The measure of minor arc is 84 degree
The expression for the an angle inscribed in a circle, then the measurement of the angle is equal to the half of the measure of its intercepted arc.
[tex]\text{Angle}=\frac{1}{2}m(arc)[/tex]here we have, arc length = 84 degree
[tex]\begin{gathered} m\angle ADC=\frac{1}{2}(mAC) \\ m\angle ADC=\frac{1}{2}\times84 \\ m\angle ADC=42^o \end{gathered}[/tex]Angle = 42 degree
The function g is defined as follows.=gx+5x27If the graph of g is translated vertically upward by 3 units, it becomes the graph of a function f.Find the expression for fx.
f(x) = 5x²+10
Explanations:
Given the function g(x) expressed as:
[tex]g(x)=5x^2+7[/tex]If the function g(x) is translated vertically upward by 3 units to produce f(x), the resulting translation used will be given as:
[tex]f(x)=g(x)+3[/tex]Substitute the function g(x) into the translation rule to have:
[tex]\begin{gathered} f(x)=5x^2+7+3 \\ f(x)=5x^2+10 \end{gathered}[/tex]Therefore the expression for f(x) is 5x²+10
Rebecca had $100 in her savings accountin the first week. She adds $45 each weekfor 5 weeks. The savings account balancecan be shown by a sequence.
Rebecca had $100
and each week, she add $45
Let the number of weeks is x
So, after x weeks, she will have y
y = 100 + 45x
See the following figure:
After 5 weeks, y = 100 + 45 * 5 = 325
============================================
After 1 week , y = 145
after 2 weeks , y = 190
after 3 weeks , y = 235
and so on
So, The savings account balance can be shown by a sequence.
The sequence will be: 145 , 190 , 235 , 280 , .......
The kind of this sequence will be arthimatic sequence , because there is a common defference between the terms of the sequence which = 45
The cost to manufactute a hair clip is $.50. With a markip of 200 percent,what is the selling price of this hair clip?
The selling price of this hair clip will be $ 1.50.
Cost price of the clip is = $ 0.50
Markup price = 200 percent
Mark up price = 200 % of 0.5
Mark up price = 200 / 100 × 0.50
Mark up price = 2 × 0.50
Mark up price = $ 1
Selling price of the product will be:
SP = $ 0.50 + $ 1
SP = $ 1.50
Therefore, we get that, the selling price of this hair clip will be $ 1.50.
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Your question was incomplete. Please refer the content below:
The cost to manufacture a hair clip is $0.50. With a markup of 200 percent, what is the selling price of this hair clip?
simplify 3y -(2y - 3)/4
The expression is given
[tex]\frac{3y-(2y-3)}{4}[/tex]Simplify the expression
[tex]\frac{3y-2y+3}{4}=\frac{y+3}{4}[/tex]Hence the answer is
[tex]\frac{y+3}{4}[/tex]A spring is attached to the ceiling and pulled 17 cm down from equilibrium and released. After 3 seconds the amplitude has decreased to 13 cm. The spring oscillates 14 times each second. Find a function that models the distance, D the end of the spring is below equilibrium in terms of seconds, t, since the spring was released.
The end of the spring is below equilibrium in terms of seconds, t, since the spring was released is D(t) = 17([tex]0.957^{t}[/tex])cos(28πt)
What is equilibrium?A state of balance between opposing forces or actions that is either static (as in a body acted on by forces whose resultant is zero) or dynamic (as in a reversible chemical reaction when the rates of reaction in both directions are equal).
Given that, a spring is attached to the ceiling and pulled 17 cm down from equilibrium and released. After 3 seconds, the amplitude has decreased to 13 cm. The spring oscillates 14 times each second.
Amplitude begins at 17 cm, [tex]A_{0}[/tex] = 17 cm
The amplitude decreases by 13/3 = 4.33 per second = 0.043%
The amplitude function can be then modelled as =
A(t) = [tex]A_{0}[/tex][tex](1-0.043)^{t}[/tex]
A(t) = [tex]A_{0}[/tex][tex]0.957^{t}[/tex]
The spring oscillates 14 times each second, therefore,
T = 1/14
2π/B = 1/14
B = 28π
The graphical equation is;
D(t) = [tex]A_{cos}[/tex](Bt-C)+D
Horizontal shift = 0
Vertical shift = 0
Hence, The end of the spring is below equilibrium in terms of seconds, t, since the spring was released is D(t) = 17([tex]0.957^{t}[/tex])cos(28πt)
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the rest of the question say what is the length of the tangent line labeled X
To solve this problem, consider the following picture
By the tangent secant segment theorem we have the following equation
[tex]a^2=b\cdot(b+c)[/tex]Note that in our case, we have a=x, b=3 and c=9. So if we replace this values in the equation, we have
[tex]x^2=3\cdot(3+9)=3\cdot12=36[/tex]so, applying the square root on both sides, we get
[tex]x=\sqrt[]{36}=\pm6[/tex]Since x is a distance, it should be strictly positive, so we have that
[tex]x=6[/tex]I need help with this math problem. It’s homework and I have been sitting here for 3 hours. Please please help me.
Given:
Coordinates (-3 , 2), (6 , 2), (6 , -4), (-3 , -4)
Required:
Area and Parameter
Explanation:
Formula to find the distance between two points
Distance between (-3 , 2), (6 , 2) and (6 , 2), (6 , -4)
[tex]\begin{gathered} d=\sqrt{(6-(-3))\placeholder{⬚}^2+(2-2)\placeholder{⬚}^2} \\ d=9 \end{gathered}[/tex]Final Answer:
Give the equation of the transformed quadratic toolkit function shown below.()=−(+1)2+2()=−(−1)2+2()=−(+1)2+2()=(−1)2−2
The Solution:
Given:
Required:
Determine the function of the given graph.
The required equation is:
[tex]y=-\left(x-1\right)^{2}+2[/tex]Answer:
[option 2]
7. Marco was asked to rotate thecoordinate P(3,-4) 180 degrees about theorigin. Then, he decided to perform atranslation of (x, y+2) followed by adilation of 2. Marco was convinced thatP and P'" had the same coordinates. IsMarco correct? Explain your reasoning.
Let's take this, step by step.
First step:
Rotate the coordinate 180 degrees about the origin.
When a 180 degrees rotation about the origin is performed the coordinates (x, y) changes to (-x, -y)
Thus, P(3, -4) changes to P'(-3, 4)
Second Step:
Perform a translation of (x, y+2)
P'(-3,4) = P''(-3, 4+2) = P''(-3, 6)
Third step:
Perform a dilation of 2.
P''(-3, 6) = P'''(-3*2, 6*2) = P'''(-6, 12)
We can see that,
P(3, -4) while P'''(-6, 12)
Therefore, P and P''' do not have the same coordinates
If two planes leave an airport at the same time with one flying west at 520 miles per hour and the other flying east at 540 miles per hour, how long will it take them to be 3180 miles apart?
SOLUTION:
Step 1:
In this question, we are given the following:
If two planes leave an airport at the same time with one flying west at 520 miles per hour and the other flying east at 540 miles per hour,
how long will it take them to be 3180 miles apart?
Step 2:
Let the distance of one of the planes flying west at 520 miles per hour be:
[tex]520\text{ x}[/tex]And let the distance of the other plane flying east at 540 miles per hour be:
[tex]540\text{ x}[/tex]where x , represents the time of flight in hours, such that:
[tex]\begin{gathered} 520\text{ x + 540 x = 3180} \\ 1060\text{ x = 3180} \\ \text{Divide both sides by 1060, we have that:} \\ x\text{ = }\frac{3180}{1060} \\ x\text{ = 3} \end{gathered}[/tex]CONCLUSION:
The time it will take them to be 3180 miles apart will be in 3 hours' time.
It costs mrs. barazal $245 for her and 6 people to take a day-long guided tour of the Everglades how much does the guided tour cost per person?
For Barazal and 6 persons the cost is $245
So, the number of persons = 7
so, the cost per person = 245/7 = $35
So
the guided tour cost per person = $35
6) Identifyas amonomial, binomial, or trinomial.4x2 – y + 0z4 binomial monomial Trinomial
For this problem we have the following expression given:
[tex]4x^2-y+0z^4[/tex]Since any number multiplied by 0 is 0 then our expression becomes:
[tex]4x^2-y[/tex]And since we have two terms we can categorize the expression as a binomial.
A billboard has an area of 32 square meters. Express the area in square feet.
We will use the equivalency:
[tex]\begin{gathered} 1m=3.281ft \\ \frac{3.281ft}{1m}=1 \end{gathered}[/tex]Then, if we have an area of 32 m^2, we can multiply this value by the equivalency factor we wrote (as it is equal to 1) as:
[tex]\begin{gathered} A=32m^2\cdot(\frac{3.281ft}{1m})^2 \\ A=32m^2\cdot\frac{10.765ft^2}{1m^2} \\ A=344.48ft^2 \end{gathered}[/tex]Answer: the area is 344.48 sq ft.
a recipe requires 7/8 sticks of butter for each 1 1/4 cups of flour. how many cups of flour to sticks of butter
In order to calculate the rate of cups of flour to stick of butter, just calculate the following quotient:
(1 1/4)/(7/8) = (5/4)/(7/8) = 5·8/7·4 = 40/28 = 20/14 = 10/7
Hence, the required rate is 10/7 or 10:7
that is, 10 cups of flour for 7 sticks of buttter
Solve the system of linear equations.7x + 2y = -88y = 4x
7x + 2y = -8 Equation 1.
8y = 4x Equation 2.
We solve for y in eq. 2; as follows:
y = 4x/8.
Now we replace y on eq. 1:
7x + 2(4x/8) = -8
7x + x = -8
8x = -8
x = -8/8
x = -1
Finally we replace x on eq 2:
8y = 4(-1)
8y = -4
y = -4/8
y = -1/2
In an arithmetic sequence a18 = -10 and a40= 100 , write the explicit rule, the recursive rule, and find s30
Answer:
Explicit rule [tex]a_n=5n-100[/tex]Recursive rule [tex]a_1=-95,a_n=a_{n-1}+5[/tex]Sum of the first 30 terms [tex]-675[/tex]
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Let the first term be a and common difference be d.
Use equations for nth term and sum of the first n terms[tex]a_n=a+(n-1)d\\[/tex][tex]S_n=n(a+a_n)/2[/tex]Use the first equation to find the values of a and d[tex]a_{18}=a+17d=-10[/tex][tex]a_{40}=a+39d=100[/tex]Substract the first equation from the second and solve for d39d - 17d = 100 + 1022d = 110d = 110/22d = 5Find aa + 17*5= - 10a + 85 = - 10a = - 95Explicit rule[tex]a_n=-95+5(n-1)=-95+5n-5=5n-100[/tex]Recursive rule[tex]a_1=-95,a_n=a_{n-1}+5[/tex]Sum of the first 30 terms[tex]S_{30}=(-95-95+29*5)*30/2=(-45)*15=-675[/tex]The explicit rule is a(n) = - 95 + 5 · (n - 1), whose recursive rule is [tex]a_{n+1}[/tex] = [tex]a_{n}[/tex] + 5. The 30th element of the arithmetic sequence is 50.
How to derive an arithmetic sequence
Arithmetic sequences are sets of elements generated by a formula of the form:
a(n) = a + r · (n - 1), for n ≥ 1
Where:
a - First element of the sequence.r - Common raten - Index of the n-th element of the sequence.Please notice that the common rate is the difference between any two consecutive elements of the sequence. The recursive form is described by the following form:
[tex]a_{n+1}[/tex] = [tex]a_{n}[/tex] + r
Now we should determine the elements of the explicit rule by solving the following system of linear equations:
n = 18
- 10 = a + r · (18 - 1)
a + 17 · r = - 10
n = 40
100 = a + r · (40 - 1)
a + 39 · r = 100
Then, we solve the system of linear equations by numerical methods:
(a, r) = (- 95, 5)
And the 30th element of the arithmetic series:
a(n) = - 95 + 5 · (n - 1)
a(30) = - 95 + 5 · (30 - 1)
a(30) = 50
And the recursive form is [tex]a_{n+1}[/tex] = [tex]a_{n}[/tex] + 5.
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What volume of ice cream is contained in a 10 cm-high ice cream cone with a base radius of 4 cm?
We would find the volume of the ice cream contained in the cone by applying the formula for determining the voume of a cone which is expressed as
Volume = 1/3 x pi x radius^2 x height
From the information given,
height = 10
radius = 4
pi is a constant whose value is 3.142
Thus,
Volume = 1/3 x 3.142 x 4^2 x 10
Volume = 167.57
rounding to the nearest whole number,
Volume = 168 cubic cm
I need help with number 28 I could be wrong but I think you need to use the rook to match the bishop number 25
Answer:
2 translation vectors.
[tex](A,3)\text{ }+\text{ u(4,0) }=\text{ (E,3)}[/tex][tex](E,3)\text{ + u(0,4) = (E, 7)}[/tex]Step by step explanation:
You have to move a rook from the green circle to the blue one.
Then you have to represent series of the translation vector
You should know that the tower only moves horizontally or vertically.
You first move it 4 blocks to the right
[tex](A,3)\text{ }+\text{ u(4,0) }=\text{ (E,3)}[/tex]Then you move 4 blocks up.
[tex](E,3)\text{ + u(0,4) = (E, 7)}[/tex]Hi, I'm having a really hard time doing Multi Step Equations in Math, please help me.
You have the following equation:
4x - 3 = 2x + 5
In order to solve the previous equation, proceed as follow:
4x - 3 = 2x + 5 subtract 2x both sides
4x - 2x - 3 = 5 add 3 both sides
4x - 2x = 5 + 3 simplify like terms
2x = 8 divide by 2 both sides
x = 8/2
x = 4
Hence, the solution to the given equation is x = 4
Select all the lines that are perpendicular to 3x – y = 10. A. y = 3x + 5 B. y = –13x + 17 C. x + 3y = 27 D. y – 2 = 13(3x + 36)
The lines that are perpendicular to 3x – y = 10. is option C (x+3y= 27).
Line equation:
3x - y = 10
y = 3x - 10
here slope m = 3.
perpendicular line slope = -1/m = -1/3
so the perpendicular line must have slope m = -1/3
A.
y = 3x + 5
here slope m = 3
This line is not the perpendicular to 3x - y = 10 because here slope not equal to -1/3.
B.
y = -13x + 17
here slope m = -13
This line is not the perpendicular to 3x - y = 10 because here slope not equal to -1/3.
C.
x + 3y = 27
3y = -x + 27
y = -1/3(x) + 27/3
y = -1/3(x) + 9
here slope m = -1/3
This line is perpendicular to the 3x - y = 10 because here slope is equal to -1/3.
D.
y - 2 = 13(3x+36)
y = 39x + 468 - 2
y = 39x + 466.
here slope m = 39.
So this line is not the perpendicular to 3x - y = 10 because here slope not equal to -1/3.
Therefore the lines that are perpendicular to 3x – y = 10. is option C (x+3y= 27).
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can you find the domain of a piecewise functuon
a piecewise function
x+ 4 , if -4 ≤x <3
. 3 ≤ x < 6
Then ,answer is [ -4,6)
James invests 20k in an account that offers a compound interest rate of 8.3% per year for 6 years. I need to know which one is the correct answer 1. a(6)=20,000×(1+0.83)⁶‐¹2. a(6)=20,000×(1+0.083)⁶+¹3. a(6)=20,000×(1+0.083)⁶‐¹4. a(6)=20,000×(1+0.083)⁶
Given,
The principal amount is 20k.
The rate of interest is 8.3%.
The time period is 6 Years.
Required
The amount of investment after 6 years.
The amount is calculated as,
[tex]\begin{gathered} Amount=principal\times(1+\frac{rate}{100})^{time} \\ =20000\times(1+\frac{8.3}{1000})^6 \\ =20000\times(1+0.083)^6 \\ =20000\times(1+0.083)^6 \end{gathered}[/tex]Hence, the amount after 6 years is 2000 x (1 + 0.083)^6.
Volunteer drivers are needed to bring a students to the championship baseball game. Drivers either have cars, which can eat 4 students, or vans which can seat 6 students. The equation 4c +60 80 describes the relationship between the number of carse and number of vans v that can transport exactly so students 3 Explain how you know that this graph represents this equation number of vans 2 4 6 8 10 12 14 16 18 20 22 24 number of cars
One featue of the equation is that when c = 0
[tex]\begin{gathered} 4(0)+6v=80 \\ \therefore v=13.33 \end{gathered}[/tex]The other feature is that when v = 0
[tex]\begin{gathered} 4c+6(0)=80 \\ \therefore c=20 \end{gathered}[/tex]Therefore, our graph must contain the points (0, 13.33) and (20, 0), and looking at the graph given we see that it has exactly those points; hence, the graph represents the equation given
match the following each letter may be used more than once.a. 12/15b. 15/12c. 9/15d. 9/12e. 12/9f. 15/9
We have a right triangle and we have to write some of the trigonometric ratios.
A trigonometric ratio relates a trigonometric function of an angle of the tiangle with a quotient of two of the sides of the triangle.
The basic trigonometric ratios are:
[tex]\begin{gathered} \sin (\alpha)=\frac{\text{Opposite}}{\text{Hypotenuse}} \\ \cos (\alpha)=\frac{\text{Adyacent}}{\text{Hypotenuse}} \end{gathered}[/tex]We can also write the trigonometric ratio for the tangent:
[tex]\tan (\alpha)=\frac{\sin (\alpha)}{\cos (\alpha)}=\frac{\text{Opposite}}{\text{Adyacent}}[/tex]Now, we can write sin(x):
[tex]\sin (X)=\frac{\text{Opposite}}{\text{Adyacent}}=\frac{YZ}{XZ}=\frac{12}{15}[/tex]The opposite side to X is YZ and the hypotenuse is XZ, so sin(X) = YZ/XZ = 12/15.
In the same way, we can calculate cos(x):
[tex]\cos (X)=\frac{\text{Adyacent}}{\text{Hypotenuse}}=\frac{XY}{XZ}=\frac{9}{15}[/tex]The tan(x) can be calculated as:
[tex]\tan (X)=\frac{\text{Opposite}}{\text{Adyacent}}=\frac{YZ}{XY}=\frac{12}{9}[/tex]For Z, the opposite and adyacent angles are different than for X, so we can write:
[tex]\tan (Z)=\frac{\text{Opposite}}{\text{Adyacent}}=\frac{XY}{YZ}=\frac{9}{12}[/tex]Answer:
sin(X) = 12/15
cos(X) = 9/15
tan(X) = 12/9
tan(Z) = 9/12
what should be the value of k so that the trinomial is a perfect square trinomial ?
ANSWER:
5
STEP-BY-STEP EXPLANATION:
The perfect square trinomial is given as follows:
[tex](a\pm b)^2=a^2\pm2ab+b^2[/tex]Therefore, in this case would be:
[tex]\begin{gathered} x^2+2kx+25 \\ a=x \\ b=5 \\ (x+5)^2=x^2+2\cdot5x+25 \\ k=5 \end{gathered}[/tex]Therefore the value of k is 5
simplifying like terms and distributive property7b + 2(46 - 3)
We will solve as follows:
[tex]7b+2(46-3)=7b+92-6[/tex][tex]=7b+86[/tex]So, the solution is 7b + 86.
Question 5 of 10 Which function is increasing? O A 19-(0) OB. Rx) = 5* O C. f( 10w -() OD. (X) = (0.5)
Increasin function:
f(x) = a^x
Where a must be greater than 1:
A. 1/15 = 0.06 NO
B. 5 YES
C. 1/5 NO
D. 0.5 NO
Correct option B.5
5>1
The following data points represent the number of flying saucers that are owned by each alien on planet nowhere. (a)Arrange the data from the least to greatest 1,4,2,21,8,27(b)Find the median number of flying saucers
The data that represent the number of flying saucers that are owned by each alien on planet nowhere is given below:
[tex]1,4,2,21,8,27[/tex](a)We sort the data from the least to greatest below.
[tex]1,2,4,8,21,27[/tex](b)The median is the middle number.
In this case, we have two numbers in the middle: 4 and 8
Therefore we find their average:
[tex]\begin{gathered} \text{Median}=\frac{4+8}{2} \\ =\frac{12}{2} \\ =6 \end{gathered}[/tex]Answer:
6 is the correct answer.
Step-by-step explanation:
What is the new equation 1 when youmultiply by -1?
the equation will be
-x - y = 7
Find f[2) if f(x) = (x+ 1)^2 O9O6 O5
You have the following function:
f(x) = (x + 1)²
In order to determine the value of f(2) you replace the value x = 2 in the given function and make the operations, just as follow:
f(2) = (2 + 1)² simplify inside parenthesis
f(2) = (3)² 3² is the same as 3x3=9
f(2) = 9
Hence, the value of the function when x = 2 is f(2) = 9