The dimensions of the rectangle in terms of x are (x-6) and (x+3).
What in mathematics is a quadratic equation?
x ax2 + bx + c = 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. a 0. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer could be simple or complicated.
Given that:
A = x^(2) - 3x - 18
By solving this equation we can get the values of length and breath of rectangle
A = x^(2) - 6x + 3x - 18
A = x(x-6)+3(x-6)
A = (x-6)(x+3)
Hence the area of rectangle is equal to L * W
Hence, the dimensions of the rectangle are (x-6) and (x+3).
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Alan travel 8 2/3 kilometer to get to chool. He ran 1 10/11 kilometer and walked the ret. How many kilometer were left to walk?
If Alan had ran 1 10/11 kilometer and walked the ret so his remaining distance from school is 6 5/11 kilometer.
What is called distance?Distance is the sum of an object's movements, regardless of direction. Distance can be defined as the amount of space an object has covered, regardless of its starting or ending position.
What is the formula for distance?Learn how to apply the Pythagorean theorem to find the distance between two points using the distance formula. The Pythagorean theorem can be rewritten as d=√((x_2-x_1)²+(y_2-y_1)²) to calculate the separation between any two locations.
As the total travel of alan from his school is
=8 2/3 kilometer
according to given condition;
he has traveled;
=1 10/11 kilometer
so his remaining travel from his school is;
=8 2/3 kilometer-1 10/11 kilometer
= 6 5/11 kilometer
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Mr. Dyson works at a music camp. he has $90 to spend on guitar strings for his students. a pack of bronze strings cost $6. A pack of nickel strings cost $4.50. The equation 6x + 4.5y = 90 represents the situation. how many packs of nickel strings does he buy if he only buys nickel strings and no bronze strings.
By evaluating the linear equation, we will see that Mr. Dyson will buy 20 packs of nickel strings.
How many packs of nickel strings does he buy?We know that the linear equation:
6x + 4.5*y = 90
Represents the given situation, where the variable x is the number of bronze strings and y is the number of nickel strings.
We want to find the number of packs of nickel strings that he will buy if he does not buy any bronze strings, so we need to evaluate in x = 0.
We will get:
6*0 + 4.5*y = 90
4.5*y = 90
y = 90/4.5 = 20
He will buy 20 packs of nickel strings.
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Triangle JKL is similar to triangle STU. What is the length of side LK?
Using mathematical operations, we can conclude that the length of LK is 1.25 units in triangle JKL.
What are mathematical operations?
A mathematical "operation" is indeed the method by which a value utilizes operands and a math operator.
The supplied operands or numbers must conform to a set of predefined rules that are connected to the symbol of the math operator.
Parentheses, Exponents, Arithmetic, Division, and Addition Simple arithmetic is also known as PEMDAS (from left to right).
So, we know that the given triangles are similar:
Then, the length of line LK will be:
JK/ST = LK/UT
Solve this as follows:
JK/ST = LK/UT
2.5/10 = LK/5
10LK = 2.5(5)
10LK = 12.5
LK = 12.5/10
LK = 1.25
Therefore, using mathematical operations, we can conclude that the length of LK is 1.25 units in triangle JKL.
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Hello, can someone help me out with this question please!?!?!
Answer: C
Step-by-step explanation:
Distributive property 2. combine like terms 3. subtraction proerty of equality 4 division of equality.
What is the 9th term of the sequence 2,8,32,128
Answer: 131072
Step-by-step explanation:
Basically the sequence is just being multiplied by 4, like 2(4)=8 and 8 is the next number in the sequence or 32(4)=128 which then again is the next number in the sequence.
Use Pythagoras' theorem to work out the length of
the side AD in the rectangle below.
Give your answer in centimetres to 2 d.p.
B
A
6.3 cm
с
4 cm
D
The value of AD in one decimal place for the given triangle is 9.8 cm.
What is a triangle?A triangle is a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices.
Triangle is a very common figure to deal with our daily life for example in our daily life to measure the height of any tower then there is a huge application of the right angle triangle.
As per the given by triangle ΔADE
By Pythagoras' theorem,
(AD)² = (AE)² + (ED)²
(AD)² = 4² + 9²
(AD)² = 97
AD = 9.8
Hence "The value of AD in one decimal place for the given triangle is 9.8 cm".
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The missing image is attached below,
If Y varies directly with X and X=5 and Y=15 what would be the value of Y if X=12
Answer:
i think 3
Step-by-step explanation:
Helen thinks of two numbers. The highest common factor of her two numbers is 5. The lowest common multiple of her two numbers is a multiple of 12. Write down two possible numbers that Helen could be thinking of.
It is evident from the steps above that it is impossible to be have two numbers with the same LCM and HCF as 12 and 5, respectively.
Explain the term LCM and HCF?The entire form of the Least Common Multiple in mathematics is LCM, whereas the official name of the Highest Common Factor is HCF. The L.C.M. indicates the least number that is precisely divisible by 2 or more numbers, while the H.C.F. describes the biggest factor existing between any given pair of 2 or more numbers.The given condition are-
Helen considers two numbers that fit the following criteria:
Five is the two integers' largest common factor.Twelve is the least frequent multiple of a two numbers.The steps to solve the condition are-
1. It is assumed that when Helen considers of two numbers, they have corresponding HCF and LCM values of 5 and 12.
2. A smallest common multiple shared by two numbers is referred to as the least common number.
LCM of 4 with 6 is 12, for instance.
3. The highest number which divides the two selected numbers, leaving a residue of 0, is referred to as the highest common factor.
HCF of 6 and 8 is 2, for instance.
4. Given that the LCM of Helen's two chosen numbers is 12, even multiples of 12 are indeed the two numbers' common multiples. In light of this, 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, and so forth.
5. The only numbers that may be divided by 5 are 60 and 120. All other numbers have HCF values apart from 5. 60 and 120 have an HCF of 60, but not 5.
6. As a result, it is evident from the steps above that it is impossible to be have two numbers with the same LCM and HCF as 12 and 5, respectively.
Therefore, the aforementioned criteria cannot exist mathematically.
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suppose the lifetime of a particular brand of tire for cars is approximately normally distributed with a mean of 48,000 miles and standard deviation of 3,000 miles. step 1 of 2: what is the probability that a single tire randomly selected from the population will have a lifetime between 46,800 and 49,200 miles? round your answer to 4 decimal places if necessary.
0.3108 is the probability that a single tire randomly selected from the population will have a lifetime between 46,800 and 49,200 miles
What is probability?Probability is a mathematical discipline that concerns with numerical figures of how probable an occurrence is to occur or how probably a statement is to be true. A number between 0 and 1 is the probability of an occurrence, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.
X ~ N ( µ = 48000 , σ = 3000 )
As we know, P ( 46800 < X < 49200 )
Standardizing the value, we get -
Z = ( X - µ ) / σ
Z = ( 46800 - 48000 ) / 3000
Z = -0.4
Z = ( 49200 - 48000 ) / 3000
Z = 0.4
Also,
P ( -0.4 < Z < 0.4 )
P ( 46800 < X < 49200 ) = P ( Z < 0.4 ) - P ( Z < -0.4 )
P ( 46800 < X < 49200 ) = 0.6554 - 0.3446 (Probability calculated from Z table)
P ( 46800 < X < 49200 ) = 0.3108
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A truth erum ha the property that 90% of the guilty upect are properly judged while, of coure, 10% of the guilty upect are improperly found inno cent. On the other hand, innocent upect are mi judged 1% of the time. If the upect wa elected from a group of upect of which only 5% have ever committed a crime, and the erum indicate that he i guilty, what i the probability that he i innocent
Therefore in this question the probability that he is innocent is 0.1743
What is probability?The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a claim to be true. A number between 0 and 1 is the probability of an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.
Here,
In this case, let G represent the state of guilt and H represent the state of innocence.
and Let K stand for the situation where the truth serum shows that someone is guilty.
We are aware that 90% of the guilty suspects receive just verdicts, i.e. P(K|G)=0.9.
Additionally, we know that innocent suspects are mistakenly identified 1% of the time, or P(K|H)=0.01.
When a suspect is chosen from a group of suspects, of whom 5% committed a crime, and the serum suggests that the suspect is guilty, we must determine the likelihood that the suspect is innocent.
We must therefore determine the probability P(H|K).
A group of people was chosen for the suspect, of which 5% were criminals.
so the probability that selected person is guilty is
P(G) = 0.05
Therefore, the probability that selected person is not guilty is
P(H) = 1 – P(G) = 1 – 0.05 = 0.95
Then,
Using Bayes' Theorem, we get
P(H|K) =[tex]\frac{P(H)P(K|H)}{P(H)P(K|H) + P(G)P(K|G)}[/tex]
= [tex]\frac{0.95*0.01}{0.95*0.01 + 0.05*0.9}[/tex] =0.1743
Therefore in this question the probability that he is innocent is 0.1743
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Line c has an equation of y= 1 /5 x–3. Line d, which is parallel to line c, includes the point (– 1,1). What is the equation of line d?
Answer:
[tex]y=\frac{1}{5}x+\frac{6}{5}[/tex]
Step-by-step explanation:
Parallel lines have the same slope, so the slope of line [tex]d[/tex] is [tex]1/5[/tex].
So, the equation of line [tex]d[/tex] is:
[tex]y-1=\frac{1}{5}(x+1) \\ \\ y-1=\frac{1}{5}x+\frac{1}{5} \\ \\ y=\frac{1}{5}x+\frac{6}{5}[/tex]
assume a single spin of the roulette wheel is made. find the probability of the marble landing on a 00 or even slot.
By applying this theory, it is discovered that there is an 0.5 = 50% chance that the marble will land on a 00 or even slot.
What is the definition of the term probability?Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is.A probability is calculated by dividing the entire number of possible outcomes by the desired outcomes.
In this issue:
There are thus 38 positions; T =3818 of them are even, plus 00, so D = 19The preferred likelihood is:
P = D/T
P = 19/38 = 0.5
Thus, the probability that the marble will land on a 00 or even slot is 50%, or 0.5.
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The complete question is-
When playing American roulette, the croupier (attendant) spins a marble that lands in one of the 38 slots in a revolving turntable. The slots are numbered 1 to 36, with two additional slots labeled 0 and 00 that are painted green. Consider the numbers 0 and 00 as neither even nor odd. Half the remaining slots are colored red and half are black. Assume a single spin of the roulette wheel is made. Find the probability of the marble landing on a 00 or even slot.
Help me with ixl please
A straight line = 180°. You have: 58° , 40°, and q so:
q = 180° - (58° + 40°)
q = 82°
Answer:
82
Step-by-step explanation:
180 i s the line length so
180-40=140
140-58=82
line L has y- intercept at (0,4) and an x- intercept at (10,0)
Answer:
y = -2/5 x + 4
Step-by-step explanation:
slope = (0-4)/(10-0)
-4/10
-2/5
y intercept = 4
y = -2/5 x + 4
determine whether a triangle with the given vertices is a scalene, isosceles, or equilateral triangle. check all that apply
Answer: the first one(triangle ABC) is scalene, the second one(triangle TRI) is Isosceles, and the last one(triangle PQR) is
Isosceles
Step-by-step explanation: graph each joint is Desmos online calculator
A sandwich store charges a $10 delivery fee, and $4.50 for each sandwich.
a. What is the total cost (sandwiches and delivery charge) if an office orders 6 sandwiches?
Type the answer in the box below.
$
b. What is the total cost for x sandwiches?
Type the answer in the box below.
A clothing company has 4,630 shirts to ship. It can fit 130 shirts in a shipping box .How many boxes are to ship all the shirts?
Answer: 36 boxes
Step-by-step explanation:
4630 divided by 130 = 35.6 boxes
Then we ground up to 36 boxes
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The sales tax is $53 on the purchase of a dining room set for $1060. Find the sales tax rate.
Answer: Sale tax rate is 5%
Step-by-step explanation:
Take $53 divided by $1060, then time 100% = 5%
I have 2/3 L (litre) of liquid detergent. I ued 3/4 of thi to wah my heet on the weekend. How much liquid detergent do I have left?
Liquid detergent do I have left is 8/9.
What is detergent ?
When washing items like clothing or dishes, detergent is a chemical compound that is often in the form of a powder or liquid. Alternatives include washing liquid, soap powder, and cleaner. More detergent synonyms. More detergent synonyms.
I have 2/3 L (litre) of liquid detergent. I ued 3/4 of thi to wah my heet on the weekend.
[tex]\frac{\frac{2}{3}}{\frac{3}{4}}$$[/tex]
Apply the fraction rule: [tex]$\frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a \cdot d}{b \cdot c}$[/tex]
[tex]=\frac{2 \cdot 4}{3 \cdot 3}$$[/tex]
Multiply the numbers: 2-4=8
[tex]=\frac{8}{3 \cdot 3}$$[/tex]
Multiply the numbers: 3-3=9
[tex]=\frac{8}{9}$$[/tex]
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*NOT A QUIZ QUESTION JUST REGULAR HOMEWORK*
Two figures are similar when they have some common properties. The value of PQ as required is 28 units.
Similar triangles are two or more which have a series of common properties. This may be in relations to the length of their sides or measure of their angles.
In the given triangle PQR,
ΔPQS ll ΔSTR
Given that PS = RS, and QT = RT.
Then we can say that;
[tex]\frac{RS}{ST}[/tex] = [tex]\frac{PQ}{PQ}[/tex]
But, PR = 2RS;
[tex]\frac{RS}{ST}[/tex] = [tex]\frac{2RS}{PQ}[/tex]
[tex]\frac{1}{ST}[/tex] = [tex]\frac{2}{PQ}[/tex]
2ST = PQ
2(-22 + 9x) = 9x - 8
-44 + 18x = 9x - 8
18x - 9x = -8 + 44
9x = 36
x = 4
So that,
PQ = 9x - 8
= 9(4) - 8
PQ = 36 - 8
= 28
Thus, the length of PQ is 28 units.
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Leslie creates designer bracelets with gemstones. Her most recent order included a total of 7 bracelets. It takes 14 stones to make one bracelet. Write and solve an equation that represents how many stones were used for the order.
7s = 14; s = 2 stones
s/14 = 7 ; s = 98 stones
s + 7 = 14; s = 7 stones
s − 7 = 14; s = 21 stones
An expression that represents the number of bracelet Leslie designs is
s/14 = 7 ; s = 98 stonesHow to find the number of stones used for the orderInformation from the question include
Her most recent order included a total of 7 bracelets
It takes 14 stones to make one bracelet
let s represent stone
It takes 14 stones to make one bracelet means that one bracelet = 14 s
hence if 1 bracelet is 14 stones then 7 bracelet will be
1 bracelet = 14 s
7 bracelet = ?
cross multiplying
1 * ? = 7 * 14
? = 98 stones
the equation is written as
s/14 = 7 ; s = 98 stones
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Find the additive inverse of -[tex]\frac{1}{2}[/tex]
Answer: 1/2
Step-by-step explanation:
Let N be any number and M be the additive inverse of N
N + M = 0 = M + N
that additive inverse of N is - N
x + ( - 1/2 ) = 0
x - 1/2 = 0
x = 1/2
the additive inverse of -1/2 is 1/2
HELP ASAP!!
A quadrilateral has 4 sides. One angle of a regular quadrilateral measures (6w+13) Determine the value of w. Round to the nearest whole number
Ow=13
Ow=23
Ow=59
Ow=90
Answer:
(a) w = 13
Step-by-step explanation:
You have a regular quadrilateral with interior angle measure (6w+13)°, and you want the value of w to the nearest integer.
Regular quadrilateralA regular quadrilateral is a square. Its interior angles are 90°, so we have ...
6w +13 = 90
6w = 77
w = 12.833...
w ≈ 13
The value of w to the nearest whole number is 13.
Whitch one is correct a b c or d
Answer:
Step-by-step explanation:
u got it right the first time it is D
a box of frozen vegetables weighing 144kg 780g was delivered at a grocery shop. If there were 15 packets of equal inside the box, what was the weight of each bag?
Answer:
9.652 kg
Step-by-step explanation:
144 kg 780 g = 144.78 kg
if there are 15 packets in the box then:
144.78 ÷ 15 = x
x = 9.652 kg
Therefore the weight of each bag is 9.652 kg
A store sells new video games for $45 each and used video games for $14 each. Jerry is buying 3 new video games and xused video games?
forty-five times three equals one-hundred-thirty-five
45x3=135
A lorry leave a factory on a journey of 195km at 08 45 , travelling at an average peed of 52 km/h. A) Find the time at which the lorry the time taken arrive at it detination. B) on the return journey, the lorry leave at 14 55 and arrive at the factory at 18 15. Calculatge the time taken and the average peed of the lorry on the return journey
The time at which the lorry the time taken arrive at it destination is 12.20.
Given :
A lorry leave a factory on a journey of 195km at 08 45 , travelling at an average speed of 52 km/h.
here,
Distance = 195 km
Speed = 52 km/h
we know that ,
speed = distance / time
on cross muliplicating
speed * time = distance
time = distance / speed
substitute the values
time = 195 / 52
= 3.75 hours
destination time = 8.45 + 3.75
= 12.20
Therefore the time at which the lorry the time taken arrive at it destination is 12.20
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the tens digit of a two-digit number exceeds the units digit by 1. if the number is divided by the sum of its digits, the quotient is 6. what is the number?
The reqiured two digit number is 54
Let, a two-digit number be n
the digit at tens place as x and the digit at unit place be y
The tens digit of a two-digit number exceeds the units digit by 1.
x = y + 1 .............(1)
if the number is divided by the sum of its digits, the quotient is 6.
(10x + y)/(x + y) = 6
Substitute above value of x in this equation.
(10(y + 1) + y) = 6(y + 1 + y)
10y + 10 + y = 6(2y + 1)
11y + 10 = 12y + 6
y = 4
Substitute above value of y in equation (1),
x = 4 + 1
x = 5
So, the number would be, 10x + y = 50 + 4
= 54
Therefore, the number is 54
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The figure is made up of 10 identical squares. The perimeter is y cm. What is the side
of each square in terms of y?
(answer in cm)
The side of each square in terms of y is y/16.
What is a perimeter?
The complete length of a shape's boundary is referred to as the perimeter in geometry. A shape's perimeter is calculated by adding the lengths of all of its sides and edges.
Here, we have
The figure is made up of 10 identical squares. The perimeter is y cm.
The number of outer sides is 16
Let the side be x
then
16x = y
x = y/16
Hence, the side of each square in terms of y is y/16.
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a trucker driver can expect to make $us55,065 per year in the us. assuming that this driver works 70 hours per week and 52 weeks per year, what is the equivalent salary in canadian dollars per hour?
The equivalent salary in Canadian dollars per hour of the driver is $28.13/hour.
To convert the annual salary of a truck driver in the US from US dollars to Canadian dollars, you can use the current exchange rate between the two currencies. The exchange rate fluctuates constantly, so you will need to use the most current rate.
Assuming the current exchange rate is 1 US dollar to 1.26 Canadian dollars, the annual salary of a truck driver in the US, $55,065, is equivalent to 71,040.90 Canadian dollars. If the truck driver works 70 hours per week and 52 weeks per year, their hourly wage in Canadian dollars would be $28.13.
Here's the calculation:
Annual salary in Canadian dollars = $55,065 * 1.26 = $71,040.90
Hourly wage in Canadian dollars = $71,040.90 / (70 hours/week * 52 weeks/year) = $28.13/hour
Keep in mind that this is just a rough estimate, as the exchange rate can change over time, and the actual wage may vary depending on the driver's experience, location, and other factors.
So, the equivalent salary in Canadian dollars per hour of the driver is $28.13/hour.
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