The measure of the arc of the sinkhole that falls within the restaurants property is -21°
Measure of angles subtendedLet x be the angle at the dollar store at the intersection
Now the angle of the grocery store at the intersection, y is 2/3 that of the dollar store. So, y = 2x/3
Since both x and y are supplementary,
x + y = 180°
x + 2x/3 = 180°
5x/3 = 180°
x = 180° × 3/5
x = 36° × 3
x = 108°
Angle subtended by gas station at sinkholeThe gas station has the same angle at the intersection but has 88° more of the sinkhole edge to stabilize. So, the angle the gas station store subtends at the sinkhole is z = x + 88°
Angle subtended by grocery store at sinkholeAlso, since the grocery stores property has 2/3 of the angle in the intersection at the dollar store has, but has 5° more of the sinkhole edge to stabilize. The angle the grocery store subtends at the sinkhole is k = y + 5° = 2x/3 + 5°
Measure of arc subtented by restuarantLet k' be the angle subtended by the restuarant at the sinkhole.
Since the sinkhole is a circle, we have that
x + z + k + k' = 360°
x + x + 88° + 2x/3 + 5° + k' = 360°
8x/3 + 93° + k' = 360°
8x/3 + k' = 360° - 93°
8x/3 + k' = 267°
So, making k' subject of the formula, we have
k' = 267° - 8x/3
Substituting the values of the variables into the equation, we have
k' = 267° - 8 × 108°/3
k' = 267° - 288°
k' = -21°
So, the measure of the arc of the sinkhole that falls within the restaurants property is -21°
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Convert the unit of weight. Use 1 lb = 16 oz. Express your answer in exact simplest form. 3 lb = _____ oz
3lb= ⋅ = _____oz ?
Answer:
48
Step-by-step explanation:
one pound equals 16 ounces so multiply each side by three and you get that 3 lb equals 48 ounces
Answer:
48 oz
Step-by-step explanation:
We know 1 lb = 16 oz. That means that to find how many oz are in 3 lbs, you have to multiply 16 by 3. That equals 48.
Write an inequality for the graph shown below.
User for your variable.
X
o
?
Answer:
3 > x
Step-by-step explanation:
3 is larger than all of the values on the line, of which the arrow is pointing. The circle is open, so it means that it is not greater than or equal to.
I hope this helps!
-No one
Can someone please help with this. I’m stuck.
Answer:
567 ghbvc. the high but
Step-by-step explanation:
solve accordingly to the picture
hope it helps
SOMEONE PLEAASE HELP ME ASAP THIS IS DUE SOON
14. Now simplify the y-terms to get the equation of the parabolic path. You do not need to expand the x-term. (2 points) Hint: Square both sides to get rid of the square root
______________
√ (x - 7)^2 + (y - 9)^2 = (y - 4)
Answer:
Assuming a vertical axis of symmetry, the equation would be of the form y = ax^2 + bx + c which can also be written as y = a(x - h)^2 + k. Case 1: If the two points have the same y value, then the axis of symmetry will pass through the midpoint of the segment between them.
Step-by-step explanation:
An equation is formed of two equal expressions. The given equation can be simplified for y as y=(x²-14x+114)/10.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
The given equation √[(x-7)²+(y-9)²]=(y-4) can be simplified for y as shown below,
[tex]\sqrt{\left(x\:-\:7\right)^2\:+\:\left(y\:-\:9\right)^2}=\left(y\:-\:4\right)[/tex]
(x - 7)² + (y - 9)² = (y - 4)²
(x - 7)² = (y - 4²) - (y - 9)²
(x² + 49 - 14x) = (y² + 16 - 8y) - (y² + 81 - 18y)
x² + 49 - 14x = y² + 16 - 8y - y² - 81 + 18y
x² + 49 - 14x = 10y - 65
x² - 14x + 49 + 65 = 10y
x² - 14x + 114 = 10y
y = (x² - 14x + 114)/10
Hence, the given equation √[(x-7)²+(y-9)²]=(y-4) can be simplified for y as y=(x²-14x+114)/10.
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simplify 5/9x4 3/5x6 3/11x6/10 and 3 4/5x7 1/2
Answer:
529/55 and 57/2
Step-by-step explanation:
The graph of f(x) = 8 - x and line l which is tangent to f at x =1 is
shown in the figure to the right. The equation for line l is y =-3x +10.
Region R is the shaded region between line l, the graph off and the
y-axis while S is the shaded region between line l, the graph off and
the x-axis.
(a) Find the area of the shaded region R.
By taking the integral of the difference between the two given lines, we will see that R = 0.75.
How to find the area of the region R?Notice that the area will be given by the integral of the difference between the line L and our function on the interval [0, 1]
Then we just need to compute:
[tex]R = \int\limits^1_0 {-3x + 10 - (8 - x^3)} \, dx[/tex]
Solving that we will get:
[tex]R = \int\limits^1_0 {-3x + 10 - (8 - x^3)} \, dx = \int\limits^1_0 ({-3x + 10 - 8 + x^3} )dx\\\\\R = \int\limits^1_0 ({-3x + 2 + x^3} )dx\\\\\\[/tex]
[tex]R = \int\limits^1_0 ({-3x + 2 + x^3} )dx\\\\R = \frac{-3}{2}*(1)^2 + 2*1 + \frac{1^4}{4} = 0.75[/tex]
So the area of region R is 0.75 square units.
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Solve the equation.
−10x + 1 + 7x = 37
x = −15
x = −12
x = 12
x = 15
Help picture below problem 13
The Pythagorean theorem is the idea that the sum of the two legs which are both squared is equal to the hypotenuse's length squared.
*look at the image I attached for a better explanation
By looking at the picture, we are missing the leg's length, and by using the Pythagorean theorem, we get the equation
[tex]?^2+5^2 = 13^2\\?^2 + 25 = 169\\?^2 = 144\\? = 12[/tex]
Thus the missing side length is 12 cm
Hope that helps!
solve this sum urgent no spam
Answer:
Step-by-step explanation:
YES IS THE ANSWER BECAUSE X=9
AND 11+3=87
Write the number in standard form
and word form.
7 x 10 + 5 x 1 + 6 x (1/100) + 2 x
(1/1,000)
Answer:
75.062
Step-by-step explanation:
just add and multiply then remember that 1/100 or 1/1000 is just 0.001 or 0.01
The number of men and women participating in the Winter Olympic Games has been steadily increasing in recent years. In the 19th Winter Olympics, 1389 men and 787 women participated. 1660 men and 1121 women participated in the 22nd Winter Olympics.
Part A
Which system describes the number of men and women participating if x represents the number of winter games after the 22nd Winter Olympics?
Multiple choice question.
A)
y=1389x+1660y=787x+1121
B)
y=2713x+1121y=3343x+1660
C)
y=2713x+1389y=3343x+787
D)
y=2713x+1660y=3343x+1121
Using a system of equations, it is found that the correct option is:
A) 1389x+1660y=787x+1121y.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, considering the amounts in each olympics(1389 men and 787 women participated on the 19th, 1660 men and 1121 women in the 22th), the system is:
A) 1389x+1660y=787x+1121y.
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Name three synonyms for "Solution": _____________,___________,______________
Answer:
1 quick fix 2 solving 3 result
Step-by-step explanation:
hope it helps
PLEASE HELP PLEASE help
Answer:
Q. Equal
Step-by-step explanation:
"The same" means equal. Its kind of like equations.
1 is equal to 1 they are the same number
answer: Equal
Step-by-step explanation: being the same in quantity, size, degree, or value.
If 4–(x – 4) = 1 over 16 what is the value of x?
Answer:
4x+4=16
4x= 16–4
4x= 12
x= 12/4
x= 3
Alternatively,
4x+4=16
Taking 4 common,
4 (x+1) = 16
x+1 = 16/4
x+1 = 4
x = 4–1
x = 3
Step-by-step explanation:
The value of x is 68.
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Parts of an Equation
There are different parts of an equation which include coefficients, variables, operators, constants, terms, expressions, and an equal to sign. When we write an equation, it is mandatory to have an "=" sign, and terms on both sides. Both sides should be equal to each other. An equation doesn't need to have multiple terms on either of the sides, having variables, and operators. An equation can be formed without these as well, for example, 5 + 10 = 15. This is an arithmetic equation with no variables. As opposed to this, an equation with variables is an algebraic equation.
Given equation:
4/(x - 4) = 1 /16
Now, solving for x
4/(x - 4) = 1 /16
64 = x - 4
x= 68
Hence, the value of x is 68.
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Find the sum of a finite arithmetic sequence from n=1 to n=5 using the expression -3(4)^n-1
Answer:
Step-by-step explanation:
Arithmetic sequaence:
[tex]\sf a_n = -3(4)^n - 1\\\\a_1=-3*4^1 -1\\\\ = -3*4 - 1\\\\ = -12 - 1\\\\a_1=-13[/tex]
[tex]a_2 = -3*4^2-1\\[/tex]
= -3*16 -1
= -48 - 1
= -49
difference = second term - first term
= -49 -(-13)
= -49 + 13
d = -36
[tex]\boxed{S_n=\dfrac{n}{2}[2a + (n-1)d]}[/tex]
[tex]\sf S_5=\dfrac{5}{2}*[2*(-13} + 4*(-36)]\\\\ =\dfrac{5}{2}[-26-144]\\\\=\dfrac{5}{2}*(-270)[/tex]
= 5*(-135)
= -675
Please help me to answer this
If AC= 8x-14 and EC = 2x + 11, solve for x.
Step-by-step explanation:
AC= 8x-14
AC+14=8x
x=(AC+14)÷8
EC=2x+11
EC-11=2x
x=(EC-11)÷2
Answer:
Isolate the variable by dividing each side by factors that don't contain the variable.
Step-by-step explanation:
You randomly draw twice from this deck of cards
0 с G|F. D C G
What is the probability of not drawing a C, then not drawing a C,
without replacing the first card? Write your answer as a decimal
rounded to the nearest hundredth.
The probability of not drawing C in neither draw is P = 0.5
How to get the probability?
All the cards have the same probability of being drawn, in this case, our set of cards is {F, D, C, G}
The probability of not drawing C is equal to the probability of drawing F, D or G. So we have 3 options out of 4, then the probability is:
p = 3/4.
Now we draw another, this time there are 3 cards, one of these is C, and the other two cards are not C. Then the probability of not drawing C again is equal to 2 over 3.
q = 2/3.
The joint probability (for both of these events to happen) is equal to the product of the individual probabilities:
P = p*q = (3/4)*(2/3) = 0.5
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Write a function in vertex form that is translated 3 units down and 3 units to the right of f (x) = x^2
f (x) =
Answer:
f(x)= (x-3)^2-3
Step-by-step explanation:
Vertex Form: y= a(x-h)^2+k
a is the reflection
h and k are the vertex so in an ordered pair (x,y) = (h,k)
Since it is translating 3 units down it is going to be a negative 3. If it was translating up it would be positive 3. This represents the "k" because it is moving on the y-axis.
Since it is translating 3 units to the right it is going to be positive 3. If it was translating left it would be negative 3. This represents the "h" because it is moving on the x-axis.
After plugging it into the vertex form formula: f(x)= (x-3)^2-3
*notice when I plugged the "h" in it became negative because x-(3)= x-3*
Antonio weighs four pounds more than twice his brother weight. If Antonio weighs 97 pounds, how much does his brother weigh? Write and solve equation.
Answer:
The bother's weight is 46.5 lb.
Step-by-step explanation:
Let the brother's weight be b.
Antonio's weight is 2b + 4.
Antonio's weight is 97 lb.
2b + 4 = 97
2b = 93
b = 46.5 lb
Answer: The bother's weight is 46.5 lb.
Reflect the given triangle over
the x-axis.
[_
3 6 31
-3 3 3.
3 [?]
13
UD
[
[3 6 3]
( 3 3. 3]
THIS ANSWER IS CORRECT
Solution:
[tex]\sf \left[\begin{array}{ccc}3&6&3\\3&-3&-3\end{array}\right][/tex]
Explanation:[tex]\sf \left[\begin{array}{ccc}3&6&3\\-3&3&3\\\end{array}\right][/tex]
The rule for a reflection over the x -axis is (x,y) → (x,−y)
===============================================================
or multiply the matrix with: [tex]\left[\begin{array}{ccc}1&0\\0&-1\end{array}\right][/tex]
[tex]\dashrightarrow \ \sf \begin{pmatrix}1\cdot \:3+0\cdot \left(-3\right)&1\cdot \:6+0\cdot \:3&1\cdot \:3+0\cdot \:3\\ 0\cdot \:3+\left(-1\right)\left(-3\right)&0\cdot \:6+\left(-1\right)\cdot \:3&0\cdot \:3+\left(-1\right)\cdot \:3\end{pmatrix}[/tex]
Final answer:[tex]\sf \left[\begin{array}{ccc}3&6&3\\3&-3&-3\end{array}\right][/tex]
Find the value of x. AB=20 BC=6 CD=8
Step-by-step explanation:
there is the rule
outside length × (outside length + inside length) is the same for all lines originating from the same point.
so, we have
CD(CD + x) = BC(BC + AB) = 6(6+20) = 6×26 = 156
8(8 + x) = 156
8 + x = 19.5
x = 11.5
hello, id like to order3 halves of a cupcake for my family plus some extra for my 2 friends.
Answer:
They'll each want a quarter of a cupcake.
Step-by-step explanation:
The number of people in the family is 14.
The number of cupcakes ordered is 4.
What is a fraction?A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator.
Example: 1/2, 1/3 is a fraction.
We have,
Number of cakes for the family = 3 (1/2)
Number of friends = 2
Now,
Each person's amount of cake = 1/4
The number of people in the family.
= 3(1/2) ÷ 1/4
= 7/2 x 4
= 14
The total number of cupcakes ordered.
= 2 x 1/4 +3(1/2)
= 1/2 + 3(1/2)
= 1/2 + 7/2
= 8/2
= 4
Thus,
There are 14 people in the family.
The total number of cupcakes ordered is 4.
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The complete question is:
Hello, id like to order3 halves of a cupcake for my family plus some extra for my 2 friends.
They'll each want a quarter of a cupcake.
Some students are sharing pens among themselves. If each gets 5, no pens will be left. If each gets 3, 12 pens will be left. How many students are there?
Answer:
6 students
Step-by-step explanation:
Let x = number of students
Let y = total number of pens
Given:
If each student gets 5 pens, no pens will be left⇒ 5x = y
Given:
If each students gets 3, 12 pens will be left.⇒ 3x = y - 12
Substitute 5x = y into 3x = y - 12 and solve for x:
⇒ 3x = 5x - 12
⇒ 12 = 5x - 3x
⇒ 2x = 12
⇒ x = 6
Therefore, there are 6 students.
so urgent pls
Answer:
B
because if you were looking for time that is less than and equal to you would have to choose (c) as you answerPLEASE HELP WILL GIVE BRANLIEST
What is the equation for the circle with center (-9, 5) and radius 4
Answer:
[tex]\sf (x+9)^2+(y-5)^2=16[/tex]
Step-by-step explanation:
Standard equation of a circle: [tex]\sf (x-h)^2+(y-k)^2=r^2[/tex]
(where (h, k) is the center of the circle and r is the radius)
Given:
center = (-9, 5)radius = 4Substituting given values into the equation:
[tex]\sf \implies (x-(-9))^2+(y-5)^2=4^2[/tex]
[tex]\sf \implies (x+9)^2+(y-5)^2=16[/tex]
Equation:-
(x-h)²+(y-k)²=r^2(x-(-9))2+(y-5)^2=4^2(x+9)^2+(y-5)^2=16x^2+18x+81+y^2-10x+25=16[/tex][tex]\\ \rm\rightarrowtail x^2+y^2+8x+90=0[/tex]I NEED HELP WITH MY HOMEWORK
Answer:
I-9I
Step-by-step explanation:
Absolute value (the straight brackets) is how far away the number is from zero, this makes -9 into positive 9
Answer:
C. |-9|
Step-by-step explanation:
|-9| = 9
9 > 7 > |5| (5) > -12
Find all the factors of 18.
A) 2, 9
B) 1, 2, 3, 6, 9, 18
C) 1, 2, 3, 4, 6, 8, 9, 18
Answer:
B)1, 2, 3, 6, 9, 18
Step-by-step explanation:
1×18
2×9
3×6
HOPE IT HELPS YOU
-5 x + 10 -20 need help with this
Answer:
-5(x+2)
Step-by-step explanation: