Wouldn’t it be 36.7 because that’s the arch am I right?
Answer:
The measure of arc CD is 114.6°.
Step-by-step explanation:
Let the center of the circle be O and OP is perpendicular to CD at point point P.
The perpendicular line from the center of circle divide each chord in two equal parts. so, CP=DP.
[tex]CP=\frac{CD}{2}=\frac{36.7}{2}=18.35[/tex]
In a right angles triangle,
[tex]\sin\theta =\frac{opposite}{hypotenuse}[/tex]
In a right angles triangle OPC,
[tex]\sin\angle POC =\frac{18.35}{21.8}[/tex]
[tex]\angle POC =\sin^{-1} (\frac{18.35}{21.8})[/tex]
[tex]\angle POC \approx 57.3[/tex]
In triangle OPC and OPD,
[tex]OC=OD[/tex] (Radius)
[tex]OP=OP[/tex] (Reflexive property)
[tex]CP=DP[/tex] (Altitude on chord from center)
By SSS postulate
[tex]\triangle OPC\cong \triangle OPD[/tex]
[tex]\angle POC\cong \angle POD[/tex] (CPCTC)
[tex]\angle POC=\angle POD[/tex]
The measure of angle COD is
[tex]\angle COD=\angle POC+\angle POD[/tex]
[tex]\angle COD=2\angle POC[/tex]
[tex]\angle COD=2(57.3)[/tex]
[tex]\angle COD=114.6[/tex]
Therefore the measure of arc CD is 114.6°.
Which of the following could be folded to produce the object above?
Answer:
answer is Z
Step-by-step explanation:
An ice cream shop makes 14 different flavors of ice cream. You can get each flavor in a waffle cone, sugar cone, cake cone, or a cup. If you are daring you can add one of these toppings rainbow sprinkles, cookie crumbs, or peanuts as a topping. How many different outcomes are possible? show work
14×3×3=126. So 126 is your answer.
Answer:
14*4*3 168
Step-by-step explanat
15. Scott and Tara were asked to find the
area of this trapezoid:
16 cm
18 cm
24 cm
Scott wrote A = 2(24 + 16)(8).
Tara wrote A = (16 + 24)(8)
Which student is correct? Explain.
Answer:
Both Scott and Tara have responded correctly.
Step-by-step explanation:
we know that
The area of a trapezoid is equal to
A=(1/2)[b1+b2]h
we have
b1=16 cm
b2=24 cm
h=8 cm -----> Note The height is 8 cm instead of 18 cm
substitute
A=(1/2)[16+24](8)
A=160 cm²
Verify Scott 's work
Note Scott wrote A = (1/2)(24 + 16)(8) instead of A = 2(24 + 16)(8)
Remember that the Commutative Property establishes "The order of the addends does not alter its result"
so
(24+16)=(16+24)
A = (1/2)(24 + 16)(8)=160 cm²
Verify Tara's work
Note Tara wrote A = (1/2)(16+24)(8) instead of A = (16 + 24)(8)
A = (1/2)(16+24)(8)=160 cm²
The admission fee at an amusement park is $4.50 for children and $13 for adults. On a certain day, 249 people enter the park, and the admission fees collected totaled $2,013.00 how many children and how many adults were admitted?
Answer:
154 adults 94kids
Step-by-step explanation:
Solve the system of equations. y = -5x + 24 y = 4x - 21 a. ( -5, -1) c. ( -1, 5) b. ( 5, -1) d. No solution
y = -5x + 24
y = 4x - 21
Since both of these equations are equal to Y, theyre equal to each other.
So we can make an equation with y = -5x + 24 in one side and y = 4x - 21 on the other.
-5x + 24 = 4x - 21
Now in order to get the value of x we need to isolate it in one side of the equation. We can do this by subtracting 24 from both sides of the equation:
-5x + 24 - 24 = 4x - 21 - 24
-5x = 4x - 45
Now we subtract 4x from both sides so the 4x shift to the other side
-5x - 4x = 4x - 4x - 45
-9x = -45
Finally divide both sides by -9 so x is by itself
(-9)÷(-9x) = -(45)÷(-9)
x = 5
Since we did all of this to BOTH sides of the equation, both sides are still equal to each other and the equation still is true.
Now apply x = 5 to either of the initial equations to find the value of Y
y = -5x + 24 or y = 4x - 21
(I'll do both but u only need one)
y = -5(5) + 24
y = -25 + 24
y = -1
y = 4(5) - 21
y = 20 - 21
y = -1
Either way, X is 5 and Y is -1
Answer (5, -1)
Final answer:
The solution to the system of equations is (5, -1), matching option b. This is found by setting both equations equal to each other, combining like terms, solving for x, and then using that value to find y.
Explanation:
To solve the system of equations, set the two equations equal to each other since they both equal y:
y = -5x + 24
y = 4x - 21
Now equate them:
-5x + 24 = 4x - 21
Add 5x to both sides:
24 = 9x - 21
Add 21 to both sides:
45 = 9x
Now divide by 9 to solve for x:
x = 5
Substitute x back into either original equation to find y:
y = -5(5) + 24
y = -25 + 24
y = -1
The solution is (5, -1), which corresponds to option b.
To check the solution, we can substitute x = 5 into both of the original equations to verify that they are true. For the first equation:
-5(5) + 24 = -25 + 24 = -1
For the second equation:
4(5) - 21 = 20 - 21 = -1
Since both substitutions lead to an identity, the solution is correct. The final answer is (5, -1), or option b.
Which fact would help you to solve for x in the diagram shown?
A) Angles in an equilateral triangle are congruent.
B) The sum of the interior angles in a quadrilateral is 360°.
C) Alternate interior angles formed by a transversal and parallel lines are congruent.
D) The exterior angle of a triangle is equal to the sum of the two remote interior angles.
The answer is A, Angles in an equilateral triangle are congruent.
Which fact would help you to solve for x in the diagram shown?
A) Angles in an equilateral triangle are congruent.
Which line passes through the origin?
(A) y = 3
(B) y = x − 3
(C) y = −3x
(D) y = 2x + 1
Answer:
c. y=-3x
Step-by-step explanation:
Plug in x=0 and y=0.
0=-3(0)
0=0...the origin
Solve for x: 3x - 5 = 9x + 8 - 5x
Answer:
X= -13
Step-by-step explanation:
Your first goal is to get all the X’s to one side of the equation.
So:
3x - 5 = 9x + 8 - 5x
+5x +5x
8x - 5 = 9x + 8
-9x -9x
-1x - 5 = 8
Now that you have all the X variables simplified and on one side, you make sure all of you constant terms are on the other side.
-1x - 5 = 8
+5 +5
-1x = 13
Because you can’t have a negative X, you divide the entire equation by -1.
-1x = 13
-1
x = -13
Dividing by -1 will give you the inverse of the equation which is positive one x equals negative thirteen.
Solve the inequality n/-3+ 8 > 6.
A.) n > -6
B.)n > 42
C.)n < 6
D.)n > -42
Answer:
C.) n < 6
Step-by-step explanation:
Subtract 8:
n/-3 > -2
Multiply by -3. The negative multiplier requires the comparison be reversed:
n < 6
To solve the inequality n/-3 + 8 > 6, we first subtract 8 from both sides of the inequality and then multiply by -3. This reveals that n < 6, which corresponds to option C.
Explanation:To solve the inequality n/-3 + 8 > 6, we first isolate the term containing n by subtracting 8 from both sides of the inequality:
n/-3 + 8 - 8 > 6 - 8
n/-3 > -2
Now, we can multiply both sides of the inequality by -3 to find the value of n. Remember, when you multiply or divide both sides of an inequality by a negative number, you must reverse the inequality sign:
n/-3 × -3 < -2 × -3
n < 6
Thus, the correct answer to the inequality n/-3 + 8 > 6 is n < 6, which corresponds to option C.
Find the solution of this system of equations. Separate the x- and the y- values with a comma. X=6+y -8x+9y=-29
Answer:
x= 25, y = 19
Step-by-step explanation:
Solve the following system:
{x = y + 6 | (equation 1)
9 y - 8 x = -29 | (equation 2)
Express the system in standard form:
{x - y = 6 | (equation 1)
-(8 x) + 9 y = -29 | (equation 2)
Swap equation 1 with equation 2:
{-(8 x) + 9 y = -29 | (equation 1)
x - y = 6 | (equation 2)
Add 1/8 × (equation 1) to equation 2:
{-(8 x) + 9 y = -29 | (equation 1)
0 x+y/8 = 19/8 | (equation 2)
Multiply equation 2 by 8:
{-(8 x) + 9 y = -29 | (equation 1)
0 x+y = 19 | (equation 2)
Subtract 9 × (equation 2) from equation 1:
{-(8 x)+0 y = -200 | (equation 1)
0 x+y = 19 | (equation 2)
Divide equation 1 by -8:
{x+0 y = 25 | (equation 1)
0 x+y = 19 | (equation 2)
Collect results:
Answer: {x = 25 , y = 19
Answer: X= -29, Y= -267 over 10
Step-by-step explanation:
X= -29, substitute the value of X into the equation 6+y-8(-29)+9y an then solve for Y...
Hope this helps!
what is the sum of an 8-term geometric series if the first term is -11, the last term is 180, 224, and the common ratio is -4
Answer:
The sum is [tex]144,177[/tex]
Step-by-step explanation:
we know that
The formula of the sum in a geometric sequence is equal to
[tex]S=a1[\frac{1-r^{n}}{1-r}][/tex]
where
a1 is the first term
r is the common ratio
n is the number of terms
we have
a1=-11
r=-4
n=8
substitute the values
[tex]S=(-11)[\frac{1-(-4)^{8}}{1-(-4)}][/tex]
[tex]S=(-11)[\frac{1-(65.536)}{5}][/tex]
[tex]S=144,177[/tex]
Which statement is true about the solution to √2x-1==1
Answer:
There are no real number solutions to this question.
The statement which is true for the equation[tex]\sqrt{2x-1} =-1[/tex] is option C which is that x=1.
What is an equation?It is a relationship between variables and it can be in the form of one variable also.
How to solve the problem?We have been given [tex]\sqrt{2x-1} =-1[/tex]
squaring both sides we get
2x-1=1
2x=1+1
2x=2
x=1
Hence the solution of the equation is x=1.
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Which verbal description, when graphed has the same slope as y= -2x+6
A. Teo has read 6 books. He reads 2 per day, X is the number of days and y is the total number of books read
B. Caroline is 6 miles from home. She walks towards home at 2 miles per hour, X is the number of hours and Y is the number of miles from Home
C. Ned deposits $6 per week into his saving account, which already has $2 in it, X is the number of weeks and Y is the total of dollars
Answer: i say its A but i could be wrong
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
what is y+5=7(x-8) written in standard form
Answer:
7x-y=61
Step-by-step explanation:
The standard form is Ax+By=C.
Let's simplify the equation first.
1. Distribute: y+5=7x-56
2. Subtract 5: y=7x-61
3. Arrange into standard form: 7x-y=61
Answer
-7x+y=-61
Its the same as 7x-y=61, but in a different form
Find the number of even-numbered subsets that have only even numbers from the set (1,2,3,4,5,6...100)
I would greatly appreciate a quick answer
Answer:
Step-by-step explanation:
You could use the 'brute force' method, which would be to simply write out all the possible subsets. We could avoid repetition within the subsets.
{2} would be the first subset; it contains one even number.
Next would be {2, 4}, next {2, 4, 6} ... {2, 4, 6, ... 94, 96, 98, 100}. Provided that we correctly understand what this problem is asking for, writing out and then counting all these subsets should answer the question.
ASAP PLEASE HELP ME !!!!
Answer:
The correct answer is third option
The sum of any number and its opposite is 0
Step-by-step explanation:
It is given an expression,
8.29 * (-5.62 + 5.62)/5.62
To find the correct reason
Here - 5.62 + 5.62 = 0
5.62 is opposite to - 5.62
because sum of a number and its opposite is 0.
Therefore the correct answer is third option.
The sum of any number and its opposite is 0
HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! evaluate ^3√343/512
Answer:
Step-by-step explanation:
7/8 0r 0.875
A French class has a total of
42
students. The number of males is
8
more than the number of females. How many males and how many females are in the class?
Their are 34 females in the class.
If 42 is the total amount of French students; subtract the amount of males(8) from the whole class to receive how many females their are in the class. Which is 34.
Simplify the following expression.
A.49
B.1/14
C.1/49
D.14
Answer:
C
Step-by-step explanation:
Using the rules of exponents
• [tex]a^{m}[/tex] × [tex]a^{n}[/tex] ⇔ [tex]a^{(m+n)}[/tex]
• [tex]a^{-m}[/tex] ⇔ [tex]\frac{1}{a^{m} }[/tex]
Hence
[tex]7^{-5/6-7/6}[/tex] = [tex]7^{-\frac{12}{6} }[/tex] = [tex]7^{-2}[/tex], then
[tex]7^{-2}[/tex] = [tex]\frac{1}{7^{2} }[/tex] = [tex]\frac{1}{49}[/tex] → C
ANSWER
C. 1/49
EXPLANATION
The given expression is
[tex] {7}^{ - \frac{5}{6} } \times {7}^{ - \frac{7}{6} } [/tex]
Recall that:
[tex] {a}^{m} \times {a}^{n} = {a}^{m + n} [/tex]
We apply this product rule of exponents to get:
[tex] {7}^{ - \frac{5}{6} } \times {7}^{ - \frac{7}{6} } = {7}^{ - \frac{5}{6} + - \frac{7}{6} } [/tex]
This implies that:
[tex] {7}^{ - \frac{5}{6} } \times {7}^{ - \frac{7}{6} } = {7}^{ - \frac{12}{6} } [/tex]
[tex]{7}^{ - \frac{5}{6} } \times {7}^{ - \frac{7}{6} } = {7}^{ - 2} [/tex]
Recall again that:
[tex] {a}^{ - m} = \frac{1}{ {a}^{m} } [/tex]
We apply this rule to get:
[tex]{7}^{ - \frac{5}{6} } \times {7}^{ - \frac{7}{6} } = \frac{1}{ {7}^{2} } [/tex]
This simplifies to:
[tex]{7}^{ - \frac{5}{6} } \times {7}^{ - \frac{7}{6} } = \frac{1}{49} [/tex]
15% of 20 is
Ο 30
Ο 300
Answer:
3
Step-by-step explanation:
Is means equals and of means multiply
15% * 20 = ?
Change to decimal form
.15 * 20 = ?
3 = ?
15% of 20 is 3
Can someone please help me out
Answer:
D
Step-by-step explanation:
Look at where the two functions intersect.
[tex](-3,-3)[/tex] and [tex](0,6)[/tex].
Those are the solutions.
What are these Ratios in order from greatest to least? 23:24, 11:12, 7:8
Answer:
From greatest to least is 23:24 , 11:12, 7:8
Step-by-step explanation:
Hope this helps!!!
The point (−3, 1) is on the terminal side of angle θ, in standard position. What are the values of sine, cosine, and tangent of θ? Make sure to show all work.
ANSWER
See below
EXPLANATION
The given point (-3,1) lies in the second quadrant.
In this quadrant only sine is positive.
The length of the hypotenuse formed by the right angle triangle is
[tex] {h}^{2} = {3}^{2} + {1}^{2} [/tex]
[tex] {h}^{2} = 9 + 1[/tex]
[tex]{h}^{2} = 10[/tex]
[tex]h = \sqrt{10} [/tex]
The side opposite to θ, is 1 units.
The adjacent side is 3 units.
[tex] \sin( \theta) = \frac{opposite}{hypotenuse} [/tex]
[tex]\sin( \theta) = \frac{1}{ \sqrt{10} } = \frac{ \sqrt{10} }{10} [/tex]
[tex]\cos( \theta) = - \frac{adjacent}{hypotenuse} [/tex]
[tex]\cos( \theta) = - \frac{3}{ \sqrt{10} } = - \frac{3 \sqrt{10} }{10} [/tex]
[tex] \tan( \theta) = - \frac{opposite}{adjacent} [/tex]
[tex]\tan( \theta) = - \frac{1}{3} [/tex]
The values of sine, cosine and tangent of θ are; 1/√10, -3/√10 and -1/3 respectively.
Sine, Cosine and Tangent of anglesFrom the task content, it follows from Pythagoras theorem that;
hypothenuse = √((-3)²+1²)hypothenuse = √10On this note;
Sin θ = 1/√10Cos θ = (-3)/√10Tan θ = -1/3Read more on Trigonometric identities;
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what is 2 3/2 equal to?
A) Two times the square root of 8
B) three times the square root of 8
C) Three times the square root of 16
D) Two times the square root of 16
The expression '2 3/2' is a mixed number. Converting this to an improper fraction results in 7/2, which simplifies to 3.5. This does not match any of the provided options.
Explanation:The expression '2 3/2' implies that we are dealing with mixed numbers, meaning you have a whole number and a fraction combined. When you see this, you should convert the mixed number into an improper fraction. The way to do this is to multiply the whole number by the denominator of the fraction and then add the numerator to this product. In this case that would be (2*2) + 3 which equals 7. Your new fraction would be 7/2 which equals 3.5 when simplified to a decimal. This does not correspond to any of the provided options (A, B, C, D), signifying that the original question may have been misinterpreted or contains a typographical error.
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2 3/2 is equal to 7/2 or D) Two times the square root of 16.
Explanation:When we have a whole number followed by a fraction, we can convert it to an improper fraction.
To do this, we multiply the whole number by the denominator of the fraction and add the numerator.
So in this case, 2 x 2 + 3 = 7.
Therefore, 2 3/2 is equal to 7/2 or D) Two times the square root of 16.
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What number is 20%of 40
Answer:
20% of the number 40 is 8
20% x 40=800 divide 100 =8
Can someone plzz help me
For this case we have that by definition of trigonometric relations of a rectangular triangle that, the sine of an angle is given by the opposite leg to the angle on the hypotenuse of the triangle.
That is to say:
[tex]Sin (30) = \frac {IR} {14}[/tex]
We clear the length of the leg:
[tex]IR = 14 * sin (30)\\IR = 14 * \frac {1} {2}\\IR = 7 \ in[/tex]
Answer:
[tex]IR = 7 \ in[/tex]
(PLEASE HELP) Question is worth 30 points:) The following function represents the production cost F(x) In dollars for x numbers of units produced by company 1: F(x)=0.05x^2-7x+300 The Following table represents the production cost g(x) in dollars, for x number of units produced by company 2: x: 0.6,0.8,1, 1.2, 1.4 G(x): 899.58,899.52,899.50,899.52, 899.58 based on the given information, the minimum production cost for company ____ is greater [put 1 or 2 in blank space]
Answer:
production cost f(x), in dollars, for x number of units produced by company 1:
f(x) = 0.05x^2 − 7x + 300
2) Table that represents the production cost g(x), in dollars, for x number of units produced by company 2:
x g(x)
0.6 899.58
0.8 899.52
1 899.50
1.2 899.52
1.4 899.58
3) Comparison: do a table for f(x) with the same x-values of the table for g(x).
x f(x) = 0.05x^2 − 7x + 300 g(x)
0.6 295.818 899.58
0.8 294.432 899.52
1 293.05 899.50
1.2 291.672 899.52
1.4 290.298 899.58
As you can see the values of f(x) are consistently lower than the values of g(x) for the same x-values.
The minimum production cost for company 2 is around 899.50 at x = 1, while the minimum production cost of company 1 is defintely lower (lower than 292.298 for sure, in fact if you find the vertex it is 55).
Answer: Based on the given information, the minimum production cost for company 2 is greater.
Step-by-step explanation:
how many pennies would be on the square labled H?
square A: 1 penny 2^0
square B: 2 pennies 2^1
square c: 4 pennies 2^2
[tex]\bf \begin{array}{|lllllllll|ll} \cline{1-9} label&A&B&C&D&E&F&G&H\\ &&&&&&&&&\\ pennies&2^0&2^1&2^2&2^3&2^4&2^5&2^6&2^7\implies 128\\ \cline{1-9} \end{array}[/tex]
Answer: part 2: 2n-1
Step-by-step explanation:
what is the best next step in the construction of a line that passes through B and is perpendicular to line A?
A. set the compass to be equal to CD
B. set the co pass to be wider than it was when placed at point B to draw the arc that passes through C and D
C. set the compass to be greater than CD
D. keep the compass setting the same width as when it was placed at point B to draw the arc that passes through C and D
Answer:The answe is D
Step-by-step explanation:
The correct next step is to keep the compass at the same width used at point B to draw an arc through points C and D, enabling the construction of a perpendicular line. Hence correct option D.
The best next step in the construction of a line that passes through point B and is perpendicular to line A is to keep the compass setting the same width as when it was placed at point B to draw the arc that passes through points C and D. This ensures that the arcs intersect the line A at points that are equidistant from B, which is essential in establishing a perpendicular line.
a submarine is at a depth of 2 1/3 km below sea level and if it starts ascending at the rate of 800m/h.then find its position after 2 hours?
Answer:
66 ⅔ m
Step-by-step explanation:
2 ⅓ km can be written in improper form as 5/3 km.
There's 1000 m in 1 km, so we can convert this:
5/3 km × (1000 m / km) = 5000/3 m
The submarine rises at 800 m/h. So after 2 hours:
distance = rate × time
d = 800 m/h × 2 h
d = 1600 m
So the new position is:
5000/3 m − 1600 m
5000/3 m − 4800/3 m
200/3 m
66 ⅔ m
Final answer:
After ascending at a rate of 800 meters per hour for 2 hours from a depth of 2 1/3 kilometers, the position of the submarine would be 733.3 meters below sea level.
Explanation:
The student has asked to find the position of a submarine after it ascends from a depth of 2 1/3 km below sea level at a rate of 800 m/h for 2 hours.
Firstly, we convert the depth of the submarine from kilometers to meters to match the ascent rate's unit. There are 1,000 meters in a kilometer, so 2 1/3 km is equivalent to 2,333.3 meters (since 2 km = 2000 m and 1/3 km = 333.3 m).
The submarine ascends at a rate of 800 meters per hour. After 2 hours, the total ascent will be 800 m/h * 2 h = 1,600 meters.
To find the new position, we subtract the ascent distance from the original depth: 2,333.3 m - 1,600 m = 733.3 meters below sea level.
Therefore, after 2 hours, the position of the submarine would be 733.3 meters below sea level.