Using the definition of the secant, the angle is given as follows:
θ = 112.6º.
How to calculate the secant of an angle?The secant of an angle θ is given by one divided by the cosine of the angle θ, that is:
sec(θ) = 1/cos(θ).
In the context of this problem, the numeric value of the secant of the angle is given as follows:
sec(θ) = -13/5.
This means that the following relation can be established:
1/cos(θ) = -13/5.
Hence we can solve to find the angle measure as follows, applying cross multiplication:
-13cos(θ) = 5
cos(θ) = -5/13.
Applying the inverse cosine, we have that:
θ = arccos(-5/13).
θ = 112.6º.
This angle has equivalent on other quadrants, as for example, in the third quadrant the cosine is also negative. However, in the third quadrant, the tangent is positive and we want a negative tangent, which is why the measure is of θ = 112.6º.
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Between 10 P.M. and 7:45 A.M., the water level in a swimming pool decreased by
3/8 in. Assuming that the water level decreased at a constant rate, how much did the water level drop each hour?
Please help asap
The water level drop each hour by 0.0384 inch
Firstly, the deacrease in water level is takes as per the question
Decrease = 3/8 inches
Decrease=0.375 inches
Then the time interval is calculated
From 10 pm to 7:45 hours will be 9.45 hours
Time interval= (9 + 45/60) hours
Time interval=9.75 hours
Now, the drop in water level per hour is determined, to do so, total water level decreased is divided by the time taken to decrease that water level
that is 0.375/9.75 inches/hour
= 0.03846 inches/hour
Therefore, if between 10 P.M. and 7:45 A.M., the water level in a swimming pool decreased by 3/8 inches and the water level decreased at a constant rate, the water level drop each hour is 0.03846
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omar will run at least 28 miles this week, so far he has run 12 miles. What are the possible numbers of additional miles he will run? use t for the number of additional miles he will run white your answer as an inequality solved for t
The inequality that will define Omar's run is 12 + m ≥ 28.
An inequality in algebra is a mathematical statement that employs the inequality symbol to show how two expressions relate to one another. The phrases on either side of an inequality symbol are not equal. The phrase on the left should be larger or smaller than the expression on the right, or vice versa, according to this symbol. Relationships between two algebraic expressions that are represented by the inequality symbols are known as literal inequalities. The relationship is known as an inequality when the symbols ">", "", "", or "" are used to link two real numbers or algebraic expressions.
For this issue, it is said that Omar would run at least 28 miles this week; he may run more, but 28 miles is his minimum objective.
He had already covered 12 miles.
Afterward, the inequality symbol will be "."
The inequality is therefore 12 + m 28.
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HELP PLS DUE TOMORROW
What are the similarities and differences between these two problems?
For example:
Similar: both arithmetic/linear/common difference
Different: #1 is discrete #2 is continuous
WILL GIVE BRAIN
Answer:
Step-by-step explanation:
Similarity:Both equations are linear equations with one variable.
Difference:
Problem1: Linear equation uses discrete variable. Money can be counted.
Problem 2: Linear equation uses continuous variable. water can be measured.
HELP
What is the slope of the line?
Answer: -8/3
Step-by-step explanation:
slope is rise/run or y2-y1/x2-x1
so, the two points are (4,-4), (1,4)
-4-4/4-3= -8/3
find the 1st term, 3rd term and 12th term of series whose nth term is 3n-5/4
Based on the given task content; the first term of the series whose nth term is 3n-5/4 is -1/2.
The 12th term of the series is 7.75How to find the nth term of a series?nth term = (3n - 5) /4
Where,
n = number of termsFirst term, a = (3n - 5) / 4
substitute n = 1 into the equation= (3n - 5) / 4
= {3(1) - 5} / 4
= (3 - 5) / 4
= -2/4
= -1/2
The first term of the series whose nth term is 3n-5/4 is -1/2
When n = 12(3n - 5) / 4
= {3(12) - 5} / 4
= 36 - 5 / 4
= 31/4
= 7.75
Therefore, the 12th term of the series whose nth term is 3n-5/4 is 7.75
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Graph the line -3 with slope (-4,-2) passing through the point
The linear equation of the line that passes through point (-4,-2) and has a slope of -3 is y = -3x - 14.
What is the graph of the line with the given slope and point?The formula for equation of line is expressed as;
y = mx + b
Where m is slope and b is y-intercept.
Given the data in the question;
Point ( -4, -2 )
x = -4y = -2Slope m = -3First we calculate the y-intercept 'b' using the equation of line formula.
y = mx + b
Plug in point ( -4, -2 ) and slope -3.
-2 = -3(-4) + b
-2 = 12 + b
b = -2 - 12
b = -14
Now that we have the values of slope m and y-intercept b, plug these into y = mx + b to determine the equation of the line.
y = mx + b
y = -3(x) + ( -14 )
y = -3x - 14
Therefore, the equation of the line is y = -3x - 14.
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A small container of paint will cover 20,000cm².
Luke wants to paint all the faces of fifty 8cm cubes.
Is one container of paint enough?
One paint container is enough to paint all the faces of fifty 8 cm cubes.
Given
The paint can cover 20,000 [tex]cm^{2}[/tex]
Side of square = 8 cm
As the Total surface area of a cube is [tex]6a^{2}[/tex],
where a is the side of the cube.
The total surface area of one cube = 6 x [tex]8^{2}[/tex]
= 384 [tex]cm^{2}[/tex]
Since there are fifty such cubes,
384 x 50
Total area to be painted = 19200 [tex]cm^{2}[/tex]
Since 19,200 [tex]cm^{2}[/tex] is less than 20,000 [tex]cm^{2}[/tex] , it is possible to paint all the cubes.
Hence one paint container is enough to paint all cubes.
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The midpoint of FG is M(6, 9). One endpoint is F(4, 9). Find the coordinates of the other
endpoint G.
Write the coordinates as decimals or integers.
Answer:
G= (8,9)
Step-by-step explanation:
Write the equation in slope-intercept form:
6x−3y=−18
The equation in slope-intercept form is y = 2x + 6
How to determine the slope-intercept form of the equation?The equation is given as
6x - 3y = -18
The above equation is a linear function, and it is in its general form
To determine the slope-intercept form of the equation, we simply make y the subject of the formula in the equation
So, we have
6x - 3y = -18
Divide through the equation by -3
So, we have
-2x + y = 6
Add 2x to both sides
y = 2x + 6
Hence, the slope-intercept form of the equation is y = 2x + 6
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△PGH is an equilateral, PG=x+5, GH=2x-5 and PH=3x-15. Find the value of x and the perimeter of the triangle.
The value of x is 10
The perimeter of the triangle is 30 units
What is an equilateral triangle?An equilateral triangle can be defined as a triangle which has all its sides equal or congruent to each other.
The properties of an equilateral triangle includes;
From the information given, we have the sides as;
PG=x+5 GH=2x-5 PH=3x-15Since all of its sides are equal, we have to equate two side, we have;
x + 5 = 2x - 5
collect like terms
x - 2x = -5 - 5
subtract the like terms
-x = -10
make 'x' the subject
x = 10
But the perimeter of an equilateral triangle = 3a = 3(10) = 30 units
Thus, the value is 10
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Victoria's car used of a gallon to travel 21 miles. At what rate doesthe car use gas, in miles per gallon?
Answer:
26 1/4 miles per gallon
Explanation:
We are told that the car travels 21 miles per 4/5 gallons. Therefore, the rate at which the car uses the gas is
[tex]\frac{21\text{ miles}}{4/5\text{ miles}}[/tex]which can also be written as (by taking the reciprocal of the denominator)
[tex][/tex]what is 5 + 2 =??? i need to know now
Answer: 5 + 2 = 7
Step-by-step explanation: its easy
What is the area of trapezoid ABCD?
Enter your answer as a decimal or whole number in the box. Do not round at any steps.
units²
Trapezoid A B C D on a coordinate plane with vertex A at negative 3 comma 2, vertex B at 1 comma 5, vertex C at negative 7 comma negative 3, and vertex D at 0 comma negative 2. Angle B is shown to be a right angle.
Given the coordinates above, the area of the trapezoid is approximately 41. See the explanation below.
What is a Trapezoid?A trapezoid is a quadrilateral with at least one set of parallel sides in American and Canadian English. A trapezoid is known as a trapezium in British and other varieties of English.
For the calculation showing the above solution:
Step 1 - Given:
A = (-3,2)
B = (1, 5) = ⊥
C = (-7, -3)
D = (0.-2)
Step 2 - To get the distance between the points we need to use the formula for Distance between two points which is given as:
d=√((x2 – x1)² + (y2 – y1)²).
Distance of Line AB =
√((1 – (-3))² + (5 – 2)²).
= √[(4)² + (3)²]
= √( 16 + 9)
= √25
AB= 5
Repeat this for BC, CD, DA and we'd get the following
BC = 11.313708498985
CD = 7.0710678118655
DA = 5
Step 3 - From the above structure, [see attached] we then apply the formula for the area of a Trapezoid (Trapezium) which is given as:
A = [(a+b)/2] h
Where a = 5
b = 11.313708498985
h = 5
= [(5+11.313708498985)/2] 5
= 40.7842712475
[tex]\approx[/tex] 41
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Which comparison is correct?
A |-3| > |-4|
B |5| > 7
C 7 < |7|
D -5 <-4
Please help!! I need the answer quick as possible thank you!
The comparison of the inequalities that is correct among the given options is; D: -5 < -4
What is the comparison of the absolute values?We want to compare absolute values.
The absolute value (or modulus) | x | of a real number x is the non-negative value of x without regard to its sign. For example, the absolute value of 3 is 3, and the absolute value of −3 is also 3.
The absolute value of a number can also be described as its distance from zero along real number line.
A) |-3| > |-4|; This is incorrect because the absolute value of - 3 is 3 and the absolute value of - 4 is 4 and 4 is greater than 3 not the other way round.
B) Again, this is incorrect as the absolute value of 5 is 5 which is less than 7.
C) This is incorrect with the same reason as above.
D) This is correct because on a number line, - 5 is less than - 4
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An eastbound train and a westbound train meet each other on parallel tracks heading in opposite directions. The eastbound train travels 18 miles per hour faster than the westbound train. After 2.5 hours, they are 280 miles apart. At what speeds are the two trains traveling?
Answer: The eastbound train is traveling at 65mph while the westbound train travels at 47mph.
Step-by-step explanation:
You would use x as the variable for the speed of the westbound train. The eastbound train would be 18+x. your equation would be 2.5(18+x+x)=280
You would find that x=47 for the westbound train. You would then add 18 to get the speed of the eastbound train which would be 65.
can a percent of change be greater than 100%?
What is the ratio of the two quantities? 17 seconds to 7 min HELP PLSS WILL BE BRAINLYEST
Answer:
17 : 420
Step-by-step explanation:
Ratio of two quantities:When finding the ratio of two quantities, both quantities should be in same type.
Convert 7 minutes to seconds.
7minutes = 7 * 60
= 420 seconds
17 seconds : 7 minutes = 17 : 420
What is the domain of this relation?
Answer:
(-5, -3, 1, 2, 3) .... the fourth one
Step-by-step explanation:
the domain is all the x values.
so look at your points and look at the x values ( the number on the X-axis) for those points!
If the perimeter of the rectangle is 46, what is the value of x?
Answer: 5
Step-by-step explanation:
perimeter = 2 x length + 2 x width
plug in the values
46 = 2(3x+2)+2(x+1)
distribute the 2 into the fraction by multiplying
46 = 6x+4+2x+2
add similar components
46 = 8x+6
subtract 6 to both sides
40 = 8x
divide by 8
5 = x
Can someone help me solve for
If you're talking about the lower case m, which sporadically appears before a specific angle, like m ANGLE A-B-C. The m denotes the angle ABC's "measure" (angular measure in degrees).
Here the angle m ∠UVX = [tex]52^{0}[/tex].
What is the m ∠?The measure of an angle is sometimes represented by the symbol m. Different names can be given to an angle . The same angle is known by several names. The angle might be identified by the letter of the vertex, in which case it would be called A. ABC stands for the actual physical angle and mABC for its measure. There is no distinction between the two, and any one may be used without a doubt.If you're talking about the lower case m, which sporadically appears before a specific angle, like m ANGLE A-B-C. The m denotes the angle ABC's "measure" (angular measure in degrees).To learn more about : Angular measure in degrees
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Mrs. [Name] has 56 pencils and 42 erasers. If she wants to make sets of pencils. erasers for her class so that each student has the same number of pencils and erasers, what is the greatest number of students she can have in her class so there are none left over? How many pencils and erasers will each student have
[re post]
Answer:
there must be 14 students and each one can get 4 pencils and 3 erasers
Step-by-step explanation:
56 goes into 14 4 times. 42 goes into 14 3 times none left over
simplify 5(x+4)-2(x-3)
Answer:
3x +26
Step-by-step explanation:
A parallelogram has four angles. You know that one angle is 96. What is the other three angles
Can you help me please
Which statement describes the graph?
Answer:
b
Step-by-step explanation:
the depth of the water in a tank after t minutes is modeled by f l(t) =3+2.5t measured in inches.find the interpret f(5)
The function f(5) equals 15.5 inches
What is a function?
A function from either a set X to a set Y provides precisely one item of Y to each item of X. The set X is known as the function's domain, while the set Y is known as the function's codomain. The Persian mathematicians Al-Biruni and Sharaf al-Din al-Tusi are credited with the first known attempt to the concept of function. Initially, functions were the idealized vision of how a variable quantity depended on another quantity. A planet's location, for example, is a function of time. Historically, the notion was developed with the infinitesimal calculus at the end of the 17th century, and the functions investigated were differentiable until the 19th century.
The function is solved as
f(5) = 3 + 2.5(5) = 3 + 12.5 = 15.5 inches
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Add 6.2 to the difference between 4.1 and 1.9 then divide the result by 3
Difference: the outcome of subtraction.
Let's just start of with the difference between 4.1 and 1.9, because we need the result of this before we do anything else.
1. 4.1-1.9=2.2
2.2 is the difference of 4.1 and 1.9.
2. It says to add 6.2 next.
6.2+2.2= 8.4
Next we need to divide by 3.
3. 8.4/3=2.8.
4. 2.8 is the answer!!
----------------------------
i think this was simple, so good luck!! much love! <33
1/3(2x-3/7)+1/6x=4/7 find x
If the equation is 1/3(2x - 3/7)+(1/6)x = 4/7 , then the value of x is 3/7.
The given equation is
1/3(2x - 3/7)+(1/6)x = 4/7
First we have to apply the distributive property of subtraction in the equation
1/3(2x - 3/7)+(1/6)x = 4/7
(3/2)x - 1/7 + (1/6)x = 4/7
Here we have to rearrange the terms and group the like terms
Move the 1/7 to right hand side of the equation
(3/2)x + (1/6)x = (4/7)+(1/7)
Addition of like terms
(5/3)x = 5/7
Move the 5/3 to the right hand side of the equation
x = 5/7 ÷ 5/3
x = 5/7 × 3/5
x = 3/7
Hence, if the equation is 1/3(2x - 3/7)+(1/6)x = 4/7 , then the value of x is 3/7
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Petra always keeps her 6 bedrooms in her house clean it takes her 15 minutes to clean a single room how many hours will it take her to clean all 6 bedrooms
Answer:
90 minutes(1hour 30 minutes)
Step-by-step explanation:
If 1 room=15 minutes
Then 6 rooms= ?
=6×15/1
=90 minutes
=1hour 30 minutes
what is the simplest form of the square root of 75
Transform the basic function f(x)=x2 as follows. complete each transformation separately in the order they are given. shift down 5 units and left 77 units. reflect about the y -axis compress vertically by a factor of 2.
The transformed function becomes; f'(x) = (1/2)[(-x - 77)² - 5] after its shifting and compression.
What is the procedure for obtaining a new function from a parent function?Let us suppose we have such a parent function y=f (x). By simply introducing a constant c, a new function y=g(x) can be generated from the parent function.The following are the function transformation / translation principles: f (x) + b multiplies the function by b.f (x) + b shifts a function b units upward.f (x) − b shifts a function b units downward.f (x + b) shifts a function b units to the left.f (x − b) shifts a function b units to the right.−f (x) reflects a function in x-axis (that is, upside-down)For the given question;
The parent function is given as; f(x) = x².The function is shifted 5 units down, then y coordinates will get reduced by 5 units as; f(x) = x² - 5.Now, there is a shift of 77 to the right, then x coordinates will get reduced by 77 units; f(x) = (x - 77)² - 5.There is a reflection of function about y-axis, then value of x coordinates will change to its negative; f(x) = (-x - 77)² - 5.At last, there is a vertical compress by a factor 2, reduced the function to its half; f'(x) = (1/2)[(-x - 77)² - 5].Thus, the transformed function becomes; f'(x) = (1/2)[(-x - 77)² - 5].
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