The radius of the circle is
[tex] \sqrt{ {1}^{2} + {( - 3)}^{2} } = \sqrt{10} [/tex]
meaning that
[tex] \sin( \theta ) = \frac{ - 3}{ \sqrt{10} } [/tex]
Thus,
[tex] \csc \theta = - \frac{ \sqrt{10} }{3} [/tex]
The value of csc θ is √10/ (-3).
What is trigonometry?
Trigonometry is a branch of mathematics that studies relationships between the sides and angles of triangles.
As,
(1,−3) is in quadrant 4 and csc is negative.
Using Pythagoras,
H=√ 1² + (-3)²
H= √10
So, cosec θ= H/P
= √10/ (-3)
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What value of k transforms the graph of f(x)=0.5x+3 into graph g? Describe the transformation.
for 7, 8, and 9
Using translation concepts, the values of k are given as follows:
7. k = 3.8. k = -2.9. k = 2.What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
In this problem:
In graph 7, g(x) is a shift up of 3 units of f(x), hence k = 3.In graph 8, g(x) is a shift left of 2 units of f(x), that is, g(x) = f(x + 2), hence k = -2.In graph 9, g(x) is a vertical stretch by a factor of 2 of f(x), that is, g(x) = 2f(x), hence k = 2.More can be learned about translation concepts at https://brainly.com/question/27885240
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Carlita has a swimming pool in her backyard that is rectangular with a length of 26 feet and a width of 14 feet. She wants to install a concrete walkway of width c around the pool. Surrounding the walkway, she wants to have a wood deck that extends w feet on all sides. Find an expression for the perimeter of the wood deck.
Lets solve the question,
Given dimensions are:
Length = 26 feet
Width = 14 feet
concrete walkway with width = c
After installing the concrete walkway dimensions of the walkway will be,
Length = 26 + 2c
Width = 14 + 2c
She wants to build a wooden deck around the pool with a concrete walkway of width = w
Thus the dimensions of the wooden deck around the pool will be,
Length = [tex]26 + 2c + 2w[/tex]
Width = [tex]14 + 2c + 2w[/tex]
Now the perimeter of the wooden deck will be,
Perimeter = 2(length + width)
[tex]= 2[(26 +2c + 2w) + 2(14 + 2c + 2w)] = 2(40 + 4c + 4w) = (80 + 8c + 8w)[/tex]
Therefore, perimeter of the wooden deck would be: 80 + 8c + 8w
Perimeter = (80 + 8c + 8w)
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What is the product of 4 and 5g + 2.34?
The product of 4 and 5g + 2.34 is 20g + 9.36
How to determine the product?The expressions are given as:
4 and 5g + 2.34
As a product expression, we have:
4 * (5g + 2.34)
Evaluate the product
20g + 9.36
Hence, the product of 4 and 5g + 2.34 is 20g + 9.36
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The sum of ages of Clayman and Ato is 25 years. In five years' time, the age of Ato will twice the age of Clayman now. a. How old is Clayman? b. How old is Ato?
Clayman is 10 years old and Ato is 15 years old
Word problems leading to equationsLet the age of Clayman be x
Let the age of Ato be y
If the sum of ages of Clayman and Ato is 25 years. then;
x + y = 25
x = 25 - y ...... 1
In five years time;
Age of Clayman = x + 5
Age of Ato = y + 5
If in five years' time, the age of Ato will twice the age of Clayman now, then;
y+5 = 2x ............. 2
Substitute equation 1 into 2
y +5 = 2(25-y)
y + 5 = 2(30 - y)
y + 5 = 50 - 2y
3y = 45
y = 15
Since x + y = 25
x = 25 - 15
x = 10
Therefore Clayman is 10 years old and Ato is 15 years old
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insert one rational number between 5 and 5.25
Answer:
5.1
Step-by-step explanation:
A rational number is any number that can be written as a fraction, or is a decimal that terminates or repeats.
Find the value of $x$ that satisfies $\frac{1}{3x-1} = \frac{2}{x+1}$. Can someone please explain this in detail?
The value of x = 3/5 or 0.6 will satisfy the equation given.
What is an Equation ?An equation is a mathematical statement which is formed when two expressions are equated by an equal sign.
It is given that
[tex]\rm \dfrac{1}{3x-1} = \dfrac{2}{x+1}\\[/tex]
It has to be solved and the value of x has to be determined
(x+1) = 2 (3x-1)
x +1 = 6x -2
5x = 3
x = 3/5
Therefore the value of x = 3/5 or 0.6 will satisfy the equation given.
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Find the tables with unit rates greater than the unit rate in the graph then arrange these tables in order from least to greatest unit rate
Table 3,4,5,6,7 has a greater value of the unit rate than the unit rate of the graph.
What is a graph?A diagram depicting the relationship between two or more variables, each measured along with one of a pair of axes at right angles.
The unit rate of the graph is;
[tex]r_g = \frac{26-0}{14-0} \\\\ r_g = \frac{13}{7} \\\\ r_g = 1.857[/tex]
The unit rate for the given tables;
[tex]\rm r_1 = \frac{26-13}{14-7}\\\\ r_1 = \frac{13}{7} \\\\ r_1 = 1.857[/tex]
[tex]\rm r_2 = \frac{26-13}{14-7} \\\\ r_2 = \frac{9}{5} \\\\ r_2 = 1.8 < 1.818[/tex]
[tex]r_3 = \frac{34-17}{18-9} \\\\r_3 = \frac{17}{9} \\\\ r_3 = 1.889 > 1.818[/tex]
[tex]\rm r_4 = \frac{42-21}{22-11} \\\\ r_4 = \frac{21}{11} \\\\ r_4 = 1.909 > 1.818[/tex]
[tex]\rm r_5 = \frac{38-19}{20-10} \\\\ r_5 = \frac{19}{10}\\\\ r_ 5 = 1.9 > 1.818[/tex]
[tex]\rm r_6 = \frac{50-25}{26-13} \\\\ r_6 = \frac{25}{13} \\\\ r_6 = 1.923 > 1.818[/tex]
[tex]r_ 7 = \frac{46-23}{24-12} \\\\ r_7 = \frac{23}{12} \\\\r_7 = 1.917 > 1.818[/tex]
Hence, table 3,4,5,6,7 has a greater value of the unit rate than the unit rate of the graph.
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What is the measure of m?
m = [?]√
Give your answer in simplest form.
Answer:
[tex]m=4\sqrt{6}[/tex]
Step-by-step explanation:
[tex]n^2 = {8*4}[/tex] (By geometric mean theorem)[tex]\rightarrow n^2={32}[/tex][tex]m=\sqrt{n^2+8^2}[/tex] (By Pythagoras Theorem)[tex]\rightarrow m=\sqrt{32+64}[/tex] [tex]\rightarrow m=\sqrt{96}[/tex] [tex]\rightarrow m=4\sqrt{6}[/tex]Step-by-step explanation:
first find the relation between n,m and x
Members of a soccer team raised $1818.50 to go to a tournament. They rented a bus for $960.50 and budgeted $35.75 per player for meals. Write and solve an equation which can be used to determine p, the number of players the team can bring to the tournament.
The equation formed by the given condition is 960.5 + 35.75p ≤ 1818.50 and the number of players they can bring is a maximum of 24.
How to form an equation?Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.
In other words, an equation is a set of variables that are constrained through a situation or case.
Given that,
The total amount that can be spent = $1818.50
Rent of bus = $960.50
Cost per player = $35.75/player
So,
Cost of bus + Cost per player × number of players ≤ The total amount that can be spent
960.50 + 35.75p ≤ 1818.50
35.75p ≤ 858
p ≤ 24
Hence "The equation formed by the given condition is 960.5 + 35.75p ≤ 1818.50 and the number of players they can bring is a maximum of 24".
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Equation:
Step-by-step explanation:
Question 9 of 30 If f(x) = 3*-¹ + 4 and g(x) = 4x-7, what is (f - g) (x) ? O A. (f - g)(x) = 3*-1 - 4x-11 B. (f - g)(x) = 3*-1 - 4x +11 C. (f - g)(x) = 3*-1 - 4x+3 O D. (f-g)(x) = 3×-¹ - 4x - 3 NEED HELP ASAP
Answer:
I really don't know
Step-by-step explanation:
what is even that
Which graph shows the solution to the system of linear inequalities? Y<2x-5 y>-3+1
Helppppp
Answer:
Is the second expression written correctly? It reduces to y>-2, since no x is in the equation.
Step-by-step explanation:
We can graph the two equations. See attached image. If y>2 is the correct expression, all points to the right.
If the equation was meant to read y=-3x+1, then graph the revised expression.
What is the solution to the linear equation?
8-10-28+7=8+d-10-36
0 d=-5
O d=1
0 d=5
Mark this and retur
Save and Exit
Next
Submit
Answer:
d = 15
Step-by-step explanation:
8 - 10 - 28 + 7 is equal to -23
8 + d - 10 - 36 is equal to -38 + d
if -23 = -38 +d
15 = d
The solution of the equation is d = 15
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The given equation is 8-10-28+7=8+d-10-36
In the equation d is the variable
We have to solve for d
8-10-28+7=8+d-10-36
-23 = -38+d
Add 38 on both sides
-23+38=d
15=d
Hence, the solution of the equation is d = 15
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19.
(05.06 MC)
The scatter plot shows the number of households, in millions, that have cable television over eight consecutive years. Which of the following is an appropriate line of best fit? (1 point)
Considering the given scatter-plot, the line of best-fit is given by:
y = 0.77857t + 3.7.
How to find the equation of the line of best-fit using a calculator?To find the equation, we need to insert the points (t,y) in the calculator.
In this problem, considering the scatter-plot, we have that:
The values of t are: 1, 2, 3, 4, 5, 6, 7.The values of y are: 3.8, 5.8, 6.2, 7.5, 7, 8.2, 9.2.Hence, using the calculator, the equation is:
y = 0.77857t + 3.7.
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Help plssssss I need this today
Answer:1 is exponential. 2 is linear. 3 is neither. 4 is linear. 5 is linear. 6 is exponential. 7a is exponential. I think 7b could be 10x + y = 10 but I'm not too sure. 7c is (8,4).
Step-by-step explanation:1. the coordinates are moving in an exponential way or something im not sure the correct wording but that is what exponential graphs look like. 2 is a straight line so it is linear. 3 is neither because the graph isn't exponential or linear. 4 is linear because the coordinates are subtracting at the same number. 5 is linear for the same reason at 4. 6 is exponential because the coordinates are multiplied by 2 each time. 7a is exponential because the coordinates are divided by 2 each time. 7b I'm not sure on. 7c is 8/4 because August is the 8th month and the month before (7) is 8 so 8 divided by 2 equals 4. So the 8th month would have to be 4. I hope that helps!
Which of the following values are in the range of the function graphed below?
Check all that apply.
first answer gets brainliest need asap!!!
Answer:
1
Step-by-step explanation:
Although you did not give me the answer choices, I believe that the only possible answer is 1 because the only y value the graph is on is 1.
please help!!! picture has the question and answer choices in it
Answer:
5x-y≥ 1
Step-by-step explanation:
Find the slope of the line to be :
y = 5x -1 <===== the shaded area is less than or equal (because it is a SOLID line...not dashed) to this :
y ≤ 5x-1 re-arrange to
5x-y ≥ 1
In which funtion is x=2 mapped to 32?
The function g(x)=4(x+3)² - 68 is mapped to 32.
What is equation?An equation is a mathematical expression in terms of one or more unknown variable.
Given are the following functions:
f(x)= - 3x² - 4
g(x)= 4(x+3)²-68
f(x)= 3x
f(x)= 2x-62
To get the mapped function, we substitute the value of x in all function,
a) f(x)=-3x²- 4
Put x=2,
f(2)= -3 (2)² - 4
f(2)= -16
It is not mapped.
b) g(x)=4(x+3)² - 68
Put x=2,
g(2) = 4(2+3)² - 68
g(x) =32
It is mapped to 32.
c) f(x)=3x
Put x=2,
f(2) = 3 x 2 =6
It is not mapped.
d) f(x)=2x - 62
Put x=2,
f(2) =2x2 -62
f(2) = -58
It is not mapped.
Therefore, the function g(x)=4(x+3)² - 68 is mapped to 32.
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Please help me do the equation and figure out the right solution. I am supposed to be correcting the one in the picture.
Answer:
The correct answer is if you want no roots in the denominator, the correct answer is [tex]\frac{2x}{y}[/tex]* [tex]\sqrt[3]{2y^{2} }[/tex]
Step-by-step explanation:
The mistake is that you can't take a cube root of a square at step 3 when [tex]y^{2}[/tex] is taken out.
Explain please .................
Answer:
See below
Step-by-step explanation:
cos 2pi/3 = -1/2
sin 2pi/3 = sqrt (3)/2
cos 1 pi/6 = sqrt(3)/2
sin 11 pi/6 = - 1/2
so when you put in these values in you will have :
(2*8) * (-1/2 + sqrt (3)/2 i )( sqrt(3)/2) + i (-1/2) )
= 16 ( - sqrt (3)4 + 1/4 i + 3/4 i - sqrt(3)/4 i^2 ) rememember i^2 = - 1
= 16 ( 1/4 i + 3/4 i )
= 16 i
what is the equation of a line that has a slope of -5 and a y intercept of -7
Answer:
y=(-5x)+(-7)
Step-by-step explanation:
The equation for slope is y=mx+b
so you would say -5x as the mx in the equation and -7 as the u intercept.
Hii!
_________________________________________________________
[tex]\rightsquigarrow\circ\boldsymbol{Answer}\circ\leftharpoonup[/tex]
y=-5x-7
[tex]\rightsquigarrow\circ\boldsymbol{Explanation}\circ\leftharpoonup[/tex]
For this question we will use the slope intercept form equation, because we are provided with the slope and the y-intercept.
The slope intercept form equation is [tex]\large\textsf{y=mx+c}[/tex]. In this formula m denotes the slope and c denotes the y-intercept.
Since we have both m and b, we can stick them into the formula. Upon doing this we obtain
[tex]\twoheadrightarrow\sf y=-5x+(-7)[/tex]
[tex]\bullet[/tex] Simplify
[tex]\twoheadrightarrow\sf y=-5x-7[/tex]
[tex]\bullet[/tex] Great job! We found the equation
--
Hope that this helped! Best wishes.
[tex]\textsl{Reach far. Aim high. Dream big.}\\\boldsymbol{-Greetings!-}[/tex]
--
The Rotation maps all 60° about O the center of the regular hexagon. State the image of B for the following rotation. R^3=
F
E
B
B will be at the place of E after all three rotations. So the correct option is B.
What is Rotation?Moving in a circular plane with respect to the fixed point is called as the rotation of the object.
If rotation maps to The three rotations for B will be
The given B after one rotation will shift in place of C
After the second rotation will shift in place of D
After the third rotation will shift in place of E
B will be at the place of E after all three rotations. So the correct option is B.
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kacee spent half of the money in her bank account, then deposited $15 more. if she now has $29, how much did she have begin with.
Answer:
Step-by-step explanation:
Solution
Before she put anything back into her account, she had 29 - 15 = 14 dollars.
She started with 2 * 14 = 28 dollars.
Answer: 28 dollars.
Given right triangle QRS, what is the value of sin(30°)?
The value of sin(30°) is 1/2.
What is Trigonometry?The branch of mathematics concerned with specific functions of angles and their application to calculations.
The diagram is attached below:
We know,
sin 30= Perpendicular/ Hypotenuse.
As, the hypotenuse is the opposite side of the right angle and the perpendicular is opposite to the given angle.
So,
sin 30 = 5/10
sin 30 = 1/2
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Applying the the properties of Congruence.
Quadrilateral GHJK = Quadrilateral LMNP.
Find the given side length or angle measure.
PLEASE HELP NO Scams pleaseeeee !!
Answer:
[tex]LM = 35cm[/tex] and [tex]m \angle H = 98^o[/tex]
Step-by-step explanation:
For this problem, it is critical to understand what the opening statement means.
[tex]Quadrilateral GHJK \cong quadrilateral LMNP[/tex] means that each pair of corresponding sides between shapes are congruent (they have equal length), and each pair of corresponding angles between shapes are congruent (they have equal measure -- or same number of degrees when measured with a protractor).
So, it's important to be able to determine which pairs are the corresponding parts. When the congruence is given like [tex]Quadrilateral GHJK \cong quadrilateral LMNP[/tex] the letters are in a particular order. That order explains the order in which the shape is drawn out, and they put them in the same order for both shapes to mean that those are the letters that correspond with each other.
So, the first letter of each are a corresponding pair, the second letter of each are a corresponding pair, ... etc
In other words, point G and L correspond, point H and K correspond, etc.
Part 1 -- Find LMTo find the corresponding sides, the sides for these shapes are defined by a two adjacent letters (two letters next to each other in the name, or ... as it wraps around the end of the name... the first and last letter).
[tex]\overline{GH} \cong \overline{LM}\\ \overline{HJ} \cong \overline{MN} \\\overline{JK} \cong \overline{NP}\\\overline{KG} \cong \overline{PL}[/tex]
While all of that is true, we only have a few sides with any information in them. Notice that side GH in the first shape, and sides PL & LM in the second shape are the only sides with anything written. So, we just need to determine which sides correspond (and thus, are congruent), so that we know how to move forward. Looking at the list of congruent sides above, we see that [tex]\overline{GH} \cong \overline{LM}[/tex]
Since the sides (line segments) are congruent, their lengths are equal
[tex]GH = LM[/tex]
...so we can substitute the expressions for each angle into the equation and solve for the unknown value "x"
[tex]GH = LM\\(4x+3)=(6x-13)[/tex]
[tex](4x+3)+13=(6x-13)+13\\4x+16=6x[/tex]
[tex](4x+16)-4x=(6x)-4x\\16=2x[/tex]
divide both sides by 2
[tex]\frac{16}{2}=\frac{2x}{2}\\8=x[/tex]
So, to find the length, LM, we just need to look back at the expression for LM:
[tex]LM = 6x-13\\LM = 6(8)-13\\LM = 48-13\\LM = 35[/tex]
remembering that the lengths are measured in centimeters (as indicated on the diagram): [tex]LM = 35cm[/tex]
Part 2 -- Find m∠HTo find the corresponding angles, the angles for these shapes are defined by a single letter, so since the points correspond in order, the names of the shapes tell which angles are congruent.
[tex]\angle G \cong \angle L\\\angle H \cong \angle M\\\angle J \cong \angle N\\\angle K \cong \angle P[/tex]
While all of that is true, we only have a few angles with any information in them. Notice that ∠H in the first shape, and ∠L & ∠M in the second shape are the only angles with anything written. So, we just need to determine which angles correspond (and thus, are congruent), so that we know how to move forward. Looking at the list of congruent angles above, we see that
[tex]\angle H \cong \angle M[/tex]
Since the angles are congruent, their measures are equal
[tex]m\angle H = m\angle M[/tex]
...so we can substitute the expressions for each angle into the equation and solve for the unknown value "y"
[tex]m\angle H = m\angle M\\(9y+17)=(11y-1)[/tex]
subtract 1 from both sides
[tex](9y+17)+1=(11y-1)+1\\9y+18=11y[/tex]
subtract 9y from both sides
[tex]\\(9y+18)-9y=(11y)-9y\\18=2y[/tex]
divide both sides by 2
[tex]\frac{18}{2}=\frac{2y}{2}\\9=y[/tex]
So, to find angle H, we just need to look back at the expression for the measure of angle H:
[tex]m\angle H = 9y+17\\m\angle H = 9(9)+17\\m\angle H = 81+17\\m\angle H = 98[/tex]
remembering that the angle is measured in degrees (as indicated on the diagram): [tex]m \angle H = 98^o[/tex]
Work out, giving your answer in its simplest form:
2/3 x 3 3/5
Answer: 12/5
Step-by-step explanation:
[tex]3 \frac{3}{5}=\frac{18}{5}\\\\\implies \frac{2}{3} \times 3 \frac{3}{5}=\frac{2}{3} \times \frac{18}{5}\\\\=\frac{36}{15}\\\\=\boxed{\frac{12}{5}}[/tex]
please help me its math
The value of f(x) = 3x² - 2x at x = 4 is 40.
What is function?The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x. Mapping or transformation is used to denote a function in math.
Here, the given function;
f(x) = 3x² - 2x
put the value of x = 4, we get
f(4) = 3 X 4² - 2 X 4
f(4) = 3 X 16 - 8
f(4) = 48 - 8
f(4) = 40
Thus, the value of f(x) = 3x² - 2x at x = 4 is 40.
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The equation a^-4= is equal to what?
Answer:
a⁻⁴ = 1/a⁴
Step-by-step explanation:
1/a⁴
Which table represents an arithmetic sequence?
An arithmetic sequence is a sequence of integers with its adjacent terms differing with one common difference. The table that represents an arithmetic sequence is the third table.
What is arithmetic sequence?An arithmetic sequence is a sequence of integers with its adjacent terms differing with one common difference.
The explicit formula for any arithmetic series is given by the formula,
aₓ = a₁ + (x-1)d
where d is the difference and a₁ is the first term of the sequence.
For the table to be in an arithmetic sequence, the difference between any two consecutive terms must be equal.
For the first table, the difference between the first two terms is -6, while for the next two terms it is -12. Thus, it is not an arithmetic sequence.In the second table, the difference between the first two terms is 2 while the difference between the next two terms is 4. Thus, it is not an arithmetic sequence.In the third table, the difference between the first two terms is 1.4, the difference between the next two terms is 1.4. Also, it last two terms the difference is 1.4. Thus, it is an arithmetic sequence.Hence, the table that represents an arithmetic sequence is the third table.
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The difference of a number and 6is the same as 5 times
Answer:
let difference be x
Step-by-step explanation:
you can solve for x by keeping the 2 statesments as conditions.
then you solve for both equations together by adding subtracting or multiplying.
eg: let x be the number.
the. proceed with conditions as equations
then solve
then your answer is here
Expand . ( 3x –2 ) 2 need an answer ASAP.
Answer:
6x - 4
Step-by-step explanation:
For expanding (3x -2) 2 , (3x - 2) is to be multiplied with 2.
(3x - 2) × 2 = 6x - 4
