Answer:
See below.
Step-by-step explanation:
[tex]\cos(20)-\sin(20)=\sqrt{2}\sin(25)[/tex]
First, use the co-function identity:
[tex]\sin(90-x)=\cos(x)[/tex]
We can turn the second term into cosine:
[tex]\sin(20)=\sin(90-70)=\cos(70)[/tex]
Substitute:
[tex]\cos(20)-\cos(70)=\sqrt{2}\sin(25)[/tex]
Now, use the sum to product formulas. We will use the following:
[tex]\cos(x)-\cos(y)=-2\sin(\frac{x+y}{2})\sin(\frac{x-y}{2})[/tex]
Substitute:
[tex]\cos(20)-\cos(70)=-2\sin(\frac{20+70}{2})\sin(\frac{20-70}{2})\\\cos(20)-\cos(70) =-2\sin(45)\sin(-25)\\\cos(20)-\cos(70)=-2(\frac{\sqrt{2}}{2})\sin(-25)\\ \cos(20)-\cos(70)=-\sqrt{2}\sin(-25)[/tex]
Use the even-odd identity:
[tex]\sin(-x)=-\sin(x)[/tex]
Therefore:
[tex]\cos(20)-\cos(70)=-\sqrt{2}\sin(-25)\\\cos(20)-\cos(70)=-\sqrt{2}\cdot-\sin(25)\\\cos(20)-\cos(70)=\sqrt{2}\sin(25)[/tex]
Replace the second term with the original term:
[tex]\cos(20)-\sin(20)=\sqrt{2}\sin(25)[/tex]
Proof complete.
PLSSS HELP I would appreciate it
Answer:
x = 12.6 degrees
Step-by-step explanation:
Using the property of alternate interior angles, we can say that m<A is equivalent to m<E.
m<A = m<E
63 = 5x
12.6 = x
So, x = 12.6 degrees
Cheers.
A tent is in the form of a right circular cylinder and cone. The radius of the cone and cylinder is 4 meters. The height of the cylinder and cone are 4.5 meters and 3 meters respectively. Find the outer surface area of the tent. (Assume π = 22 /7)
Answer:
176m²
Step-by-step explanation:
When we are asked to find the outer surface area of a geometric shape, it means to find the Lateral or Curved Surface Area of the shape. We are given two shapes above.
Step 1
Find the Outer surface area of the cone
Outer / Lateral surface area of a cone =
πrl
Where l = √r² + h²
r = 4 m
h = 3m
Outer surface area = 22/7 ×√4² + 3²
= 22/7 × √16 + 9
= 22/7 × √25
= 22/7 × 5
= 62.83185m²
Step 2
Find the outer surface area of a cylinder
= 2πrh
π = 22/7
r = 4m
h = 4.5
π = 22/7
Outer surface area of a cylinder = 2 × 22/7 × 4 × 4.5
= 113.09734m²
Step 3
The Outer Surface Area of the Tent = Outer Surface Area of the cone + Outer Surface Area of the cylinder
= 62.83185m² + 113.09734m²
= 175.92919m²
Approximately ≈ 176m²
Therefore, the outer surface area of the tent = 176m²
2. A cylinder has a height of 4.5 cm and a diameter of 1.5 cm. What is the surface area of the cylinder in square centimeters? Use 3.14 for pi.
21.2
31.8
7.9
24.7
Answer:
[tex] SA = 24.73~cm^3 [/tex]
Step-by-step explanation:
[tex] SA = 2\pi r^2 + 2\pi r h [/tex]
r = d/2 = (1.5 cm)/2 = 0.75 cm
[tex] SA = 2(3.14)(0.75~cm)^2 + 2(3.14)(0.75~cm)(4.5~cm) [/tex]
[tex] SA = 24.73~cm^3 [/tex]
Answer:
24.7
Step-by-step explanation:
took this exam and got it right
Briefly explain your knowledge of sine, cosine, and tangent.
Answer:
Sine, Cosine and Tangent are main functions used in Trigonometry .
They are based on a Right-Angled Triangle.
It helps to give a name to each side of a right triangle:
"Opposite" ; side opposite to the angle θ
"Adjacent"; side adjacent (next to) to the angle θ,
"Hypotenuse" ; the longest side
Step-by-step explanation:
Sine, Cosine and Tangent (are often shortened as sin, cos and tan)
They are used in calculation by;
[tex]Sin \alpha = \frac{Opposite}{Hypotenuse}\\ \\Cos \alpha = \frac{Adjacent}{Hypotenuse}\\ \\Tan \alpha = \frac{Opposite}{Adjacent}[/tex]
To remember how to apply them , we use
SOHCAHTOA
soh
Sin = Opposite / Hypotenusecah
Cosine = Adjacent / Hypotenusetoa
Tangent = Opposite / AdjacentI hope it helps :)What are the solutions to the equation 3(x – 4)(x + 5) = 0? x = –4 or x = 5 x = 3, x = 4, or x = –5 x = 3, x = –4, or x = 5 x = 4 or x = –5
Answer:
x= 4 x = -5
Step-by-step explanation:
3(x – 4)(x + 5) = 0
Using the zero product property
(x – 4)=0 (x + 5) = 0
x= 4 x = -5
What are the solutions to the equation 3(x – 4)(x + 5) = 0?
x = –4 or x = 5
x = 3, x = 4, or x = –5
x = 3, x = –4, or x = 5
x = 4 or x = –5
Answer:
D. x = 4 or x = –5
Step-by-step explanation:
Solve the equation for all values of x in simplest form: (x-9)^2 = 15
[tex](x-9)^2=15\\x-9=\sqrt{15} \vee x-9=-\sqrt{15}\\x=9+\sqrt{15} \vee x=9-\sqrt{15}[/tex]
What is the standard form of function f ?
Answer:
f(x) = 4x² + 48x + 149
Step-by-step explanation:
f(x) = 4(x + 6)² + 5
The above expression can be written as: f(x) = ax² + bx + c, by doing the following:
1. Expand (x + 6)²
(x + 6)² = (x + 6)(x + 6)
(x + 6)(x + 6)
x(x + 6) + 6(x +6)
x² + 6x + 6x + 36
x² + 12x + 36
(x + 6)² = x² + 12x + 36
2. Substitute x² + 12x + 36 for (x + 6)² in
f(x) = 4(x + 6)² + 5
This is illustrated below:
f(x) = 4(x + 6)² + 5
(x + 6)² = x² + 12x + 36
f(x) = 4(x² + 12x + 36) + 5
Clear bracket
f(x) = 4x² + 48x + 144 + 5
f(x) = 4x² + 48x + 149
Therefore, the standard of the function:
f(x) = 4(x + 6)² + 5
is
f(x) = 4x² + 48x + 149
How to do this question plz answer me step by step plzz plz
Answer:
4 cm
Step-by-step explanation:
Volume of milk
LBH
L= 8, B= 5 and H =12
5×8×12=480
After rotation
L= 8, B=15 and H=x
V=LBH
480=8×15×x
480=120x
x=4cm
Answer:
The depth of the milk is 4cm when turned
Step-by-step explanation:
First we need to figure out how much milk is inside the container. We can do this by finding the volume it takes up. The milk's depth is 12cm so the height is 12 instead of 15. The length and width remain the same (5 and 8)
5x8x12=480 cm^3
The volume of the milk is 480, so when the carton is turned, the milk's volume still is the same
When it is turned, the base changes. Now it is 8 and 15 for the length and width. We just need to find the height.
8x15xh=480
120h=480
h=4
The depth of the milk is 4cm when turned
Suppose the radius of a circle is 2. What is its circumference?
Answer:
12.57
Step-by-step explanation:
The formula to solve the circumference of a circle is:
2 x PI x R (radius)
=> 2 x PI x 2
=> 4 PI or 12.57
need help...!! plzzz
If f(x)= Square root of X +12 and g(x)= 2 Square root of X what is the value of (f-g)(144)
Answer:
0
Step-by-step explanation:
Give another name plane L
Answer:
Any one of these three works:
plane MOU
plane MNU
plane NOU
Step-by-step explanation:
A plane can be named by a single letter, such as L in this problem, or by any three non-collinear points that lie on the plane. Non-collinear points are points that do not all lie in a single line.
Points M, N, O, and U lie on plane L, so you can choose any 3 of the 4 points to name the plane with, but make sure all 3 points are non-collinear.
To name plane L with points, you cannot use points MNO together since they are collinear, but you can name it using point U plus any two of the points M, N, and O.
plane L can be named
plane MOU
plane MNU
plane NOU
Do not name it plane MNO
In 1 through 3, what is the relationship between the values of the given digits?
1. The 7s in 7,700
2. The 2's in 522
Answer:
7000 (7 thousand)
700 (7 hundred)
20 (2 tens)
2 (2 units)
Step-by-step explanation:
what is the relationship between the values of the given digits?
1. The 7s in 7,700
2. The 2's in 522
From the knowledge of place values;
7,700 could be broken down thus :
7000 + 700 + 0 + 0
The first 7 depicts thousands as it has 3 trailing digits (7000)
The second 7 depicts hundred as it has 2 trailing digits (700)
522 could be broken down thus :
500 + 20 + 2
From 522
The first '2' has one trailing digit = tens
The ending / last digit ia always = Unit value
URGENT WILL GIVE BRAINLIEST TO FIRST RESPONDER You are visiting a Redwood tree forest and want to verify the height of one of the trees. You measure its shadow along the ground and use trig to calculate the height. The shadow measures 500 feet and you calculate the angle of elevation to be 35 degrees. This forms a right triangle. a. What is the measure of the other acute angle? b. What is the height of the tree? c. You are standing at the end of the tree's shadow and want to take a picture of the tree but your camera can only focus at distance less than 500 feet. When you hold the camera to take the picture it is 5 feet above the ground. What is the distance from the end of the shadow to the top of the tree? d. Can you take a clear picture of the top of the tree from where you are standing?
Answer:
a) 55 degrees
b) 350 ft.
Step-by-step explanation:
a- the sum of angles of triangle=180
( since it is right angle , one angle is 90 degrees), x be the acute angle
x+35+90=180
x=180-125
x=55 degrees
b) tan 35= height of a tree/ length of a shadow
height of a tree=tan35*500=350.103≅350 ft ( rounded to nearest tens)
c) hypotenuse²=350.1²+500²
c=√350.1²+500²
c=610.385 ft
d) no because the distance is more than 500
In the given figure if p||q what is the value of b?
Answer:
120°
Step-by-step explanation:
We can see that b=a by opposite exteriors.
So a+1/2a=180
1.5a=180
a=180/1.5=120
And since b and a are equal, b also equals 120°
A student estimated the sum 7.95 + 8.11 + 78.5 + 8.05 + 79.4 + 0.815 as: All the numbers begin with a 7 or 8, so use cluster estimation. 8 + 8 + 80 + 8 + 80 + 0.8 = 184.8
Answer: this not correct ,because in the expression it is not clear , the numbers are neither exactly rounded to nearest tens or tenths.
Step-by-step explanation:
Our total add is
= 7.95 + 8.11 + 78.5 + 8.05 + 79.4 + 0.815
When we spherical it up to nearest tens
7.95 = 8.00
8.11 = 8.00
78.5 = 79
8.05 = 8.00
79.4 = 79.0
0.815 = 1
when we estimate the rational numbers with an extra operation once done,our results is
= eight + eight + eighty + eight + eighty + zero.8 = 184.8, isn't correct ,because within the expression it's not clear , the numbers area unit neither precisely rounded to nearest tens or tenths.
for example ,79.4 once rounded to nearest tens = seventy nine,but within the expression eighty (80) is written,which isn't correct.
Similarly,when rounded to nearest tens, 0.815 = 1, however within the expression 0.8 is written,which is wrong.
Similarly,when rounded to nearest tens ,78.5 = 79 , however within the expression eighty ( 80 ), is written,which is wrong
Which products result in a difference of squares? Select three options. A. (x minus y)(y minus x) B. (6 minus y)(6 minus y) C. (3 + x z)(negative 3 + x z) D. (y squared minus x y)(y squared + x y) E. (64 y squared + x squared)(negative x squared + 64 y squared)
Answer:
C D E
Step-by-step explanation:
Edg
Out of the given options, options C, D and E are a difference of squares.
What is the difference of squares?Difference of Squares, two terms that are squared and separated by a subtraction sign.
Given are, options,
D) (y squared minus x y)(y squared + x y) = (y²-xy)(y²+xy) = y⁴-(xy)²
E) (64 y squared + x squared)(negative x squared + 64 y squared) = (64y²+x²)(64y²-x²) = (64y)⁴-x⁴
C) (3 + x z)(negative 3 + x z) = (3+xz)(3-xz) = 3²-(xz)²
Hence, out of the given options, options C, D and E are a difference of squares.
For more references on difference of squares, click;
https://brainly.com/question/11801811
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in this figure ST || QR, PT = 4cm, TR = 8cm, area of PQR = 90cm^2. Find PT:TR please help me
Answer: The required ratio is PT:TR = 1:2.
Step-by-step explanation:
Given: In triangle PQR, ST || QR, PT = 4cm, TR = 8cm, area of PQR = 90 cm².
To find : PT:TR
.i.e. Ratio of PT to TR.
Here, PT:TR[tex]=\dfrac{PT}{TR}[/tex]
[tex]=\dfrac{4\ cm}{8\ cm}[/tex]
Divide numerator and denominator by 4 , we get
[tex]\dfrac{1}{2}[/tex]
Therefore, the required ratio is PT:TR = 1:2.
Based on the table, which best predicts the end
behavior of the graph of f(x)?
Answer:
approaching negative infinity
Step-by-step explanation:
Since as x increases, the values of f(x) are approaching infinity, the function approaches negative infinity as the end behavior.
Answer:
Below.
Step-step-explanation:
As x increases from negative infinity f(x) decreases in value .
As x increases to positive infinity f(x) decreases in value.
For values of x on the negative side the graph rises to the left and on the positive x -axis it falls to the right.
La madre de rosita se ha comprado una mascarilla por un valor de 1 25 dolares al mismo tiempo se ha comprado un paquete de jabones de 2 00 dolares y luego compra un gel de alcohol en 3 00 dolares después de pagar le queda 7 65 dolares que debemos saber que tengo que hacer para obtener el resultaron
Answer:
La cantidad inicial que tenía la madre de Rosita antes, comprando los artículos es de $13.90
Step-by-step explanation:
La información dada son;
El valor de la máscara = $ 1.25
El valor del paquete de jabones = $ 2.00
El valor del gel de alcohol = $ 3.00
La cantidad que le quedaba después de pagar = $ 7.65
Por lo tanto, tenemos;
La cantidad inicial que tenía la madre de Rosita antes, comprando los artículos = La cantidad que le quedaba después de pagar + El valor del gel de alcohol + El valor del paquete de jabones + El valor de la mascarilla
Por lo tanto;
La cantidad inicial que tenía la madre de Rosita antes, comprando los artículos = $ 7.65 + $ 3.00 + $ 2.00 + $ 1.25 = $ 13.90.
a businessman bought three machines at rs 5400 each and spent 4000 on rearing and sold the machines for Rs Rs 7000 each, how much profit didi he make?
Answer:
[tex] \boxed{Rs \: 800}[/tex]Step-by-step explanation:
Cost price of three machines with repairment charge ( CP ) = 5400 × 3 + 4000
= Rs 20200
Selling price of 1 machine = Rs 7000
Selling price of 3 machines ( S.P )= Rs 7000 × 3
= Rs 21000
Since , SP > CP , he made a profit
Profit = SP - CP
= Rs 21000 - Rs 20200
= Rs 800
--------------------------------------------------------------
Further more explanation
Profit and loss
In any business , owners have intension to have profit by selling articles. The price at which an article is purchased is called it's Cost price ( C.P ) and the price at which it is sold is called Selling price ( S.P ).
If the selling price is less than cost price of an article then there is a loss.
[tex] \mathrm{Loss \: = \: Cost \: Price \: (C.P) - Selling \: Price \: (S.P)}[/tex]
If the selling price is more than cost price of an article then there is a profit ( gain )
[tex] \mathrm{Profit = Selling \: Price \: (S.P) - Cost \: Price \: (C.P)}[/tex]
So, If S.P > C.P, there is profit in dealing.
If C.P > SP , there is loss in dealing.
Hope I helped!
Best regards!!
A physiological psychologist has performed an experiment to determine if a particular drug, smartozine, affects maze learning in rats. Three groups of 8 rats each are injected with one of three different doses of smartozine, while a fourth group of 6 rats is injected with a saline solution as a control. After the injection, rats in all four groups are timed in how long it takes them to learn to traverse a maze. The results of the experiment are presented below. Did smartozine affect how quickly the rats learned the maze. Use a level of significance of.05 SSB 610 SSW = 1742 What is the critical value of F for this situation?
Answer:
The critical value of F for this situation is 2.975.
Step-by-step explanation:
A test is being performed to determine if a particular drug, smartozine, affects maze learning in rats.
The groups are divided as follows:
Three groups of 8 rats each are injected with one of three different doses of smartozine.The fourth group of 6 rats is injected with a saline solution as a control.So, there were in total k = 4 groups with n = 30 rats.
The significance level of the test is, α = 0.05.
Compute the critical value of F as follows:
[tex]F_{\alpha, (k-1, n-k)}=F_{0.05, (4-1, 30-4)}=F_{0.05, (3,26)}=2.975[/tex]
*Use the F-table.
Thus, the critical value of F for this situation is 2.975.
The critical value of F for this situation has been 2.975.
The F value has been the statistical factor that has been used for the determination of the significance of the test.
The high F value has been the representation of the rejected null hypothesis, while the low F value represents the accepted hypothesis. The study that has been performed with the rats has:
Number of groups of rats = k = 4
Total number of rats = n = 30
The 0.05 significance test has been performed, thus the value of α has been 0.05.
The value of F can be given as:
Critical value = [tex]\rm F_\alpha_\;_,(_k_-_1,_n_-_k_)[/tex]
Substituting the values:
Critical value = [tex]\rm F_0._0_5,_(_4_-_1,_3_0_-_4_)[/tex]
Critical value = 2.975
Thus, the critical value of F for this situation has been 2.975.
For more information about the F value, refer to the link:
https://brainly.com/question/11566053
Which equation represents a population of 320 animals that decreases at an annual rate of 19% ?
A. p=320(1.19)t
B. p=320(0.81)t
C. p=320(0.19)t
D. p=320(1.81)t
Use the ^ symbol to indicate exponents. So for instance 4^2 = 4 squared.
A decrease of 19% means we have r = -0.19 and 1+r = 1+(-0.19) = 0.81 as the base of the exponent. A decrease of 19% means the population retains 81% each year.
Is 3+(-4) the same as -4+3 ? Explain
Newly planted seedlings approximately double their weight every week. If a seedling weighing 5 grams is planted at time t=0 weeks, which equation best describes its weight, W, during the first few weeks of its life?
Answer:
[tex]W(t)=5(2^t)[/tex]
Step-by-step explanation:
Given that the Newly planted seedlings approximately double their weight every week and a seedling weighing 5 grams is planted at time t = 0 weeks. This represent an exponential function with an equation in the form:
[tex]W(t)=ab^t[/tex].
W(t) is the weight in t weeks, t is the weeks and a is the weight when t = 0. At t = 0, W = 5 g:
[tex]W(t)=ab^t\\W(0)=ab^0\\5=ab^0\\a=5[/tex]
Since the weight double every week, b = 2. The exponential function is given as:
[tex]W(t)=ab^t\\\\W(t)=5(2^t)[/tex]
PLS ANSWER I WILL GIVE BRAINLIST AND A THANK YOU
Answer:
x= 6 degrees
Step-by-step explanation:
x+x+54 = 90
2x+54 = 90
x= 90- 54 /2
x =6
Answer:
x = 6
Step-by-step explanation:
90 - 54 = 36
x + 5x = 6x
36 + 6x = 90
90 - 36 = 6x
36/6x = 6
x = 6
algebraic expression twice the difference of a number and 5. with x being "a number"
Answer:
2(x-5)
Step-by-step explanation:
Answer:
the answer to your question is 5xa^2
or you can use symbolab calculator online
The phone company offers to long-distance plans the first charges a flat value of five dollars per month plus $.99 each minute used and the second charge is $10 a month plus $.79 for each minute used if X represents the number of minutes use each month which system each of equations represent the amount of money why are you spin
Answer:
The systems of equation for the amount spent are as follows
[tex]Y= 0.99x+5[/tex]
[tex]Y= 0.79x+10[/tex]
Step-by-step explanation:
In this problem we are expect to give a model or an equation that represents the amount of money spent per month given a fix subscription amount and a variable fee which is based on extra minutes spent.
let Y represent the amount of money spent in total for the month
The first case:
Subscription =$5
charges per minutes = $0.99
therefore the amount spent can be modeled as
[tex]Y= 0.99x+5[/tex]
The second case:
Subscription =$10
charges per minutes = $0.79
therefore the amount spent can be modeled as
[tex]Y= 0.79x+10[/tex]
Find the missing factor D that makes the equality true -15y^4=(D)(3y^2)
Answer:
[tex]D=-5y^2[/tex]
Step-by-step explanation:
We have the equation:
[tex]\displaystyle -15y^4=D(3y^2)[/tex]
And we want to find D such that the equation is true.
So, we can divide both sides by 3y². This will yield:
[tex]\displaystyle D=\frac{-15y^4}{3y^2}[/tex]
We can split this into:
[tex]\displaystyle D=\frac{-15}{3}\cdot\frac{y^4}{y^2}[/tex]
Simplify. Hence:
[tex]D=-5y^2[/tex]
multiple choice
a. 126 pie cm^3
b. 84 pie cm^3
c. 504 pie cm*3
Answer:
a. 126 pie cm^3
Step-by-step explanation:
Area of a circle = pi*r²
Volume = area*height
(pi*r²)*14
Since your answers are with Pi omit the Pi and times 3² * 14 = 126 pie cm³
Answer:
A. 126pi cm^3
Step-by-step explanation:
The volume of a cylinder can be found using the following formula.
[tex]v=\pi r^2 h[/tex]
First, we must find the radius. The radius is half of the diameter.
[tex]r=\frac{d}{2}[/tex]
The diameter of the cylinder is 6 cm.
[tex]r=\frac{6cm}{2}[/tex]
[tex]r= 3cm[/tex]
The radius is 3 cm.
Now, we can substitute values into the formula.
[tex]v=\pi r^2 h[/tex]
[tex]r= 3cm\\h=14 cm[/tex]
[tex]v=\pi (3cm)^2*14 cm[/tex]
Evaluate the exponent.
[tex](3cm)^2=3cm*3cm=9cm^2[/tex]
[tex]v=\pi*9cm^2*14cm[/tex]
Multiply 9 cm^2 and 14 cm
[tex]9 cm^2*14cm=126cm^3[/tex]
[tex]v=\pi*126cm^3[/tex]
The answer choices are in terms of pi, so we can simply rearrange our answer:
[tex]v=126\pi cm^3[/tex]
The volume of the cylinder is 126pi cubic centimeters and A is the correct answer.
