Answer:
When the terminal side is in the first quadrant (angles from 0° to 90°), our reference angle is the same as our given angle. This makes sense, since all the angles in the first quadrant are less than 90°. So, if our given angle is 33°, then its reference angle is also 33°.
When the terminal side is in the second quadrant (angles from 90° to 180°), our reference angle is 180° minus our given angle. So, if our given angle is 110°, then its reference angle is 180° – 110° = 70°.
When the terminal side is in the third quadrant (angles from 180° to 270°), our reference angle is our given angle minus 180°. So, if our given angle is 214°, then its reference angle is 214° – 180° = 34°.
When the terminal side is in the fourth quadrant (angles from 270° to 360°), our reference angle is 360° minus our given angle. So, if our given angle is 332°, then its reference angle is 360° – 332° = 28°.
find last years salary if after a 2% pay raise this years salary is $40,290
Answer:
2/100*40290
=805.8
40290 - 805.8
=$39484. 2
Write fraction that represents the parts shaded red (indicated by "R*) in the figure shown below.
R
R
R
R
R
W
R
R
W
The fraction that represents the parts shaded red (indicated by "R*) is 7/9
How to write the fraction that represents the parts shaded red (indicated by "R*)?The figure is represented by the following list of characters
RRRRRWRRW
In the above list of characters, we have
n(R) = 7
Total = 9
The fraction that represents the parts shaded red (indicated by "R*) is then calculated as
Fraction = n(R)/Total
So, we have
Fraction = 7/9
Hence, the fraction that represents the parts shaded red (indicated by "R*) is 7/9
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how do we write repeated multiplication as powers and how do we evaluate powers
Answer:
[tex]5 { \\ }^{2} [/tex]
Step-by-step explanation:
exponents are ways to write multiplication powers 5
[tex]5 {}^{2} [/tex]
= 5×5 = 25
Answer:
the exponent signifies the number of times the base is a factorpowers can be evaluated by performing the multiplicationsStep-by-step explanation:
You want to know how multiplication and powers are related, and how powers can be evaluated.
Repeated additionYou may be familiar with the fact that a coefficient is used to signify repeated addition:
y + y + y + y = 4y
The coefficient of 4 in 4y signifies that y is in the sum that many times.
Repeated multiplicationAn exponent is used to signify repeated multiplication:
y × y × y × y = y⁴ . . . . y to the fourth power
The exponent of 4 signifies that y is a factor in the product that many times.
In typeset text, the exponent is rendered in a superscript font. In plain text, the exponent (power) is identified using a caret (^):
y⁴ = y^4
Rules of exponentsThe rules of exponents derive from the idea of exponents signifying repeated multiplication:
[tex](x\cdot x)=x^2\\(x\cdot x\cdot x)=x^3\\(x\cdot x)\cdot(x\cdot x\cdot x)=(x\cdot x\cdot x\cdot x\cdot x)\ \Longrightarrow\ x^2\cdot x^3=x^{2+3}=x^5[/tex]
Division has a similar rule.
[tex]\dfrac{(x\cdot x\cdot x\cdot x\cdot x)}{(x\cdot x)}=(x\cdot x\cdot x)\ \Longrightarrow\ \dfrac{x^5}{x^2}=x^{5-2}=x^3[/tex]
This supports the idea that a positive exponent in the denominator is the same as a negative exponent in the numerator, and vice versa.
Evaluating powersPowers can be evaluated in a straightforward way by carrying out the multiplications.
In general, the number of significant digits in the result will be the product of the exponent and the number of significant digits in the base.
For example, 9.2^5 could be expected to have 2×5 = 10 significant digits:
9.2^5 = 9.2×9.2×9.2×9.2×9.2 = 65,908.15232
Most calculators are limited to 12 digits or less, and most spreadsheets are limited to 16 digits or less. Some special-purpose calculators have "variable" precision, so are able to properly render higher powers of numbers with more than 1 or 2 significant digits.
A calculator may use any of several techniques for evaluating powers. Among them might be ...
logarithmsrepeated squaring.LogarithmsLogarithms turn a power problem into a multiplication problem:
log(9.2^5) = 5·log(9.2)
Of course, once the logarithm is found, the issue of evaluating powers comes back:
9.2^5 = 10^(5×log(9.2)) ≈ 10^(4.818939136727776)
Fortunately, there are methods of evaluating antilogs that simplify this part of raising to a power. The difficulty is that precision may be lost. Here, using the rounded value 10^(4.81893913673) gives the result 65,908.152320337..., which is in error after the 10th digit.
Repeated squaringAn integer power can be written as a sum of powers of 2. For example, ...
37 = 32 +4 +1 = (8 +1)4 +1
Then ...
9.2^37 = (((((9.2^2)^2)^2 · 9.2)^2)^2) · 9.2
This requires only 7 multiplications, not 36
__
Additional comment
Only the first token after the caret is considered to be the exponent:
y^4x = (y^4)(x) . . . . . the first token is 4
y^1/2 = (y^1)/2 = y/2 . . . . the first token is 1
If the exponent has multiple parts, they should be enclosed in parentheses:
[tex]y^{3x+1}[/tex]
will be written in plain text as ...
y^(3x+1)
and ...
y^(1/2) = √y
You also need to be careful writing multiple exponents using the caret symbol. Parentheses are usually required. The Order of Operations has you evaluate multiple exponents right to left.
3^4^5 = 3^(4^5) = 3^1024
(3^4)^5 = 3^20
Solve the system of equations by graphing.
x+y=-7
4x+1=19
Answer: look at the graph below
Step-by-step explanation:
Consider the given system of equation
x + y = -7 ........(1)
4x + y = 19 ..........(2)
Consider the equation (1)
x + y = -7
We first find different values of x and y that satisfies (1),
1) x = 1 , y = -7-1 = -8
We get one point as (1,-8)
2) x= 2 , y = -7 -2 = -9
We get point as (2 ,-9)
3) x = 0 , y = -7
We get point as (0 ,-7)
Similarly, find different values of x and y that satisfies (2),
4x + y = 19
1) x = 2 , y = 19 - 8 = 11
We get point as (0,11)
2) x= 3 , y = 19 - 12 = 7
We get point as (3 , 7)
3) x= 4 , y = 19 - 16 = 3
We get point as (4 ,3)
Now , we plot these point on the graph paper, we obtained graph as, (as attached below)
what is the common fact or 9 12 15 and 18
Answer:
3 is the common factor
Step-by-step explanation:
3 x 3 =9
3 x 4= 12
3 x 5 =15
3 x 6 =18
hope it helps
Answer:
Factors for 9: 1, 3, and 9
Factors for 12: 1, 2, 3, 4, 6, and 12
Factors for 15: 1, 3, 5, and 15
Prime Factors for 9: 3 and 3
Prime Factors for 12: 2, 2, and 3
Prime Factors for 15: 3 and 5
GCF = 3
Ahmad is loading a pallet with boxes that each
weighs 45 pounds. The pallet can safely
support no more than 900 pounds. How many
boxes can Ahmad safely load onto the pallet?
A square with side lengths of 4 units is translated on
the coordinate plane. One vertex of the image is at (2,
1).
Which ordered pair could represent another vertex of
the image?
Why 6:4 and 18:8 are not equivalent ratios?
The simplest form of the ratios are not the same, hence, the ratios 6:4 and 18:8 are not equivalent ratios
In order to show why the given ratios are not equivalent ratios, we need to express them in their simplest form as shown:
For the ratio of 6:4
6:4 = 6/4
simplify.
= 3/2
= 3×2/2×2
= 3/2
= 3:2
For the ratio of 18:8
18:8 = 18/8
simplify.
= 9/4
= 9×2/4×2
= 9/4
= 9:4
Since the simplest form of the ratios are not the same, hence, the ratios 6:4 and 18:8 are not equivalent ratios.
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PLEASE HELP What are the coordinates of point Q?
(0,3)
(0,-3)
(-3,0)
(3,0)
Answer:
(0, -3)
Step-by-step explanation:
.
2 x 2 x 2 x 2 ( 5.2 - 3.2 ) divided by 4
Answer:
8
Step-by-step explanation:
you first do operation in the brackets and then multiply and then divide:
2*2*2*2*2 / 4 = 8
At a party, a number of guests were served
15 litres of champagne. Each guest had 2
glasses of champagne and each glass held
150 millilitres. Assuming no spillage, how
many guests were at the party?
50 guests were there at the party
One unit means one thing. A unit rate means the ratio of something. Write this rate as a ratio with a denominator of 1. For example, if you run 70 meters in 10 seconds, on average you walk 7 meters in 1 second. Both reporting 70 meters in 10 seconds and 7 meters in 1 second are rates, but 7 meters in 1 second is the unit price. The unitary method is a method of finding the value of one unit and then finding the value of the required number of units.Suppose you go to the market to buy six apples. The trader tells you that he is selling 10 apples for 100 rupees. In this case the apple is the unit and the price of the apple is the value.
Total champagne available = 15 litres
1 litre = 1000 ml
15 litres = 15000 ml
Total = 15000 ml
Each guest had 2 glasses of 150 ml = 300 ml, which means each guest was served 300 ml of champagne
Total no of guests = Total champagne / champagne served to each
= 15000 / 300
= 50
50 guests were there at the party
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a scuba trip costs $80 plus $45 for each diver. write and evaluate an expression to find the total cost for 6 divers
Answer:
$350.00
Step-by-step explanation:
80 + 6(45) = ?
What do we get when we break apart 818+167 using place value?
Which system of inequalities is represented by this graph?
Responses
{y>−2x−4
y≤x+1
{y<−2x−4
y≤x+1
{y<−2x−4
y −2x−4
y
the graphed system of inequalities is:
y > − 2x − 4
y ≤ x + 1
Which is the first option.
Which system of inequalities is represented by the given graph?
On the image in the quesitonw e cans ee the graph of a system of inequalities. There we can see two lines.
One of the lines has a positive slope and we can see that it is a solid line, and we also can see that the region below that line is shaded, so one of the inequalities is of the form:
y ≤ line with positive slope.
The whole opposite happens for the other line, it has a negative slope, it is dashed (so this time we use the symbols > or <) and the region shaded is above the line, so this time we have an inequality of the form:
y > line with negative slope.
Then the system of inequalities is:
y ≤ line with positive slope.
y > line with negative slope.
By looking at the options, the only one with this form is:
y > − 2x − 4
y ≤ x + 1
Which is the first option
Finally, we conclude that the graphed system of inequalities is:
y > − 2x − 4
y ≤ x + 1
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a translation of T2, –7(x, y) is applied to ΔABC, what are the coordinates of B'?
If a translation of T (2, -7) is applied to the triangle ABC as shown in the figure attached hereby for reference, and B (1, 5) gets repositioned to B', then the current coordinates of B' are (3, -2).
As per the question statement, a translation of T (2, -7) is applied to the triangle ABC as shown in the figure attached hereby for reference, and B (1, 5) gets repositioned to B'.
We are required to calculate the coordinates of B'.
To solve this question, we need to know what Translation (a, b) to (x, y) and (-a, -b) to (x, y) means. Translation (a, b) to (x, y) means the abscissa "x" is to be shifted to the right by "a" units while the ordinate "y" is to be shifted to the right by "b" units, i.e., after translation, the new coordinates become [(a + x), (b + x)]. On the other hand, Translation (-a, -b) to (x, y) means the abscissa "x" is to be shifted to the left by "a" units while the ordinate "y" is to be shifted to the left by "b" units, i.e., after translation, the new coordinates become [(a - x), (b - x)].
Here, as per the above mentioned concept, a translation of T (2, -7) if applied to the point B (1, 5), the new point B' will be at [tex][(1+2), (5+(-7)]=[3, (-2)][/tex].
Translation: In Coordinate Geometry, a translation is a repositioning of a point or a figure from one location to another location without changing its size, shape or orientation.Coordinates: The coordinates of a point are a pair of numbers that define its exact location on a two-dimensional coordinate plane by using the horizontal and vertical distances from the two reference axesTo learn more about Translation, click on the link below.
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Answer: D (3,-12)
Step-by-step explanation:
If a car rolled down a 25 meter ramp, continued rolling another 20 meters at the bottom, then reversed and went back to the top of the ramp, what is the car's displacement? What is the car's distance traveled? Explain.
The car's displacement according to the description given is; 0 meters while it's distance travelled is; 90 meters.
What is the difference between displacement and distance?It follows from definition that, displacement which is a vector quantity is a measure of the change in position of a body after undergoing motion while the distance travelled which is a measure of magnitude only (scalar) is a measure of the space covered over the course of time.
Hence, the displacement is zero as the start position is same as the end position.
Also, the distance is the space covered= 25 +20 +20 +25 = 90 meters.
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how to construct a population data set for which N=6 u=5
A population with 6 elements and mean 5 is given by:
4, 4, 5, 5, 6, 6
What is the mean?The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations.
Hence, for this problem, we need 6 observations which add to 30, hence one possible population is:
4, 4, 5, 5, 6, 6
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PLEASE HELP ME I WILL GIVE YOU 100 POINT PLEASE HELP AND MARK BRAINLETS AND STOP REPORTING ME I ALREADY LOST 100 POINTS
The graphs of the functions and relations gives;
4. The graph of y(x) = x² represents a function and the graph of y² = x represents a relation
5. In equation, y² = x, the value x = 9, gives two y–values y = 3 or -3, therefore y² = x is a relation rather than a function.
6. The domain and range are both [-8, 8]
7. From the equation,x = √(8 - y²), each x– value gives two y–values, therefore x² + y² = 8 is a relation not a function
What are the functions and relations?The given equations of the graphs are;
y(x) = x²y² = xWhere;
x = The input or independent variable
y = The output or dependent variable
In a function each input or value of x can give only one output or value of y, such that a vertical line drawn from each x–value crosses the graph only once.
Therefore;
The graph of y(x) = x², represent a function, given the each x–value has only one y–value, or the value of x determines the y–value.
The graph of y² = x represents a relation given that one x–value can give two y–values (a vertical line drawn at a point, x > 0, crosses the graph twice.
5. Let 9 represent the value chosen from the domain of both y(x) = x² and y² = x, we have;
y(9) = 9² = 81
Therefore, the x–value, x = 9 has only one y–value, which is 89Therefore, the equation, y(x) = x² is a function
In the relation, y² = x, we have;
y² = 9
y = ±3
Therefore, when x = 9, y = 3, or y = -3, which are two outputs or y–value for one input or x–value.
Which makes y² = x a relation rather than a function.
6. The equation of the graph is the equation of a circle, x² + y² = 8
Where;
8 = The square of the radius of the circle
(h, k) = (0, 0), the center of the circle is at the origin.
Therefore;
The coordinates of the edges of the circle on the x–axis are;
(-√8, 0), and (√8, 0)
The domain is therefore [-8, 8]
Similarly, the range, which are the possible y–values is also [-8, 8]
7. The equation x² + y² = 8, and therefore, the graph is not a function given that we have;
x² + y² = 8x = √(8 - y²)Given that y²y(x) = x²is always positive, each x - value gives two y-values, which does not conform with the mapping relationship of a function
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I need help with this question
Answer:
(-5, 5)
Step-by-step explanation:
The function increases from x = -11 to x = -5.
The function decreases from x = -5 to x = 5.
the function increases from x = 5 to x = 11.
Answer: (-5, 5)
Solve F(x)=2x²+3x+5
Help please, very difficult.
Answer:
No Solution
Step-by-step explanation:
Find the circumference and area of the figure If each unit on the graph measures 1 centimeter. Round answers to the nearest tenth, If necessary.
The circumference and area of the circular figure as given in the task content are; 31.4 and 78.5 respectively.
What is the circumference and area of the figure?Since each unit on the graph measures one centimeter, it follows that the radius of the circle which is described by line PQ can be determined as; 5units = 5 centimetres.
On this note, the circumference of the figure; 2πr = 2 × 3.14 × 5
Circumference = 31.4 cm.
Also, the area of the circle in discuss can be determined from; πr² = 3.14 × 5²
Area = 3.14 × 25
Area = 78.5cm²
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Find the sum..
7/4 − (−1/2)
Please Help! I need it now!
Answer:
1.25
Step-by-step explanation:
Answer:1.25
Step-by-step explanation:
13[6 squared divided by (5 squared minus 4 squared)+9]
The answer to the given question is 169.
A subfield of mathematics called algebra uses mathematical expressions to depict issues or circumstances. To create a meaningful mathematical expression, variables like x, y, and z are used together with operations like addition, subtraction, multiplication, and division. All branches of mathematics, such as trigonometry, calculus, and coordinate geometry, involve the use of algebra. A simple example of an expression in algebra is 2x + 4 = 8. Algebra deals with symbols, which are linked together using operators It is not just a mathematical concept, but a skill that we all use in our daily lives without even realizing it.These symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations in order to determine their values..
13 * (((6 square) / (( 5 squared ) - (4 square))) + 9)
= 169
Therefore, the correct value of the given question is 169
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Can you figure out the sequence/progression of the circle?
Answer:
i the middle
Step-by-step explanation:
Which of the following equations shows a slope of 5 for the line the equation represents
The equation shows a slope of 5 for the line the equation represents of that given line will be y = 5x:
Given that
slope of the line = 5To find
The equation of lineSo according the question
We have
slope = 5We know that
Slope-intercept form of a line's equation is written as
y = mx+c.Where
The slope of the line is m, andc is the intercept.From question
m = 5 , and c = 0.so the equation of that given line will be
y = 5x + 0 ory = 5xThe equation of that given line will be y = 5xTo learn more about Equation of line please click on the link:
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can someone please help me with this hw question for pre calc
Answer: 15. f(1)=3
16. g(3)=1
Step-by-step explanation:
15. (fog)(1)=
f(g(1))=
f(1)=3
16. (gof)(5)=
g(f(5))=
g(3)=1
Mariam took a taxi from her house to the airport. The taxi company charged a pick-
up fee of $2.90 plus $1.25 per mile. The total fare was $6.65, not including the tip.
Write and solve an equation which can be used to determine m, the number of miles
in the taxi ride.
The equation is 2.90 + 1.25m= 6.65
The number of miles in the taxi ride is 3 miles
How to calculate the number of miles in the taxi ride ?
The airport charged a pick up fee of $2.90
$1.24 was charged per mile
The total fare was $6.65
The equation can be expressed as
2.90 + 1.25m= 6.65
collect the like terms
1.25m= 6.65 - 2.90
1.25m= 3.75
divide by the coefficient of m which is 1.25
m= 3.75/1.25
m= 3
Hence the number of miles of the taxi ride is 3
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When adding and subtracting numbers in Scientific Notation, the powers of the base 10 must be the same exponent so that you have "like terms". When multiplying and dividing numbers in Scientific Notation, you do not have to have the same power of the base 10. You can simply follow the exponent rules for multiplying and dividing with the like base 10. True or False I NEED HELP NOW
Answer:
The answer is true!
Step-by-step explanation
What is the equation solve it
Answer:
12x + 9 = 4x + 7
Group likely terms
12x - 4x = 7 - 9
8x = -2
Now we need to isolate x
Therefore; Divide both side by the coefficient of x thus 8
Hence x = -1/4
Answer:
[tex]x = \bf -\frac{1}{4}[/tex]
Step-by-step explanation:
We are given the following equation:
[tex]12x + 9 = 4x + 7[/tex]
In order to solve this equation, we have to rearrange it to make [tex]x[/tex] the subject of the equation:
[tex]12x + 9 = 4x + 7[/tex]
⇒ [tex]12x + 9 - 4x = 4x + 7 - 4x[/tex] [Subtracting [tex]4x[/tex] from both sides]
⇒ [tex]8x + 9 = 7[/tex]
⇒ [tex]8x + 9 - 9 = 7 - 9[/tex] [Subtracting 9 from both sides]
⇒ [tex]8x = -2[/tex]
⇒ [tex]\frac{8}{8} x = -\frac{2}{8}[/tex] [Dividing both sides by 8]
⇒ [tex]x = -\frac{2}{8}[/tex]
⇒ [tex]x = \bf -\frac{1}{4}[/tex] [Simplifying the fraction]
Brian spent 14 minutes washing the dishes. That was 35% of the total number of minutes he spent doing chores. How many minutes did Brian spend doing chores?