Answer:
Step-by-step explanation:
STEP
1
:
9
Simplify —
4
Equation at the end of step
1
:
9
((x2) - 5x) - (0 - —) = 0
4
STEP
2
:
Rewriting the whole as an Equivalent Fraction
2.1 Subtracting a fraction from a whole
Rewrite the whole as a fraction using 4 as the denominator :
x2 - 5x (x2 - 5x) • 4
x2 - 5x = ——————— = —————————————
1 4
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole
Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator
STEP
3
:
Pulling out like terms
3.1 Pull out like factors :
x2 - 5x = x • (x - 5)
Adding fractions that have a common denominator :
3.2 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
x • (x-5) • 4 - (-9) 4x2 - 20x + 9
———————————————————— = —————————————
4 4
Trying to factor by splitting the middle term
3.3 Factoring 4x2 - 20x + 9
The first term is, 4x2 its coefficient is 4 .
The middle term is, -20x its coefficient is -20 .
The last term, "the constant", is +9
Step-1 : Multiply the coefficient of the first term by the constant 4 • 9 = 36
Step-2 : Find two factors of 36 whose sum equals the coefficient of the middle term, which is -20 .
-36 + -1 = -37
-18 + -2 = -20 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -18 and -2
4x2 - 18x - 2x - 9
Step-4 : Add up the first 2 terms, pulling out like factors :
2x • (2x-9)
Add up the last 2 terms, pulling out common factors :
1 • (2x-9)
Step-5 : Add up the four terms of step 4 :
(2x-1) • (2x-9)
Which is the desired factorization
Equation at the end of step
3
:
(2x - 9) • (2x - 1)
——————————————————— = 0
4
STEP
4
:
When a fraction equals zero :
4.1 When a fraction equals zero ...
Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.
Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.
Here's how:
(2x-9)•(2x-1)
————————————— • 4 = 0 • 4
4
Now, on the left hand side, the 4 cancels out the denominator, while, on the right hand side, zero times anything is still zero.
The equation now takes the shape :
(2x-9) • (2x-1) = 0
Theory - Roots of a product :
4.2 A product of several terms equals zero.
When a product of two or more terms equals zero, then at least one of the terms must be zero.
We shall now solve each term = 0 separately
In other words, we are going to solve as many equations as there are terms in the product
Any solution of term = 0 solves product = 0 as well.
Solving a Single Variable Equation:
4.3 Solve : 2x-9 = 0
Add 9 to both sides of the equation :
2x = 9
Divide both sides of the equation by 2:
x = 9/2 = 4.500
Solving a Single Variable Equation:
4.4 Solve : 2x-1 = 0
Add 1 to both sides of the equation :
2x = 1
Divide both sides of the equation by 2:
x = 1/2 = 0.500
Supplement : Solving Quadratic Equation Directly
Solving 4x2-20x+9 = 0 directly
Earlier we factored this polynomial by splitting the middle term. let us now solve the equation by Completing The Square and by using the Quadratic Formula
Parabola, Finding the Vertex:
5.1 Find the Vertex of y = 4x2-20x+9
Parabolas have a highest or a lowest point called the Vertex . Our parabola opens up and accordingly has a lowest point (AKA absolute minimum) . We know this even before plotting "y" because the coefficient of the first term, 4 , is positive (greater than zero).
Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions.
Parabolas can model many real life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that object, thrown upwards, can reach. For this reason we want to be able to find the coordinates of the vertex.
For any parabola,Ax2+Bx+C,the x -coordinate of the vertex is given by -B/(2A) . In our case the x coordinate is 2.5000
Plugging into the parabola formula 2.5000 for x we can calculate the y -coordinate :
y = 4.0 * 2.50 * 2.50 - 20.0 * 2.50 + 9.0
or y = -16.000
Parabola, Graphing Vertex and X-Intercepts :
Root plot for : y = 4x2-20x+9
Axis of Symmetry (dashed) {x}={ 2.50}
Vertex at {x,y} = { 2.50,-16.00}
x -Intercepts (Roots) :
Root 1 at {x,y} = { 0.50, 0.00}
Root 2 at {x,y} = { 4.50, 0.00}
When constructing a confidence interval for the population mean using the standard deviation of the sample, the degrees of freedom for the t distribution equals.
The t distribution's degrees of freedom are equal to n - 1 by standard deviation.
What does math standard deviation mean?
The standard deviation shows the average level of variability in your dataset. It provides the standard deviation of every statistic. A low standard deviation indicates that values are frequently within a certain distance of the mean, whereas a high standard deviation indicates that values are frequently outside of this range. Consider the information below: 2, 1, 3, 2, 4. The deviations from the mean of the observations will be represented by the average and the sum of squares, which will be 2.4 and 5.2, respectively. This indicates that the standard deviation will be (5.2/5) = 1.01.The degrees of freedom for the t distribution when creating a confidence interval for the population mean using the sample's standard deviation equals n - 1.
Degrees of freedom = n - 1
Learn more about standard deviation
brainly.com/question/13905583
#SPJ4
peter deposited $7,790 into an account that earns 4 5/8% interest, compounded annually. calculate the interest peter will earn after 42 months. how much will peter have in his account after 42 months?
The interest earned by Peter after 42 months is $1,335.60 and the total amount in his account is $9,125.60.
How to determine the accrued ( A ) and interest ( I ) amount in a compound interest?The formula for compound interest is expressed as;
A = P(1 + r/n)^nt
Where A is accrued amount, P is principal, r is interest rate, n is compound, and t is time period.
Given the data in the question;
Principal P = $7,790Annual interest r = 4 5/8%Compounded annually n = 1Time t = 42 monthsAccrued amount A = ?Interest I = ?First, convert the interest rate to decimal.
Rate r = 4 5/8% = (4×8 + 5 )/8%
Rate r = 37/8%
Rate r = 4.625%
Rate r = 4.625/100 = 0.04625 per pear
Next, convert time from months to years
Time t = 42 month = ( 42/12 )years
Time t = 3.5 years
To determine the accrued amount, plug the given values into the compound interest formula and solve for A.
A = P(1 + r/n)^nt
A = $7,790(1 + 0.04625/1)^( 1 × 3.5 )
A = $7,790(1 + 0.04625 )^( 3.5 )
A = $7,790(1.04625 )^( 3.5 )
Accrued amount A = $9,125.60
Note that; Accrued amount A = Principal P + Interest I
Hence;
Interest I = A - P
Interest = $9,125.60 - $7,790
Interest = $1,335.60
Amount in the account after 42 months is the same as the accrued amount A, this is $9,125.60.
Therefore, the interest earned is $1,335.60 and the accrued amount is $9,125.60.
Learn more about compound interest here: brainly.com/question/27589784
#SPJ1
What does K =
2(k-3)/k+9 = 3/5
The value of k in the equation is 6.
How to solve equation?An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.
Therefore, the equation can be solved as follows;
[tex]\frac{2k-3}{k+9}=\frac{3}{5}[/tex]
cross multiply
5(2k - 3) = 3(k + 9)
10k - 15 = 3k + 27
add 15 to both sides of the equation
10k - 15 = 3k + 27
10k - 15 + 15 = 3k + 27 + 15
10k = 3k + 42
subtract 3k from both sides of the equation
10k = 3k + 42
10k - 3k = 3k - 3k + 42
7k = 42
divide both sides by 7
k = 42 / 7
k = 6
learn more on equation here: https://brainly.com/question/17471243
#SPJ1
a fruit basket contains 5 apples, 6 oranges, and 3 peaches. if 3 fruit are selected and consumed, then compute the chance that all 3 fruits are not apples. write the answer as a decimal number rounded to third place value. group of answer choices
All three fruits are not apples is 0.027
Probability sampling is the process of selecting a sample from a population when the selection is based on the randomization principle, often known as chance or random selection.
P (X) = n/N
Given :
A fruit basket contains 5 apples
oranges=6
peaches=3
To find :
compute the chance that all 3 fruits are not apples ?
Solution :
P(all 3 are apples) =(5x4x3)/(14x13x12)
⇒ 60/ 2184
⇒ 0.027
the chance that all 3 fruits are not apples is 0.027
To know more about the probability that all three are not same visit :
https://brainly.com/question/9230883
#SPJ4
I don't understand this: beth wants to paint a circular tabletop that has a radius of 3 feet. a small can of paint covers 15 square feet. how many cans will beth need to buy?
The required number of cans would be 2 for painting a circular tabletop that has a radius of 3 feet.
What is the area of the circle?The area of the circle is equal to the product of the square of the radius of the circle and pi.
A = πr²
where 'r' is the radius of the circle
We have been given that beth wants to paint a circular tabletop that has a radius of 3 feet. a small can of paint covers 15 square feet.
Firstly, we need to calculate the area of a given circular tabletop which is equal to the area of a circle with a radius of 3 feet.
area of the circular tabletop = the area of a circle
area of the circular tabletop = π r²
Here r = 3 feet
area of the circular tabletop = π (3)²
area of the circular tabletop = 9π
area of the circular tabletop = 28.27 square feet
Required number of cans = 28.27 / 15
Required number of cans = 1.88 ≈ 2
Therefore, the required number of cans would be 2.
Learn more about the area of the circle here:
brainly.com/question/19794723
#SPJ2
write as a single fraction:
2/x+2 + 3/2x+1
Answer:
3x2+6x+4 2x
hope this helps !!
HAVE A AMAZING DAY
Answer:
(6x+7)/2x
Step-by-step explanation:
2/x+2 + 3/2x+1
2/x+2x/x + 3/2x+x/x [Convert the bolded numbers into fractions with x in the denominator.
2/x+2x/x + 3/2x + x/x [Convert the bolded numbers so that the denominator becomes 2x]
4/2x+4x/2x + 3/2x + 2x/2x
4/2x+4x/2x + 3/2x + 2x/2x [Now that all numbers have the same denominator, we can add the numerators]
(4+4x + 3 + 2x)
(6x+7)
(6x+7)/2x [Place the denominator, 2x, back into the fraction]
Conrad has 6 more marbles than Rory. If r represents the numbers of marbles that Rory has, which expression represents the number of marbles that Conrad has?
6r
r – 6
6 – r
r + 6
r + 6 expression represents the number of marbles that Conrad has.
Algebraic expression
An algebraic expression in mathematics is an expression which is made up of variables and constants, along with algebraic operations (addition, subtraction, etc.). An algebraic expression is an expression built up from integer constants, variables, and the algebraic operations.
For example, 3x² − 2xy + c is an algebraic expression.
Given that Conrad has 6 more marbles than Rory. If r represents the numbers of marbles that Rory has.
Number of marbles Rory has = r
Therefore number of marbles Conrad has = r + 6
r + 6 expression represents the number of marbles that Conrad has.
To learn more about algebraic expression visit:
brainly.com/question/953809
#SPJ1
Solve for variable c
6c x 88 - 93 = 67
6c X 88 = 93+67
528c=160
C=0,303030303030303
what would happen if you divide 8/5 instead of 4/5
Answer:
The value would double
Step-by-step explanation:
4/5 is half of 8/5
Answer:
4/5 is half of 8/5 so it got doubled
5−−4=
Pls help it’s due in 20 mins
NEGATIVE TIMES NEGATIVE GIVES POSITIVE
[tex]5 - ( - 4) \\ = 5 + 4 \\ = 9[/tex]
ATTACHED IS THE SOLUTION
Answer:9
Step-by-step explanation:
-- = + ( 5+4)
++= +
-+ = -
+- = -
Find the unit rate. Enter your answer as a mixed number.
A fertilizer covers
5/8
square foot in
1/6
hour.
The unit rate is square feet per hour.
The unit rate is the change of a quantity over one unit of another thus the unit rate of fertilizer covers is (30/8) foot per hour.
What is the rate of change?The rate of change is the change of a quantity over 1 unit of another quantity.
Most of the time the rate of change is the change with respect to time.
For example the speed 3meter/second.
As per the given,
A fertilizer covers 5/8 square feet in 1/6 hour.
5/8 square feet ⇒ 1/6 hour
Multiply both sides by 6
6 × 5/8 square feet ⇒ 6/6 hour
30/8 square feet ⇒ 1 hour.
Hence "The unit rate is the change of a quantity over one unit of another thus the unit rate of fertilizer covers is (30/8) foot per hour".
To learn more about the rate of change here,
https://brainly.com/question/12786410
#SPJ1
In finding the solution of the equation: 5 - 3x = 2 + 9, 3x is added to both sides of the equation first. Which of the following should be done next?
add -9
add -5
add -2x
The next step in solving the equation 5 - 3x = 2 + 9 is (a) add -9
How to determine the first step?From the question, we have the following equation that can be used in our computation:
5 - 3x = 2 + 9
When 3x is added to both sides, the equation becomes
5 = 2 + 9 + 3x
The next step is to eliminate 9 or 2 from the variable term
This can be done by adding -9 to both sides
So, we have:
-9 + 5 = 2 + 3x
Hence, the next step is (a) add -9
Read more about equations at
https://brainly.com/question/2476251
#SPJ1
de
Identify the Base and Height of Triangles
A formula for calculating the area of a triangle is A=bh, where b is the length of the
or length of an altitude, of the triangle.
Identify the base and sketch in the height on each type of triangle.
Right triangle
and his the
Acute triangle
Obtuse triangle
A formula for calculating the area of a triangle is A=1/2(b*h), where b is the length of the base and h is the height of or length of the altitude, of the triangle.
Identify the base and sketch in the height on each type of triangle.
right triangle - One of the sides that touches the 90-degree angle constitutes the foundation of a right triangle.
The height of a triangle is measured from its base to its highest point, and in a right triangle, that height can be determined from the side that forms a right angle to the base.
acute triangle - Three sides and three vertices make up the fundamental polygon known as the triangle. It has three sides, which results in three interior angles. An acute angle is one that is between 0° and 90° in length. When all three of the triangle's internal angles are acute, the triangle is said to be acute.
obtuse triangle - In an obtuse triangle, the height or altitude from the acute angles is outside the triangle. To find the height of the obtuse triangle, we extend the base as illustrated.
what is a triangle?
Three edges and three vertices make up a triangle, which is a polygon. It is among the fundamental shapes in geometry. Triangle ABC refers to a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear identify a distinct triangle and a distinct plane at the same time.
To learn more about triangles visit:
https://brainly.com/question/1058720
#SPJ13
LEMON SQUASH 1 part concentrate to 2 parts water If you put 25 ml of concentrate in a glass, how much water should be added? ml
A carpenter is building a triangular frame. She has three pieces of wood measuring 5 feet, 6 feet, and 12 feet.
The carpenter
build the triangular frame with the three pieces of wood. She could cut the
Piece by
To create a triangular frame
Answer: Cannot, 12 foot , 2 feet
Step-by-step explanation:
5/5 on test
The carpenter can cut the 12 feet wood by 2feet to make triangular frame.
What is triangle?A polygon with three vertices and three edges is called a triangle. Geometry's most fundamental shape is this one. Triangle ABC is a triangle with A, B, and C as its vertices.
Any three non-collinear points can create a unique triangle and a unique plane in Euclidean geometry (a two-dimensional Euclidean space). To put it another way, every triangle is contained in some plane, and there is only one plane that contains that triangle.
Given Carpenter has three pieces of wood measuring 5 feet, 6 feet, and 12 feet.
and wants to make a triangular frame,
with these wood pieces he can not make the triangular frame because it does not follow the property of triangle,
which says the sum of two sides of triangle should always greater than the larger side,
here large side is 12 feet and 5 + 6 is less than 12,
so to make a triangular frame he should decrease the larger side which should be less than 11
by cutting 12 feet piece by 2 feet it will be 10 feet and carpenter can make the triangular frame.
Hence the carpenter need to cut 12 feet long piece by 2 feet, to make triangular frame.
Learn more about triangle;
https://brainly.com/question/29083884
#SPJ2
Please help ASAP!! This is overdue!
The equation of each line is labelled as shown in the image attached below, where:
y = 2x + 7 is line b
x + 5y = 10 is line d.
x + y = -9 is line f.
y = x is line c.
x = -5 is line a.
y = -5 is line e.
What is the Equation of a Line?The equation of a line can be rewritten as y = mx + b, if the line has a slope of m and a y-intercept of b.
For vertical lines, the equation is written as x = b, where b is where the line cuts across the x-axis.
For horizontal lines, the equation is written as y = b, where b is the point on the y-axis the line intercepts.
The equation y = 2x + 7 is a line that has a slope of 2 and a y-intercept of 7. This line is labelled as line b in the image below.
x + 5y = 10 is rewritten as y = -1/5x + 2. The slope is 1/5 and the y-intercept is 2. This equation is labelled as line d.
x + y = -9 is rewritten as y = -x - 9. The slope is -1 and the y-intercept is -9. It is represented by the line labelled line f.
y = x has a slope of 1 and passes through the origin, (0, 0). It is labelled as line c.
x = -5 is the vertical line that is labelled as line a.
y = -5 is the horizontal line that is labeled as line e.
See image below.
Learn more about equation of a line on:
https://brainly.com/question/13763238
#SPJ1
Select equivalent or not equivalent for each pair of expressions
Equivalent or not equivalent result for each pair of given expressions are as follow:
a.5x-7+3x and 3x-7 +5x is equivalent.
b. 4y +9 +3y and 3y + 9 + 4y is equivalent.
c. 6z -2z +4 and 4 +2z-6z is not equivalent.
As given in the question,
Each pair of given expressions are equivalent or not equivalent :
a. 5x-7+3x and 3x-7 +5x
5x-7+3x
=(5x +3x) -7
= 8x -7
3x-7 +5x
= (3x +5x) -7
= 8x -7
This pair is equivalent.
b. 4y +9 +3y and 3y + 9 + 4y
4y +9 +3y
=(4y+3y)+9
= 7y +9
3y + 9 + 4y
=(3y +4y) +9
= 7y +9
This pair is equivalent.
c. 6z -2z +4 and 4 +2z-6z
6z -2z +4
=4z + 4
4 +2z-6z
= 4 -4z
This pair is not equivalent.
Therefore, equivalent or not equivalent result for each pair of given expressions are as follow:
a.5x-7+3x and 3x-7 +5x is equivalent.
b. 4y +9 +3y and 3y + 9 + 4y is equivalent.
c. 6z -2z +4 and 4 +2z-6z is not equivalent.
Learn more about equivalent here
brainly.com/question/14672772
#SPJ1
A baseball team won 16 of their first 20 games. If they win half of the rest of their games, how many more
games will they have to play in order to win 75% of the total number of games?
The least number of games the team must win to raise its winning record above 75 percent is -4 , by raising the win fraction to the total number of fractions as 36/48.
What is meant by fractions?There are ratios of fractions that represent a portion of the whole. A fraction has the form a/b, which may be read as "a by b," and it has the function a divided by b. The denominator is referred to as b, and the numerator is known as a.
To transform a percentage to a fraction, we divide it by 100.
Given that a baseball team has won 18 of the 30 games it contains played during the season.
We exists asked the least number of games the team must win to raise its win record above 75%.
Let the number of games needed to be x.
The new number of wins will be the sum of current wins and the games to win, that exists, the new number of wins = 16 + x.
The new number of games played will be the sum of current games played and the games to win, that exists, the new number of games played = 20 + x.
Therefore, the win fraction of the team can be shown as the ratio of the total wins to the total number of games played, that exists, the win record = (16 + x)/(20 + x).
We exists asked to make sure that the win record should be at least 75%,
This percentage can be described as the fraction 75/100 = 3/4.
Therefore, we get the equation:
(16 + x)/(20 + x) = 3/4,
simplifying the above equation, we get
4x - 3x = 3x - 4x - 4,
x = -4.
Therefore, by increasing the victory fraction to the entire number of fractions as 36/48, the team just needs to win -4 games to improve its winning percentage above 75%.
To learn more about fractions refer to:
brainly.com/question/1622425
#SPJ13
Y-intercept = 4 Slope = 2
Answer:
y=2x+4
Step-by-step explanation:
Guessing you need an equation?
Find the unit rate. It took Timothy four days to finish 1/5 of his book. How much of the book did he read per day?
Group of answer choices
1/20 of the book
4/5 of the book
5/3 of the book
3/4 of the book
Answer:
Timothy read 1/20 of the book each day
the positive difference between the product of 78 and 36 and their sum is
Answer:
2694
Step-by-step explanation:
product of 78 and 36=78*36=2808
sum =78+36=114
difference between them =2808-114=2694
Find AX. A(-4, 5), X(1, −2)
The distance of AX, A(-4, 5), X(1, -2) is 8.6
The distance formula is used to find the distance (shortest path) between two points.
The distance formula is
[tex]d = \sqrt{(x_2 - x_1)^{2} + (y_2 - y_1)^{2} } \\d = \sqrt{(-4 - 1)^{2} + (5 - (-2))^{2} } \\d = \sqrt{(-5)^{2} + (7)^{2} } \\d = \sqrt{25 + 49}\\ d = \sqrt{74}[/tex]
d = 8.6
Therefore, the distance of AX, A(-4, 5), X(1, -2) is 8.6
To learn more about distance formula refer here
https://brainly.com/question/7243416
#SPJ1
is y=1000x proportional?
Answer:
has a proportional relationship with a constant of proportionality of 1000.c
Step-by-step explanation:
y=1,000x,y=1,000x
evaluate the expression 2⋅(|3.4−6|−1.8)÷2 1/2+(−2)^3.
On evaluating the given expression we get -9.6. We use the BEDMAS rule where we solve Brackets, Exponents, Division, Multiplication, Addition and Subtraction in a given expression in this order.
We evaluate the the problem using BEDMAS rule:
2.(|3.4-6|-1.8)÷2 1/2+(-2)^3
= 2.(|12-6|-8) ÷ 5/2 + (-8)
= 2.(6-8) ÷ 5/2 - 8
=2.(-2) ÷ 5/2 - 8
= -4 ÷ 5/2 - 8
= -8/5 - 8
= -48/5
= -9.6
Thus the answer of the the given expression we get after evaluating it is -9.6
Another problem on evaluating the expression using BEDMAS
brainly.com/question/24105090
#SPJ4
Look at the two histograms below. They give you information about the heights of players on two basketball teams, the Tigers and the Panthers. Use the histograms to answer the following questions.
The most appropriate choice for histogram will be given by-
a) Team tigers has taller players than team panthers
Team panthers has shorter players than team tigers.
b) team tigers have height that vary more.
c) So team panthers have more players about the same height.
What is histogram?
Histogram is a type of bar graph which makes use of the range of classes in the horizontal x axis and the frequency of classes in the vertical y axis.
Here,
a) The bars in the histogram of team tigers are relatively taller than the bars in the histogram of team panthers. So, team tigers has taller players than team panthers.
The bars in the histogram of team panthers are relatively shorter than the bars in the histogram of team tigers. So, team panthers has shorter players than team tigers.
b) For team tigers, there are no players between 66-69 inches height and, two players between 69-72 inches height and five players between 72-75 inches height. So fluctuations between the heights of two consecutive bars for team tigers is more.
For team panthers, it can be seen that the fluctuation between the heights of heights of two consecutive bars is not that much.
So team tigers have height that vary more.
c) In team panthers, there are one player in 63-66 inches and 69-72 inches, three players in 66-69 inches and 75-78 inches and two players between 72-75 inches and 78-81 inches. So team panthers have more players about the same height.
To learn more about histogram, refer to the link-
https://brainly.com/question/2962546
Complete Question
The diagram has been attached here
Look at the two histograms below. They give you information about the heights of players on two basketball teams, the Tigers and the Panthers. Use the histograms to answer the following questions.
a)Which team has taller players? Which has shorter players? Explain your thinking.
b)Which team has heights that vary more? Explain your thinking.
c)Which team has more players that are about the same height?
#SPJ9
Solve 7x 8 = 3x
x = …
please
I need help with the following question.
Answer:
A
(Look at the screenshots below)
1st screenshots shows the "moved down to two units"
2nd screenshot shows the"flipped over a vertical line that lines halfway between the two triangles"
find two positive integers whose product is 24,999,999 and whose positive difference is as small as possible. explain how you discovered them
Answer:
5001 and 4999
Step-by-step explanation:
25,000,000 is the square of 5,000 and 24,999,999 is one less than it. Notice that the situation resembles the expression [tex]x^2-1[/tex] in which x would be 5,000.
[tex]x^2-1[/tex] can be factored into [tex](x+1)(x-1)[/tex], and substituting x with 5000 yields: [tex](5000+1)(5000-1)[/tex]. This can also be written as [tex](5001)(4999)[/tex]. Therefore, the integers would be 5001 and 4999.
R is directly proportional to T. If R = 60 when T = 10, Calculate the value of T when R = 54
Answer:
T=9
Step-by-step explanation:
if R is proportional to T
[tex] t = rk [/tex]
Where k is a constant
[tex]10 = 60k[/tex]
[tex]k = \frac{1}{6} [/tex]
Therefore,
[tex]54 \times \frac{1}{6} = t[/tex]
[tex]t = 9[/tex]
Question 8 of 8 Pls answer quickly pls and thank you
What are all the possible ways to classify the following shape?
shape
A. polygon, quadrilateral, trapezoid
B. polygon, quadrilateral, parallelogram, trapezoid
C. quadrilateral, trapezoid
A polygon is a flat shape that is encircled by lines known as edges. It has a two-dimensional appearance. As a result, all of the shapes in sections a, b, and c are polygons.
A. Trapezoid, Quadrilateral - A trapezoid always forms a quadrilateral since it is a regular polygon having four sides. A trapezoid is a quadrilateral with opposing parallel sides. A right angle, also known as a right trapezoid, can have congruent sides, which are referred to as isosceles.
B. Polygons, quadrilaterals, parallelograms, and trapezoids - A quadrilateral is a four-sided shape. A parallelogram is a form with four parallel and equal-length sides. A parallelogram's area is equal to the base multiplied by the height. A trapezoid is a shape that has at least one set of opposite ends that are parallel.
C. quadrilateral, trapezoid - A trapezoid is a quadrilateral with several parallel opposed sides. Although the right angles of square trapezoids and isosceles triangles can be included which is an isosceles quadrilateral.
Learn more about shapes at
https://brainly.com/question/23231268?referrer=searchResults
#SPJ9