Answer:
She is partially correct. There are 2 possible answers to this problem, and x - 2 = 3 is one of the answers. When applying the square root to both sides, the resulting answer could be either negative or positive. Therefore, applying the square root to both sides leads to the two following equations: x - 2 = 3 or x - 2 = -3.
What’s the answer help???
Answer:
a = 5 cm, b = 2 cm.Step-by-step explanation:
[tex]\text{We have:}\\\\A_{PQRS}=45\ cm^2\\\\A_{PQRS}=a(7+b)\\\\A_{PXYS}=10\ cm^2\\\\A_{PXYS}=ab\\\\\text{Therefore we have the system of equations:}\\\\\left\{\begin{array}{ccc}a(7+b)=45&\text{use the distributive property}\\ab=10\end{array}\right\\\left\{\begin{array}{ccc}7a+ab=45&(1)\\ab=10&(2)\end{array}\right\\\\\text{Substitute (2) to (1):}\\7a+10=45\qquad\text{subtract 10 from both sides}\\7a=35\qquad\text{divide both sides by 7}\\a=5\\\text{Put it to (2):}\\5b=10\qquad\text{divide both sides by 5}\\b=2[/tex]
Solve for x: 2/x-2+7/x2-4=5/x
Answer:
x = 11/6
Step-by-step explanation:
You need to reduce this fraction to the lowest terms.
This can be done by dividing out those factors that appear both in the numerator and in the denominator.
Please mark brainliest and have a great day!
Answer: [tex]\bold{x=-\dfrac{4}{3}\qquad x=5}[/tex]
Step-by-step explanation:
[tex]\dfrac{2}{x-2}+\dfrac{7}{x^2-4}=\dfrac{5}{x}\\\\\\\text{Multiply each term by the LCD x(x-2)(x+2) to clear the denominator:}\\\dfrac{2}{x-2}[x(x-2)(x+2)]+\dfrac{7}{x^2-4}[x(x-2)(x+2)]=\dfrac{5}{x}[x(x-2)(x+2)]\\\\\\\text{Simplify - cross out like terms:}\\2[x(x+2)]+7[x]=5[(x-2)(x-2)]\\\\\\\text{Distribute:}\\2x^2+4x+7x=5x^2-20\\\\\\\text{Set equation equal to zero and Add like terms:}\\0=5x^2-2x^2-7x-4x-20\\0=3x^2-11x-20\\\\\text{Factor, set each factor equal to zero, and solve for x:}[/tex]
[tex]0=(3x+4)(x-5)\\0=3x+4\qquad 0=x-5\\\large\boxed{x=-\dfrac{4}{3}\qquad x=5}[/tex]
The invoice date is August 1st. The terms are 5/10 EOM. What is the percent of the cash discount being offered?
The percent of the cash discount being offered is 5%.
Explanation:The terms 5/10 EOM mean that the customer is eligible for a cash discount of 5% if the invoice is paid within 10 days from the end of the month. In this case, the invoice date is August 1st, so the end of the month is August 31st. To calculate the number of days allowed for the cash discount, we subtract 10 days from August 31st, which gives us August 21st. Therefore, the cash discount is valid until August 21st and the percent of the cash discount being offered is 5%.
PLEASE HELP, I WILL MARK BRAINLIEST
Ted creates a box plot using 14, 13, 21, 10, 28, 30, and 35 as the data. Which of the following box plots shows the data accurately? A box plot is drawn with end points at 10 and 35.The box extends from 13 to 30 and a vertical line is drawn inside the box at 21. A box plot is drawn with end points at 10 and 35.The box extends from 15 to 32 and a vertical line is drawn inside the box at 23. A box plot is drawn with end points at 10 and 35.The box extends from 11 to 28 and a vertical line is drawn inside the box at 19. A box plot is drawn with end points at 10 and 35.The box extends from 17 to 34 and a vertical line is drawn inside the box at 25.
PLEASE HELP
a box plot is drawn with end points at 10 and 35. The box extends from 13 to 30 and a vertical line is drawn inside the box at 21.
which expression is equivalent to 4 square root 6 divided by 3 root 2
The equivalent expression to 4 √6 divided by 3 √2 is 4/3 × √3. This is achieved by expressing the square roots as fractional exponents and simplifying.
Explanation:The student is asking which expression is equivalent to the following mathematical expression: √(4 √6) / (3 √2).
To simplify this expression, we'll use the properties of exponents and radicals.
The square root of a number x can be written as x raised to the power of 0.5, so:
√6 = 60.5
√2 = 20.5
The given expression thus becomes:
(4 × 60.5) / (3 × 20.5) = 4/3 × 60.5/20.5
Since the exponents are the same, we can simplify the radicals by dividing the numbers inside the radicals:
4/3 × (6/2)0.5 = 4/3 × (3)0.5
And as (3)0.5 is the square root of 3:
4/3 × √3
Therefore, the equivalent expression is 4/3 × √3.
which sequences are arithmetic? select three options
Answer:
The sequences are arithmetic
1).-8.6, -5.0, -1.4, 2.2, 5.8
2). 5, 1, -3, -7, -11
3). -3, 3, 9, 15, 21
Step-by-step explanation:
If a sequence is a an AP then there is a common difference d.
1) Check sequence 1
-8.6, -5.0, -1.4, 2.2, 5.8
-5.0 - - 8.6 = 3.6
-1.4 - -5.4 = 3.6 It is an AP
2) Check sequence 2
2, -2.2,2.42, -2.662, 2.9282
-2.2 - 2 = -4.2
-2.662 - 2.42 = -5.082 Not AP
Similarly AP sequences are
5, 1, -3, -7, -11
-3, 3, 9, 15, 21
The sequence that are arithmetic are as follows:
5, 1, -3, -7, -11.
-3, 3, 9, 15, 21
-8.6, - 5.0, -1.4, 2.2, 5.8
What is arithmetic sequence?Arithmetic sequence is a list of numbers with a definite pattern. Therefore, let's find the sequence with a definite pattern.
5, 1, -3, -7, -11.
This is a sequence as it as a definite pattern. The value are reduced by 4. Therefore, the common difference is 4.
1 - 4 = 4-3 - (-1) = 4...-3, 3, 9, 15, 21
This is a sequence because it has a common difference of 6.
3 - (-3) = 69 - 3 = 615 - 9 = 6...-8.6, - 5.0, -1.4, 2.2, 5.8
This is a sequence because it has a common difference of 3.6.
-5.0 - (-8.6) = 3.6-1.4 - (-5.0) = 3.6learn more on sequence here: https://brainly.com/question/17627016
Subtract 8 1/6 - 4 5/6 . Simplify the answer and write as a mixed number.
Answer:
3 1/3
Step-by-step explanation:
8 1/6 - 4 5/6 Borrow 1 or 6/6 from the 8 so you have something to subtract.
7 7/6 - 4 5/6 Subtract the whole numbers.
7 - 4 = 3 Subtract the fractions.
7/6 - 5/6 Do the subtraction
2/6 Reduce
2/6 = 1/3 Put the two parts together.
3 1/3
the result of subtracting the two mixed numbers is [tex]3\frac{1}{3}[/tex]
To subtract the mixed numbers [tex]8\frac{1}{6}[/tex] and [tex]4\frac{5}{6}[/tex] we need to first understand how to subtract it. To subtract mixed numbers we need to first convert them to improper fraction. For the new fraction, the denominator remains same but new numerator is calculated by finding the product of whole number and denominator and then adding it to the numerator. This can be done as follows:
[tex]8\frac{1}{6} = \frac{ 8 \times 6 +1}{6} = \frac{49}{6}[/tex]
[tex]4\frac{5}{6} = \frac{ 4 \times 6 +5}{6} = \frac{29}{6}[/tex]
Now we subtract them as follows:
[tex]\frac{49}{6} - \frac{29}{6} = \frac{20}{6} = \frac{10}{3}[/tex]
To convert this back into mixed fraction we divide 10 by 3 and the quotient becomes the whole number while the remainder becomes numerator and 3 remains as denominator
[tex]\frac{10}{3} = 3\frac{1}{3}[/tex]
Therefore, the result of subtracting the two mixed numbers is [tex]3\frac{1}{3}[/tex]
Identify the values of a, b, and c that would be used in the quadratic
formula to solve the equation
- x2 + 5x = 7.
A) a = -1, b = 5, c = 0
B) a = 1, b = 5, c = 7
C) a = -1, b = 5, c = -7
D) a = 1, b = -5, c = 0
Answer:
C) a= -1, b=5, c= -7
Step-by-step explanation:
To get the values of a, b and c we must first write the equation in the form
ax²+bx+c=0 where a b and c are the coefficients.
Therefore, -x² +5x=7 can also be written as:
-x²+5x-7=0
a= -1 ( coefficient of x²)
b=5 (coefficient of x)
c= -7 ( the constant in the equation)
Answer:
a=-1, b=5 and c=-7
Step-by-step explanation:
We have the following equation:
[tex]-x^{2} + 5x = 7[/tex] → [tex]-x^{2} + 5x - 7 = 0[/tex]
Given the equation of a parabola: [tex]ax^{2} +bx + c = 0[/tex]. By comparison, we know that:
a=-1, b=5 and c=-7
So the correct option is Option C.
sin30°=1/2 and cos30°=(sqrt3)/2
true or false?
Answer:
True.
Step-by-step explanation:
It's true.
The sin of 30 in degrees equals 1/2 and the cos of 30 degrees equals sqrt(3)/2.
I am attaching a table that can be useful for remembering the values of the cosine and sine of some angles.
Answer:
True
Step-by-step explanation:
evaluate the expression 3x +(z+2y)-12 if x=3,y=8 and z=5
Answer:
18
Step-by-step explanation:
First you need to plug in the numbers for each variable.
3(3)+(5+2(8))-12
Now you solve
3(3)+(21)-12
9+21-12
18
Least common multiple (3,10)
Answer: 30
Step-by-step explanation: Start off by multiplying the two numbers.
3 x 10 = 30.
30 is a common multiple. Find any multiples below 30. Let’s start off using the biggest number of the two, which is 10, to see what other numbers can be multiples. 10, 20, and 30 can be. 3 can’t be divided into 10 or 20, so your least common multiple is 30.
HELPP SOS!!!!! THANK YOU SO MUCH WHOEVER ANSWERS WITH ACCURACY
•The parent function of the graph of f(x) is the square root function, which was reflected across the x-axis. Which of the following is the equation of f(x)?
The equation of f(x) is B. F(x) = -√x. Therefore , B. F(x) = -√x is correct.
Here's why:
The parent function of the graph is the square root function, which means the original equation is f(x) = √x.
The graph is reflected across the x-axis.
This means that the y-values are multiplied by -1. In other words, if the original point was (x, √x), the reflected point would be (x, -√x).
Therefore, the equation of the reflected function is f(x) = -√x.
The other options are incorrect because:
A. F(x) = √x is the original equation, not the reflected equation.
C. F(x) = √x - 1 shifts the graph down one unit, but it does not reflect it across the x-axis.
D. F(x) = √x + 1 shifts the graph up one unit, but it does not reflect it across the x-axis.
The first ferris wheel was 250 feet in diameter. It was invented by John Ferris in 1893. Assuming it made one revolution every 30 seconds, what was the linear speed of a passenger ( assuming the passenger is on the edge of the ferris wheel) in feet per minute.
Step-by-step explanation:
The wheel has a diameter of 250 feet, so its circumference is:
C = 2πr = πD
C = 250π feet
It makes one revolution in 30 seconds, or half a minute, so the linear speed of the passenger is:
v = d / t
v = 250π / 0.5
v = 500π ft/min
v ≈ 1571 ft/min
This is about the same as 17.9 mph.
Final answer:
The linear speed of a passenger on the original Ferris wheel with a diameter of 250 feet, making one revolution every 30 seconds, was approximately 1570.8 feet per minute.
Explanation:
The question asks to calculate the linear speed of a passenger on the edge of the first Ferris wheel, which was 250 feet in diameter, and made one revolution every 30 seconds. To find the linear speed, we first need to determine the circumference of the Ferris wheel, which can be done by using the formula for the circumference of a circle, C = πd, where d is the diameter.
For the first Ferris wheel:
Diameter (d) = 250 feet
Circumference (C) = π * 250 feet = 785.398163 feet (approximately)
Time for one revolution = 30 seconds
Since the question requires the speed in feet per minute, we need to convert the time for one revolution to minutes:
30 seconds = 0.5 minutes
The linear speed (v) can be found using the formula v = C / time. Substituting our values in:
v = 785.398163 feet / 0.5 minutes = 1570.79633 feet per minute
Therefore, the linear speed of a passenger at the edge of the Ferris wheel was approximately 1570.8 feet per minute.
let f(x)=x+3 and g(x)=1/2 the graph of (f•g)(x) is shown below
Answer:
(1/2)x+3/2
or
0.5x+1.5
Step-by-step explanation:
Hopefully you mean to have that dot between f and g closed because if it open it means something totally different.
So closed dot means multiplication
Open dot means you are composing a function with another one
So here you are just doing (x+3) * (1/2)
Just use distributive property (1/2)x+(1/2)(3)
(1/2)x +3/2
or
0.5x+1.5
What is the Least Common Multiple of 8 and 24
Answer: 24
Step-by-step explanation:
Break down the numbers until they have no way to be broken down anymore
8 = 4*2 = 2*2*2
24 = 6*4 = 3*2*2*2
The one that has more products is 24, so, it is 24.
What is the solution to this equation?
x + 19 = 26
A. X = 45
B. x= 17
c. x = 5
D. X = 7
x+19= 26
x+19-19= 26-19
x= 7
Check answer by using substitution method
x+19= 26
7+19= 26
26= 26
Answer is x= 7 (D.)
To find the solution we need to solve for x
We need to get x alone to solve for x.
To remove any number, always do the opposite operation
Opposite of +19 is -19
To remove +19 , subtract 19 from both sides
x+19=26
x+19 -19 =26-19 =7
x=7
So the value of x=7
The solution to this equation Option D. x=7
What is an example of an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. For example, 3x – 5 = 16 is an equation. Solving this equation, we get the value of the variable x as x = 7.
What are the 3 types of equations?There are three major forms of linear equations: point-slope form, standard form, and slope-intercept form.
What is not an equation?An equation is a mathematical statement that two things are equal. It consists of two expressions, one on each side of an 'equals' sign. For example x=y is an equation where two expressions x and y are equal. Whereas f(x)=x is a function with variable x and hence f(x)=x is not an equation.
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How to slove the equation 6.8x+9.3=-9.4+3.4(2-5x)
1. In a 30-60-90 triangle, the length of the hypotenuse is 6. What is the length of the shortest
side?
a. 2
b. 3
c. 3.12
d. 31/3
e, 6-3
Answer:
b. 3
Step-by-step explanation:
In a 30°-60°-90° triangle, the short side is ½ the hypotenuse [the long side is double the short side].
30°-60°-90° Triangles
x√3 → long side
x → short side
2x → hypotenuse
45°-45°-90° Triangles
x → two legs
x√2 → hypotenuse
I am joyous to assist you anytime.
Three runners competed in a race. Data were collected at each mile mark for each runner. If the runner ran at a constant pace, the data would be linear. A regression line fitted to their data. Uses the residual plots to decide which data set is best fit by the regression line, and then identify the runner that kept the most consistent pace.
Linear data is data lying across a straight line. The runner which kept the most consistent pace was runner B.
How does linear regression works?Firstly, there is a data set. Then, we try to fit a line which will tell about the linear trend. This line is made using the least squares method.
For the given case, the second runner(runner B)'s data is almost forming a linear trend, whereas, for the first runner, its more spread, and the third graph, its a quadratic trend.
For non-linear trends like in third graph(runner C), we use polynomial regression to fit polynomial curves of higher degrees.
Thus, as the runner B's data set is lying more near to a line than other runners, thus,
The runner which kept the most consistent pace was runner B.
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What is 6 more than 5 times the measure number of mn , what is m np
Answer:
6 more than 5 times the measure of mn is (5mn + 6)
Step-by-step explanation:
Which shows the factored form of x2-12x-45?
Answer:
(x - 15)(x + 3)
Step-by-step explanation:
Consider the factors of the constant term (- 45) which sum to give the coefficient of the x- term (- 12)
The factors are - 15 and + 3, since
- 15 × 3 = - 45 and - 15 + 3 = - 12, hence
x² - 12x - 45 = (x - 15)(x + 3)
There are 3 measures of music that are played 3 times in a song. If the first measure has 8 notes, the second measure has 16 notes and the third measure has 4 notes, how many notes are played throughout the song?
Answer:
82 notes
Step-by-step explanation:
3×8=24
16×3=48
4×3=12
24+48+12=84
Final answer:
To find the total number of notes played throughout the song, add the notes from each measure (8 + 16 + 4 = 28) and multiply by the times they are played (28 x 3), resulting in 84 notes played in total.
Explanation:
The question pertains to calculating the total number of notes played in a song where specific measures of music are repeated a certain number of times. First, we need to calculate the number of notes in a single iteration of the three measures:
Measure 1: 8 notes
Measure 2: 16 notes
Measure 3: 4 notes
Adding these together, we get a total of 28 notes for one iteration of the 3 measures. Since these measures are played 3 times throughout the song, we multiply 28 by 3, which equals 84 notes. Therefore, 84 notes are played throughout the song.
Help with this!!
thank you
Answer:
9
Step-by-step explanation:
Whatever you do to the denominator, you've got to do to the numerator, and vice versa. So for 8 to become 24, you multiply by 3. do that to the numerator 3 as well. 3 × 3 is 9.
For the sake of showing work I will replace the empty space with an x like so...
[tex]\frac{3}{8} =\frac{x}{24}[/tex]
To find out what x is you must cross multiply (aka butterfly)
***Image of this step is attached below
3*24 = 8*x
72 = 8x
Next divide 8 to both sides to finish isolating x. Since 8 is being multiplied by x, division (the opposite of multiplication) will cancel 8 out (in this case it will make 8 one) from the right side and bring it over to the left side.
72 ÷ 8 = 8x ÷ 8
9 = 1x
9 = x
To make these fractions equivalent the empty spot must be 9
[tex]\frac{3}{8} = \frac{9}{24}[/tex]
Hope this helped!
~Just a girl in love with Shawn Mendes
the segments shown below could form a triangle
Answer:
False
Step-by-step explanation:
a^2+b^2=c^2 so the biggest number would be c and that would be 11 9^2=81 4^2=16 adding these together gets 97. 97=/=11^2 which is 121
Answer:
A. True.
Step-by-step explanation:
We have been given lengths of three segments. We are asked to determine whether the given segments could form a triangle or not.
Triangle inequality theorem states that sum of two sides of triangle must be greater than third side of the triangle.
Using triangle inequality theorem, we will get:
[tex]9+4>11[/tex]
[tex]13>11[/tex] True
[tex]9+11>4[/tex]
[tex]20>4[/tex] True
[tex]4+11>9[/tex]
[tex]15>9[/tex] True
Since our given segments satisfies triangle inequality theorem, therefore, the given segments could form a triangle.
Each granola bar costs $1. Write an expression that shows the total cost of the granola bars. Use the variable you identified in question 1. Btw I used the variable "g". Thanks!
Answer:
$[tex]1g[/tex]
Explanation:
If the number of granola bars is represented by the variable [tex]g[/tex], and each granola bar costs $1, then we need to multiply the amount per granola bar by the number of granola bars.
This is $[tex]1 * g[/tex], or $[tex]1g[/tex].
In this scenario, the total cost of the granola bars can be represented by the mathematical expression 'g', as each granola bar costs $1.
Explanation:If each granola bar costs $1 and 'g' is representing the number of granola bars, then the total cost of the granola bars can be represented by the expression 1 * g or simply g. This is because for every granola bar you buy, you are adding $1 to your total. So if you bought 'g' granola bars, your total cost would be $1 times the number of granola bars 'g'. This is an example of direct proportionality, where the total cost increases with the increase in number of granola bars.
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If (x) = 3х + 2, what is (5)?
ОА. 10
OB. 1
Ос. 13
OD. 17.
Answer:
D
Step-by-step explanation:
To evaluate f(5) substitute x = 5 into f(x)
f(5) = (3 × 5) + 2 = 15 + 2 = 17 → D
[tex]f(5)=3\cdot5+2=17\Rightarrow\text{D}[/tex]
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Three roots of a fifth degree polynomial function f(x) are –2, 2, and 4 + i. Which statement describes the number and nature of all roots for this function?
A. f(x) has two real roots and one imaginary root.
B. f(x) has three real roots.
C. f(x) has five real roots.
D. f(x) has three real roots and two imaginary roots.
A fifth-degree polynomial has three real roots and two imaginary roots.
Explanation:The given polynomial function f(x) is a fifth-degree polynomial, meaning it has five roots. We are given three of the roots: -2, 2, and 4 + i. Since the coefficients of a polynomial with real coefficients are either real or come in conjugate pairs for complex roots, the remaining two roots must be the complex conjugates of 4 + i, which are 4 - i. Therefore, f(x) has three real roots -2, 2, and 4, and two complex roots 4 + i and 4 - i.
Answer: D. f(x) has three real roots and two imaginary roots.
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The function f(x), a fifth degree polynomial, has three real roots and two complex (imaginary) roots due to the Conjugate Root Theorem. The roots are –2, 2, 4, 4 + i and 4 - i. Therefore, option D is correct.
Explanation:The function f(x) is a fifth degree polynomial. Given the roots available, –2, 2, and 4 + i, we already have three roots, two real and one complex (or imaginary). From the Conjugate Root Theorem, which states that if a polynomial has real coefficients, then any imaginary root must have its conjugate as a root. Thus, the conjugate of 4 + i, which is 4 - i, is also a root of this function. Therefore, the fifth degree polynomial has three real roots –2, 2, and 4, and two imaginary roots 4 + i and 4 - i, indicating that option D: 'f(x) has three real roots and two imaginary roots' is correct.
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While shopping at a clearance sale, Samantha finds a $60.00 dress on sale for 25% off. Samantha also has a 50% off coupon. Which statement correctly summarizes her savings?
Answer:
Samantha will save $37.50 because she must first find the 25% sale price before taking the extra 50% reduction
Step-by-step explanation:
Samantha will be offered the choice of using the coupon or the sale discount. If she chooses tht 50% coupon, her savings will be $30. If she chooses the marked sale discount, her savings will be $15.
The scenario above assumes she gets 50% off the sale price of $45, so saves $15+22.50 = $37.50 off the original price.
Answer: Samantha will save $37.50 because she must first find the 25% sale price before taking the extra 50% reduction so the answer is B
Step-by-step explanation:
hurry 50 pts
what dose this =
[15 ÷ 5 • 3 + (23 – 3)] + [4 • (36 – 33)]
Answer:
1155
Step-by-step explanation:
Answer:
41
Step-by-step explanation:
:))
Which absolute value inequality represents the given graph?
A. 18x + 91 < 57
B. 18x + 91 > 57
C. 18x +91 557
D. 18x +9 57
Answer:
Distribute the -9 into the values in the parentheses.
STEP BY STEP
-9(-2x-3)
-9*-2x=18x
-9*-3=27
Therefore, the equation then becomes: 18x+27.
The answer is the first choice, or A.