Using the pythagorean identity, [tex]\cos^2{\theta} + \sin^2{\theta} = 1[/tex]. Since [tex]\theta[/tex] is in quadrant ||, we know that [tex]\cos{\theta}[/tex] is negative. Solving the equation [tex]\cos^2{\theta} + (\frac{4}{5})^2 = 1[/tex] for [tex]\cos{\theta}[/tex], we get that [tex]\cos{\theta} = -\frac{3}{5}[/tex].
[tex]\tan{\theta}[/tex] is equal to [tex]\frac{\sin{\theta}}{\cos{\theta}}[/tex], which is [tex]-\frac{4}{3}[/tex].
The value of cos θ and tan θ will be negative 0.60 and negative 0.75, respectively.
What is trigonometry?Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.
If sin θ = 4/5.
The value of the cosine is negative. Then the cosine of angle θ is given as,
cos θ = -√(1 - sin²θ)
cos θ = - √[1 - (4/5)²]
cos θ = - √[9/25]
cos θ = - 3/5
θ = 143.13°
The value of the tangent of angle θ is calculated as,
⇒ tan θ
⇒ tan 143.13
⇒ - 0.75
The value of cos θ and tan θ will be negative 0.60 and negative 0.75, respectively.
More about the trigonometry link is given below.
https://brainly.com/question/22698523
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Pleas help with step by step. Thank you
Answer:
ok
Step-by-step explanation:
8, 18, 11, 15, 5, 4, 14, 9, 19, 1, 7, 17, 6, 16, ? , ?, ?, ?, ? Now, the only numbers used are in the range of 1 to 19. No numbers can be repeated. Now, there is a pattern to the sequence of numbers, and your keen powers of observation will be able to note that the last five numbers used in the sequence will be some combination of 13, 12, 10, 3, and 2. (If you’re more into logic brain-busters, a MIT professor called this puzzle “the hardest ever.”) Any luck? Here are a few hints: The sequence doesn’t obey any mathematical rule, and it is not counting any particular group of things. The only way to figure out the problem, according to Spencer, is to think of the numbers as words and write them out. The completed sequence is as follows: 8, 18, 11, 15, 5, 4, 14, 9, 19, 1, 7, 17, 6, 16, 10, 13, 3, 12, 2. Numerically, the sequence’s order is meaningless. That’s because they’re actually just listed in alphabetical order. While you’re in puzzle-mode, a bunch of raccoons solved this ancient Greek riddle—can you figure it out?
Answer:
8, 18, 11, 15, 5, 4, 14, 9, 19, 1, 7, 17, 6, 16, 10, 13, 3, 12, 2
Step-by-step explanation:
The answer is actually very simple: the numbers are placed in alphabetical order.
E ight
E ighteen
E leven
F ifteen
F our
F ourteen
N ineteen
O ne
S even
S eventeen
S ix
S ixteen
T en
T hirteen
T hree
T welve
T wo
please answer question 10
Answer:
Length = 5 units, Area = 51 unit squared
Step-by-step explanation:
For the length of the midsection (I think this is what you're talking about):
Method 1.
Draw the graph and count the units across for the length.
Method 2.
The lowest y coordinates are the 0 from point A and the 0 from point B: this means that the line between point A and B is the bottom line of the trapezoid.
The highest y coordinates are the 6 from point C and the 6 from point D: this means that the line between point C and D is the top line of the trapezoid (parallel to line AB).
Since the length of the midsection is essentially the shorter line of the two parallel lines, it is the length between point C and point D.
(10, 6) - (5, 6) = 5, so the length of the midsection is 5 units.
For the area:
Step 1. Add the lengths of the pair of parallel lines.
5 units + 12 units = 17 units
Step 2. Divide the answer to step 1 by 2.
17 units ÷ 2 = 8.5 units
Step 3. Multiply the answer to step 2 by the height between the two parallel lines.
6.5 units x 6 units = 51 units squared
Hopefully this was what you were looking for!
Bluey :)
Please help me with this geometry question :((
Step-by-step explanation:
the proportion that contains BC and FI :
BC / FG = proportion
8/4= proportion
2= proportion
BC/FI=8/3
Find the volume of a box whose width is 5 units, height and length are 2 units.
Answer:
20 units^3
Step-by-step explanation:
Well the formula for the volume of a box is,
l*w*h
l = 2
h = 2
w = 5
2*2*5
= 20 units^3
Hope this helps :)
Answer:
The volume of a box is:
20 units³
Step-by-step explanation:
The volume formula is:
v = height*width*length
v = 2*5*2
v = 20 units³
Leo had a $30 gift card to use at a coffee shop. He used the entire balance to buy regular-sized coffees, which cost $2, and large coffees, which cost $3. If he bought 13 coffees in total, how many large coffees did he buy? 2 3 4 9
Answer:
4 Large coffees
Step-by-step explanation:
4 X $3.00 = $12.00
9 x $2.00 = $18.00
$18.00 (9 small coffees) + $12.00 (4 Large Coffees ) = $30.00
Answer:
4
Step-by-step explanation:
took the test
Need help asap plz ill rate 5 star (only right answer please)
Answer:
[tex]6x^2 -x - 1[/tex]
By degree: Quadratic
By number of terms: Trinomial
[tex]3x + 4[/tex]
By degree: Linear
By number of terms: Binomial
[tex]2[/tex]
By degree: Constant
By number of terms: Monomial
Step-by-step explanation:
Given
[tex](x - \frac{1}{2})(6x + 2)[/tex]
[tex](7x^2 + 3x) -\frac{1}{3}(21x^2 - 12)[/tex]
[tex]4(5x^2-9x+7)+2(-10x^2+18x-13)[/tex]
Required
Simplify and categorize the result based on their degree and number of terms
Simplifying [tex](x - \frac{1}{2})(6x + 2)[/tex]
[tex]x(6x + 2) - \frac{1}{2}(6x + 2)[/tex]
Open bracket
[tex]6x^2 + 2x - 3x - 1[/tex]
[tex]6x^2 -x - 1[/tex]
By degree: Quadratic
By number of terms: Trinomial
Simplifying [tex](7x^2 + 3x) -\frac{1}{3}(21x^2 - 12)[/tex]
Open bracket
[tex]7x^2 + 3x -\frac{1}{3} * 21x^2 -\frac{1}{3}*- 12[/tex]
[tex]7x^2 + 3x -7x^2 + 4[/tex]
Collect like terms
[tex]7x^2-7x^2 + 3x + 4[/tex]
[tex]3x + 4[/tex]
By degree: Linear
By number of terms: Binomial
Simplifying [tex]4(5x^2-9x+7)+2(-10x^2+18x-13)[/tex]
Open brackets
[tex]4*5x^2-4*9x+4*7+2*-10x^2+2*18x-2*13[/tex]
[tex]20x^2-36x+28-20x^2+36x-26[/tex]
Collect like terms
[tex]20x^2-20x^2-36x+36x+28-26[/tex]
[tex]2[/tex]
By degree: Constant
By number of terms: Monomial
A rocket is launched from a tower. The height of the rocket, y in feet, is related to the time after launch, x in seconds, by the given equation. Using this equation, find the time that the rocket will hit the ground. y=-16x^2+266x+102 The amount of time it takes for the rocket to hit the ground is ____ seconds
Answer:
17 seconds
Step-by-step explanation:
Solution:-
The trajectory of a rocket launched is modeled by a parabolic path via a quadratic equation as follows:
[tex]y = -16x^2 + 266x +102[/tex]
Where,
y: The height of the rocket from ground
x: The time taken since rocket launch
We are to determine the time ( x ) it takes for the rocket to hit the ground. This can be determined by setting the quantity ( y ) to zero as follows
[tex]y = -16x^2 + 266x +102 = 0\\\\ -16x^2 + 266x +102 = 0[/tex]
solve the quadratic equation using quadratic formula as follows:
[tex]x = \frac{-b +/- \sqrt{b^2 - 4ac} }{2a} \\\\x = \frac{-266 +/- \sqrt{266^2 - 4*(-16)*(102)} }{2*(-16)} \\\\x = \frac{-266 +/- 278 }{-32} \\\\x = 8.3125 +/- 8.6875\\\\x = 17 , -0.375[/tex]
Answer: Ignore the negative value for time " -0.375 ". Hence, the rocket hits the ground at time t = 17 seconds
What’s the slope for this graphed?
A.1/2
B.-2
C.2
D.-3
Answer:
the answer is just 2
Step-by-step explanation:
start at the -3 and move right 3 and up 6 this is a inclined line so the answer will be positive the fraction put the numbers into a rise over run fraction which will be 6/3 which will reduce to 2/1 which is 2.
Which is the graph of g(x) = [X + 3]
Answer:
The "top center" one
Step-by-step explanation:
-y=x+3
-Use the slope-intercept form to find the slope and y-intercept. (y=mx+b)
m=1 b=3
-Slope: 1 , y-intercept: 3
X | y
-3 | 0
0 | 3
Then you can use a graphing calculator if you'd like !
Comeplete the table for the given rule. Rule: y = x/4
Answer:
x=16
x=8
x=36
Step-by-step explanation:
16÷4=4
8÷4=2
36÷4=9
Answer:
please see the attached picture.
Hope it helps..
Best regards!!
FIRST GETS BRAINLLEST If the rectangle below is enlarged by a scale factor of 1.2, what will be the area of the new rectangle? 62 square units 66 square units 72 square units 76 square units
Answer:
72 square units.
Step-by-step explanation: You have to multiply both sides by the scale factor. 5 times 1.2 is 6, and 10 times 1.2 is 12. Then, multiply 6 by 12 to get your area of 66 square units.
Cutting equilateral triangle BFC out of square ABCD and translating it to the left of the square creates the shaded figure ABFCDE. The perimeter of square ABCD was 48 inches. What is the perimeter, in inches, of ABFCDE?
Answer: 72 inches
Step-by-step explanation:
You are given that equilateral triangle BFC is cut out of square ABCD, since it is an equilateral triangle, that is all sides are equal to each other, we can therefore find the side of a triangle.
Given that the perimeter of square ABCD was 48 inches.
Perimeter of a square = 4L
Substitute 48 into the formula
48 = 4L
L = 48/4 = 12 inches
That means each length = 12 inch
Perimeter P of the shaded figure ABFCDE will be
P = AB + BF + FC + CD + DE + EA
P = 12 + 12 + 12 + 12 + 12 + 12
P = 72 inches
Therefore, the perimeter of ABFCDE is 72 inches.
Answer:
72
Step-by-step explanation:
We know that each side of a square is equal so if the perimeter is 48 then 48/4 = 12 and knowing the bottom of that triangle cut out is 12 we can solve each side 12 since its a equilateral triangle.
12*6= 72 = answer
Name the prism in each case given that all lateral faces are rectangles and the bases are: Squares
Answer:
Rectangular Cuboid
Step-by-step explanation:
A rectangular cuboid has 4 faces that are rectangles and 2 faces that are squares. Since a square is a rectangle, this shape is technically built of 6 rectangles and is creates a 3-dimensional shape. Hence, we have the prism, rectangular cuboid.
i need an explanation for this question!
Answer:
D
Step-by-step explanation:
2/5 is 40%, so we need to find 40% of 25. .40 x 25 = 10. We see that 31 - 40 has 8 values and 41 to 50 has to, and 8 + 2 = 10, so our answer is D.
SO I HAVE A QUESTION IS THE EQUATION Y-Y1=M(X-X1) AND Y=MX+B SAME GIVE EXAMPLES PLSSSSSSSSSS
Both of these are ways to express linear equations.
[tex]y - y_1 = m(x - x_1)[/tex] is the equation for a line with slope m which contains the point [tex](x_1,y_1)[/tex]. This is called point-slope form.
[tex]y = mx + b[/tex] is the equation for a line with slope m and y-intercept b. That is, it contains the point (0, b). This is called slope-intercept form.
Both of these are perfectly valid ways of writing lines, though sometimes one will be easier to use than the other.
Answer:
Hey there!
Both of these can be used to write the equation of the line. However, for the Y-Y1=M(X-X1) equation, we must know one point on the line (X1, Y1) and the slope of the line, while in the Y=MX+B equation, we need to know the slope and the x or y intercept.
For example, we can convert from Y-Y1=M(X-X1) to Y=MX+B
For example, say the point is (2, 3) and the slope is 1
Then, we have Y-3=1(x-2)
This simplifies to Y-3=1x-2
And to Y=X+1
So it is very possible to change from one form to another.
Let me know if you need more help.
1. What solid is represented by this net? (Image 1). A. cylinder B. triangular pyramid C. rectangular prism D. triangular prism E. cone F. rectangular pyramid 2. Choose all the solids from the list below. A. Rectangle B. Circle C. Cone D. Pyramid E. Prism F. Cylinder 3. The volume of the following figure = ___________ cm3. (Image 2) A. 288 B. 72 C. 216 D. 144
Answer:
c rectangular prism i think
Step-by-step explanation:
The formula for any arithmetic sequence is an = a1 + d(n - 1), where an represents the value of the nth term, a1 represents the value of the first term, d represents the common difference, and n represents the term number. What is the formula for the sequence -15, -11, -7, ...? an = -15 + (-4)(n - 1) an = -15 + (n - 1) an = 4 + (-15)(n - 1) an = -15 + 4(n - 1)
Answer:
4th choice
Step-by-step explanation:
First we would just solve the equation since that is the easiest way. So 15 would be our a1 or first term and each time the number is being added by 4 so we would get an = -15 + 4(n - 1) for our final answer or the 4th choice
Answer:
option 4
Step-by-step explanation:
-15, -11 , -7 ,......
First term = [tex]a_{1}[/tex] = -15
Common difference = d = 2nd term - 1st term
= -11 - [-15]
= -11 + 15 = 4
Plug in the values of [tex]a_{1}[/tex] & d in the formula
[tex]a_{n} = a_{1} + d (n-1)\\\\a_{n} = -15 + 4*(n-1)[/tex]
Triangle ABC has vertex coordinates A(–5, 2), B(–1, 3), and C(–1, 1). It is rotated 90° clockwise around the origin. What are the coordinates of B'?
Answer:
(3,1)
Step-by-step explanation:
The rule for a 90 degree clockwise rotation:
[tex](x,y)\rightarrow(y,-x)[/tex]
B is (-1, 3).
Apply the rule:
[tex]\frac{(-1,3)\rightarrow\boxed{(3,1)}}{(x,y)\rightarrow(y,-x)}\\\\3 * 1 = 3\\\\-1 * -1 = 1[/tex]
Option D should be the correct answer.
1/90 times -1/3 please give a explanation! ( if you give the reciprocal of the product for this equation Ill give brainliest)
Answer:
[see below]
Step-by-step explanation:
[tex]\frac{1}{90}*-\frac{1}{3}\\\\\frac{1*-1}{90*3}\\\\\frac{-1}{270}\\\\\boxed{-\frac{1}{270}}[/tex]
If a number gets multiplied by it's reciprocal, the product would be one.
[tex]\frac{x}{y}*\frac{y}{x}=1\\\\-\frac{1}{270}*-\frac{270}{1}= 1[/tex]
The reciprocal of the product of the equation is [tex]-\frac{270}{1}[/tex].
Hope this helps.
Which of the following is a statistical question? A. How many students attend Natasha's school? B. How many players are on Greg's football team? C. What volume of milk is used to make cupcakes according to Paula's cookbook? D. What are the checking account balances of the shoppers in a grocery store?
Answer:
Step-by-step explanation:
Find the radius of the circle whose equation is (x - 2)2 + (y - 4)2 = 9.
O 81
09
3
Answer:
3
Step-by-step explanation:
(x - 2)^2 + (y - 4)^2 = 9
The equation of a circle is written as
(x-h)^2+ (y-k)^2 = r^2
where ( h,k) is the center and r is the radius
(x - 2)^2 + (y - 4)^2 = 3^2
The center is ( 2,4) and the radius is 3
Answer:
r = 3
Step-by-step explanation:
The stock equation for a circle of center (h, k) and radius r is
(x - h)^2 + (y - k)^2 = r^2. Comparing this with the given (x - 2)^2 + (y - 4)^2 = 9, we see that r^2 must be 9 and therefore r = 3.
There are 3 different roads from city A to city B and 2 different roads from city B to city C. In how many ways can someone go from city A to city C passing by city B and then return back to A? 36, 10, 5, 24
Answer:
36
Step-by-step explanation:
There are 3 * 2 = 6 ways to go from A to C and then 2 * 3 = 6 ways to go from C to A so the answer is 6 * 6 = 36.
Pls help With this question thank you
Answer:
[tex]CD=4 \text{ cm }[/tex]
Step-by-step explanation:
We have a similarity of triangles. Once the side BC and ED are parallel,
[tex]$\frac{BC}{AC} =\frac{ED}{AD} $[/tex]
[tex]$\frac{10}{AC} =\frac{5}{4} $[/tex]
Once [tex]AC=AD+CD \Rightarrow AC=4+CD[/tex]
[tex]$\frac{10}{4+CD} =\frac{5}{4} $[/tex]
[tex]5CD+20=40[/tex]
[tex]5CD=20[/tex]
[tex]CD=4 \text{ cm }[/tex]
which number line represents the solution to [x-5]=1
Answer:
Step-by-step explanation:
If there are illustrations to given problems, please share those illustrations. Thank you.
The only value of x for which [x-5]=1 is true is 6: [6-5]=1
Steps to solve:
x - 5 = 1
~Add 5 to both sides
x - 5 + 5 = 1 + 5
~Simplify
x = 6
Best of Luck!
Anna is saving to buy some souvenirs on a family vacation. She has already saved $125, and she saves another $2 from her allowance every day. Formulate and then graph the equation that models the total amount Anna saves, y, in terms of the number of days she adds to her savings, X.
Answer:
y = 2x + 125
Step-by-step explanation:
y = mx + c
c in this problem is $125.
It is the amount of money she has already saved, that is not going to change, so this is the y intercept.
She saves $2 every day, with the number of days being x.
So she saves $2 × x = 2x
2x is the gradient.
On your graph, your straight lien should run through 125 on the y-axis.
The line should have a gradient, or slope, of 2x.
Make sure to plot carefully, looking at the scale of the graph.
The equation is that the total amount Anna saves will be y = 2x + 125. And the graph of the line is drawn below.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
Anna is saving to get a few keepsakes on a family excursion. She has previously saved $125, and she saves another $2 from her remittance consistently.
Let 'x' be the number of days and 'y' be the total cost. Then the equation is given as,
y = 2x + 125
The equation is that the total amount Anna saves will be y = 2x + 125. And the graph of the line is drawn below.
More about the linear equation link is given below.
https://brainly.com/question/11897796
#SPJ2
The bending of a bean varies directly as its mas. A beam is bent 20mm by a mass 0f 40kg. how much will the beam bend with a mass of 100kg?
Answer:
The beam will bend by 50 mm with a mass of 100kg?
Step-by-step explanation:
The first step in solving the problem of direct variation is setting up the relation mathematically.
We can do this as follows:
The bending of the beam varies directly as its mass.
[tex]20 \alpha 40kg[/tex]
[tex]\alpha[/tex] here is the symbol representing direct variation. To remove this and replace it with an equality sign, we have to introduce a constant of proportionality, k
[tex]20 = k \times 40[/tex]
k = 20 /40 = 0.5
We can now use this to find the distance the beam will bend with a mass of 100kg?
This will be
[tex]Bending = 0.5 \times 100 =50mm[/tex]
There fore, the beam will bend by 50 mm with a mass of 100kg?
I need help doing this can anyone help?
You posted a lot of questions. I'll do the first four problems to get you started.
============================
Problem 1
This sequence is arithmetic because we add the same amount (4) each time to get the next term. The first term is -2. The first five terms are: -2, 2, 6, 10, 14
============================
Problem 2
This sequence is geometric. We multiply each term by 1/4 to get the next term. We start with 8 as the first term. The first five terms are 8, 2, 1/2, 1/8, 1/32.
============================
Problem 3
Similar to problem 1. This time we're adding -19 to each term to get the next one. The starting term is -6. This sequence is arithmetic and the first five terms are -6, -25, -44, -63, -82
============================
Problem 4
Similar to problem 2. This sequence is geometric with common ratio 2/3. First term is 6. The first five terms are 6, 4, 8/3, 16/9, 32/27
If 4 pounds of sugar cost $2, the cost of 1 pound of sugar is $ and the cost of 10 pounds of sugar is $ Bryan drives at an average speed of 60 miles per hour. At this rate, it will take him 3 hours to drive how many miles does Bryan
Answer:
The cost of one pound of sugar is $0.5 and the cost of 10lbs of sugar is $5
Bryan is driving 180 miles
Step-by-step explanation:
If you're good at trigonometry please help meeee
On a 30-60 set square, the side opposite the 60 degree angle is 80mm long. Find the length of the longest side to the nearest millimetre
Answer:
[tex]\boxed{92 \: \mathrm{mm}}[/tex]
Step-by-step explanation:
sin θ = [tex]\frac{opposite}{hypotenuse}[/tex]
sin (60) = [tex]\frac{80}{x}[/tex]
x = [tex]\frac{80}{\mathrm{sin} (60)}[/tex]
x = 92.37604307...
x ≈ 92
Using the base dimension and either given angle you can solve for x
Sin(angle) = opposite leg/ hypotenuse
Sin(60) = 80/x
X = 80/sin(60)
X = 80/ sqrt(3)/2
X = 160/3 x sqrt(3). (This is exact answer)
For a decimal answer: 160/3 = 53 1/3
Multiplied by sqrt(3) = 92.376 mm
Rounded to nearest mm = 92