By using trigonometric rules and expressions we find that the expression [tex]x = \sqrt{\frac{1-\cos 170^{\circ}}{2} }[/tex] is equivalent to single trigonometric expression x = sin 85°.
How to simplify a trigonometric expression
In this question we must apply trigonometric rules to simplify a given number, in which case we can take advantage of this expression:
[tex]\sin \frac{\theta}{2} = \sqrt{\frac{1 - \cos \theta}{2} }[/tex]
If we know that [tex]x = \sqrt{\frac{1-\cos 170^{\circ}}{2} }[/tex], then the rewritten expression is:
x = sin 85°
By using trigonometric rules and expressions we find that the expression [tex]x = \sqrt{\frac{1-\cos 170^{\circ}}{2} }[/tex] is equivalent to single trigonometric expression x = sin 85°.
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The diagonals of parallelogram abcd intersect at point e. to prove that bae= dce, all of the following could be used, except for which
a.the sum of measures of the interior angles of abcd is 360 degrees
b. abc = cda by sss
c. abc = cde by sss
d. given two parallel lines by transversal, alternates interior angles are congruent.
The only option that cannot be used to prove that the diagonals of parallelogram abcd intersect at point e is; Option C
How to determine quadrilateral proof?
A) The sum of the interior angles of any quadrilateral is 360° and so this is true about the parallelogram.
B) AB = CD and BC = DA from opposite sides of a parallelogram are equal. Also AC = CA because of reflexive property of congruence. Thus, ∠ABC ≅ ∠CDA
C) This is not true because ∠ABC ≅ ∠CDA instead of ∠ABC ≅ ∠CDE.
D) This is true because of the definition of a transversal.
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2. Liam can work at most 20 hours a week but he needs to earn at least $125. His dog-walking job pays.
$7 per hour and his job as a car-wash attendant pays $11 dollars an hour. How can he earn $125? I
Write a system of inequalities to represent this situation.
Answer:
Look down below and you will know the answer↓:
Step-by-step explanation:
He will have to work as between the range (of 20,0) and (0,20) points to earn more than $125.
So, What is inequality?
Inequality means is the relationship between two expressions that are not equal, so employing a sign such as ≠ “is not equal to,” > “greater than,” or < “less than.”.
Since then: Liam can work at most 20 hours a week, but he also needs to earn at least $125. His dog-walking job pays $7 per hour and his job as a car-wash attendant pays $11 dollars an hour. How can he earn $125.
He Let the Dog walking hours are represented by x and Car wash hours will be represented by y. The inequality will be formed as:
7x + 11y ≥ 125
x+y = 20
When we plot these two equations on the graph, we will get the range for the time from (20,0) and (0,20).
We Suppose that we will take a random point-like (5,15) when we put this value in the inequality, we get the total earning greater than $125.
7x + 11y ≥ 125
7 (5) + 11 ( 15 ) ≥ 125
35 + 165 ≥ 125
200 ≥ 125
Therefore, He has to work between the range (of 20,0) and (0,20) points to earn more than $125.
Mark me as brainlist, thanks me, and rate. Hope it helps you!!!need help with work would give more points but poor
Answer:
Step-by-step explanation:
2.5
4 quarts per gallon
8 quarts per 2 gallons
2 quarts is half a gallon since 4 quarts is a full gallon
answer: 2.5
Thankyou guys for all your help….I need help with one more plsss
Round to the nearest tenth
I don't understand your question
What are the solutions to the quadratic equation below in factored form?
(10x + 5)(11x - 44) = 0
= ½, x = 4
0x=
0 x = 2, x = -4
0x = 2, x = 4
○ x = − ½, x = 4
Answer:
D.) x = − ½, x = 4
Explanation:
[tex]\rightarrow \sf (10x + 5)(11x - 44) = 0[/tex]
set the factors to zero
[tex]\rightarrow \sf 10x + 5 = 0, \ 11x - 44 = 0[/tex]
exchange the sides
[tex]\rightarrow \sf 10x = -5, \ 11x = 44[/tex]
exchange the sides
[tex]\rightarrow \sf x = -\dfrac{5}{10} , \ x = \dfrac{44}{11}[/tex]
simplify the following
[tex]\rightarrow \sf x = -\dfrac{1}{2} , \ x =4[/tex]
On solving
x=-1/2 or x=41-sinA+cosA / sinA+cosA-1 = 1+cosA/sinA
Solution:
[tex]\dfrac{\left[\left(\sin ^{2} A+2 \times \sin A \times (1-\cos A)+(1-\cos A)^{2}\right]\right.}{\left[\left(1-\cos ^{2} A\right)-(1-\cos A)^{2}\right]}[/tex]
[tex]\dfrac{\left[\left(1-\cos ^{2} A\right)+2 \times \sin A \times (1-\cos A)+(1-\cos A)^{2}\right]}{\left[(1-\cos A)(1+\cos A)-(1-\cos A)^{2}\right]} [/tex]
[tex]\dfrac{(1-\cos A)[1+\cos A+2 \sin A+1-\cos A]}{[1-\cos A][1+\cos A-1+\cos A]} [/tex]
[tex]\dfrac{[2+2 \sin A]}{[2 \times \cos A]}[/tex]
[tex]\dfrac{2(1+\sin A)}{2 \times \cos A}[/tex]
[tex]\dfrac{1+\cos A}{\sin A} [/tex]
Hence Proved.
A contractor is purchasing some stone tiles for a new patio, each tile costs $3 and he wants to spend less than $1000 the size of each tile is 1 square foot, write and inequality that represents the number of tiles he can purchase with a $1000 limit, and the figure out how large the stone patio can be
Answer:
333.333 Tiles and 333.333 Square Foot
Step-by-step explanation:
3X <= 1000
X <= 1000/3
X <= 333.333 Tiles
Then
333.333* 1sqt2 = 333.333 Square Foot
What is the height of a triangle whose
base is 8.2 centimeters and whose area
is 173.43 square centimeters?
Answer:
42.3cm
Step-by-step explanation:
I think this is right :)
Please help!!!!!
The equation of a circle is x² + y² – 8x + 10y + 37 = 0. What is the center and the radius of the circle? Show all your work.
Let's take this problem step-by-step:
Let's convert the equation back into the standard form:
⇒ standard form: (x-h)² +(y-k)² = r²
(h, k): center's coordinater: radius[tex]x^2+y^2-8x+10y + 37 = 0\\\rm \hookrightarrow x^2 - 8x + y^2+10y = -37\\\rm \hookrightarrow (x^2 - 8x) + (y^2 + 10y) = -37\\\rm \hookrightarrow (x^2-8x+16) + (y^2+10y+25) = -37 + 16 +25\\\rm \hookrightarrow (x-4)^2 + (y+5)^2 = 4\\\rm \hookrightarrow (x-4)^2 + (y+5)^2 = 2^2[/tex]
Based on the equation found
⇒ center: (4, -5)
⇒ radius: 2
Answer:
center: (4, -5)radius: 2Hope that helps!
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Which output in this table is incorrect
Answer:
B
Step-by-step explanation:
This is quite a trial and error question.
Given from the table
$1 cost of item = $0.08 tax on item
$2 cost of item = ($0.08x2) tax on item = $0.16 tax on item
$3 cost of item = ($0.08x3) tax on item = $0.24 tax on item
$8.50 cost of item = ($0.08x8.50) tax on item = $0.68 tax on item
$10 cost of item = ($0.08x10) tax on item = $0.80 tax on item
The only one that is different is the incorrect value therefore $0.64 is the incorrect one.
Two friends, Vani and Shaquana, took summer jobs. The equation y=28.8xy=28.8x represents Vani's earnings in dollars and cents, yy, for working xx hours. Shaquana earned $653.40 in 33 hours.
How much less per hour does Shaquana earn than Vani?
An equation is formed of two equal expressions. Shaquana earns $10 less per hour than Vani.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
The equation y=28.8x represents Vani's earnings in dollars and cents, y, for working x hours.
y = 28.8x
y/x = 28.8
Hence, Vani is paid $28.8 per hour.
The amount that Shaquana earned was $653.40 in 33 hours. Therefore, per hour she was paid
Amount per hour = $653.40/33 = $19.8 per hour
The difference between the two is,
Difference = $28.8 - $19.8 = $10
Hence, Shaquana earns $10 less per hour than Vani.
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Vani - 28.8
y=28.8x
Vani earns $28.80 per hour.
Shaquana -
653.40 / 33 = $19.80 per hour
Shaquana earns $19.80 per hour.
Vani − Shaquana = $28.80
$28.80−$19.80
=$9
Shaquana earns $9 less per hour than Vani.
Bryan is making a wooden cube to hold his little sister's jewelry. The volumes the cube is
3
512 in ³. What is the length of one side of the jewelry box?
Answer:
8 in
Step-by-step explanation:
Volume of Cube = 512 in³
Formula : -
Volume of cube = side x side x side = side³
512 = 8 x 8 x 8 = 8³
So,
The length of one side of the jewelry box is 8 in.
MisterBrainly (also known as Enstine) lets out 100 feet of string on a kite from a hand height of 3 feet. The angle between horizontal hand height and the kite is 25º. Find the height of the kite above the ground, to the nearest foot.
Answer: I love the picture example
Step-by-step explanation:
We will first find the heigh of the kite from his hand to a point in the air.
Then, we will add 3 feet to the result.
So, how to find the vertical line of the right triangle?
Well, we have the vertical line = x
We also got the hypothenuse, equal to 100 feet
And also theta, equal to 25 degrees.
We can calculate sine because the sine of 25 degrees = opposite side (the height line) over (divided by) the hypothenuse
sin(25) = x/100 feet
multiply 100 feet on both sides, to cancel to 100 feet on the right side.
100sin(25) = x
100(0.442) = x
x = 42.2 feet
Height = 42.2 + 3 feet (the yoda's hand =) = 45.2 feet (total)
Rounded to the nearest tenth.
I also did the verification, so it is the correct answer.
Easy as that =]]
Height of the kite from 3ft above the ground
[tex]\\ \rm\Rrightarrow sin\Theta=\dfrac{Perpendicular}{Hypotenuse}[/tex]
[tex]\\ \rm\Rrightarrow sin25=\dfrac{P}{100}[/tex]
[tex]\\ \rm\Rrightarrow P=100sin25[/tex]
[tex]\\ \rm\Rrightarrow P=42.26\approx 42ft[/tex]
Height from the ground
42+345ft(Rounded)True OR False
------------------------
x - 62 = 44, x = 106
Answer:
True
Step-by-step explanation:
Step 1: We can plug 106 into x in the equation x - 62 = 44.
Step 2: Check if 106 - 62 = 44. It’s correct, so the answer is TRUE!!
Please mark me as Brainliest. Thanks[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \:True [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex]\qquad \tt \rightarrow \: x - 62 = 44[/tex]
[ add 62 on both sides ]
[tex]\qquad \tt \rightarrow \: x - 62 + 62 = 44 + 62[/tex]
[tex]\qquad \tt \rightarrow \: x = 106[/tex]
The proved value is same as that of statement, hence the statement is correct.
A 11 gram sample of a substance that’s used to treat thyroid disorders has a k- value of 0.125
The substance's half-life is 5.5 days if the 11-gram sample of a substance that’s used to treat thyroid disorders has a k- the value of 0.125
What is exponential decay?During exponential decay, a quantity falls slowly at first before rapidly decreasing. The exponential decay formula is used to calculate population decline and can also be used to calculate half-life.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
We have an exponential function:
[tex]\rm N = N_oe^{-kt}[/tex]
Plug N = N⁰/2
[tex]\rm N_o/2 = N_oe^{-kt}[/tex]
[tex]\rm \dfrac{1}{2} = e^{-0.125t}[/tex]
Solving for t:
t = 5.54 ≈ 5.5 days
Thus, the substance's half-life is 5.5 days if the 11-gram sample of a substance that’s used to treat thyroid disorders has a k- the value of 0.125
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Find the equation of the parabola with its focus at (6,2) and its directrix y = 0.
Consider parallel lines cut by a transversal.
Parallel lines q and s are cut by transversal r. On line q where it intersects line r, 4 angles are created. Labeled clockwise, from uppercase left: angle 1, angle 2, angle 4, angle 3. On line s where it intersects line r, 4 angles are created. Labeled clockwise, from uppercase left: angle 5, angle 6, angle 8, angle 7.
Explain which theorems, definitions, or combinations of both can be used to prove that alternate exterior angles are congruent.
When two parallel lines are cut by a transverse. the angles formed on the exterior of the parallel lines, on the opposite sides of the transverse are known as the Alternate Exterior Angle.
What are Alternate exterior angles?When two parallel lines are cut by a transverse. the angles formed on the exterior of the parallel lines, on the opposite sides of the transverse are known as the Alternate Exterior Angle.
Firstly, ∠1 and ∠7 are alternate exterior angles as shown in the image, now to prove if these two angles will be congruent we can use the below proof.
First Method:
∠1 + ∠2 = 180° {Supplementary angles because both lies on the line q}
∠2 = (180° - ∠1)
Similarly, ∠2 = ∠6 = (180° - ∠1), corresponding angles are equal,
∠6 + ∠7 = 180° {Supplementary angles because both lies on the line r}
∠7 = 180° - ∠6
∠7 = 180° - (180° - ∠1)
∠7 = 180° - 180° + ∠1
∠7 = ∠1
OR
Second Method:
∠1 = ∠3 {Vertical angles formed by intersecting lines q and r}
∠3 = ∠5 {Alternate Interior angles}
∠5 = ∠7 {Vertical angles formed by intersecting lines s and r}
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A carpenter started with a board that was 31 inches long. he cut 2 pieces that were each 3 inches long. he then cut 3 pieces that were each
Answer:
i don't know
Step-by-step explanation:
i
Determine the value of y, if x is 81.
Y=/x+6
The value of y for the given equation at x=81 is 87.
What is Equation?Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign.
Here, given equation;
y = x + 6
Put x = 81, we get
y = 81 + 6
y = 87
Thus, the value of y for the given equation at x=81 is 87.
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Simplify. Rewrite the expression in the form 9^n9
n
9, start superscript, n, end superscript.
(9^{-3})(9^{12})=(9
−3
)(9
12
)
[tex] {3}^{18n} [/tex]
Answer:
9^10
Step-by-step explanation:
khan
add the following rational number7/-27 and 11/18
Answer:
19/54
Step-by-step explanation:
- 7/27 + 11/18
LCM of the 27, 18 is 54
- 7/27 * (2/2) + 11/18 * (3/3)
- 14/54 + 33/54
33 - 14/54
19/54
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Can someone please help me
quadrilateral ABCD is similar to quadrilateral EFGH find the measure of side EF round your answer to the nearest tenth if necessary
Answer:
EF = 2.9
Step-by-step explanation:
The geometric figures are similar so we can use the similarity ratio to calculate the length of EF:
GF/ CB = EF/AB
5/29 = EF/17 cross multiply expressions
29EF = 85 divide both sides by 29
EF = 2.9 approximately
19% of 49 in a decimal
Answer:
[tex] 19\% \: of \: 49[/tex]
[tex] \frac{19}{100} \times 49[/tex]
[tex]0.19 \times 49[/tex]
[tex]9.13[/tex]
Answer:
39.69
Step-by-step explanation:
A percentage is on a scale of 100 so we divide 19 by 100
that makes 0.19.
Then multiply 49 with 0.19 that makes 9.31 (this is 19% of 49)
49 - 9.31 = 39.69
A 210-N mass is suspended from a horizontal beam by two cables that make angles of 29 degrees and 53 degrees with the beam. Find, using vectors, the tension in the cables.
The tension in both cables are calculated as; T₁ = 127.63 N and T₂ = 185.48 N
Resolving forces in the y direction gives us;
T₁ sin 29° + T₂ sin 53° = 210 ------(eq 1)
Resolving forces in the horizontal direction gives;
T₁ cos 29° = T₂ cos 53° ----(eq 2)
T₁ = T₂ cos 53°/cos 29°
Thus;
(T₂ cos 53°/cos 29°)sin 29° + T₂ sin 53° = 210
0.3336T₂ + 0.7986T₂ = 210
T₂ = 210/1.1322
T₂ = 185.48 N
Thus;
T₁ = 185.48 cos 53°/cos 29°
T₁ = 127.63 N
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Hi my name is aughhhhhhhhhhh
Answer:
Hello auggggh nice to meet you!
Step-by-step explanation:
which shows the best use of the associative and commutative properties to make simplifying -1/3 - 10 +7 + 2/3 +5 easier A.[5+(-1/3)+(-10]+(2/3+7) B.[-1/3+7+(-10)]+(5+2/3 C.[-1/3+(-10)]+[7+2/3+5] D.(-1/3+2/3)+[5+7+(-10)]
The answer choice which best uses the associative and commutative properties is; Choice C; [-1/3+(-10)]+[7+2/3+5].
Which best shows the use of associative and commutative properties?It follows from the answer choices that the best application of the associative and commutative properties is that which sums up all negative numbers and sums up all positive numbers and hence, choice C is the correct answer choice.
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How are rays and angles related? a ray , and an angle is two . the measure of an angle related to the length of its sides. so, the measure of an angle the same at all distances from its vertex.
A ray is a part of a line that starts at a point (called the endpoint) and extends infinitely in one direction. An angle is formed when two rays share a common endpoint (vertex).
A ray has one endpoint: A ray is a one-dimensional figure that starts at a single point (the endpoint) and extends infinitely in one direction. On the other hand, an angle is formed by two rays, each with its own endpoint, meeting at a common vertex.
An angle is two rays: As mentioned earlier, an angle is created when two rays share a common endpoint. The two rays are referred to as the sides of the angle, and the endpoint they share is called the vertex.
The measure of an angle is determined by the amount of rotation: The measure of an angle is not dependent on the lengths of its sides but rather on the amount of rotation between its two rays. To measure an angle, we compare it to a standard unit of angle measurement, usually degrees. One full rotation (360 degrees) corresponds to a complete circle, and angles are measured based on the fraction of a full circle they represent.
The measure of an angle remains the same at all distances from its vertex: The measure of an angle is independent of the length of its sides or how far away an observer is from the vertex. For example, a 60-degree angle remains a 60-degree angle whether you look at it from up close or from a distance. This is because the measure of an angle depends only on the relative positions of its two rays, not on the size of the shape it forms.
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here is an illustration of a bedroom. the striped wall and the floor intersect at a
Fully simply 15x^4y^4(−5x^3y^5)
Answer:
[tex]-75x^{7}y^{9}[/tex]
Step-by-step explanation: