Answer:
[tex]-\frac{17}{15}[/tex]
Step-by-step explanation:
By definition, [tex]\cot \theta=\frac{1}{\tan \theta}[/tex] and [tex]\sec \theta=\frac{1}{\cos \theta}[/tex]. Since since [tex]\cot \theta[/tex] is negative, [tex]\tan \theta[/tex] must also be negative, and since [tex]\sin \theta[/tex] is positive, we must be in Quadrant II.
In a right triangle, the sine of an angle is equal to its opposite side divided by the hypotenuse. The cosine of an angle in a right triangle is equal to its adjacent side divided by the hypotenuse. Therefore, we can draw a right triangle in Quadrant II, where the opposite side to angle theta is 8 and the hypotenuse of the triangle is 17.
To find the remaining leg, use to the Pythagorean Theorem, where [tex]a^2+b^2=c^2[/tex], where [tex]c[/tex] is the hypotenuse, or longest side, of the right triangle and [tex]a[/tex] and [tex]b[/tex] are the two legs of the right triangle.
Solving, we get:
[tex]8^2+b^2=17^2,\\b^2=17^2-8^2,\\b^2=\sqrt{17^2-8^2}=\sqrt{225}=15[/tex]
Since all values of cosine theta are negative in Quadrant II, all values of secant theta must also be negative in Quadrant II.
Thus, we have:
[tex]\sec\theta=\frac{1}{\cos \theta}=-\frac{1}{\frac{15}{17}}=\boxed{-\frac{17}{15}}[/tex]
Which glide reflection describes the mapping ABC to DEF?
(x, y) (x + 6, y – 1) and reflected across x = 0
(x, y) (x + 6, y − 1) and reflected across y = 0
(x, y) (x, y + 6) and reflected across y = 0
(x, y) (x + 7, y) and reflected across x = 0
Answer:
Option (2)
Step-by-step explanation:
To get the transformation applied in triangle ABC to map triangle DEF we will apply the following rules.
If a point A of triangle ABC maps the point D of triangle DEF,
Coordinates of point A → (-4, -5)
Coordinates of point D → (2, 6)
First point A is shifted to quadrant (4) from quadrant (3),
Rule for the translation,
A(x, y) → A'(x + 6, y - 1)
A(-4, -5) → A'(2, -6)
Followed by reflection across x-axis (y = 0)
A'(x, y) → D(x, -y)
A'(2, -6) → D(2, 6)
Therefore, Option (2) will be the answer.
The graph of the function f(x) = (x + 2)(x − 4) is shown. On a coordinate plane, a parabola opens up. It goes through (negative 2, 0), has a vertex at (1, negative 9), and goes through (4, 0). Which describes all of the values for which the graph is negative and increasing? all real values of x where x < −2 all real values of x where −2 < x < 4 all real values of x where 1 < x < 4 all real values of x where x < 0
Answer:
c
Step-by-step explanation:
all real values of x where 1 < x < 4
Answer:
c
Step-by-step explanation:
trust me
5) Last week a Pizza Hut sold 36 cheese pizzas, 64 pepperoni pizzas, and 20 veggie pizzas. Based on these data, which number is closest to the probability that the next customer will order a cheese pizza?
Answer:
[tex]P(Cheese) = 0.30[/tex]
Step-by-step explanation:
Given
[tex]Cheese = 36[/tex]
[tex]Pepperoni = 64[/tex]
[tex]Veggie = 20[/tex]
Required
[tex]P(Cheese)[/tex]
This is calculated as:
[tex]P(Cheese) = \frac{Cheese}{Total}[/tex]
[tex]P(Cheese) = \frac{36}{36+64+20}[/tex]
[tex]P(Cheese) = \frac{36}{120}\\[/tex]
[tex]P(Cheese) = 0.30[/tex]
Write the equation of the line that passes through (−3, 5) and (2, 10) in slope-intercept form.
Answer:
gradient =y2-y1÷x2-x1
=10-5÷2-(-3)
1
y-y1=m(x-x1)
y-5=1(x-(-3))
y=x+2
what are 2 consecutive odd integers whose sum is 36.
Two consecutive odd integers with a sum of 36 are 17 and 19.
Hope it helps you I'm from ph❤️
Answer:
Two consecutive odd integers with a sum of 36 are 17 and 19.
Step-by-step explanation:
hope i helped
The length of the base of an isosceles triangle is x. The length of a leg is 3x-4. The perimeter of the triangle is 97. Find x.
Answer:
x = 15
Step-by-step explanation:
Given that,
The length of the base of an isosceles triangle is x.
The length of a leg is 3x-4.
Perimeter, P = 97
An isosceles triangle has one base. The perimeter of a triangle is given by :
97=x+3x-4+3x-4
97 = 7x-8
97+8=7x
105 = 7x
x = 15
So, the value of x is 15.
Need answer to this maths question plssss
Answer:
The fourth angles is 105
Step-by-step explanation:
The sum of the angles of a quadrilateral is 360
3*85 = 225
Let the fourth angle be x
225 +x = 360
x = 360 -225
x =105
7. The Waltz family are planning to repave their driveway. The length of their driveway is 7 feet
longer than its width. The area of the driveway is 144 square feet. Write a quadratic equation in
standard form representing the area of the driveway.
Find the dimensions of the driveway in feet.
Width
Length =
Answer:
Dimensions Of The Driveway is Length=16 Feet & Width=9 Feet
Step-by-step explanation:
According To Question,We Have Given
Length of Driveway Is 7 feet longer than its Width
Let the Width be X Feet . So Length is (X+7)Feet
Area Of Driveway = 144 sq. Feet
X * (X+7) = 144
[tex]X^{2}[/tex]+7X=144
[tex]X^{2}[/tex]+16X-9X-144=0
X(X+16)-9(X+16)=0
X = -16 & +9 (Neglect -16 because Width=X, that Can Never be in Negative)
So X = +9
Now Put this value, We get Width = 9 Feet & Length =16 Feet
Write an equation that you could use to solve for X.
THE CORRECT EQUATION IS..
(8X+3)°=(7X+12)°
[BEING VERTICALLY OPPOSITE ANGLES ARE ALWAYS EQUAL ]
HOPE THIS HELPS YOU...
Answer:
8x + 3 = 7x + 12
8x -7x= 12-3
x=9
I need help finding the distince.
Answer:
guessing that the area of the inner rectangle is 10m²
and the other rectangle is 16m*10m= 160m²
we can say that
(16-x) * (10-x) = 10
for the area of the inner rectangle
let's calculate the lefthand side of the equation
160 - 16x -10x + x² = 10
160 -26x +x² = 10
subtract 10 on both sides
150 -26x +x² = 0
rearrange
x² -26x + 150 = 0
looks like something we can throw the pq formula on to solve for x
with p = -26 and q = 150
[tex]x = - \frac{ - 26}{2} \frac{ + }{ - } \sqrt{( \frac{ - 26}{2})^{2} - 150 } [/tex]
[tex]x = 13 \frac{ + }{ - } \sqrt{169 - 150 } [/tex]
[tex]x = 13 \frac{ + }{ - } \sqrt{19 } [/tex]
[tex]x1 = 8.64[/tex]
[tex]x2 =17.36 [/tex]
we need to interpret this solutions
but to be sure on this, I need the unreadable text of the photographed problem
Express x^2 + 4x - 7 in the form (x + a)^2 - b where a and b are intergers
Answer:
[tex]a = 2 \\ b = 11[/tex]
Step-by-step explanation:
[tex] {x}^{2} + 4x + 4 - 4 - 7 = {(x + 2)}^{2} - 11[/tex]
Which function vertex form is equivalent to f(x)=x^2+6x+3?
Answer:
y = (x + 3)² - 6
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
Given
f(x) = x² + 6x + 3
Using the method of completing the square
add/subtract ( half the coefficient of the x- term)² to x² + 6x
f(x) = x² + 2(3)x + 9 - 9 + 3
= (x + 3)² - 6 ← in vertex form
Which system of equations has one solution?
Select the correct answer from the drop-down menu. A vertical pole is supported by two ropes staked to the ground on opposite sides of the pole. One rope is 8 meters long, and the other is 7 meters. The distance between the stakes is 6 meters, and the height of the pole is meters.
Answer:
6.78 m
Step-by-step explanation:
Since the set up forms a triangle with length of ropes two sides of the triangle a = 8 m and b = 7 m respectively, the distance between them which is c = 6 m forms the third side of the triangle.
To find the height of the pole, we need to find the angle between any of the ropes and the ground. So, choosing the 8 m long rope side and using the cosine rule,
b² = a² + c² - 2accosФ where Ф is the angle opposite the 7 m long side which is also the angle between the 8 m long side and the ground.
So, making, Ф subject of the formula, we have
b² - (a² + c²) = 2accosФ
cosФ = [b² - (a² + c²)]/2ac
Ф = cos⁻¹{[b² - (a² + c²)]/2ac}
substituting the values of the variables into the equation, we have
Ф = cos⁻¹{[b² - (a² + c²)]/2ac}
Ф = cos⁻¹{[7² - (8² + 6²)]/2(8)(6)}
Ф = cos⁻¹{[49 - (64 + 36)]/96}
Ф = cos⁻¹{[49 - 100]/96}
Ф = cos⁻¹{-51/96}
Ф = cos⁻¹{-0.53125}
Ф = 122.09°
Since the height of the pole, h is a perpendicular bisector to the base of the triangle, and the 8 m long side form a triangle with it and the ground and the 8 m long side being the hypotenuse side of this triangle, we have that
sinФ = h/a where a = 8 m and Ф = 122.09° = the angle between the 8 m long side and the ground.
h = asinФ
substituting the values of the variables into the equation, we have
h = asinФ
h = (8 m)sin122.09°
h = 8 m × 0.8472
h = 6.78 m
Consider the quadratic function that has x-intercepts of–1 and –7 and passes through the point (-2,-20). What is the
value of a in the factored form of this function?
1, 2,3,4?
the sum of the digits of a two-digit number is 15. the unit digit is one less than the tens digit. find the number. let x be the tens digit. show the equation!
Answer: 87.
Step-by-step explanation:
Let x be the tens digit, then (x - 1) - unit digit.
x + x - 1 = 15
2x - 1 = 15
2x = 15 + 1
2x = 16
x = 16 ÷ 2
x = 8 - the tens digit.
8 - 1 = 7 - the units digit.
87 - the number.
Anyone know the answer?
Answer:
Determine AC with the pythagorean theorem, then you can find CD by subtracting AD.
with DC and BC, you can find BD. again, with the pythagorean theorem
Answer:
20
Step-by-step explanation:
Find AC
[tex]\sqrt{65^{2} -16^{2} } = 63[/tex]
Substract
63 - AD = 12
Find "?"
[tex]\sqrt{12^{2} +16^{2} } = 20[/tex]
how long will it take a 1500 W motor to lift a 300 kg piano to a sixth-story window 20 m above?
Answer:
39.24 sec
How long will it take a 1500 W motor to lift a 300 kg piano to a sixth-story window 20 m above? All tutors are evaluated by Course Hero as an expert in their subject area. Answer is t = 39.24 sec
Step-by-step explanation:
It will take the motor 39.2 seconds to lift the piano to the sixth-story window.
Given the following data;
Power = 1500 WattsMass = 300 kgHeight = 20 metersWe know that acceleration due to gravity is equal to 9.8 m/s².
To find how long it will take to lift the piano to the sixth-story window;
First of all, we would have to determine the gravitational potential energy required to lift the piano up.
Mathematically, gravitational potential energy is given by the formula;
[tex]G.P.E = mgh[/tex]
where:
G.P.E is the gravitational potential energy of an object.m is the mass of the object.g is the acceleration due to gravity.h is the height of the object.Substituting into the formula, we have;
[tex]G.P.E = 300*9.8*20[/tex]
G.P.E = 58,800 Joules
Next, we would determine the time using the following formula;
[tex]Time = \frac{Energy}{Power}[/tex]
Substituting the values into the formula, we have;
[tex]Time = \frac{58800}{1500}[/tex]
Time = 39.2 seconds.
Therefore, it will take the motor 39.2 seconds to lift the piano to the sixth-story window.
Find more on power, time and energy here: https://brainly.com/question/20488953
In ΔOPQ, PQ = 14, QO = 13, and OP = 20. Which list has the angles of ΔOPQ in order from smallest to largest?
Answer:
The answer is A, that's the correct one
Write the equation of the line that passes through
the points (-1, 2) and (63) in slope-intercept form.
Step 1: Choose (21. Y1).
Answer:
y=63x+65
Step-by-step explanation:
write the formula for the coefficient of quartile deviation
Step-by-step explanation:
How to Calculate the Semi Interquartile Range / Quartile Deviation. As the SIR is half of the Interquartile Range, all you need to do is find the IQR and then divide your answer by 2. Note: You might see the formula QD = 1/2(Q3 – Q1). Algebraically they are the same.
An economist tracks the relationship between the change in the value of the U.S. dollar (a measure known as the dollar index) and the price of corn per bushel. The relationship is modeled by a quadratic function whose values are also shown in the table. For what change in the dollar index is the minimum corn price
31/24 menos 5/8 cuanto es?
Answer:
31/24 menos 5/8 cuanto es 2/3
Step-by-step explanation:
=31/24- 5/8
=31-15/24
= 16/24
=2/3
Hence the final answer is 2/3
Helpppppppppp what’s the angleeeee plz tell me tytytytyytyttytytytg
Answer:
looks like 154 degrees to me
Step-by-step explanation:
The blue dot is at what value on the number line?
Answer:
The blue dot is at 3.
What is the perimeter square above
A.882 square centimeters
B.42 square centimeters
C.441 square centimeters
D. 84 square centimeters
Answer:
option D
Step-by-step explanation:
length of a square = 21 cm
perimeter of a square = 4l
=4*21
=84 centimeters
Answer:
C
Step-by-step explanation:
The square looks like it has equivalent sides so
21 x 21 = 441 square centimeters
If k is a non-zero constant, determine the vertex of the function y = x2 - 2kx + 3 in terms of k.
Answer:
Set y = 0, evaluate the quadratic at h=−b2a and solve for k.
k=9 I think..... I'm not completely sure but I think that's how it is
Answer:
[tex]\displaystyle \text{Vertex} = \left(k, 3-k^2\right)[/tex]
Step-by-step explanation:
We are given the quadratic equation:
[tex]y=x^2-2kx+3[/tex]
Where k is a non-zero constant.
And we want to determine the vertex of the parabola in terms of k.
The vertex of a parabola is given by the formulas:
[tex]\displaystyle \text{Vertex}=\left(-\frac{b}{2a}, f\left(-\frac{b}{2a}\right)\right)[/tex]
In this case, a = 1, b = -2k, and c = 3.
Find the x-coorinate of the vertex:
[tex]\displaystyle x=-\frac{(-2k)}{2(1)}=\frac{2k}{2}=k[/tex]
To find the y-coordinate, we substitute the value we acquired back into the equation. So:
[tex]\displaystyle \begin{aligned} y(k)&=(k)^2-2k(k)+3\\&=k^2-2k^2+3\\&=3-k^2\end{aligned}[/tex]
Therefore, our vertex in terms of k is:
[tex]\displaystyle \text{Vertex} = \left(k,3-k^2\right)[/tex]
express 42 base 7 in base 10
Answer:
correct 42 in bsae 10 is 60
Help
Will
Give
Brainlist
Answer:
3.14 million
Step-by-step explanation:
10.676 - 7.536 = 3.14
To check
7.536 + 3.14 = 10.676
Answer:
3.14 million is the correct answer
Find the lengths of the missing pieces of the triangle. (Picture attached). Thank you!!
Step-by-step explanation:
my answer is in the image above
Answer:
I've attached the Answer here