Answer:
2
Step-by-step explanation:
Determine whether the function is linear or quadratic. Identify the quadratic, linear, and constant terms.
y = (x - 1)(4x + 2) - 4x2
Answer:
Quadratic. But what is 4x2?
Step-by-step explanation:
During the trip, the Morales family drove on several different highways. Gabriela and Luis noticed that sometimes the mile markers were increasing, and other times the mile markers were decreasing.
On one highway, Gabriela noticed that they passed mile marker 123 at 1:00. She then saw that they reached mile marker 277at 3:00. Since Mr. Morales was driving at a constant speed, their mile-marker location over time can be represented by a line where the time in hours is the independent variable and the mile marker is the dependent variable. The points (1,123) and (3,277) are two points on this line.
What is the value of the slope of this line?
Enter your answer as the correct value, like this: 42
If your answer is a fraction, use the / symbol. For example, if your answer is 314, enter your answer like this: 3/14
Answer:
The slope of the line is 77
Explanation:
We know the speed is constant and that the mile-marker location over time can be represented by a line. This means that the equation is linear.
The slope can, therefore, be calculated as follows:
[tex]slope = \frac{y_2-y_1}{x_2-x_1}[/tex]
where (x₁ , y₁) and (x₂ , y₂) are two points on the line
We are given that the two points (1, 123) and (3, 277) are two points in the line
Substitute with them in the above equation to get the slope as follows:
[tex]slope = \frac{277-123}{3-2}=77[/tex]
Hope this helps :)
The slope of a line represents the rate of change between two variables. The value of the slope in this scenario is 77/2.
The slope of a line represents the rate of change between two variables. In this case, the slope can be calculated using the formula:
slope = (change in y) / (change in x).
Given the points (1,123) and (3,277), the slope can be calculated as follows:
slope = (277 - 123) / (3 - 1).
Therefore, the value of the slope of the line representing the Morales family's mile-marker locations over time is 77/2.
Solve the following equation for x
Answer:
C
Step-by-step explanation:
Using the laws of logarithms
• log x + log y ⇔ log(xy)
• log x = log y ⇒ x = y
Given
logx + log(x - 3) = log 3x
log x(x - 3) = log 3x, hence
x(x - 3) = 3x
x² - 3x = 3x ( subtract 3x from both sides )
x² - 6x = 0 ← factor out x from each term
x(x - 6) = 0
Equate each factor to zero and solve for x
x = 0
x - 6 = 0 ⇒ x = 6
Solutions are x = 0, x = 6 → C
Answer: OPTION A
Step-by-step explanation:
You need to remember the logarithms properties:
[tex]log(a)+log(b)=log(ab)\\\\log(a)-log(b)=log(\frac{a}{b})\\\\log(a)^b=b*log(a)[/tex]
Rewrite the equation:
[tex]log(x(x-3))=log(3)+log(x)[/tex]
Like this logarithm has base 10, you can make this procedure:
[tex]log(x(x-3))-log(x)=log(3)[/tex]
[tex]log\frac{(x(x-3))}{(x)}=log(3)[/tex]
[tex]log(x-3)=log(3)[/tex]
[tex]10^{log((x-3))}=10^{log(3)}[/tex]
Then:
[tex](x-3)=3[/tex]
Now you need to solve for the variable "x":
[tex]x=3+3\\x=6[/tex]
addison walked 6 miles in 4 hours what was her walking rate in hours per mile
Answer:
2/3 hour per mile.
Step-by-step explanation:
Hours per mile
= hours taken / miles walked
= 4/6 = 2/3 hour per mile.
Answer:
she walked 1.5 miles for every hour
Step-by-step explanation:
Divide the miles by the hours: 6/4 =1.5
To make sure this is correct multiply 1.5 times 4(the hours) and you will get 6(the miles she walked
Hope this helped:3
What is the volume of this cylinder? (Round to the nearest inch ) 7( radius)
14( height)
Please help me
Answer:
The formula for the volume of a cylinder is:
V= pi * radius^2 * height
When the values are plugged in, you would have:
V= pi * 7^2 * 14
Then simplified....
V= pi * 49 * 14
V= pi * 686
V= 2155.13256036
and when rounded to the nearest inch...
the volume would be approximately 2155 inches.
what is the parent function of
f(x)=2/5(-x-5)^5 +2
Answer:
Parent function: [tex]x^{5}[/tex]
Step-by-step explanation:
Parent function is the simplest form of the type of function given
for equation: [tex]\frac{2}{5} (-x -5)^{5} +2[/tex]
the simplest form is: [tex]x^{5}[/tex]
the set of all points in a plane that are equidistant from two points is an
A midpoint.
It is a set of points (single point) that is equidistant from point A and point B.
In other words the distance between point A and midpoint M is equal to the distance between point M and point B.
Answer:
The set of all points in a plane that are equidistant from two points is a Perpendicular Bisector.
Step-by-step explanation:
Given: Two points on the plane.
We need to find what has set of all such point which is equidistant from two given fixed point.
Point which is equidistant from two fixed point is known as mid point of the line segment formed by joining the fixed points.
So, all the point which is equidistant from fixed points form a perpendicular bisector.
Therefore, The set of all points in a plane that are equidistant from two points is a Perpendicular Bisector.
What is the value of x?
x=15
x=30
x=37.5
x=52.5
Answer:
x = 15Step-by-step explanation:
[tex]\text{If}\ \angle1\ \text{and}\ \angle2\ \text{are complementary, then}\ \angle1+\angle2=90^o.\\\\\text{We have:}\\\\\angle1=x^o\\\angle2=(3x+30)^o\\\\\text{Substitute:}\\\\x+(3x+30)=90\\\\(x+3x)+30=90\qquad\text{subtract 30 from both sides}\\\\4x=60\qquad\text{divide both sides by 4}\\\\x=15[/tex]
The value of x is 52.5.
Explanation:The value of x can be determined by examining the given equations:
x = 15x = 30x = 37.5x = 52.5Since x is a variable, it can take on different values. In this case, the value of x is 52.5 because that is the only value that satisfies the given equations.Learn more about Value of x here:https://brainly.com/question/26914436
#SPJ11
A ball is dropped from the top of a building that is 1,000 feet high. Its height, in feet, as a function of the time, x, in seconds, after the ball was dropped, is given by the following equation, ƒ(x) = 1,000 - 16x 2. Which set of numbers is appropriate as the domain for this function?
Real numbers from 0 to sqrt(1000/16) = 0 to 2.5sqrt(10).
Before 0, it hadn't been dropped. After 2.5sqrt(10), it has hit the ground and stopped falling.Positive Real Numbers. This includes fractions of seconds, the other two don't.
The appropriate domain for the function describing the height of a ball dropped from a 1,000 feet high building as a function of time is 0 <= x <= 25 seconds, indicating the ball's descent time until it hits the ground.
The student has asked about the appropriate domain for a function describing a ball dropped from a height of 1,000 feet, given by the equation f(x) = 1,000 - 16x². To find the domain, we need to understand when the ball hits the ground, marking the end of its free fall and the function's practical use.
The height (f(x)) becomes 0 when the ball reaches the ground. Setting the equation to zero gives us 0 = 1,000 - 16x². Solving for x, we find x = 25 seconds. This means the ball will hit the ground after 25 seconds, indicating the end of its descent and the maximum value of x in the domain. Therefore, the appropriate domain for this function, representing the time from when the ball was dropped until it hits the ground, is 0 ≤ x ≤ 25 seconds.
please answer me x and y
Answer: x=5√3(you've got it correct!)
y=15
In∆ADC,
Cos 60°=DC/10
DC=5
y=20-5
y=15
Answer:
x = 5√3y = 15Step-by-step explanation:
Look at the picture.
ΔABC, ΔDBA and ΔDAC are the triangles 30° - 60° - 90°. The sides are in ratio 1 : √3 : 2.
Therefore
in ΔDAC:DC : AD : AC = 1 : √3 : 2
If AC = 10, then DC = 10 : 2 = 5 and AD = x = 5√3
in ΔDBA:AD : BD : AB = 1 : √3 : 2
If AD = 5√3, then AB = 2 · 5√3 = 10√3 and BD = y = 5√3 · √3 = 5 · 3 = 15
Find the difference. Express your answer in simplest form. 7r/s - 4r/s
[tex]7 \frac{r}{s} \: - 4 \frac{r}{s} \\ taking \: common \: factor \: ( \frac{r}{s} ) \\ = \frac{r}{s} (7 - 4) \\ =3 \frac{r}{s} [/tex]
Hope it helps...
Regards;
Leukonov/Olegion.
Need help with these questions please help!!
Answer:
C) 8+x > 10
Step-by-step explanation:
I think C is the correct answer because it's an open circle, it can't equal to 2 and it must be higher than 2.
Answer:-
Q no.8 :
9, 13, 17 can merely be the correct option.
Explanation:-
• The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third.
For instance:-
1) Calculation: 9 + 13 = 22 which is greater than the third side (the hypotenuse) that was 17. And hence is correct.
2) Calculation: 10 + 10 = 20 which is equal to the third/hypotenuse side that was also 20. Therefore it doesn’t fit the theorem and is unable to form a triangle.
3)Calculation: 6+8 = 14 which is less than the greatest/hypotenuse/third side or the side of measure 15. Thence, it isn’t the correct also. No accurate triangle can be formed from all these(6, 8, 15) measurements.
4) Calculation: 2+3 = 6 which is equal to the third /hypotenuse side of measure 6 also. And therefrom no triangle can be constructed from the given sides(2, 3, 6).
• The third important property of triangles is the triangle inequality rule, which states:
“The length of a side of a triangle is less than the sum of the lengths of the other two sides and greater than the difference of the lengths of the other two sides”.
(Note: I honestly prefer you to understand from the first point which is far much clearer than the second one).
In a standard deck of cards there are four suits: spades, clubs, hearts, and diamonds. Each suit has one each of 13 cards: ace, king, queen, jack, 2, 3, 4, 5, 6, 7, 8, 9, and 10.
If event A is choosing a king, event B is choosing a heart, and event C is choosing a jack, which Venn diagram could represent this description?
Answer:
The answer would be graph A.
Step-by-step explanation:
Since the cards all belong to four suites, the king can be a heart as well as the jack, but they cannot be the same card. So the choice is graph A.
A Venn diagram displaying events A, B, and C, with overlaps representing the king of hearts (A intersect B) and the jack of hearts (B intersect C), correctly describes the description given.
The Venn diagram that represents the description given should consist of three overlapping circles, one for each event: choosing a king (event A), choosing a heart (event B), and choosing a jack (event C).
Since there is one king and one jack in the hearts suit, the events are not mutually exclusive and the intersections between the circles will represent these possibilities.
There will be an overlap between events A and B, which represents the king of hearts, and an overlap between events B and C, which represents the jack of hearts. However, there will not be an overlap between events A and C since a card cannot be a king and a jack simultaneously.
Which of the following points lies on the graph of f(x) = -x 2?
(-4, 2)
(-2, -4)
(-2, 4)
(4, -2)
Answer:
(-2, -4)
Step-by-step explanation:
we have
[tex]f(x)=-x^{2}[/tex]
we know that
If a ordered pair lies on the graph, then the ordered pair must satisfy the equation of f(x)
Verify each ordered pair
case A) (-4, 2)
Substitute the value ox x and the value of y in the equation and then compare the results
[tex]2=-(-4)^{2}[/tex]
[tex]2=-16[/tex] ------> is not true
therefore
The point not lies on the graph
case B) (-2, -4)
Substitute the value ox x and the value of y in the equation and then compare the results
[tex]-4=-(-2)^{2}[/tex]
[tex]-4=-4[/tex] ------> is true
therefore
The point lies on the graph
case C) (-2, 4)
Substitute the value ox x and the value of y in the equation and then compare the results
[tex]4=-(-2)^{2}[/tex]
[tex]4=-4[/tex] ------> is not true
therefore
The point not lies on the graph
case D) (4, -2)
Substitute the value ox x and the value of y in the equation and then compare the results
[tex]-2=-(4)^{2}[/tex]
[tex]-2=-16[/tex] ------> is not true
therefore
The point not lies on the graph
what is k equal to if 7.6/2 =9.5/k
Answer:
k=2.5
Step-by-step explanation:
7.6/2 = 3.8
9.5/3.8 = 2.5
Answer:
Step-by-step explanation:
7.6/2 =9.5/k
7.6k=2×9.5
k = (2×9.5)/7.6
k = 19/7.6
k= 2.5
vrify : 7.6/2 = 3.8 and 9.5/2.5 = 3.8 .....true
Gold has a density of 19.32 grams per cubic centimeters and is worth $40.26 per gram. The figure shows the dimensions of a particular bar of gold. What is this bar of gold worth?
Do 19.32 x 40.26 which should equal $777.82
The bar graph shown here provides the numbers of scoops of different ice cream flavors that were sold during school lunch today.
How many more scoops of strawberry were sold than vanilla?
A) 2
B) 3
C) 4
D) 5
The number of more scoops of strawberry were sold than vanilla is 4. Therefore, option C is the correct answer.
What is bar graph?A bar graph is a graph that shows complete data with rectangular bars and the heights of bars are proportional to the values that they represent. The bars in the graph can be shown vertically or horizontally. Bar graphs are also known as bar charts and it is a pictorial representation of grouped data.
From the given graph, number of scoops of strawberry sold is 10 and the number of scoops of Vanilla sold is 6.
Difference = 10-6
= 4
Therefore, option C is the correct answer.
Learn more about the bar graph here:
https://brainly.com/question/8644324.
#SPJ2
Use completing the square to solve for x in the equation x^2-10x+25=35.
It actually has 2 answers
x =(10+√140)/2=5+√ 35 = 10.916
or:
x =(10-√140)/2=5-√ 35 = -0.916
ANSWER
[tex]x =5 \pm \sqrt{35} [/tex]
EXPLANATION
The given quadratic equation is:
[tex] {x}^{2} - 10x + 25 = 35[/tex]
Group the constants on the RHS,
[tex] {x}^{2} - 10x= 35 - 25[/tex]
[tex] {x}^{2} - 10x= 10[/tex]
Add the square of half the coefficient of x to both sides of the equation,
[tex]{x}^{2} - 10x + ( - {5)}^{2} = 10 + ( - {5)}^{2} [/tex]
[tex]{x}^{2} - 10x + 25= 10 + 25[/tex]
We factor the perfect square to get:
[tex]{(x - 5)}^{2} =35[/tex]
[tex]x - 5 = \pm \sqrt{35} [/tex]
[tex]x =5 \pm \sqrt{35} [/tex]
An annular solar eclipse occurs when the moon is at its farthest point from the earth during a total eclipse. True False
-Hello There-
The Answer To This Question Would Be "TRUE"
Have A Great Day!
The question is a picture.
Answer:
904.32 cm³Step-by-step explanation:
The formula of a volume of a cylinder:
[tex]V=\pi r^2H[/tex]
r - radius
H - height
We have r = 6cm and H = 8cm. Substitute:
[tex]V=\pi(6^2)(8)=\pi(36)(8)=288\pi\ cm^3[/tex]
[tex]\pi\approx3.14\to V\approx(288)(3.14)=904.32\ cm^3[/tex]
Answer:
904.32 cm³
Step-by-step explanation:
The volume (V) of a cylinder is calculated using the formula
V = πr²h ( r is the radius of the base and h the height )
here r = 6 and h = 8, so
V = 3.14 × 6² × 8
= 3.14 × 36 × 8 ≈ 904.32 cm³
What is the exponential form of 3*3*3*3*x*x*x*z*z?
3*3*3*3 = 3^4 = 81
x*x*x = x^3
z*z = z^2
3*3*3*3*x*x*x*z*z =
3^4x^3z^2 =
81x^3z^2
Answer:
9xz√x
Step-by-step explanation:
you take two 3's you pair them up you do the two time witch gives you three times three or nine you then pair up the x's giving you 9x and that leaves one x to go on the inside of the sq root symbol then you pair up the z's and because there are only two z's put them together on the outside equaling 9xz√x
What is the constant term of −3x4−7x+2
-
3
x
4
-
7
x
+
2
?
Answer:
The constant term is 2
Step-by-step explanation:
The given polynomial is [tex]-3x^4-7x+2[/tex].
To find the constant term, we must make sure the polynomial is in standard form.
The constant term is the term that is independent of x.
Considering [tex]-3x^4-7x+2[/tex], the term that is independent of x is the last term which is 2.
Therefore the constant term is [tex]2[/tex].
What is the missing measure on the small rectangle?
Answer:
4 inches
Step-by-step explanation:
If you divide 18 by 6, the answer is three, so it is scaled down 3x.
So, you have to divide 12 by 3, and the answer is 4.
Answer: 4 Inches
Step-by-step explanation: The rectangle on the left shows that the length is 18 inches and the height is 12 inches. Now, to find the height on the right, First we must realize what changed has been made from the left to the right. We know that our length has decreased to 6 inches from 18. 18 can be divided by 3 and that will give us the quotient of 6. Now, we must divide our height on our original rectangle by 3 as well. Once we divide, our new height of our rectangle also known as X will be 4 Inches Long.
Have A Great Day!
Need Help Please!!!!!!!!!!:>
divide by 2 for each of the numbers
32/2=16
16/2=8
8/2= 4
Answer is 4
ANSWER
The next term in the given geometric sequence is 4.
EXPLANATION
We want to find the next term in the geometric sequence
32,16,8,
We can observe that there is a common ratio of
[tex] \frac{16}{32} = \frac{1}{2} [/tex]
This implies that, we obtain the subsequent terms by multiplying the previous terms by ½.
To obtain the next term after 8, we multiply 8 by half to get.
[tex] 8 \times \frac{1}{2} = 4[/tex]
Therefore the next term is 4.
In March, volunteers for a charity walkathon in Toronto raised $89,351. Volunteers in Montreal raised $102,459. Volunteers in Edmonton raised $78,505.
a. Round each amount to the nearest thousand dollars.
b. Add the rounded amounts to estimate the total amount of money raised.
c. Use the estimate to choose the exact total from among the following.
(1) $250,615 (2) $350,615 (3) $270,315 (4) $170,015
In your question, we are trying to find the total amount of money raised when the money is rounded to the nearest thousands.
Answer: (3) 270,315In order to solve the problem, we would need to round the money raised to the thousands place.
The thousands place would be the number before the comma. (_),000.
Lets round for Part A:
89,351. The thousands place would be 9 in this case, when you look at the number to the right of it (3), it's not big enough to make 9 bigger, so we would keep the thousands place the same. It would end up as 89,000.
102,459. The thousands place would be 2, the number to the right of it is not big enough to be rounded up, so we would keep it the same. It would end up as 102,000.
78,505. The thousands place would be 8. The number to the right of it is a big enough number to let the number 8 be rounded, therefore we would round the 8 up to 9. It would end up as 79,000.
Part B
Our current values would be 89,000, 102,000, and 79,000.
Now, for part B, we would add the rounded values to get an estimate of the money saved:
[tex]89,000+102,000+79,000 =270,000[/tex]
You should get 270,000. Remember, that's just an estimate number.
Part C:
The answer choice that's close to that number is answer choice (3), $270,315.
Your FINAL answer should be (3) $270,315.
-y-2=3y+5 what is the answer
Answer:
y= -7/4
Step-by-step explanation:
-2-y=3y+5 (subtract 5 from both sides)
-7-y=3y (add 1y to both sides)
-7=4y (divide by 4)
y= -7/4
Answer:
y = -7/4
Step-by-step explanation:
Step 1: Isolate x by combining like terms
4y = -7
Step 2: Simplify
y = -7/4
Hank's pickup can travel 68 miles on 4 gallons of gas. How many gallons will Hank's pickup need to travel 51 miles?
Answer:
3
Step-by-step explanation:
68/4 to get how many miles per gallon
17
51/17 to see how many gallons of gas
3 gallons of gas
Based on the information given, Hank's pickup has a fuel efficiency of 17 miles per gallon. Therefore, it will require approximately 3 gallons of gas to travel 51 miles.
Explanation:To determine how many gallons of gas Hank's pickup will need to travel 51 miles, we first establish the rate of gas consumption for the vehicle. As per the given data, Hank's pickup can travel 68 miles on 4 gallons. This gives us a rate of 68 miles/4 gallons = 17 miles per gallon.
Now, to find out how many gallons are required to travel 51 miles, we divide 51 miles by the rate of 17 miles per gallon. So, the calculation is as follows:
51 miles ÷ 17 miles/gallon = 3 gallons.
Therefore, Hank's pickup will require approximately 3 gallons to travel 51 miles.
Learn more about Fuel Efficiency here:https://brainly.com/question/13347135
#SPJ3
Nine less than the quotient of two and a number xxx.
the expression to represent "Nine less than the quotient of two and a number ( x )" is:[tex]\[ \frac{2}{x} - 9 \][/tex]
To represent "Nine less than the quotient of two and a number ( x )", we first need to find the quotient of two and ( x ), and then subtract nine from it.
Let's break it down:
1. Quotient of two and a number ( x ):
This is represented as [tex]\( \frac{2}{x} \).[/tex]
2. Nine less than the quotient:
Subtracting nine from the quotient gives [tex]\( \frac{2}{x} - 9 \).[/tex]
So, the expression to represent "Nine less than the quotient of two and a number ( x )" is:
[tex]\[ \frac{2}{x} - 9 \][/tex]
complete question given below:
Write an expression to represent: Nine less than the quotient of two and a number xxx.
An engineer is designing a roller coaster. The tallest peak is 310 feet high.
The roller coaster travels 155 horizontal feet as it descends the hill.
What is the slope of the hill?
The answer is:
The slope of the hill is equal to 2.
Why?To solve the problem, we need to remember that the slope of a line, is the rate of increase or decrease of the line.
From the statement we know that the tallest peak of the roller coaster is 310 feet (y), while the roller coaster travels 155 horizontal feet (x), so, calculating we have:
[tex]Slope=\frac{height}{base}=\frac{y}{x}[/tex]
Then, substituting the given information and calculating, we have:
[tex]Slope=\frac{310ft}{155ft}=2[/tex]
We have that the slope of the hill is equal to 2.
Have a nice day!
Answer:
The slope of the hill is equal to 2
Step-by-step explanation:
Savvas realize benchmark test
PLEASE HELP! 8 points!! Find the first 5 terms.
Answer:
2, 6, 12, 20, 30
Step-by-step explanation:
To find the first 5 terms, substitute n = 1, 2, 3, 4, 5 into the rule
a₁ = 1² + 1 = 1 + 1 = 2
a₂ = 2² + 2 = 4 + 2 = 6
a₃ = 3² + 3 = 9 + 3 = 12
a₄ = 4² + 4 = 16 + 4 = 20
a₅ = 5² + 5 = 25 + 5 = 30