The quadrants in which the tangent is positive are I and III.
Option B is the correct answer.
What are trigonometric identities?There are three commonly used trigonometric identities.
Sin x = Perpendicular / Hypotenuse
Cosec = Hypotenuse / Perpendicular
Cos x = Base / Hypotenuse
Sec x = Hypotenuse / Base
Tan x = Perpendicular / Base
Cot x = Base / Perpendicular
We have,
Tangent is defined as the ratio of the opposite side to the adjacent side of a right triangle.
It is positive when the opposite side and the adjacent side are both positive or both negative.
In the first quadrant (I), both the opposite and adjacent sides are positive, so the tangent is positive.
In the second quadrant (II), the opposite side is positive and the adjacent side is negative, so the tangent is negative.
In the third quadrant (III), both the opposite and adjacent sides are negative, so the tangent is positive.
In the fourth quadrant (IV), the opposite side is negative and the adjacent side is positive, so the tangent is negative.
Therefore,
The quadrants in which the tangent is positive are I and III.
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Find the value of x
A 20
B 60
C 50
D 45
E 30
Answer:
the answer is letter E.
see the attachment.
Urgent help!!!
Write equation in slope intercept form.
1.25 (25) = 31.25
The equation in slope intercept form is,[tex]31.25 = 1.25 \times 25 +0[/tex]. The given equation is obtained by comparing the standard equation of the straight line.
What is a slope of a straight line?
A straight line is a combination of endless points joined on both sides of the point.
The slope 'm' of any straight line is given by:
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
The given equation is;
1.25 (25) = 31.25
31.25=1.25 (25)
The standard equation of the slope intercept form. is;
[tex]\rm y = mx +x[/tex]
On comparing the given equation with the above equation, we get;
y=31.25
m=1.25
x=25
c=0
The equation in slope intercept form is;
[tex]31.25 = 1.25 \times 25 +0[/tex]
Hence, the above equation is the slope intercept form.
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Hi Guys I'm stuck on this question
write x^2-4x+2 in the form (x-A)^2+B
Answer:
(x-2)^2-2
Step-by-step explanation:
x^2-4x+2
take the x out
x(x-4) + 2
(x-2)^2-2
because (x-2)^2 is
x^2-4x+4
its like completing the square
Answer:
(x-2)² -2
Step-by-step explanation:
Consider that (a+b)² = a²+2ab+b²
To find the form (x-A)²+B compare x²-4x+2 with a²+2ab+b²
x² - 4x +2
a² + 2 a b+ b², so a= x and b = (-2)
x²+ 2· x ·(-2)+ (-2)² - 2 = (x-2)² -2 is in the form (x-A)²+B
Check our answer:
(x-2)² -2= (x²-2·2x+4)-2 = x²-4x +2 ✅
This figure represents a small keepsake box. Holly wants to cover 35 of the surface with stickers.
How much of the total surface will be covered with stickers?
Enter your answer as a decimal or mixed number in simplest form in the box.
The amount of the surface area covered with stickers is 0.6 or 60%
How to determine the covered area?The amount of area to cover is given as:
Covered area = 3/5
Express as percentage
Covered area = 3/5 * 100%
Divide 3 by 5
Covered area = 0.6 * 100%
Evaluate the product
Covered area = 60%
Hence, the amount of the surface area covered with stickers is 0.6 or 60%
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Answer:
135.93
Step-by-step explanation:
I took the test
Find F Write your answer in simplest radical form.
Answer:
f= 5.2 or 3[tex]\sqrt{3}[/tex]
Step-by-step explanation:
Cot(60) = 3/f
0.58 =3/f
0.58f = 3
f= 5.2 or 3[tex]\sqrt{3}[/tex]
At another park in Chicago, neighbors get together to plan a community garden. Plans for the community garden are shown below. celery tomatoes 6 yds spinach carrots watermelon 12 yds red peppers 8 yds a) The members of the gardening group plan to build a walkway through the garden as formed by the hypotenuse of each of the four triangles in the drawing. That way, the gardeners will be able to access all sections of the garden. Calculate the length of the entire walkway to the nearest hundredth of a yard. Show your work. (4 points-1 point for each length calculation and 1 point for the total distance) *** 15 yds
Answer:
we can use the pythagorean theorem to each of those right triangles to find the lengths of the pathways
Step-by-step explanation:
for the spinach celery walkway,
d=[tex]\sqrt{6^{2}+8^{2}[/tex] = 10 yd
for each watermelon walkway,
d=[tex]\sqrt{8^{2}+12^{2}[/tex] = 14.42 yd
from the carrots red peppers walkway,
[tex]b^{2}+12^{2} = 15^{2}[/tex]
b=[tex]\sqrt{15^{2}-12^{2}[/tex]= 9yd
for each tomatoes walkway;
d=[tex]\sqrt{6^{2}+9^{2}[/tex] = 10.82 yd
so the total length of the walkway is = 10+14.42+15+10.82 = 50.24 yd
Multiply 9/8 x 7/8 what is it fraction?
Answer:
63/8
Step-by-step explanation:
For this question all you have to do is times the 9 and 7 and put the denominator(in this case 8) underneath to make a fraction. The answer totals as 63/8 or 7 and 7/8.
Which number is equal to 4/2?
The number that is equal to [tex]\frac{4}{2}[/tex] is 2
How to find the number that is equal to 2
When you ask "What is 4/2 as a whole number?" you are asking to convert the fraction [tex]\frac{4}{2}[/tex] to a whole number.
The fraction [tex]\frac{4}{2}[/tex] has a numerator of [tex]4[/tex] and a denominator of [tex]2[/tex]. To convert [tex]\frac{4}{2}[/tex] to a whole number, you simply divide the numerator by the denominator.
Given that:
[tex]\frac{4/2=2}{2/2=1} =\frac{2}{1}=2[/tex]
Therefore, The number that is equal to [tex]\frac{4}{2}[/tex] is 2
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How do I do the math here? I am not sure how to set it up with having only one angle to work with.
Answer:
angle A = 112 degrees
Step-by-step explanation:
Angle ADC is bisected (given) ...so angle 1 = angle 2
then angle D = 68 degrees
now you have to remember that adjacent corners (angles on the same LEG) of a trapezoid sum to 180 (they are 'supplementary' )
angle A = 180 - 68 = 112 degrees
Determine two coterminal angles in radian measure (one positive and one negative) for each angle.
The two coterminal angles in radian measure (one positive and one negative) for each angle for figure 1 and 2 are,[(13π/4),(-π/4) and [(7π/4),(-17π/4) rad] respectively.
What is coterminal angle ?Angles having the same terminal side at standard position are called coterminal angles.
Although the magnitudes of coterminal angles varies, they all have the same sides and vertices.
Positive or negative coterminal angles are possible. The positive coterminal is obtained by adding 2 rad or 360° to the negative coterminal, while the negative coterminal is obtained by removing 2 rad or 360°.
For figure 1;
The positive coterminal angle is found as;
[tex]\rm \rightarrow \theta + 2 \pi \\\\ \rightarrow \frac{5 \pi}{4} + 2 \pi \\\\ \rightarrow\frac{13 \pi}{4} \ rad[/tex]
The negative coterminal angle is found as;
[tex]\rm \rightarrow \theta - 2 \pi \\\\ \rightarrow \frac{5 \pi}{4} - 2 \pi \\\\ \rightarrow\frac{-3 \pi}{4} \ rad[/tex]
For figure 2;
The positive coterminal angle is found as;
[tex]\rm \rightarrow \theta + 2 \pi \\\\ \rightarrow \frac{-9\pi}{4} + 2 \pi \\\\ \rightarrow\frac{7 \pi}{4} \ rad[/tex]
The negative coterminal angle is found as;
[tex]\rm \rightarrow \theta - 2 \pi \\\\ \rightarrow \frac{-9 \pi}{4} - 2 \pi \\\\ \rightarrow\frac{-17 \pi}{4} \ rad[/tex]
Hence,the two coterminal angles in radian measure (one positive and one negative) for each angle for figure 1 and 2 are,[(13π/4),(-π/4) and [(7π/4),(-17π/4)] respectively.
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how many liters each of a 50% acid solution and a 65% acid solution must be used to produce 60 liters of a 55% acid solution?
Answer:
178
Step-by-step explanation:
100 plus 78 equal s 179
What is the value of 3(a-9) when a =6
Answer:
-9
Step-by-step explanation:
We are given the value of "a", which is 6. Let us substitute the value of "a" into the expression to determine a numerical value of 3(a - 9).
⇒ 3(a - 9)⇒ 3[(6) - 9] . . . . . . . . {a = 6}Open the parentheses to simplify the expression inside the long brackets [ ].
⇒ 3[(6) - 9] . . . . . . . . {a = 6}⇒ 3[6 - 9]Subtract the expression inside the long brackets [ ]
⇒ 3[6 - 9]⇒ 3[-3]Finally, simplify the product of 3 and -3.
⇒ 3[-3] ⇒ 3 × -3 = -9Therefore, -9 is the value of 3(a - 9) when a = 6.
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[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{3(a - 9)}\\\\\mathsf{= 3(\bold{6} - 9)}\\\\\mathsf{= 3(6) + 3(-9)}\\\\\mathsf{= 18 - 27}\\\\\large\text{OR EVEN \rm{3(-3)}}\\\\\mathsf{= 3(-3)}\\\\\mathsf{= -9}\\\\\\\\\huge\text{Therefore, the answer is: \boxed{\mathsf{-9}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
From the top of a cliff, the angle of depression of a boat on the sea is 22°. If the height of the cliff above sea level is 40 m, calculate, correct to two significant figures, the horizontal distance of the boat from the bottom of the cliff.
Answer:
= 25√3/3
Step-by-step explanation:
x/25 = tan 30o
x = 25/√3
= 25√3/3
Manny buys a new grill that costs $375. The grill is discounted 22% and sales tax is 6.5%. How much does Manny pay for the grill? ( NEED HELP ASAP!!)
Answer:
$310.05
Step-by-step explanation:
Method 1: Find the amount of 22% discount and subtract from original price, and find the amount of 6% tax and add to discounted price.
Original price: $375
Discount of 22%
22% of $375 = 0.22 × $375 = $82.50
Price after discount (but before tax): $375 - $82.50 = $292.50
Sales tax of 6%
6% of $292.50 = 0.06 × $292.50 = $17.55
Price after discount and tax: $292.50 + $17.55 = $310.05
Method 2: Add and subtract the discount percent and the tax percent first, then multiply.
Original price: $375
The discount is 22%.
The original price is 100%.
Subtract 22% from 100%: 100% - 22% = 78%
The discounted price is 78% of the original price.
Once you have the discounted price, tax is 6%.
The new discounted price is 100%. Add 6% to get 106%.
The price with tax is 106% of the discounted price.
106% of 78% of $375 = 1.06 × 0.78 × $375 = $310.05
Answer: $310.05
A line passes through the points (-4,8) and (3,-7). Answer all parts of the question. Part A: what is the slope of the line that passes through these points (-4,8) and (3,-7).
Answer: [tex]y=\frac{-15}{7}x-\frac{4}{7}[/tex]
Slope: -15/7
y-int:-4/7
Step-by-step explanation:
slope: rise/run
[tex]\frac{x^2-x^1}{y^2-y^1}[/tex]
[tex]\frac{-7-8}{-4-3}=\frac{-15}{-7} =\frac{-15}{7}[/tex]
thats the answer :)
~rere
Find the surface area and volume of the prism.
10 cm
6 cm
8 cm
The surface area of the prism is
The volume of the prism is
17 cm
cm².
cm³.
I’ll mark you as Brainly please help
PLEASE HELP ME FOR BRAINLIEST
Answer: The answer is d
Step-by-step explanation:
Determine the equation of the line tha has an x-intercept of 4 and a y intercept of-3
Answer:
[tex]y=\frac{3}{4} x-3[/tex]
Step-by-step explanation:
Given information: x-int: 4 and y-int:-3
x-int point : (4,0).
y-int point : (0,-3).
Plug this information to point-slope form to solve for m and then convert that to slope-intercept form.
[tex]y-y_0=m(x-x_0)\\0-(-3)=m(4-0)\\3=4m\\m=\frac{3}{4} \\[/tex]
[tex]y-y_0=m(x-x_0)\\y-(-3)=\frac{3}{4} (x-0)\\y+3=\frac{3}{4}x\\y=\frac{3}{4}x-3[/tex]
Please help me with this really please
Answer:
You need 443.2 square inches of wrapping paper to completely cover the prism.
Step-by-step explanation:
Calculate the area of each side.
Triangles:
Base * Height * 1/2
10 in. * 8.7 in. * 1/2
87 in.^2 * 1/2
43.5 in.^2
There are two sides with the triangle so we multiply the 43.5 in.^2 by two
(43.5 in.^2) * 2
87 in.^2
Side Rectangles:
Length * Width
13 in. * 8.7 in.
113.1 in.^2
There are two sides with this size rectangle so we multiply the 113.1 in.^2 by two
(113.1 in.^2) * 2
226.2 in.^2
Bottom Rectangle
Length * Width
13 in. * 10 in.
130 in.^2
There is only one side with the bottom rectangle.
Add up all the calculate areas.
Triangles + Side Rectangles + Bottom Rectangle
87 in.^2 + 226.2 in.^2 + 130 in.^2
443.2 in.^2
XY is dilated by a scale factor of to form X'Y'. X'Y' measures 2. What
is the measure of XY?
Answer:
11
Step-by-step explanation:
if the other things are the XY and XY, then the other one needs to measure 11.
How to simplify the problem in the photo?
Answer:
2^3 a^5 b^4
4b^2 c^3
2^(3-2) a^5 b^(4-2)
c^3
2a^5 b^2
2a^5 b^2 c^3
PLEASE HELP PLEASE HELP
Answer: 20:21
Step-by-step explanation: The Greatest Common Factor is 4, 80 divided by 4 is 20 and 84 divided by 4 is 21
Hope this helps
Answer:
20:21
Step-by-step explanation:
Expressing a number or more in their simplest form simply means expressing them to their lowest terms. You can divide 80:84 with 2 or 4. To make it faster, just divide both by 4 and you'll get 20:21 which is the final answer, no other number can divide 20:21.
I hope this helps.
What multiplication problem is represented by this grid?
The multiplication problem represented by this grid is 0.7 x 0.4 = 0.28
Sure hope this helps you
At the school track meet, Dita ran 100 meters at a rate of 6.25 meters per second.
Time = StartFraction distance Over rate EndFraction
How long did it take Dita to finish the race?
16 seconds
93.75 seconds
106.25 seconds
625 seconds
original equation
[tex]v=\frac{d}{t}[/tex]
solve for t
[tex]t=\frac{d}{v}\\\\t=\frac{100}{6.25} \\\\t=16[/tex]
It took Dita 16 seconds to finish the race
Answer:
a
Step-by-step explanation:
aaaaaaa
its a
16 seconds
You invested money in two funds. Last year, the first fund paid a dividend of 9% and the second a dividend of 3%, and you received a total of $858. This year, the first fund paid a 10% dividend and the second only 1%, and you received a total of $867. How much money did you invest in each fund?
The amount that was invested in the first fund is $8300.
The amount that was invested in the second fund is 3700.
What are the linear equations that represent the question?0.09a + 0.03b = $858 equation 1
0.1a + 0.01b = $867 equation 2
Where:
a = amount invested in the first fund b = amount invested in the second fund How much was invested in the second fund?Multiply equation 2 by 0.9:
0.09a + 0.009b = 780.30 equation 3
Subtract equation 1 from equation 3
0.021b = 77.70
Divide both sides by 0.021
b = $3700
How much was invested in the first fund?
Substitute for b in equation 1: 0.09a + 0.03(3700) = $858
0.09a + 111 = 858
a = (858 - 111) / 0.09
a = $8300
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What is the common difference if the arithmetic sequence below? -5,-1,3,7…..
Answer:
4
Step-by-step explanation:
-1 - (-5) = 4
3 - (-1) = 4
7 - 3 = 4
Ali and Mo share a sum of money in the ratio Ali:Mo = 9:7 . Ali recieves $600 more than Mo. Calculate how much each recieves.
Answer:
A = 2700 M = 2100 dollars
Step-by-step explanation:
9 + 7 = 16 shares
2 shares more = 600
1 share = 300
9 shares * 300 = 2700
7 shares x 300 = 2100
Area for 10 1/4 and 10 1/2
Mrs. Cox measured the height of seven students. What is the combined height of the tallest and shortest student?
Answer:
8 feet
Step-by-step explanation:
3 + 5 = 8
..................................................
write two equations that when graphed look like this *see image*. please help its due soon and i will give ya 75 points for answering CORRECTLY thanks, 5 stars, and brainlist. Thank ya
The graph is showing the equation of circle x²+y²=4
What is a circle?A circle is a two-dimensional geometry on the plane having a centre point and the circular line is drawn equidistant from the centre point.
The given graph in the question represents the equation of the circle cutting the points on the x-axis and y-axis at 4 which is the radius of the circle.
The equation will be as follows:-
x²+y²=4
Hence the graph is showing the equation of circle x²+y²=4
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