The factor form of quadratic equations are listed below:
(x + 4) · (x + 5) (x + 3) · (x + 4) (x + 3) · (x + 5) (x + 3) · (x + 4) (x + 10) · (x + 1) (x + 6) · (x + 1) (x + 5) · (x + 1) (x + 7) · (x + 3) (x + 8) · (x + 2) (x + 10) · (x - 1) (x + 10) · (x + 2) (x + 14) · (x + 1) (x + 6) · (x + 7) (x + 6) · (x + 3) (x + 10) · (x + 6)How to determine the binomial factors of quadratic equations
In this problem we find fifteen cases of quadratic equations of the form x² + b · x + c, where b, c are real coefficients. This kind of quadratic equation can be modified into factor form by means of the following rule:
x² - (r₁ + r₂) · x + r₁ · r₂ = (x - r₁) · (x - r₂)
- r₁ - r₂ = b
r₁ · r₂ = c
Where r₁, r₂ are roots of the polynomial.
Now we proceed to find the binomial factors:
Case 1
x² + 9 · x + 20 = (x + 4) · (x + 5)
Case 2
x² + 7 · x + 12 = (x + 3) · (x + 4)
Case 3
x² + 8 · x + 15 = (x + 3) · (x + 5)
Case 4
x² + 7 · x + 12 = (x + 3) · (x + 4)
Case 5
x² + 11 · x + 10 = (x + 10) · (x + 1)
Case 6
x² + 7 · x + 6 = (x + 6) · (x + 1)
Case 7
x² + 5 · x + 4 = (x + 5) · (x + 1)
Case 8
x² + 10 · x + 21 = (x + 7) · (x + 3)
Case 9
x² + 10 · x + 16 = (x + 8) · (x + 2)
Case 10
x² + 10 · x + 9 = (x + 10) · (x - 1)
Case 11
x² + 12 · x + 20 = (x + 10) · (x + 2)
Case 12
x² + 15 · x + 14 = (x + 14) · (x + 1)
Case 13
x² + 13 · x + 42 = (x + 6) · (x + 7)
Case 14
x² + 9 · x + 18 = (x + 6) · (x + 3)
Case 15
x² + 16 · x + 60 = (x + 10) · (x + 6)
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16. c= vλ. If c = 2.998 x 10^8 m/s, v= 4.41 x 10¹4 s-¹; find a value for λ.
Answer:
6.80 x 10⁻⁷ m
Step-by-step explanation:
You can find the value of λ by inserting the given values into the equation and simplifying.
c = vλ <----- Given equation
2.998 x 10⁸ m/s = (4.41 x 10¹⁴ s⁻¹)λ <----- Insert values
6.80 x 10⁻⁷ m = λ <----- Divide both sides by 4.41 x 10¹⁴
On purchasing a cell phone, Tia got an offer and got the cell phone for $35\%$ less than the tag price. If she saved $\$140$ on that cell phone. Then price on the tag must be $\$$
On purchasing a cell phone, Tia got an offer and got the cell phone for 35% less than the tag price. If she saved 140 on that cell phone. Then price on the tag is 400.
Since, the cell pone is sold with 35% discount on it.
Tia got that phone at selling price with 35% discount on tag price. Also, she saved around 140 on buying the cell phone.
Therefore, the discount on the cell phone on the tag price is her saving on buying the cell phone.
Hence,
35% discount on tag price=Saved amount
(35/100)×T=140
where T is the tag price.
T=(140×100)35
T=14000/34
T=400
Therefore, on buying the cell phone with 35% discount on tag price costs around 140. Then the tag price is 400.
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the diagonal of the rectangle is 15 cm and one of its sides is 9 cm. find the area of the rectangle.
The area of the rectangle is 108 square centimeters.
Given Information
The following information has been given in the question,
Length of the diagonal of the rectangle, l = 15 cm
Length of one of the sides of the rectangle, a = 9 cm
Let the other side of the rectangle be b.
Finding the Other Side of the Rectangle
According to Pythagoras Theorem,
(hypotenuse)² = (base)² + (perpendicular)²
Applying this theorem in the right-angle triangle formed by the diagonal and 9cm side of the rectangle, we get,
l² = a² + b² [∵ The diagonal makes the hypotenuse]
(15)² = (9)² + b²
b² = (15)² - (9)²
b² = 225 - 81
b² = 144
b = √144
b = 12 cm
Calculating the Area of the Rectangle
Area of the rectangle, A = a × b
A = 9 × 12
A = 108 cm²
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At 3:20, what is the measure in degrees of the lesser angle formed by the hour hand and the minute hand
Answer: 30 degrees
Step-by-step explanation:
(Refer to the attached image)
Answer:
D. 10
Step-by-step explanation:
To find the distance between two points, use the distance formula:
Distance between two points
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]\textsf{where }(x_1,y_1) \textsf{ and }(x_2,y_2)\:\textsf{are the two points}[/tex]
Define the two points:
[tex]\textsf{Let }(x_1,y_1)=(4,-3)[/tex]
[tex]\textsf{Let }(x_2,y_2)=(-4,3)[/tex]
Substitute the two defined points into the distance formula and solve for d:
[tex]\implies d=\sqrt{(-4-4)^2+(3-(-3))^2}[/tex]
[tex]\implies d=\sqrt{(-4-4)^2+(3+3)^2}[/tex]
[tex]\implies d=\sqrt{(-8)^2+6^2}[/tex]
[tex]\implies d=\sqrt{64+36}[/tex]
[tex]\implies d=\sqrt{100}[/tex]
[tex]\implies d=\sqrt{10^2}[/tex]
[tex]\implies d=10[/tex]
Therefore, the distance between the two given points is 10 units.
Formula given by
[tex]\boxed{\sf Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}}[/tex]
[tex]\\ \tt{:}\longrightarrow D=\sqrt{(-4-4)^2+(3+3)^2}[/tex]
[tex]\\ \tt{:}\longrightarrow D=\sqrt{8^2+6^2}[/tex]
[tex]\\ \tt{:}\longrightarrow D=\sqrt{10^2}[/tex]
[tex]\\ \tt{:}\longrightarrow D=10units[/tex]
Option D
Write as a decimal the number that is exactly halfway between 1 100 and 1 10
Answer:
605
Step-by-step explanation:
We are starting at 110 and not zero, so I need to find have the distance between 110 and 110 and add that to 110.
110 + 1/2(1100 - 110) Subtract what is in the parentheses
110 + 1/2(990) Find 1/2 of 990
110 + 495
604
Find the area of the figure.
Answer:
60 ft^2
Step-by-step explanation:
1. Find the pattern in this sequence. Then write
the next three terms in the sequence.
5,2,1,...
Answer:
-1,-3,-4 it is just subtracting the same amount.
Step-by-step explanation:
Nina thought of a number. she added 24 , tripled the result, subtracted 18 , multiplied the result by 2 and got 120 . what was nina's number?
Answer:
Step-by-step explanation:
If we subtract 3 from the unknown number, we get just as much as if we subtracted 7 from the unknown number and we multiplied the result by 2
Drag the tiles to the correct boxes to complete the pairs. Suppose you roll a fair six-sided die. Then you roll a fair eight-sided die. Match each probability to its correct value. the probability that both numbers are odd numbers and their product is greater than 10 the probability that the second number is twice the first number the probability of getting numbers whose sum is a multiple of 4 the probability that the sum of the two numbers is greater than 11 the probability that the second number rolled is less than the first number arrowRight arrowRight arrowRight arrowRight arrowRight
The probability will be:
Case 1 matches with 5/48.
Case 2 matches with 1/12.
Case 3 matches with 1/4.
Case 4 matches with 1/8.
Case 5 matches with 5/16.
How to illustrate the probability?We have a total sample space of six-sided die and an eight sided die.
(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(1,8)
(2,1),(2,2),(2,3),(2,4),(2,5),(2,6),(2,7),(2,8)
(3,1),(3,2),(3,3),(3,4),(3,5),(3,6),(3,7),(3,8)
(4,1),(4,2),(4,3),(4,4),(4,5),(4,6),(4,7),(4,8)
(5,1),(5,2),(5,3),(5,4),(5,5),(5,6),(5,7),(5,8)
(6,1),(6,2),(6,3),(6,4),(6,5),(6,6),(6,7),(6,8)
Case 1: The Probability that both numbers are odd numbers and their product is greater than 10. are: (3,5),(3,7),(5,3),(5,5),(5,7)
And the total number of outcomes are: 48.
The required probability is 5/48.
Case 2: The probability that the second number is twice the first number are:
(1,2),(2,4),(3,6),(4,8)
And the total number of outcomes are 48.
So, the required probability is 1/12.
Case 3: The probability of a number whose sum is a multiple of 4 are:
(1,3),(1,7),(2,2),(2,6),(3,1),(3,5),(4,4),(4,8),(5,3),(5,7),(6,2),(6,6).
And the total number of outcomes are: 48.
The required probability is 12/48 = 1/4
Case 4: The probability that the sum of two numbers is greater than 11.
(4,8),(5,8),(6,7),(6,8),(5,7),(6,6)
And a total number of outcomes are 48.
So, the required probability is 6/48 = 1/8.
Case 5: The probability that the second number rolled is less than the first number are:
(2,1),(3,1),(3,2),(4,1),(4,2),(4,3),(5,1),(5,2),(5,3),(5,4),(6,1),(6,2),(6,3),(6,4),(6,5)
And the total number of outcomes are: 48.
The required probability is 15/48 = 5/16.
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A helicopter is 665 feet above the ground. A girl is looking up at the helicopter to form a line. Her line of sight is 5 feet off the ground. The distance between the girl and the helicopter is 280 feet.
A helicopter flies 665 feet above ground. What is the measure of the angle of depression from the helicopter to the girl’s line of sight? Round to the nearest degree.
23°
25°
65°
67°
The measure of the angle of depression from the helicopter to the girl’s line of sight is 67 degrees.
What is a right angle triangle?A right angle triangle has one of its angle as 90 degrees. The sides and angles can be found using trigonometric ratios.
Therefore, angle of depression from the helicopter can be found as follows:
tan x = opposite / adjacent
where
x = angle of depression
Hence,
tan x = 660 / 280
tan x = 2.35714285714
x = tan⁻¹ 2.35714285714
x = 67.1231281953
x = 67°
Therefore, the measure of the angle of depression from the helicopter to the girl’s line of sight is 67 degrees.
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Answer:
D = 67
Step-by-step explanation:
How would you describe the graph for the equation |x| <4?
a.) An open circle on 4 with a solid line drawn to an open circle on -4.
b.) A closed circle on 4 with a solid line drawn to a closed circle on -4.
c.) A closed circle on 4 with a solid line drawn to an open circle on -4.
d.) An open circle on 4 with a solid line drawn to a closed circle on -4.
Answer:
a.) An open circle on 4 with a solid line drawn to an open circle on -4.
Explanation:
Open circles are used for signs: < and >
Closed circles are used for signs: ≤ and ≥
Here in the given expression: |x| < 4
[<] sign is used so open circle is used
If |y| < a then -a < y < a
so here, -4 < x < 4
Both circles should be opened, drawn with a solid line from -4 to 4.
A bag contains lettered tiles. the theoretical probability of choosing a vowel is 40%. the bag contains 78 consonants. how many tiles are in the bag?
The total number of ties present in the bag are 130.
What is probability?Calculating or estimating how likely something is to occur is what probability is all about. The likelihood of an event occurring can be expressed using words like "certain," "impossible," or "probable."
Formula for probability is -
Probability(Event) = Favourable Outcomes/Total Outcomes
It P(E) is the probability for occurring any event.
'x' be the favourable outcome.
'n' be the total outcome.
Then,
P(E) = x/n.
Calculation for the total tiles present the bag.
The probability of choosing a vowel is 40% = 0.4.
Then, the probability of choosing a consonants will be 1 - 0.4 = 0.6 or 60%.
Let P(E) be the probability of the occurrence of the consonants.
Then,
P(E) = total number of consonants/total tiles in the bag.
Let 'T' be the total tiles in the bag.
0.6 = 78/T
T = 78/0.6
T = 130
Therefore, the total tiles present in the bag are 130.
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A plane can cover 9904 km in 8 hours how mucb distance will it cover in 1 hour?
In one hour the plane will cover a distance of 1238 km.
What is a linear equation?
A linear equation has one or two variables. No variable in a linear equation is raised to a power greater than 1.No variable is used as the denominator of a fraction. A linear equation is defined as an equation that is written in the form of ax+by=c. When solving the system of linear equations, we will get the values of the variable, which is called the solution of a linear equation.
solving this we will get the valve of Y is x is given.
calculation:-
today distance = 9904 km.
total time is taken = 8 hours.
∴total distance covered in one hour = 9904/8
= 1238 km.
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Im very confused about my precourse work for AP environmental science.
The conversion method given on the paper is something I am not used to and I cant seem to find any information about anything like this. I only need help with #3 and #4.
The computation shows that the values are 64000 acres and 563 metric tons.
How to compute the values?1. A 100 square mile area of national forest is how many acres?
1 mile square = 640 acres
100 square miles = 100 × 640 = 64000 acres.
2. Fifty eight thousand kilograms of solid waste is equivalent to how many metric tons?
1 metric ton = 103kg
58000 kg = 58000/103 = 563 metric tons
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The weights of certain machine components are normally distributed with a mean of 7.75 ounces and a standard deviation of 0.07 ounces. Find the two weights that separate the top 4% and the bottom 4%. These weights could serve as limits used to identify which components should be rejected. Round your answer to the nearest hundredth, if necessary.
The weight that separates the top 4% is x = 7.87 (round nearest hundredth) .
The weight that separates the bottom 4% is x = 7.63 (round nearest hundredth).
What is normal distribution?The majority of the observations are centred around the middle peak of the normal distribution, which is a continuous distribution of probability that really is symmetrical around in its mean.
The probability for values that are farther from of the mean tapered down equally both in directions.
Now, use z-chart to find the z-value for that separates the top 4% and the bottom 4%.
The values of z = +1.75 and z = -1.75
Let the weight of the machines be 'x'.
Use the formula for z- value
z = (x - μ)/ σ
Where,
σ is standard deviation = 0.07 ounces.
μ is mean = 7.75 ounces.
Substitute all the values and calculate the weight.
case 1: when z = +1.75
1.75 = (x - 7.75)/0.07
x = (1.75×0.07) + 7.75
x = 7.872
x = 7.87 (round nearest hundredth)
case 2: when z = -1.75
-1.75 = (x - 7.75)/0.07
x = (-1.75×0.07) + 7.75
x = 7.6275
x = 7.63 (round nearest hundredth)
Therefore,
x = 7.87 (round nearest hundredth) is weight which separates top 4%.
x = 7.63 (round nearest hundredth) is weight which separates bottom 4%.
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Select the correct answer
The area of a triangle whose height is 1 more than 6 times its base is 13 square feet. If the base of the triangle is xfeet, which equation models
this situation?
A 6x²+x-12=0
B. 6x²+x -13=0
C 6x²+x-26=0
D. 36x² +6x-26= 0
Answer:
Step-by-step explanation:
The area for a triangle is
[tex]A=\frac{1}{2}bh[/tex]
Our base is given as x, the height is given as 1 more than 6 times the base which looks like this: 6x + 1. We know that the area is 13, so filling in everything:
[tex]13=\frac{1}{2} (6x+1)(x)[/tex]
We can get rid of the denominator of 2 by multiplying it on both sides to get:
[tex]26=(6x+1)(x)[/tex] and simplifying a bit:
[tex]26=6x^2+x[/tex]
Now we can move over the 26 and put the expression into standard quadratic form by setting it equal to 0:
[tex]6x^2+x-26=0[/tex] which is choice C
find the value of x from the figure
Answer:
x = 30
Step-by-step explanation:
110 and 3x - 20 are supplementary angles, sum to 180° , then
110 + 3x - 20 = 180
90 + 3x = 180 ( subtract 90 from both sides )
3x = 90 ( divide both sides by 3 )
x = 30
Answer:
x = 30
Step-by-step explanation:
Please refer to the attached photo. (Apologies for the terrible drawing.)
For this question, you must be clear of the angle properties.
z + 110 = 180 (Sum of Angles on a straight line)
z = 180 - 110 = 70
z = 3x - 20 (Corresponding Angles)
3x - 20 = z
3x - 20 = 70
3x = 70 + 20
3x = 90
x = 90 / 3 = 30
When solving an equation, Anne's first step is shown below. Which property justifies
Anne's first step?
The justification used is multiplicative property of equality because both sides are multiplied by the same value
Solving linear equationsGiven the expression below
-1/3(4x^2 - 3) - 3 = 5x^2 - 2
We are to determine the justification by Anne to get the step 2 as shown
(4x^2 - 3) - 3 = -3(5x^2 - 2)
Expand
(4x^2 - 3) - 3 = -15x^2 + 6
Hence the justification used is multiplicative property of equality because both sides are multiplied by the same value
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Select the equivalent expression. 2^-4 = ?
Answer:
1/16
Step-by-step explanation:
This means 1/2x2x2x2 = 1/16
The probability is .80 that a standard normal random variable is between -z and +z. The value of z is approximately:________
The z value for the probability in the standard normal table is 1.29.
In this question,
Z-Score, also known as the standard score, indicates how many standard deviations an entity is, from the mean. A standard normal table (also called the unit normal table or z-score table) is a mathematical table for the values of ϕ, indicating the values of the cumulative distribution function of the normal distribution.
The value of probability is 0.80
A standard normal random variable is between -z and +z, So
P(-z < 0 < z) = 0.80
⇒ 2P(0 < z) = 0.80
⇒ P(0 < z) = [tex]\frac{0.80}{2}[/tex]
⇒ P(0 < z) = 0.40
From the standard normal table, z value for the probability 0.40 is
⇒ z = 1.29
Thus P(0 < 1.29) = 0.40
Hence we can conclude that the z value for the probability in the standard normal table is 1.29.
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Convenience sampling Multiple Choice is the same as simple random sampling. ensures that samples are representative of the population. is an unbiased sampling method. collects sample information from groups that are easy to obtain.
Option (d) is correct. Convenience sampling collects sample information from easy-to-collect groups.
Given convenient sampling.
Convenience sampling is defined as a method adopted by researchers in which they collect market research data from a pre-existing group of respondents. This is the most commonly used sampling technique because it is extremely fast, simple and economical. In many cases, members are easily accessible to be part of the template. It is non-probability sampling and therefore different from random sampling. Since the samples are taken for convenience, the samples are not always representative of the population and therefore have bias. In this case, people were sampled simply because they were convenient.
Thus, convenience sampling collects sample information from easy-to-collect groups.
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Question 12
From the given graph, use two points to write an equation in point-
slope form and then change to slope-intercept form.
Step 1: Use the two points to find the slope.
Step 2: Use the slope and one point to complete point-slope form.
y-y₁ = m(x-x₁)
Step 3: Change point-slope form into slope intercept form by solving
for y. Show your work!
y=mx+b
To find the quotient of 3 divided by one-sixtto find the quotient three-fourths divided by one-eighth,h, multiply 3 by
The quotient of 3 by 1/ 6 and that of 3/4 by 1/ 8 is 1/2 and 4 respectively
How to find the quotientFrom the given equation, we have to find
= 3/4 ÷ 1/8
First , we take the denominator of the second fraction to be the numerator, we have
=
[tex] \frac{3}{4} \times \frac{8}{1} [/tex]
Multiply through
=
[tex] \frac{24}{4} [/tex]
=
[tex]6[/tex]
To find the quotient of 3 by 1/6
=
[tex]3 \times \frac{1}{6} [/tex]
=
[tex] \frac{3}{6} [/tex]
=
[tex] \frac{1}{2} [/tex]
Thus, the quotient of 3 by 1/ 6 and that of 3/4 by 1/ 8 is 1/2 and 4 respectively
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mel cuts a slice of cake if her slice is 4/15 of the cake, what is the central angle of her slice, please give answer in degrees
Answer:
Below in bold.
Step-by-step explanation:
That would be 4/15 * 360 as there are 360 degrees in a circle
= 96 degrees.
Read the following description of a relationship:
Ron is making a banner by stringing letters on a cord. The cord weighs 8
ounces, and each letter weighs 10 ounces.
Let n represent the number of letters and w represent the weight of the banner.
This relationship can also be shown in a table. Complete the equation that represents the
relationship between n and w
The equation that represents the relationship between n and w is w = 10n + 8.
How to illustrate the expression?From the information, Ron is making a banner by stringing letters on a cord and the cord weighs 8
ounces and each letter weighs 10 ounces.
Let represent the number of letters
Let w represent the weight of the banner.
In this case, when n = 6, w = 68 and when n = 7, w = 78.
Therefore, the relationship will be:
w = 10n + 8
To confirm let's use n = 6
10n + 8
10(6) + 8
= 68
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Answer:
Step-by-step explanation:
w=10n+8
In standard form, 7 (10°) + 4 (10-3) + 5 (10³) is equal to?
in standard form, 7 (10°) + 4 (10-3) + 5 (10³) is equal to 5. 04 × 10 ^3
What is standard form?Standard form is simply a value with an exponential powerl
Given the values;
It is important to note that any number to the power of O is equivalent to 1
So, we have
10^ 0 = 1
4( 10^-3) = 37
5(10^3) = 5000
Now, let's substitute the values
(10°) + 4 (10-3) + 5 (10³)
It is equivalent to
⇒1 + 4 × 10^-3 + 5 × 10^3
⇒1 + 37 + 5000
Add the values
= 5038
Let's convert it to standard form, we have
= 5. 04 × 10 ^3
Thus, in standard form, 7 (10°) + 4 (10-3) + 5 (10³) is equal to 5. 04 × 10 ^3
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What addition/subtraction equation should I put?
Answer:
7 - 10
Step-by-step explanation:
Because it is -3 and 7 - 10 = -3
Quick please!!
What’s the distance between the following points?
Answer:
answer is 6^2 × 6^2 = squate root 72
distance equals 8.485
Answer:
6[tex]\sqrt{2}[/tex] ≈ 8.49 units
Step-by-step explanation:
calculate the distance d using the distance formula
d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = (2, - 3 ) and (x₂, y₂ ) = ( 8, - 9 )
d = [tex]\sqrt{(8-2)^2+(-9-(-3))^2}[/tex]
= [tex]\sqrt{6^2+(-9+3)^2}[/tex]
= [tex]\sqrt{36+(-6)^2}[/tex]
= [tex]\sqrt{36+36}[/tex]
= [tex]\sqrt{72}[/tex]
= [tex]\sqrt{36(2)}[/tex]
= [tex]\sqrt{36}[/tex] × [tex]\sqrt{2}[/tex]
= 6[tex]\sqrt{2}[/tex] units ← exact length
≈ 8.49 units ( to 2 dec. places )
Can someone help me please
Answer:
y = x + 2
Step-by-step explanation:
You can find the slant asymptote using polynomial long division because the numerator is one degree higher than the denominator.
(x^2+x+4)/(x-1)
I'm not sure how to show long division but you should get:
x+2 with remainder 6
Then your slant asymptote is y = x + 2
You can graph it on Desmos to verify