FTime (hr) Amount Earned3$27.006$54.0010$90.00Student GTime (hr) Amount Earned1$8.504$34.007S59.50According to the tables, which statement is true?Student E cams the most amount of money per hourStudent E cars more money per hour than studentStudent Goarns the least amount of money per hourStudent G earns less money per hour than student F
Answers
the answer is:
Student G earns less money per hour than student F
The table gives a set of outcomes and their probabilities. Let A be the event the outcome is divisible by 3". Find P(A). 12 Outcome Probability Tim elaps 1 0.14 PAUS 2 0.02 3 0.19 Smart out of 4 0.01 5 0.04 7 6 0.17 7 0.15 8 0.28
Answers
Here, we want to get the probability that a selected outcome is divisible by 3
What we have to do here is ti select numbers that are multiples of 3 and add their probabilities
From the given table, the outcomes that are multiples of 3 are;
3 and 6 only
So, we proceed to add the probabilities of these outcomes
Mathematically, we have this as;
[tex]P(A)\text{ = 0.19 + 0.17 = 0.36}[/tex]A body is moving in simple harmonic motion with position function
s(t) =2 + 2 cos t
where s is in meters and t is in seconds. Find the at time t.
Answers
The velocity of the body under simple harmonic motion (SHM) at time t is equal to -2sint. (Option D)
A type of self-sustaining periodic motion known as simple harmonic motion.
It is observed by the formula:
y = y' + Δy · cos ωt ....1.
Where,
y' = Initial position
Δy = Amplitude
ω = Angular frequency.
t = Time
To find the equation for the velocity of the body in simple harmonic motion differentiating equation w.r.t time (1),
then we get
v = - ω · Δy · sin ωt ....2.
If we know that ω = 1, t = t and Δt = 2, then the velocity of the body is:
v = - 1 · 2 · sin t
v = -2sint
The velocity is equal to -2sint
The velocity of the body under simple harmonic motion (SHM) at time t is equal to -2sint. (Option D)
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? Question
Rachel and Jeffery are both opening savings accounts. Rachel deposits $1,500 in a savings account that earns 1.5% interest,
compounded annually. Jeffery deposits $1,200 in a savings account that earns 1% interest per year, compounded
continuously.
If y represents the account balance after t years, which two equations form the system that best models this situation?
Answers
For the conditions stated, y=1500+2250t and y=1200+1200t, respectively, will be necessary equations because both Rachel and Jeffery are opening savings accounts. Rachel places $1,500 in a savings account that accrues annual compound interest of 1.5%. Jeffery places $1,200 in a savings account that accrues continuously compounded interest of 1% per year.
What is equation?A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.
Here,
according to given condition,
y=1500+1500*1.5t
y=1500+2250t
y=1200+1200*1t
y=1200+1200t
So the required equation will be y=1500+2250t and y=1200+1200t for the conditions given as Rachel and Jeffery are both opening savings accounts. Rachel deposits $1,500 in a savings account that earns 1.5% interest, compounded annually. Jeffery deposits $1,200 in a savings account that earns 1% interest per year, compounded continuously.
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Mrs. Brown is putting different colored sand into cups for her 4 daughters to make sand art bottles. The total amount of each color she has is shown in the table. Sand Color Weight (lb) Blue 1516 Pink 34 Purple 12 Turquoise 78 If each color is divided equally among the daughters, how much more pink sand will be available for each girl than purple sand? Write in simplest fraction form
Answers
Answer:
11/2 lb
Step-by-step explanation:
If 34 lb of pink sand and 12 lb of purple sand are equally divided among 4 daughters, you want to know how much more pink sand each girl receives.
DifferenceThe difference in amounts seen by each daughter will be ...
difference in amounts / number of daughters = (34 lb -12 lb)/(4 daughters)
= 22/4 lb/daughter = 11/2 lb/daughter
Each girl will have 11/2 more pounds of pink sand than purple sand.
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Help please.
We have the equation negative 9 minus this whole expression, 9x minus 6—this whole thing is being subtracted from negative 9—is equal to 3 times this whole expression, 4x plus 6.
Solve the Equation
Answers
The value of x in the equation given is x = -4/7.
What is an equation?A mathematical equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
The information given will be illustrated as:
9 - (9x - 6) - 9 = 3(4x + 6)
9 - 9x + 6 - 9 = 12x + 18
Collect like terms
-9x + 6 = 12x + 18
-9x - 12x = 18 - 6
-21x = 12
Divide
x = 12/-21
x = -4/7
This illustrates the concept of equations.
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Fifty people in a room are wearing clothes either in red orwhite or a combination of the two colors. Thirty are wearingonly red and 16 are wearing a combination of both red andwhite. How many are wearing clothes that have white in them?
Answers
SOLUTION
We will solve the question using a Venn diagram
Let R represents people wearing clothes that have red
Let W represents people wearing clothes that have white
We have the Venn diagram as follow
So from the Venn diagram small letter w represent those wearing clothes that have only white. So we have that
[tex]\begin{gathered} 30+16+w=50 \\ 46+w=50 \\ w=50-46 \\ w=4 \end{gathered}[/tex]So those for "only" white is 4.
But those wearing clothes that have white in them will be only white plus those wearing combination of red and white. We have
[tex]16+4=20[/tex]Hence the answer is 20
What is the center of the circle simplify any fractions
Answers
Answer:
[tex](x,y)\rightarrow(0,4)[/tex]Explanation: We have to find the center of the circle, the equation of the circle is as follows:
[tex]x^2+y^2-8y-48=0\rightarrow(0)[/tex]Ploting the equation (0) gives the following result:
Therefore the center of the circle has the coordinates (0,4).
The drama club was selling ticketsto the school play. Adult ticketscost $8.00 each, and studenttickets cost $5.00 each. The littletheater holds 142 people and wassold out for both Friday andSaturday. The total sales for thetwo days was $1,948.00.1. How many adult tickets weresold out over the two days?2. How many student tickets weresold out over the two days?
Answers
We are given a problem that can be solved using a system of linear equations. Let A, be the number of adults, and S the number of students. Since there are in total 142 people and there were two days, this means that the sum of the number of adults and the number of students must be 284, which can be written mathematically as follows:
[tex]A+S=284,(1)[/tex]This is our first equation. The second equation is found using the total sales of $1948. Since the ticket per adult is $8 and per student is $5, we have the following equations:
[tex]8A+5S=1948,(2)[/tex]To solve this equation we will solve for A in equation (1), by subtracting S to both sides;
[tex]\begin{gathered} A+S-S=284-S \\ A=284-S \end{gathered}[/tex]Now we will replace this value in equation (2):
[tex]8(284-S)+5S=1948[/tex]Now we will apply the distributive property:
[tex]2272-8S+5S=1948[/tex]Addins like terms:
[tex]2272-3S=1948[/tex]Subtracting 2272 to both sides;
[tex]\begin{gathered} 2272-2272-3S=1948-2272 \\ -3S=-324 \end{gathered}[/tex]Dividing both sides by -3:
[tex]S=-\frac{324}{-3}=108[/tex]Now we replace this value in equation (1), where we have already solved for A:
[tex]\begin{gathered} A=248-108 \\ A=140 \end{gathered}[/tex]Therefore, there were sold 108 student tickets and 140 adult tickets.
I need help on this
Answers
To answer this question, we need to evaluate each function in x=66, this way:
[tex]\begin{gathered} y=7(66) \\ y=462 \\ y=(66)^2-12(66)+84 \\ y=3648 \\ y=1.1317^{66} \\ y=3517.76 \end{gathered}[/tex]In this case, the function that has a greater value at x=66 is the one in the second option:
[tex]y=x^2-12x+84[/tex]How do I solve for x? Would my answer be 27?
Answers
SOLUTION
Exterior property of a triangle
An exterior angle of a triangle is equal to the sum of its two opposite non-adjacent interior angles.
Hence,
[tex](5x+13)^0=(4x+2)^0+(2x-9)^0[/tex]Simplify and evaluate for x
[tex]\begin{gathered} 5x+13^0=4x+2^0+2x-9^0 \\ 5x+13^0=4x+2x+2^0-9^0 \\ 5x+13^0=6x-7^0 \\ \text{Collect like terms} \\ 13^0+7^0=6x-5x \\ 20^0=x \\ \therefore x=20^0 \end{gathered}[/tex]Therefore,
[tex]x=20^0[/tex]the line AB is drawn on the grid.(i) Write down the coordinates of A
Answers
The coordinate of point A = (0, 1)
Explanation:Given:
the line AB is drawn on the grid
To find:
the coordinates of A
The coordinates of a point is in the form: (x, y)
To determine the coordinates of A, we will trace the y axis and x-axis.
At point A, x = 0, y = 1
The coordinate of point A = (0, 1)
A firm incurs $70,000 in interest expenses each year. If the tax rate of the firm is 30%, what is the effective after-tax interest rate expense for the firm?
Answers
Answer:
After tax interest expenses = Interest expenses x (100 - Tax Rate)
= 70000 x (100 - 30)%
= 70000 x 70%
= $49,000.00
Step-by-step explanation:
Find the formula for an exponential function that passes through the 2 points given
Answers
The form of the exponential function is
[tex]f(x)=a(b)^x[/tex]a is the initial value (value f(x) at x = 0)
b is the growth/decay factor
Since the function has points (0, 6) and (3, 48), then
Substitute x by 0 and f(x) by 6 to find the value of a
[tex]\begin{gathered} x=0,f(x)=6 \\ 6=a(b)^0 \\ (b)^0=1 \\ 6=a(1) \\ 6=a \end{gathered}[/tex]Substitute the value of a in the equation above
[tex]f(x)=6(b)^x[/tex]Now, we will use the 2nd point
Substitute x by 3 and f(x) by 48
[tex]\begin{gathered} x=3,f(x)=48 \\ 48=6(b)^3 \end{gathered}[/tex]Divide both sides by 6
[tex]\begin{gathered} \frac{48}{6}=\frac{6(b)^3}{6} \\ 8=b^3 \end{gathered}[/tex]Since 8 = 2 x 2 x 2, then
[tex]8=2^3[/tex]Change 8 to 2^3
[tex]2^3=b^3[/tex]Since the powers are equal then the bases must be equal
[tex]2=b[/tex]Substitute the value of b in the function
[tex]f(x)=6(2)^x[/tex]The answer is:
The formula of the exponential function is
[tex]f(x)=6(2)^x[/tex]Find the mzEFH, given that mzEFG = 50°. F E G . I
Answers
By theorem, we will have that m
m
=> m
=>2m
Then, we replace values and solve:
2m m
So, we have that m
A shop, had a sale.
(a) In the sale, normal prices were reduced by 15%.
The normal price of a chair was reduced in the sale by $24.
Work out the normal price of the chair.
Answers
Answer:
$160
Step-by-step explanation:
A shop, had a sale. In the sale, normal prices were reduced by 15%. The normal price of a chair was reduced in the sale by $24. Work out the normal price of the chair.
if 15% of normal price equals $24 then:
24/15% or 24/0.15 = $160 normal price
CHECK:
$160 * 0.15 = $24
Answer:
$160
Step-by-step explanation:
We want to know the price of the chair
So:
24 / 0.15 = 160$
or
24 / 15% = 160
Sofia got a raise from her annual salary of $43,000 to $44,505. whay percent was her raise?
Answers
4x- 1/2+ 2/3x combine like terms
Answers
Okay, here we heve this:
We need to combine like terms in the following equation:
[tex]\begin{gathered} 4x-\frac{1}{2}+\frac{2}{3}x \\ =(4x+\frac{2}{3}x)-\frac{1}{2} \\ =\frac{14}{3}x-\frac{1}{2} \end{gathered}[/tex]Find the midpoint of the line segment IJ where I (3,-9) and J (-10,-5)
Answers
Answer:
M (-7/2, -7)
Explanation:
Given the coordinates as I(3, - 9) and J(-10, -5), we can go ahead and determine the midpoint of the line segment IJ using the midpoint formula stated below;
[tex]M(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]So we have that x1 = 3, x2 = -10, y1 = -9, and y2 = -5.
Let's go ahead and substitute the above values into our formula and simplify;
[tex]\begin{gathered} M\lbrack\frac{3+(-10)}{2},\frac{-9+(-5)}{2}\rbrack \\ =M(\frac{3-10}{2},\frac{-9-5}{2}) \\ =M(-\frac{7}{2},\frac{-14}{2}) \\ =M(-\frac{7}{2},-7) \end{gathered}[/tex]In the national park, the ratio of black bear bears to grizzly bears is 3:1. If the park had 12 grizzly bears, how many black bears would it have?
Answers
The number of black bears in the national park is 36
Here, given the ratio of black bears to grizzly bears, and the number of grizzly bears, we want to find the number of blackbears the national park has
Let the number of black bears be x
what this mean is that the total number of bears in the park is (x + 12)
The total ratio of the two is 3 + 1 = 4
Matematically;
[tex]\begin{gathered} \frac{3}{4}\text{ }\times\text{ (x + 12) = x} \\ \\ 3(x\text{ + 12) = 4 }\times\text{ x} \\ \\ 3x\text{ + 36 = 4x} \\ 4x-3x\text{ = 36} \\ \\ x\text{ = 36} \end{gathered}[/tex]Please give me the answers asap the time is running down
Answers
Explanation
Given the question
[tex]|x|<13[/tex]To get the values of x, we will consider two possibilities which are:
[tex]\begin{gathered} x\text{ being positive},\text{ so that} \\ x<13 \end{gathered}[/tex]And
[tex]\begin{gathered} x\text{ being negative} \\ -x<13 \\ x>-13 \end{gathered}[/tex]Therefore, the value of x is
[tex]\begin{bmatrix}\mathrm{Solution\colon}\: & \: -13So the correct option is
[tex]\begin{bmatrix}\mathrm{Solution\colon}\mleft\lbrace x|\: \mright? & \: -13Option A is correctThe first option is correct
Jan is looking at a mapof Roaring River. The map wascreated using the scale 1 inch :25 miles. If the river is 5.5inches long on the map, then itis actuallymiles long.
Answers
The map of Roaring River shows1 inch to be an equivalent of 25 miles. If therefore, the river is shown as 5.5 inches long on the map;
[tex]\begin{gathered} \text{Scale; 1 inch=25 miles} \\ 5.5\text{ inches=25 x 5.5 miles} \\ 5.5\text{ inches=137.5miles} \end{gathered}[/tex]The river is "actually" 137.5 miles long
I need help on a problem
Answers
Those are similar triangles, which means, they are related by a ratio
For example in this case,
7: 10
to find x
10 / 7 = x/3
x= 10*3 /7
x= 30/ 7
x= 4.29
____________
Four times a number decreased by three is between -15 and 41?
Answers
Answer:
The number will lie between -3 and 11
Step-by-step explanation:
Let the number be 'x'
According to the question,
-15 < 4x - 3 < 41
-12 < 4x < 44 (Adding 3)
-3 < x < 11 (Dividing by 4)
INT. ALGEBRA: Write an equation that passes through (-10,-30) and is perpendicular to 12y-4x=8
Thank you for your help, and please do show work! I will be looking to give the Brainliest answer to someone!
Answers
The equation of the perpendicular line is y = -3x - 60
How to determine the line equation?The equation is given as
12y - 4x = 8
Make y the subject
12y= 4x + 8
y = 1/3x + 2/3
The point is also given as
Point = (-10, -30)
The equation of a line can be represented as
y = mx + c
Where
Slope = m
By comparing the equations, we have the following
m = 1/3
This means that the slope of 12y - 4x = 8 is 1/3
So, we have
m = 1/3
The slopes of perpendicular lines are opposite reciprocals
This means that the slope of the other line is -3
The equation of the perpendicular lines is then calculated as
y = m(x - x₁) +y₁
Where
m = -3
(x₁, y₁) = (-10, -30)
So, we have
y = -3(x + 10) - 30
Evaluate
y = -3x - 30 - 30
y = -3x - 60
Hence, the perpendicular line has an equation of y = -3x - 60
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Please help me asap with both I’ll mark you brainly
Answers
1. The scholar made a mistake in the last step
where he said x=3.5
[tex]0.5x = 7 \\ \frac{0.5x}{0.5} = \frac{7}{0.5} \\ x = 14[/tex]
SCHOLA DIVIDED 7 BY 2 INSTEAD OF DIVIDING BY 0.5
2.TO CHECK IF 3 as a solution satisfies the equation I will first look in what the LHS is equal to by plugging in 3 in the place of n. SO THAT n=3 SATISFIES THE EQUATION LHS=RHS
[tex]lhs = - \frac{1}{2} (2(3) - 8) + 3 \\ lhs = - \frac{1}{2} (6 - 8) + 3 \\ lhs = - \frac{ 1}{2} ( - 2) + 3 \\ lhs = 1 + 3 \\ lhs = 4[/tex]
Now I will check what The RHS IS EQUAL TO BY ALSO PLUGGING IN 3 IN THE PLACE OF n
[tex]rhs = \frac{1}{4} (8(3) - 4) - 1 \\ rhs = \frac{1}{4} (24 - 4) -1 \\ rhs = \frac{1}{4} (20) - 1 \\ rhs = 5 - 41\\ rhs = 4[/tex]
FROM WHAT I FOUND LHS=RHS THIS MEANS THAT n=3 SATISFIES THE EQUATION BECAUSE IT IS BALANCED. WHAT IS ON THE LEFT HAND SIDE IS EQUAL WITH WHAT IS ON THE RIGHT HAND SIDE.
I HOPE THIS HELPS.
In the figure, m < 1= (x-6)º and m2 2= (5x).
Answers
We have the measure of angles 1 and angle 2, as we can see from the diagram in the image, angles 1 and 2 added form the right angle (90°) in the figure.
Thus, the sum of x-6 and 5x, must be equal to 90°.
(a) Write an equation:
[tex]x-6+5x=90[/tex](b) To find the degree measure of each angle, first we need to solve for the value of x in the equation.
Combining like terms:
[tex]6x-6=90[/tex]Adding 6 from both sides:
[tex]\begin{gathered} 6x-6+6=90+6 \\ 6x=96 \\ \end{gathered}[/tex]Divide both sides by 6:
[tex]\begin{gathered} \frac{6x}{6}=\frac{96}{6} \\ x=16 \end{gathered}[/tex]Now that we have x, we find angle 1:
[tex]m\angle1=x-6=16-6=10[/tex]And the measure of angle 2:
[tex]m\angle2=5x=5(16)=80[/tex]The formula for the perimeter of a
rectangle is P = 2l + 2w. Solve the formula for
w.
Answers
P = 2( l + w )
P/2 = 2( l + w ) /2
P/2 = l + w
answer: w = P/2 - 1
What is the answer to this question?
Answers
The reflection of a point P over a line as in the P' if the line m is the "perpendicular bisector" of line PP'. Point P' is called the "image" of point P.
What is termed as the reflection of the point?A reflection point represents when a figure is built around a single point recognized as point of reflection or the figure's center. On the other side, per each point in the graph, some other point is observed directly opposite it.For the given question.
Line m is the line along which reflection of point P is taken.
Then, line m is called the "perpendicular bisector" of line PP'.
P is the object and P' will be the image of the point P.
Thus, the complete definition of the reflection is given as-
The reflection of a point P over a line as in the P' if the line m is the "perpendicular bisector" of line PP'. Point P' is called the "image" of point P.
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