an airplane travels 600 miles against the wind in 5 hours, and makes the return trip with the same wind in 2 hours. find the rate of the wind.
Answer:
The speed of wind is 75 miles / hour
Step-by-step explanation:
Let's assume
speed of airplane is x miles /hour
speed of wind is y miles /hour
An airplane travels 600 miles against the wind in 4 hours
against wind means resultant speed will be less
so, speed =x-y
total distance traveled in 4 hour is
and this has to be equal to 600
Divide both sides by 4
makes the return trip with then same wind in 2 hours
with wind means resultant speed will be more
so, speed =x+y
total distance traveled in 2 hour is
and this has to be equal to 600
Divide both sides by 2
So, we get system of equations
now, we can solve it by adding both equations
now, we can solve for x
now, we can find y by plugging x into any one equation
a lion sprints after a giraffe. the lions speed is 22.4 meters per second (50 mph). how far will the lion get in fifteen seconds
Answer:
1100 feet, or 335.28 meters
Work out the area and the perimeter of each semicircle. Give your answer correct to two decimal places (2 d.p.).
diameter = 24mm
The area of this semi-circle is 38.28 cm² and this can be determined by using the formula of area of the semi-circle.
Given :
The diameter of the semi-circle is 10 cm.
The area of the circle is given by the formula:
A=[tex]\pi[/tex]r²
where r is the radius of the circle.
So, the area of the circle whose radius is 5cm is given by:
A=[tex]\pi[/tex]×(5)²
A=25[tex]\pi[/tex]
The area of the circle is 25[tex]\pi[/tex] then the area of the semicircle whose radius is 5cm is given by:
A[tex]s[/tex]= 25/2([tex]\pi[/tex])
A[tex]s[/tex]=12.5[tex]\pi[/tex]
Now, substitute the value of [tex]\pi[/tex] in the above equation.
A[tex]s[/tex]=12.5×3.142
A[tex]s[/tex]=39.28cm²
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Solve |x+ 4| = -6 im struggling with this problem
Recall that:
[tex]\begin{gathered} |a|\ge0 \\ \text{for all a}\in\R. \end{gathered}[/tex]Therefore the given equation has no solutions.
Answer: Option B.
A. Put the following values in order from least to greatest:
4²,-√4, √4²,-2√4, 6-47, √
The order of values in ascending order will be -4<-2<2<2.64<4<16 as the definition of ascending order says, "When numbers are arranged in ascending order, they are done so from smallest to largest".
What is ascending order?When numbers are arranged in ascending order, they are done so from smallest to largest. Climbing down the stairs of numbers starting with their highest value is another way to think of descending. The slide is descended while moving down it. Ascending order, in which the numbers are arranged from lower value to higher value, is the opposite of descending order. A number can be arranged in ascending order by going from smallest to largest from left to right.
Here,
4²=16
-√4=-2
√4²=4
-2√4=-4
6-4=2
√7=2.64
-4<-2<2<2.64<4<16
According to the definition of ascending order, "When numbers are arranged in ascending order, they are done so from smallest to largest," the order of values in ascending order will be -4<-2<2<2.64<4<16.
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A car rental company's standard charge includes an initial fee plus an additional fee for each mile driven. (READ PICTURE FOR RESTc=
Theequation ^4 +^3 −−1=0a. Has four unequal complex rootsb. Has two equal real roots and two equal complex rootsc. Has two unequal real roots and two unequal complex rootsd. Has one real root of multiplicity 2 and a second real root of multiplicity 2e. Is not solvable
Answer:
Alternative C - Has two unequal real roots and two unequal complex roots
Step-by-step explanation:
The roots of this equation are:
(solved using the computer):
[tex]1,\text{ -1, }\frac{1-i\sqrt[]{3}}{2},\text{ }\frac{1+i\sqrt[]{3}}{2}[/tex]As we can see, we have two unequal real roots and two unequal complex roots.
Alternative C.
What is 66253/19
please help this must be turned in by tonight
Answer:
3487
Step-by-step explanation:
In the equation g(x)--2x^2(x-4)(2x-3) you are tasked to find the roots of the equation, how would you go about solving (2x-3)?
I would solve 2x-3 by first off multiplying, then subtracting. Make sure to start with the equations in the parentheses.
what is the y and x intercept of 5x-7y= -8
SOLUTION
Write out the equation given
[tex]5x-7y=-8[/tex]To find y-intercept, we replace x with 0, hence
[tex]\begin{gathered} \text{for x=0} \\ 5(0)-7y=-8 \\ -7y=-8 \\ \text{Divide both sides by -7} \\ -\frac{7y}{-7}=-\frac{8}{-7} \\ \text{Hence } \\ y=\frac{8}{7} \\ \end{gathered}[/tex]Hence
Y - intercept is ( 0, 8/7 )
Similarly, for x-intercept, we replace y with 0 and find x
[tex]\begin{gathered} \text{for y=0} \\ 5x-7(0)=-8 \\ \text{Hence } \\ 5x=-8 \\ \text{Divide both sides by 5, } \\ \frac{5x}{5}=-\frac{8}{5} \\ \text{Hence } \\ x=-\frac{8}{5} \end{gathered}[/tex]Hence
x- intercept is ( - 8/5 , 0 )
A report card shows that a student earns 21 points on a test with a total of 25 points. What percentage of the total points has the
student earned on the test?
Answer: The student got an 84%
Step-by-step explanation:
This one is comparatively simple because 25 is a factor of 100,
we just have to multiply each side by 4 so we get 81 out of 100
Cheers!
Rsmbro
The table shows the results of the men’s long jump in a recent Olympics. Use the table for exercises 1-3.
1. We need to find the distance jumped by the Gold winner, we know that the total distance jumped by three athletes is 25.04, so we can subtract the distances from the Silver and Bronze winners in order to determine what we want. This is done below:
[tex]\begin{gathered} \text{Gold}=25.04-8.37-8.29 \\ \text{Gold}=8.38 \end{gathered}[/tex]Now we need to represent this number as a fraction in its simplest form.
[tex]\text{Gold}=\frac{838}{100}=\frac{419}{50}[/tex]2. In order to determine which medal he would receive, we need to add the distance he actually jumped by 0.06 and compare to the table. We have:
[tex]d=8.25+0.06=8.31[/tex]He would win a Bronze medal.
3. In order to determine how farther Athlete B jumped more than Athlete D, we need to subtract their distances.
[tex]d=8.37-8.11=0.26[/tex]The athlete B jumped 0.26 meters farther than Athlete D.
Rebecca is playing a video game that involves planting and cutting down trees. She moves up an energy level for each tree she plants, and she moves down a level for each tree she cuts. If Rebecca reaches energy level 10, she will earn bonus points.
Rebecca is currently at energy level 4. The results of her next 3 turns are:
Turn 1: 6 trees cut
Turn 2: 8 trees planted
Turn 3: 1 tree cut
Answer the questions to find out whether Rebecca earned bonus points in the next 3 turns. Use the number line to help you add.
(You can go into the negetives)
The points she will have using the given inequalities are;
1) After the three turns is; 4 + (-6) + 8 + (-1)
2) After turn one she will have 0 points
3) After turn 2 she will have 8 points
4) After turn 3 she will have 7 points; She will not earn bonus points because she could not reach ten points
How to interpret inequality lines graph?We are told that the rule for Rebecca's movement is that
She moves up an energy level for each tree she plants.
She moves down a level for each tree she cuts.
If she reaches energy level 10, she will earn bonus points.
Now, we are told that she is at level 4.
A) Turn 1 = 6 trees cut
Turn 2 = 8 trees planted
Turn 3 = 1 tree cut.
The expression that represents Rebecca's energy level after the three turns is;
4 + (-6) + 8 + (-1)
B) Rebecca's energy level after the first turn is; 0 points because she cut 6 trees
C) Rebecca's energy level after the second turn is; 8 points because she planted 8 trees
D) Rebecca's energy after turn 3 is; 8 + (-1) = 7
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An online furniture store sells chairs for $150 each and tables for $650 each. Every day, the store can ship at most 16 pieces of furniture and must sell no less than $3900 worth of chairs and tables. If x represents the number of tables sold and y represents the number of chairs sold, write and solve a system of inequalities graphically and determine one possible solution.
Using graphical method to solve the system of linear inequalities, the solution are (x, y) 3, 13.
System of Linear InequalitiesA system of linear inequalities in two variables consists of at least two linear inequalities in the same variables. The solution of a linear inequality is the ordered pair that is a solution to all inequalities in the system and the graph of the linear inequality is the graph of all solutions of the system.
To solve this, we can write out the equations as
x + y ≤ 16 ...eq(i)
650x + 150y ≥ 3900 ...eq(ii)
Solving both equations with a graph.
Kindly find the attached graph to the problem.
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If AC=13x-17, find x. Round your answer to the nearest tenth if necessary AB= 2x+4 BC= 19
x=3.7
1) Given that AC is the line segment made up by AB + BC We can set this equation:
AC=AB+BC
13x-17=2x+4+19 Combining like terms
13x-2x -17=2x-2x+23
11x -17=23
11x -17+17 = 23 +17
11x = 40 Dividing both sides by 11
x=3.63 Round to the nearest tenth
x=3.7
Can someone help? :)
Answer:
The equation of the line is -1/3x + 4
Step-by-step explanation:
You would do rise over run or use the slope formula
y2-y1/x2-x1=
2-4/6-0 = -2/6 = -1/3
The y-intercept is when the line hits the y-axis so it would be (0,4) or 4
The sum of three numbers is 11. Two times the smallest is 1 less than the largest, while the sum of the largest and smallest is 7.Use a linear system in three variables to find the three numbers.
ANSWER:
The numbers are 2, 4 and 5
STEP-BY-STEP EXPLANATION:
let x be the smallest, y the one that follows and z the largest
we have the following equations
[tex]\begin{gathered} x+y+z=11 \\ z-1=2x \\ x+z=7 \end{gathered}[/tex]We solve the system of equations as follows
[tex]\begin{gathered} z-1=2x\rightarrow z=2x+1 \\ x+z=7\rightarrow z=7-x \\ \text{ we equate noth equations} \\ 2x+1=7-x \\ 2x+x=7-1 \\ 3x=6 \\ x=\frac{6}{3}=2 \end{gathered}[/tex]now, for z:
[tex]\begin{gathered} z=7-2 \\ z=5 \end{gathered}[/tex]for y:
[tex]\begin{gathered} 2+y+5=11 \\ y=11-5-2 \\ y=4 \end{gathered}[/tex]help meeeeeeeeeeeeeee pleaseeeeeee
Answer: 19.6 feet
Step-by-step explanation:
Using the Pythagorean theorem,
[tex]x^2 +(x+6)^2 =48^2\\\\x^2 +x^2 +12x+36=2304\\\\2x^2 +12x-2268=0\\\\x^2 +6x-1134=0\\\\x=\frac{-6 \pm \sqrt{6^2 -4(1)(-1134)}}{2(1)}\\\\x \approx 30.8 \text{ } (x > 0)\\\\\implies x+(x+6) \approx 67.6\\\\\therefore (x+(x+6))-48 \approx 19.6[/tex]
suppose that g(x) = f(x) -7 which statement best compares the graph of g(x) with the graph of f(x)
It implies that when F(x) shifts 7 units to the left, we get the value equal to G. (x). As a result, the graph of G(x) is the graph of F(x) with 7 units added to the left.
How is the graph of G related to the graph of f?The graph of g is the reflection of the graph of f. If g(x) = f(-x), then the graph of g is obtained from the graph of f by reflecting about the y-axis.
For instance, the result of multiplying f(x) and g(x) is h(x) = fg (x), or h(x)=f(x)g (x). if f is the function denoted by f(x) = x2 and g is the function denoted by g(x) = x + 3.
Therefore,
The Correct answer is : The two functions G(x) and F are provided to us (x).
We must determine which assertion most accurately contrasts the graphs of G(x) and F(x).
Suppose
F(x) = x [/ tex]
G(x) = x-7
When x = 1 is substituted
So, F(x) = 1
G(x) = 1-7 = -6
It implies that we obtain the value equal to the value of G when F(x) shifts 7 units to the left (x).
The graph of G(x) is therefore the graph of F(x) with 7 units added to the left.
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Kareem wants to give $11 to help kids who need school supplies. he also wants to buy a pair of shoes for $39. at least, how much money does he need to earn? brainly
If 9% of a number equals 3, find 36% of that number.
PLEASE HELP NOW!: QS is a perpendicular bisector.Find the value of x.Find the value of y.
Since QS is perpendicular:
[tex]\begin{gathered} 4y=90 \\ \text{solve for y:} \\ y=\frac{90}{4} \\ y=22.5 \end{gathered}[/tex]geometry homework.....help me
Answer:
1. Acute Isosceles Triangle
2. Equiangular Equilateral Triangle
3. Obtuse Scalene Triangle
Step-by-step explanation:
Triangle 1:
It is given that there are two congruent sides. By the definition of an Isosceles Triangle, where at least two or more sides are congruent, it is an Isosceles Triangle.
An acute angle is less than 90 degrees. A right angle is 90 degrees. An obtuse angle is greater than 90 degrees. An equiangular triangle is a triangle whose angles are all of the same measure.
By these definitions, Triangle 1 is an acute Isosceles Triangle.
Triangle 2:
It is given that all three sides are congruent. By the definition of an Equilateral Triangle, where all the sides must be congruent, this is an Equilateral Triangle.
An equilateral triangle is also equiangular. So, Triangle 2 is an equiangular Equilateral Triangle.
Triangle 3:
It is given that none of the sides are congruent. By the definition of a Scalene Triangle, where none of the sides are congruent, this is a Scalene Triangle.
By the angle definitions above, as one of the angles are greater than 90 degrees, this is an obtuse triangle.
So, Triangle 3 is an obtuse Scalene Triangle.
Set up and solve. Round answers to the nearest tenth.A young giraffe casts a shadow of 27 feet when the angle of elevation of the sun is 20°. Draw and label a picture that represents the given information then find the height of the giraffe.
Given,
The length of the shadow is 27 feet.
The angle of elevation is 20 degree.
Required:
The height of the giraffe.
The diagram of the giraffe and shadow is,
The height of the giraffe is:
[tex]\begin{gathered} tan\theta=\frac{side\text{ opposite to }\theta}{side\text{ adjacent to }\theta} \\ tan20^{\circ}=\frac{AB}{BC} \\ BC=tan20^{\circ}\times AB \\ BC=27\times0.36397 \\ BC=9.8\text{ feet} \end{gathered}[/tex]Hence, the height of giraffe is 9.8 feet.
Solve the following exponential 4e^3x-1 = 5
Given
[tex]4e^{3x}-1=5[/tex]
Solving, step-by-step
[tex]\begin{gathered} 4e^{3x}-1=5 \\ e^{3x}=6/3 \\ 3x=\ln 1.5 \\ x=\frac{\ln 1.5}{3} \\ \end{gathered}[/tex]In a right triangle one of the acute angles is 1/4 the size of the other acute angle find the measure of the larger angle
In a right triangle, there are 2 acute angles and 1 right angle.
Let x be the measure of the larger acute angle, using the triangle sum theorem (that states that the sum of the interior angles of a triangle is 180) we have that:
[tex]\begin{gathered} x+\frac{1}{4}x+90=180 \\ \frac{5}{4}x=180-90 \\ \frac{5}{4}x=90 \\ 5x=360 \\ x=\frac{360}{5} \\ x=72 \end{gathered}[/tex]The larger acute angle measures 72°.
Use the drop-down menus to complete each statement to show why 65–√ is between 12 and 18.
it is proven that 6√5 between 12 and 18, Irrational numbers
What are Irrational numbers?
The group of real numbers known as irrational numbers are those that cannot be written as a fraction of the form p/q, where p and q are integers. Additionally, the decimal expansion of an irrational integer is neither terminating nor recurring.
Irrational numbers are real numbers that cannot be expressed as a straightforward fraction. These cannot be stated as ratios, such as p/q, where p and q are integers, q0. It is a contradiction of rational numbers.
It has been given in question 4 < 5 < 9 and we have to show 6√5 is between 12 and 18.
For box number 1.
4 < 5 < 9 ⇒ √4 < √5 < √9
For the box number 2.
√4 < √5 < √9 ⇒ 2 < √5 < 3
For the box number 3.
we multiply the inequality by 6.
6×(2 < √5 < 3)
⇒ 6×2 < 6×√5 < 6×3
So the 6×2 < 6×√5 < 6×3
⇒ 12 < 6√5 < 18
Hence it is proven that 6√5 between 12 and 18.
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Betsie is going to buy 250 envelopes.
Here is some information about the cost of envelopes in two shops.
Value World
Pack of 10 envelopes for £1.99
Buy 2 packs get 1 pack free
Letters2go
Pack of 25 envelopes for £3.19
Betsie wants to buy the envelopes for the best possible price.
Which shop should Betsie buy the 250 envelopes from?
You must show how you get your answer.
The shop for which Betsie should buy the 250 envelopes from, using proportions, is Value World.
What is a proportion?A proportion is a fraction of a total amount, and this fraction is used to build relations, using basic arithmetic operations such as multiplication or division, to obtain the desired measures.
In this problem, the final price is obtained as follows:
Divide the price by the number of packs to find the unit rate.Multiply the unit rate by 250.Hence the final price at Value World is given as follows:
1.99/10 = 0.119.
She will pay for 2/3 of the 250 packs, as she buys 2 and gets one free, hence:
2/3 x 250 x 0.119 = £19.83.
At Letters2go, the final price is obtained as follows:
3.19/25 x 250 = £31.90.
Due to the lower price, she should purchase her envelopes at Value World.
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A yearly coffee club subscription costs $65. Avery received an offer for 30 % off the subscription cost. What is the sale price of the subscription?
Answer:
$45.50
Step-by-step explanation:
We want to find 70% of the original cost.
[tex].70 \times 65 = 45.50[/tex]
What is the percent change from 112 to 96
well, the change is just 112 - 96 = 16.
now if we take 112 as the 100%, what's 16 off of it in percentage?
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 112 & 100\\ 16& x \end{array} \implies \cfrac{112}{16}~~=~~\cfrac{100}{x} \\\\\\ 7=\cfrac{100}{x}\implies 7x=100\implies x=\cfrac{100}{7}\implies x\approx 14.29[/tex]