Answer:
[tex]3(2x + 5)(3x - 1)[/tex]
Step-by-step explanation:
Hello!
We can first factor out the greatest common factor between the coefficients: 3.
[tex]f(x) = 18x^2 + 39x - 15[/tex][tex]f(x) = 3(6x^2 + 13x - 5)[/tex]Now, let's work with what we have inside the brackets.
Standard form of a quadratic: [tex]ax^2 + bx+ c = 0[/tex]
Given our equation: [tex]6x^2 + 13x - 5[/tex]
a = 6b = 13c = -5We need to find two numbers that add up to b (13) and multiply to ac (-30).
The two numbers are 15 and -2. Expand 13x to 15x and -2x and factor by grouping.
Factor by Grouping[tex]6x^2 + 13x - 5[/tex][tex]6x^2 -2x + 15x - 5[/tex][tex]2x(3x- 1) +5(3x - 1)[/tex][tex](2x +5)(3x - 1)[/tex]
Now, we simply add the other factor, 3, to the final factored form.
Factored Solution: [tex]3(2x + 5)(3x - 1)[/tex]
Rearrange this expression into quadratic form, 2++=0 , and identify the values of , , and . 0.20=2/75−x
Rearranging the given expression into quadratic form gives x² + 0.2x - 15 = 0.
The values of a, b, and c include the following:
a = 1
b = 0.2
c = -15
What is a quadratic function?In Mathematics, the standard form of a quadratic function is given by this mathematical expression;
ax² + bx + c = 0
Where:
a and b represents the coefficients of the first and second term in the quadratic function. c represents the constant.Next, we would multiply both sides of the quadratic function by (75 - x) as follows;
0.20 × (75 - x) = x²/(75 - x) × (75 - x)
0.20 × (75 - x) = x²
By applying the distributive property to the mathematical expression, we have the following:
0.20(75) - 0.20(x) = x²
15 - 0.2x = x²
By rearranging the mathematical expression, we have the following:
x² + 0.2x - 15 = 0
Therefore, the quadratic function is equal to x² + 0.2x - 15 = 0.
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Anything would be great
Please please please help. I'm in honor's geometry and if I don't get my grade at least to a C, I'm going to fail
In the diagram below, m is the perpendicular bisector of BC.
If BK = 5x, AC = 6x + 7, CP = 4x, AB = 9x – 14. Find BC
Answer:
BC = 56 units
Step-by-step explanation:
since the main diagonal AK bisects the diagonal BC , then the figure is a kite.
• the disjoint pairs of consecutive sides are congruent in a kite, that is
AB = AC and BK = CK
using the pair AB = AC to solve for x
9x - 14 = 6x + 7 ( subtract 6x from both sides )
3x - 14 = 7 ( add 14 to both sides )
3x = 21 ( divide both sides by 3 )
x = 7
Since m bisects BC , then
CP = PB and
BC = CP + PB = 4x + 4x = 8x
then
BC = 8x = 8 × 7 = 56
Solve 4x-2y=-10 y=x+1 using the substitution method
(-4,-3)
x=-4,y=-3
Step-by-step explanation:
solve for the first variable in one of the equations, then substitute the results into the other equation. point form:
The 65 students in a classical music lecture class were polled, with the following results: 36 like Wolfgang Amadeus Mozart 37 like Ludwig van Beethoven 32 like Franz Joseph Haydn 14 like Mozart and Beethoven 20 like Mozart and Haydn 15 like Beethoven and Haydn 8 like all three composers. How many of these students like:________.
a. exactly two of these composers?
b. exactly one of these composers?
c. like only Mozart?
d. like haydn and exactly one of the other two?
e. like none of these composers?
The following are the solutions for the student data:
a. 25 students like exactly two of the composers
b. 31 students like exactly one these composers
c. 10 students like only Mozart
d. 19 students like haydn and exactly one of the other two composers
e. Only one student like none of these composers.
What is Venn diagramVenn diagrams are commonly used in mathematics, statistics, and logic to illustrate relationships between sets of data. It consists of circles that overlap to show the similarities and differences between the sets like in the case of students data.
Students who like:
All three composers = 8
Only Mozart and Beethoven = 14 - 8 = 6
Only Mozart and Haydn = 20 - 8 = 12
Only Beethoven and Haydn = 15 - 8 = 7
Only Mozart = 36 - (6 + 12 + 8) = 10
Only Beethoven = 37 - (6 + 7 + 8) = 16
Only Haydn = 32 - (12 + 7 + 8) = 5
Students who like none of the composers:
65 - (10 + 16 + 5 + 12 + 6 + 7 + 8)
65 - 64 = 1
Therefore, students who like:
exactly two of the composers = 12 + 6 7 = 25 students
exactly one these composers = 10 + 16 + 5 = 31 students
only Mozart = 10 students
Haydn and exactly one of the other two composers = 12 + 7 = 19 students
none of the composers = 1 student
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Which of the arithmetic mean, median, mode, and geometric mean are resistant measures of central tendency?
a) The arithmetic mean and median only.
b) The median and mode only.
c) The mode and geometric mean only.
d) The arithmetic mean and mode only.
The median and mode only are resistant measures of central tendency.
The correct option is B.
Statistics that are resistant to outliers don't change as a result. We assert that the median is a resistive measure of centre, in contrast to the mean, which is not. In a way, the median is able to reject distant values whereas the mean is drawn to them. It cannot withstand the impact of excessive values. The measurement that is least subject to sample variation is the median, which is defined as the middle of ranking data, where 50% of values are above it and 50% below it. As a result, the extreme figures have no bearing on the median. For symmetric data, nonresistant measures perform better because they are less affected by skewness and outliers. Resistant measures can be used since they are less negatively influenced.
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All students in Ridgewood Junior High School either get their lunch in the school cafeteria or brought it from home on Tuesday. 25% of students brought their lunch. 50 students brought their lunch. How many students in total are in Ridgewood Junior High School?
Answer:
125
Step-by-step explanation:
What is the value of the expression d (20+d) d when =8
36
84
168
224
Answer:
Option D: 224
Step-by-step explanation:
[tex] \sf (20 + d)d[/tex]
Insert the value d = 8
[tex] \sf(20 + 8)8[/tex]
Add
[tex] \sf (28)8[/tex]
multiply
[tex] \sf 224[/tex]
HELLPPPP ITS DO TOMORROW
The place value of the digit 6 in the given number is 0.006
What is place value?Place value can be defined as the value represented by a digit in a number on the basis of its position in the number. For example, the place value of 7 in 3,743 is 7 hundreds or 700. However, the place value of 7 in 7,432 is 7 thousands or 7,000.
Given that, California receives average rainfall of 0.476 m per year, we need to find the place value of 6 in the number given,
The number is 0.476
We know that, the first digit after the decimal represents the tenths place. The next digit after the decimal represents the hundredths place. The remaining digits continue to fill in the place values until there are no digits left.
Here, the place of 6 is after 2 digits after the decimal,
Therefore, the place of 6 is thousandths place,
Therefore, the digit 6 has value = 6 × 1/1000 = 0.006
Hence, the place value of the digit 6 in the given number is 0.006
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Which equation is represented by the graphed line? (Image: graph of a line) y = x + 5 y = 5x y = x - 5
The graphed line is y = 5x passing through points (0, 0) and (1, 5)
What is an equation?An equation is an expression that shows the relationship between variables and numbers.
The linear equation is in the form:
y = mx + b
where m is the rate of change and b is the y intercept.
The graphed line passes through (0, 0) and (1, 5), hence the equation is:
y - 0 = [(5-0)/(1 - 0)](x - 0)
y = 5x
The graphed line is y = 5x.
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the water tank of mang peter was full with 10000 liters of water on monday. he used 1500 liters that day.How much water was left on tuesday?
Therefore , the solution of subtraction after subtraction, amount of water left on Tuesday is 98500 liters.
What is difference?One of the most crucial mathematical operations, which is obtained by removing two numbers, produces difference in mathematics. It reveals how much one number deviates from another. To determine how many numbers are between the two given numbers is the goal of finding the difference in math.
Here,
Given:
Amount of water on Monday=10000
Amount of water used=1500
Water left on Tuesday=10000-1500=98500
Thus , amount of water left on Tuesday is 98500 liters.
Therefore , the solution of subtraction after subtraction, amount of water left on Tuesday is 98500 liters.
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78-(x-60)=30 What does x equal?
Answer:
x = 108
Step-by-step explanation:
78-(x-60)=30
Solving for x,
x = 78-30+60
x = 108
If Jill makes $90 commission on $300 in sales, at the same commission rate,
how much will she make on $480 in sales?
The commission made by Jill for a $480 sale at the rate of commission 30% is $144.
What is meant by the rate of commission?
A commission is a payment made to a salesperson by a company in exchange for his or her assistance in facilitating or closing a sale. The design of the underlying commission agreement determines how a sales commission is calculated.
The rate of commission is a percentage or fixed sum that is linked to a specific amount of sales.
Given,
Sales = $300
Commission = $90
Then, rate of commission = (Commission/ sales) * 100
= ( 90/300) * 100 = 30%
For this rate of commission, the commission she makes for a $480 sale is
= 480 * (30/100) = 480 * 0.3 = $144
Therefore, the commission made by Jill for a $480 sale at the rate of commission 30% is $144.
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Evaluate the function over the domain {-2, -1, 0, 1, 2}. As the values of the domain
y = 2.5*
increase, do the values of the range increase or decrease?
The range of the function is {0.16, 0.4, 1, 2.5, 6.25}. With an increase in the value of the domain, the range of the function is increasing.
What is a function?
A function from a set X to a set Y allocates exactly one element of Y to each element of X. The set X is known as the function's domain, while the set Y is known as the function's codomain.
The given function is
f(x) = 2.5^x.
Given domain is {-2, -1, 0, 1, 2}.
Now putting x = -2, -1, 0, 1, 2 in the function f(x) = 2.5^x.
When x = -2:
f(-2) = 2.5^(-2)
f(-2) = 0.16.
When x = -1:
f(-1) = 2.5^(-1)
f(-1) = 0.4
When x = 0:
f(0) = 2.5^(0)
f(0) = 1.
When x = 1:
f(1) = 2.5^(1)
f(1) = 2.5
When x = 2:
f(2) = 2.5^(2)
f(2) = 6.25
The range of the function is {0.16, 0.4, 1, 2.5, 6.25}
The values of the range increase with the increase of domain.
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Which graph shows the solution to the system of linear inequalities?
x – 4y < 4
y < x + 1
Answer: we have
--------> inequality A
--------> inequality B
Using a graphing tool
the solution of the inequality A is the shaded area above the dashed line
see the attached figure N
the solution of the inequality B is the shaded area below the dashed line
see the attached figure N
therefore
the solution of the compound system of inequalities is the shaded area between the two dashed lines
see the attached figure N
therefor
the answer in the attached figure N
Triangle Theorems, What Is The Value Of X?
A triangle's x value is 120°. Using a triangle angle characteristics, an unknown angle can be found.
How to find the value of x in a triangle?The triangle in question is an equilateral triangle.Thus, all angles are equivalent to 60 degrees.So, for a triangle, we know that Interior angle + neighbouring outside angle = 180°, 60° + x = 180°, and x = 180° - 60° = 120°.Thus, a triangle's x value is 120°.From 180 degrees, deduct the sum of the two angles. A triangle's total angle measure is always 180 degrees. When you subtracted the sum of the two angles from 180 degrees, you discovered a difference. Note this difference down. The value of X is this.Bring the variable to the left side and the other values to the right side in order to find the value of x. To determine the answer, simplify the values.To learn more about triangle refer to:
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HELPPPPPPPPP ASP PLS
25% percent of Amanda's day was spent on either meals or homework.
How to solve the percentage in pie chart?Pie charts are a great way to visualize data and percentages. To solve the percentage in a pie chart, you must first identify the total amount represented by the pie chart. Then, divide the value of each section of the pie chart by the total amount and multiply the result by 100 to calculate the percentage of the total that each section represents. For example, if a pie chart has 3 sections with values of 15, 25, and 60, the total would be 100. Then, 15 divided by 100 is 0.15, or 15%, 25 divided by 100 is 0.25, or 25%, and 60 divided by 100 is 0.6, or 60%. Therefore, the pie chart would have 3 sections representing 15%, 25%, and 60% of the total.To learn more about circle graph refer to:
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If the mean time between unscheduled maintenance of LCD displays in a hospital's CT scan facility is 4,000 operating hours, what is the probability of unscheduled maintenance in exactly 5,000 hours?
The probability of unscheduled maintenance in exactly 5,000 hours is 4/5.
What is the probability?
We know that the probability deals with the fact that an event may or many not occur. It deals with a chance event. In this case, we have been told that the hospital's CT scan facility is 4,000 operating hours.
We know that the probability can be obtained from;
P = Number of unscheduled maintenance hours/Total operating hours
This would now give us that;
P = 4000/5000
P = 4/5
Hence, there is a probability of 4/5.
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HELP PLSSS 70 POINTS GOD BLESS WILL GIVE BRAINLIEST
PICTURE BELOW
Answer:
the correct answer is -1/16 i believe
a cube has 6 faces top bottom and all 4 sides.
IMPORTANT: Given the triangles below are similar, find the missing side length. Show the work that
Answer:
x=15
Step-by-step explanation:
6(5)=30
3(5)=15
The length of the missing side Triangle is 3
As it is given that the given triangle is similar which shows all three sides of both the triangle will be in the same ratio by CPST (corresponding parts of similar Triangles).
so
15/x=30/6 ................. the ratio of two sides of the triangle
x = 15*6/30
x= 3
here the value of x is 3.
Also, the ratio of the side comes out to be 5:1 as 6 and 30 are the length so the first triangle has a side of 15 and the length of another triangle will be 3 to make the ratio 5:1.
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What is the equivalent of 3(x - 6)
Answer:
3x-18
Step-by-step explanation:
Joe pushes a 200 kg car with a force of 125 N. In what scenario
would Joe not be doing work or the car?
O when the car moves
O when the car does not move
O when there is no friction
O when the power is too large
9 This is a required question
The chart below shows the force applied on four different
2 pol
Joe pushes a 200 kg car with a force of 125 N, In the scenario when the car does not move, Joe not be doing work or the car.
Which four types of friction are there?Static friction, sliding friction, rolling friction, and fluid friction are the four main categories of friction. Normal force and friction are independent of the hardness of the contacting surfaces and are directly proportional to the contacting surfaces.
How is the friction work calculated?The tiny bumps push against each other as two surfaces slide over one another. A surface is subject to a force from friction equivalent that opposes the direction of the surface's motion. Application of lubricants can reduce friction.
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1 week is 5 miles 2 weeks is 6 miles 3 weeks is 7 miles 4 weeks is 8 miles write an equation while w is weeks and m is miles m=w...
The automobile travels at an average speed of 65.71 mph.
Find the car's average speed ?Put r = d/t to use.You are moving at a rate of 12 miles per hour since 24 miles are multiplied by two hours.Become familiar with the distance formula, a Pythagorean theorem application that can be used to determine the separation between two places.
Sal Khan and the CK-12 Foundation created it.
The car's average speed is 65.71 miles per hour.
the settings provided;Initially, the automobile is traveling at 50 mph.
motion time, t = 3 hours
v = 70 mph is the motion's final speed.
motion time, t = 11 hours
The following formula is used to determine the car's average speed:
average speed = total distance /total speed
Total distance traveled divided by total motion duration equals average speed.
The entire distance is equal to 920 miles (50 x 3 + 70 x 11).
The duration of the motion was (3 + 11) hours, or 14 hours.
The car's typical speed is;
Consequently, the car's average speed is 65.71 mph.
average speed =920/14
= 65.71 mph.
Find out more here:The automobile travels at an average speed of 65.71 mph.
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If you buy one ticket in the provincial lottery, the probability that you will win a prize is 0.11. If you buy one ticket each month for three months, what is the probability that you will win at least one prize?
The probability that you will win at least one prize if you buy one ticket each month for three months is 0.314 or 31.4%.
How to find the probability?The probability of not winning a prize in one drawing is 1 - 0.11 = 0.89.
If we assume that the draws are independent events, the probability of not winning a prize in three consecutive months is 0.89^3 = 0.686.
Therefore, the probability of winning at least one prize in three months is 1 - 0.686
= 0.314 or 31.4%.
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Given: Line a and line b intersect Prove: <1 = <3Which statement and reason best completes the proof?
When lines a and b overlap, angle 1 equals angle 3.
What is intersecting lines?The intersection of two lines in Euclidean geometry might be the empty set, a point, or another line. Distinguishing these circumstances and locating the intersection have applications in computer graphics, motion planning, and collision detection, among others. When two or more lines intersect on a plane, they are referred to as intersecting lines. The crossing lines have a common point, which exists on all of them and is known as the point of intersection. The intersecting lines are two lines that have precisely one common point. The crossing lines have a point in common. The point of intersection is the common point that exists on all intersecting lines.
Here,
To prove ∠1 ≅ ∠ 3, we can use the congruent supplements theorem. According to the congruent supplements theorem, If two angles are supplements of the same angle then two angles are congruent.
Line a and line b intersect (given)
∠3 is supplementary to ∠2 because of linear pair theorem (given)
So, if we take ∠2 as the common angle
And ∠1 is supplementary to ∠2 by linear pair theorem ( option D)
Then, ∠1 is supplementary to ∠2 which is supplementary to ∠3
Therefore, ∠1 ≅ ∠3 (according to the congruent supplements theorem)
This is proved when line a and line b intersect, angle 1=angle 3.
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On another ring, the number of rubies is 4 times the number of diamonds, write the ratio of rubies to diamonds
The ratio of rubies to diamonds is 4:1.
What is the ratio?The ratio is the relative size of one value compared to another.
The ratio shows the quantity of a variable or number contained in another.
We depict ratios as fractional values, like proportions.
Fractional values can be represented as fractions, decimals, or percentages.
The number of rubies = 4x
The number of diamonds = x
The sum of ratios = 5x (4x + x)
The ratio of rubies to diamonds = 4:1
Thus, on this other ring, we can conclude that the ratio of rubies to diamonds is 4:1, meaning that rubies outnumber diamonds by 4 times.
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The average person spends about 1/10 of their walking hours with their eyes closed. If Mrs. James was awake for 15 1/2 hours today, how much more time did she have her eyes open than closed.? PLEASE HELP
The time that Mrs James have her eyes open than closed will be 13 19/20 hours.
How to calculate the Fraction?A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split.
From the information, the average person spends about 1/10 of their walking hours with their eyes closed. If Mrs. James was awake for 15 1/2 hours today.
The more time that she have her eyes open than closed will be:
= 15 1/2 - (1/10 × 15 1/2)
= 15 1/2 - 1 11/20
= 13 19/20
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The cylindrical and the cuboidal containers shown below have the same height. the same amount of water was poured into each container. The water filled 1/2 of the cylindrical container and 1/3 of the cuboidal container. If the base are of the cylindrical container is 154 sq cm, what is the base area of the cuboidal container?
Note that where the cylindrical and the cuboidal containers shown below have the same height. the same amount of water was poured into each container. The water filled 1/2 of the cylindrical container and 1/3 of the cuboidal container. If the base area of the cylindrical container is 154 sq cm, the base area of the Cuboidal Container is 15.2
What is the justification for the above?Let the height of the cylinder and cuboidal container be h m
We know that the base of the cylinder container is given as: 154 sq cm.
Recall that the volume for a cylinder is = Base x Height
That means in this case:
The volume for the cylinder is = 154 x Height
Thus,
1/2 * 154h = 1/3h³
77h = 1/3h³; divide both side by h to get
77 = 1/3h²
Collecting like terms and make h subject of the formula, we have;
h² = 77 * 3
h² = 231
h = √231
h= 15.1986841536
h = 15.199 or [tex]\approx[/tex] 15.2
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Question 3 of 10
What is the value of x?
37⁰
75"
The value of x in the figure is 40°.
What is linear pair?When two lines meet at a single point, a pair of linear angles is created. If the angles follow the point where the two lines cross, they are considered to be linear. A linear pair's angles add up to 180° in every case. These angles are additionally referred to as. A linear pair is made up of two angles that are next to one another and whose non-common sides form a line. All angles that create a linear pair are supplementary, however not all supplementary angles have to be linear pairs.In a linear pair, the total of two angles is always 180°. All neighboring angles are linear pairs, however not all adjacent angles are linear pairs.
∠DBA + ∠ABC = 180° ( ∵ linear pair)
∠100° + ∠ABC = 180°
∠ABC = 180° - 100°
∠ABC = 80°
The sum of angles of a triangle is 180° .
So, in triangle ABC
∠A + ∠B + ∠C = 180°
x + 80 + 60 = 180°
x + 140 = 180°
x = 180° - 140°
x = 40°
So, ∠A = x = 40°
The complete question is,
Find the value of x in the figure below :
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