The correct answer is [tex]$\sqrt{3}$[/tex]. Hence the correct option is d.
To find the value of [tex]$\tan 60^\circ$[/tex] using the unit circle, follow these steps:
Draw the unit circle, which is a circle with a radius of 1 unit centered at the origin (0,0) on the Cartesian coordinate plane.
Identify the point on the unit circle corresponding to [tex]$60^\circ$[/tex]. This point is located in the first quadrant and makes an angle of [tex]$60^\circ$[/tex]with the positive x-axis.
Since the unit circle has a radius of 1, the coordinates of the point corresponding to 60 are:
[tex]$x$-coordinate: $\cos(60^\circ) = \frac{1}{2}$\\$y$-coordinate: $\sin(60^\circ) = \frac{\sqrt{3}}{2}$[/tex]
Now, we'll use the definition of tangent to find [tex]$\tan(60^\circ)$[/tex]:
[tex]$\tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}$\\Substitute the values of $\sin(60^\circ)$ and $\cos(60^\circ)$ into the formula:$\tan(60^\circ) = \frac{\frac{\sqrt{3}}{2}}{\frac{1}{2}}$[/tex]
Simplify the expression:
[tex]$\tan(60^\circ) = \left(\frac{\sqrt{3}}{2}\right) \cdot \left(\frac{2}{1}\right)$$\tan(60^\circ) = \sqrt{3}$[/tex]
So, the correct answer is [tex]$\sqrt{3}$[/tex]. Hence the correct option is d.
Complete question:
Use the unit circle to find tan 60°.
a. square root 3/3
c. 2 square root 3/3
b. square root 3/2
d. square root 3
What did I do wrong here?
Answer:
You put 8i^2 instead of 12i^2. You multiply -6i by -2i which equal -12i^2
Step-by-step explanation:
-7 + 6i - 14i+ 12i^2
-7 - 8i - 12
-19 - 8i
Solve each inequality
1/4x + 9 > 17
Answer:
x>32
Step-by-step explanation:
1/4x+9>17
1/4x>17-9
1/4x>8
x>8/(1/4)
x>8(4/1)
x>32
Answer:
6/4
Step-by-step explanation:
9-17=6
1/4*6
6/4
I hope this helps
How do you find the circumference and diameter of a circle? Please make this quick for a quiz tomorrow! thank you friends!
Answer:
Diameter of a circle is twice the value of the radius
And to calculate the value of the circumference which could also be said to be the perimetre...
The formlae is given by: 2(pie)r.
Where pie = 22/7
And r = radius of the circle
So everytging is multiplied together
Step-by-step explanation:
Work out the new amount after a 15% decrease
A) 50ml
B) 44kg
C) $320
D) £210
Answer:
A= 37.5ml
B= 37.4kg
C= $272
D= £199.50
Step-by-step explanation:
You have to find 15% of all of them and then minus 15% from the amount you were given.
5 times 7/10
The product lies between - and -
Answer:
5 x 7/10 is equal to 3.5, therefore it lies between the whole numbers of 3 and 4.
The product of 5 times 7/10 is exactly 3.5.
To calculate 5 times 7/10, we multiply 5 by the fraction 7/10. This can be done using simple multiplication of the numerator (5 * 7 = 35) followed by dividing the result by the denominator (35/10), which simplifies to 3.5. Thus, 5 times 7/10 is 3.5.
When we are asked where the product lies between, it actually means we are looking for a range. Since we already know 5 times 7/10 equals 3.5, it would be accurate to say that the product lies between numbers that are smaller and greater than 3.5. However, the question seems to be incomplete because it does not provide the specific range to work within, so based on the provided calculation, we can only state the exact answer which is 3.5.
A rectangle is eight inch long and its diagonal is ten inches. What’s the width of the rectangle?
Answer:
6 inch
Step-According to the Pythagorean theorem, the square length of the rectangle + the square width of the rectangle = the square length of the diagonal. So， 8 square + ? Square = 10 square, so 64 +? = 100. 100-64 = 36, 36 is the square of 6, so the answer is 6. Hope is correct. :)
Look at the pic and answwe
Answer:
CD/RQ = AB/PN
8/6 = AB/10
6AB = 80
AB = 40/3, so x = AD = (1/2)(40/3) = 20/3
The correct answer is B.
The value of length AD in the similar triangles is determined as 20/3. (Option B).
How to calculate the length of AD?The length of segment AD is calculated by applying proportion formula as follows;
CD/RQ = AB/PN
The given parameters include;
Length CD = 8Length RQ = 6Length PN = 10The value of length AB is calculated as;
8/6 = AB/10
6AB = 80
AB = 40/3
The value of length AD is calculated as;
x = AD
AD = 1/2AB
AD = (1/2)(40/3)
AD = 20/3
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in triangle ABC , p is midpoint of BC and Q is the midpoint of AC . if b (2,7) , p (-1,5) and a (4,-5) are the known points , then find the co ordinates of c and q.
Answer:
c（-4，-17）q（0，-11）
Step-by-step explanation:
draw picture
While Jane was visiting her sister in Winchester, she bought a wooden bench that was marked down 25% from an original price of $80. If the sales tax in Winchester is 10%, what was the total cost of the wooden bench?
Answer:
Step-by-step explanation:
The total cost of the bench would be $72 after the markdown being 10% from the orginal proce which was $80.
Given the function f(x)=4x+10 and g(x), which function has a greater slope
the first one because it has a slope of 4/1 where the second one has a slope of 0
The interior angles formed by the sides of a quadrilateral have measures that some to 360°
What is the value of x?
Answer:
Value of x is 34
Step-by-step explanation:
The figure is a quadrilateral;
Angles given are; 2x°, 88°,108° and (3x - 6)°
We already know that the interior angles of a quadrilateral add up to 360°
Therefore, to get the value of x;
2x° + 88° + 108° + (3x - 6)° = 360
5x° + 190° = 360°
5x° = 170°
x = 34°
Thus, the value of x is 34
PLZZ HELP MEHH Sara graphs each quadratic equation. Which graph is the narrowest?
A) y = x2
B) y = 2x2
C) y =1/2x^2
D) y =1/4x^2
Answer:
(B) y=2x^2
Step-by-step explanation:
(1/2) and (1/4) make the graph wider
2 makes it narrower
Final answer:
The narrowest graph among the given options is the graph of the equation with the largest coefficient, which is y = 2x² , which is option B.
Explanation:
The width of the parabola's graph is determined by the coefficient of the x² term in a quadratic equation of the form y = ax². The larger the absolute value of coefficient a, the narrower the parabola. Therefore, we can compare the coefficients in the given equations:
y = x² has a coefficient of 1.
y = 2x² has a coefficient of 2, which makes it narrower than the first equation.
y = 1/2x² has a coefficient of 1/2, which makes it wider than the first equation.
y = 1/4x² has a coefficient of 1/4, which makes it the widest among all.
Consequently, the graph of equation B, y = 2x², is the narrowest because it has the largest coefficient.
through:(3,5), parallel to y=9/5x+5
Answer:
False
Step-by-step explanation:
5=9/5.3+5
5=45.3+5
5= 135+5
5 does not =140
Slope is 2 and goes through the point (0,-11)
Answer:
y = 2x - 1
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Here m = 2
The line crosses the y- axis at (0, - 1) ⇒ c = - 1
y = 2x - 1 ← equation of line
Please help me solve this by substitution:
y=x+2
3x+3y=6
Answer:
x = 0, y = 2
Step-by-step explanation:
solve the equation for x3x + 3(x + 2) = 6
2. Substitute the given value of x into the simplest equation y= x + 2
y = 0 + 2
3. Solve the equation for y
y= 2
4. The possible solution of the system is the ordered pair ( x, y)
( x, y) = ( 0, 2)
3. Changing the opacity of the image and changing colors is a basic way of performing color correction. (1 point)
True
False
Answer: True
Step-by-step explanation: Just took the test
If G = {(-1, 7),(-8, 2),(0, 0),(6, 6)), then the range of G is
A (7, -1),(2, -8),(0, 0),(6, 6)]
B (-8,-1,0, 6)
C (0, 2, 6, 7)
Answer:
B) {-8,-1,0,6)
Step-by-step explanation:
range is always y
express problem in simplest form
1) 3-1/2-1/6
2)2 3/4 + 3 2/5
Answer:
hi
Step-by-step explanation: srry
A shopper paid $2.52 for 4.5 pounds of potatoes, $7.75 for 2.5 pounds of broccoli, and $2.45 for 2.5 pounds of pears. what is the unit price of each item she brought
Answer:
a) UNIT PRICE of potatoes is $0.56
b) UNIT PRICE of broccoli is $3.1
c) UNIT PRICE of broccoli is $0.98
Step-by-step explanation:
UNIT PRICE is defined as the price of 1 unit.
[tex]\textrm{Unit Price} = \frac{\textrm{Total cost on n products}}{\textrm{n}}[/tex]
Now, here in the given question:
1. Cost of 4.5 pounds of potatoes is $2.52
So, the unit price of potatoes [tex]= \frac{\textrm{2.52}}{\textrm{4.5}} = 0.56[/tex]
⇒ 1 pound of potatoes cost $0.56
Hence,UNIT PRICE of potatoes is $0.56
2 Cost of 2.5 pounds of broccoli is $7.75.
So, the cost of 1 pound of broccoli [tex]= \frac{\textrm{7.75}}{\textrm{2.5}} = 3.1[/tex]
⇒ 1 pound of broccoli cost $3.1
Hence,UNIT PRICE of broccoli is $3.1
3. Cost of 2.5 pounds of pears is $2.45.
So, the cost of 1 pound of pears [tex]= \frac{\textrm{2.45}}{\textrm{2.5}} = 0.98[/tex]
⇒ 1 pound of pears cost $0.98
Hence,UNIT PRICE of broccoli is $0.98
Answer:
Potatoes - $0.56/pound.
Broccoli - $3.1/pound.
Pears - $0.98/pound.
Step-by-step explanation:
A shopper paid $2.52 for 4.5 pounds of potatoes.
So, the unit price of potatoes is [tex]\frac{2.52}{4.5} = 0.56[/tex] dollars per pound.
A shopper paid $7.75 for 2.5 pounds of broccoli.
So, the unit price of broccoli is [tex]\frac{7.75}{2.5} = 3.1[/tex] dollars per pound.
A shopper paid $2.45 for 2.5 pounds of pears.
So, the unit price of pears is [tex]\frac{2.45}{2.5} = 0.98[/tex] dollars per pound. (Answer)
Vince went on a 3 day hiking trip. Each day, he walked 3/4the distance that he walked the day before. He walked 83.25 kilometers total on the trip. How far did Vince walk on the 1st day of the trip?
Answer
36 km
Step-by-step explanation:
Suppose he walked n km on the first day
We create the following equation
n + 3/4 n + (3/4)^2 n = 83.25
n + 0.75n + 0.5625n = 83.25
2.3125n = 83.25
n = 36 km
Answer:
36
Step-by-step explanation:
Jess new pool holds 1,624 gallons of water he can fill the pool at a rate of 112 per hour how many hours will it take Jess to fill his pool
14.5 hours will it take Jess to fill his pool.
What is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Jess new pool holds 1,624 gallons of water he can fill the pool at a rate of 112 per hour.
So, the number of hours taken to fill the pool
= 1624 / 112
= 14.5 hour.
Thus, the time taken 14.5 hour.
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A pie was cut into two equal pieces. Each of the pieces of pie was cut into halves again, and each of those smaller pieces was cut into two equal pieces If two of the pieces of the pie are eaten, what portion of the pie remains?
Answer:
6 pieces, 6/8
Step-by-step explanation:
You have 8 pieces you take away 2 you get 6.
8-2=6
Answer:
3/4 of the pie is left.
Step-by-step explanation:
Step 1: Cut the pie into 2 equal pieces. Each piece is 1/2 of the pie.
Step 2: Cut each half in half. Each new smallest piece is now 1/4 of the pie.
Step 3. Cut each 1/4 pie in half. Each new smallest piece is 1/8 of the pie.
Now 2 of the smallest pieces are eaten.
That means 2 of the 1/8 pie size are eaten.
2 * 1/8 = 2/1 * 1/8 = 1/4
1/4 of the pie was eaten.
The remaining part is 1 pie minus 1/4 pie.
1 - 1/4 = 1/1 - 1/4 = 4/4 - 1/4 = 3/4
Answer: 3/4 of the pie is left.
Which inequality is equivalent to |X-41<9?
0 -9 > x-4<9
09
O X -4<-9 or x - 4< 9
O x-4> -9 or x - 4<9
Answer:
x - 4 > -9 or x -4 < 9
Step-by-step explanation:
Let's see the definition of absolute value inequality.
i) If lxl < b, then -b < x < b
ii) If lxl > b, then x > b or x < -b
We are given the inequality lx - 4l<9
Here we have to use the first case.
Using the above definition of inequality, we can write the given inequality as follows:
-9 < (x - 4) < 9
So the third option is correct.
x - 4 > -9 or x -4 < 9
A game designer must decide how to color four buildings that are in a row. Using only the colors yellow, green, red, and blue, each building must be painted with exactly one color. Any two neighboring buildings must be different colors, and the first and last buildings must be different colors. How many ways are there to paint the four buildings?
Answer:
The number of ways are there to paint the four buildings is 48.
Step-by-step explanation:
I) let the first building be any color. Therefore the first building can be painted with any of the 4 colors.
Therefore the first building can be colored in 4 ways.
ii) the second building can be colored in 3 ways since it cannot be colored the
same color as the first building.
iii) the third building can also be colored in 3 ways.
iv) the last building can be colored in 2 ways because it cannot be the same color as the first building or the color of the adjacent building.
Therefore the total number of ways the buildings can be colored = 4 [tex]\times[/tex] 3 [tex]\times[/tex] 3 [tex]\times[/tex] 2 = 48.
There are 108 different ways for the game designer to paint the four buildings using the colors yellow, green, red, and blue, with the requirement that neighboring buildings and the first and last buildings must be different colors.
Explanation:The game designer has four choices of colors for the first building (yellow, green, red, or blue). For each choice of the first color, the second building has three choices, as it cannot be the same color as the first one. Similarly, the third building will have three choices, as it cannot be the same color as the second building. Finally, the fourth building also has three choices as it must differ from the third one and cannot be the same color as the first building. Therefore, the calculation will be 4 options for the first times 3 options for the second, times 3 options for the third, times 3 options for the fourth: 4 × 3 × 3 × 3 = 108 ways to paint the four buildings.
To summarize, the first building can be any of the four colors. The subsequent buildings each have three options excluding the color of the immediate previous building. Since the first and last buildings must be different, the last building also cannot be the color of the first one, giving us a total of 108 ways to paint the buildings.
Unit rate of 15 pounds in 6 weeks
Please help me!!! Will mark as brainiest!
1. Write an equation to represent the measures of the angles.
2. Solve the equation to find the measures of the unknown angle.
x=41
Step-by-step explanation:
139+x=180
180-139=41
x=41
Two angles whose sum is 180° are called supplementary angles. The measure of the unknown angle is 41°.
What are supplementary angles?
Two angles whose sum is 180° are called supplementary angles. If a straight line is intersected by a line, then there are two angles form on each of the sides of the considered straight line. Those two-two angles are two pairs of supplementary angles. That means, if supplementary angles are aligned adjacent to each other, their exterior sides will make a straight line.
The two of the given angles form a linear pair. Thus, the measure of the two angles together will be equal to 180°.
1.) An equation to represent the measures of the angles.
x + 139° = 180°
2.) Solving the equation to find the measures of the unknown angle,
x + 139° = 180°
x = 180° - 139°
x = 41°
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solve the system of equations by substitution -6x+7y=23, -5x+y=24
Answer:
x = -5, y = -1
Step-by-step explanation:
You're given 2 equations:
-6x + 7y = 23
-5x + y = 24
you choose the equation that is easier to isolate a single variable to use as your substitution. I chose -5x + y = 24 because the 'y' is already by itself. Now solve for 'y'.
-5x + y = 24
y = 24 + 5x
Use this y-value to substitute into your other equation
-6x + 7y = 23
-6x + 7(24 + 5x) = 23
-6x + 168 + 35x = 23
29x = 23 - 168
29x = -145
x = -5
We found the value of 'x', so plug it back in to any of the two given equation to solve for y.
-5x + y = 24
-5(-5) + y = 24
25 + y = 24
y = 24 - 25
y = -1
Answer:
(-5,-1)
Step-by-step explanation:
First you must get a variable on one side alone. For example I done Y on the 2nd one. So to move it, you would take the 5x and move/add to the other side so Y=5x+24.
Then the substitution comes in. So you take
-6x+7(5x+24)=23 so you would plug in what Y equals. Then after you distribute the seven you would combine like terms. Then you take and move/subtract 168 from 23 which equals -145. Then you would divide by the number attached to the variable which is 29, therefore giving you x=-5
Then to get Y you simply plug what X equals into the X space.
Y=5(-5)+24
Y= -25+24
Y=-1
Four times the difference of k and three
Answer:
4 (k-3)
Step-by-step explanation:
Which statement explains why √2 is an irrational number?
Answer:
it is a repetitive decimal
Step-by-step explanation:
Answer:
it is a repetitive decimal
Step-by-step explanation:
Brian, Chris, and Damien took a math test that had 20 questions. The number of questions Brian got right is 14 more than the number of questions Chris got right. Damien correctly answered 2 less than the number of questions Chris answered correctly. If Brian and Damien have the same score, which statement is true?
A.
Brian and Damien both answered 2 fewer questions correctly than Chris did.
B.
Brian and Damien both answered 4 more questions correctly than Chris did.
C.
Brian and Damien both answered 2 more questions correctly than Chris did.
D.
Brian and Damien both answered 4 fewer questions correctly than Chris did.
Question:
Brian, Chris, and Damien took a math test that had 20 questions. The number of questions Brian got right is 14 more than 1/4 the number of questions Chris got right. Damien correctly answered 2 less than 5/4 the number of questions Chris answered correctly. If Brian and Damien have the same score, which statement is true?
A) Brian and Damien both answered 2 fewer questions correctly than Chris did.
B) Brian and Damien both answered 4 more questions correctly than Chris did.
C) Brian and Damien both answered 2 more questions correctly than Chris did.
D) Brian and Damien both answered 4 fewer questions correctly than Chris did.
Answer:
Option C
Brian and Damien both answered 2 more questions correctly than Chris did
Solution:
Let "x" be the number of correct answers of Brian
Let "y" be the number of correct answers of Chris
Let "z" be the number of correct answers of Damien
The number of questions Brian got right is 14 more than 1/4 the number of questions Chris got right
[tex]x = 14 + \frac{1}{4}y\\[/tex] ---------- eqn 1
Damien correctly answered 2 less than 5/4 the number of questions Chris answered correctly
[tex]z = \frac{5}{4}y - 2[/tex] ---------- eqn 2
Brian and Damien have the same score
x = z -------- eqn 3
Therefore,
[tex]14 + \frac{1}{4}y = \frac{5}{4}y - 2\\\\\frac{5}{4}y - \frac{1}{4}y = 14+2\\\\y = 16[/tex]
Substitute y = 16 in eqn 1
[tex]x = 14 + \frac{16}{4}\\\\x = 14 + 4\\\\x = 18[/tex]
Therefore, by eqn 3,
z = 18
Thus we get,
Number of correct answers of Brian = 18
Number of correct answers of chris = 16
Number of correct answers of Damien = 18
Therefore, correct statement is:
Brian and Damien both answered 2 more questions correctly than Chris did
Answer:
Brian and Damien both answered 2 more questions correctly than Chris did.-B
Step-by-step explanation: