Answer: x=-2, x=3+[tex]\sqrt{2}[/tex], 3-[tex]\sqrt{2}[/tex]
Step-by-step explanation:
f(x) = x³ - 4x² - 5x + 14
-2 | 1 -4 -5 14
-2 12 -14
1 -6 7 0
x³ - 4x² - 5x + 14 = (x+2)(x²-6x+7)
x²-6x+7=0
x²-6x+9-2=0
(x²-6x+9)-2=0
x²-6x+9=2
x²-3x-3x+9=2
x(x-3)-3(x-3)=2
(x-3)²=2
x-3=[tex]\sqrt{2}[/tex], -[tex]\sqrt{2}[/tex]
x=3+[tex]\sqrt{2}[/tex], 3-[tex]\sqrt{2}[/tex]
Hence, zeroes are x=-2, x=3+[tex]\sqrt{2}[/tex], 3-[tex]\sqrt{2}[/tex]
Step-by-step explanation:
our first "suspicion" for a factoring is an integer factor of the constant term : 14.
14 = 2 × 7 or -2 × -7
I started to try 2 or -2 and found that -2 is indeed a zero solution.
so, the first factors are
f(x) = (x + 2)(x² + ...)
let's divide (x³ - 4x² - 5x + 14) by (x + 2) to get the x² term.
x³ - 4x² - 5x + 14 ÷ x + 2 = x² - 6x + 7
- x³ + 2x²
--------------
0 -6x² - 5x
- -6x² - 12x
----------------
0 7x + 14
- 7x + 14
------------
0 0
f(x) = (x + 2)(x² - 6x + 7)
the zeros for x² - 6x + 7 we get from the general solution for a quadratic equation
ax² + bx + c = 0
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
x = (6 ± sqrt((-6)² - 4×1×7))/(2×1) =
= (6 ± sqrt(36 - 28))/2 = (6 ± sqrt(8))/2 =
= 3 ± sqrt(8/4) = 3 ± sqrt(2)
x1 = 3 + sqrt(2)
x2 = 3 - sqrt(2)
so, the zeros are
-2, 3 - sqrt(2), 3 + sqrt(2)
Determine whether the polygons to the right are similar.
Answer:
A the scale factor is 2 from LMN to CDF (or 1/2 from CDF to LMN).
Step-by-step explanation:
shadows are similar, when they have the same angles, abd if there is one scale factor for all sides and other lengths from one shape to the other.
8×2 = 17
15×2 = 30
17×2 = 34
5y=15x+10 but in standard form?
Answer:
y=3x+2
Step-by-step explanation:
Divide by 5 on all sides.
3x-y=-2
Step-by-step explanation:
What is the average hourly pay of someone making 45,000 per year? Assume a 40 hour workweek and a 52 week year.
The average hourly pay of person making 4500 per year is 21.63 per hour.
Given that,
we have to find what does a person making $45,000 a year make per hour on average, Assume a 52-week year and a 40-hour workweek.
To calculate this
The ratio of the sum of the values in a given set to all the values in the set is the mean value, which is the definition of the average.
We have to multiply 52-week year and a 40-hour work week.
40×52
2080
Now, divide 45000 by 2080
45000/2080
21.63
Therefore, The average hourly pay of person making 4500 per year is 21.63 per hour.
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Mrs. Reed is buying seeds to start a vegetable garden. She purchases 12 packets of bean seeds, 15
packets of carrot seeds, and 2 packets of corn seeds. Choose Yes or No to tell if each statement about
the purchase is correct.
Step-by-step explanation:
Mrs. Reed is buying seeds to start a vegetable garden. She purchases 12 packets of bean seeds, 15
packets of carrot seeds, and 2 packets of corn seeds. Choose Yes or No to tell if each statement about
the purchase is correct.
The blood types of 200 people are collected at a doctor’s office. The table shows the breakdown of patients by blood type.
If a person from this group is selected at random, what is the probability that this person has type AB blood? Express your answer as a fraction in lowest terms or as a decimal rounded to the nearest millionth (if necessary).
Blood Type Survey Results
Blood Type Number of Patients
A 45
B 65
O 75
AB 15
Answer:
[tex]\frac{3}{40}=0.075[/tex]
Step-by-step explanation:
The probability of a person selected at random from this group having type AB blood is 15 out of 200 total people. Therefore:
[tex]\frac{15}{200}=\frac{3}{40}=0.075=7.5\%[/tex]
Question 3(Multiple Choice Worth 1 points)
(02.04 MC)
In triangle DEF, if mZD = (2x)°, mZE = (2x - 4)º, and mZF = (x + 9)°, what is the value of x?
A)35
B)37
C)44
D)71
By using property of triangle and trapezium, it is obtained that
a) value of x is 35°
b) Third option is correct
What is a triangle and trapezium?
Triangle is a three sided two dimensional figure.
Trapezium is a quadrilateral whose one pair of opposite side is parallel and another pair of opposite side is non parallel
Here property of triangle is used
[tex]m \angle D = (2x)^{\circ}, \ m\angle E = (2x - 4)^{\circ}, m \angle F = (x +9)^{\circ}[/tex]
[tex]m \angle D + m\angle E + m \angle F = 180\\2x + 2x - 4 + x + 9 = 180\\5x + 5 = 180\\5x = 180 - 5\\5x = 175\\x = \frac{175}{5}\\x = 35^{\circ}[/tex]
In the second question, if the trapezoid is rotated 90° clockwise, then (x, y ) will change to (y, -x) and new coordinate of A is (1, 5)
Third option is correct
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2 1/7:15a=5/14:0.8. solve
The value of a from the equation is a = 0.32
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be 2 1/7 : 15a = 5/14 : 0.8
Now , on simplifying the equation , we get
15/7 : 15a = 5/14 : 0.8
Multiply by 14 on both sides of the equation , we get
( 15 x 2 ) : 15a = 5 : 0.8
30 : 15a = 5 : 0.8
So , on simplifying the equation , we get
30 / 15a = 5 / 0.8
Divide by 5 on both sides , we get
6 / 15a = 1 / 0.8
Multiply by 0.8 on both sides of the equation , we get
15a = 6 x 0.8
15a = 4.8
Divide by 15 on both sides , we get
a = 4.8 / 15
a = 0.32
Therefore , the value of a = 0.32 or a = 8 / 25
Hence , the value of a in the equation is a = 0.32
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A trust company offers 3-year compund interest GIC earning annual interest of 5.50% compounded monthly or 5.70% compounded semi-annually. Which rate should an investor choose?
As per the given interest rate and types of annual interest , investor should choose compounded monthly as it gives interest more frequently .
As given in the question,
Time period to calculate the compound interest = 3years
Interest rate compounded monthly = 5.50%
Each month interest output is 5.64079
Rate of interest compounded semi- annually = 5.70%
Each month interest output is 5.78123
Compounded monthly gives interest every month and semi-annually gives twice a year.
Monthly is more frequent compare to semi-annually.
Investor should choose monthly.
Therefore, as per the given interest rate and types of annual interest , investor should choose compounded monthly as it is more frequent .
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Write a coordinate rule for the composition 
Answer:
so basically u do that and then u do that and then
Step-by-step explanation:
8
PLEASE answer ill give BRAINLIEST
1.What is the measure of CBA?
2.What is the measure of CAB?
3.When these 3 interior angles of a triangle are added together, what does it equal.
The measure of CBA is 44° , the measure of CAB is 46° and the sum of the three interior angles of the triangle is 180°.
According to the question,
We have the following information:
Angle CAB = 2x
Angle CBA = 3x-20
And the given triangle is a right-angled triangle which means that one of its angle is 90°.
Now, we know that the sum of three angles of a triangle is 180°.
So, we have the following expression:
2x+3x-20+90 = 180°
5x+70 = 180
5x = 180-70
5x = 110
x = 110/5
x = 22°
Now, putting the value of x in given angles:
Angle CAB = 2x
Angle CAB = 2*22
Angle CAB = 44°
Angle CBA = 3x-20
Angle CBA = 3*22-20
Angle CBA = 66-20
Angle CBA = 46°
Hence, the measure of CBA is 44° , the measure of CAB is 46° and the sum of the three interior angles of the triangle is 180°.
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K=2; f(x)=-x^3 -2x ^2+3 answer
The value of the function f(x) = [tex]x^3-2x^2+3[/tex] when x = 2 is f(2) = 3
The given function is
f(x) = [tex]x^3-2x^2+3[/tex]
The function is the mathematical statement which represents the relationship between one variable and another variable. If one variable is dependent variable the other variable will be independent variable.
The given function is
f(x) = [tex]x^3-2x^2+3[/tex]
The value of x = 2
Then substitute the value of x in the function
f(x) = [tex]x^3-2x^2+3[/tex]
f(2) = [tex]2^3-2(2)^2+3[/tex]
Solve the power of each terms
f(2) = 8 - 8 + 3
Do the arithmetic operations
f(2) = 3
Hence, the value of the function f(x) = [tex]x^3-2x^2+3[/tex] when x = 2 is f(2) = 3
The complete question is:
Find the value of f(x) = [tex]x^3-2x^2+3[/tex] , when x = 2
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A rectangular-prism-shaped toy chest is 2 \text { m}2 m2, start text, space, m, end text by 1 \text { m}1 m1, start text, space, m, end text by 1 \text { m}1 m1, start text, space, m, end text.
A shipping crate is packed with 181818 of these toy chests. There is no extra space in the crate.
What is the volume of the crate?
The volume of the crate if there is no extra space in the crate is 36m³.
How calculate the volume?From the information illustrated, the prism is 2m by 1m by 1m abd the shipping crate is packed with 18 of these.
In this case, the volume will be:
= Length × Width × Height
= 2 × 1 × 1
= 2m³
Since there are 18 crates, the total volume will be:
= 2m³ × 18
= 36m³
The volume is 36m³.
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Complete question
A rectangular-prism-shaped toy chest is 2m by 1m by 1m. A shipping crate is packed with 18 of these toy chests. There is no extra space in the crate. What is the volume of the crate?
QUEST
Find the median of the numbers in the following list.
Select the correct answer below:
O22
O 21
26
O24
O 14
26, 13, 39, 22, 42, 39, 18, 21, 32, 14
Step-by-step explanation:
first order them from least to greatest
13,14,18,21,22,26,32,39,39,42
then just look for the term in the middle
sunset there are 2 numbers in the middle you will add them both and subtract them by 2
42+39 then / 2 =40.5
Find the measure of EACH numbered angle. 18° m
The measure of the angle 1, angle 2, angle 3 is 68°, 94°, 25° respectively.
What is angle?
An angle is created where two straight lines or rays meet at a single point. The point from where two lines converge is known as an angle's vertex. The name "angle" comes from the Latin word "angulus," which meaning "corner."
Let's firstly find angle 1,
We know that, the sum of the all three angles of a triangle is 180°.
So,
18° + 94° + angle 1 = 180°
112° + angle 1 = 180°
angle 1 = 180° - 112°
angle 1 = 68°
Now, we know that, opposite angle are always equal
Therefore,
angle 2 = 94°
Now, again applying the property of triangle that sum of all three angles are equal:
Therefore,
angle 3 + angle 2 + 61° = 180°
angle 3 + 94° + 61° = 180°
angle 3 = 25°
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Three of the 30 computers are out of service. What percent of the computers are not working?
The percentage of computers not working is 10%.
What is the percentage?The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.
Given that there are three of the 30 computers are out of service.
The percentage of the computers which are out of service will be calculated as,
P = 3 / 30
P = 0.1
P = 0.1x 100
P = 10%
Therefore, the percentage of computers not working is 10%.
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Mia was out at a restaurant for dinner when the bill came. Her dinner came to $28. After adding in a tip, before tax, she paid $37.24. Find the percent tip.
The percentage of the tip will be equal to 24.81%.
What is the percentage?The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.
Given that Mia was out at a restaurant for dinner when the bill came. Her dinner came to $28. After adding in a tip, before tax, she paid $37.24.
The percentage tip will be calculated as,
P = ( (37.24 - 28 ) / 37.24
P = 9.24 / 37.24
P = 0.2481 x 100
P = 24.81%
Therefore, the percentage of the tip will be equal to 24.81%.
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Find missing side length given two similar triangles
Answer: 49
Step-by-step explanation:
by using triangle ABC and the known values of triangle XYZ, we can divide side XY/AB, 28/4=7. By doing the same with YZ/BC, 56/8=7, we find that the scale factor is 7. With this information, we multiply side CA by the scale factor, 7x7=49.
Given the coordinate, perform the following transformation and give the new coordinates.
12. Reflect (2, 3) over the x axis: (
13. Reflect (7, -2) over the y axis: (
14. Rotate (4, 5) 90° about the origin: (
15. Rotate (-3, -2) 270° about the origin:
16. Reflect (17, -23) over the line y=x.
The reflection of the point (2,3) over the x-axis is (2,-3). The reflection of the point (7,-2) over the y-axis is (-7,-2).
What is a reflection?A reflection is referred to as a flip in geometry. A reflection is the shape's mirror image. A line, called the line of reflection, will allow an image to reflect through it. Every point in a figure is said to reflect the other figure when they are all equally spaced apart from one another.
The reflection of the point (2,3) over the x-axis is calculated as,
(2,3) ⇒ (2,-3)
The reflection of the point (7,-2) over the y-axis is calculated as,
(7,-2) ⇒ (-7,-2)
Therefore, the reflection of the point (2,3) over the x-axis is (2,-3). The reflection of the point (7,-2) over the y-axis is (-7,-2).
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The radius of a circle is 8 ft. Find its area in terms of pi
Answer:
Step-by-step explanation:
201.06ft²
Answer:
Step-by-step explanation:
Please help :(
Solve each equation for x. Show all steps.
1) log base4 (x^2 -12x+48) =2
2) 27^(4x-6) = (1/9)^(2x-7)
The values of x in the equations are as follows:
1. x = 8 or 4
2. x = 2
How to solve equations?Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign.
Therefore, let's solve the equation as follows:
log₄ x² - 12x + 48 = 2
using law of logarithm
4² = x² - 12x + 48
16 = x² - 12x + 48
x² - 12x + 48 - 16 = 0
x² - 12x + 32 = 0
x² - 4x - 8x + 32 = 0
x(x - 4) - 8(x - 4) = 0
(x - 8)(x - 4) = 0
Therefore,
x = 8 or x = 4
[tex]27^{(4x-6)}=(\frac{1}{9})^{2x-7}[/tex]
[tex]27^{(4x-6)}=(3^{-2} )^{2x-7}[/tex]
[tex]3^{3(4x-6)}=3^{-4x+14}[/tex]
[tex]3^{12x-18} =3^{-4x+14}[/tex]
Cancel the base
Therefore,
12x - 18 = - 4x + 14
12x + 4x = 14 + 18
16x = 32
x = 32 / 16
x = 2
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Given that capital is fixed, what do you figure is the marginal cost or additional cost of producing another:
haircut
sandwich
Ferris Wheel ride
The marginal cost is the labor utilized in order to provide an additional cost of a haircut.
What is the marginal cost?The marginal cost is the extra cost of generating one additional unit of output.
The example of a haircut, the marginal cost is the labor utilized in order to provide an additional haircut; employees offer their time, which is valued in pay, resulting in the marginal cost of labor.
Thus, in all circumstances, such as the sandwich and Ferris Wheel, there will be an additional labor cost because labor is necessary to make each of the items.
Change in cost / Change in quantity Equals Marginal cost.
The firm will incur an increased labor expense because of one more haircut, and the laborer will be paid more because of the rise in one more quantity of haircut delivered. This pay rise is the marginal cost.
Thus, the marginal cost is the labor utilized in order to provide an additional cost of a haircut.
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Karen is waiting for a pot of soup to cook off before serving it. After 4 3/4 min the soup has cooled from 100°C to 78° C. What was the average change in temperature each minute.
Answer:
Karen is waiting for a pot of soup to cool off before serving it. After 4 min the soup has cooled from 100°C to 78°C. What was the average change in temperature each minute?
✓ Answer:It went down 5.5°C a minute.Step-by-step explanation:You have to look for the difference of 100 and 78, which is …
Solve for j ??????????????????????????
Answer:
j=24
Step-by-step explanation:
j/8 - 2 = 1
j/8 - 2 + 2 = 1 + 2
j/8 = 3
8 * j/8 = 8 * 3
j=24
Subtract and simplify.
With the help of subtraction we can say that the answer is =21/15
What is subtraction?The process of subtracting one number from another is called subtraction. The way to calculate the difference between two numbers is by using the basic arithmetic operation of subtraction, which is represented by the symbol (-).The operation of subtraction is used to calculate the difference between two numbers. If you remove a few items from a collection of things, the group will get smaller.Acc to the question-
32/15 - 11/15as the denominator is same21/15more simplifying we get = 1.4Hence,The answer is = 21/15
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Answer:
21/15
Step-by-step explanation:
Given problem,
→ (32/15) - (11/15)
Let's solve the given problem,
→ (32/15) - (11/15)
→ (32 - 11)/15
→ 21/15
Hence, the answer is 21/15.
A transversal intersects two lines. Which condition would always make the two lines parallel?
If a transversal intersects two lines such that a pair of alternate interior angles is equal , then the two lines are parallel.
What do you mean by traversal line?
A transversal is a line that, at two different locations in the geometry, cuts through two lines in the same plane. Various sorts of angles in pairs, including successive internal angles, corresponding angles, and alternate angles, are produced by a transversal intersection with two lines.
What do you mean by angle?
An angle is defined as the figure, in which two rays meet at a common point called the vertex. The angle is denoted using the symbol “∠”.
From the figure,
x + 1 = 180°
y + 2 = 180°
Adding above equations,
x + y + 1 + 2 = 360°
Given ,
x + y = 1 +2
x + y + x + y = 360°
2(x + y) = 360°
x + y = 180°
Angles made on same side of transversal is supplementary . So the lines are parallel.
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what is -112 = -7(v + 4) ?
Answer:
Step-by-step explanation:
1.) -112*-7=784
784=v+4
2.)784-4=780
v=780
Answer:
v = 12
Step-by-step explanation:
-112 = -7v -28
7v = 112 - 28
7v = 84
7/7 v = 84/7
v = 12
A solution contains 7% salt. How much water should be added to 30 ounces of this solution to make a 5% solution?
12 ounces of water.
Step-by-step explanation:1. Set the initial values.Total mass of the solution: 30 ounces.
Total mass of salt (solute): (30*0.07)= 2.1 ounces.
Total mass of water (solvent): (30*0.93) 27.9 ounces.
2. Find an equation that relates amount of water and percentage of salt.
Since we know that the amount of salt is 2.1 ounces, and it has to remain constant, we have to create a function such that the variable is the amount of water and it gives us the percentage of solution we are looking for. The function should look like this:
[tex]\frac{2.1}{x} =0.05[/tex]; where x is the mass of the water in the solution.
Side note: The number "0.05" is 5% converted into a decimal.
3. Solve the equation for x.[tex]\frac{2.1}{x} =0.05\\ \\\frac{x}{2.1} =\frac{1}{0.05} \\ \\x=\frac{2.1}{0.05} \\ \\x=42[/tex]
42 would be the total amount of ounces the solution should have in order to be a 5% solution. Therefore, 12 ounces (42-30) have to be added.
4. Conclude.12 ounces of water have to be added to this solution in order to make it a 5% solution, where 2.1 ounces is salt and 39.9 is water.
Pls help 3z2-6z for z=5
Answer:
0
Step-by-step explanation:
to me you use the exponent first and then add the variable after, 30-30=0 and if you do the variable first 225-30=195. But my answer would be 0.
Answer: 78
Step-by-step explanation:
3z2-6z for z=5
I dont understand, please help
The slope is 5 and the y-intercept is -2000.
(b) The slope tells us about the rate of change in weekly profit and the y-intercept tells us about the minimum profit.
(c) The situation can be modeled as y = 5x -200. Here, y= profit per week and x= number of customers per week.
(d) If the state world roller rink reached a maximum capacity of 2,500 customers per week then the weekly profit will be $10,500.
What is meant by slope intercept form?In order to make the y-intercept (where the line crosses the vertical y-axis) and slope (steepness) immediately apparent, a line's equation must be written in the slope-intercept form. This version is frequently known as y = mx + b. the equation of a straight line in the form of y = mx + b, where m is the line's slope and b is its y-intercept. The slope intercept formula y = mx + b is used when you know the line's slope and the provided point is also the line's y-intercept (0, b). y = mx + b, where m represents the line's slope, is the slope-intercept form of a line.
(a) Consider two points
(x₁, y₁) = (400, 0)
(x₂, y₂) = (500, 500)
The slope is given as
m = (y₂ - y₁)/ (x₂ - x₁)
= (500-0)/(500-400)
= 500/100
= 5
To find y- intercept put (x, y) = (400,0) in y= mx+b (slope-intercept form of a line)
0 = 5(400)+b
0 = 2000 + b
b= - 2000
(b) The slope tells us about the rate of change in weekly profit and the y-intercept tells us about the minimum profit.
(c) Let the number of customers per week = x
And the profit per week = y
Then, the situation can be modeled using slope-intercept form as
y = 5x -200
(d) Put x= 2500 in y = 5x -200
y = 5(2500)-2000
= 12,500-2000
= 10,500
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4). $1,200, 3.9%, 8 months
The simple interest on $1,200, 3.9%, 8 months is $31.356.
How to calculate the interest?From the informationm, we want to calculate the simple interest of the amount that is given.
The simple interest is calculated thus:
Simple interest = PRT / 100
where
P = Principal = $1200
R = Rate = 3.9%
T = Time = 8 months = 8/12 = 0.67 years
The interest will be:
Simple interest = PRT / 100
Simple interest = (1200 × 3.9 × 0.67) / 100
Simple interest = 31.356
The interest is $31.356.
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Complete question
Calculate the simple interest on $1,200, 3.9%, 8 months
