Answer:
Step-by-step explanation:
3x²=15-4x
divide by 3 on both sides
x²=5-[tex]\frac{4}{3}[/tex]x
move everything to one side
x²+[tex]\frac{4}{3}[/tex]x -5 = 0
add the square of 1/2 the middle term of [tex]\frac{4}{3}[/tex] but also subtract it too
x²+[tex]\frac{4}{3}[/tex]x +[tex]( \frac{2}{3} )^{2}[/tex]-5-[tex]( \frac{2}{3} )^{2}[/tex] = 0
now use the property of a perfect square to rewrite
[tex](x+\frac{2}{3}) ^{2}[/tex] -5 -[tex]\frac{4}{9}[/tex] = 0
rewrite 5 as a fraction
[tex](x+\frac{2}{3}) ^{2}[/tex] - [tex]\frac{45}{9}[/tex]- [tex]\frac{4}{9}[/tex] = 0
add up the fractions
[tex](x+\frac{2}{3}) ^{2}[/tex] - [tex]\frac{49}{9}[/tex] = 0
move to the other side
[tex](x+\frac{2}{3}) ^{2}[/tex] = [tex]\frac{49}{9}[/tex]
take the square root of both sides :P
[tex]\sqrt{((x+\frac{2}{3}) ^{2} }[/tex] = [tex]\sqrt{\frac{49}{9} }[/tex]
much easier looking now, just use algebra to solve for x
x + [tex]\frac{2}{3}[/tex] = [tex]\frac{7}{3}[/tex]
subtract [tex]\frac{2}{3}[/tex] from both sides
x + [tex]\frac{2}{3}[/tex] - [tex]\frac{2}{3}[/tex] = [tex]\frac{7}{3}[/tex] - [tex]\frac{2}{3}[/tex]
x = [tex]\frac{5}{3}[/tex]
:)
Answer:
x = - 3, x = [tex]\frac{5}{3}[/tex]
Step-by-step explanation:
Given
3x² =15 - 4x ( add 4x to both sides )
3x² + 4x = 15 ← factor out 3 from each term on the left side
3(x² + [tex]\frac{4}{3}[/tex] x) = 15
To complete the square
add/subtract ( half the coefficient of the x- term)² to x² + [tex]\frac{4}{3}[/tex] x
3(x² + 2([tex]\frac{2}{3}[/tex] )x + [tex]\frac{4}{9}[/tex] - [tex]\frac{4}{9}[/tex] ) = 15
3(x + [tex]\frac{2}{3}[/tex] )² - [tex]\frac{4}{3}[/tex] = 15 ( add [tex]\frac{4}{3}[/tex] to both sides )
3(x + [tex]\frac{2}{3}[/tex] )² = 15 + [tex]\frac{4}{3}[/tex] = [tex]\frac{49}{3}[/tex] ( divide both sides by 3 )
(x + [tex]\frac{2}{3}[/tex] )² = [tex]\frac{49}{9}[/tex] ( take the square root of both sides )
x + [tex]\frac{2}{3}[/tex] = ± [tex]\sqrt{\frac{49}{9} }[/tex] = ± [tex]\frac{7}{3}[/tex] ( subtract [tex]\frac{2}{3}[/tex] from both sides )
x = - [tex]\frac{2}{3}[/tex] ± [tex]\frac{7}{3}[/tex], then
x = - [tex]\frac{2}{3}[/tex] - [tex]\frac{7}{3}[/tex] = - 3
x = - [tex]\frac{2}{3}[/tex] + [tex]\frac{7}{3}[/tex] = [tex]\frac{5}{3}[/tex]
50 POINTS
Use the function f(x) to answer the questions.
f(x) = −16x2 + 22x + 3
Part A: What are the x-intercepts of the graph of f(x)? Show your work. (2 points)
Part B: Is the vertex of the graph of f(x) going to be a maximum or a minimum? What are the coordinates of the vertex? Justify your answers and show your work. (3 points)
Part C: What are the steps you would use to graph f(x)? Justify that you can use the answers obtained in Part A and Part B to draw the graph. (5 points)
work and answers below
Answer:
[tex]\text{Part A.}\\(-\frac{1}{8},0),\\(\frac{3}{2},0)\\\\\text{Part B.}\\(\frac{11}{16},\frac{169}{16})\\\\\text{Part C.}[/tex]
Draw a parabola concave down with vertex at [tex](\frac{11}{16},\frac{169}{16})[/tex]. Since the leading coefficient of the equation is -16, the parabola should appear thinner than its parent function [tex]y=x^2[/tex]. Ensure that the parabola passes through the points [tex](\(-\frac{1}{8},0)[/tex] and [tex](\frac{3}{2},0)[/tex].
Step-by-step explanation:
Part A:
The x-intercepts of a function occur at [tex]y=0[/tex]. Therefore, let [tex]y=0[/tex] and solve for all values of [tex]x[/tex]:
[tex]0=-16x^2+22x+3[/tex]
The quadratic formula states that the real and nonreal solutions to a quadratic in standard form [tex]ax^2+bx+c[/tex] is equal to [tex]x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex].
In [tex]-16x^2+22x+3[/tex], assign:
[tex]a\implies -16[/tex] [tex]b\implies 22[/tex] [tex]c\implies 3[/tex]Therefore, the solutions to this quadratic are:
[tex]x=\frac{-22\pm\sqrt{22^2-4(-16)(3)}}{2(-16)},\\x=\frac{-22\pm 26}{-32},\\\begin{cases}x=\frac{-22+26}{-32}=\frac{4}{-32}=\boxed{-\frac{1}{8}},\\x=\frac{-22-26}{-32}=\frac{-48}{-32}=\boxed{\frac{3}{2}}\end{cases}[/tex]
The x-intercepts are then [tex]\boxed{(-\frac{1}{8},0)}[/tex] and [tex]\boxed{(\frac{3}{2},0)}[/tex].
Part B:
The a-term is negative and therefore the parabola is concave down. Thus, the vertex will be the maximum of the graph. The x-coordinate of the vertex of a quadratic in standard form [tex]ax^2+bx+c[/tex] is equal to [tex]x=\frac{-b}{2a}[/tex]. Using the same variables we assigned earlier, we get:
[tex]x=\frac{-22}{2(-16)}=\frac{-22}{-32}=\frac{11}{16}[/tex]
Substitute this into the equation of the parabola to get the y-value:
[tex]f(11/16)=-16(11/16)^2+22(11/16)+3,\\f(11/16)=\frac{169}{16}[/tex]
Therefore, the vertex of the parabola is located at [tex]\boxed{(\frac{11}{16},\frac{169}{16})}[/tex]
help pls!!!!!
What is the inequality for this verbal description?
The value of y is greater than or equal to the sum of five times the value of x
and negative three.
Answer:
y ≥ 5x+ (-3)
Step-by-step explanation:
greater than or equal to ≥
The sum means add
y ≥ 5x+ (-3)
Answer:
Option D, y ≥ 5x + (-3)
Step-by-step explanation:
Step 1: Make an expression
The value of y is greater than or equal to the sum of five times the value of x and negative three.
The value of y is greater than or equal to ← y ≥
The sum of five times the value of x and negative three ← 5x + (-3)
y ≥ 5x + (-3)
Answer: Option D, y ≥ 5x + (-3)
A driveway is in the shape of a rectangle 20 feet wide by 25 feet long.
(a)
Find the perimeter in feet.
(b)
Find the area in square feet.
You have one of each type of coin (pennies are not included) and one each of $5, $10, $20, and $50 bill. How many sums of money are there?
Answer:
$85.40
Step-by-step explanation:
All the US coin types, excluding pennies, are:
- nickels
- dimes
- quarters
Nickels are equal to 5 cents, or $0.05
Dimes are equal to 10 cents, or $0.10
Quarters are equal to 25 cents, or $0.25
Because there are only one of each coin (excluding pennies), we can just add the values written above:
$0.05 + $0.10 + $0.25 = $0.40
Next, let's add one of each bill listed in the question:
$5 + $10 + $20 + $50 = $85
Finally, let's add the value of the coins and the value of the bills to find the sum:
$85 + $0.40 = $85.40
The answer is $85.40
Hope it helps (●'◡'●)
I need help!!
A B C D
Answer:
[tex]f(x) = \sqrt{x} - 2[/tex]
Step-by-step explanation:
The starting point of the graph starts in the negative y axis. This means we must have either a horinzontial reflection, a negative vertical stretch or compression, or a negative vertical shift.
The first option is the only sign of the starting point be negative so that is the answer.
Which graph represents a function with direct variation? A coordinate plane with a U shaped line graphed with the minimum at (0, 0). A coordinate plane with a V shaped line graphed with the minimum at (0, 0). A coordinate plane with a line passing through (negative 4, 2), (0, 0) and (4, negative 2). A coordinate plane with a line passing through (negative 2, negative 3), (0, 1) and (1, 3).
left 3, up 4
right 3, down 4
left 3, down 4
right 3, up 4
Answer:
a line passing through (negative 4, 2), (0, 0) and (4, negative 2).
Step-by-step explanation:
A function exhibiting direct variation MUST pass through the origin, (0, 0), and the graph must be a straight line. The answer that satisfies these requirements is
a line passing through (negative 4, 2), (0, 0) and (4, negative 2).
Use the Empirical Rule to answer the questions below:
The distribution of weights for newborn babies is approximately normally distributed with a mean of 7.6 pounds and a standard deviation of 0.7 pounds.
1. What percent of newborn babies weigh more than 8.3 pounds? %
2. The middle 95% of newborn babies weigh between and pounds.
3. What percent of newborn babies weigh less than 6.2 pounds? %
4. Approximately 50% of newborn babies weigh more than pounds.
5. What percent of newborn babies weigh between 6.9 and 9.7 pounds? %
Answer:
1. 16%
2. The middle 95% of newborn babies weigh between 6.2 and 9 pounds.
3. 2.5%
4. Approximately 50% of newborn babies weigh more than 7.6 pounds.
5. 83.85%
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.
Approximately 95% of the measures are within 2 standard deviations of the mean.
Approximately 99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean of 7.6 pounds, standard deviation of 0.7 pounds
1. What percent of newborn babies weigh more than 8.3 pounds?
7.6 + 0.7 = 8.3.
So more than 1 standard deviation above the mean.
The normal distribution is symmetric, which means that 50% of the measures are below the mean and 50% are above.
Of those above the mean, 100 - 68 = 32% are more than one standard deviation above the mean. So
[tex]0.32*0.5 = 0.16[/tex]
16% of newborn babies weigh more than 8.3 pounds.
2. The middle 95% of newborn babies weigh between and pounds.
Within 2 standard deviations of the mean, so:
7.6 - 2*0.7 = 6.2 pounds
7.6 + 2*0.7 = 9 pounds.
The middle 95% of newborn babies weigh between 6.2 and 9 pounds.
3. What percent of newborn babies weigh less than 6.2 pounds?
More than 2 standard deviations below the mean, which is 5% of the 50% below the mean, so:
[tex]p = 0.05*0.5 = 0.025[/tex]
2.5% of newborn babies weigh less than 6.2 pounds.
4. Approximately 50% of newborn babies weigh more than pounds.
Due to the symmetry of the normal distribution, the mean, so 7.6 pounds.
Approximately 50% of newborn babies weigh more than 7.6 pounds.
5. What percent of newborn babies weigh between 6.9 and 9.7 pounds?
6.9 = 7.6 - 0.7
9.7 = 7.6 + 3*0.7
Within 1 standard deviation below the mean(68% of the 50% below) and 3 standard deviations above the mean(99.7% of the 50% above). So
[tex]p = 0.68*0.5 + 0.997*0.5 = 0.8385[/tex]
83.85% of newborn babies weigh between 6.9 and 9.7 pounds.
Think of a situation in the real world where a relationship occurs between two sets. For example, I could list several different people and then list their birthdays. I could then form a relationship between these sets. First, illustrate the relationship using arrows. Then determine if the relationship is a function or not. State why?
Answer:
See Explanation
Step-by-step explanation:
Required
Determine if a real life situation is a function or not
I will give 2 instances
(1) Students and their ID
The relationship is as follows:
Student 1 -----> ID-1
Student 2 -----> ID-2
Student 3 -----> ID-3
Student 4 -----> ID-4
---------
----
--
Student n -----> ID-n
The above is a function because every student has a unique student ID.
In fact, the relation is a one-on-one function because no two students will have the same ID
(2) People and their year of birth
The relationship is as follows:
Person 1 -----> 2000
Person 2 -----> 2001
Person 3 -----> 2002
Person 4 -----> 2001
---------
----
Person n -----> 2005
The above is not a function because there is a possibility that a more than one person will have the same year of birth.
What is the y-intercept of the line y+11= -2(x+5)?
Answer:
y-intercept is (0, -21)
Step-by-step explanation:
For y-intercept, x = 0:
[tex]{ \sf{y + 11 = - 2(0 + 5)}} \\ { \sf{y + 11 = - 10}} \\ { \sf{y = - 21}}[/tex]
100 Points + Brainliest Again. They deleted my other for being too easy :P
What is the circumference of a circle with a radius of 20 inches?
Answer:
125.66 inches
Step-by-step explanation:
Step 1: Calculate the circumference
The circumference formula is: C = πd
Another way of saying that is: C = 2πr
C = 2π(20)
C = 40π
C ≈ 125.66 inches
Answer: 125.66 inches
I need help solving 10gallons = miles
Answer:
50?
Step-by-step explanation:
Because its 50 miles per gallon, so gallon time 50 will be the miles? I'm not sure but i think it is
What is the value if x
Answer:
Step-by-step explanation:
Simplify (5^-2)^4. Plsss help
Answer:
1/5^8
Step-by-step explanation:
We know that a^b^c = a^(b*c)
(5^-2)^4
5^(2*-4)
5^-8
We know that a^-b = 1/a^b
1/5^8
Determine if the function f is an exponential function. If so, identify the base. If not, why not?
f(x)=(1/e)^x
A. This is not an exponential function because the variable is in the exponent position.
B. The base is x.
C. This is a polynomial.
D. The base is e^−1.
Answer: D) The base is e^(-1)
We use the rule that x^(-k) = 1/(x^k). That allows us to say e^(-1) = 1/(e^1) = 1/e
The 1/e is the base of the exponential (1/e)^x
In general, the exponential b^x has base b.
There are 43 students in the orchestra and twice that number in the band. There are 31 boys and 10 girls in the choir. If each student only participates in one group, how many students total are there in the orchestra, the band, and the choir?
Answer:
170 students total
Step-by-step explanation:
43x2=86
86+43+31+10=170
For the next school year, you must take math, English, science, and one elective. You must take all four classes in one day. How many class schedules are possible if the math class cannot be the first class of the day?
18
4
12
24
Answer:
24
Step-by-step explanation:
which
Which of the following lines is perpendicular to y = 3x + 2?
A.
1
y = 3x --
2
B.
-1
= — X+6
3
C.
1
y = -x +2
3
D.
1
y = 3x +-
2
What is the volume of the cylinder shown below?
Answer:
c. 1500pi cubic units
The planet Mercury travels in an elliptical orbit with eccentricity 0.203. Its minimum distance from the Sun is 4.5 x 10^7 km. If the perihelion distance from a planet to the Sun is a(1 - e) and the aphelion distance is a(1 + e), find the maximum distance (in km) from Mercury to the Sun.Pick from the following:1. 7.7 x 10^7 km.2. 6.6 x 10^7 km.3. 6.8 x 10^7 km.
Answer:
Option C
Step-by-step explanation:
From the question we are told that:
Eccentricity [tex]e=0.203[/tex]
Minimum distance from the Sun [tex]d_s= 4.5 x 10^7 km[/tex]
Perihelion distance from a planet to the Sun is [tex]r= a(1 - e)[/tex]
Aphelion distance [tex]r'=a(1 + e)[/tex]
Generally the equation for Perihelion distance is mathematically given by
[tex]4.5 * 10^7= a(1 - 0.203)[/tex]
[tex]4.5 * 10^7 = 0.797a[/tex]
[tex]a = 56.46 * 10^6 km[/tex]
Generally the equation for Aperihelion distance is mathematically given by
[tex]r' = a(1 + e)[/tex]
[tex]r' = 56.4617 * 10^6 (1 + 0.203)[/tex]
[tex]r'=6.8 * 10^7 km[/tex]
Option C
What is the solution to -41-2x + 6 = -24?
O x = 0
O x = 0 or x = -6
0 x = 0 or x = 6
Ono solution
Hello!
-41 - 2x + 6 = -24 <=>
<=> -35 - 2x = -24 <=>
<=> -2x = -24 + 35 <=>
<=> -2x = 11 <=>
<=> x = -11/2 or -5.5
Good luck! :)
The solution of the equation is only one solution.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
We have,
-41 - 2x + 6 = -24
Now, solving for x we get
-41 + 6 -2x = -24
-35 - 2x = -24
-2x = -24 + 35
-2x = 11
x = -11/2
x= -5.5
As, the equation of linear and have x= -5.5.
Thus, the equation have only one solution.
Learn more about Equation here:
https://brainly.com/question/29538993
#SPJ7
If m ∥ n and n ⊥ p, then _____
Answer:
If m is parallel to n and n is perpendicular to p, then m is perpendicular to p.
Step-by-step explanation:
If you draw m parallel to n and then you run a line p through n such that n and p are perpendicular. The line p will also cross over m since lines go on forever and it will be perpendicular to m as well.
help with number 4 part a and b?
Part A
The vertex of a parabola is the lowest or highest point. The vertex in this graph is (2,-1).
Part B
You need to find the rate of change between the points when x=2 and x=3. When x=2, y=-1, and when x=3, y=0.5. You can find the average rate of change between these points by putting the difference of y over the difference of x. 0.5--1=1.5 and 3-2=1. The average rate of change is 1.5/1, or just 1.5.
The measures of the exterior angles of a convex pentagon can be represented as follows: angle 1=X, angle 2= 2x+9, angle 3=3x+4, angle 4=4x+11, angle 5=5x+18
Find the measure of each angle
Can someone help me find the answer?
Answer: C. is the correct answer.
What is the simplest form of
Picture!
Answer:
Step-by-step explanation:
Factor the radicand.
Pls help me? I’m struggling
Answer: Number 1 is 150
Step-by-step explanation: If you put 72 / 48% in your calculator, you will get your answer.
What is the area if measurements are 6m x 5.2m
Answer:
33.00 355.2
5.0m x 6.7m 33.50 360.6
5.0m x 6.8m 34.00 366.0
5.0m x 6.9m 34.50 371.4
5.1m x 6.0m 30.60 329.4
5.1m x 6.1m 31.11 334.9
5.1m x 6.2m 31.62 340.4
5.1m x 6.3m 32.13 345.8
5.1m x 6.4m 32.64 351.3
5.1m x 6.5m 33.15 356.8
5.1m x 6.6m 33.66 362.3
5.1m x 6.7m 34.17 367.8
5.1m x 6.8m 34.68 373.3
5.1m x 6.9m 35.19 378.8
Which equation does the graph represent?
A. x^2 + y^2 = 4
B. x^2/3^2 + y^2/4^2 = 1
C. (X - 1)^2 / 3^2 + y^2/4^2 = 1
D.X^2 / 4^2 + (y + 1)^2 / 3^2 = 1
9514 1404 393
Answer:
B. x^2/3^2 + y^2/4^2 = 1
Step-by-step explanation:
The graph looks like a circle, but is not. It is a unit circle scaled by a factor of 3 in the x-direction and a factor of 4 in the y-direction. Thus, its equation is ...
(x/3)^2 +(y/4)^2 = 1
x^2/3^2 +y^2/4^2 = 1
f(x+h)-f(x)
Find the difference quotient
h
where h# 0, for the function below.
f(x) = 4x? -
-8
Simplify your answer as much as possible.
f(x + h) - f(x)
:
h
Х
Okay
9514 1404 393
Answer:
8x +4h
Step-by-step explanation:
[tex]\dfrac{f(x+h)-f(x)}{h}=\dfrac{(4(x+h)^2-8)-(4x^2-8)}{h}\\\\=\dfrac{(4x^2 +8xh+4h^2)-(4x^2-8)}{h}=\dfrac{8xh+4h^2}{h}\\\\=\boxed{8x+4h}[/tex]
ESSE
Combine these radicals.
27-3
O √24
O 23
O-23
0 -3/2
here's the answer to your question
