The exact value of secθ in simplest radical for is 1.083
What are trigonometric identities?Trigonometric identities are the functions that include trigonometric functions such as sine, cosine, tangents, secant, and, cot.
We are Given θ is an angle in standard position.
Its terminal side passes through the point (12, -5).
To find the exact value of secθ in simplest radical form.
When θ is an angle in standard position and its terminal side passes through the point (x,y), then the exact value of secθ is:
So, we have x = 12 and y = -5 which is in the first quadrant.
Therefore,
r² = x² + y²
r² = ( 12 )² + ( -5 )²
r² = 144 + 25
r² = 169
r = 13
Then,
sec θ = 1/cosθ
sec θ = [ 1/(x/r) ]
sec θ = r/x
sec θ = 13/12
sec θ = 1.083
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Suppose $PABCD$ is a right square pyramid with apex $P$ and base $ABCD$. If $PBD$ is an equilateral triangle with side length 6, then what is the volume of $PABCD$
The volume of a right square pyramid PABCD is 50.91 cubic units
Let l be the side length of right squared pyramid and h be the height.
We know that the formula for the volume of the right squared pyramid.
V = a²h / 3
And the formula for the height of right squared pyramid.
h = (1/√2)a
Here, the side length (a) = 6 units
So, using above formula of height,
h = (1/√2) × 6
h = 6/√2
h = 3√2 units
Now using the formula for the volume of the right squared pyramid, the volume of pyramid PABCD would be,
V = (6² × 3√2) / 3
V = 6² × √2
V = 36√2
V = 50.91 cubic units
Therefore, the volume of PABCD is 50.91 cubic units
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Lin is solving the inequality 15-x< 14. She knows the solution to the
equation 15 - x = 14 is x = 1
How can Lin determine whether x > 1 or x < 1 is the solution to the
inequality?
If Lin is solving the inequality [tex]15-x < 14[/tex] and she know the solution is x = 1 , then the solution of inequality is [tex]x > 1[/tex] .
The inequality that Line is solving is [tex]15-x < 14[/tex] ,
the solution of the equation [tex]15-x = 14[/tex] is given as x = 1 ;
we have to find the value of x for which the given inequality expression is true ,
Case(i) , let us take [tex]x > 1[/tex] ,
So , putting x = 2 , in the inequality ,
we get ; [tex]15-2 < 14[/tex]
= 13 < 14 , that is TRUE .
Case(ii) , let us take [tex]x < 1[/tex] ,
So , putting x = 0 in the inequality ,
we get ; [tex]15-0 < 14[/tex]
= 15 < 14 , that is FALSE .
Therefore , the solution of the inequality is x > 1 .
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Simplify the following using law of indices. a) 12x⁷ ÷ 4x³
b) (2x)² × (2x)³ × (2x)⁵
Answer:
a) 3[tex]x^{4}[/tex]
b) 1024[tex]x^{10}[/tex]
Step-by-step explanation:
[tex]\frac{12x^{7} }{4x^{3} }[/tex]
[tex]\frac{3(4)xxxxxxx}{4xxx}[/tex] We can cancel out a 4 and 3 x's. That leaves
3xxxx
or 3[tex]x^{4}[/tex]
[tex](2x)^{2}[/tex] x [tex](2x)^{3}[/tex] x [tex](2x)^{5}[/tex] can be written in expanded form
[(2)(2)xx] x [(2)(2)(2)xxx] x [(2)(2)(2)(2)(2)xxxxx]
(2)(2)(2)(2)(2)(2)(2)(2)(2)(2)xxxxxxxxxx
1024[tex]x^{10}[/tex]
Which fraction is equivalent to - 3/2?
3/-2
-(3/-2)
-3/-2
-(-3/2)
Answer: -(-3/2 is equivalent also
Step-by-step explanation:
The reason why is because you take it out of the parentheses you will still have a negative fraction
Sal brought 2 dozen apples to a science club meeting. He divided the apples equally among the 8 people there. How many apples did he give each person?
Division is the antithesis of multiplication. When you divide twelve into three equal groups, you get four in each group when you multiply three groups of four to create twelve.
How do you explain division?The opposite of multiplication is division. When you multiply three groups of four to produce twelve, you get four in each group when you split twelve into three equal groups. The basic objective of splitting is to determine how many equal groups are created or how many people are in each group after a fair distribution.
The phrase to use is "divide in half," not "divide by half," when discussing splitting something into two equal portions. In mathematics, multiplying by two is equivalent to dividing by half. Additionally, see "multiply by two."
The French term "douzaine," which denotes a group of 12, is where the word "dozen" originates.
2 dozen apples equals 24, and 24 divided by 8 is 3.
Therefore, the answer is 3.
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`y=7/(1,000)-(9x)/8` is this proportional or nonproportional
Tom and his friend are driving to Louisville, Kentucky, next week. They figure that the trip will be about 432 miles round trip. If his car gets 31 mpg and the current cost of gasoline is $2.79, how much will they spend on gas? $51.61 $44.46 $38.88 $31.00
=====================================================
Explanation:
Let x be the number of gallons used up. It's some positive real number.
We'll use the formula
miles = (mpg)*(number of gallons)
to help figure out how much fuel is used. The trip is 432 miles, and the mpg rating is 31
So,
miles = (mpg)*(number of gallons)
432 = 31*x
31x = 432
x = 432/31
x = 13.9354838709678 which is approximate.
Multiply that with the 2.79 to get the final answer.
2.79*x = 2.79*13.9354838709678 = 38.8800000000001
The 1 at the very end is probably due to some rounding error, but then again it may be accurate. Either way, that value rounds to 38.88
Side note: The 31 mpg rating is very likely an average value and not the same throughout the trip. This is due to the car changing speeds at different points of the journey. In reality, the true answer will vary slightly from the 38.88 figure we just calculated (but it should be fairly close).
The total amount of money that Tom and his friend would spend on gas during the trip is $38.88.
How much would be spent on gas?
The first step is to determine the total amount of gas that would be needed during the trip.
Gas that would be needed = 432 / 31 = 13.94
The second step is to multiply the gas that would be needed by the cost of gasoline: $2.79 x 13.94= $38.88
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Atiker wants to uile a rectangular wall which reasures Ambuy 2.5 m,
achtile measures 16 cm by 10 cm,
How many tiles will he need for the wall?
Tik
2.5 m
10 cm
16 cm
Answer:
Step-by-step explanation:
There are 100 cm in 1 meter. the dimensions are 400cm by 250cm. depending on which way you turn them, they will fit better. if you take 400 divided by 16, you will have a row of 25 wide and if you divide 250 by 10, you will have a length of 25. you now have 25 rows of 25. 25x25 is 625 tiles.
Hope this helps
Tammy already has $565 dollars in her savings account. If she puts $5 per week in her account, write and solve an inequality to find out how many weeks she must save to have at least $100 in her account. Let w represent the number of weeks.
Answer:
Since she already has $565, her goal is $665.
5 × 20 = 100
w = 20 weeks
HELP DUE IN 15 MINS!
x=??
Answer:
Step-by-step explanation:
Remark
The angle formed by the intersection of a tangent to a circle and an intersecting secant is 1/2 (Arc PS - arc PR)
PS = 208
PR = 74
Solution
x = 1/2 (208 - 74)
x = 1/2 (134)
x = 67
please help solve this its for geometry
Answer:
Step-by-step explanation:
1.RS+ST=RT. so 9y+2+2y+7=15y-11
2.11y+9=15y-11
3.15y-11y=11+9
4.4y=20
finally we find the answer is y=5
Find the product of the factors 8.075*0.08
Answer: 8.075: gotta get somebody else to do this one...sorry. and 0.08 = 8
Step-by-step explanation:
Did this with a classmate couple months ago. Hope this helps. :)
pls help, 20 points!
Answer:
13
Step-by-step explanation:
7x -4 = 87
7x = 87+4 = 91
x = 91/7 = 13
if you can buy one bunch of cilantro for $1.60 how many can you buy with $38.40?
Answer: 24 bunches of cilantro
Step-by-step explanation:
1. Set a proportion with the given information, which should be 1/1.60 = x/38.40.
2. Cross multiply. Now the equation should 1.60x = 38.40.
3. Divide by 1.60 to get x alone to find out how many bunches of cilantro you can buy with $38.40. This should give you x = 24 bunches of cilantro.
Answer:
24 bunches
Step-by-step explanation:
The person below is correct
Mr.Rosado is making a stop at his favorite ice cream shop.
He can choose on flavor of ice cream: chocolate, strawberry, vanilla or rocky road.
He can put his ice cream in a sugar cone, waffle cone or a cup.
What is the p(chocolate ice cream AND a waffle cone)?
Answer:
1/12
Step-by-step explanation:
Assuming his choices are equally likely (important: he's choosing randomly)...
Probability of selecting chocolate: 1/4 (1 of 4 equally likely choices)
Probability of selecting waffle cone: 1/3
Probability of selecting both: 1/4 x 1/3 = 1/12
Now, if you'll excuse me, I'm off to get ice cream! :-)
Find the area of the sector.
195°
9 m
Answer:B
Step-by-step explanation: Because it right
What is the result when the number 80 is decreased by 50%?
NO LINKS OR I'LL REPORT
Find the area of the figure. Round your answer to the nearest tenth.
Be sure to sketch the polygon and the associated triangle.
Given: A regular hexagon with radius = 8
Answer:
17.3 if I am right mark me brainless pls
GIVEN: GH (congruent JH and FH (congruent) HI
PROVE: FG (congruent) IJ
Hence proved that FG = IJ with CPCT theorem for ΔGHF ≅ ΔJHI by SAS Congruency rule.
What is Congruency of triangles?Triangle congruence: Two triangles are deemed to be congruent if all three of their corresponding sides and angles have the same magnitude. Slides, rotations, flips, and turns can be used to make these triangles appear identical. They would be in alignment if they were moved. Congruence is represented by the letter "≅".
When two figures are similar to one another in terms of their size and shape, this is what mathematicians mean by congruence. It can be demonstrated that two triangles are congruent using four congruence rules in general. Finding all six dimensions is necessary, though.
Given that,
GH ≅ JH
FH ≅ HI
And,
∠GHF = ∠JHI
Therefore,
ΔGHF ≅ ΔJHI (SAS Congruency)
∴ FG = IJ (CPCT theorem)
Hence proved that FG = IJ with CPCT theorem for ΔGHF ≅ ΔJHI by SAS Congruency rule.
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Factor this polynomial completely.
x2 + 3x - 18
A. (x - 2)(x+9)
B. (x+3)(x - 6)
C. (x - 3)(x + 6)
D. (x - 3)(x-6)
help please I don't know this one
Answer:
21
Step-by-step explanation:
As the ball rolls downhill, its kinetic energy ___________
Maximum
Minimum
Answer:
Maximum
Step-by-step explanation:
Answer:
Maximum
Step-by-step explanation:
Two ropes are used to stake a new tree. If they are each tied 3 feet up from the ground and 4 feet from the base of the tree. How many feet of rope do you need total?
Answer:
7
Step-by-step explanation:
I’ll mark u as brainliest plz answer this !!!
Answer:
the answer is 20. 50% of 20 is 10 so if 10 preferred the one juice then there's 20 people total
Answer:20
Step-by-step explanation:
If x=all beings on Vreet
0.5x=10
x=10/0.5
x=20
Colleen and Amy go shopping. The function below represents how much money each girl spent based on the number of hours they were shopping. If Colleen and Amy each go shopping for 3 hours, how much money did they spend together?
p(x)3x^4=x^4-3x^2+5
$32
$86
$248
$302
Answer:
$302
Step-by-step explanation:
p(x) 3x^4 = x^4-3x^2+5
We put 3 in for x and solve
3(3)^4 = 3^4 -3(3)^2 + 5
3(81) = 81 -3(9) + 5
243 = 81 - 27 + 5
243 = 59
Then we add 243 with 59 and get
$243 + $59 = $302
So, they spend together $302
If you can, please give me a Brainliest; thank you!
Can u please help...............
A graph of ΔABC with vertices A(0, 0), B (3, 3), and C (4, 0) and its image after a 90° rotation about the origin is shown in the image attached below.
What is a rotation?In Geometry, the rotation of a point 90° about the center (origin) in a counterclockwise (anticlockwise) direction would produce a point that has these coordinates (-y, x).
By applying a rotation of 90° counterclockwise to the vertices of triangle ABC (∆ABC), the coordinates of the vertices of the image (∆A′B′C′) are as follows:
(x, y) → (-y, x)
Ordered pair A = (0, 0) → Ordered pair A' = (0, 0)
Ordered pair B = (3, 3) → Ordered pair B' = (-3, 3)
Ordered pair C = (4, 0) → Ordered pair C' = (0, 4)
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factorise fully -b -20
Answer:
−(b+20)
Step-by-step explanation:
The only thing we could possibly do is factor out the negative since there are no factors no squared numbers.
PLS MARK BRAINLIEST
PLEASE HELP ME ASAP!!! WILL MAKE YOU BRAINLIEST!!!!
Which of the following postulates or properties of spherical geometry are true?
A) The sum of the measures of a triangle is 180.
B) No two lines are parallel.
C) Through any two points there is exactly one line.
D) Two lines intersect in exactly one point.
Answer:A
Step-by-step explanation:
Taliban
For each equation determine whether it has no solutions, exactly one solution, or is true
for all values of x (and has infinitely many solutions). If an equation has one solution, solve
to find the value of x that makes the statement true.
a. 6r+8 = 7x + 13
b6r + 8 = 2(3x + 4)
c. 6r+8 = 6r+ 13
For the given equations , the solutions are as follows :
(a) the equation [tex]6x + 8 = 7x + 13[/tex] has exactly one solution , and the solution is .
(b) the equation [tex]6x + 8 = 2(3x + 4)[/tex] has Infinitely Many Solutions .
(c) the equation [tex]6x + 8 = 6x + 13[/tex] has No Solution .
Equation (a) ;
the equation is given as [tex]6x + 8 = 7x + 13[/tex] , we solve the equation further ,
we get ;
[tex]7x - 6x = 13 - 8[/tex] ;
[tex]x = 5[/tex] ;
So , the equation has exactly one solution and the solution is [tex]x = 5[/tex] .
Equation (b) ;
the equation is given as [tex]6x + 8 = 2(3x + 4)[/tex] , we solve equation further ,
we get ;
[tex]6x + 8 = 6x + 8[/tex] ;
On solving further ,
we have ;
[tex]8 = 8[/tex] ;
So , the equation has infinitely many solutions .
Equation (c) ;
the equation is given as [tex]6x + 8 = 6x + 13[/tex] , we solve equation further ,
we get ;
[tex]8 = 13[/tex] ;
and we know that [tex]8\neq 3[/tex] ,
So , the equation have No Solution .
The given question is incomplete , the complete question is
For each equation determine whether it has no solutions, exactly one solution, or is true . for all values of x (and has infinitely many solutions). If an equation has one solution, solve to find the value of x that makes the statement true.
(a) 6x + 8 = 7x + 13
(b) 6x + 8 = 2(3x + 4)
(c) 6x + 8 = 6x + 13
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Building blocks are in the shape of a cube. The dimensions of the building blocks are based on the length of the packaging box, which is defined as [tex]\frac{1}{12} x^{2}[/tex] centimeters, where x is the length of the packaging box. What is the volume of a building block in terms of x?
ily whoever answers right <3
The volume of the building block in terms of x is V = x⁶/1728
What is volume?Volume is the amount of space a substance occupies.
What is the volume of a building block in terms of x?Since building blocks are in the shape of a cube. The dimensions of the building blocks are based on the length of the packaging box, which is defined as x²/12 centimeters, where x is the length of the packaging box.
Since the building blocks are in the shape of a cube, its volume is the volume of a cube.
What is the volume of a cube?The volume of a cube is given by V = L³ where L = length of side of cube.
To find the volume of the building block, since the length of the building block is L = x²/12, then we find the volume of the building block by substituting L into V.
So, V = L³
V = (x²/12)³
= x⁶/12³
= x⁶/1728
So, the volume of the building block is V = x⁶/1728
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