Given data:
The given area of the triangle is A=5.
The first side given is a=4.1.
The second side given is b=2.5.
The expression for the area of triangle is,
[tex]A=\frac{1}{2}ab\sin C[/tex]Substitute the given values in the above expression.
[tex]\begin{gathered} 5=\frac{1}{2}(4.1)(2.5)\text{ sin C} \\ \sin C=0.97561 \\ C=102.7^{\circ} \end{gathered}[/tex]Thus, the value of the angle is 102.7 degrees.
Suppose it is believed that the probability a patient will recover from a disease following medication is 0.8. In a group of twenty such patients, the number who recover would have mean and variance respectively given by (to one decimal place):
Based on the number of patients and the probability that a patient will recover from the disease, the mean 16 patients would be and the variance would be 1.79
How to find out mean and the variance?The mean can be found by the formula:
= Number of patients in group x Probability that patient will recover
= 20 x 0.8
= 16 patients
The Variance is:
= Number of people x probability of recovery x (1 - probability of recover)
= 20 x 0.8 x (1 - 0.8)
= 3.2
So the standard deviation is:
= √3.2
= 1.79
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which ordered pair is a solution of the equation 7x−5=4y−6?PLEASE HURRY THIS IS DUE NOW A. only (2,4)B. only (3,6)C. both A and BD. neither A or B
To answer this question, we can take the coordinates (2, 4), and (3, 6) and substitute each of them in the given equation. Then, we can determine which of these ordered pairs is a solution of the equation 7x - 5 = 4y - 6. Then, we have:
1. Case: Ordered pair (2, 4):
[tex]7\cdot(2)-5=4\cdot(4)-6\Rightarrow14-5=16-6\Rightarrow9\ne10[/tex]This ordered pair is NOT a solution.
2. Case: Ordered pair (3, 6):
[tex]7\cdot(3)-5=4\cdot(6)-6\Rightarrow21-5=24-6\Rightarrow16\ne18[/tex]This ordered pair is NOT a solution.
Therefore, neither the ordered pair (2, 4) nor (3, 6) are solutions to the given equation (Option D).
In parallelogram ABCD… Justify your answer with the applicable property.
Solution
For this case we have the following measures:
m <1= x+12
m < 2= 6x -18
We can set up both angles equal:
x +12 = 6x -18
Solving for x we have:
12+18 = 5x
5x = 30
x= 30/5= 6
Then the value of m< 2 is:
m< 2= 6*6 -18= 36-18= 18
the best second answer is:
If a quadrilateral is ||gram the opposite angles are congruent
How can use theorem 7-4 to find missing segments? (7-4 is similarity) :)
Given
AD = 6.4
BD = 3.6
Find
AC,BC and DC
Explanation
Using Pythogoras theorem in triangle ADC
[tex]AC^2=DC^2+6.4^2------(1)[/tex]Using PT in triangle BDC
[tex]BC^2=DC^2+3.6^2-------(2)[/tex]Adding equation (1) and (2)
[tex]\begin{gathered} AC^2+BC^2=DC^2+3.6^2+DC^2+6.4^2 \\ AC^2+BC^2=2DC^2+53.92 \end{gathered}[/tex]Using PT in triangle ABC
[tex]10^2=AC^2+BC^2[/tex]Equating above 2 equations
[tex]\begin{gathered} 100=2DC^2+53.92 \\ DC^2=23.04 \\ DC=4.8 \end{gathered}[/tex]Putting this value of DC in equation (2)
[tex]\begin{gathered} BC^2=4.8^2+3.6^2 \\ BC^2=23.04+12.96 \\ BC=6 \end{gathered}[/tex][tex]\begin{gathered} 10^2=AC^2+BC^2 \\ 100=AC^2+36 \\ AC=8 \end{gathered}[/tex]Final Answer
AC = 8
BC = 6
DC = 4.8
A hummingbird's brain has a weight of approximately 2.94 x 10- ounces. An elephant's brain has a weight ofapproximately 1.76 x 102 ounces.Approximately how many times heavier is the elephant's brain than the hummingbird's brain?A) 60B) 600C) 6,000D) 60,000
Given the information on the problem,we have to divide the weight of the elephant's brain by the weight of the bird's brain, then, using the rules of exponents, we have the following:
[tex]undefined[/tex]a road is 4/7 of a mile long. a crew needs to replace 4/5 of the road. how long is the section that needs to be repaired
To solve this problem we need to find the fraction of a fraction, for that we just have to multiply them. This is done below:
[tex]\frac{4}{7}\cdot\frac{4}{5}=\frac{16}{35}\text{ of a mile}[/tex]The section is 16/35 of a mile long.
Solve T=C(8+AB) for A
If a price changes from $105,300 to $104,399 will that be a percentincrease or decrease?
If the price changes from $105,300 to $104,399, It means that there is a decrease in price.
Decrease = 105,300 - 104,399 = $901
The percentage decrease is gotten by dividing the decrease by the initial price and multiplying by 100. It becomes
[tex]\frac{901}{105300}\text{ }\times\text{ 100 = 0.8557\%}[/tex]By rounding up to the nearest whole number, it becomes 1%
The percent decrease is 1%
A local pizza parlor has the following list of toppings available for selection. The parlor is running a special to encourage patrons to try new combinations of toppings. They list all possible three topping pizzas (3 distinct toppings) on individual cards and give away a free pizza every hour to a lucky winner. Find the probability that the first winner randomly selects the card for the pizza topped with spicy italian sausage, banana peppers and beef. Express your answer as a fractionPizza toppings: Green peppers, onions, kalamata olives, sausage, mushrooms, black olives, pepperoni, spicy italian sausage, roma tomatoes, green olives, ham, grilled chicken, jalapeño peppers, banana peppers, beef, chicken fingers, red peppers
First, we need to find out how many possible combinations of pizza toppings there would be.
To do this, we will use the formula for Combination.
Combination is all the possible arrangements of things in which order does not matter. In our example, this would mean that a pizza topped with spicy Italian sausage, banana pepper, and beef is the same as a pizza topped with banana pepper, beef, and Italian sausage.
The formula for combination is
[tex]C(n,r)=^nC_r=_nC_r=\frac{n!}{r!(n-r)!}[/tex]From our given, n would be 17, since there are a total of 17 toppings (including spicy Italian sausage, banana peppers, and beef) and r would be 3 since there are three toppings that you chose.
Substituting it in the formula,
[tex]C(n,r)=\frac{n!}{r!(n-r)!}[/tex][tex]C(17,3)=\frac{17!}{3!(17-3)!}[/tex][tex]C(17,3)=680[/tex]Now, since we know that there are a total of 680 combinations of pizza toppings, we can now solve the probability of the first winner selecting a pizza topped with Italian sausage, banana peppers, and beef.
Write the standard form of the equation of the circle described below
Given:
Center ( 8, -4)
Radius (r) = 3
Find-:
Standard equation of a circle
Explanation-:
The standard equation of a circle:
[tex](x-h)^2+(y-k)^2=r^2[/tex]Where,
[tex]\begin{gathered} (h,k)=\text{ Center} \\ \\ r=\text{ Radius} \end{gathered}[/tex]So equation of circle is:
[tex]\begin{gathered} (x-h)^2+(y-k)^2=r^2 \\ \\ (h,k)=(8,-4) \\ \\ r=3 \end{gathered}[/tex][tex]\begin{gathered} (x-h)^2+(y-k)^2=r^2 \\ \\ (x-8)^2+(y-(-4))^2=3^2 \\ \\ (x-8)^2+(y+4)^2=9 \end{gathered}[/tex]Line Graph: This time you will not have the numbers on the x and y axis. You will need to decide which number to use (1, 2, 3... or 2,4,5.... Or 5, 10, 15...) 3: Creating Graphs Create a single line graph using the following table. Time goes on the x axis Rainfall goes on the y axis Make sure to do the following: Label the x and y axis Create a title 10 15 20 Time (minutes) 25 30 35 40 25 55 45 60 50 35 40 Speed (of car) (km/min)
Line Graph:
A line graph is used to show how the data points are changing with respect to time.
For Example:
A line graph may be used to show the average rainfall over the entire month.
For the given scenario we have,
X-axis = Time in minutes
Y-axis = Speed of car in km/min
Title of graph = Speed of Car Vs Time
Data points for time = 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60
Data points for speed = 25, 30, 35, 40, 25, 55, 45, 60 50 35 40
This is how the line graph looks like.
It is showing the speed of the car in km/min over an interval of 60 minutes in steps of 5 minutes.n steps of
Procedure:
• Draw and label the x-axis and y-axis.
,• Label the data points on both axis.
,• Draw the data points.
,• Join the data points with a line.
,• We are done.
,•
The length of a rectangle is given by a number, x (metres). The width is two metres longer than the length. The area of the rectangle is 120 m^2
metersGiven:
a.) The length of a rectangle is given by a number, x (meters).
b.) The width is two meters longer than the length.
c.) The area of the rectangle is 120 m^2.
Let's first recall the formula for getting the area of the triangle.
Area = L x W
Where,
L = Length
W = Width
The width is two meters longer than the length. Therefore, we can say that:
W = L + 2
Let's now determine the measure of the dimension of the rectangle:
Let,
x = length of the rectangle
We get,
[tex]\begin{gathered} \text{ A = L x W} \\ 120\text{ = L x (L + 2)} \\ 120=L^2\text{ + 2L} \\ L^2\text{ + 2L - 120 = 0} \\ (L\text{ - 10)(L + 12) = 0} \end{gathered}[/tex]Based on the relationships given, the Length of the rectangle has two possible measures.
L - 10 = 0
L = 10 m
L + 12 = 0
L = -12 m
Since a length must never be a negative value, the length of the rectangle must be 10 m.
For the width, we get:
W = L + 2 = 10 + 2 = 12 m
Summary:
Length = 10 m
Width = 12 m
Find the midpoint M of the line segment joining the points C=(6,2) and D=(2,8).
Given
[tex]point\text{ C \lparen6,2\rparen and Point \lparen2,8\rparen}[/tex]Solution
Formula
[tex]\begin{gathered} M=(\frac{x_1+x_2}{2},\text{ }\frac{y_1+y_2}{2}) \\ \end{gathered}[/tex][tex]\begin{gathered} x_1=6 \\ x_2=2 \\ y_1=2 \\ y_2=8 \end{gathered}[/tex]Now
[tex]\begin{gathered} M=(\frac{6+2}{2},\text{ }\frac{2+8}{2}) \\ \\ M=(\frac{8}{2},\frac{10}{\text{2}}) \\ \\ M=(4,5) \end{gathered}[/tex]The midpoint M of the line segment joining the points C=(6,2) and D=(2,8). is
[tex]M=(4,5)[/tex]Bella drove her car 81 km and used 9 liters of fuel. She wants to know how many kilometers (x) she can drive on 22 liters of fuel. She assumes her car will continue consuming fuel at the same rate.
Find the proportion between liters of fuel
that is find 22/9 = 2.444
thats how much liters have more to consume
now multiply 2.444 by 81 , the kilometers she has drived
It gives as result 2.444 x 81 = 198 kilometers
55mL of hardener to each container of resin. How much hardener should be added to 14 containers of resin?Write your answer in liters.
The amount of hardener added to 1 container of resin = 55mL.
The amount of hardener added to 14 containers is calculated as,
[tex]\begin{gathered} \text{Amount of hardener = 55 }\times\text{ 14 } \\ \text{Amount of hardener = 770 mL} \\ \text{Amount of hardener = 0.770 L} \end{gathered}[/tex]Thus 0.770 litres of hardener must be added to 14 containers of resin.
For which value(s) of x will the rational expression below equal zero? Che all that apply. (x - 5)(x+2) x + 1 A.-5 B. 2 c. 1 1 D. -1 E. 5 F. -2
The rational expression we have is:
[tex]\frac{(x-5)(x+2)}{x+1}[/tex]For a rational expression to be equal to 0, the numerator of the expression has to be equal to 0.
The numerator is: (x-5)(x+2)
That has to be equal to 0:
[tex](x-5)(x+2)=0[/tex]Here, we apply the zero product property, which tells us that if a product is equal to 0, one of the two elements, or the two elements, are equal to 0:
[tex]\begin{gathered} x-5=0 \\ x+2=0 \end{gathered}[/tex]We solve the two equations, and get the two values that will make the rational equation equal to 0:
[tex]\begin{gathered} x=5 \\ x=-2 \end{gathered}[/tex]Answer:
E. 5
F. -2
The safe load, L, of a wooden beam of width w, height h, and length l, supported at both ends, varies directly as the product of the width and the square of the height, and inversely as the length. A wooden beam 5 inches wide, 8 inches high, and 216 inches long can hold a load of 7670 pounds. What load would a beam 3 inches wide, 5 inches high, and 240 inches long of the same material, support? Round your answer to the nearest integer if necessary.
we know that
L=KW(h^2)/l
we have that
W=5 in
h=8 in
l=216 in
L=7670 pounds
step 1
Find the value of K (constant of proportionality)
substitute the given values in the equation
7670=K(5)(8^2)/216
7670=k(1.4815)
k=5,177.25
step 2
we have the equation
L=(5,177.25)W(h^2)/l
for
W=3 in
h=5 in
l=240 in
substitute in the equation and solve for L
L=(5,177.25)(3)(5^2)/240
L=1,617.89 pounds
Round your answer to the nearest integer
so
L=1,618 pounds
3/4 = m + 1/4
What is m? m = ?
Answer 3/4 = m + 1/4 is 2/4
Explanation.3/4 = m + 1/4
m = 3/4 - 1/4
m = (3 - 1)/4
m = [tex]\frac{2}{4}[/tex]
__________________
Class: Elementary School
Lesson: Fractions
[tex]\boxed{ \colorbox{lightblue}{ \sf{ \color{blue}{ Answer By\:Cyberpresents}}}}[/tex]
A rectangular garden has a walkway around it. The area of the garden is 2(4.5x +1.5). Thecombined area of the garden and the walkway is 3.5(8x + 4). Find the area of the walkway aroundthe garden as the sum of two terms.The area of the walkway around the garden is(Simplify your answer. Use integers or decimals for any numbers in the expression.)
In this case, we'll have to carry out several steps to find the solution.
Step 01:
DataL
garden area = 2(4.5x +1.5)
garden + walkway area = 3.5(8x + 4)
walkway area = ?
Step 02:
walkway area:
walkway area = 3.5(8x + 4) - 2(4.5x +1.5)
= 28x + 14 - 9x - 3
= 19x + 11
The answer is:
The area of the walkway around the garden is 19x + 11
Elijah is snorkeling above a shipwreck. The ship has an elevation of -105 feet. Elijah is snorkeling at 2/15 of the ship's elevation. What is Elijah's elevation?
Elijah's elevation when Elijah is snorkeling above a shipwreck is -14.
What is elevation?Elevation simply has to do with the height above sea level.
In this case, Elijah is snorkeling above a shipwreck and the ship has an elevation of -105 feet. Elijah is snorkeling at 2/15 of the ship's elevation.
Elijah's elevation will be:
= Fraction of his snorkeling × Ship's elevation
= 2/15 × (-105)
= -14
This shows the elevation of Elijah.
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Fill in the blank with the correct inequality symbol. State which property of inequalities is being utilized.If x-8>10, then x_18.
GIVEN
The inequality:
[tex]x-8>10[/tex]SOLUTION
The inequality is to be solved.
Add 8 to both sides of the inequality. This follows the Addition Property of Inequalities:
[tex]if\text{ }xTherefore:[tex]\begin{gathered} x-8+8>10+8 \\ x>18 \end{gathered}[/tex]ANSWER
[tex]x>18[/tex]A third friend wants to offer Rebecca andSteve some of the animal models she hasalready made. The model she has of thegiant squid is 5 inches tall. Using thesame scale (2 in:5ft), how tall would thegiant squid be in real life?
From the present question, it is said that the scale of a model is equal to:
[tex]e=\frac{2in}{5ft}[/tex]It means that the ratio of the size of the model and the real size of the giant squid must be always this same value. It was given that the size of the model is 5 in. Because we don't know the size of the real-life giant squid, we will use it as x. From this, we can write the following relation:
[tex]\frac{5in}{x}=\frac{2in}{5ft}[/tex]Now, we just need to isolate x in the present relation to find how tall would be a giant squid in real life.
[tex]\begin{gathered} \to2in\times x=5in\times5ft \\ x=\frac{5in\times5ft}{2in}=\frac{25}{2}ft=12.5ft \end{gathered}[/tex]From the solution developed above, we conclude that the real-life giant squid would be 12.5 ft tall.
Can you help me with question number 4 and double check all my other work. (I don’t really understand functions.)
SOLUTION
The relation is a function because each x-value has a unique y-value. That is each domain has only one image. Therefore, the relation is a function
O GRAPHS AND FUNCTIONSGraphically solving a system of linear equations
(-3,4)
Explanationhere we have a system of 2 linear functions, To solve a system of linear equations graphically we graph both equations in the same coordinate system. The solution to the system will be in the point where the two lines intersect.
so
Step 1
graph the function (1)
a)
[tex]y=-\frac{1}{3}x+3[/tex]to graph the line we need 2 poins, so
i) P1, when x=0
[tex]\begin{gathered} y=-\frac{1}{3}x+3 \\ y=-\frac{1}{3}(0)+3=3 \\ so \\ P1=(0,3) \end{gathered}[/tex]ii) P2; when x= 3
[tex]\begin{gathered} y=-\frac{1}{3}(3)+3=-1+3=2 \\ so \\ P2;\text{ \lparen3,2\rparen} \end{gathered}[/tex]iii) now, draw a line that passes trought P1 and P2
Step 2
now, graph line 2 ( function 2)
i) P3, when x= 0
[tex]\begin{gathered} 3x+y=-5 \\ replace\text{ and solve for y} \\ 3(0)+y=-5 \\ y=5 \\ so,P3=(0,-5) \end{gathered}[/tex]ii) P5, when x= 2
[tex]\begin{gathered} 3x+y=-5 \\ replace\text{ and solve for y} \\ 3(2)+y=-5 \\ 6+y=-5 \\ subtract\text{ 6 in both sides} \\ y=-6-5=-11 \\ y=-11 \\ so,\text{ P4=\lparen2,-11\rparen} \end{gathered}[/tex]iii) now, draw a line that passes trought P3 and P4
Step 3
finally, the solution is the orderede pair where the lines intersect each other
therefore, the solution is
(-3,4)
I hope this helps you
graph the inequality 3x+y<4
Subsituting (0,0) in the inequality,
[tex]\begin{gathered} 3\times0+0<4 \\ 0<4 \end{gathered}[/tex]Hence the line 3x+y=4, demarcating the plane contains the origin.
Thus, the above graph gives the required region of inequality.
use the formula Sn to find the sum of the first five terms of the geometric sequence.
First, find the common ratio r:
-4/9 : 4/3 = -1/3
4/3 : -4 = -1/3
-4:12 = -1/3
r= -1/3
[tex]Sn=\frac{a(r^n-1)}{r-1}[/tex]Where:
a= first term = 12
n= number of terms = 5
Replacing:
[tex]Sn=\frac{12(-\frac{1^{}}{3}^5-1)}{-\frac{1}{3}-1}[/tex]Sn= 244/27 = 9 1/27
Frank makes 8 dollars for each hour of work. Write an equation to represent his total pay p after working h hours
The equation will be
P = 8h
here, P = total pay
h= working hours.
3. Solve the system using elimination (not substitution or matrices). negative 2 x plus y minus 2 z equals negative 8A N D7 x plus y plus z equals negative 1A N D5 x plus 2 y minus z equals negative 91. If the system has a single solution, write the solution as an ordered triple, (x, y, z).2. If the system has infinite solutions, write the solutions IN TERMS OF z.The solution should look something like left parenthesis 3 minus 3 z comma space minus 1 plus 7 z comma space z right parenthesis but not like left parenthesis negative 6 plus 3 y comma space y comma space 2 minus 5 y right parenthesis or not like left parenthesis x comma space 3 plus 5 x comma space minus 1 plus 4 x right parenthesis. None of these are the solution, they are just examples of what the answer could look like and not look like.3. Be sure to show all appropriate work. Extraneous work may be counted against you. Your handwritten work should include the steps used to find the solution. You should label your steps with how you combined your equations, like 2E1+E3. Solutions with no work will receive no credit.
Given the system of equation
[tex]\begin{gathered} -2x+y-2z=-8\ldots\ldots\ldots\text{.}(1) \\ 7x+y+z=-1\ldots\ldots\ldots\text{..}(2) \\ 5x+2y-z=-9\ldots\ldots\ldots\text{.}(3) \end{gathered}[/tex]step 1: Make z the subject of the formula in equations (2)
[tex]z=-1-7x-y\ldots\ldots\ldots(2)[/tex]step 2: Substitute the value of z obtained into equation (1)
10
step 3: Substitute the value of z obtained in step 1 into equation (3)
[tex]\begin{gathered} 5x+2y-(-1-7x-y)=-9 \\ 5x+2y+1+7x+y=-9 \\ 12x+3y=-10\ldots\ldots\ldots\text{.}(5) \end{gathered}[/tex]step 4: Solve equations (4) and (5) simultaneously,
[tex]\begin{gathered} 12x+3y=-10\ldots\ldots\ldots\text{.}(4) \\ 12x+3y=-10\ldots\ldots\ldots\text{.}(5) \\ \text{subtract equation (5) from (4)} \\ (12x-12x)+(3y-3y)=-10-(-8) \\ 0\text{ + 0 = }-10+10 \\ 0=0 \end{gathered}[/tex]Therefore, the system has infinite solutions
The solution in terms of z is
[tex]\begin{gathered} x=-\frac{1}{3}z+\frac{7}{9} \\ y=\frac{4}{3}z-\frac{58}{9} \\ z=z \end{gathered}[/tex]What is the position of see on the number line belowWrite your answer as a fraction or mixed number
Answer:
1/3
Explanation:
We can see that from 0 to 1 the number line is divided into 6 parts and the point is right after the second part. Therefore, the fraction that represents point C is 2/6
This fraction is also equal to 1/3 because we can divide the line from 0 to 1 into 3 parts and take the first. The point will be at the exact same position of C.
Therefore, the answer is:
1/3
Which equation is the best approximation of the trend line
approximatesThe equation of a line is given by
[tex]\begin{gathered} y=mx+c \\ m=\frac{change\text{ in y}}{change\text{ in x}}=\frac{y_2-y_1}{x_2-x_1}=\frac{y-y_1}{x-x_1} \end{gathered}[/tex]Taking two points from the line of best fit
Point A(14,200) and Point B (18,400)
[tex]\begin{gathered} x_1=14;y_1=200;x_2=18;y_2=400 \\ \frac{y_2-y_1}{x_2-x_1}=\frac{y-y_1}{x-x_1} \\ \frac{400-200}{18-14}=\frac{y-200}{x-14} \\ \frac{200}{4}=\frac{y-200}{x-14} \\ \frac{50}{1}=\frac{y-200}{x-14} \\ y-200=50(x-14) \\ y-200=50x-700 \\ y=50x-700+200 \\ y=50x-500 \end{gathered}[/tex]Hence, the equation that best approximate the trend line is y=50x-500
