Answer:
Yes, (2, -1) is a solution.
Step-by-step explanation:
Plug in 2 for x and -1 in for y and see if it is a true statement.
2x - y = 5
2(2) - (-1) = 5
4 - (-1) = 5 Subtracting a negative number is the same as adding a positive number
4 + 1 = 5
5 = 5 Since this statement is true, (2,-1) is a solution.
A certain school's enrollment increased 6% this year over last year's enrollment. If the school now has 1378 students enrolled, how many students were enrolled last year?
A. 1295
B. 1300
C. 1350
D. 1460
E. 1500
If the school now has 1,378 students enrolled, last year, the number of students enrolled was B. 1,300.
How is the number of students determined?Using the mathematical operations of addition, subtraction, division, and multiplication, we can determine the number of students.
Mathematical operations help us to determine unknown values, given a known domain.
Data and Calculations:Increase in school enrollment over last year's = 6%
Enrollment for the current year = 1,378
Let last year's enrollment = 100%
And the current year's = 1.06 (100 + 6)
Therefore, the enrollment last year = 1,300 (1,378/1.06)
Thus, the enrollment (number) last school year was B. 1,300.
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State the domain and range of the sin, cos, tan, functions. State the domain
and range of the inverse sin, cos, and tangent functions.
The domain and range of trigonometric functions are as follows;
Function Domain Range
sin(x). All real numbers [-1, 1]
cos(x). All real numbers [-1, 1]
tan(x). {x| x ≠ -3•π/2, -π/2, π/2, } R
The domain and range of the inverse sine, cosine, and tangent are;
Function Domain Range
arcsin(x). (-1, 1) [-π/2, π/2]
arccos(x). (-1, 1) [0, π]
arctan(x) (-∞, ∞). [-π/2, π/2]
What are the domains and ranges of the trigonometric functions?sin(x)
The domain of sin(x) is the set of possible values for x, for which sin(x) is defined, which is;
All real numbers.The range of sin(x) is the set of possible values output values of sin(x) is, which is; -1 ≤ sin(x) ≤ 1
The range is therefore; [-1, 1]cos(x)
Similarly;
The domain of cos(x) is the set of all real numbersThe range of cos(x) is; -1 ≤ cos(x) ≤ 1tan(x)
tan(x) = sin(x)/cos(x), however, cos(x) = 0, when x = -3•π/2, -π/2, π/2, 3•π/2...
The domain of tan(x) is therefore;
{x| x ≠ -3•π/2, -π/2, π/2, 3•π/2...}sin(x) increases as cos(x) decreases, therefore;
The range of tan(x) = sin(x)/cos(x) is therefore;
-∞ < tan(x) < ∞ which is {-∞, ∞}arcsin(x)
The input of arcsin(x) is sin(x)
sin(x) = opposite/hypotenuse
Given that the magnitude of hypotenuse > opposite, the ratio, opposite/hypotenuse is < 1 in magnitude
The domain of arcsin(x) is therefore;
-1 < sin(x) < 1, which is (-1, 1)The range is the set of possible outputs, which is [-π/2, π/2], given that sin(x) is positive and negative from -π/2, π/2
The range is [-π/2, π/2]arccos(x)
Similarly;
The domain of arccos (x) is (-1, 1) The range is [0, π]arctan(x)
The input of arctan(x) is tan(x)
tan(x) = sin(x)/cos(x)
The domain of arctan(x) is therefore;
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\Which set does not contain –3?
the set of all real numbers
the set of all integers
the set of all whole numbers
the set of all rational numbers
Answer:
The set of all whole numbers
Step-by-step explanation:
Real numbers, integers, and rational numbers can all contain negative numbers. Whole numbers include numbers from 0 and up.
Hope this helps!
Have a nice day
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Triangle DEF has vertices D(-2, -1), E(0, 1), and F(1, -3). Graph the
triangle and its image after a dilation with a scale factor of 3.
The image after a dilation with a scale factor of 3 is A(-6, -3), B(0, 3), and C(3, -9) of triangle ABC.
Here, the coordinates are,
D = (-2, -1)
E = (0 , 1)
F = (1, -3)
After dilating triangle DEF using a scale factor of 3 and a center of dilation at the origin to form triangle ABC.
A = (-2 x 3, -1 x 3) = (-6, -3)
B = (0 x 3, 1 x 3) = (0, 3)
C = (1 x 3, -3 x 3) = (3, -9)
Line segments,
AB = 8.48
BC = 12.36
CD = 10.81
Therefore, after dilation by using a scale factor of 3 is A(-6, -3), B(0, 3), and C(3, -9).
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Which is the solution set of the inequality 15y - 9 < 36?
A. y > 9/5
B. y < 9/5
C. y > 3
D. y < 3
Answer:
D
Step-by-step explanation:
y < 3
Two pounds of grapes cost `\$5`. jordan says that's `2.5` pounds per dollar. emika says it's `0.4` pounds per dollar. which rate is correct?
The rate of grapes said by Emika i.e., 0.4 pounds per dollar is the correct rate.
We know that the rate is nothing but the ratio of two different quantities which have different units.
In this question, we have been given two pounds of grapes cost $5
First we find the rate in pounds per dollar.
2 pounds of grapes = $5
As rate is the ratio of two different quantities, we find the ratio (pounds per dollar).
= 2 pounds /5 dollars
= (2/5) pounds per dollar
= 0.4 pounds per dollar .......(1)
This means the rate of grapes is 0.4 pounds per dollar.
In this question, we have been given Jordan says that's 2.5 pounds per dollar and Emika says it's 0.4 pounds per dollar.
From (1), we can clearly say that Emika is correct.
Therefore, the rate of grapes said by Emika i.e., 0.4 pounds per dollar is the correct rate.
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248 miners need to ride the elevator to the bottom of the mine. The elevator can hold 9 miners at a time. How many miners will be in the elevator on its last trip?
write a two-column proof to verity each conjecture. If -3r+1/2= 4 the r=-7/6
If -3r + 1/2 = 4, then it is true that r=-7/6
How to write a two-column proof to verity each conjecture?The equation is given as:
-3r + 1/2 = 4
And the solution is given as
r=-7/6
The two-column proof is as follows:
-3r + 1/2 = 4 ---- Given-3r = 4 - 1/2 ----- Subtract property of equation-3r = 3 1/2 ----- Subtract property of equation-3r = 7/2 ----- Convert to improper fractionr = -7/6 ----- Division property of equationHence, if -3r + 1/2 = 4, then it is true that r=-7/6
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simplify three square root of five end root minus two square root of seven end root plus square root of forty five end root minus square root of twenty eight. (1 point)
The expression is simplified to 6√5 - 4√7
How to simplify the expressionFrom the information given, we have that;
[tex]3\sqrt{5} - 2\sqrt{7} + \sqrt{45} - \sqrt{28}[/tex]
Let's find the surd forms with perfect squares and add into the formula
3√5 - 2√7 + √9 ×5 - √7× 4
Find the perfect squares of the expression
3√5 - 2√7 + 3√5 - 2√7
collect like terms
3√5 + 3√5 - 2√7 - 2√7
Add like terms
6√5 - 4√7
Thus, the expression is simplified to 6√5 - 4√7
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A large polymeric molecule that is nonpolar over most of its structure but very polar at one end:_____.
A large polymeric molecule that is nonpolar over most of its structure but very polar at one end DNA and Phospholipid.
DNA and phospholipid were two examples of huge polymeric molecules that would be polar solely on a single end although nonpolar on the majority of their structure, as opposed to the other alternatives, which would be all monomeric compounds. Nucleotides are used to help DNA create its polymeric structure. Phosphodiester linkage aids in the arrangement of the nucleotides.
The polar molecule would only be found in one area of the vast strand-like polymeric structure. At one extremity of the strand, there is a polar phosphate link; with its assistance, some other monomeric units were joined, generating the phosphodiester bonds. Two fatty acids and the first molecule of glycerol work together to generate the structure known as the phosphodiester.
The phosphate group is present in the polar head region of the phosphate group. This help in the polarity of the phospholipid structure making the head region of the polymeric molecule hydrophilic.
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b. a quality control randomly selects two of five parts to test for defects. in a group of five parts, how many combinations of two parts can be selected?
10 combinations of two parts can be selected.
Combination is defined as the number of arrangements in a collection of items where the order of selection does not matter.
denoted by C(n,x)= ⁿcₓ=[tex]\frac{n!}{(x!)(n-x)!}[/tex] ,
where n is the total number of elements in the set.
x is the number of selected objects.
According to the Question
Total number of elements = 5 = n
Number of objects to be selected = 2 = x
Substituting the values in the above formula
C(5,2)=[tex]\frac{5!}{2!*3!}[/tex]
[tex]=\frac{5*4*3!}{2*3!} \\ \\ =\frac{20}{2} \\ \\ =10[/tex]
Therefore , 10 combinations of two parts can be selected.
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Cam someone help plss
Answer:
let y=0
3x+6(0)=18
3x=18
x=6
(6;0)
Answer: 3
Step-by-step explanation: If you solve the equation, like I did in the attached image, you will see that the x-intercept is 3.
11. The circlex²+y² = 26 and the line y = x + 4 meet at two points P and Q
a) show that the x co-ordinates of P and Q satisfy the equation x² + 4x-5=0
b) hence find the co-ordinates of P and Q
a)The x co-ordinates of P and Q satisfy the equation x² + 4x - 5 = 0.
b)The co-ordinates of P and Q are (-5, -1) and Q = (1, 5).
What is defined as the equation of the circle?(x-h)² + (y-k)² = r² is the equation for a circle with (h, k) center and r radius. This is the equation's standard form. Thereby, if we recognise the coordinates of the circle's center and radius, we can usually find its equation.The given equation of the circle is;
x² + y² = 26.
Th circle satisfies the line y = x + 4.
Thus, Put the value of y in the main equation.
x² + (x + 4)² = 26.
Simplify the equation;
x² + x² + 16 + 8x = 26
2x² + 8x - 10 = 0
Divide the equation by 2.
x² + 4x - 5 = 0
Part a: This shows that x co-ordinates of P and Q satisfy the equation x² + 4x - 5 = 0.
Part b: Now, do the factorization of x² + 4x - 5 = 0.
(x + 5)(x - 1) = 0
x = -5 and 1.
For x = -5; y = -1
Point P = (-5, -1)
For x = 1; y = 5
Point Q = (1, 5)
Thus, the requires points P and Q are obtained.
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2(2x + 3) + 5x + 1 = -11
Answer:
-2
Step-by-step explanation:
2(2x + 3) + 5x + 1 = -11
x = -2
2(2× +3) + 5× +1 = -11
Multiply the 2 to what is in the bracket
4×+ 6 + 5× +1 = -11
Group liketerms
4× + 5× = -11 - 1 -6
simply it
9× = - 18
we will divide them by the co-efficient of ×
9× = - 18
________
9 9
x = - 2
PLEASE HELP ASAP! Solve the system of equations by graphing on your own paper. Write the solution as an ordered pair (x, y)
y=2x+1
y=4x-5
Answer:
Step-by-step explanation:
its 6 2 + 5 = 9-2 = 6
The length of a bacterial cell is about 5 x 10−6 m, and the length of an amoeba cell is about 3.5 x 10−4 m. how many times smaller is the bacterial cell than the amoeba cell? write the final answer in scientific notation with the correct number of significant digits. 1.4 x 101 7 x 101 143 x 101 7 x 103
The bacterial cell is about 7 × 10^(1) times smaller than the amoeba cell in scientific notations.
What are scientific notations?
Scientific notations are a way of representing either a very small or a very large number in the powers of 10. Scientific notations comprise digits from 1 to 9 with powers of 10.
Calculation of the amount by which a bacterial cell is smaller than the amoeba cell
Given the length of amoeba cell in scientific notations is 3.5 × 10^(- 4)
The length of a bacterial cell in scientific notations is 5 × 10^(- 6)
To obtain how small the bacterial cell is from the amoeba cell, we need to divide both the lengths i.e.
= 3.5 × 10^(- 4) / 5 × 10^(- 6)
= 0.7 × 10^(2)
= 7 × 10^(1)
Hence, the bacterial cell is about 7 × 10^(1) times smaller than the amoeba cell in scientific notations.
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Todd wants to make a cheesecake for a birthday party. The recipe calls for a 9-inch diameter round pan. Todd only has square pans. He has an 8 -inch square pan, a 9-inch square pan, and a 10 -inch square pan. Which pan comes closest in area to the one that the recipe suggests?
The pan that comes closest in area is the 8-inch square pan.
What pan comes closest?A circle is a bounded figure which points from its center to its circumference is equidistant.
Area of a circle = πr²
Where :
π = pi = 22/7
R = radius = diameter / 2 = 9/2 = 4.5 inches
22/7 x 4.5² = 63.64 in²
A square is a quadrilateral with four equal sides.
Area of a square = length²
8² = 64 in²
9² = 81 in²
10² = 100 in²
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ILL GIVE BRAINLIEST !!!!!!
Answer:
See explanation
Step-by-step explanation:
a. [tex]\sqrt{49}[/tex]=7
b. 0, [tex]\sqrt{49}[/tex] ==> 0 is a whole number, not a natural number
c. -9, 0, [tex]\sqrt{49}[/tex]
d. -9, -3/7, 0, 0.25, 6.7, [tex]\sqrt{49}[/tex]
e. [tex]\sqrt{2}[/tex] since it has an infinite number of digits and can't be given as a ratio of two integers.
f. -9, -3/7, 0, 0.25, [tex]\sqrt{2}[/tex], 6.7, [tex]\sqrt{49}[/tex] ==> Real numbers consist of both rational and irrational numbers
Which statement about the product is true? (1 point)
5.643 x 4.6
O The product is irrational.
The product is neither rational nor irrational.
O The nature of the product cannot be determined.
O The product is rational.
Answer:
The product is rational.
Step-by-step explanation:
609+283+97 pls help help helpp
Answer:
989
Step-by-step explanation:
Answer:
986
DO NOT HAVE A GOOD DAYHAVE A GREAT DAYThe height, in meters, of a machine piston can be modeled by the regression equation y = 4.4sin(0.4x -1.7) +2.3,
where x represents time, in seconds.
To the nearest tenth of a meter, what is the height of the piston after 10 seconds?
O 1.6 m
O 25m
O 3.3 m
O
5.6 m
The height of the machine piston after 10 seconds is 2. 5m . Option B
How to determine the value
Given the function;
y = 4.4 sin (0.4x -1.7) +2.3,
Where;
x represents time in secondsy is the height of the machine pistonGiven x as 10 seconds
y = 4. 4 sin ( 0.4(10) - 1. 7) + 2. 3
y = 4. 4 sin ( 4 - 1. 7) + 2. 3
y = 4. 4 sin (2. 3) + 2. 3
y = 4. 4(0. 04013) + 2. 3
y = 2. 47
y = 2. 5 meters in the nearest tenth
Thus, the height of the machine piston after 10 seconds is 2. 5m . Option B
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Answer:
D. 5.6 m
Step-by-step explanation:
Use your context clues.
All the other answers had O, like an X, so I put D, which was correct. *Wink*
The following table presents the time taken to review articles that were submitted for publication to a particular journal during a recent year. A few articles took longer than 6 months to review; these are omitted from the table. Consider the data to be a population.
A) Variance = 10.24
B) Standard Deviation = 3.2
One of the measurements of dispersion is the standard deviation, which is exclusively used for quantitative data. It aids in determining if the data's mean is a suitable measurement to reflect the core value.
TIME FREQUENCY(f) MIDPOINT(x) d d² fd fd²
0 - 0.9 43 0.45 -3 9 -129 387
1.0 - 1.9 17 1.45 -2 4 -34 68
2.0 - 2.9 19 2.45 -1 1 -19 19
3.0 - 3.9 18 3.45 0 0 0 0
4.0 - 4.9 14 4.45 1 1 14 14
5.0 -5.9 16 5.45 2 4 32 64
∑f = 127
∑fd = -136
∑fd² = 552
[tex]d = \frac{x - 3.45}{1}[/tex]
Standard Deviation = [tex]\sqrt \frac{fd^{2} }{N} - \sqrt \frac{(fd)^{2} }{N} * i[/tex]
[tex]\sqrt \frac{552}{127} -\sqrt (\frac{-136}{127})^{2} * 1[/tex]
√4.35 - √1.15
Standard Deviation = 3.2
(SD)² = (3.2)² = 10.24
Variance = 10.24
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Explain why (4) × (-5) = 20. Use patterns, an example from the Integer Game, or the properties of operations to support your reasoning.
Multiplying (-4) × (-5) we get 20. Here is the reason.
There are a few properties of integers which determine its operations. These principles or properties help us to solve many equations. To recall, integers are any positive or negative numbers, including zero. Properties of these integers will help to simplify and answer a series of operations on integers quickly.
All properties and identities for addition, subtraction, multiplication and division of numbers are also applicable to all the integers. Integers include the set of positive numbers, zero and negative numbers which are denoted with the letter Z.
Z= ( -5, -4,-3,-2,-1,0,1,2,3,4,5)
Integers have 5 main properties of operation which are:
Closure Property
Associative Property
Commutative Property
Distributive Property
Identity Property
While doing multiplication we use the following rules:
Minus multiply plus= minusMinus multiply minus= plusPlus multiply minus = minusPlus multiply plus = plusSo using second rule we can write (-4×-5)= 20.
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Here is the histogram of a data distribution.
What is the shape of this distribution?
O A. Unimodal skewed
• B. Bimodal symmetric
• C. Unimodal symmetric
• D. Bimodal skewed
O E. Uniform
Answer: your answer would be unimodal skewed. This graph only has one maxima, thus it can't be bimodal. However, it's not symmetric, meaning that it is skewed
Hope this helps you
Step-by-step explanation:
The histogram is solved and it is uni-modal skewed
What is Histogram?A graph called a histogram is used to show the frequency distribution of a small number of data points for a single variable.
A histogram displays the frequency distribution of a set of continuous data. It is useful for visualizing the shape of the data distribution, such as whether it is symmetrical or skewed, and identifying any outliers or gaps in the data.
Given data ,
Let the histogram be represented as A
Now , the value of A is plotted on the graph
A. Unimodal skewed: This distribution has one peak (mode) and the tail of the distribution extends to one side. Depending on which side the tail is longer, it can be either positively skewed (tail extends to the right) or negatively skewed (tail extends to the left).
B. Bimodal symmetric: This distribution has two distinct peaks (modes) and is symmetric, meaning the left and right sides of the distribution are roughly mirror images of each other.
C. Unimodal symmetric: This distribution has one peak (mode) and is roughly symmetric, meaning the left and right sides of the distribution are roughly mirror images of each other.
D. Bimodal skewed: This distribution has two distinct peaks (modes) and the tail of the distribution extends to one side for each peak. Depending on which side each tail is longer, it can be either positively skewed (tail of one peak extends to the right and the other to the left) or negatively skewed (tail of one peak extends to the left and the other to the right).
E. Uniform: This distribution is flat and has roughly equal frequency for all values in the range of the dataset.
Hence , the histogram is unimodal skewed
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-4b+5=-27 is what because i have no idea
Answer:
b=8
Step-by-step explanation:
-4b + 5 = -27
Move the 5 to the right side by subtraction, subtract five from the right side as well.
Now you should have:
-4b = -32
Now divide by -4 to get ‘b’ isolated, do this on both sides.
You should be left with:
b=8
Evaluate the function h(x) =13-x when x=-3,0, and 8
Answer:
16, 13, 5
Step-by-step explanation:
h(-3)=13-(-3)
h(-3)=13+3
h(-3)=16
h(0)=13-(0)
h(0)=13
h(8)=13-(8)
h(8)=5
Hope this helps.
She pays a total of $59.53. She pays a total of $6.49 for the ice cream. She buys 8 bags of oranges that each cost the same amount.
Answer:
price of oranges is 6.63
Step-by-step explanation:
1)59.53-6.49=53.04
2) 53.04/8=6.63
Solve for x. Please show work.
2x + 6 = -3x - 14
A) 16 Miss Violet was in the cafeteria.
B) -16 Mrs. Teal was in the library.
C) 3.2 Mr. Brown was in the auditorium.
D) -4 Ms. Ivory was in the student center.
E) 4 Prof. Gray was in the library.
Answer:
D
Step-by-step explanation:
2x+6=-3x-14
2x+3x=-14-6
5x=-20
x=-4
Answer:
X = -4
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
I need help I’m confused please, anyone?
Answer:
-2.
Step-by-step explanation:
x = 0 where the line passes through the y axis.
So, from the diagram we see that at x = 0, f(x) = -2.
What is the first step to solving
the following equation?
3(3x 8) = 4x+6
Is it Combine Like Terms
Subtraction Property of Equality
Or
Distribution Property
Division Property of Equality