If x = a, y = b is the solution of the pair of equations x - y = 2 and x + y = 4, find the values of a and b.
Answer: a = 3, b = 1
Step-by-step explanation: There is nothing to be done except solving the equation together:
x - y = 2 => x - 2 = y (Equation 1)
x + y = 4 => 4 - x = y (Equation 2)
x - 2 = 4 - x ==> x should be 3 in this case. (a = 3)
If x or a is equal to 3, we can use this value to find y (or b).
Solving for the first equation:
x - y = 2 ==> (3 - y = 2)
y is equal to 1.
Copy and complete the table of values for
y = x² + 4x = 2.
-
What numbers replace A, B and C?
Answer:
A = -5
B = -2
C = 3
if g(x) = x to the power of 2 + 3, find g(4)
Answer:
19
Step-by-step explanation:
If g(x) = [tex]x^{2} + 3[/tex], then we will substitute 4 in for x, giving us:
[tex]4^{2} + 3[/tex]
Simplifying:
[tex]16 + 3 = 19[/tex]
So g(4) = 19.
Hope this helped!
Add the polynomial. 2a+b-c-d and 4a-3b-2c+5d
Answer:
6a-2b-3c+4d
Step-by-step explanation:
2a+4a = 6a
b-3b = -2b
-c-2c = -3c
-d+5d = 4d
Answer:
6a - b - 3c + 4d
Step-by-step explanation:
⭐What is a polynomial?
if "poly" means "many" and "nomial" means "terms", then polynomial means "many terms"Whenever you add polynomials, the only terms you can perform addition or subtraction on are like terms.
⭐What are like terms?
terms with the same variable AND exponentWe are asked to add the two given polynomials. Therefore, we have to add the like terms.
[tex]2a + b - c - d + (4a - 3b - 2c + 5d)[/tex]
a and a, b and b, c and c, and d and d all have the same variable with an exponent of 1.
When adding, make sure to utilize the correct addition rules.
⭐What are the rules for adding real numbers?
NEGATIVE + positive = NEGATIVEnegative + POSITIVE = POSITIVEPOSITIVE + POSITIVE = POSITIVENEGATIVE + NEGATIVE = NEGATIVE2a and 4a are positive. Therefore, 2a + 4a = 6a.
-3b is negative, but b is positive. -3b > b. Therefore, -3b + b = -2b.
-c and -2c are both negative. Therefore, -2c - c = -3c.
-d is negative, but 5d is positive. 5d > -d. Therefore, -d + 5d = 4d.
∴ [tex]2a + b - c - d + (4a - 3b - 2c + 5d) = 6a -b -3c + 4d[/tex]
⭐if this response helped you, please mark it the "brainliest"!⭐
Why is it difficult to classify protists? Select three options.
There are many varying characteristics and exceptions to each type of protist.
They have been previously categorized based on what they are not.
They are all eukaryotes composed of one or more cells that contain nuclei.
There are no exceptions to the characteristics of each type of protist.
They are microscopic and therefore too small to study accurately.
Recent studies show that protists have not descended from one common ancestor.
Answer:
There are many varying characteristics and exceptions to each type of protist.
They have been previously categorized based on what they are not.
Recent studies show that protists have not descended from one common ancestor.
Step-by-step explanation:
find the minimum amount of time (in seconds) it takes for a vehicle to pass through the zone without exceeding the posted speed limit of miles per hour.
The minimum amount of time (in seconds) it takes for a vehicle to pass through the zone without exceeding the posted speed limit of miles per hour is 4.8708 seconds.
We can solve this problem easily by using the Pythagorean Theorem. This is because the distances from the cop car to the road form two legs of a right triangle. This makes the total length of this zone the hypotenuse of this triangle and thus, this problem can be solved using the Pythagoras theorem.
= (150)^2 + (200)^2 = h^2
= 62500 = h^2
= h = 250
Our distance is in feet, but our speed is in miles per hour. Let's convert this distance into miles as well.
= 250 feet × 1 mile/5280 feet = 0.04735 miles
Then, when we use the formula d = rt
= 0.04735 = 35t
= 0.04735/ 35 ≈ 0.001353
Since our speed was in miles per hour, this time is also in hours. We need to convert this to seconds before we can state our final answer.
= 0.001353 hours × 60 minutes/1 hour × 60 seconds/1 minute = 4.8708 sec
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toddler triplets whose names are red, green and blue each have a coat whose colour is given by their name, but they aren't clear on which coat belongs to which of them. when they go out, red chooses a coat at random among the three coats, green chooses a coat at random among the remaining two coats and blue is left to take the remaining coat. how many ways are there for exactly one of the toddler triplets to end up with their coat?
Answer:
Step-by-step explanation:
A way for one of the toddler triplets to end up with their coat is if the other two toddler triplets each get one another coat.
making it a 33% chance of one of the toddler triplets to end up with their own coat.
100% divided by 3 = 0.33
There is exactly a 33% chance for one of the toddler triplets to end up with their coat.
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
Example:
50% = 50/100 = 1/2
25% = 25/100 = 1/4
20% = 20/100 = 1/5
10% = 10/100 = 1/10
We have,
Number of coat = 3
Red, green, and blue.
Now,
Each of them picks up a coat at random and goes out.
The chance of each of them getting their own coat.
= 1/3 x 100
= 33%
Thus,
There is a 33% chance that one of the toddler triplets ends up with their coat.
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The answer and explanation
The requried value of 'a' in the given expression is a = -12.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
here,
8⁻⁵⁵ / 8ᵃ = 8⁻⁴³
8ᵃ = 8⁻⁵⁵ / 8⁻⁴³
8ᵃ = 8 ⁻⁵⁵ ⁺ ⁴³
8ᵃ = 8⁻¹²
Taking logs on both sides
a ln 8 = -12 ln 8 [lnbˣ = x lnb]
a = -12
Thus, the requried value of 'a' in the given expression is a = -12.
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PLEASE HURRYYY THIS IS AN 70% GRADE!!!!!! The graph shows how many centimeters a bamboo plant can grow (g ) and the number of hours (t ) that the plant has been growing.
Part B: Determine the constant of proportionality. Explain how you determined k.
Answer:
5 cm per hour
if this helps
Step-by-step explanation:
On a coordinate plane, a parabola opens down. It goes through (negative 2, negative 2), has a vertex at (1.5, 10), and goes through (5, negative 2).
Over which interval is the graph of f(x) = –x2 + 3x + 8 increasing?
This simplifies to x<3/2. So the graph of f(x) = –x^2 + 3x + 8 is increasing over the interval (-infinity,3/2)
What is the interval?Generally, The vertex form of a parabola that opens downward is
f(x) = a(x-h)^2 + k,
where (h,k) is the vertex of the parabola.
We know that the vertex of the parabola is at (1.5, 10) so we can use that to find the value of a and h. So,
f(x) = a(x-1.5)^2 + 10
Given that the parabola goes through (- 2, - 2) and (5, - 2), we can substitute these points into the equation to find a and k.
Substituting (-2, -2) into the equation:
-2 = a((-2) - 1.5)^2 + 10
Substituting (5, - 2) into the equation:
-2 = a(5 - 1.5)^2 + 10
Solving these two equations will give you a = -1/2 and k = -8
So the equation is f(x) = -1/2(x-1.5)^2 - 8
The graph of a parabola is increasing on the interval where the derivative is greater than 0.
To find the derivative, we use the power rule and the chain rule:
f'(x) = -1/2(2x-3)
= -x+3/2
So, the graph of f(x) is increasing when -x+3/2 > 0
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Wesley wants to run 19 miles this week. If he runs 4.2 miles each day, how many days does he need to run to meet his goal?
The mileage of Alyssa's car is a measure of how far the car has traveled per unit fuel.The best method and reasoning to calculate the gas mileage is: D. 243.8 miles ÷ 7.71 gallon s
How many days must he run to reach his objective?The mileage of Alyssa's car is a measure of how far the car has traveled per unit fuel.
The best method and reasoning to calculate the gas mileage is:
D. 243.8 miles ÷ 7.71 gallon s
because dividing a quantity with units of miles by a quantity with units of gallons gives a quantity with units of miles per gallon.
The mileage of the car is calculated by dividing the number of miles traveled by the amount of gas used.
mileage
= 243.8 /7.71
From the given parameters;
The unit of miles traveled is miles
The unit of gallons used is gallons
Because the miles traveled is divided by the gallons used, then the unit of the mileage would be miles per gallon
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A day is a unit of time and cannot be divided into a fraction, Therefore Wesley would need to run for at least 5 days to meet his goal of 19 miles.
How many days Wesley needs to run?To find out how many days Wesley needs to run to meet his goal, we need to divide the total distance he wants to run (19 miles) by the distance he runs each day (4.2 miles):
19 miles ÷ 4.2 miles/day = 4.52 days
Since a day is a unit of time and cannot be divided into a fraction, Wesley would need to run for at least 5 days to meet his goal of 19 miles.
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How do you find a ratio in math 8th grade?
To find a ratio in 8th grade math, you need to divide one number by another number to get the ratio. For example, if you want to find the ratio of 10 to 8, you would divide 10 by 8 to get a ratio of 1.25.
1. Identify the two numbers you want to compare as the numerator and denominator
2. Divide the numerator by the denominator
3. The resulting answer is the ratio of the two numbers
To find a ratio in 8th grade math, divide the numerator by the denominator to get the ratio.
To find a ratio in 8th grade math, you need to divide one number by another number to get the ratio. For example, if you want to find the ratio of 10 to 8, you would divide 10 by 8 to get a ratio of 1.25.
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y+4=3(x-3) rewrite in Ax+By=C
Answer:
0=3x-y=-13
Step-by-step explanation:
Answer:
In the equation y+4=3(x-3), we can see that x and y are the variables and 4 and -3 are the constants.
To convert the equation to the form Ax + By = C, we'll first distribute the 3 on the right side:
y + 4 = 3x - 9
Next, we'll move all the terms with x to one side of the equation and all the terms with y to the other side:
-3x + y = - 13
Now we have the equation in the form Ax + By = C, where A = -3, B = 1, and C = -13.
the u.s. post office is interested in estimating the mean weight of packages shipped using the overnight service. they plan to sample 300 packages. a pilot sample taken last year showed that the standard deviation in weight was about 0.15 pound. if they are interested in an estimate that has 95 percent confidence, what margin of error can they expect?
Margin of error is 0.017 pound(approximately.)
Now, According to the question:
We know that:
Formula of margin of error :
E = [tex]z^*[/tex] × [tex]\frac{s}{\sqrt{n} }[/tex]
where:
z* = critical value for confidence interval
s= standard deviation
n= sample size.
We have:
s= 0.15 pound
n= 300
Critical value for 95% confidence = 1.96
Then, Margin of error for 95% confidence interval will be :
E = (1.96)[tex]\frac{0.15}{\sqrt{300} }[/tex]
E = 0.0169740971 ≈ 0.017
Hence, Margin of error is 0.017 pound (approximately.)
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An airplane flies 1200 km in 1 1/2 hours. what is its average speed in kilometers per hour?
Answer:
800 km/h
Step-by-step explanation:
speed = distance ÷ time
=1200km ÷ 1½
=800 km/h
A simple random sample of 40 items resulted in a sample mean of 25. The population standard deviation is 5.a. What is the standard error of the mean? round answer to 2 decimal place.b. At 95% confidence, what is the margin of error? round answer to 2 decimal place
The standard error of the mean 0.79
The margin of error 1.55
The standard error of the mean is one of the components of the margin of error.
The margin of error is the multiplication of standard error of the mean and critical value. Margin of error is denoted by E
sample size, n= 40,
Sample mean, = 25 and
population standard deviation, [tex]\alpha[/tex]= 5
[tex]SE_{x}[/tex]
The standard error of the mean, [tex]SE_{x}[/tex]
[tex]SE_{x}[/tex] = [tex]\alpha[/tex]/√n
[tex]SE_{x}[/tex] = 5/√40
[tex]SE_{x}[/tex] = 5/6.3246
[tex]SE_{x}[/tex] = 0.79
We have to find the critical value
[tex]\alpha[/tex]/2 = 0.05/2 = 0.025 is ± 1.96
The margin of error, E
E = [tex]Z_{\alpha /2 }[/tex] * [tex]SE_{x}[/tex]
E= 1.96×0.79
E= 1.55
The standard error of the mean 0.79
The margin of error 1.55
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At a deli counter someone bought 1 3/4 pounds of ham for $14. 50 someone bought 2 1/2 pounds of turkey for $26. 25 someone bought 3/8 pounds of roast beef for $5. 50 which meat is the least expensive per pound
The per-pound cost of ham, turkey, and roast beef is $8.29, $10.5, and $14.67. Here, ham is the least expensive meat.
The ratio is defined as the relationship between two magnitudes of similar size in terms of how often the first contains the second.
The cost of 1.75 pounds of ham is given as $14. 50. Let's consider the cost per pound of ham is x and this is calculated as follows,
[tex]\begin{aligned}\frac{1.75}{\$14.50}&=\frac{1}{x}\\1.75\times x&=\$14.50\\x&=\$8.29\end{aligned}[/tex]
The cost of 2.5 pounds of turkey is given as $26. Let's consider the cost per pound of turkey as y and this is calculated as follows,
[tex]\begin{aligned}\frac{2.5}{\$26.25}&=\frac{1}{y}\\2.5\times y&=\$26.25\\y&=\$10.5\end{aligned}[/tex]
The cost of 0.375 pounds of roast beef is $5.50. Let's consider the cost per pound of roast beef as z and this is calculated as follows,
[tex]\begin{aligned}\frac{0.375}{\$5.50}&=\frac{1}{z}\\0.375\times z&=\$5.50\\z&=\$14.67\end{aligned}[/tex]
From the above values we conclude, z>y>x. So the cost of ham is the least expensive.
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How to find the height of a triangle using Pythagorean Theorem?
Answer:
Step-by-step explanation:
We can find height of triangle by using pythagoras theorem
By theorem (hypotenuse)^2 = (perpendicular or height)^2 + (base)^2
=> Height of triangle = sqrt{(hypotenuse)^{2} - (base)^{2}
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Using probability the value of p + q = -0.4
What is probability?Probability is the likelihood of an event.
How to find the value of p + q?Given the Venn diagram and that the probabilities are independent events.
The probability of A or B is given by
P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
Also, the probability of A and B is given by P(A ∩ B) = P(A)P(B)
So, we have that
P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
P(A ∪ B) = P(A) + P(B) - P(A)P(B)
From the Venn diagram, we have that
P(A) = p + q
P(B) = q + 0.6
P(A ∩ B) = q
P(A ∪ B) = 0.2
So, substituting these into the equation, we have that
P(A ∪ B) = P(A) + P(B) - P(A)P(B)
0.2 = p + q + q + 0.6 - q
0.2 = p + 2q - q + 0.6
0.2 - 0.6 = p + q
-0.4 = p + q
So, the value of p + q = -0.4
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Use tracing paper to answer each of these questions for both sets of shapes below:
A
C
B
D
Which figure appears to be the exception?
What makes that shape different from the others?
●
What do the other three shapes have in common?
Solve for x and y.
2x + 5y = 8
4x + 3y = 2
Ax = 2, y = -2
Bx = 1, y = 2
Cx = -1, y = 2
Dx = -2, y =
4
Answer:
C) x = -1, y = 2
Step-by-step explanation:
Given system of linear equations:
[tex]\begin{cases}2x + 5y = 8\\4x + 3y = 2\end{cases}[/tex]
Multiply the first equation by -2:
[tex]\implies -2 \cdot 2x -2 \cdot 5y=-2 \cdot 8[/tex]
[tex]\implies -4x-10y=-16[/tex]
Add this to the second equation to eliminate x:
[tex]\begin{array}{crcrcr}& 4x & + & 3y & = & 2\\+&(-4x & - &10y&=&-16\\\cline{2-6}&&-&7y&=&-14\end{array}[/tex]
Solve for y:
[tex]\implies -7y=-14[/tex]
[tex]\implies \dfrac{-7y}{-7}=\dfrac{-14}{-7}[/tex]
[tex]\implies y=2[/tex]
Substitute the found value of y into one of the equations and solve for x:
[tex]\implies 2x+5(2)=8[/tex]
[tex]\implies 2x+10=8[/tex]
[tex]\implies 2x=-2[/tex]
[tex]\implies x=-1[/tex]
Therefore the solution to the given system of linear equations is:
x = -1, y = 2Answer:
c
Step-by-step explanation:
just trust me
a gazebo in the shape of a regular octagon has equal sides of 9 feet and an apothem of 10.9 feet. a. if one side of a gazebo is open, and the other sides have a railing, find the cost of the railing if it sells for $7.90 per foot. b. find the area of the gazebo. (express your answer in square feet) c. find the cost of the gazebo's flooring if it costs $3 per square foot. round to the nearest hundred dollars
The maximum number of pens he can buy now is 71.
We are given that;
A regular octagon has equal sides = 9 feet and an apothem of 10.9 feet
The cost of the railing if it sells = $7.90 per foot
Now,
Let’s assume that the person has bought x pens.
The total cost of the pens would be 9x dollars.
The shopkeeper has given a discount of 70 dollars. So the total cost of the pens after discount would be 9x - 70 dollars.
We need to find the maximum number of pens he can buy now.
we need to find the maximum value of x such that 9x - 70 ≤ 0.
Solving this inequality gives us x ≤ 70/9 ≈ 7.78.
Therefore, by algebra the answer will be 71.
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Rick's Phone Service charges $20.79 for an activation fee plus $4 for every gigabyte (g) used. Which of the following graphs models the situation?
The equation representing the situation is y = 20.79+4x, where y is total cost and x is GB used.
What is an equation?An equation is a mathematical statement that shows that two mathematical expressions are equal.
Given that, Rick's Phone Service charges $20.79 for an activation fee plus $4 for every gigabyte (g) used.
If total charge for x GB used is y, then the equation to represent the situation is ;
y = 4x + 20.79
The graph of the equation is attached.
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i have 18 distinguishable socks in my drawer: 8 white, 6 brown, and 4 blue. in how many ways can i choose a pair of socks, provided that i get two socks of the same color?
The required number of ways to choose a pair of socks, provided that i get two socks of the same color are 50.
What is combination?Combinations are ways to choose elements from a collection in mathematics where the order of the selection is irrelevant. Let's say we have a trio of numbers: P, Q, and R. Then, combination determines how many ways we can choose two numbers from each group.
According to question:We have,
8 white, 6 brown, and 4 blue
So, We need to choose a pair of socks, provided that i get two socks of the same color.
The number of ways are;
Ways to choose 2 white = C(8,2) = 28
Ways to choose 2 brown = C(6,2) = 16
Ways to choose 2 blue = C(4,2) = 6
So
28 + 16 + 6 =
50 ways
Thus, required total number of ways are 50.
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A pizza parlor has six different toppings. How many different one- and two-topping pizzas can you order
You can order 6 different one-topping pizzas. You can order 15 different one-topping pizzas.
What is the combination?
A combination is a method of selecting items from a collection where the order of selection is irrelevant.
The combination is defined as "an arrangement of objects in which the order in which the objects are chosen is unimportant." The combination means "selection of things," where the order is irrelevant.
The formula of combination is nCr = n!/[r!(n-r)!]
Where n is the total number of objects and r is the number of objects those are selected.
Case 1: one-topping pizzas
The number of different toppings is 6.
Selecting one topping is ₆C₁ = 6!/[1!5!] = 6
Case 2: two-topping pizzas
The number of different toppings is 6.
Selecting two topping is ₆C₂ = 6!/[2!4!] = 15
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factors of 12 that are also squared in numbers
please answer my mock rev question !!
Answer:
(a) 8800000
(b) Barcelona had the least population in 2018
(c) The difference in population is 2.9 x [tex]10^{7}[/tex]
Step-by-step explanation:
(a) Since '10' is raised to a positive power, the decimal will be moving in the forward direction, In other words, it will move towards the right. Therefore, the decimal will be moving 6 places forward. After which, the empty slot(s) will be occupied by zeros
8.8 x [tex]10^{6}[/tex] = 8800000
(b) First notice that three out of the five cities have population expressed in [tex]10^{6}[/tex] (where 6 is the least power). Then notice that out of those three cities, the smallest number corresponds to Barcelona (i.e. 5.5).
Therefore, Barcelona had the least population in 2018
(c) Population of:
Tokyo: 3.7 x [tex]10^{7}[/tex]
Ahmedabad: 7.7 x [tex]10^{6}[/tex]
First, make sure the two numbers are expressed in the same standard form (meaning 10 is raised to the same power in both cases):
Tokyo: 3.7 x [tex]10^{7}[/tex] = 3.7 x 10 x [tex]10^{6}[/tex] =37 x [tex]10^{6}[/tex]
Ahmedabad: 7.7 x [tex]10^{6}[/tex]
Next step:
37 x [tex]10^{6}[/tex] - 7.7 x [tex]10^{6}[/tex]
= (37 - 7.7) x [tex]10^{6}[/tex]
= 29.3 x [tex]10^{6}[/tex]
= 29 x [tex]10^{6}[/tex] (Corrected to 3 significant figures)
= 2.9 x 10 x [tex]10^{6}[/tex]
= 2.9 x [tex]10^{7}[/tex]
amar keeps picking playing cards out of a standard deck of 52 cards in the hopes that he will draw a spade there are 13 spades in the deck after looking at each card he places it back in the deck what is probability that amar will draw a spade in the first five attempts
The probability of Amar drawing a spade in the first five attempts is approximately 24.5%, as there are 13 spades in a deck of 52 cards.
The probability of drawing a spade in the first attempt is 13/52 or 25%.
The probability of drawing a spade in the second attempt is 12/51 or 23.5%.
The probability of drawing a spade in the third attempt is 11/50 or 22%.
The probability of drawing a spade in the fourth attempt is 10/49 or 20.4%.
The probability of drawing a spade in the fifth attempt is 9/48 or 18.8%.
The total probability of drawing a spade in the first five attempts is the sum of the above probabilities, which is 24.5%.
The probability of drawing a spade in the first five attempts is 24.5%, calculated by summing the separate probabilities.
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Write an equation for the sentence.
33 less than g is 56.
Answer: 33 - g = 56
less than means -
is means =
1. An angle is in standard position such that sin Ø-5/9. What are the possible values of Ø, to the nearest degree if 0 ≤0360? State the larger of
the two angles.
The larger possible angle of sin Ф = (5/9) is 34°.
What are trigonometric identities?There are three commonly used trigonometric identities.
Sin x = 1/ cosec x
Cos x = 1/ sec x
Tan x = 1/ cot x or sin x / cos x
Cot x = cos x / sin x
We have,
sin Ф = 5/9
Ф = [tex]sin^{-1}[/tex] (5/9)
Ф = 33.75
This means,
Ф =33° or 34°
Thus,
The larger angle is 34°.
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