Answer:
x = - 7 , x = 2 , x = 1
Step-by-step explanation:
note that
p(1) = 1³ + 4(1)² - 19(1) + 14 = 1 + 4 - 19 + 14 = 0
since p(1) = 0 , then x = 1 is a zero
using synthetic division
1 | 1 4 - 19 14
↓ 1 5 - 14
------------------------
1 5 - 14 0
quotient is x² + 5x - 14
equating quotient to zero
x² + 5x - 14 = 0
(x + 7)(x - 2) = 0
equate each factor to zero and solve for x
x + 7 = 0 ⇒ x = - 7
x - 2 = 0 ⇒ x = 2
then zeros are x = - 7, x = 2 , x = 1
Answer:
[tex]x = 1\\\\x =2\\\\x = -7[/tex]
Step-by-step explanation:
[tex]~~~~~~~x^3 +4x^2 -19x +14=0\\\\\implies x^3- x^2+5x^2 -5x -14x+14=0\\\\\implies x^2(x-1) +5x (x-1)-14 (x-1)=0\\\\\implies (x-1)(x^2 +5x -14) = 0\\\\\implies (x-1) (x^2 +7x -2x -14) = 0\\\\\implies (x-1) \textbf{[}x(x+7) -2(x+7) \textvf{]}=0\\\\\implies (x-1)(x-2)(x+7)=0\\\\\implies x = 1,~ x =2,~ x = -7[/tex]
For questions 1 and 2, multiple answers may be selected
1. Circle the data that represents discrete data: The weight of cows The number of books in your apartment The color of your hair The ounces of water that you drink each day.
2. Circle the data that represents continuous data: The weight of cows The number of books in your apartment The color of your hair The ounces of water that you drink each day
The discrete data is (b) while the continuous data are (a) and (d)
What are discrete data?These are data that can be represented using positive whole numbers.
Using the above definition as a guide, the discrete data is (b) The number of books in your apartment
What are continuous data?These are data that can be represented using decimal numbers.
Using the above definition as a guide, the continuous data are (a) The weight of cows and (d) The ounces of water that you drink each day
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6 x (3+2) divided by 10
1. Marco got an amazing deal for 60% off a pair of running shoes. He paid $28 for the shoes (before taxes).
a.
Find the original price of the running shoes.
b. The sale price is
% less than the original price.
% of the original price.
C.
The sale price is
times the original price.
d.
The sale price is
Answer:
B
Step-by-step explanation:
You can not know the original price unless you know the taxes percentage.
6) Suppose you deposit $6000 in a savings account that pays interest at an annual rate of 4% compounded
continuously. How many years will it take for the balance in your savings account to reach $8000? Round
your answer up to the nearest number of years.
Answer:
7 years
Step-by-step explanation:
Find the distance between the pair of coordinates: (-4, -3) and (-8, 7). A 10.77 B 3.74 C 04 D 12.65 Question
[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-4}~,~\stackrel{y_1}{-3})\qquad (\stackrel{x_2}{-8}~,~\stackrel{y_2}{7})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{[-8 - (-4)]^2 + [7 - (-3)]^2}\implies d=\sqrt{(-8+4)^2 + (7+3)^2} \\\\\\ d=\sqrt{(-4)^2 + 10^2}\implies d=\sqrt{116}\implies d\approx 10.77[/tex]
At a highschool in a class of 235 students, 90 pass Mathematics, 85 pass English and 78 pass both courses. What’s the probability that a random student passed either Mathematics or English or both? ((Union question)
Answer:
41.3%
Step-by-step explanation:
The probability of interest is found by dividing the number of students passing either course by the total number of students.
The number passing only one of the courses is the number passing that course, less the number passing both courses. This is shown in the attached 2-way table.
__
The number passing either course will be the sum of the number passing one course (including the number passing both courses), and the number passing only the other course. It can also be found as the sum of the numbers passing either course, less the number passing both courses (since the latter would be counted twice).
Here those passing either (or both) Math or English will be ...
90 +(85 -78) = 85 +(90 -78) = (90 +85) -78 = 97
So, the probability is ...
p(passing either M or E) = 97/235 = 0.41277 ≈ 41.3%
Situation:
Tina wants to save money for school.
Tina invests $400 in an account that
pays an interest rate of 8%.
A = P(1+r)¹
P= amount of money invested
r = interest rate percentage in decimal form
t = time in years
A = total money in the account at timet
How many years will it take for the account to
reach $5,500? Round your answer to the nearest
hundredth.
Enter the correct answer.
DONE
It will take 4 year for the account to reach $5,500.
How to find the amount?The formula we use to calculate the amount is
A = P(1+r)¹
Where, P= amount of money invested
r = interest rate percentage in decimal form
t = time in years
A = total money in the account at time
Tina wants to save money for school.
Tina invests $400 in an account that pays an interest rate of 8%.
A = P(1+r)¹
5500 = 400(( 1 + 0.08)^t
5500/ 400 = ( 1 + 0.08)^t
55/ 4 = (1.08)^t
13.75 = (1.08)^t
t = 4
It will take 4 year for the account to reach $5,500.
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In South Africa, musicians who perform along the streets are called buskers, and must get a permit, which costs $30. They can make an average of $45 per night (n), depending on the area. Some choose not to get this permit, but need to stay in less populated areas in order to not get caught without a permit so they may only make an average of $15 per night. How many nights of work would have the performers making an equal amount total?
The number of night of work each performers will have equal amount is 1 night
How to find the time of work that the performers will have equal amount?The buskers gets permit which cost $30. They can make an average of $45 per night (n),
Therefore,
y = 45n - 30
Without a permit they may only make an average of $15 per night.
Therefore,
y = 15n
The number of night the money made are both equal.
45n - 30 = 15n
45n - 15n = 30
30n = 30
n = 30 / 30
n = 1
Therefore, the number of night of work each performers will have equal amount is 1 night
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A leak in a pool causes the height of the water to decrease by 0.25 foot over 2 hours. After the leak is fixed, the height of the water is 4.75 feet. The equation 4.75 = x + (negative 0.25) can be used to find x, the original height of the water in a pool.
What was the original height of the water in the pool in feet?
4.5
5.0
6.5
7.0
The original height of the water in a pool is 5 ft , Option B is the correct answer.
What is an Equation ?An equation can be defined as a mathematical statement when two algebraic expressions are equated using an equal sign.
It is given in the question that
A leak in a pool causes the height of the water to decrease by 0.25 foot over 2 hours.
the height of the water is 4.75 feet.
The equation
4.75 = x + (negative 0.25)
can be used to find x, the original height of the water in a pool.
4.75 = x - 0.25
x = 5
Therefore the original height of the water in a pool is 5 ft , Option B is the correct answer.
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Answer:
B
Step-by-step explanation:
What is the circumference of the circle below? (Round your answer to the nearest tenth.)
OA. 56.5 cm
OB. 113.1 cm
OC. 254.5 cm
OD. 28.3 cm
Answer:
A. 56.5 cm
Step-by-step explanation:
circumference of the circle is Pi times diameter
diameter is radius times 2
diameter is 9 times 2
diameter is 18
circumference of the circle is Pi times 18
circumference of the circle is 3.14 times 18
circumference of the circle is 56.52
Select the correct answer.
This system of equations relates the ticket price, in dollars, for seats in the silver (x) and gold (y) sections at a rock concert.
x + 2y = 82
3x + y = 96
By how much does the price of a ticket for the gold section exceed the price for a ticket for the silver section?
A.
$6
B.
$8
C.
$10
D.
$12
E.
$14
Answer:
$12
Step-by-step explanation:
x+2y=82........(1)
3x+y=96.........(2)
y=96-3x...........(3)
x+2y=82
x+2(96-3x)=82
x+192-6x=82
-5x=82-192
-5x=-110
x=-110÷-5
x=22
y=96-3x
y=96-3(22)
y=96-66
y=30
Therefore,x=22 and Y=30
so silver= x =22
gold= y = 30
y=30;x=22
=30-22
-12
Therefore $12
Is √13 + 4 rational or irrational?
Answer:
irrational
Step-by-step explanation:
what are rational numbers ?
every number that can be expressed as a/b, with a and b being integer numbers, and b different to 0.
the square root of any number that is not a squared rational number is then an irrational number.
I am not sure, if the expression here is
sqrt(13) + 4
or
sqrt(13 + 4), which would then be sqrt(17).
but in both cases we are creating the square root of a not- squared rational number.
neither 13 nor 17 are the result of a multiplication of a rational number with itself.
in fact, 13 and 17 are prime numbers with no other factors than either 1 or themselves.
so, both, sqrt(13) and sqrt(17) are irrational numbers.
adding or subtracting rational numbers to irrational numbers result again in irrational numbers.
Hi student, let me help you out! :)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
We are asked to find out if [tex]\pmb{\sqrt{13} +4}[/tex] is rational or irrational.
[tex]\triangle~\fbox{\bf{KEY:}}[/tex]
Irrational numbers cannot be expressed as fractions (in [tex]\pmb{\cfrac{p}{q}}[/tex] form).So, can we write [tex]\pmb{\sqrt{13} +4}[/tex] as a fraction? We can write 4 as a fraction, but we cannot write [tex]\pmb{\sqrt{13}}[/tex] as a fraction, because this number has infinitely many digits after the decimal point, and they never repeat; there's no pattern at all!
And even if we add 4, which is a rational number, to [tex]\pmb{\sqrt{13}}[/tex], we'll still get an irrational number.
Thus, [tex]\pmb{\sqrt{13}+4}[/tex] is irrational.
Hope it helps you out! :D
Ask in comments if any queries arise.
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~Just a smiley person helping fellow students out :)
4 less than a number times 2
Answer:
x-4*2
Step-by-step explanation:
Since we dont know the number, we can make it a variable. So, x is the unknown number.
4 less will mean subtraction. So. x-4.
Next we have to multiply with 2.
So, the expression is x-4*2.
A light in a park can illuminate effectively up to a distance of 100 m. A point on a bike path is 150 m from the light. The sight line to the light makes an angle of 23° with the bike path. What length of the bike path, to the nearest metre, is effectively illuminated by the light?
The length of the bike path, to the nearest meter, is effectively illuminated by the light is 138 m
The missing diagram is attached with the answer.
What is Angle of elevation ?The angle formed between the horizontal line and line of sight is called Angle of Elevation.
It can be seen in the diagram that
It is a right angled triangle if extended and
cos 23 degree = (length of the bike path)/Hypotenuse
Hypotenuse here is the point on a bike path is 150 m from the light
Therefore
cos 23 ° = x / 150
x = 0.92 * 150
x = 138 m
Therefore The length of the bike path, to the nearest meter, is effectively illuminated by the light is 138 m.
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If a car can go 204 miles in 3 7/8 hours, how far can it go in 2 1/5 hours
Answer:
115.5
Step-by-step explanation:
the car is traveling at precisely 52.5 miles an hour
please help me fast write the answer in picture
Step-by-step explanation:
hope you can understand
11,9,36,28,7,41 what is the mean absolute deviation
Answer:
The mean absolute deviation of this sample is 13.
Step-by-step explanation:
Mean absolute deviation is the sum of the absolute value of the differences between data values and the mean, divided by the sample size.
HELP!!
3. Explain why all circles are similar. Use transformations in your explanation. You may also refer to the below image
All circles are similar because radius is constant throughout the circle.
What is similarity of circles?Every point on a circle's perimeter is equidistant from its center. We utilize the radii to get the scale factor since the size of each circle is specified by its radius.
A quality of at least two forms in relation to each other is similarity. When two forms are similar, their qualities in relation to one another remain the same.
A circle is characterized by two properties: its center and radius.Because similarity is unaffected by location the similarity of circles is solely determined by their radii.
Hence,all circles are similar because radius is constant throughout the circle.
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How do we solve this?
(No need to find x)
Answer:
Hi,
Step-by-step explanation:
We can't solve that but reduce it to the same denominator.
[tex]\dfrac{x+5}{x}+\dfrac{x+8}{x-1}\\\\=\dfrac{(x+5)(x-1)+x(x+8)}{x(x-1)}\\\\=\dfrac{x^2+5x-x-5+x^2+8x}{x(x-1)}\\\\=\dfrac{2x^2+12x-5}{x(x-1)}\\[/tex]
PLEASE ANSWER DUE IN 30 MINS ALSO BRAINLIEST THANK YOU
write these as an algebraic expression:
42 is the product of 6 and y
The difference of x and 15 is 62.
Step-by-step explanation:
part 1
6y = 42
part 2
x - 15 = 62
product means multiplication and difference means subtraction.
hope this helps
Find the rule, and type the missing number in the sequence.
96, 192, ____, 384
Answer:
Missing number is 288, and the rule is +96
Step-by-step explanation:
First subtract 96 from 192, which is 96
then add that to 192 and the missing value is 288
you should also add 96 to 288 just to make sure it gets you to the last number which is 384.
The pyramid below has a square base.
24.4 cm
17.2 cm
Vol = x area of base. x perpendicular height
Work out the volume of the pyramid.
The volume of the pyramid would be 2406.16 cubic cm.
How to find the volume of a square-based right pyramid?Supposing that:
The length of the sides of the square base of the pyramid has = b units
The height of the considered square-based pyramid = h units,
The pyramid below has a square base.
h = 24.4 cm
b = 17.2 cm
Then, its volume is given by:
[tex]V = \dfrac{1}{3} \times b^2 \times h \: \rm unit^3[/tex]
[tex]V = \dfrac{1}{3} \times 17.2^2 \times 24.4 \: \rm unit^3\\\\V = 2406.16[/tex]
Therefore, the volume of the pyramid would be 2406.16 cubic cm.
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Which of the following is the solution to | x1-5 ≤ -13?
OA. All values are solutions
OB. x≤-8.and x 28
OC. x≤ -8
OD. No solution
Answer:
C
Step-by-step explanation:
[tex]\textsf {Given :}[/tex]
[tex]\mathsf {x - 5 \leq -13}[/tex]
[tex]\textsf {Add 5 to each side of the inequality : }[/tex]
[tex]\mathsf {x - 5 + 5 \leq -13 + 5}[/tex]
[tex]\mathsf {x \leq -8}[/tex]
Write the equation for a line with a y-intercept of 3 and an x-intercept of 5.
Answer:
it's 15
Step-by-step explanation:
just do ( 5× 2) = (10+5)=15
Can someone lend a hand?
Answer:
B. y=-0.5x + 1
Step-by-step explanation:
first look at the slope: slop = rise over run. for every 2 units right, the point goes 1 unit down. so the slope if -1/2 or -0.5
next look at the y-intercept. the y-intercept of this graph is 1
plug these into the equation y= mx + b to get y = -0.5x + 1
Answer:
A. y = -0.5x + 1
Step-by-step explanation:
Hello!
An equation of a line is written in slope-intercept form: [tex]y = mx + b[/tex]
y = output, y-value, ordinatem = slope, rise over run, rate of changex = input, x-value, abscissab = y-intercept, starting valueY-interceptThe y-intercept is found when x=0, or then the line crosses the y-axis.
Over here, we can see that the line crosses the y-axis at point (0,1), so the y-intercept is positive 1.
SlopeSlope is calculated by rise over run, or the ratio of how much the graph rises over how much the graph runs. Use points to determine how the graph changes. (For simple calculations, use integer points, such as (0,1) and (0,2)
[tex]\frac{\text{rise}}{\text{run}}[/tex][tex]\frac{-1}{2}[/tex][tex]-0.5[/tex]Now that we have the slope and the y-intercept, we can plug those values to make our equation.
[tex]y = mx + b[/tex][tex]y = -0.5x + 1[/tex]The correct answer is Option A. y = -0.5x + 1
Daryl was prescribed 14 antibiotic take one tablet daily for 14 days there's 8 pills left what fraction of the prescription has he taken
Answer:
3/7
Step-by-step explanation:
He took 6 out of 14 so that is 6/14 then simplify it to 3/7
5.259 to the thenths place
Answer:
5.3 is 5.259 rounded into the tenths place.
On the April 12 billing date, Michaelle Chappell had a balance due of 1451.54 on her credit card. From April 12 through May 11 , Michaelle charged an additional 393.03 and made a payment of 700.00
The finance charge on May 12 is?
Answer:
$1,144.57
Step-by-step explanation:
1,451.54 + 393.03 = 1844.57
1,844.57 - 700 = 1,144
The picture below shows the path a bon flies from the top of a 9.5 foot tall sunflower to a point
on the ground 5 feet away. What is the measure of angle x that the sunflower makes with the
ground?
Answer:
100.05
Step-by-step explanation:
9.5 and multiple it by 5
The population of a certain city was 4001 in 1999. It is expected to decrease by about 0.37% per year. Write an exponential decay function, and use it to approximate the population in 2027
An exponential decay function, and use it to approximate the population in 2027 is P(t) = 4001e^-(0.0037)(28) = P(t) = 4001e^-0.1036
Exponential equationThe standard exponential function is expressed as:
P(t) = P0e^-rt
P0 is the initial population = 4001r is the rate. = 0.37% = 0.0037t is the timeSubstitute
P(t) = 4001e^-(0.0037)t
If t = 28 (by 2027)
An exponential decay function, and use it to approximate the population in 2027 is P(t) = 4001e^-(0.0037)(28) = P(t) = 4001e^-0.1036
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