Use synthetic division to solve these problems
5 | 1 -4 -7 10
| v 5 5 -10
1 1 -2 0
This leads to x^2+x-2
Next we find what adds to 1 and multiplies to -2
The factors of f(x) are 2 and -1, written out as (x+2) and (x-1)
-1/2 | 2 3 -23 -12
| v -1 -1 12
2 2 -24 0
This leads to 2x^2+2x-24
Next, multiply the 2 from the a value (since a is the value with x^2 and c is the value without any x) with -24, which is -48
Now find what adds to 2 and multiplies to -48
The values for this are 8 and -6, but keep in mind, when multiplying the value of a by c, you now have to add the values in place of what you tried adding it to, this time in the problem we found using synthetic division, in this case the 2 in the b value (the middle of the equation, or the value with only one x)
2x^2+8x-6x-24
When group factoring, you'd get 2x(x+4) -6 (x+4)
So, the factors of g(x) are (x+4) and (2x-6)
Jasmine is a receptionist at a doctors office . She books 36 appointments each day. Four out of every 24 appointments are cancelled. How many appointments are cancelled each day?
Answer:
6 appointments are cancelled per day
Step-by-step explanation:
Question says 4 out of 24 appointments are cancelled.
It means out of 1 appointment , the cancelled appointments = [tex]\frac{4}{24}[/tex]
=[tex]\frac{1}{6}[/tex]
Now the questions says each day there are 36 appointments
And we have to find how many appointments got cancelled each day,
It means we have to find how many appointments got cancelled out of 36 appointments each day
So we multiply 36 by [tex]\frac{1}{6}[/tex]
=[tex]36 * \frac{1}{6}[/tex]
= 6
Hence , 6 appointments got cancelled each day.
Jasmine has 6 appointments cancelled per day, determined by scaling the given cancellation ratio (4 out of every 24) to match the number of daily appointments she books (36).
Explanation:To answer this question, we first need to understand the rate at which appointments are cancelled. The problem states that 4 out of every 24 appointments are cancelled. To find out how many appointments are cancelled each day, we use this ratio and apply it to the 36 appointments that Jasmine books each day.
First, we need to scale the ratio to match Jasmine's daily bookings. To do this, we multiply the numerator and denominator of the ratio by 36/24, which is 1.5. This gives us a new ratio of 6 cancellations for every 36 appointments.
So, each day, out of the 36 appointments that Jasmine books, 6 appointments are cancelled.
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Which function passes through the points (2, 15) and (3, 26)? A. y = 11x + 7 B. y = 11x − 7 C. y = 7x + 11 D. y = -11x − 7 E. y = 7x − 11
Answer:
B is the correct answer.
The function that passes through the points (2, 15) and (3, 26) is B) y = 11x - 7.
Explanation:To find the function that passes through the points (2, 15) and (3, 26), we can use the point-slope form of a linear equation, y - y1 = m(x - x1). Using the first point (2, 15), we can substitute the values into the equation and solve for the slope, m. Then, we can use the slope to find the y-intercept, b, by substituting the values of a point into the slope-intercept form of a linear equation, y = mx + b.The function that passes through the given points is B) y = 11x - 7.
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What is the answer and work too the equation 4x+9+3x=30
Nine less than a number n n is written as
"Less than" means subtraction
The order they appear in tells me to subtract 9 from N.
n - 9
There were 13,501 visitors to a museum in june.What is this number rounded to nearest ten thousand ?Explain how
13,501 rounded to the nearest ten thousand is 14,000. This is because if you look at the 3, the number next to it is 5, causing it to round up. Numbers 0-4 are rounded down, and numbers 5-9 are rounded up.
Answer:
10,000
Step-by-step explanation:
When we round a number to the nearest ten thousand we check the digit at the thousand place,
If the digit ≥ 5,
The number is rounded to next ten thousand,
If the digit < 5,
The number is rounded to previous ten thousand.
Here, the given number,
13,501,
Digit at thousand place = 3 ( < 5 )
Thus, 13,501 ≈ 10,000 ( nearest ten thousand )
A line segment whose endpoints are (4,2) and (3,7) is translated to the right 5 units and up one unit. Which of the following matrix sums represents this translation?
5 units right: x + 5
1 unit up: y + 1
(x, y) → (x + 5, y + 1)
(4, 2) → (4 + 5, 2 + 1) = (9, 3)
(3, 7) → (3 + 5, 7 + 1) = (8, 8)
[tex]\begin{array}{ccc}\ \ x&y\end{array}\ \ \ \ \begin{array}{ccc}\ \ x&y\end{array}\\\left[\begin{array}{ccc}4&2\\3&7\end{array}\right]+\left[\begin{array}{ccc}5&1\\5&1\end{array}\right]=\left[\begin{array}{ccc}9&3\\8&8\end{array}\right][/tex]
Answer:
[tex]\left[\begin{array}{ccc}4&2\\3&7\end{array}\right]+\left[\begin{array}{ccc}5&1\\5&1\end{array}\right][/tex]
what is the y-intercept of 6x+ 12y= 60?
A. 5
B. 10
C .60
What is the slope of the line that contains the points (1, −1) and (−2, 8)?
A. −3
B. 7 over 3 negative
C. 1 over 3 negative
Problem 1
Plug in x = 0 and solve for y to get the y intercept
6x+12y = 60
6(0)+12y = 60
12y = 60
12y/12 = 60/12 ... divide both sides by 12
y = 5
Answer: A) 5
======================================
Problem 2
Use the slope formula.
The two points are (x,1, y1) = (1, -1) and (x2, y2) = (-2, 8)
m = (y2-y1)/(x2-x1)
m = (8-(-1))/(-2-1)
m = (8+1)/(-2-1)
m = 9/(-3)
m = -3
Answer: A) -3
An artist wants to frame a square painting with an area of 400 square inches if x is the length of the one side of the painting what equation ca you set up to find the length of a side how many solutions does the equation have?
There is only one solution to the equation. A quadratic equation has 2 solutions a positive and a negative, but since we are looking for length, the answer can only be postive. Area= side^2
400= x^2
sqrt(400)=x
20 inches = x
The length of one side is 20 inches
check: 20*20 = 400, which is the area of the square painting.
I'd really appreciate it if anyone helped! :)
Which statement best explains why y=4−6x is a function?
It is a linear equation.
The solutions to the equation can be written as ordered pairs.
The slope is a factor of the y-intercept.
Each x value has one and only one y value.
D, Each x value has one and only one y value.; This is because if an x-value repeats itself then it is not a function. You can test this on a graph by drawing a vertical line on it. If the vertical line intercepts the line more than once anywhere on the graph, then it is not a function.
Answer:
Each x value has one and only one y value.
Step-by-step explanation:
y = f(x) can be called a function if, and only if
f(a) = f(b) means that a = b.
That is, each x value has one and only one y value.
y = 4 - 6x
f(a) = f(b)
4 - 6a = 4 - 6b
6b = 6a
b = a
So the correct answer is:
Each x value has one and only one y value.
Josie watched a beetle on the sidewalk. It crawled 2/6 of a yard, then rested for a bit, and then crawled 1/4 of a yard farther. How far did the beetle crawl in all?
John is 24 years old. Two years ago, he was twice Shane's age at that time. How old is Shane now?
Answer:
Present age of john= 24 years
Let Shane's age= x years
Two years ago
John's age = 24-2= 22 years
Shane's age = (x-2) years
Writing in terms of equation,to the above statements
⇒22= 2(x-2)
⇒22= 2 x- 4
⇒22+4 = 2 x
⇒ 2 x= 26
⇒ x= 26÷2
⇒ x =13
Present age of son = 13 years
At the start of 2014 lucy's house was worth ?200000. The value of the house increased by 5% each year. Work the value of the house at the start of 2017
Answer:
Value of house in 2017 = 231525$
Explanation:
At the start of 2014 worth of Lucy's house = 200000$
Rate of increase of the value of the house = 5% = 0.05
Value of house in 2015 = 200000+0.05*200000 = 210000$
Value of house in 2016 = 210000+0.05*210000 = 220500$
Value of house in 2017 = 220500+0.05*220500 = 231525$
Number of years in between 2014 and 2017 = 2017 - 2014 = 3 years.
Value of house in 2017 [tex]=200000*1.05^3=231525$[/tex]
Find the area of a rectangle with length (2x + 3) and width (x - 4). A) 2x2 - 11x - 12 B) 2x2 - 5x + 12 C) 2x2 + 11x + 12 D) 2x2 - 5x - 12
D
area of a rectangle = length × width
area = (2x + 3)(x - 4) ( expand using FOIL )
= 2x² - 8x + 3x - 12 = 2x² - 5x - 12 → D
What is the correct word name for the given decimal 5.89
What is the mode of this data set 55 78 43 39 78 61 75 50 43 78
Mode means MOST. Which number is displayed the most?
39, 43, 43, 50, 55, 61, 75, 78, 78, 78
Answer: 78
Note: I placed the data set into numerical order because it will help you to easily find the mode and also the median (middle number).
Is it possible for a number to be a rational number that is not an interger but is a whole number. Explain
Whole numbers are a subset of integers, which in turn are a subset of rational numbers.
So, every whole number is an integer, and every integer is a rational number.
So, it is possible for a rational number not to be an integer. Think of any decimal number: 1.356 is a rational number, but it's not an integer.
On the other hand, if a number is not an integer, it can't be a whole number, because all whole numbers are integers.
A function is shown.
f(x)=x2+2x−1
Which graph represents the function?
The fourth graph represents the function.
We have to rewrite the given function into the standard form of a parabola.
What is a parabola?A parabola is a U-shaped plane curve that is symmetrical about its vertex.
What is the standard form of a parabola?The standard form of a parabola is given by:
y = (x-h)²+k
Where (h,k) is the vertex of the parabola.
The given function is rewritten in its standard form:f(x) = x²+2x-1
We can rewrite this as:
f(x) = x²+2x+1-2
f(x) =( x+1)²-2
By observing the function in standard form, we can see that the vertex of the parabola is (-1,-2).Now compare this with the given graphs. The only graph that has its vertex at (-1,-2) is the fourth graph.
We have found the graph that represents the function f(x) = x²+2x-1 to be the fourth graph.
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Sierra drives for h hours at a rate of 2x miles per hour. Which expression shows the distance that she drives after h hours
Answer:
Distance traveled by Sierra in h hours at a rate of 2x miles per hour = 2xh
Explanation:
Distance traveled by a body = Velocity of the body * Time taken by the body
Here velocity of Sierra = 2x miles per hour
Time taken by Sierra = h hours.
Distance traveled by Sierra = 2x * h = 2xh
So distance traveled by Sierra in h hours at a rate of 2x miles per hour = 2xh
What operations are needed to solve this word problem? Joe has 8 Dalmatians. Sarah has 3 fewer Dalmatians than Joe. How many Dalmatians do they have together?
Final answer:
To solve the word problem, subtract 3 from 8 to find the number of Dalmatians Sarah has, then add that number to Joe's 8 Dalmatians to determine the total number of Dalmatians they have together, which is 13.
Explanation:
To solve the word problem presented, we need to perform two primary operations: subtraction and addition. Joe has 8 Dalmatians, and Sarah has 3 fewer Dalmatians than Joe.
First, we determine how many Dalmatians Sarah has by subtracting 3 from 8. Once we know how many Dalmatians Sarah has, we add that number to Joe's 8 Dalmatians to find out the total number they have together.
Step 1: Calculate the number of Dalmatians Sarah has.
Sarah's Dalmatians = Joe's Dalmatians - 3
Sarah's Dalmatians = 8 - 3
Sarah's Dalmatians = 5
Step 2: Calculate the total number of Dalmatians they have together.
Total Dalmatians = Joe's Dalmatians + Sarah's Dalmatians
Total Dalmatians = 8 + 5
Total Dalmatians = 13
Therefore, Joe and Sarah have a total of 13 Dalmatians together.
A piece of wood is divided into three pieces in the ratio 6:8:4. The length of the longest pieces is 144cm. Calculate the length of the wood.
3.24m
the longest piece will be associated with 8 parts of the ratio.
divide 144 by 8 to find 1 part of the ration then multiply this value by 6 and 4 for the remaining parts of the ratio
[tex]\frac{144}{8}[/tex] = 18 cm ← 1 part
6 parts = 6 × 18 = 108 cm
4 parts = 4 × 18 = 72 cm
length = 144 + 108 + 72 = 324 cm = 3.24m
Answer: 324 cm
Step-by-step explanation:
6 : 8 : 4
x18 x18 x18
108 144 72
108 + 144 + 72 = 324
Please solve
-1/3x > 5
A) x < -15
B) x > -15
C) x > -5/3
D) x<-5/3
Step 1. Simplify 1/3x to x/3
-x/3 > 5
Step 2. Multiply both sides by 3
-x > 5 * 3
Step 3. Simplify 5 * 3 to 15
-x > 15
Step 4. Multiply both sides by -1
x < -15
Your answer is A.
The ratio of boys to girls at a rock concert was about 7 to 6. If there were, 1092 boys at the concert, how many girls were there?
Would a length of 650 feet meet the requirements for the runners' corral? If so, what would the width be? Justify your response with calculations.
The question in the photo is already answered but I need the question Above answered
The photo is just to give you guys the data for the coral.
Let
x-----------> the length of the rectangular corral
y-----------> the width of the rectangular corral
we know that
the area of the rectangular corral is equal to
[tex]A=x*y\\ A\geq 29,040\ ft^{2}[/tex]
so
[tex]x*y \geq 29,040[/tex] -------> inequality A
the perimeter of the rectangular corral is equal to
[tex]P=2x+y\\P \leq 1,364 ft[/tex]
so
[tex]2x+y \leq 1,364[/tex] -----> inequality B
using a graphing tool --------> resolve the compound system inequalities
see the attached figure
the solution is the shaded area
so
the length of 650 feet does meet the requirements of the runners corral
and the width is 64 ft-------> see the graph
the answer is
a) the length of 650 feet does meet the requirements of the runners corral
Fill in the blank. Given O below, you can conclude that OH is congruent to _____.
A. OE
B. O
C. LE
D. TG
Answer:
(A) OE
Step-by-step explanation:
From the given figure, it can be seen that TG and LI are the chords of the circle with center O such that TG=LI=10.4 which means that TG is congruent to LI.
Also, OE and OH gives the shortest distance(perpendicular) of the chord LI and TG respectively from center of circle O.
And, We know that "the congruent chords are equidistant from the center of a circle."
Therefore, we can conclude that, OH is congruent to OE.
Hence, option (A) is correct.
From the figure we can conclude that OH is congruent to OE.
Further Explanation:
Given:
The options are as follows,
A. OH is congruent to OE.
B. OH is congruent to OE.
C. OH is congruent to OE.
D. OH is congruent to OE.
Explanation:
A point is a location on the graph or at any surface.
A line is the distance between the two points that extends to infinite in both directions.
A ray is defined as the distance between the two points that extends to infinite in one direction.
Plane extends in two dimensions.
The length of TG and LI is [tex]10.4{\text{ units}}.[/tex]
LI and TG are the chords of the circle with same length.
OE and OH are the perpendicular bisector of the chords LI and TG respectively.
The given chords of the circle are equidistant from the center of the circle.
From the figure we can conclude that OH is congruent to OE.
Learn more:
If the clothing maker bought 500 m2 of this fabric, how much money did he lose? use 1tepiz=0.625dollar and 0.9144m=1yard https://brainly.com/question/2479097. Suppose that you find the volume of all the oceans to be 1.4×109km3 in a reference book. to find the mass, you can use the density of water, also found in this reference book, but first you must convert the volume to cubic meters. what is this volume in cubic meters? https://brainly.com/question/1446243.
Answer details:
Grade: High School
Subject: Mathematics
Chapter: Line and Rays
Keywords: congruent, fill, blank, conclude, OH, OE, chord, tangent, displacement, two chords, radius, center, circle, equidistant,
A store buys a jacket for $20.00 then sells it to customers 80% more than that what is he selling price of the jacket
The selling price of the jacket, after the store increases its purchasing price by 80%, is $36.
Explanation:The subject of this question is mathematics, specifically a practical application of percentages. The store buys the jacket for $20 and then increases the sale price by 80% for its customers. First, to calculate the 80% of the cost price, you multiply 20 (the cost price) by 0.80 (the percentage increase represented as a decimal). This results in $16. The selling price is then calculated by adding this calculated value to the original cost price which gives us $20 + $16 = $36. So, the store sells the jacket for $36.
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Simplify the expression.
{(-1)^3/(-3)^-3}^2
a. 1/729
b.3^-18
c. 729
d. 3^18
What is the slope of the line shown below?
answer B or 1/6 should be right.
Answer: The correct option is
(B) [tex]\dfrac{1}{6}.[/tex]
Step-by-step explanation: We are given to find the slope of the straight line shown in the graph.
From the graph, we see that the line passes through the points (-6, 3) and (12, 6).
The SLOPE of a line passing through the points (a, b) and (c, d) is given by
[tex]m=\dfrac{d-b}{c-a}.[/tex]
Therefore, the slope of the given line is
[tex]m=\dfrac{6-3}{12-(-6)}=\dfrac{3}{12+6}=\dfrac{3}{18}=\dfrac{1}{6}.[/tex]
Thus, the slope of the given line is [tex]\dfrac{1}{6}.[/tex]
Option (B) is CORRECT.
There are 144 people in line. There are twice as many adults as children in line .How many children in line and how many adults are in line?
48 children and 96 adults
let x be the number of children then number of adults = 2x and
x + 2x = 144
3x = 144 ( divide both sides by 3 )
x = [tex]\frac{144}{3}[/tex] = 48
There are 48 children and ( 2 × 48 ) = 96 adults
There are 48 children and 96 adults in line.
Explanation:To find how many children and adults are in line, we can use algebraic equations and solve for each variable. Let's assume the number of children in line is x. Since there are twice as many adults as children, the number of adults in line would be 2x. According to the given information, the total number of people in line is 144. Therefore, we can set up the equation x + 2x = 144. Simplifying the equation, we get 3x = 144. Dividing both sides by 3, we find x = 48. So, there are 48 children and 2 * 48 = 96 adults in line.
What number multiplied by itself 2 times equals 1/100
Question 9 Unsaved For all x, (2x+3)^2=? Question 9 options: 4x^2+9 4x^2+6x+9 4x^2+6 4x^2+12x+9
Use [tex](a+b)^2=a^2+2ab+b^2[/tex]
[tex](2x+3)^2=(2x)^2+2(2x)(3)+3^2=4x^2+12x+9[/tex]