Answers
either x = 5 or x = -1 (second option)
Explanation:
We are asked to use the u substitution. This means that we will assume that:
u = x - 3
Substitute in the given expression:
u^2 + 2u - 8 = 0
(u-2)(u+4) = 0
either u = 2
or u = -4
Now, we have:
u = x- 3
at u = 2:
x - 3 = 2
x = 2 + 3 = 5
at u = -4:
x - 3 = -4
x = -4 + 3 = -1
Hope this helps :)
Using substitution we have:
u = x-3
We rewrite:
(u) ^ 2 + 2 (u) -8 = 0
We are looking for roots:
u1 = 2
u2 = -4
We return the change:
u1 = 2 = x-3
x1 = 3 + 2 = 5
u2 = -4 = x-3
x2 = -4 + 3 = -1
Answer:
x1 = 5
x2 = -1
(option2)
Related Questions
Find the constant of variation k for the inverse variation. Then write an equation for the inverse variation. Y=4.5 when x = 3
Answers
Construction is under way at an airport. This map shows where the construction is taking place. If Road A and Road B are parallel, what is the distance from P to Q on Road C?
Answers
650(2000) = 800x + 800(650)
x = 975 ft
A sine function has the following key features:
Period = 12
Amplitude = 4
Midline: y = 1
y-intercept: (0, 1)
The function is not a reflection of its parent function over the x-axis.
How would this graph look??
Answers
Final answer:
A sine function with an amplitude of 4, period of 12, midline of y = 1, and y-intercept of (0, 1) would oscillate between 5 and -3, with a wave repeating every 12 units along the x-axis and starting upward from the y-intercept.
Explanation:
The graph of the sine function with the given properties will have the following characteristics:
The amplitude is 4, which means the function will oscillate 4 units above and below the midline.
The period is 12, indicating that it takes 12 units along the x-axis for the function to repeat its pattern.
The midline is y = 1, so the center of oscillation is not at the x-axis but is shifted upwards by 1 unit.
The y-intercept is (0, 1), which means the function starts at the midline.
Since the function is not a reflection over the x-axis, it means that it starts off going upwards from the midline.
Mapping these points, we can sketch the sine graph starting from the point (0, 1), curving up to a maximum of 5 (midline + amplitude), then down through the midline, reaching a minimum of -3 (midline - amplitude), and back to the midline at (12, 1), completing one full cycle.
can someone help me with this?
Answers
6+7 = 13 individuals under age 12
7+4 = 11 individuals 13 to 30 years old
13+11 = 24 people total from the two groups
There are 6+7+7+4+4+1 = 29 people total from the entire survey
So the final answer is 24/29. It cannot be reduced further.
PLEASE HELP
8.04b
1. Eliminate the parameter.
x = 5t, y = t + 8
A) y = 5x + 8
B) y = x divided by five + 8
C) y = 5x - 8
D) y = x divided by five - 8
2. Eliminate the parameter.
x = square root of x , y = 3t + 7
A) y = 3x2 + 7
B) y = 3 square root of x + 7, x ≥0
C) y = 3 square root of x - 7, x ≥0
D) y = 3x2 - 7
3. Eliminate the parameter.
x = t2 + 2, y = t2 - 4
A) y = x - 6, x ≥ 1
B) y = x + 6, x ≥ 1
C) y = x2 - 6, x ≥1
D) y = x2 + 6, x ≥1
4. Eliminate the parameter.
x = 4 cos t, y = 4 sin t
Answers
Question 1. Eliminate the parameter. x = 5t, y = t + 8
Answer: option B: y = (x / 5) + 8 ↔ x divided by 5 + 8
Explanation:
1) From x = 5t => t = x / 5
2) Substitute t in y = t + 8 => y = (x / 5) + 8
Which is the option B) y = the division of x by 5, added to 8.
Question 2. Eliminate the parameter.
There is an error in the question, because it says x = √x
If the righ question is x = √t , y = 3t + 7 , then the answer is the option A) y = 3x^2 + 7
Explanation:
1) Given: x = √t , y = 3t + 7
2) from x = √t => t = x^2
3) Substitute t = x^2 in y = 3t + 7
=> y = 3 x^2 + 7 ↔ option A) y = x^2 + 7
Question 3. Eliminate the parameter.
x = t^2 + 2, y = t^2 - 4
Answer: option A) y = x - 6
Explanation:
1) From x = t^2 + 2 => t^2 = x - 2
2) Substitute t^2 in y = t^2 - 4
=> y = x - 2 - 4
=> y = x - 6, since t^2 is ≥ 0, then x ≥ 0
=> option A) y = x - 6, x ≥ 1
Question 4. Eliminate the parameter.
x = 4 cos t, y = 4 sin t
Answer: x^2 + y^2 = 16
Explanation:
1) Square both sides of x = 4 cost
=> x^2 = (4 cos t)^2
x^2 = 16 (cos t)^2
2) Square both sides of y = 4 sin t
y^2 = 16 (sin t)^2
3) Add x^2 and y^2
x^2 + y^2 = 16(cos t)^2 + 16 (sin t)^2
=> x^2 + y^2 = 16 [ (cos t)^2 + (sin t)^2 ]
4) since (cos t)^2 + (sin t)^2 = 1
x^2 + y^2 = 16
50 POINTS!
A high school coach wants to buy new shirts for the 25 members of the track team. The coach must spend less than $300 on the shirts and needs to figure out how much he can spend per shirt, s. Which of the following must be true about the inequality and the resulting graph? Check all that apply
A)The inequality should be written as 25s<300.
B)The inequality should be written as 25s>300.
C)The circle is open.
D)The circle is closed.
E)The arrow points left.
F)The arrow points right
Answers
Answer:
Step-by-step explanation:
A,C,E
What are the roots of the polynomial equation?
x2−14x−32=0
Answers
We can easily factor that into:
(x +2) * (x -16) = 0
x1 = -2
x2 = 16
We are given the quadratic equation :
[tex] x^{2} -14x-32=0 [/tex]
Now let us use AC method to factorise it.
Step 1:
Find product of A and C
A=1 and C =-32
A*C =-32
Step 2:
Find factors of -32 such that they add up to give -14.
Factors of -32 that add up to give -14 are -16 and 2.
Step 3:
Rewrite the equation using factors found in step 2.
[tex] x^{2} -16x +2x -32 =0 [/tex]
Step 4:
Factoring by grouping.
[tex] x(x-16) +2(x -16) =0 [/tex]
[tex] (x-16) (x+2) =0 [/tex]
Step 5:
Find roots.
x-16=0 gives x=16
x+2=0 gives x=-2
Answer : Roots of the given Polynomial equation are 16 and -2.
We are given the quadratic equation :
[tex] x^{2} -14x-32=0 [/tex]
Now let us use AC method to factorise it.
Step 1:
Find product of A and C
A=1 and C =-32
A*C =-32
Step 2:
Find factors of -32 such that they add up to give -14.
Factors of -32 that add up to give -14 are -16 and 2.
Step 3:
Rewrite the equation using factors found in step 2.
[tex] x^{2} -16x +2x -32 =0 [/tex]
Step 4:
Factoring by grouping.
[tex] x(x-16) +2(x -16) =0 [/tex]
[tex] (x-16) (x+2) =0 [/tex]
Step 5:
Find roots.
x-16=0 gives x=16
x+2=0 gives x=-2
Answer : Roots of the given Polynomial equation are 16 and -2.
The measure of Angle E, the angle of elevation from point A to point B, is ( 3 x plus 1 ). The measure of Angle D, the angle of depression from point B to point A, is 2 ( x plus 8 ) Find the measure of each angle.
Answers
E----------------> angle of elevation
D----------------> angle of depression
we know that
E=(3x+1)
D=2(x+8)
remember that
angle of elevation is equals to angle of depression------> by alternate angles
then
E=D
(3x+1)=2(x+8)-----------> 3x+1=2x+16----------> 3x-2x=16-1-----> x=15
E=3*15+1-------> 46°
D=2*15+16-----> 46°
the answer is
the measure of angle of elevation and angle of depression is 46°
please help attachment on please don't skip any parts
will get brainliest
Answers
Picture included!
What is the slope of the line shown in the graph?
A.) -1
B.) -2
C.) 1/2
D.) 2
Answers
:D
[tex]\bf \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ % (a,b) &&(~ 0 &,& 3~) % (c,d) &&(~ 1 &,& 1~) \end{array} \\\\\\ % slope = m slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{1-3}{1-0}\implies \cfrac{-2}{1}\implies -2[/tex]
Zach uses his car for business and must keep accurate driving records so that his company will reimburse him for car expenses. When he started his trip, the odometer read 26.645, When he returned home, the odometer read 28,017. Zach's car gets about 48 miles per gallon. If the tank was full at the beginning of the trip and it cost $62.28 to fill the tank at the end of the trip, what price did Zach pay per gallon?
Answers
We can divide that by his average mpg to figure out how many gallons of gas he bought:
1372/48 = 28.583 gallons.
Now divide the amount he paid by this to get the price per gallon:
62.28/28.583 = $2.179 per gallon of gas.
Find the range of ƒ(x) = –2x – 5 for the domain {–2, –1, 1, 2}.
Answers
By substituting each value of the domain of x in the function and solving it we will get the range of the function for respective domain
The given function is :
f(x) = -2x - 5
For x = -2 , f(x) is:
f(-2) = (-2*-2) - 5 = 4 - 5 = -1
For x = -1, f(x) is :
f(-1) = (-2*-1) - 5 = 2 - 5 = -3
For x = 1 , f(x) is
f(1) = (-2*1) - 5 = -2 -5 = -7
For x = 2, f(x) is
f(2) = (-2*2) - 5 = -4 -5 = -9
The range is -1 , -3 , -7 , -9
Hope this helps ..!!
Thank you :)
Eugene knows the circumference of a circle is 125.6 meters. Does he have enough information to find the area?
Answers
Answer:
the answer is aStep-by-step explanation:
i did the test
Graph the following inequality and then select the correct graph below.
y ≤ x - 2
Answers
Hope it helps.
Answer:
The graph in the attached figure
Step-by-step explanation:
we have
[tex]y\leq x-2[/tex]
The solution of the inequality is the shaded area below the solid line
The equation of the line is [tex]y= x-2[/tex]
The slope of the line is positive [tex]m=1[/tex]
The y-intercept of the line is the point [tex](0,-2)[/tex]
The x-intercept of the line is the point [tex](2,0)[/tex]
therefore
the graph in the attached figure
Choose the option that correctly completes the statement.
A triangle must have _____ one acute angle.
at most
at least
Answers
Find the simplified form of the expression. Give your answer in scientific notation.
(9 x 10 5)(6 x 10 -7)
A. 5.4 x 10 -34
B. 1.5 x 10 -1
C. 5.4 x 10 -1
D. 1.5 x 10 -34
Answers
Now we get: [tex](9*10^5)(6*10^{-7})=9*6*10^5*10^{-7}[/tex] by associativity of multiplication.
This is equal to: [tex]54*10^{5+(-7)}=54*10^{-2}[/tex] by the property we stated above, for a=10. Scientific notation requires that the coeeficient in fron tof the power of 10 is between 1-10 and thus since 54=10*5.4, we have that the expression is equal to: 5.4*10*[tex]10^{-2}[/tex]=[tex]5.4*10^{-1}[/tex]. Hence the correct answer is C
Using the completing-the-square method, rewrite f(x) = x2 + 10x + 7 in vertex form.
Answers
f(x) - 7 = x² + 10x
Next let's add (half of 10)² to both sides of the equation: btw that is 25 but on the right side we will leave it as 5² because it will make the factoring easier
f(x) - 7 + 25 = x² + 10x + 5²
Lets simplify the left side a bit and factor the perfect square trinomial on the right.
f(x) + 18 = (x + 5)²
Finally move the constant back to the side with the binomial
f(x) = (x + 5)² - 18
The vertex is (-5, -18)
Using the completing-the-square method the vertex form of the function
f(x) = x² + 10x + 7 is f(x) = (x + 5)² - 18
The given function is:
f(x) = x² + 10x + 7
Comparing f(x) = x² + 10x + 7 with f(x) = ax² + bx + c
a = 1, b = 10, c = 7
(b/2)² = (10/2)² = 5²
Add and subtract 5² to the right hand side of the equation
f(x) = x² + 10x + 5² + 7 - 5²
f(x) = x² + 10x + 5² + 7 - 25
f(x) = x² + 10x + 5² - 18
f(x) = (x + 5)² - 18
f(x) = (x + 5)² - 18 is of the form f(x) = a(x - h)² + k which is the vertex form of a quadratic equation
Therefore, the vertex form of the function f(x) = x² + 10x + 7 is
f(x) = (x + 5)² - 18
Learn more here: https://brainly.com/question/19105786
helpppppppppppppppppppppppppppppp
Answers
-------------------------------
-x³+5x² (x²+4x+3)----------- > the quotient q(x)
4x²-17x-15
-4x²+20x
3x-15
-3x+15
the quotient q(x) is x²+4x+3
the answer is the option x²+4x+3
Sylvia is going to pick out a souvenir hat while she is on vacation. She knows the price of the hat will increase by 5% when she pays sales tax. She writes the expression h + 0.05h to find the total amount she will pay for the hat if it costs h dollars. Jin correctly writes another expression, 1.05h, that will also find the the total amount Sylvia will pay for the hat if it costs h dollars. Use the drop-down menus to explain what each part of Sylvia's and Jin's expressions mean.
Answers
Sylvia's espression:
h + 0.05h
h: Original hat price.
0.05h: Increase of 5% due to sales tax.
Jin's expressions:
1.05h
h: Original hat price.
1.05: Factor for which you must multiply the original price to add 5% due to sales tax.
Answer:
Step-by-step explanation:
Sylvia's expression
H: Price of hat
0.05: percent sales tax
0.05 h: amount of sales tax Sylvia will pay
h+0.5 h: total amount Sylvia will pay
Jin's Expression
1.05: One whole plus percent sales tax
H: price of hat
1.05 h: total amount Sylvia will pay
helppppppppppppppppppppppp
Answers
10.3 units
Explanation:
Triangle ABC is a right-angled triangle. This means that we can apply special trig functions.
We are given that:
angle B = 25 degrees and AB = 4 units
Therefore:
cos(B) = adjacent / hypotenuse
cos(25) = 4 / BC
BC = 4.414 units
tan(B) = opposite / adjacent
tan(25) = AC / 4
AC = 1.865
Finally, we can get the perimeter as follows:
perimeter = AB + BC + AC
perimeter = 4 + 4.414 + 1.865
perimeter = 10.279 which is approximately 10.3 units
Hope this helps :)
Side c = 4
Angle B = 25°
Step #1: Find angle C by subtracting the other 2 angles from 180°.
C = 180° - A° - B°
C = 180° - 90° - 25°
C = 65°
Step #2: Use the Law of Sines to find side a.
a / sin(A) = c / sin(C)
a / sin(90°) = 4 / sin(65°)
a = (sin(90°) x 4) / sin(65°)
a = 4.414
Step #3: Use the Law of Sines to find side b.
b / sin(B) = c / sin(C)
b / sin(25°) = 4 / sin(65°)
b = (sin(25°) x 4) / sin(65°)
b = 1.865
So you have the sides
c = 4
b = 1.865
a = 4.414
The perimeter is all the sides added up
P = 4 + 1.865 + 4.414
P = 10.279
That can be rounded to 10.3 units
Hope this helps!
Which statement about this product is true?
0.44 ×(−5 3/4)
It is equal to 0 because 0.44 rounded to the nearest whole number is 0, and 0 times any number is 0.
It is equal to −5 3/4 because 4/4 is equal to 1, and 1 times any number equals that number.
It is greater than −3 because 0.44 × 5 3/4 is less than 1/2 × 6
It is less than −5 3/4 because multiplying by a number less than 1 gives a smaller number.
Answers
Answer:
It is greater than −3 because 0.44 × 5 3/4 is less than 1/2 × 6
Step-by-step explanation:
i guessed it and it was right so ye.
find the arithmetic mean an of an-1 = 3.9 and an+1 = 7.1
a. 11
b. 5.5
c. 3.7
d. 1.6
Answers
Answer:
Step-by-step explanation:
Alright, lets get started.
We are asked to find arithmetic mean of two terms given.
For finding arithmetic mean, we add up the values and divide the sum by the number of values.
Here we have given two numbers , below
[tex]a_{n-1}=3.9[/tex]
[tex]a_{n+1}=7.1[/tex]
So, mean of these two numbers will be = [tex]\frac{3.9+7.1}{2}[/tex]
So, mean of these two numbers will be = [tex]\frac{11}{2}=5.5[/tex]
So, arithmetic mean for given two numbers are 5.5 : Answer (b)
Hope it will help :)
b. 5.5
Step-by-step explanation:FOR LEARNING ONLY.. not necessary to read, but I hope it helps!
you start with:
[tex]a_{n-1}=3.9\\a_{n-1}=7.1[/tex]
arithmetic questions like this are like finding an average.
so you add the values while dividing by the total of values there are.
in this case:
[tex]\frac{7.1+3.9}{2}[/tex]
which is simplified to:
[tex]\frac{11}{2}[/tex]
then decimal:
[tex]5.5[/tex]
Calculate the principal amount which earns $500 simple interest over 3 Years at a rate of 8% p.a round to the nearest cent
Answers
so, to find one year
500 ÷ 3 = $166.67
Interest for one year is $166.67
Interest rate for one year is 8%
8% = 166.67
1% = $20.83
100% = $2083.33
Principal amount is $2083.33
Final answer:
To find the principal amount that would earn $500 in simple interest over 3 years at an 8% annual rate, divide the interest by the product of the rate and period. The principal amount is $2083.33.
Explanation:
Calculating the Principal Amount from Simple Interest
To calculate the principal amount that earns $500 in simple interest over 3 years at a rate of 8% per annum, we can utilize the simple interest formula:
Interest = Principal × rate × time. Plugging in the known values, we get $500 = Principal × 0.08 × 3. This yields the equation $500 = Principal × 0.24.
To find the Principal, we divide $500 by 0.24, which gives us approximately $2083.33. Therefore, the initial principal amount is $2083.33.
What is the area of this polygon?
Answers
The polygon has a rectangle and a triangle
Area of triangle FSCW
= Length × width
= 9 × 2
= 18 square units
area of triangle FNS
= 1/2 × base× height
= 1/2 × 9 × 6
= 27 square units
Therefore the area of the polygon is
= 27 + 18
= 45 square units
.help please and thank you
Answers
Mrs. Rodriguez has 18 packages of pens in stock at her store on monday. On tuesday, she has 5/6 the number of pens she had on monday. On Wednesday, she has 2/5 of the number of pens she had on tuesday. How many packages of pens does she hve on Wednesday?
Answers
Mrs. Rodriguez has 18 packages of pens in stock at her store on Monday.
[tex] Number \; of\; packages\; of \; Pens\; on\; Monday=18\\ \\ [/tex]
On Tuesday, she has 5/6 the number of pens she had on Monday, which means...
[tex] Number \; of\; packages\; of \; Pens\; on\; Tuesday=\frac{5}{6} \; of \ 18 = \frac{5}{6} \times 18=\frac{90}{6}=15\\ [/tex]
On Wednesday, she has 2/5 of the number of pens she had on Tuesday, which means...
\\ Number \; of\; packages\; of \; Pens\; on\; Wednesday = \frac{2}{5} \; of \ 15=\frac{2}{5} \times 15=\frac{30}{5}=6
Conclusion:
Number of packages of pens does she have on Wednesday is 6 Packages
A jar contains 17 orange,7 pink, and 4 black marbles. A marble is drawn at random.What is the probability that the marble is pink or orange
Answers
P(pink) = 7/28
P(orange) = 17/28
P(pink or orange) = P(pink) + P(orange)
P(pink or orange) = 7/28 + 17/28
P(pink or orange) = 24/28
P(pink or orange) = 6/7 or 0.857143 or 85.7%
Graph this function f(x)=x^2-4x-5
Answers
Answer:
Step 1: a = 1, b = -4
Step 2: x = 2, f(2) = -9
Step 4: (5,0) and (-1,0)
Step 6: f(0) = -5
On the graph the points plotted are (-1,0) , (0,-5) , (2,-9) , and (5,0)
The data set represents a bimonthly progression of gasoline prices over the course of several months in an unspecified city. Use a graphing calculator to determine the quadratic regression equation for this data set. x 0 2 4 6 8 y 2.86 2.89 2.93 3.04 3.11 a. c. b. d.
Answers
Answer:
y = 0.0027*x^2 + 0.0111*x + 2.8574
Step-by-step explanation:
Using Excel the procedure is:
First, insert x and y values in a table format, as can be seen in the figure
Then, select data
Next, go to insert tab and inside charts options select scatter plot without any lines
Finally, select a point in the plot, right-click, add trend line, polynomial order 2 and check display equation option
What is the simplest form of (8x2)3?
Answers
[tex] = 8^3 \times (x^2)^3 [/tex]
[tex] = 512x^{2 \times 3} [/tex]
[tex] = 512x^6 [/tex]