We want to find the angle A. For doing that, we need to use something called The Law of Sines. It relates the angles and measures of its opposite edges. Applying it in this particular case gives us:
[tex]\frac{\sin(A)}{25}=\frac{\sin (62\degree)}{28}[/tex]Note that A is the opposite angle of the edge BC, and 62° is the opposite angle of the edge CA (They must be opposite!).
Just remains to solve the equation. Let's solve it:
[tex]\sin (A)=25\cdot\frac{\sin(62\degree)}{28}=(\frac{25}{28})\cdot\sin (62\degree)[/tex]The next step is just to use a calculator. Let's put the right-hand side within an inverse sin (sin^-1):
[tex]A=\sin ^{-1}((\frac{25}{28})\cdot\sin (62\degree))\approx52.03\degree[/tex]
I need help seeing if I got them all right. I’m not 100% sure I did them right and am confused a little
Triangle A has three different angles, therefore all three sides have different lengths, so the triangle is scalene.
Triangle B has all three sides with the same length, therefore the triangle is equilateral.
Triangle C has all three angles congruent, therefore all three sides are also congruent, so the triangle is equilateral.
Triangle D has two sides with the same length, therefore the triangle is isosceles.
Which lines has a constant of proportional between y and x of 3
Given:
The three lines are given in the graph.
To find the line that has a constant of proportional between y and x of 3:
Let us consider the blue line.
When x=0, we get y=0
W
The solutions obtained after plotting the quadratic equationy = –2x^2 + 3x-1 in the coordinate plane are ?
The solutions are:
[tex]\begin{gathered} (0.5,0) \\ and \\ (1,0) \end{gathered}[/tex]Solutions:
[tex]\begin{gathered} x=\frac{1}{2}=0.5 \\ x=1 \end{gathered}[/tex]How many days did Amelia record the the time she spent working in the yard ? Step
SOLUTION:
7) The times recorded, you count the number of strokes. Total number of strokes = 5 strokes.
8)
fractions (1/4, 3/4, 6/4, 6/4, 6/4)
[tex]\begin{gathered} \frac{1}{4}+\text{ }\frac{3}{4}+\text{ 1}\frac{2}{4}+\text{ 1}\frac{2}{4}+\text{ 1}\frac{2}{4} \\ \text{Total whole number= 1+1+1= 3} \\ \text{Total fractions= }\frac{1}{4}+\frac{3}{4}+\frac{2}{4}+\frac{2}{4}+\frac{2}{4} \\ \text{Total fractions= }\frac{1+3+2+2+2}{4} \\ T\text{otal fractions= }\frac{10}{4} \\ \text{otal fractions= 2}\frac{2}{4}\text{ OR 2}\frac{1}{2}\text{ hours} \end{gathered}[/tex][tex]\begin{gathered} \text{Total hours: 2+2}\frac{1}{2} \\ \text{Total hours: 5}\frac{1}{2}\text{ hours} \end{gathered}[/tex]9) To calculate the average hours. We add all the hours and divide by 5
[tex]\begin{gathered} 5\frac{1}{2}\div5 \\ \frac{11}{2}\div\frac{5}{1} \\ \frac{11}{2}\times\frac{1}{5} \\ \frac{11}{10} \\ 1\frac{1}{10}\text{ hours} \end{gathered}[/tex]Final answers:
7) 5 days
8) 5 and half hours
9) 1 and tenth hours
I need help what is 160 ÷7/8
Solve the division this way:
[tex]\frac{160}{\frac{7}{8}}=\frac{8\cdot160}{7}=182.86[/tex]The answer is 182.86
State the coordinates of the endpoints of a line segment that intersects the y-axis
According to the question statement, we need to find the endpoints of a line segment that cuts the y axis.
Those can be any points. The only condition is that one of the points has to have a positive x coordinate and the other one has to have a negative x coordinate.
It means that the answer can be: (4,3) and (-7,9)
12) Ms. Baker made chocolate chip cookies and gingerbread cookies to give to her coworkers for theholidays. She baked 6 batches total, and each batch had 12 cookies. There were one third as manygingerbread cookies as chocolate chip cookies. How many of each cookie did she bake?
It is given that Ms. Baker baked 6 batches total, and each batch had 12 cookies.
The total number of cookies=6 time 12
[tex]=6\times12[/tex][tex]=72[/tex]The total number of cookies is 72.
Let x be the number of gingerbread cookies.
The given that ne third as many gingerbread cookies as chocolate chip cookies.
The number of chocolate chip cookies =1/3 of x
[tex]=\frac{1}{3}x[/tex]The total number of cookies=the number of gingerbread cookies+the number of chocolate chip cookies.
Substitute values, we get
[tex]72=x+\frac{1}{3}x[/tex][tex]72=x(1+\frac{1}{3})[/tex][tex]72=x(\frac{1\times3}{3}+\frac{1}{3})[/tex][tex]72=x(\frac{3}{3}+\frac{1}{3})[/tex][tex]72=x(\frac{3+1}{3})[/tex][tex]72=x(\frac{4}{3})[/tex]Transferring 4/3 to the left-hand side, we get
[tex]72\times\frac{3}{4}=x[/tex][tex]18\times3=x[/tex][tex]x=54[/tex]Hence the number of gingerbread cookies =54 cookies.
The number of chocolate chip cookies =1/3 of x
[tex]=\frac{1}{3}\times54=18[/tex]The number of chocolate chip cookies = 18 cookies.
Put the following equation of a line into slope-intercept form, simplifying allfractions.2y - x = -8
Slope intercept form :
y=mx+b
Solving for y:
2y-x=-8
2y=-8+x
y= (-8+x)/2
y= -4+1/2x
y= 1/2x-4
Write an equation of the line passes through (4, 1) and is parallel to y = -2x + 7 40
The given equation is
[tex]y=-2x+7[/tex]Notice that this equation has a slope of -2 because that's the coefficient of x.
It's important to know that parallel lines have equal slopes. So, the new line has a slope of -2 too.
Then, we use the given point (4, 1), the slope -2, and the point-slope formula to find the equation
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-1=-2(x-4) \\ y-1=-2x+8 \\ y=-2x+8+7 \\ y=-2x+15 \end{gathered}[/tex]Hence, the equation of the new parallel line is y = -2x + 15.Question is down below 1st drop down menu answer choices A. At the center of B. On C. Outside 2nd drop down answer choices A. On B. Inside C. Outside 3rd drop down answer choices A. Half B. Twice C. One third
Given:
There are given that the central angles and described angles to fid difference.
Explanation:
According to the concept of a central angle, the vertex of the central angles has located at the center of the circle.
And,
According to the concept of inscribed angles, the vertex of the inscribed angle has located on the circumference of the circle.
And,
The measurement of for inscribed angle is defined by half the measure of the intercepted arc.
Final answer:
Hence, for the first box, the answer will be (A) At the center of, for the second box the answer will be (A) On. and for the third box, the answer will be (A) Half
A construction crew needs to pave a road that is 206 miles long. The crew paves 7 miles of the road each day. The length L (in miles), that is left to be paved after d days is given by the following function. L (d) = 207-7dHow many miles of road does the crew have left to pave for 13 days?If 143 miles of road is left to be paved, how many days has the crew been paving the road?
Answer:
Explanation:
Given:
L (d) = 207-7d
where:
L (d) = the length L (in miles), that is left to be paved after d days
d= number of days
To find the amount of miles of road that the crew have left to pave for 13 days, we plug in the given number of days into the equation:
L (d) = 207-7d
=207-7(13)
=116 miles
So, the crew have left 116 miles to pave for 13 days.
If 143 miles of road is left to be paved, the amount of days that the crew have been paving the road is:
L (d) = 207-7d
143 miles = 207-7d
Simplify and rearrange
7d=207-143
7d=64
d=64/7
d=9.14 days
Therefore, the crew have been paving for 9.14 days if 143 miles of road is left to be paved.
PART A. The set of ordered pairs below represents a linear function. {(-2, -3), (0, -2), (2, -1), (x, y)}What is one other pair of coordinates that could be the missing ordered pair, (x, y), in this set? x=____y=____PART B. Show your work or explain how you got your answers in Part A.
Answer:
x=4, y=0
Explanation:
Part A
In this set, one other pair of coordinates that could be the missing ordered pair, (x, y), is:
[tex]\begin{gathered} (4,0) \\ x=4 \\ y=0 \end{gathered}[/tex]Part B
Observe that:
• The x-value increases by 2.
,• The y-value increases by 1.
Therefore, the next pair will be:
[tex](2+2,-1+1)=(4,0)[/tex]The point P' (2, -9) is reflected in the line y=x. What are the coordinates of P'?
You have the point P(2,-9)
When any point is reflected around the line y=x, its coordinaes changes as follow: x coordinate becomes y coordinate, and y coodinate becomes x coordinate.
In this case you have that the reflected point will be:
P' (-9,2)
The great Khafre Pyramid, the second tallest and second largest of the three ancient pyramids of Egypt, is 448 feet tall, and the length of a side at the base is 706 feet. The base of the pyramid is a square. What is its volume, rounded to the nearest cubic foot?
The volume of a pyramid can be calculated with the following formula:
[tex]\text{volume =}\frac{1}{3}\times(area\text{ of base)}\times height[/tex]The base of the pyramid is a square, so its area will be:
[tex]\begin{gathered} \text{area of base =side}\times side \\ \text{area of the base=706}\times706 \\ \text{area of base =}498,436\text{ ft²} \end{gathered}[/tex]Let's plug that result in the formula for the volume:
[tex]\begin{gathered} \text{volume}=\frac{1}{3}\times(498,496)\times448 \\ \text{volume}=74,433,109\text{ ft³} \end{gathered}[/tex]So our final answer will be:
[tex]\text{volume = 74,433,109 ft}^3[/tex]-. Your annual salary is $75,000. You can choose to be paid semimonthly or biweekly. Does it matter which option you choose?
Problem
Your annual salary is $75,000. You can choose to be paid semimonthly or biweekly. Does it matter which option you choose?
Solution
For this case if he/she select semimonthly the total payments are:
2*12 = 24 paychecks
with Payment = 75000/24= 3125 each one
And if he/she select biweekly we have
(52weeks/4)*2 = 26 paychecks
with Payment = 75000/26= 2884.62 each one
And is a different since with the biweekly payment you recive less amount on each payment but in general he/she will recive the same amount at the end of the yea r
For the given function value, write a corresponding ordered pair.G(0)= -5/8What is the corresponding ordered pair?
Assumung an expression of g is a function of x a shown;
[tex]g(x)=y[/tex]where
• x is the input value
,• y is the output
The ordered pair for the function is written as (x, y)
Given the function value;
[tex]G(0)=-\frac{5}{8}[/tex]On comparing with the expression above:
x = 0 and y = -5/8
Therefore a corresponding ordered pair for the function value will be (0, -5/8)
Can you please help me
ANSWER
[tex]125.7in^2[/tex]EXPLANATION
The lateral area of a cylinder is given as:
[tex]A=2\pi rh[/tex]where r = radius; h = height
Therefore, the lateral area for the given cylinder is:
[tex]\begin{gathered} A=2\cdot\pi\cdot5\cdot4 \\ A=125.7in^2 \end{gathered}[/tex]a large container holds 5 gallons of water it begins leaking at a constant rate after 15 minutes the container has 2 gallons of water left. how many minutes will it take for the container to go from full to empty?
Use the graph to answer the question.For which value of a is f(x) discontinuous?
Given:
a graph of the function is given.
Find:
To find the value of a at which function f(x) is discontinuous.
Explanation:
we know a function f(x) is said to be continuous , if one can draw the graph of the function continuously without lifting the pen, and if the graph of the function breaks at some point, that point is known as point of discontinuity.
From the given graph, it is clear that the graph of the function f(x) is discontinuous at x = -1,.
Conclusion:
therefore the value of a is -1.
Given a Cost of $12.00 and a Markup of $7.20 find the Selling Price.
Question
Given a Cost of $12.00 and a Markup of $7.20 find the Selling Price.
Solution
We are given
Cost = $12.00
Markup (Profit) = $7.20
We want to find the Selling Price.
The formula for selling price (S.P.) is given by
[tex]S.P\mathrm{}\text{ = Cost + Markup}[/tex][tex]\begin{gathered} S\mathrm{}P\text{. = \$12.00 + \$7.20} \\ S\mathrm{}P\text{. = \$19.20} \end{gathered}[/tex]Therefore, the selling price is $19.20
Use the intermediate value theorem for polynomials to show that the polynomial function has a real zero between the numbers given.f(x)= -8x^5+5x^3-6x^2+1;-1 and 0
Solution:
The intermediate value theorem for polynomials states that when a polynomial function changes from a negative value to a positive value, the function must cross the x-axis.
To prove it has a real zero, it must cross the x-axis.
The theorem thus states mathematically that;
[tex]\begin{gathered} f(a)Given:[tex]\begin{gathered} a=-1 \\ b=0 \\ f(x)=-8x^5+5x^3-6x^2+1 \end{gathered}[/tex]We test for the continuity of the polynomial at x = a and x = b
Hence,
[tex]\begin{gathered} f(a)=f(-1) \\ f(x)=-8x^5+5x^3-6x^2+1 \\ f(-1)=-8(-1^5)+5(-1^3)-6(-1^2)+1 \\ f(-1)=8-5-6+1 \\ f(-1)=-2 \end{gathered}[/tex][tex]\begin{gathered} f(b)=f(0) \\ f(x)=-8x^5+5x^3-6x^2+1 \\ f(0)=-8(0^5)+5(0^3)-6(0^2)+1 \\ f(0)=1 \\ f(0)=1 \end{gathered}[/tex]
From the above, since the value of the output of the function at the input (intervals) -1 and 0 changes from negative to positive (i.e, from -2 to 1), then it should pass through the x-axis.
Once the function passes through the x-axis, then it will have a real zero between the interval given.
Convert 3 7/8 into a decimal
We need to convert 3 7/8 to a decimal number
So,
[tex]\begin{gathered} 3\frac{7}{8}=3+\frac{7}{8} \\ \\ \frac{7}{8}=0.875 \\ \\ 3\frac{7}{8}=3+\frac{7}{8}=3+0.875=3.875 \end{gathered}[/tex]
For the following right triangle, find the side length x.XO68
Using the Pythagoras theorem,
opposite² + adjacent² = hypotenuse²
From the figure given,
opposite =6 adjacent=8 hypotenuse=x
Substitute the values and evaluate
6² + 8² = x²
36 + 64 = x²
100 = x²
Take the square root of both-side
10 = x
Provide me three coordinate points for the following, given the Slope and Y-intercept. 4. Slope = 15, Y intercept = -1 (give me 3 coordinate points)
The coordinates can be
[tex](1,14)(2,29)(3,44)[/tex]elloFitte: Weather in MichiganDateJanuary 20January 21January 22January 23January 24January 25Temperature("F/"C)32/030/-128/-232/023/-530/-1TOThe weather in Detroit,Michigan in January tends to becold and snowy. Use the datatable to the left to graph thetemperature for six days. Youcan use Fahrenheit or Celsiusunits. Remember- Yourindependent variable goes onthe x-axis and your dependentvariable will be on the y-axis.Make sure that label both axis',include units, and provide a title.
Step 1: We determine the dependent and independent variables. Since the temperature depends on the day it is registered, the independent variable (x) is the date, and the dependent variable (y) is the temperature.
Step 2: We graph the ordered pairs (x,y), considering the given information in the table. If we use Fahrenheit degrees, we have:
Step 3: We add the axis labels and the title of the graph.
Answerestimates by first rounding each number to the place value. 8.3×36
We are asked to estimate the result of the given multiplication problem
[tex]8.3\times36[/tex]As you can see, the number 8.3 is in decimal and we need to round it off to the nearest place value.
Let us round off 8.3 to 8
[tex]8\times36=288[/tex]Therefore, the estimated result is 288
Which of the following represents the solutions x^2 -4x+12=6x-2
Given the equation:
[tex]x^2-4x+12=6x-2[/tex]Let's find the solution to the given equation.
Move all terms to the left and equate to zero.
Ad 2 and subtract 6x to both sides:
[tex]\begin{gathered} x^2-4x-6x+12+2=6x-6x-2+2_{} \\ \\ x^2-10x+14=0 \end{gathered}[/tex]Let's solve usingbthe quadratic formula:
[tex]x=\frac{-b^{}\pm\sqrt[]{b^2-4ax}}{2a}[/tex]Apply the general formula to find the values of a, b, and c:
[tex]\begin{gathered} ax^2+bx+c=0 \\ \\ x^2-10x+14=0 \end{gathered}[/tex]Thus, we have:
a = 1
b = -10
c = 14
Substitute the values into the quadratic formula:
[tex]\begin{gathered} x=\frac{-(-10)\pm\sqrt[]{-10^2+4(1)(14)}}{2(1)} \\ \\ x=\frac{10\pm\sqrt[]{100+56_{}}}{2} \\ \\ x=\frac{10\pm\sqrt[]{44}}{2} \\ \\ x=\frac{10\pm\sqrt[]{4\ast11}}{2} \\ \\ x=\frac{10\pm\sqrt[]{2^2\ast11}}{2} \\ \\ x=\frac{10\pm2\sqrt[]{11}}{2} \\ \\ x=5\pm\sqrt[]{11} \end{gathered}[/tex]Solving further:
[tex]\begin{gathered} x=5+\sqrt[]{11},\text{ 5-}\sqrt[]{11} \\ \\ x=5+3.317,\text{ 5-3.31}7 \\ \\ x=8.317,\text{ 1.683} \end{gathered}[/tex]Therefore, the solutions are:
x = 8.317, 1.683
ANSWER:
8.137 and 1.683
Which situation can be represented by this inequality? (7.10C, SS, RC2) 145 < 15n + 17 A Ann has made 15 necklaces. She will make 17 more necklaces every week. Ann makes necklaces for n weeks. For what values of n will Ann have made at most 145 necklaces? B Ann has made 17 necklaces. She will make 15 more necklaces every week. Ann makes necklaces for n weeks. For what values of n will Ann have made at most 145 necklaces? C Ann has made 15 necklaces. She will make 17 more necklaces every week. Ann makes necklaces for a weeks. For what values of n will Ann have made at least 145 necklaces? D Ann has made 17 necklaces. She will make 15 more necklaces every week. Ann makes necklaces for n weeks. For what values of n will Ann have made at least 145 necklaces?
Answer:
D. Ann has made 17 necklaces. She will make 15 more necklaces every week. Ann makes necklaces for n weeks. For what values of n will Ann have made at least 145 necklaces?
Explanation:
The inequality is:
145 ≤ 15n + 17
Then, the expression on the right side indicates that there is a fixed quantity of 17 and there is a variable quantity 15n that depends on the variable n. So, the situation that can represent this expression is that Ann has made 17 necklaces (fixed quantity) and she will make 15 more necklaces every week (a variable quantity).
So, if 15n + 17 represents the number of necklaces that Ann made after n weeks, the complete expression 145 ≤ 15n + 17 represents that this number of necklaces should be greater than or equal to 145.
Therefore, the correct answer is:
D. Ann has made 17 necklaces. She will make 15 more necklaces every week. Ann makes necklaces for n weeks. For what values of n will Ann have made at least 145 necklaces?
How many 2/5s can go into 1 1/2
The number of (2/5)s in 1 and 1/2 are 15/4 or 3.75.
Let the number of (2/5)s in 1 and 1/2 be x.
Hence, we can write,
(2/5)x = 1 and 1/2.
We can write the mixed fraction 1 and 1/2 as improper fraction 3/2.
Hence,
(2/5)x = 3/2
x = (3/2) ÷ (2/5)
x = (3/2) * (5/2)
x = (3*5/2*2) = 15/4 = 3.75.
Hence, the number of (2/5)s in 1 and 1/2 are 15/4 or 3.75.
Improper fraction
An improper fraction is defined as a fraction whose numerator is greater than the denominator. Suppose, x/y is an improper fraction, such that x > y. It is therefore, the improper fraction is always greater than one.
To learn more about improper fraction, here:-
https://brainly.com/question/21449807
#SPJ1
write an equation to describe the relationship between T and the number of tickets and seeds in the total cost of tickets
c = 55t
Explanation:To find the relationship between the cost (c) and the number of ticket (t), the first thing we do is find the rate of change
The rate of change = slope = change in c/change in t
using points (t, c): (2, 110) and (5, 275)
The rate of change = (275-110)/(5 - 2)
The rate of change = 165/3
The rate of change = 55
Using proportional equation:
y = kx
where k = constant of poroportionality
The equation:
y = kx
where y = cost of ticket = c
x = numer of tickets = t
k = constant of poroportionality = rate of change
k = 55
Our equation becomes:
c = kt
Th equation that describes the relationship:
c = 55t