Answers
Given the following:
plane A flies 4375 miles
plane B flies 4550 miles
plane B is flying 35 mph more than plan A.
We are should find the amount of time it takes each plane to atravel their respective distances.
The time equation is:
4375 = 4550
x x + 35
Lets cross multipy
4375(x + 35) = x(4550)
4375x + 153125 = 4550x
153125 = 4550x - 4375x
153125 = 175x
175x = 153125
x = 153125/175
x = 875
x is the speed of plane A
Speed of plane B = 875 + 35 = 910
The amount of time plane A will use is = 4375/875 = 5
The amount of time plane B will use is = 4550/910 = 5
Related Questions
What is the system of inequalities associated with the following graph?A) {y<−1x {+y>1 B) {y>−1 {x+y≥1 C) {y<−1 {x+y≥1 D) {y < -1 {x + y <1
Answers
SOLUTION:
Step 1:
In this question, we are given the following:
What is the system of inequalities associated with the following graph?
Step 2:
The details of the solution are as follows:
CONCLUSION:
The final answer is:
C) {y<−1
{x+y≥1
which inequality best represents that ice cream at -3 degrees C is cooler than ice cream at 1 degrees C
Answers
that ice cream at -3 degrees C is cooler than ice cream at 1 degrees C:
[tex]-3C^{\circ}<1C^{\circ}[/tex]a smmall rectangular tray measures 16 cm by 18 cm determine the length of the diagonal . round you're answer to the nearest tenth.m
Answers
Given the dimension of the rectangle:
16 cm by 18 cm
We have the image of the rectangle below:
To find the length of the diagonal AC, use pythagorean theorem since ACD form a right triangle.
Thus, we have:
[tex]\begin{gathered} AC^2=AD^2+DC^2 \\ \\ AC=\sqrt[]{AD^2+DC^2} \end{gathered}[/tex]Input values into the formula:
[tex]\begin{gathered} AC=\sqrt[]{18^2+16^2} \\ \\ AC=\sqrt[]{324+256} \\ \\ AC=\sqrt[]{580} \\ \\ AC=24.08\approx24.1\text{ cm} \end{gathered}[/tex]Therefore, the length of the diagonal is 24.1 cm
ANSWER:
24.1 cm
Find the area of a regular heptagon with an apothem of 5 cm. Round to the nearest tenth.
Answers
Answer:
[tex]84.3\text{ cm}^2[/tex]Explanation:
Here, we want to calculate the area of the regular heptagon
Mathematically, we use the formula below:
[tex]A\text{ = a}^2n\text{ tan\lparen}\frac{180}{n})[/tex]where:
a is the length of the apothem which is 5 cm
n is the number of sides of the polygon which is 7 (heptagon is a 7-sides polygon)
Substituting the values, we have it that:
[tex]\begin{gathered} A\text{ = 5}^2\times7\text{ }\times\text{ tan }\frac{180}{7} \\ \\ A\text{ = 84.3 cm}^2 \end{gathered}[/tex]18/10 [blank] x/12 x =
Answers
18/10 = x/12
(18/10)* 12 = (x/12)* 12
18*12/ 10 = x (12/12)
216/ 10 = x
x= 108/5
x = 21.6
Completing the square to find the zeros3. a^2+2a-3=0
Answers
Answer:
1 and -3.
Explanation:
Given the quadratic polynomial:
[tex]a^2+2a-3=0[/tex]To use the completing the square method to find the zeros, follow the steps below:
Step 1: Take the constant to the right-hand side.
[tex]a^2+2a=3[/tex]Step 2: Divide the coefficient of a by 2, square it and add it to both sides.
[tex]a^2+2a+(1)^2=3+(1)^2[/tex]Step 3: Write the left-hand side as a perfect square.
[tex](a+1)^2=4[/tex]Step 4: Take the square root of both sides.
[tex]a+1=\pm\sqrt[]{4}[/tex]Step 5: Solve for a.
[tex]\begin{gathered} a=-1\pm\sqrt[]{4} \\ a=-1\pm2 \\ a=-1+2\text{ or }a=-1-2 \\ a=1\text{ or }a=-3 \end{gathered}[/tex]The zeros of the quadratic equation are 1 and -3.
A plane has a speed of 400mi/h. On a windy day, theplane could fly 75 mi with thewind in the same time it tookto fly 65mi against the samewind. What is the rate of thewind?
Answers
The plane has a top speed of 400 miles per hour. That means if it travelled at this same speed on a windy day, it would cover
[tex]undefined[/tex]To show that you can identify implied mul-tiplication, rewrite this algebraic equationusing the times symbol wherever multipli-cation is implied.
Answers
In general, if a and b are two numbers,
[tex]\begin{gathered} ab=a*b \\ and \\ a(b)=a*b \end{gathered}[/tex]Therefore, in our case,
[tex]\begin{gathered} bc=b*c \\ \Rightarrow3(bc)=3*(b*c)=3*b*c \\ and \\ 2d=2*d \end{gathered}[/tex]Thus, the answer is[tex]3*b*c=2*d[/tex]3*b*c=2*dWyatt's eraser box is shaped as a rectangular prism. His erasers are cubes with 1-centimeter sides. The
bottom of the box can hold 14 erasers, and the box is 6 centimeters tall. How many erasers can Wyatt fit
in his box?
Answers
Each eraser has the shape of a cube with a side length of 1 cm.
The eraser box is a rectangular prism (a rectangular box).
We know the bottom of the box can hold 14 erasers. If we lay 14 more erasers on top of it, we would have used 2 cm of the box's height.
We can do it a total of 6 times until we top up the box, thus the total number of erasers that fit the box is 6*14 = 84 erasers
Suppose that y varies jointly with w and x and inversely with z and y = 24 when w = 8, X= 9 and z = 6. Write the equation that models the relationship. Then find y when w = 2, X= 20 and z = 8.
Answers
We would have the following:
[tex]24=\frac{8\cdot9}{6}\cdot2[/tex]From this, we will have the following expression:
[tex]z=2\cdot\frac{w\cdot x}{y}[/tex]Now, we determine the values after replacing the ones given:
[tex]8=2\cdot\frac{2\cdot20}{y}\Rightarrow y=\frac{4\cdot20}{8}\Rightarrow y=10[/tex]The value of y is 10.
33. A coin is tossed and a die with numbers 1-6 is rolled. What is P(head and 3)a. 1/12b. 1/4C.1/3d. 2/334. Two cards are selected from a deck of cards numbered 1 - 10. Once a card isselected, it is replaced. What is P(two even numbers)?a. 1/4b. 2/9c. 1/2d. 135. Which of the following in NOT an example of independent events?a. rolling a die and spinning a spinnerb. tossing a coin two timesc. picking two cards from a deck with replacement of first cardd. selecting two marbles one at a time without replacement36. A club has 25 members, 20 boys and 5 girls. Two members are selected atrandom to serve as president and vice president. What is the probability that bothwill be girls?b. 1/25c. 1/30d. *a. 1/537. One marble is randomly drawn and then replaced from a jar containing twowhite marbles and one black marble. A second marble is drawn. What is theprobability of drawing a white and then a black?b. 2/9c. 3/8a. 1/3d. 1/638. Maria rolls a pair of dice. What is the probability that she obtains a sum that iseither a multiple of 3 OR a multiple of 4?a. 5/9b. 7/12c. 1/36d. 7/3639. Events A and B are independent. The P(A) = 3/5, and P(not B) = 2/3. What isP(A and B)?c. 4/15d. 2/15b. 1/5a. 2/5
Answers
SOLUTION
(33) The question says a coin is tossed and a die with 6 faces is rolled, what is the probability of getting a head and a 3.
Probability is given as
[tex]Probability=\frac{expected\text{ outcome}}{total\text{ outcome }}[/tex]Now, a coin has two faces, a head and a tail. So, total outcome is 2 faces.
We want to get the probability of getting a head. This becomes
[tex]\begin{gathered} Probability\text{ of head = }\frac{expected\text{ outcome}}{total\text{ outcome}}=\frac{1\text{ head}}{2\text{ faces}} \\ =\frac{1}{2} \\ P(head)=\frac{1}{2} \end{gathered}[/tex]So, probability of getting a head is 1/2
A die has 6 faces labelled 1, 2, 3, 4, 5 and 6
Probability of getting a 3 should be
[tex]\begin{gathered} Probability\text{ of getting 3 = }\frac{one\text{ face showing 3}}{6\text{ faces}} \\ that\text{ is }\frac{1}{6} \end{gathered}[/tex]So, probability of getting a 3 is 1/6
Now probability of getting a head and a 3, that is P(head and 3), means we multiply both probabilities, we have
[tex]\begin{gathered} P(head\text{ and 3\rparen = }\frac{1}{2}\times\frac{1}{6} \\ =\frac{1}{12} \end{gathered}[/tex]Hence the answer is
[tex]\frac{1}{12}[/tex]A toddler is jumping on another pogo stick whose length of their spring can be represented by the function g of theta equals 1 minus sine squared theta plus radical 3 period At what times are the springs from the original pogo stick and the toddler's pogo stick lengths equal?
Answers
The springs from the original pogo stick and the toddler's pogo stick length are equal after 1 second and 0.9994 second.
Explanation:The given functions are:
[tex]\begin{gathered} f(\theta)=2\cos \theta+\sqrt[]{3} \\ g(\theta)=1-\sin ^2\theta+\sqrt[]{3} \end{gathered}[/tex]The springs from the original pogo stick and the toddler's pogo stick length are equal when both functions coincide
That is;
[tex]\begin{gathered} f(\theta)=g(\theta) \\ \Rightarrow2\cos \theta+\sqrt[]{3}=1-\sin ^2\theta+\sqrt[]{3} \end{gathered}[/tex]Solving the equation, we have:
[tex]\begin{gathered} 2\cos \theta+\sqrt[]{3}=1-\sin ^2\theta+\sqrt[]{3} \\ Subtract\sqrt[]{3}\text{ from both sides} \\ 2\cos \theta=1-\sin ^2\theta \end{gathered}[/tex]Note the identity below:
[tex]\begin{gathered} \cos ^2\theta+\sin ^2\theta=1 \\ \cos ^2\theta=1-\sin ^2\theta \end{gathered}[/tex]This means
[tex]\begin{gathered} 2\cos \theta=\cos ^2\theta \\ \cos ^2\theta-2\cos \theta=0 \\ \cos \theta(\cos \theta-2)=0 \\ \cos \theta=0 \\ \Rightarrow\theta=\cos ^{-1}(0)=1 \\ \\ OR \\ \cos \theta-2=0 \\ \cos \theta=2 \\ \theta=\cos ^{-1}(2)=0.9994 \end{gathered}[/tex]The springs from the original pogo stick and the toddler's pogo stick length are equal after 1 second and 0.9994 second.
I need help to find X for my warm up paper. I'll include the photo as it doesnt fit:) 2 brainly tutors tried to help but they just told me they couldnt and I really need help:/
Answers
The inscribed angle SKQ intercepts the arc SQ. The next equation relates their measures:
[tex]\begin{gathered} \angle SKQ=\frac{1}{2}\hat{SQ} \\ 75=\frac{1}{2}\hat{SQ} \\ 75\cdot2=\hat{SQ} \\ 150\text{ \degree}=\hat{SQ} \end{gathered}[/tex]Arc SQ can be expressed as the addition of arcs SR and RQ.
[tex]\begin{gathered} \hat{SQ}=\hat{SR}+\hat{RQ} \\ 150=\hat{SR}+60 \\ 150-60=\hat{SR} \\ 90\text{ \degree}=\hat{SR} \end{gathered}[/tex]The inscribed angle KQR intercepts the arc KR. The next equation relates their measures:
[tex]\begin{gathered} \angle KQR=\frac{1}{2}\hat{KR} \\ 78=\frac{1}{2}\hat{KR} \\ 78\cdot2=\hat{KR} \\ 156\text{ \degree}=\hat{KR} \end{gathered}[/tex]Arc KR can be expressed as the addition of arcs KS and SR.
[tex]\begin{gathered} \hat{KR}=\hat{KS}+\hat{SR} \\ 156=\hat{KS}+90 \\ 156-90=\hat{KS} \\ 66\text{ \degree}=\hat{KS} \end{gathered}[/tex]Finally,
[tex]\begin{gathered} \hat{KS}=11x \\ 66=11x \\ \frac{66}{11}=x \\ 6=x \end{gathered}[/tex]What is a discrete set?Is option d and e and possibly c?
Answers
Discrete sets are sets which members are countable and distinct.
That is, they are separable and can only have a certain value.
For example, the number of players in a rugby team is discrete because they are countable.
Hence, options C, Dare applicable.
SI unit conversion Could you please help me with exercise number 12 please and explain the process? I copied exercise 11 from the board and trued to solve #13 but not sure if it’s correct
Answers
Given:-
[tex]9468mg=\ldots kg[/tex]To find the required solution.
So we use the formula,
[tex]1\operatorname{kg}=1000000mg[/tex]So now we substitute,
[tex]\frac{9468}{1000000}=0.009468[/tex]So the required solution is 0.009468 kg.
determine the degree of the polynomial[tex] - 65b + {53x}^{3}y[/tex]
Answers
Determine the degree of the polynomial
656+ 3x^3 y
Degree of the polynomial = 4 = (3 + 1)
3x^3 grade (3)
y grade (1)
________________
The degree of the polynomial is 4
Can decimals be constants?
Answers
Constants refer to a number and a decimal is a number expressed in decimal notation, therefore, decimals can be constants.
What is a decimal?A decimal number is the expression of a fraction in terms of the quotient of the fraction, for example, 1/4 in decimal form is 0.25.
The standard form or system for representing numbers that are integers and numbers that are non integers is the decimal number system which is based on the Hindu-Arabic number system.
When numbers (integers and non integers) are expressed as decimals, the numbers are cited as being in decimal notation.
The location of a number in decimal notation is between the ones and tenth place of the number.
A constant is a value in an expression or equation that remains the same in an equation.
A constant is therefore expressed quantitatively as a number.
Therefore, decimals, which are also numbers can be constants.
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An investment of R2000 is made at 10 %per year simple interest for 3 years. The amount earned is there invested for 5 years at 16 %simple interest calculator the value of the investment at the end of 8 year
Answers
Explanation
We are asked to calculate the value of the investment at the end of 8 years
For the first part, we will find how much R2000 will yield after 3 years
[tex]\begin{gathered} A=P(1+rt) \\ P=2000 \\ r=10\text{ \% =0.1} \\ t=3 \\ \\ A=2000(1+0.1\times3) \\ A=2000(1+0.3) \\ A=2000(1.3) \\ \\ A=R2600 \end{gathered}[/tex]For the second part, we will have to know how much R2600 will yield after 5 years
[tex]\begin{gathered} P=2600 \\ t=5\text{ years} \\ r=16\text{ \%=0.16} \\ \\ A=2600(1+0.16(5)) \\ A=2600(1+0.8) \\ A=R4680 \\ \end{gathered}[/tex]At the end of the 8 years, the value of the investment will be R4680
Write an equation for the conic in the xy-plane for
Answers
Given:
[tex]\frac{(x^{\prime})^2}{15}-\frac{(y^{\prime})^2}{6}=1\text{ at }\theta=30^o[/tex]To find:
We need to find an equation for the conic in the xy-plane.
Explanation:
We can find the conic equation by using the following equation.
[tex]x^{\prime}=x\cos \theta+y\sin \theta\text{ and }y^{\prime}=y\cos \theta-x\sin \theta[/tex][tex]\text{Substitute }\theta=30^o\text{ in the eqatuions.}[/tex][tex]x^{\prime}=x\cos 30^o+y\sin 30^o\text{ and }y^{\prime}=y\cos 30^o-x\sin 30^o\text{.}[/tex][tex]\text{Use }\cos 30^o=\frac{\sqrt[]{3}}{2}\text{ and }\sin 30^o=\frac{1}{2}\text{.}[/tex][tex]x^{\prime}=x(\frac{\sqrt[]{3}}{2})+y(\frac{1}{2})\text{ and }y^{\prime}=y(\frac{\sqrt[]{3}}{2})-x(\frac{1}{2})[/tex][tex]x^{\prime}=\frac{\sqrt[]{3}}{2}x+\frac{1}{2}y\text{ and }y^{\prime}=\frac{\sqrt[]{3}}{2}y-\frac{1}{2}x[/tex][tex]\text{ Substitute }x^{\prime}=\frac{\sqrt[]{3}}{2}x+\frac{1}{2}y\text{ and }y^{\prime}=\frac{\sqrt[]{3}}{2}y-\frac{1}{2}x\text{ in the given equation.}[/tex][tex]\frac{(\frac{\sqrt[]{3}}{2}x+\frac{1}{2}y)^2}{15}-\frac{(\frac{\sqrt[]{3}}{2}y-\frac{1}{2}x)^2}{6}=1[/tex][tex]\frac{1}{15}(\frac{\sqrt[]{3}}{2}x+\frac{1}{2}y)^2-\frac{1}{6}(\frac{\sqrt[]{3}}{2}y-\frac{1}{2}x)^2=1[/tex][tex]\frac{1}{15}\mleft\lbrace(\frac{\sqrt[]{3}x}{2})^2+(2\times\frac{\sqrt[]{3}x}{2}\times\frac{y}{2})+(\frac{y}{2})^2\mright\rbrace-\frac{1}{6}\mleft\lbrace(\frac{\sqrt[]{3}y}{2})^2-2\times\frac{\sqrt[]{3}y}{2}\times\frac{x}{2}+(\frac{x}{2})^2\mright\rbrace=1[/tex][tex]\frac{1}{15}\mleft\lbrace\frac{3x}{4}^2+\frac{\sqrt[]{3}xy}{2}+\frac{y^2}{4}^{}\mright\rbrace-\frac{1}{6}\mleft\lbrace\frac{3y}{4}^2-\frac{\sqrt[]{3}xy}{2}+\frac{x}{4}^2\mright\rbrace=1[/tex][tex]\frac{3x^2}{15\times4}^{}+\frac{\sqrt[]{3}xy}{15\times2}+\frac{y^2}{15\times4}^{}-\frac{3y^2}{6\times4}^{}+\frac{\sqrt[]{3}xy}{6\times2}-\frac{x}{6\times4}^2=1[/tex][tex]\frac{x^2}{20}^{}+\frac{\sqrt[]{3}xy}{30}+\frac{y^2}{60}^{}-\frac{y^2}{8}^{}+\frac{\sqrt[]{3}xy}{12}-\frac{x^2}{24}^{}=1[/tex]Here LCM is 360, making the denominator 360.
[tex]18x^2+12\sqrt[]{3}xy+6y^2-45y^2+30\sqrt[]{3}xy-15x^2=360[/tex][tex]3x^2+42\sqrt[]{3}xy-39y^2-360=0[/tex]Final answer:
The equation for the conic in the xy-plane is
[tex]3x^2+42\sqrt[]{3}xy-39y^2-360=0[/tex]What is the component form of resultant of 4b⃗ −2aa = (7 , -5)b = ( -4 , 4)
Answers
1) Since we have this expression, let's do it in parts.
[tex]\begin{gathered} 4\langle-4,4\rangle-2\langle7,-5\rangle \\ x-component=4(-4)-2(7)=-16-14=-30 \\ y-component=4(4)-2(-5)=16+10=26 \\ \end{gathered}[/tex]Note that since each vector has two components x, and y. The resultant will be the vector:
[tex]\langle-30,26\rangle[/tex]convert the following from degrees to radians (use × 180/pi)(-2pi)/7
Answers
Use the conversion 180/pi
[tex]-\frac{2\pi}{7}\cdot\frac{180}{\pi}=-\frac{360}{7}=-51.43[/tex]in the diagram ,EF and AB are parallel .Line CD is a transversal PartA:Describe the transformation that will take
Answers
The described transformation is a translation and a reflection that is dilation.
By rotating, reflecting, or translating a shape on a coordinate plane, a transformation is made.
The transformation, i.e., f: X X, is a function, f, that maps to itself. Following the transformation, the pre-image X changes into the image X. Any operation, including translation, rotation, reflection, and dilation, may be used to create this transformation. A function can be moved in one direction or another by translation, rotated around a point by rotation, reflected in its mirror image by reflection, and scaled by dilation.
The dilation is the transformation that causes the 2-d shape to stretch or contract vertically or horizontally by a fixed amount. The equation y = a.f. yields the vertical stretch (x). The function stretches in relation to the y-axis if a > 1.
Hence we get the required answer.
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-3x + 5y = -155x - 2y = -101. Find the solution2. Write an equation to replace the second equation so that the system will have infinitely many solutions.
Answers
Problem
-3x + 5y = -15
5x - 2y = -10
Solution
For this case we can solve x from the first equation and we got:
3x = 5y +15
x= (5y+15)/3
Now we can replace this value into the second equation and we got:
5((5y+15)/3) -2y = -10
25/3y +25 -2y= -10
And solving for y we got:
(25/3 -2)y =-10-25
19/3 y = -35
y= -105/19
And then we can solve for x and we got:
x= (5*(-105/19) +15)/3 = -80/19
What is the simplified value of 3/4 5/12 fraction
Answers
Thus, the final value is 5/16.
Find the slope of the line shown on the graph to the right.What is the slope of the line? The slop of the line is ___
Answers
The formula for determining slope is expressed as
slope = (y2 - y1)/(x2 - x1)
where
y1 and y2 are the y coordinates of initial and final points on the line
x1 and x2 are the x coordinates of initial and final points on the line
From the graph,
when x1 = - 4, y1 = 0
when x2 = 2, y2 = 4
slope = (4 - 0)/(2 - - 4) = 4/(2 + 4) = 4/6
Simplifying 4/6 to its lowest term
slope = 2/3
Tina babysits and cuts lawns to earn money. For one week, she babysits for 5 hours. She earns $8.25 per hour babysitting If Tina earns $92 this week, how much does tina earn cutting lawns? 1) $10.152) $16.753) $41.254( $50.75
Answers
Answer:
[tex]\text{ \$50.75}[/tex]Explanation:
Here, we want to calculate how much Tina earns cutting lawns
From the question, she earns $8.25 per hour for 5 hours cutting lawns
What she earned in totality that week would be:
[tex]\text{ 5 }\times\text{ \$8.25 = \$41.25}[/tex]What she earned cutting lawns would be the total earned minus what she earned cutting lawns
Mathematically, we have that as:
[tex]\text{ \$92 - \$41.25 = \$50.75}[/tex]A given circle has an approximate area of 78.5 square units. How long is the circles diameter?
Answers
Remember that
The area of a circle is equal to
[tex]A=\pi\cdot r^2[/tex]we have
A=78.5 unit2
I will assume pi=3.14
substitute in the formula
[tex]\begin{gathered} 78.5=3.14\cdot r^2 \\ r^2=\frac{78.5}{3.14} \\ r=5\text{ units} \end{gathered}[/tex]the diameter is two times the radius
so
D=2(5)=10 units
therefore
The diameter is 10 unitsHow do you write 1.9 x 102 in standard form?
Answers
We are given the following number in scientific notation.
[tex]1.9\times10^2[/tex]We are asked to write this number in standard form.
Method 1:
Simply multiply 1.9 by 10²
[tex]1.9\times10^2=1.9\times(10\times10)=1.9\times100=190[/tex]Method 2:
Simply move the decimal point to the right by 2 places (since the exponent is 2
picture with question
Answers
In order to determine if the given triangles are similar, it is necessary to find the values of the missing angles.
Take into account that the sum of the interior angles of a triangle is equal to 180°, the for the missing angles you have:
180° - 90° - 46° = 44°
180° - 38° - 46° = 96°
AS YOU CAN NOTICE THE THREE ANGLES ARE NOT EQUAL.
Then, the triangles are NOT similar because it is necessary that the three angles are equal.
Circle C and circle J are congruent, what is NM?
Answers
Ok, so
We know that two circles are congruent. This makes that the triangles there, are cogruent.
Let me draw the situation here below:
If both triangles are congruent, that means that their sides and angles are equal.
Now if we notice, we realize that side DG and side NM will be equal.
So, DG = NM
Which is the same that
14t - 26 = 5t + 1
If we solve the equation for t:
14t - 5t = 26 + 1
9t = 27
And t = 3
Now, we want to find NM measure.
And we just have to replace t=3 in the expression 5t+1
This will be 5(3) + 1, which is 16.
Therefore, NM measures 16.