Final answer:
The tangent of ∠Y in ΔXYZ is the ratio of the length of side XZ to the length of side ZY, which is 65/72.
Explanation:
In ΔXYZ, we are given that ∠Z = 90°, YX = 97, XZ = 65, and ZY = 72. To find the tangent of ∠Y, we use the definition of the tangent function in a right triangle, which is the ratio of the length of the opposite side to the length of the adjacent side for the given angle.
Since ∠Z is the right angle and we are interested in a tangent of ∠Y, the opposite side to ∠Y is XZ (which measures 65), and the adjacent side to ∠Y is ZY (which measures 72).
Therefore, the tangent of ∠Y is given by the ratio:
tan(∠Y) = opposite/adjacent = XZ/ZY = 65/72.
Isolate the identity
cos 2x - cos 8x
cos 2x + cos 8x
HELP PLS
Answer:
Cos 2x = Cos (5x-3x)
Cos(5x)Cos(3x) + Sin(5x)Sin(3x)
Cos 8x = Cos (5x + 3x)
Cos(5x)Cos(3x) - Sin(5x)Sin(3x)
Cos 2x - Cos 8x
= Cos(5x)Cos(3x) + Sin(5x)Sin(3x) -
[Cos(5x)Cos(3x) - Sin(5x)Sin(3x)]
= 2Sin(5x)Sin(3x)
Cos 2x + Cos 8x
= Cos(5x)Cos(3x) + Sin(5x)Sin(3x) +
[Cos(5x)Cos(3x) - Sin(5x)Sin(3x)]
= 2Cos(5x)Cos(3x)
= 2Sin(5x)Sin(3x) ÷ 2Cos(5x)Cos(3x)
2 gets cancelled out
Sin(5x)/Cos(5x) is Tan(5x)
Sin(3x)/Cos(3x) is Tan(3x)
Hence the fraction is identical to
Tan(5x)Tan(3x)
what is (5a+2)(a+4) in polynomial standard form
Answer:
5a²+22a+8
Step-by-step explanation:
(5a+2)(a+4)
5a² + 20a + 2a + 8
5a² + 22a + 8
6q-11=13
What does q equal to?
Answer:
q=4
Step-by-step explanation:
brainlest would be epic owo
Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
6*q-11-(13)=0
Step by step solution :
Step 1 :
Pulling out like terms :
1.1 Pull out like factors :
6q - 24 = 6 • (q - 4)
Equation at the end of step 1 :
Step 2 :
Equations which are never true :
2.1 Solve : 6 = 0
This equation has no solution.
A a non-zero constant never equals zero.
Solving a Single Variable Equation :
2.2 Solve : q-4 = 0
Add 4 to both sides of the equation :
q = 4
Answer:
q=4
Step-by-step explanation:
6q-11=13 first you have to get all the like terms together so add 11 to both sides
6q=24 Now divide both sides by 6 so you just have q on one side
q=4
Kyle is renting a jetski for the day. If he can rent the jetski in 1-hour increments, what is the minimum number of hours must he rent the jetski for option 2 to be a better deal than option 1? A) 2 hours B) 3 hours C) 4 hours D) 5 hours
Complete Question:
Option 1: $30 an hour plus a non-refundable deposit of $50.
Option 2: $20 an hour plus a non-refundable deposit of $75.
Kyle is renting a jetski for the day. If he can rent the jetski in 1-hour increments, what is the minimum number of hours must he rent the jetski for option 2 to be a better deal than option 1?
Answer:
Kyle must rent the jetski for three hours for option 2 to be a better deal than option 1
Solution:
Let "x" be the number of hours
Option 1: $30 an hour plus a non-refundable deposit of $50.Therefore,
Charge for option 1: 50 + 30x
For 1 hour,
Charge = 50 + 30(1) = 80
For 2 hours,
Charge = 30(2) + 50 = 110
For 3 hours,
Charge = 30(3) + 50 = 140
For 4 hours,
Charge = 30(4) + 50 = 160
Option 2: $20 an hour plus a non-refundable deposit of $75Charge for option 2 : 75 + 20x
For 1 hour,
Charge = 20(1) + 75 = 95
For 2 hours ,
Charge = 20(2) + 75 = 115
For 3 hours,
Charge = 20(3) + 75 = 135
For 4 hours,
Charge = 20(4) + 75 = 155
For the first two hours , the charge of option 2 is more than the rent of option 1
From 3 hours, option 2 will be better deal than option 1
Select all the complex numbers in the given table
The complex number from the table are
[tex]1+\sqrt{-3}, \ 4-3 \sqrt{-16}, \ \frac{3+2 \sqrt{-9}}{7}, \ 9 \sqrt{-\frac{7}{5}}[/tex]
Solution:
Let us solve and identify the complex number.
(A) [tex]5-\sqrt{\frac{9}{4}}[/tex]
[tex]5-\sqrt{\frac{9}{4}}= 5-\sqrt{\frac{3^2}{2^2}}[/tex]
[tex]= 5-\frac{3}{2}[/tex]
= 3.5
This is not a complex number.
(B) [tex]1+\sqrt{-3}[/tex]
[tex]1+\sqrt{-3}=1+\sqrt{-1\times 3}[/tex]
We know that [tex]\sqrt{-1} =i[/tex].
[tex]1+\sqrt{-3}=1+\sqrt{3}i[/tex]
This is a complex number.
(C) [tex]4-3 \sqrt{-16}[/tex]
[tex]4-3 \sqrt{-16}=4-3 \sqrt{-1\times 4^2}[/tex]
[tex]4-3 \sqrt{-16}=4-3\times4 \sqrt{-1}[/tex]
We know that [tex]\sqrt{-1} =i[/tex].
[tex]4-3 \sqrt{-16}=4-12i[/tex]
This is a complex number.
(D) [tex]\frac{2-\sqrt{12}}{5}[/tex]
[tex]\frac{2-\sqrt{12}}{5}=\frac{2-2\sqrt{3}}{5}[/tex]
There is no –1 in the root.
This is not a complex number.
(E) [tex]\frac{3+2 \sqrt{-9}}{7}[/tex]
[tex]\frac{3+2 \sqrt{-9}}{7}=\frac{3+2 \sqrt{-1\times 3^2}}{7}[/tex]
We know that [tex]\sqrt{-1} =i[/tex].
[tex]=\frac{3+6i}{7}[/tex]
This is a complex number.
(F) [tex]9 \sqrt{-\frac{7}{5}}[/tex]
[tex]9 \sqrt{-\frac{7}{5}}=9 \sqrt{-1 \times \frac{7}{5}}[/tex]
We know that [tex]\sqrt{-1} =i[/tex].
[tex]9 \sqrt{-\frac{7}{5}}=9 \sqrt{ \frac{7}{5}}i[/tex]
This is a complex number.
Hence the complex number from the table are
[tex]1+\sqrt{-3}, \ 4-3 \sqrt{-16}, \ \frac{3+2 \sqrt{-9}}{7}, \ 9 \sqrt{-\frac{7}{5}}[/tex]
degree of inverse tangent of 0.83
Answer:
39.69 degrees
Step-by-step explanation:
Let
x ----> the measure of the angle
we have that
[tex]tan(X)=0.83[/tex]
using a calculator
[tex]m\angle X=tan^{-1}(0.83)=39.69^o[/tex]
What is the answer to 7x=3x+24
Answer:
7x=3x+24
4x=24
x=6
Answer:
[tex]x=6\\[/tex]
Step-by-step explanation:
[tex]7x=3x+24[/tex]
[tex]7x-3x=3x-3x+24[/tex]
[tex]4x=24[/tex]
[tex]\frac{4x}{4} =\frac{24}{4}[/tex]
[tex]x=6[/tex]
3.
Performance Task A person is planning a
weekly workout schedule of cardio and yoga.
He has at most 12 hours per week to work out.
The amounts of time he wants to spend on
cardio and yoga are shown.
Whrite a system of linear inequalities to represent this situation
Answer:
2/3 ≥ 3/6
Step-by-step explanation:
Cross Multiply
f/g=h/i
f×i=g×h
2×6> 3×3
12> 9
If s represents speed write an inequality to represent how fast a person can legally dive a vehicle in a school zone with a speed limit of 25 mph ?
two friends bought a $14 pizza. Each person bought their own drink. The total cost of the food can be represented by the expression $2x + $14. What expression represents the cost of food for one person
What is the shape of the horizontal cross section of the given prism?
Answer:
pentagon
Step-by-step explanation:
In this problem we have a pentagonal prism
so
The solid has two pentagonal bases and five lateral rectangular faces
we know that
A plane parallel to the base of a pentagonal prism will intersect a cross section that is the same shape as its bases
so
The shape of the horizontal cross section of the given prism, is a pentagon
Answer: Pentagon
Step-by-step explanation:
Beverly is starting a new diet. Her current weight is 160 pounds. She expects to lose 4 pounds per month. If x represents the number of months Beverly is on the diet, which linear function models the situation?
Find the product of 2x2(6x + 3). 12x3 12x3 + 3 12x3 + 6x2 2x2 + 6x + 3
Answer:
C. 12x³ + 6x²
Step-by-step explanation:
I'm an FLVS kid and got the question right, so I wanted to explain my answer:
You just have to use the distributive property for this one. Multiply 2x² by each term in the brackets.
2x²(6x + 3) ← original question for ref.
2x²(6x) = 12x³
2 · 6 = 12x² · x = x³("x" techniqually has a placeholder exponent of 1. To multiply two exponents with the same base, you just add the exponents. So x2 + x1 = x3.)2x²(3) = 6x²
2 · 3 = 6Keep the variable and exponent the sameSo the new terms are 12x³ + 6x²
The answer is C.
Solve the equation
-4(8+y)=9
Answer:
[tex]-\frac{41}{4}[/tex]
Step-by-step explanation:
-4(8+y)=9
Distribute:
-32-4y=9
Add 32 on both sides:
-4y=41
Divide -4 with 41:
y=-41/4
Answer:
[tex]y = - \frac{41}{4} = - 10 \frac{1}{4} \\ [/tex]
Step-by-step explanation:
[tex]-4(8+y)=9 \\ - 32 - 4y = 9 \\ - 4y = 9 + 32 \\ - 4y = 41 \\ \\ y = - \frac{41}{4} = - 10 \frac{1}{4} [/tex]
2. On rectangle ABCD below, if A is located at
(3, 4) and B is located at (7,6), is the slope
of BC ?
Answer: The slope of BC is -2.
Step-by-step explanation:
We know that a rectangle has all opposite sides equal and parallel.
Each interior angle is a right angle.
Therefore , if rectangle ABCD is a rectangle then , AB should perpendicular to BC. [ ∵ Angle between AB and BC is 90° .] (1)
Also , slope of line passing through (a,b) and (c,d) : [tex]\dfrac{d-b}{c-a}[/tex]
If A is located at (3, 4) and B is located at (7,6) .
Then , The slope of AB = [tex]\dfrac{6-4}{7-3}=\dfrac{2}{4}=\dfrac{1}{2}[/tex]
Also, the product of slopes of two perpendicular lines is -1.
Then , (Slope of AB) x (Slope of BC) = -1 [From (1)]
[tex]\Rightarrow\ \dfrac{1}{2}\times (\text{Slope of BC})= -1\\\\\Rightarrow\ \text{Slope of BC}=-2[/tex]
Hence, the slope of BC is -2.
credit card customer owes $523.85. They
re only able to make a payment of $184.50. How
much money does the customer still owe?
Answer:
$339.25
Step-by-step explanation:
Since the credit card customer owes $523.85 and is only able to make a payment of $184.50
Amount still owed
= $523.85 - $184.60
= $339.25
The customer still owes $339.25
M=-2 (-3,4) how do you write it into slope intercept
Answer:
y = -2x - 2
Plug the x- and y-values into the appropriate spaces in the slope-intercept form and see which value for b would make the equation true:
4 = -2(-3) +/- ?
4 = 6 - 2
4 = 4
I don't know if this makes sense, I'm sorry if it doesn't but the answer is correct because it goes through the point (-3,4)
The answer is y = -2x - 2
You have to first plug the x- and y-values into the correct spots in the slope-intercept form and see which value for b would make the equation true.
4 = -2(-3) +/- ?
4 = 6 - 2
4 = 4
Hope to help.
Which expressions are equivalent? Check all that apply.
3^9 3^4 -9^2 9^9 81^1
Answer:
3^4 and 81^1
Step-by-step explanation:
A TV sells for 290$. If it's discounted at 15%, what is the discount
The discount is $43.50, making the price of the discounted TV $246.50.
15% = .15
.15 x 290 = 43.5
$290 - $43.50 = $246.50
Describe an easy way to find the square root
when the number is not a perfect square?
The product of a rational number multiplied by itself is called as a perfect square.,we can easily find out the square root for a number which is a imperfect square
Step-by-step explanation:
using the following formula we can find a square root for a number which is a imperfect square
X = Non perfect square
√x = (square root of nearest lower perfect square +(x - perfect square)÷2×(√perfect square )
[tex]√x = (square root of nearest lower perfect square +(x - perfect square)÷2×(√perfect square )[/tex]Example
√38
the nearest perfect root is 36
36 (√36=6)
so √38 = √36 + (38-36)/2√36
= 6 + 2/12
=6 + 1/6 = 6.166 (answer)
[tex]√38 the nearest perfect root is 36 36 (√36=6)so √38 = √36 + (38-36)/2√36 = 6 + 2/12=6 + 1/6 = 6.166 (answer)[/tex]
To find the square root of a non-perfect square, use estimation techniques or the quadratic formula if in relation to an equation. Use the imaginary unit i for square roots of negative numbers, and simplify by removing perfect squares when adding or subtracting radicals.
Finding the square root of a number that is not a perfect square can be done using a few different methods. One simple non-calculator method is to use estimation and refinement; start with an approximate guess and improve it. When dealing with negative numbers, remember that we use the imaginary unit i to denote the square roots of negative numbers. For example, a₂ can be written as 2i. Adding and subtracting radicals involves simplifying each radical by removing perfect squares and combining like terms.
For equations where the square root is part of a quadratic equation, ax²+bx+c = 0, if a, b, and c are non-zero, we should use the quadratic formula to find solutions. Estimation also applies when dealing with cube roots or higher, where we can start with an initial guess and use methods like calculus to refine it.
To estimate a surd like a₃ without a calculator, consider its place on the number line between two integers, knowing that a₃ is about 1.732. This helps get an approximate value which is often sufficient for many applications.
There are (26)3⋅ 20 bacteria in a sample. What is the total number of bacteria in the sample
22
23
29
218
Answer:
29?
Step-by-step explanation:
Answer:it might be 29
Step-by-step explanation:
if you qre travelling @90 km/h how far will you travel in 42 mins? Can someone show me step by step solution pls on how to work it out.
Answer:
Distance = 63 km
Step-by-step explanation:
Speed = 90 km/h
Time = 42 mins
Time = 42 / 60 = 0.7 hrs
Distance = Speed × time
Distance = 90 km/h × 0.7 hr
Distance = 63 km
please help I NEED HELP PLS SKDJLAK
Answer: -√6 + 1
Step-by-step explanation:
[tex]\dfrac{\tan\bigg(-\dfrac{2\pi}{3}\bigg)}{\sin\bigg(\dfrac{7\pi}{4}\bigg)}-\sec(-\pi)\\\\\\=\dfrac{\tan(240^o)}{\sin(315^o)}-\sec(180^o)\\\\\\=\dfrac{\sqrt3}{-\dfrac{\sqrt2}{2}}-(-1)\\\\\\=\dfrac{-2\sqrt3}{\sqrt2}\bigg(\dfrac{\sqrt2}{\sqrt2}\bigg)+1\\\\\\=\large\boxed{-\sqrt6+1}[/tex]
If f(x) = 2x² + 5, then what is the remainder when f (x) is divided by x – 10?
Answer:
Step-by-step explanation:
x - 10 = 0
x = 10
f(10) = 2*10² + 5 = 2*100 + 5 = 200 + 5
= 205
Remainder = 205
Answer:
195 is the right answer
Step-by-step explanation:
195
7. A school supply company packages the
erasers shown below in boxes of 12. How
many cubic inches does the package contain?
2 in
.5in
Find eraser )
Answer:
5 in
Step-by-step explanation:
I don't actually the ans
Select the expression that is equivalent to the given polynomial.
16r4 – 625
O A. (2x + 5)(2x - 5)(2x + 5i) (2x – 5i)
B. (2x - 5)(2x – 5)(2x – 5i)(2x – 5i)
C. (2x - 5)(2x – 5)(2x + 5i)(2x – 5i)
D. (2x + 5)(2x + 5)(2x + 5) (21 + 5i)
Observe that [tex]16r^4[/tex] is the square of [tex]4r^2[/tex], and 625 is the square of 25.
So, your expression is a difference of squares, and as such we can rewrite it as
[tex]16r^4-625=(4r^2+25)(4r^2-25)[/tex]
Now again, [tex]4r^2[/tex] is the square of [tex]2r[/tex], and 25 is the square of 5. So, we have a sum and a difference of squares.
But if we think of 25 as [tex]-(5i)^2[/tex], we have again the difference of two squares, so we have
[tex]4r^2+25=(2r+5i)(2r-5i)[/tex]
[tex]4r^2-25=(2r+5)(2r-5)[/tex]
Option A is the correct expression equivalent to 16r⁴-625.
The options in the question must have r in place of x.
What does the imaginary number i mean?The imaginary number 'i' is the solution of the algebraic equation x²+1.
Thus, x²+1=(x+i)(x-i).
How to factorize (a²+b²)?We can observe that (a+bi)(a-bi)=(a²+b²)+i(-ab+ba)=a²+b².
Hence the factorization of a²+b² is (a+bi)(a-bi)
How to factorize the given polynomial?16r⁴-625
=(4r²-25)(4r²+25)
=(2r-5)(2r+5)(2r+5i)(2r-5i)
So, option A is the correct expression equivalent to 16r⁴-625.
To learn more about factorization visit- https://brainly.com/question/20293447?referrer=searchResults
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jack had 8 dogs each of them need them need a 30min walk how long will jack be walking his dogs.
Answer:
240 minutes or 4 hours
Step-by-step explanation:
Step 1: Multiply
8 * 30
240 min
If you want hours:
240 / 60
4 hours
Answer: 240 minutes or 4 hours
Betty is planning to give this box as a gift, so she plans to wrap it. The box is shaped like a rectangular prism, where the length is 14 inches, the width is 5 inches, and the height is 4 inches. How many square inches of paper will she need to cover the entire box?
Answer:
292 in^2
Step-by-step explanation:
Area of the top and bottom combined is 2(14 inches)(5 inches)), or 140 in^2.
Area of the two ends, combined, is 2(4 inches)(5 inches)) = 40 in^2.
Are of the two sides, combined, is 2(14 inches)(4 inches)) = 112 in^2.
Summing up these three subtotals, we get the total area 292 in^2.
Which lines best approximate the directrices of the ellipse? Round to the nearest tenth. x = −4.6 and x = 4.6 x = −3.5 and x = 3.5 y = −4.6 and y = 4.6 y = −3.5 and y = 3.5
Answer: c
Step-by-step explanation:
Answer:
C y = −4.6 and y = 4.6
Step-by-step explanation:
Edge 2023
Which situation can match the given inequality? 7x < 4x + 5
The cost of 7 journals is $5 greater than the cost of 4 journals.
The cost of 7 journals is less than the cost of 4 journals plus a $5 novel.
The cost of 7 journals is less than the cost of 4 journals with a $5 off coupon. The cost of 7 journals is greater than the cost of 4 journals plus a $5 novel.
Answer:
The cost of 7 journals is less than the cost of 4 journals plus a $5 novel.
Step-by-step explanation:
Let
x -----> the cost of a journal
Verify each case
case 1) The cost of 7 journals is $5 greater than the cost of 4 journals
In this case the equation would be
[tex]7x=4x+5[/tex]
case 2) The cost of 7 journals is less than the cost of 4 journals plus a $5 novel.
so
[tex]7x<4x+5[/tex]
solve for x
subtract 4x both sides
[tex]3x<5[/tex]
divide by 3 both sides
[tex]x<\$1.67[/tex]
so
The cost of one journal must be less than $1.67
case 3) The cost of 7 journals is less than the cost of 4 journals with a $5 off coupon.
so
The inequality would be
[tex]7x<4x-5[/tex]
case 4) The cost of 7 journals is greater than the cost of 4 journals plus a $5 novel.
so
The inequality would be
[tex]7x>4x-5[/tex]