The constant term does not have the same sign as the second expression, the two expressions are not equivalent. Also, if you substitute a value for x and evaluate each expression, the values will not be equal.
Expression 1: [tex]-0.5(3x+5)[/tex]
Using the distributive property to expand the first expression, we get
[tex]-0.5(3x+5) = -1.5x-2.5\\[/tex]
Expression 2: [tex]-1.5x + 2.5[/tex]
Since the constant term does not have the same sign as the second expression, the two expressions are not equivalent.
Also, if you substitute a value for x and evaluate each expression, the values will not be equal.
Q. Are the expressions –0.5(3x + 5) and –1.5x + 2.5 equivalent? Explain why or why not.
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Answer:Using the distributive property to expand the first expression, you would get -1.5x - 2.5. Since the constant term does not have the same sign as the second expression, the two expressions are not equivalent. Also, if you substitute in a value for x and evaluate each expression, the values will not be equal.
Step-by-step explanation: sample explanation
Clara did not want to tell Carl how old she was. All she said was that every year on her birthday, her Mom puts as many coins in her money box as how old she turned that day. Carl roughly estimated the number of coins in the box as not less that 110 but not more than 130 coins. How old is Clara?
Clara is 15 years old, and there are 120 coins on the box.
How old is Clara?Each year her mom puts as many coins in her money box as how old she turns that day.
So on her first birthday, 1 coin is put in the box.
On her second birthday, 2 coins are put in the box
And so on.
So we have the simple summation:
[tex]\sum_{n = 1} n[/tex]
We know that the outcome of that summation is a number in the interval [110, 130]
If we know that the sum goes from n = 1 to n = N (N is the age of Clara) then we can rewrite the summation as:
[tex]N*(N + 1)/2[/tex]
Now we can solve:
[tex]N*(N + 1)/2 = 110\\\\N^2 + N = 220\\\\N^2 + N - 220 = 0[/tex]
The two solutions of the quadratic equation are:
[tex]N = \frac{-1 \pm \sqrt{1^2 - 4*1*(-220)} }{2} \\\\N = (-1 \pm 29.7) /2[/tex]
If we take only the positive solution:
N = (-1 + 29.7)/2 = 14.35
Now, notice that we got this number by taking the smallest possible number of coins (110) So we can round this to the next whole number, which is 15.
If N = 15, then the number of coins in the box is:
15*(15 + 1)/2 = 120
Which lies on the wanted interval.
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pls help.... Natalie plans to run 5 miles every week for 3 weeks. The first day of the first week she ran 1 1/5 miles. How mant miles does she need to run the rest of the first week?
Answer:
3 4/5
Step-by-step explanation:
If Natalie runs 5 miles each week and she already ran 1 1/5 then she will need to run 3 4/5.
5 - 1 1/5 = 3 4/5
Simplify.
6a2−4b2+4abc−9b2−4a2+8abc
Answer:
[tex]\huge\boxed{\sf 2a^2-13b^2+12abc}[/tex]
Step-by-step explanation:
Given expression:[tex]=6a^2-4b^2+4abc-9b^2-4a^2+8abc\\\\Combine \ like \ terms\\\\=6a^2-4a^2-4b^2-9b^2+8abc+4abc\\\\=2a^2-13b^2+12abc\\\\\rule[225]{225}{2}[/tex]
Answer:
Hello! The answer is: [tex]2a^2 - 13b^2 + 12abc[/tex]
Step-by-step explanation:
[tex]6a^2 - 4b^2 + 4abc - 9b^2 - 4a^2 + 8abc[/tex]
Rearrange to combine like terms:
[tex]6a^2 - 4a^2 - 4b^2 - 9b^2 + 4abc + 8abc[/tex]
Combine like terms:
[tex]2a^2 - 13b^2 + 12abc[/tex]
Express 16.927 in standard form correct to 3 significant figures
The standard form to 3 significant figure of 16.927 is 1. 69 × 10^-1
How to determine the standard formGiven the value;
16.927 to convert to three significant figure
= 1. 69 × 10 ^ -1
Note that "2" cannot add up as 1 to '9'
Thus, the standard form to 3 significant figure of 16.927 is 1. 69 × 10^-1
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In a class of 40 students, 20% are females. How many males are in the class?
Answer:
In a class of 40 students, 20% are females. How many males are in the class?
ANSWER
= 32
if in a class of 40 students 20% are females that means 80% of the class are males...
anybody know the answer, i dont understand U_U
A function assigns the value of each element of one set to the other specific element of another set. The correct option is A.
What is the inverse of a function?Suppose that the given function is
[tex]f:X\rightarrow Y[/tex]
Then, if function 'f' is one-to-one and onto function (a needed condition for inverses to exist), then, the inverse of the considered function is
[tex]f^{-1}: Y \rightarrow X[/tex]
such that:
[tex]\forall \: x \in X : f(x) \in Y, \exists \: y \in Y : f^{-1}(y) \in X[/tex]
(and vice versa).
It simply means, the inverse of 'f' is undone operator, that takes back the effect of 'f'
The graph that represents the inverse of the given function is option A because graph A is showing more rapid growth as compared to the given graph.
Hence, the correct option is A.
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Fossils of Lystrosaurus, a dinosaur without the ability to swim or fly, can be found across Africa, India, and Antarctica.
What does this indicate?
A. That those continents were all connected during the time Lystrosaurus lived.
B. That they went extinct because they could not adapt.
C. That they later evolved either the ability to swim or the ability to fly.
D. Those continents were separated at the time Lystrosaurus lived.
Answer:
A
Step-by-step explanation:
Pangaea is the name for the land mass before the continents split. The continents would have been connected during that species life time.
Please answer with everything needed i appreciate everyones help:)0)
Answer:
1/3
Step-by-step explanation:
please mark brainliest if correct
Over which interval are the exponential and linear function approximately the same?
hard to tell but from 0.75 to 1
What does it mean to "model with mathematics"?
Answer:
See below. To model with mathematics is to test ideas using math and computer programs to simulate an object or action.
Step-by-step explanation:
To "model with mathematics" means that equations and mathematical relationships will be employed to simulate an object or action instead of using the actual object or action. One example would be the design of a roller coaster. The forces inherent on a roller coaster design can be predicted using Newton's laws and other principles of physics. F=ma may be used to predict the force pulling the car down the initial incline and that can be used to calculate speed at the bottom. A change in the car's direction will also produce forces that may be calculated, One might ask "Will this turn produce more force than the seat belt can safely handle?" Rather than building a coaster and testing it with your business partner in the seat, a mathematical model can be used to determine the risks and maximum forces. You'll have a much better chance of keeping your friend intact on the actual coaster. Mathematical models are also used to predict weather, the impact of monetary policy of the economy, and even which Netflix movie you are most likely to enjoy. The design of aircraft, ships, cars, and many other items are done using computer-aided design programs where the various forces can be modeled to determine optimum design without actually building the item. This can save enormous amounts of time and money to be able to test ideas on the computer before starting actual assembly.
During the snow storm your pipes burst you called preston the plumber who charges $50 for a serice call and $5 per hour. if your bill was for $120 total,how long did it take preston to repair your broken pipes
It takes Preston 14 hours to repair the broken pipes.
Given Information
Cost of service call charged by Preston, the plumber, S = $50
Preston charges $5/hour.
Preston's charge per hour, P = $5
The total bill, B = $120
We have to calculate the number of hours Preston take to repair the broken pipes.
Calculating the Number of Hours
Total service charge of Preston = Total bill - Service Call Charge
= B - S
∴ Number of hours Preston took to mend the broken pipe is given by,
H = (B - S)/P
H = $(120 - 50)/$5
H = 70/5
H = 14 hours
Therefore, Preston took 14 hours to repair the pipes.
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2. If (300) (30,000) = 9 x 10m, then m =
The quotient of 7 more than three times a number m and the number 27 less than n
The given statement can be modeled as an algebraic expression (3m+7)/27 < n.
What is an Expression?In mathematics, an expression is a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The statement is given as "The quotient of 7 more than three times a number m and the number 27 less than n" can be modeled as an algebraic expression.
(3m+7)/27 < n
Hence, the given statement can be modeled as an algebraic expression (3m+7)/27 < n.
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A bake shop sells twenty different kinds of pastries. Twelve of them were chocolate. Zack randomly buys eight kinds of pastries. What is the chance that four of them will be chocolate
Answer:
Just look at the other answer
Step-by-step explanation:
If gasoline costs $ 3.77 per gallon when you pay with a credit card, but $0.08 per gallon less if you pay with cash, how much do you save by filling up a 8-gallon tank and paying for it with cash?
Answer:
$0.64
Step-by-step explanation:
Cost for 8 gallons of gas
Credit Card at $3.77/gal
Cash at $(3.77 - 0.08)/gal: $3.69/gal
(8 gal)*($3.77/gal) = $30.16
(8 gal)*($3.69/gal) = $29.52
Savings is $0.64
How much simple interest is earned on an investment of 1,250 if the money is invested for 5 years at an annual interest rate of 4.5%
Work Shown:
i = P*r*t
i = 1250*0.045*5
i = 281.25
Evaluate the expression for x = 6.
12 + 2x -
5
O A. 19
O B. 79
O C. 14
O D. 54
Comparing Domain and Range
Which sets of values belong to the domain and range of a relation?
Domain
Quick
Chock
output values
values for the independent variable
input values
values for the dependent variable
Range
Mrs. Taylor is planning a pizza party for her students. She plans to purchase cheese pizza and pepperoni pizza for her students to enjoy. Cheese pizzas cost $8 each and pepperoni pizzas cost $11 each. She needs to purchase at least 12 pizzas, while spending no more than $180.
Let x represent the number of cheese pizzas purchased and y represent the number of pepperoni pizzas purchased.
What are two combinations of cheese and pepperoni pizzas that Mrs. Taylor can purchase without exceeding her spending limit?
Verify the combinations, graphically.
Verify the combinations, algebraically.
What is one combination of cheese and pepperoni pizzas that does not meet the criteria?
Verify the combination, graphically.
Verify the combination, algebraically.
The two combinations of cheese and pepperoni pizzas that Mrs. Taylor can purchase without exceeding her spending limit are; x + y ≥ 12 and
8x + 11y < 180
How to solve linear programming problems?We are told that she needs twelve pizzas. The equation below represents the number of pizzas of the type she needs to buy;
x + y ≥ 12
Where;
x represents the number of pepperoni pizzas she can buy while keeping her limit of 12 pizzas.
y represents the number of cheese pizzas she can buy while keeping her limit of 12 pizzas.
We are told that she cannot spend more than 180 dollars. Thus, our inequality is now;
8x + 11y < 180
Where;
8x represents the amount of dollars per pepperoni pizza.
11y represents the amount of dollars per cheese pizza.
These equations show all possible solutions.
The purple area in the graph attachment is verified to show the possible combinations.
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Suppose a large shipment of televisions contained 19% defectives. If a sample of size 479 is selected, what is the probability that the sample proportion will be greater than 17%
The value is P(p'-p > 0.17) = 0.09
From the question we are told that
The population proportion is p=0.19
The sample size is n = 479
Generally given that the sample size is large enough , i.e n > 30 then the mean of this sampling distribution is mathematically represent
[tex]u_{x} =p=0.19[/tex]
Generally the standard deviation is mathematically represented as
σ[tex]=\sqrt{ \frac{p(1-p)}{n}[/tex]
σ= [tex]\sqrt{ \frac{0.19(1-0.19)}{479}[/tex]
σ=0.017
Generally the the probability that the sample proportion will differ from the population proportion by greater than 17% is mathematically represented as
[tex]P(p'-p > 0.17) =P (z > \frac{0.17}{0.017} )[/tex]
[tex]P(p'-p > 0.17) =P (z > 10 )[/tex]
[tex]P(p'-p > 0.17) =P (z > 10 ) - P (z > -10 )[/tex]
From the z table the area under the normal curve to the left corresponding to 10 and - 10 is
[tex]P(p'-p > 0.17) = 0.97042 - 0.87450\\P(p'-p > 0.17) = 0.09[/tex]
So, the value of probability is greater than 17% is P(p'-p > 0.17) = 0.09
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The probability that the sample proportion will be greater than 17% is 0.8677 or 86.77%.
The true proportion of the sample or the mean of the sample = 19%, that is, μ = 19% or 0.19.
The sample size (n) = 479.
The sample proportion is to be calculated at the point 17% or 0.17.
The standard error (s) = √{μ(1 - μ)/n} = √{0.19(1 - 0.19)/479} = 0.0179.
We are asked to calculate the probability that the sample proportion is greater that 17% or 0.17.
This is written as P(X > 0.17) = P(Z > {(0.17-0.19)/0.0179}) = P(Z > -1.1173) = 1 - P(Z ≤ -1.1173) = 1 - 0.1304 = 0.8696 or 86.96%.
To calculate this using the calculator, we use the calculator function:
Normalcdf(0.17,10000000,0.19,0.0179) = 0.8677 or 86.77%.
Thus, the probability that the sample proportion will be greater than 17% is 0.8677 or 86.77%.
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Try It #4
For the function f (x) = | 2x − 1 | − 3, find the values of x such that f(x) = 0.
Answer:
x=2 or x= -1
Step-by-step explanation:
when f(x) = 0
⇒| 2x-1 | =3
case(i) (x>1/2)
2x-1=3
x=2
case(ii) (x<1/2)
-(2x-1)=3
2x-1=-3
x=-1
case(iii) (x=1/2)
[tex]0=3[/tex] absurd.
write the equation for a polynomial of least degree with integer coefficients given the following zeros: -2, -6, -10i. leave your answer in factored form, but make sure there are no irrational or imaginary numbers
The equation of the polynomial in factored form is (x+2)(x+6)(x-10) = 0
What is a polynomial?A polynomial is an algebraic equation with at least the power of its variable 3.
Analysis:
if -2, -6, -10i are the zeroes of the polynomial, it means x = -2, x = -6, x = -10i
if x = -2, (x+2) is a factor, (x+6) is a factor.
convert x = -10i to a real number,
i = [tex]\sqrt{-1}[/tex]
-10[tex]\sqrt{-1}[/tex] = 10[tex]\sqrt{- -1}[/tex] = 10[tex]\sqrt{1}[/tex] = 10
x = 10, so (x-10) is a factor.
Therefore equation of the polynomial in factored form is (x+2)(x+6)(x-10) = 0
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Please Help Asap!!!!
What is the value of sin 0 given that (3-4) is a point on the terminal side of 0
Using trigonometric relations, we will see that:
sin(θ ) = -0.8
How to get the sine of the angle?
For any point (x, y), the angle between the positive x-axis and the ray that connects the origin with the point (x, y) is:
θ = Atan(y/x)
In this case, the point is (3, -4), then the angle is:
θ = Atan(-4/3) = -53.13°
Then the sine of theta is:
sin(θ = -53.13°) = -0.8
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Which type of rigid transformation is shown? Identifying the Type of Rigid Transformation
The transformation is translation
What is Translation?Translation means the displacement of a figure or a shape from one place to another. In translation, a figure can move upward, downward, right, left or anywhere in the coordinate system. In translation, only the position of the object changes, its size remains the same.
The figure is attached below:
As per the definition the figure shows that size hasn't changed.
Hence, the transformation is translation.
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2 triangles are shown. They have one congruent side. The first triangles has angle measures of 98 degrees and 35 degrees. The second triangle has angle measures of 35 degrees and 47 degrees.
Are the triangles congruent? If so, how do you know?
yes, because all the angles of the triangles are acute
yes, because the triangles have three congruent, corresponding angles
yes, because of ASA or AAS
not enough information given
Answer:
215 is the answer of the 2 triangles
Answer: Yes because of ASA or AAS (C)
Step-by-step explanation:
Got it right on edge ")
A tablet at a local electronics store is in high demand and will only be available to customers for a limited time. The store initially has 4 cases of the tablet on hand. The store manager receives new supplies of the tablet each week. At the beginning of week 1, the store manager receives an additional order from the distributor of 5 cases of tablets. At the beginning of week 6, the manager receives another order of 10 cases. Which of the following equations best models the scenario for how many cases of the tablet the store can expect to receive each week?
Answer:
y = x + 4
Explanation:
Initially (at week 0) = 4 cases
now (at week 1) = 5 cases
now (at week 6) = 10 cases
turn them into points:
(0, 4), (1, 5), (6, 10)Find slope:
[tex]\sf slope: \dfrac{y_2 - y_1}{x_2- x_1} \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points[/tex]
[tex]\rightarrow \sf slope \ (m) : \dfrac{5-4}{1- 0 } = 1[/tex]
Find equation:
[tex]\sf y - y_1 = m(x - x_1)[/tex]
[tex]\sf \rightarrow y-4 =1(x -0)[/tex]
[tex]\sf \rightarrow y = x +4[/tex]
The school tuck-shop has milk in 700mL and 1L cartons. If there are 60 cartons and 48L of milk in total, how many 700 mL cartons are there?
60 × 48 = 2880 L
2880 ÷ 700 = 4
Answer:
20 1 Liter Cartons
40 700 ml Cartons
Step-by-step explanation:
Let A be the number of 700ml cartons.
Let B be the number of 1 L cartons
We are told that A + B = 60 cartons total
Rearrange to isolate A: A = 60 - B
700ml is 0.700L
Total volume of milk is 48L
Total volume (in liters) of the 700 ml cartons is from (0.70 L)A
Total volume from the 1L cartons is (1 L)B
Total = (0.70)A + 1B = 48 L
Now use the rearranged equation for A in the above espression:
(0.70)A + 1B = 48 L
(0.70)(60-B) + 1B = 48 L
42 - 0.70B + B = 48
0.30B = 6
B = 20
A is 60 - B or 40
=============
CHECK:
B: 20*(1 L) = 20 L
A: 40*(0.70 L) = 28 L
Total = 48 L YES
A boat can travel 408 miles on 204 gallons of gasoline how far can it travel on 169 gallons
Answer:
338 milesStep-by-step explanation:
If a boat can travel 408 miles on 204 gallons, this means that for every 2 miles, it requires 1 gallon.
So, for 169 gallons, there are 2 miles for every gallon.
So, multiply 169 * 2.
The answer is 338
Hope this helps!
PLEASE HELP THIS IS MY LAST TEST QUESTION!!!14x^5y^4+21x^3y^2/7x^3y
Answer: =2x²y³+3y.
Step-by-step explanation:
[tex]\frac{14x^5y^4+21x^3y^2}{7x^3y} =\frac{7x^3y*(2x^2y^3+3y)}{7x^3y}= 2x^2y^3+3y.[/tex]