Let x be the number of miles the family travel in 4 days
620 miles = 2 days
x = 4 days
cross-multiply
2x = 2480
Divide both-side of the equation by 2
x = 1240 miles
Solve x and express answers in simplist radical forM. 2x^2+3x-=9x+2
Hello
To solve this question, i will use quadratic formula; however, there are other methods we can use to solve this question.
Step 1
Collect like terms
[tex]\begin{gathered} 2x^2+3x=9x+2 \\ 2x^2+3x-9x-2=0 \\ 2x^2-6x-2=0 \end{gathered}[/tex]A standard quadratic equation can be represented as
[tex]\begin{gathered} ax^2+bx+c=0 \\ a=2,b=-6,c=-2 \end{gathered}[/tex]The quadratic equation is given as
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]Therefore,
[tex]\begin{gathered} x=\frac{-(-6)\pm\sqrt[]{(-6)^2-4(2)(-2)}}{2\times2} \\ x=\frac{6\pm\sqrt[]{36+16}}{4} \\ x=\frac{6\pm\sqrt[]{52}}{4} \\ x=\frac{6\pm7.2}{4} \\ x=\frac{6+7.2}{4}=3.3 \\ or \\ x=\frac{6-7.2}{4}=-0.3 \end{gathered}[/tex]From the calculations above, the value of x is either 3.3 or -0.3
Estimate the cost of putting up a decorative border in your family room if your room is 28 feet long and 16 feet wide and the border costs $8.95 for a package containing 10 feet.The estimated cost is $___
The cost of putting a border around the family room is $ 89.5 .
Dimensions of the room = 28 feet by 16 feet
Now we have to find the perimeter of the room to calculate the length of the border.
The room is a rectangle.
The perimeter of a rectangle is exactly given by
2 × (length + width)
perimeter = 2 × ( 28 + 16 ) feet
Perimeter = 88 feet
Cost of 10 feet = $ 8.95
Boxes needed = 88 / 10 = 8.8 boxes.
Now boxes cannot be taken as a fraction.
Therefore number of boxes required = 10
Cost of 10 boxes =$8.95 × 10 = $ 89.5
Therefore the cost of putting a border around the family room is $ 89.5 .
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Simplify 6a + 5a - a - 5 + 2a712a-513a-512a
By arranging similar terms, we have
[tex]\begin{gathered} 6a+5a+2a-a-5 \\ \text{which gives} \\ 13a-a-5 \end{gathered}[/tex]since 13a minus a is 12a, the answer is
[tex]12a-5[/tex]which corresponds to option 2 from top to bottom
A baseball is thrown straight upward. Describe the direction and magnitude of the velocity, force of gravity, and the varying air resistance force as the ball rises. Explain whether the net force increases, decreases, or is unaffected by the air resistance force. Repeat for the part of the motion when the ball is at maximum height and the part of the motion when the ball is moving downward.
The characteristics of the vertical throw and Newton's second law allows finding the results for the questions about the motion of the ball with air resistance are:
For the upward movement. The speed of the ball decreases with height of the ball. The forces of gravity and friction go in the same direction.
For the point of maximum height, the velocity is zero and the net force is only the force of gravity.
The ball is in a downward movement. The speed increases as the height decreases. The friction force and gravity have the opposite direction, therefore the net force decreases until reaching zero, from this point the speed remains constant.
Kinematics analyzes the movement of bodies looking for relationships between the position, velocity, and acceleration of bodies.
Newton's second law relates the net force to the mass and the acceleration of the body.
In this case, there is a vertical launch where the ball is launched with an initial velocity and is subjected to an acceleration given by the acceleration of gravity with a vertically downward direction, therefore the speed of the ball must decrease with increasing height.
v² = v₀² - 2g y
Where v and v₀ are the current and initial velocities, respectively, g is the acceleration of gravity, and y is the height of the body.
In the attached, we can see a free-body diagram of the ball, the interaction with the earth is constant and is directed towards the center of the earth, in a vertical direction. The friction force of the air is the opposition of the air to the movement of the ball and is directed opposite the direction of movement of the ball. In the case of the ascending ball, the friction force is directed downwards.
Write Newton's second law for upward motion
-W- fr = m a
-m g - fr = ma
Therefore, we see that the two forces go in the same direction, and therefore the net force increases and the acceleration in the opposite direction of the speed also increases.
At the point of maximum height, the speed of the ball is zero, therefore the friction forces of the air are also zero, at this point the acceleration is equal to the acceleration of gravity.
In the case of the ball lower. Speed increases as the ball descend.
Newton's second law is.
-W + fr = ma
- m g + fr = ma
In this case, we see that the forces go in the opposite direction, therefore the net force on the body decreases.
If the friction force with the air increases with the speed, the point where it is equal to the forces of gravity and the acceleration is zero, from this point the ball goes down with constant speed.
In conclusion with the characteristics of the vertical launch and Newton's second law, we can find the results for the questions about the motion of the ball with air resistance are:
The ball is in a downward movement. The speed increases as the height decreases. The friction force and gravity have the opposite direction, therefore the net force decreases until reaching zero, from this point the speed remains constant.
For the upward movement. The speed of the ball decreases with height of the ball. The forces of gravity and friction go in the same direction.
For the point of maximum height, the velocity is zero and the net force is only the force of gravity.
Graph the polygon with the given vertices and its image after a reflection in the given line.
J(-3, 1), K(0, 3), L(4, -1), M(1, -3); y = -2
A polygon is a plane figure characterized by a finite number of straight-line segments joined to form a closed polygonal chain in geometry.
What is a polygon?
A polygon is a plane figure characterized by a finite number of straight-line segments joined to form a closed polygonal chain in geometry. A polygon is defined as a bounded plane region, a bounding circuit, or both. A polygonal circuit's segments are known as its edges or sides.
Given coordinates are,
J(-3, 1), K(0, 3), L(4, -1), M(1, -3); y = -2
Plot all the points on a coordinate geometry in a sequence we will get the polygon of four sides.
The image of the constructed polygon with all its coordinates is attached with the answer below.
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Q.22 5.3 Write a system of linear equations that has the ordered pair of (-2,8) as it's solution.
A system of linear equations that has the ordered pair of (-2,8) as it's solution is Oy - 2x = 12 and x - 2y.
calculation:-
x = -2
for 2y - 4x = 24 plug in x = -2
2y + 8 = 24
Subtract 8 from both sides
2y + 8 - 8 = 24 - 8
2y = 16
divide both sides by 2
2y/2 = 16/2
y = 8
Therefore, the solution to the system of linear equations is:
(x, y) = (-2, 8).
A non-linear equation is such that it does not form a straight line. It looks like a curve in a graph and has a variable slope value. A linear function has one independent variable and one dependent variable. The independent variable is x and the dependent variable is y. The graph of a linear equation always forms a straight line. The definition of a linear equation is an algebraic equation in which each term has an exponent of 1.
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first test(x)=86,82,47,69,73,47,63,50,59,77,88,87second test (y)=81,71,51,75,69,44,48,48,58,68,83,77find a equation of the least squares regression line. Round the answer to three decimal places, if necessary.
To find the equation of the line, we will use the formula:
y=mx + b
The formula for calculating the slope is given as :
[tex]m=\frac{N\text{ }\Sigma(xy)-\Sigma x\Sigma y}{N\text{ }\Sigma(x^2)-(\Sigma x)^2}[/tex]how much must be deposited at the beginning of every six months in an account that pays 6% compounded semi-annually so that the account will contain 35,000 at the end of five years the semi-annual payments are___?round to 2 decimal places
In order to determine the initial investment, use the following formula for the composed interest:
[tex]I=P(1+\frac{r}{n})^{nt}[/tex]where:
P: initial investment = ?
r: interest rate = 6% = 0.06
n: number of times per time period = 6
t: time period = 5 x 2 = 10
I: final account = 35,000
replace the previous values of the parameters and solve for P, as follow:
[tex]\begin{gathered} 35000=P(1+0.06/6)^{6\cdot10}=P\cdot1.816 \\ P=35000/1.816 \\ P=19273.13 \end{gathered}[/tex]Hence, the initial investment was 19,273.13
Mabel spends 4 hours to edit a 3-minute long video. She edits at a constant rate.
How long does Mabel spend to edit a 15 minute long video?
By the concept of unitary method, she will take 20 hours to complete a video as definition of unitary method says "The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value".
What is unitary method?The unitary method is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. A single or distinct unit is referred to by the word unitary. Therefore, the goal of this method is to establish values in relation to a single unit. The unitary method, for instance, can be used to calculate how many kilometers a car will travel on one litre of gas if it travels 44 km on two litres of fuel. The unitary method refers to the process of determining the value of a single unit from the values of several other units and using that value to determine the value of the necessary number of units.
Here,
As she takes 4 hours to edit a 3 minute video,
by unitary method,
so she take 4/3 hour to edit a 1 minute video.
To edit a 15 minute video,
she will take 15*4/3 hours.
=20 hours
As stated in the definition of the unitary method, "the unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value," it will take her 20 hours to complete a video using this method.
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help with this one to
Answer:
D
Step-by-step explanation:
even
4(-x^3) = 4x^3
-4x^3 = 4x^3 (false)
odd
-4x^3 = 4(-x^3)
-4x^3 = -4x^3
Classify each figure as a line, ray, or line segment. Then, show how to write it. (a) (b) (c) Figure L K H G M Type O line O ray Oline segment O line O ray Oline segment O line Oray Oline segment How to write it 0 X Ś ?
SOLUTION
The image below shows the answer:
For a: The line in written as:
[tex]\overleftrightarrow{KJ}[/tex]For b: The ray is written as:
[tex]\overleftarrow{HG}[/tex]For c: The segment is:
[tex]\overline{LM}[/tex]What is the slope of the line that passes through the points (10, 6) and (6, 6)? Write
your answer in simplest form.
The slope of the line that passes through the points (10,6) and (6,6) is 0.
The Slope of a line can be described as a change in the y coordinate with respect to the x coordinate.
Formula to find the slope of the line that passes through the points [tex](x1,y1)[/tex] and [tex](x2,y2)[/tex] is
[tex]m= (y2-y1)/(x2-x1)[/tex]
where, m=slope
As per the given problem, let us consider
[tex](x1,y1)=(10,6)[/tex]
[tex](x2,y2)=(6,6)[/tex]
Substitute the given values such as [tex]x1=10,x2=6,y1=6,y2=6[/tex] in the formula,
[tex]m=(6-6)/(6-10)\\m=0/(-4)\\m=0[/tex]
Therefore, the slope of the line that passes through the points (10,6) and (6,6) is o.
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i cant seem to be able to solve -6(8g+4)-5+6g
Answer: -42g-29
Step-by-step explanation:
-6(8g+4) -5+6g
-48g-24 -5+6g
-48g+6g=-42g
-24-5=-29
Which of the following statements is true about the congruent triangles below?
Answer:
[tex]\angle A \cong \angle D[/tex]
Step-by-step explanation:
Let's check each statement:
1) [tex]\angle A \cong \angle D[/tex]
This is true, as both angle A and angle D are marked with double angle measure marks, signifying congruence.
2) [tex]\overline{AC} \cong \overline{EF}[/tex]
This is false, as [tex]\overline{AC}[/tex] is marked with two tick marks, while [tex]\overline{EF}[/tex] is marked with three tick marks.
3) [tex]\overline{BC} \cong \overline{ED}[/tex]
This is false, as [tex]\overline{BC}[/tex] is marked with two tick marks, while [tex]\overline{ED}[/tex] is marked with only one tick mark.
4) [tex]\angle C \cong \angle E[/tex]
This is false, as angle C is marked with three angle measure marks, while angle E is marked with only one mark.
Help with number two please highlight the answer in bold
ANSWER
Options: II and IV
EXPLANATION
Mean: Is the sum of data values divided by the total number of data values
Deviation: Is the difference between an individual data item and the set's mean.
Absolute value: Is the distance (a positive quantity) between any two points on a number line.
Variability: This relates to how dispersed (or clustered) the values in a data set are. High variability indicates that the data is dispersed. Low variability indicates that the data is grouped together (close together).
MAD: Is the average distance between each data value and the mean is the Mean Absolute Deviation (MAD) of a set of data. The higher the MAD, the more data variability there is (the data is more spread out).
Hence, II and IV are most likely to have the greatest number of values in common because they both have higher MAD (8) meaning that they have more data variability (their data is more spread out) compared to I and III which have MADs equal 4 and 2 respectively.
The population of a small city in 2010 was 36,000. In 2015, the population was 43,800. If the population growth is exponential and growth occurs at the same rate, what will be the population be in 2020? round your answer to the nearest whole number.
The population of the small city in the year 2020 using the given growth rate is; 51600 people
How to solve exponential growth rates?We are given that;
Population of the small city in the year 2010 = 36000
Population in the year 2015 = 43800
Now, we are told that the growth rate occurs at the same rate per year. Thus;
Population change from 2010 to 2015 = 43800 - 36000 = 7800
Thus, the population increases by 7800/5 = 1560 people each year.
General form of exponential function is; y = bˣ
where b is rate of growth while x is number of years
But here we will use sequence to get;
y(10) = 1560 * 10 = 15600
Thus;
Population in 2020 = 36000 + 15600 = 51600 people
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1) The Ramirez family has a new puppy! When they got it, it weighed 10 pounds. Since then it has
gained 2 pounds per week for x weeks. The puppy now weighs 16 pounds. Model this situation here.
Which equation represents this?
A 10x + 2 = 16
C 10x - 2 = 16
B 2x+10=16
D 2x-10=16
Answer:
the third one (I don’t know if you put it as b on purpose or not that’s why I’m calling it the third one)
Step-by-step explanation:
it’s says the puppy gained 2 pound for x weeks so you know that the variable (x) will be associated with the 2 and it already weighed 10 pounds so your adding from there.
Answer:
B (2x + 10 = 16)
Step-by-step explanation:
initial weight = 10 pounds
2 pounds per week for x weeks, so
2 multiplied by the number of weeks
= 2x
It now weighs 16 pounds in total
so, 10 added to it's weight per week
= 10 + 2x
= 16
so
2x + 10 = 16
At midnight, the temperature was -8'F. At noon, the temperature was 23'F. Which expression represents the increase in temperature?
increase= 31° F
Explanation
Step 1
Graph
let x represent the increase in temperature,then
[tex]-8+x=23\text{ Expression}[/tex]now, to find the increase, solve for x
[tex]\begin{gathered} -8+x=23\text{ Expression} \\ \text{add 8 in both sides} \\ -8+x+8=23+8 \\ x=31 \end{gathered}[/tex]so the increase is 31° F.
I hope this helps you
An ostrich farmer wants to enclose a rectangular area and then divide it into four pens with fencing parallel to one side of the rectangle. there are 540 feet of fencing available to complete the job. what is the largest possible total area of the four pens?
Answer:
135 feet
Step-by-step explanation:
you divide 540÷4 to get the answer
[tex]2x^{2} -3x+5=0[/tex]
The solution of the quadratic equation 2x² - 3x + 5 = 0 by completing the square is x = 3/4 ± 31i/4
What is completing the square?Completing the square method is a way of solving quadratic equations by converting them into perfect square binomials.
How to solve the quadratic equation by completing the square?Given the quadratic equation
2x² - 3x + 5 = 0, to solve by completing the square method, we first simplify by dividing through by 2.
So, 2x² - 3x + 5 = 0,
2x²/2 - 3x/2 + 5/2 = 0/2
x² - 3x/2 + 5/2 = 0
Next, we complete the square by adding half the square of the coefficient of x to both sides. That is [(-3/2)/2]² = (-3/4)²
So, x² - 3x/2 + 5/2 = 0
x² - 3x/2 + 5/2 + (-3/4)²= 0 + (-3/4)²
x² - 3x/2 + (-3/4)² + 5/2 = 0 + (-3/4)²
(x - 3/4)² + 5/2 = 0 + (-3/4)² since [x² - 3x/2 + (-3/4)² = (x - 3/4)²]
(x - 3/4)² = 9/16 - 5/2
(x - 3/4)² = (9 - 40)/16
(x - 3/4)² = -31/16
Taking square root of both sides, we have
√(x - 3/4)² = ±√(-31/16)
x - 3/4 = ±31i/4
x = 3/4 ± 31i/4
So, the solution is x = 3/4 + 31i/4
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how do you divide a number into a number with an exponent?
To divide a number into a number with an exponent
So, factor the number then put it to the power of (how many will appear)
for example :
8 = 2 * 2 * 2
so, there are 3 of the number 2
So,
8 = 2^3
Harris painted 3 times as many pictures as painted. painted 11 pictures. Select the equation that represents this situation. 3 x h = 11 0 ÷ h = 11 h = 11 x 3 h ÷ 11 = 30 its due by today
Answer:
h=11x3
Step-by-step explanation:
just answered it for someone else 30 minutes ago
tsThe table below represents the concessions sold at the last three basketball games. Thegames were held on different days and times.Friday nightSaturday morningTuesday nightTotalCandy1489478320Hot Dogs10227150279Nachos Total1084297247358163325846What is the approximately probability of a person buying a hot dog and going to a Tuesdaynight game?
Given:
The total = 846.
The number of hot dogs sold at Tuesday night = 150.
Required:
We need to find the approximate probability of a person buying a hot dog and going to a Tuesday night game.
Explanation:
The total possible outcomes = 846.
[tex]n(S)=846[/tex]Let A be the given event.
The favourable outcomes = The number of hot dogs sold at Tuesday night = 150.
[tex]n(A)=150[/tex]The approximate probability of a person buying a hot dog and going to a Tuesday night game.
[tex]P=\frac{n(A)}{n(S)}\times100[/tex][tex]P=\frac{150}{846}\times100[/tex][tex]P=17.7[/tex][tex]P=18\text{ \%}[/tex]Final answer:
[tex]P=18\text{ \%}[/tex]Evaluate the following expression. -7x7+9x -1/-1
The given expression:
[tex]-7\times7+9\times\frac{-1}{-1}[/tex]Apply BODMAS Rule : Brackets, Of, Division, Multiplication, Addition, Subtraction
According to BODMAS rule, we first simplify division:
[tex]-7\times7+9\times\frac{-1}{-1}=-7\times7+9\times1[/tex]Simplify multiplication:
[tex]-7\times7+9\times1=-49+9[/tex]Simplify addition:
[tex]-7\times7+9\times\frac{-1}{-1}=-40[/tex]Answer: -40
The sum of two numbers is 130 and their difference is 34. Let x be the first number and y be the second number. Set up a system of equations and use the elimination method to find the numbers
The numbers are 82 and 48
What is an equation?An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.
Let x represent the first number and y represent the second number.
Equation 1, sum of the numbers:
x + y = 130
Equation 2, difference of the numbers:
x - y = 34
Using the elimination method system of equations to solve:
x + y = 130
x - y = 34
-------------------
Add the two equations to eliminate the y term leaving:
2x = 164
Divide both sides by 2:
x = 82
Find y from first equation: x + y = 130
substituting 82 for x in the equation
82 + y = 130
Subtract 82 from both sides:
y = 48
The two numbers in the system of equation are 82 and 48.
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In a right triangle, the length of the hypotenuseis 14 cm and the length of one leg is 8 cm.What is the measure of the other leg?
Since it is a right triangle, we can use the Pythagorean Theorem. This one states that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse. In algebraic notation:
[tex]\begin{gathered} a^2+b^2=c^2 \\ \text{ Where a and b are the legs and c is the hypotenuse of the right triangle.} \end{gathered}[/tex]So, in this case, we have:
[tex]\begin{gathered} a=8\operatorname{cm} \\ b=? \\ c=14\operatorname{cm} \end{gathered}[/tex][tex]\begin{gathered} a^2+b^2=c^2 \\ (8cm)^2+b^2=(14cm)^2 \\ (8)^2cm^2+b^2=(14)^2cm^2 \\ 64cm^2+b^2=196cm^2 \\ \text{ Subtract }64cm^2\text{ from both sides of the equation} \\ 64cm^2+b^2-64cm^2=196cm^2-64cm^2 \\ b^2=132cm^2 \\ \text{ Apply square root to both sides of the equation} \\ \sqrt{b^2}=\sqrt{132cm^2} \\ \boldsymbol{b}\approx\boldsymbol{11.49\operatorname{cm}} \end{gathered}[/tex]Therefore, the measure of the other leg rounded to the nearest hundredth is 11.49 centimeters.
a naturalist relocated 12 wild bears in 6 months. the naturalist relocated the same number of wilde bears each month how many wild bears did the naturalist relocate per month HELP SUPER URGENT
The number of wild bears the naturalist can relocate per month is 2 wild bears.
Number of wild bears relocated by the naturalist = 12 wild bears
Time taken by the naturalist to relocate these wild bears = 6 months
Thus the number of bears the naturalist can relocate in 1 month can be found out by using unitary method
This implies that the number of bears relocated by the naturalist in 1 month or per month = 12 / 6 = 2 wild bears
Thus the number of wild bears the naturalist can relocate per month is 2 wild bears .
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I need help with this practice I’m having trouble solving itNeed some help step by step If you can. Use Desmos to graph this
Given the function:
[tex]y=-4\cos \mleft(\frac{2}{3}x+\frac{\pi}{3}\mright)-3[/tex]The graph is attached below:
• The period of the function, T = π-(-2π)=3π.
Thus, the function has been graphed to show at least one full period, the x and y-axes are also clearly labeled above.
English 6: what is characteristics?
Characteristics: special quality or trait that distinguish a person, thing, or group from others.
Find the Area of the figure below, composed of a rectangle with two semicircles
removed. Round to the nearest tenths place.
16
D). (
Submit Answer
6
attempt 1 out of 2
PLEASE HELP 20 POINTS!!!!!!!
well, we know it's a rectangle with two removed semicircle's, hmmm hold on!! two semicircles make together a whole circle, well, let's remake that circle and put it inside the rectangle, then, let's subtract that area from that of the rectangle's, Check the picture below.
[tex]\stackrel{\textit{\LARGE Areas}}{\stackrel{rectangle}{(16)(4)}~~ - ~~\stackrel{circle}{\pi (2)^2} }\implies 64~~ - ~~4\pi ~~ \approx ~~ \text{\LARGE 51.4}[/tex]