The justification of step a is common denominator and the justification of step b is multiplication property of equality
How to determine the justifications?The equation is given as:
[tex]a(x + \frac{b}{2a})^2 = -c + \frac{b^2}{4a}[/tex]
Take the LCM
This gives
[tex]a(x + \frac{b}{2a})^2 = \frac{-4ac + b^2}{4a}[/tex]
The above represents a common denominator.
Multiply both sides by 4a
[tex]4a^2(x + \frac{b}{2a})^2 = -4ac + b^2[/tex]
The above represents the multiplication property
Hence, the justifications are common denominator and multiplication property of equality
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Step A: common denominator
Step B: multiplication property of equality
The school library is (3x - 4) metres long and (2x - 3) metres wide. Find the floor area of the library in:
a) terms of x
b) square metres if x = 4
Answer:
40 meters
Step-by-step explanation:
x=4
3x-4=12-4
2x-3=8-3
12-4=8
8-3=5
8x5=40
1. Which of the following measures would NOT produce a triangle? Choose all that apply.
three sides: 3 cm, 5 cm, and 7 cm
three sides: 5 cm, 7 cm, and 9 cm
three sides: 5 cm, 9 cm, and 15 cm
three sides: 3 cm, 5 cm, and 10 cm
Answer:
I believe the answers are :
5 cm, 9cm, and 15 cm
3 cm, 5 cm, and 10 cm
Step-by-step explanation:
When 2 sides that are not the hypotenuse are added and are less than the hypotentuse, a triangle cannot be formed.
Pls help! I'm a bit confused!!
Answer:
Step-by-step explanation:
So whenever you see alphabets in math, these are called variable. Like the word suggests, variables can have different values depending on the problem.
For the first problem, the variable k equals 10, and the question asks you when k=10, what does that make k+26. All you do is substitute the value of k with the given value of k=10, and you get 10 + 26 = 36.
This way you can solve the rest of them.
Ask me if you get confused and we can work on rest of them.
Answer:
36529412.5112Step-by-step explanation:
Q1
k = 1010 + 2636Q2
n = 134(13)52Q3
a = 27 and b = 327/39Q4
x = 63(6) - 1418 - 144Q5
z = 2(2)² + 8.54 + 8.512.5Q6
x = 4 and y = 84(36 - 8)4(28)112How many balloons are in the air if there are 20 ballons and 5 pop how many are left
Answer:
15 balloons
Step-by-step explanation:
20 - 5 = 15
hope this helps:)
Answer:
15 ballons
Step-by-step explanation:
Sarah received \$55dollar sign, 5 for her birthday. She used some of that money to buy 3 shirts priced at m dollars each.
The amount of money Sarah have left written as an expression is 55 - 3m
How to write equation?Amount Sarah received for her birthday = $55Number of shirts bought = 3Cost of each shirt = $mThe amount of money Sarah have left = Amount Sarah received for her birthday - (Number of shirts bought × Cost of each shirt)
= 55 - (3 × m)
= 55 - 3m
The complete question:
Sarah received $55 dollar sign,for her birthday. She used some of that money to buy 3 shirts priced at m dollars each. How much money does Sarah have left? Write your answer as an expression.
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Find the circumference of a circle that has a 25-inch radius. Use 3.14 to approximate π.
PLEASE HELP ILL GIVE BRAINLIEST
[tex] \huge \tt \color{pink}{A}\color{blue}{n}\color{red}{s}\color{green}{w}\color{grey}{e}\color{purple}{r }[/tex]
[tex] \large\underline{ \boxed{ \sf{✰\:Important\: point's }}}[/tex]
➣ Circle:- A two-dimensional geometric figure, a line, consisting of the set of all those points in a plane that are equally distant from a given point (center).➣ Circumference:- The line that bounds a circle or other two-dimensional figure[tex]{ \rule{70mm}{2.9pt}}[/tex]
★ also circumference of a circle is also known as it's perimeter
➣To find circumference of circle when use formula[tex]{ \boxed{✜\underline{ \boxed{ \sf{\: Circumference \: of \: circle= \: 2\pi \: r}}}✜}}[/tex]
➢ r = radius (25inch.)➢ value of π is 3.14[tex]{ \rule{70mm}{2.9pt}}[/tex]
[tex] \large\underline{ \boxed{ \sf{✰\: Let's\:solve }}}[/tex]
[tex]\sf{➛ \: Circumference \: of \: circle = 2 \times 3.14 \times 25} \\ \sf{➛ \: Circumference \: of \: circle =2 \times 78.5} \\ \sf{➛ \: Circumference \: of \: circle =157inch}[/tex]
★ Hence circumference of circle=157inch
[tex] \large\underline{ \boxed{ \sf{➪\:157inch. }}}[/tex]
[tex]{ \rule{70mm}{2.9pt}}[/tex]
Hope it helps !
Vincent bought a movie ticket with a promo of free pizza, popcorn and a drink. How many possible meals can vincent choose from given that there is 8 flavors of pizza, 4 flavors of popcorn and 3 kinds of drinks?
A. 15
B. 56
C. 72
D. 96
Answer:
D. 96
Step-by-step explanation:
Using the Multiplication Principle, we multiply the number of choices for each item together:
[tex]8 \cdot 4 \cdot 3 = 96[/tex]
The set of life spans of an appliance is normally distributed with a mean mu = 48 months and a standard deviation sigma = 8 months. what is the life span of an appliance that has a z-score of –3?
Using the normal distribution, it is found that the life span of an appliance that has a z-score of –3 is of 24 months.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.In this problem, the parameters are given as follows:
[tex]\mu = 48, \sigma = 8, Z = -3[/tex].
Hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-3 = \frac{X - 48}{8}[/tex]
X - 48 = -24
X = 24.
The life span of an appliance that has a z-score of –3 is of 24 months.
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Answer:
Using the normal distribution, it is found that the life span of an appliance that has a z-score of –3 is of 24 months.
Normal Probability Distribution
The z-score of a measure X of a normally distributed variable with mean and standard deviation is given by:
The z-score measures how many standard deviations the measure is above or below the mean.
Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.
In this problem, the parameters are given as follows:
.
Hence:
X - 48 = -24
X = 24.
The life span of an appliance that has a z-score of –3 is of 24 months.
8x+21=3 need the answer please
Answer:
[tex]x=-\frac{9}{4}[/tex]
Step-by-step explanation:
Step 1: Subtract 21 from both sides
[tex]8x + 21 = 3[/tex]
[tex]8x + 21 - 21 = 3 - 21[/tex]
[tex]8x = -18[/tex]
Step 2: Divide 8 from both sides
[tex]8x = -18[/tex]
[tex]\frac{8x}{8}=-\frac{18}{8}[/tex]
[tex]x=-\frac{9}{4}[/tex]
Answer: [tex]x=-\frac{9}{4}[/tex]
PLEASE HELP CANT MOVE ON TO THE NEXT QUESTION TILL ANSWERED!!
Answer:
Step-by-step explanation:
Answer:
M = 61
nm = 31
kn = 45
L = 119
Step-by-step explanation:
its a parallelogram so everything is obvious
What is x, the height of the tree?
Answer:
21 feet
Step-by-step explanation:
It increases by a rate of 2.33333333,we know this by doing 14 divided by 6. 9 x 2.33333333 is 21
(although this might be incorrect)
Answer:
21 feet
Step-by-step explanation:
Ratio between height and distance from point on ground :
9 ft / 6 ft1.5Taking ratio between x and 14 :
1.5 = x/14x = 14 × 1.5x = 21 feetCreate a cylinder with a height of 6 cm and a radius of 10 cm. notice the volume calculation is 1,885.0 cm3. drag the orange dot to double the cylinder’s height. what do you notice about the new volume compared to the original volume?
The volume of the cylinder will be equal to V=1885 cubic cm.
What is volume?The Volume of the cone is the amount of quantity, which is obtained in the 3-dimensional space. The cylinder is the right circular object with some height like bamboo, bottles, rods etc all are cylinders.
The formula for calculating the volume of the cylinder is given as:-
V=πr²H
Here we have the radius of the cylinder r= 10 cm and the height of the cylinder is H=6 cm
V= π x (10)² x 6
V=1885 cubic cm.
Hence the volume of the cylinder will be equal to V=1885 cubic cm.
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Answer:
It doubled
Step-by-step explanation:
Got 100%
Find the value of x of a octagon with a degree of (16x+23)
A parallelogram has an area of 150 square yards and a height of 5 yards. What is the length of the base of the parallelogram? Enter your answer in the box. WILL MARK BRAINLIEST!!! 95 points!
Jake joins a soccer club. There is a registration fee of $35 dollars, and a charge of $60 a month. If m is the number of months that Jake plays in the club and c is the total amount he pays, write an equation to represent the relationship between c and m?
whats the answer??
Answer:
c=60m+35
Step-by-step explanation:
c is the cost so it should be equal to and 60 a month so 60m and +35
A story or an account of a personal experience that illustrates the central idea of a text is a(n) ______. A;anecdote B;statistic C;satire
Avery just got hired for a new job and will make $55,000 in her first year. avery was
told that she can expect to get raises of $1,500 every year going forward. how much
money in salary would avery make in her 18th year working at this job?
Avery's salary after 18 years will be equal to $82000.
What is the salary?The amount of money paid by any company to their employees on monthly basis is called salary.
Given that:-
Avery just got hired for a new job and will make $55,000 in her first yearAvery was told that she can expect to get raises of $1,500 every year going forward.The amount of salary taken by Avery in her 18th year will be:-
Per year incrememnt = $1500
So total increment in 18 years will be = 1500 x 18 = $27000
Total salary in 18th year will be = 55000 + 27000 = $82000
Therefore Avery's salary after 18 years will be equal to $82000.
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PICKING BRANILIEST HELP WITH 1
Answer:
1. x=37
2. x= 50
Step-by-step explanation:
Add up the two angles you already have, 43+100 and then subtract from 180.
180-143= 37
Do the same thing for number 2.
Add up 99+31, which is 130
The subtract from 180
180-130=50
The equation for triangles is x + (the angle measures) = 180
Hope this helps <3
Abox of chocolate candy contains 4 butter-cream-filled, 3 raspberry-
filled, 2 peanut butter-filled, 5 caramel-filled, and 6 nut-filled chocolates.
If Monica randomly selects a piece of candy, what is the probability that
she will pick a butter-cream-filled chocolate ?
A 0.10
B. 0.15
C. 0.20
D. 0.25
Answer:
0.20? sorry if im wrong
Step-by-step explanation: 4+3+2+5
can someone help me here
NONSENSE=REPORT
topic: Inscribed Quadrilateral theorem in a Circle
Answer:
Step-by-step explanation:
Remark
When a quadrilateral is inscribed in a circle, the opposite angles are supplementary. x is opposite 112 degrees. Therefore x and 112 add up to 180 degrees.
Formula
x + 112 = 180 Subtract 112 from both sides.
Solution
x + 112-112 = 180 - 112
x = 68
Answer
x = 68
Answer:
Step-by-step explanation:
#9.
x° = 200° and x = 200
y° = 100° and y = 100
#10.
x° = 68° , x = 68
y° = 99° , y = 99
[tex]\huge\color{yellow}\underline \colorbox{violet} {\color{red}{QUESTION}}[/tex]
Direction:Write TRUE if the statement is true and FALSE if not.
1.Non standard units cannot be used to measure volume.
2.To find the volume of rectangular prism multiply the length width and height.
3.When the non-standard unit used in small,more units are needed to fill a container.When the non-standard unit used is bigger.Few units are needed to fill the container.
correct answer=brainles
nice answer=rate 5 star
explanation=heart
incorrect=report
no explanation=report
Answer:
FALSETRUETRUEStep-by-step explanation:
1.
Non-standard units can be used to measure volumeExamples : m³, in³, cm³, mm³, L2.
The volume of a rectangular prism can be found by multiplying the length, width, and heightV = lwh3.
If there are smaller units, then naturally more of the units will be usedIf there are larger units, then less of the units will be useddefine angle of elevation?
The angle of elevation is the angle of which something, in simple terms, is raised from a straight plane. If it is the angle downwards, we call this the angle of depression.
An image giving an example, or a visual description, is attached.
It comes from Khan Academy.
Cereal costs $.19 per ounces. How much does 15 oz of cereal cost?
For a charity initiative, 420 t-shirts were made; in the morning 1/3 of the t-shirts is sold and in the afternoon 4/7 of the remaining ones. How many shirts are left to sell at the end of the day?
1/3 * 420 = amount of t-shirts sold in the morning
1/3 * 420 = 420/3 = 140 t-shirts
140 t-shirts were sold, so remaining is 420 - 140
420 - 140 = 280 remaining t-shirts
4/7 * 280 = amount of t-shirts sold in the afternoon
4/7 * 280 = (280/7) * 4 = 40 * 4 = 160 t-shirts
160 t-shirts were sold, so remaining is 280 - 160
the remaining t-shirts = 120 t-shirts
120 t-shirts are left to sell at the end of the day
How much profit did jamie make if he sold 87 tickets
Step-by-step explanation:
profit= revenue - cost
profit = 2(87)-69.80
=174-69.20=104.8 R
I need help on this question
Step-by-step explanation:
FIFO means "first in - first out". so, it is airways the oldest in the inventory that is sold. that means the newest or youngest items in the inventory remain.
the end inventory shows 70 units.
that means, all the November units (64) plus 6 of June are still there.
a.
the cost of the ending inventory is
576 + 6×8 = 576 + 48 = $624
b.
the cost of goods sold is then
1727 - 624 = $1,103
control :
196 + 483 + (59-6)×8 = 679 + 53×8 = 679 + 424 =
= $1,103
correct.
HELP!!!
Jay borrows $8,000 at a rate of 1.9% interest per year. What is the amount due at the end of 6 years if the interest is compounded continuously?
I'm confused.
$8,966.02 is your answer
PLease help, 100 points being given
Answer:
None of these
Step-by-step explanation:
[tex]\frac{x^{2}}{2} +\frac{y^{2}}{3} =\frac{4sin^{2}t}{2} +\frac{9sin^{2}t}{3} =5\times sin^{2}t[/tex]
[tex]x^{2}+y^{2}=13\sin^{2} t[/tex]
[tex]3x^{2}+2y^{2}=30\sin^{2} t[/tex]
i dont know how to do this one
Answer:
[tex]2\sqrt{34}[/tex]
Step-by-step explanation:
We can add a line to create a triangle and a rectangle. The triangle will have side lengths 10 and 6. Furthermore, it will be a right triangle, meaning we can apply the Pythagorean Theorem to find x, the hypotenuse.
[tex]6^2 + 10^2 = x^2\\x = \sqrt{6^2 + 10^2}\\ = \sqrt{136} \\= 2\sqrt34}[/tex]
hope this helped! :)
Choose all of the following statements that suggest a positive association.
A. The less education a person has, the less money they will likely earn.
B. The less fruits and vegetables a person eats, the lower their risk for cancer.
C. The smaller a person's shoe size, the larger their pant size.
D. The more you study, the more likely you are to earn a better grade.
Answer:
D
Step-by-step explanation:
It is only d because that is the only positive statement.