The quotient of the synthetic division problem -1 | 2 7 5 in polynomial form is 2x + 5
How to determine the quotient?The synthetic division problem is given as:
-1 | 2 7 5
Remove the number before the | sign
2 7 5
Remove the middle number
2 5
Introduce a variable starting from an exponent of 0 (let the variable be x)
2x¹ 5x⁰
Evaluate the exponents
2x 5
Express as sum
2x + 5
Hence, the quotient of -1 | 2 7 5 in polynomial form is 2x + 5
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The ideal width of a safety belt strap for a certain automobile is 6 cm. The actual width can vary by at most 0.45 cm. Write an absolute value inequality for the range of acceptable widths and solve the inequality.
Answer:
[tex]|x-6|\le 0.45[/tex]
[tex]x\in [5.55,6.45][/tex]
Step-by-step explanation:
Absolute Value Inequality
Assume the actual width of a safety belt strap for a certain automobile is x. We know the ideal width of the strap is 6 cm. This means the variation from the ideal width is x-6.
Note if x is less than 6, then the variation is negative. We usually don't care about the sign of the variation, just the number. That is why we need to use the absolute value function.
The variation (unsigned) from the ideal width is:
[tex]|x-6|[/tex]
The question requires that the variation is at most 0.45 cm. That poses the inequality:
[tex]|x-6|\le 0.45[/tex]
That is the range of acceptable widths. Let's now solve the inequality.
To solve an inequality for an absolute value less than a positive number N, we write:
[tex]-0.45\le x-6 \le 0.45[/tex]
This is a double inequality than can be easily solved by adding 6 to all the sides.
[tex]-0.45+6\le x \le 0.45+6[/tex]
Operating:
[tex]5.55\le x \le 6.45[/tex]
That is the solution in inequality form. Expressing in interval form:
[tex]\boxed{x\in [5.55,6.45]}[/tex]
Given: ∠2 ≅ ∠3 and ∠5 ≅ ∠6
Prove: PQ || RS
Answer:
sorry I need more points to ask questions and I really need the answers I know you understand, thankyou :)
ep-by-step explanation:
!50 POINTS! what is One foot as a fraction
Answer:
12/1
Step-by-step explanation:
en una guardería ay una matricula de 50 lactantes de los cuales 20 son niñas cual es la razon de niñas a niños en dicha guarderia
Answer:
La razón de niñas a niños en la guardería es de 2 niñas por cada 3 niños.
Step-by-step explanation:
Una razón es una división entre dos números, generalmente en forma racional (fraccionaria). La razón de niñas a niños en la guardería es la cantidad de niñas dividida por la cantidad de niños de la dicha guardería, Es decir:
[tex]x = \frac{20}{30}[/tex]
[tex]x = \frac{2}{3}[/tex]
La razón de niñas a niños en la guardería es de 2 niñas por cada 3 niños.
ratio 5: 12 if there are 50 trucks how many cars are there
If the 50 trucks represent the 5 in the ratio 5:12, then there are 120 cars.
An honest coin is tossed 4 times in a row. Find the probability of each of the following events. (a) E1: "The coin comes up tails exactly twice." (b) E2: "All 4 tosses come up the same." (c) E3: "Exactly one-third of the tosses come up ." (d) E4: "The first 2 tosses come up heads ."
Answer:
3/8 ; 1/8 ; 0 ; 1/4
Step-by-step explanation:
Given that:
For a coin toss :
Sample space = {HHTT, HTTT, THTT, TTTT, HHHT, HTHT, THHT, TTHT, HHTH, HTTH, THTH, TTTH, HHHH, HTHH, THHH, TTHH}
Probability = required outcome / Total possible outcomes
a) E1: "The coin comes up tails exactly twice."
p(E1) = 6/16 = 3/8
(b) E2: "All 4 tosses come up the same."
{TTTT, HHHH}
p(E2) = 2/16 = 1/8
(c) E3: "Exactly one-third of the tosses come up head."
1/3 of 4 ; p = 0 ; outcome is not a whole number
(d) E4: "The first 2 tosses come up heads ."
P(E4) = 4/16 = 1/4
What can be done to the graph of y=2x2+3 to obtain the graph of y=−2x2+3?
Answer:
Reflect over the x-axis.
Step-by-step explanation:
Assuming you meant 2x^2+3, putting a negative sign in front of the x value flips the graph over the x-axis.
Molly bought a flat. At the beginning of
the third year, the value of Molly's flat had
increased to €363 000. At the beginning of
the fifth year, the value had increased to
€439 230.
a Calculate the rate of increase.
b Calculate how many euros Molly
originally paid for the flat.
C Find how much the flat is worth at the
beginning of the ninth year.
The rate of increase is 1.1, Molly originally paid 272727 for the flat and its worth at the beginning of the ninth year. is 643076
Calculating the rate of increase.From the question, we have the following parameters that can be used in our computation:
Third year = 363000
Fifth year = 439230
So, we have
Rate² = 439230/363000
Evaluate
Rate² = 1.21
Take the square root
Rate = 1.1
Calculating how many euros Molly originally paid for the flat.An exponential function is represented as
f(x) = abˣ
Where
a = initial values
Using the values from the third year, we have
a * 1.1³ = 363000
So, we have
a = 363000/1.1³
Evaluate
a = 272727
The flat worth at the beginning of the ninth year.This means that
x = 9
So, we have
f(x) = 272727 * 1.1⁹
Evaluate
f(x) = 643076
Hence, the flat worth at the beginning of the ninth year. is 643076
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Which of the following points lies on the line whose equation is y=2x-3?
(-1,4) (1, -1)
(0,3)
Answer:
(1, -1)
Step-by-step explanation:
y - (-1) = 2 (x - 1)
y + 1 = 2x - 2
y = 2x - 2 - 1
y = 2x - 3
Answer:
Option B: (1,-1)
Step-by-step explanation:
To solve these types of questions, you must first draw the graph. Then, you can see which point is on the line.
(I personally use Desmos's Graphing Calculator for the graph. Just put the equation in, and the line is drawn for you!)
I hope this helps!
William keeps several tanks of exotic fish at his house. He feeds them 4 containers of fish food each day. Each container of fish food cost $2.00. How much money does William spend on fish food in one week?
This is for my daughters 4th grade math class....She needs to have a “plan, estimate, solve, and number model”. This is a addition and subtraction problem its can’t be multiplied!
PLEASE HELP THIS MOM WHO IS TERRIBLE WITH THIS COMMON CORE MATH!
Answer: $56
Step-by-step explanation:
Each day he feed them 4 fish food containers. How many days is a week 7. So 7x4 is 28. All we have left over is $2.00
so we just multiply 28x2. That sums up to $56!
What would be the best first step to convert 4x+10y=12 to slope intercept form?
A. -4x from both sides
B. Divide both sides by 10
C. +4x to both sides
D. -12 from both sides
Answer: A
Step-by-step explanation:
You start with -4x to get the 10y by itself
HELP ILL GIVE BRAINLIEST!! Andrea is planning on taking the train to go to the beach, a train travels at a constant speed. An equation relating the distance traveled in miles, m, to the number of minutes, t is t = 3m . If Andrea arrived at the beach in an hour and 15 minutes, how much distance did she travel?
Answer:
225 miles I think
Step-by-step explanation:
75x3=225
tl;dr: Andrea traveled 3 [tex]\frac{3}{4}[/tex] miles.
Hello!
To solve the problem, we need to understand what it means. The distance traveled in miles is represented with t, while the number of minutes is represented with m.
Now, first we need to fill in the equation with the information we're given.
t = 3m → t = 3(1 [tex]\frac{1}{4}[/tex])
Now, we solve for t.
t = 3(1 [tex]\frac{1}{4}[/tex]) → t = 3 [tex]\frac{3}{4}[/tex]
Andrea traveled 3 [tex]\frac{3}{4}[/tex] in an hour and 15 minutes.
Hope this was helpful. Have a great day! (★‿★)
Write an equation in point-slope form for the line that passes through the points (3, -5) and (1, -8).
Answer:
m = y2 - y1 / x2 - x1 -8 - (-5)/1-3
-8 +5/1-3
-3/-2
slope is 1 1/2
Step-by-step explanation:
Hope this helps :)
A pack of paper costs $3.75 including tax. Mr. Cooper wants to purchase packs of paper for his class and has a $20 budget. Write an inequality to solve for the number of packs of paper Mr. Cooper can purchase with his budget. A) $3.75x ≥ $20. B) $3.75x ≤ $20. C) $20x ≤ $3.75. D) $20x ≥ $3.75
Help!!!
The relationship between the number of pounds (lb) of cereal and the price in dollars is shown in the graph what is the unit price of cereal?
Answers:
A. $7/1 lb
B. 1 lb/ $7
C.$14/ 2 lb
D. $1/7 lb
A. $7/1 lb
The first intersection is at (7,1)
Round 56.834 to the nearest tenth
Answer:
56.8
Step-by-step explanation:
8 is the tenth
numbers that are 4 or under stay the same
numbers that are 5 or above round up
Answer:
56.8
Step-by-step explanation:
When rounding to the nearest tenth you look at the number behind the decimal. And the number in the hundredths place if it is 4 or lower you keep it the same. If it is 5-9 you up it by one.
The temperature in the late afternoon was −7.5°C. It dropped 5 degrees by early evening and then dropped another 8.5 degrees by midnight. What was the temperature at midnight?
Answer:
-21 is the correct answer
Step-by-step explanation:
-7.5 - 5 - 8.5 = -21
Answer:
-21 is the correct answer
-7.5 - 5 - 8.5 = -21
Simplify the algebraic expressions -6x(2x-5)
Answer:
-12x^2 + 30x
Step-by-step explanation:
-6x(2x-5)
(-6x * 2x)
-12x^2
(-6x * -5)
30x
What two intergers does 7 fall into
Answer:
Step-by-step explanation:
The square of 2, -2 is 4. square of 3, -3 is 9. so square root of 7 has to be less than 3 but more than 2. therefore the integers are either 2 and 3 or -3 and -2.
Answer:
2 and 3
Step-by-step explanation:
[tex]\sqrt{7}[/tex]= 2.645....
Hope this helps. Please give me brainliest.
An investigative bureau uses a laboratory method to match the lead in a bullet found at a crime scene with unexpended lead cartridges found in the possession of a suspect. The value of this evidence depends on the chance of a false positivethat is, the probability that the bureau finds a match, given that the lead at the crime scene and the lead in the possession of the suspect are actually from two different "melts," or sources. To estimate the false positive rate, the bureau collected bullets that the agency was confident all came from different melts. Then, using its established criteria, the bureau examined every possible pair of bullets and found matches. Use this information to compute the chance of a false positive.
Answer:
The correct solution will be "32.22%".
Step-by-step explanation:
The given values are:
X = 612
n = 1899
As we know,
⇒ [tex]P=\frac{X}{n}[/tex]
On substituting the above values, we get
⇒ [tex]=\frac{612}{1899}[/tex]
⇒ [tex]=0.3222[/tex]
So that the chance of false positive will be "32.22%".
Can someone please help me with this
Answer:
3.72 x 100000000= 372000000
1.2 x 100000 = 120000
Step-by-step explanation:
idek
Which statement describes A′B′?
Answer:
1 answer to your question
an architect is designing a new uilding. He makes a model of the building such that the area of the rectangular base is 12xsquared minus 11x -r
Answer:
2x2 sidhuedfhjxiijsejskfjks
Step-by-step explanation:
Answer:
................................................................................................................................
.Step-by-step explanation:
................................................................................................................................
Find the x-intercept and y-intercept of the line -8x+5y=18
x intercept is -2.25 and y intercept is 3.6
Pam is making icing for a birthday cake. The ratio of milk to powdered sugar is 2
tablespoons of milk to 15 tablespoons of powdered sugar.
If Pam uses 7 tablespoons of milk, how much powdered sugar will she need?
Answer:
She will need 52.5 table spoons of sugar
Step-by-step explanation:
2:15= 1:7.5
7tbs*1=7tbs of milk
7tbs*7.5=52.5tbs of sugar
Answer:
52.5
If you multiply the tbs of milk to the tbsp of sugar, then you will get 52.7!: )
Step-by-step explanation:
HOPE THIS HELPS~ :)
BRAINLIEST?
Please help!!
As part of a landscaping project, put in a flower bed measuring 10 feet by 20 feet. Surround the bed with a uniform border of low-growing plants.
a. Write a polynomial that describes the area of the uniform border that surrounds the flower bed.
b. The low growing plants surrounding the flower bed require 1 square foot each when mature. If there are 216 of these plants, how wide a strip around the flower bed should be prepared for the border?
Answer:
hope this helps you out.
Health insurance benefits vary by the size of the company. The sample data below show the number of companies providing health insurance for small, medium, and large companies. For purposes of this study, small companies are companies that have fewer than 100 employees. Medium-sized companies have 100 to 999 employees, and large companies have 1,000 or more employees. The questionnaire sent to 225 employees asked whether or not the employee had health insurance and then asked the employee to indicate the size of the company.
Health Insurance
Size of the Company Yes No Total
Small 36 14 50
Medium 65 10 75
Large 88 12 100
A. Conduct a test of independence to determine whether health insurance coverage is independent of the size of the company. What is the p-value? Compute the value of the χ2 test statistic (to 2 decimals). Using α .05 level of significance, what is your conclusion?
B. A newspaper article indicated employees of small companies are more likely to lack health insurance coverage. Calculate the percentages of employees without health insurance based on company size (to the nearest whole number). Based on the percentages calculated above, what can you conclude?
Answer:
A) The critical value found is 5.99 which is < the test statistic value ( 6.94 ) hence we will reject the null hypothesis (H₀)
The P-value associated is : 0.031 which is < 0.05 ( level of significance )
B) from the calculation it can be sen that employees of small companies are more likely without health insurance
Step-by-step explanation:
A) To conduct a test of independence
we apply the hypothesis test
Null hypothesis (H₀) = The health insurance coverage is independent of the size of the company
Alternative hypothesis (H₁) = The health insurance coverage is not independent of the size of the company
The test statistic is calculated as attached below
also the expected values are attached below indicating the formula used
E = expected value
O = observed value
Test statistic value ( as calculated ) = 6.94
The critical value found is 5.99 which is < the test statistic value ( 6.94 ) hence we will reject the null hypothesis (H₀)
The P-value associated is : 0.031 which is < 0.05 ( level of significance )
B) percentage of employees without health insurance
Small company : 14/50 * 100 = 28%
medium company: 10/75 * 100 = 13%
large company : 12/100 * 100 = 12%
from the above calculation it can be sen that employees of small companies are more likely without health insurance
Exponential Function:
Alternative question:
What movements has function [tex]f(x) = 5^{x-2}-4[/tex] made in relation to function [tex]g (x) = 5^{x}[/tex] ?
a) Vertical upward translation of 2 units and horizontal translation to the right of 4 units.
b) Horizontal translation to the right of 2 units and vertical translation up of 4 units.
c) Vertical downward translation of 2 units and horizontal translation to the left of 4 units.
d) Horizontal translation to the left of 2 units and vertical translation down of 4 units.
e) Horizontal translation to the right of 2 units and vertical translation down of 4 units.
f) Other
Answer:
e) Horizontal translation to the right of 2 units and vertical translation down of 4 units.Step-by-step explanation:
Given
f(x) = 5^(x-2) - 4which is the result of the transformation of the function g(x)= 5^x
We can see that
f(x) = g( x - 2) - 4This is indicating horizontal shift 2 unit to the right and vertical shift 4 units down
Correct answer option is e)
Use point-slope or slope-intercept form to match the equations in slope-intercept form with the given slope m and point (x, y)
m = 3 point (-2, 1)
y = 3x + 7
m = 3 point (1, -3)
y = 3x - 7
m = 3; point (4,5)
y = 3x - 6
Answer:
M= 3 point (-2,1) goes with y=3x+7
M=3 point (1,-3) goes with Y+3x -6
M= 3 point (4,5) goes with y=3x -7
I did the instruction
Answer:
hope I helped
Step-by-step explanation:
What is 4^7 x 4^-5 expanded
Answer:
16
Step-by-step explanation:
4^7= 16348
4^-5= 0.0009765625
16348x0.0009765625= 16