Answer:
8km /hr
1/ 8 of a litre.
Explanation:
We are told that Amelia drives 48 kilometres in 6 hours, this means the number of kilometres she drives per litre is
[tex]48\operatorname{km}\div6\text{litres}[/tex][tex]\frac{8\operatorname{km}}{\text{litre}}[/tex]Hence, Amelia drives 8 kilometres per litre.
The next question can be rephrased as, given that Amelia drives 8 km per litre, how many litres will it take to drive one kilometre?
To answer this question, we make use of the equation
[tex]\operatorname{km}\text{ travelled = 8km/litre }\cdot\text{ litres}[/tex]Now, we want
km travelled = 1 km
and the above equation gives
[tex]\begin{gathered} 1=\frac{8\operatorname{km}}{\text{litre}}\cdot\text{litres} \\ 1=8\cdot\text{litres} \end{gathered}[/tex]Dividing both sides by 8 gives
[tex]\text{litres}=\frac{1}{8}[/tex]Hence, it takes 1/8 of a litre to drive 1 kilometre.
Write an absolute value inequality that represents all real numbers more than 4 units away from x
We have to write as inequality the following
"All real numbers more than 4 units away from x""4 units away from x" means four units plus x. So, the expression would be
[tex]|x|>4[/tex]Where x represents real numbers.
This expression is referring to all real numbers more than 4 units and less than -4 units because according to the property of absolute values for inequalities, we have
[tex]|x|>x-4\rightarrow x>x-4,or,x<-(x-4)[/tex]This is represented in the following graph to see it better
For x=1
[tex]\begin{gathered} |1|>x-4\rightarrow1>1-4,or,1<-(1-4) \\ 1>-3 \\ 1<3 \end{gathered}[/tex]Both results are true.
To find this absolute value inequality we used the following property
[tex]|x|>a\rightarrow a>b,or,a<-b[/tex]Where the absolute value inequality has "more than" we rewrite the expression in two inequalities.
use and show all conversion factors to convert 352 inches per second to miles per hour. 352 inches divided by 1 second
Okay, here we have this:
We need to convert 352 inches per second to miles per hour. So we obtain the following:
[tex]\begin{gathered} \frac{352in}{1sc}\cdot\frac{1mile}{63360in}\cdot\frac{3600sc}{1h} \\ =\frac{20\text{miles}}{h} \end{gathered}[/tex]Finally we obtain that 352 inches per second 20 are miles per hour.
Covert the decimal into a fraction and reduce to the lowest terms
Solution
- The number given to us can be rewritten as follows:
[tex]92.698=92+0.698[/tex]- Thus, we already know what is in the whole number bracket; 92.
- The fraction representation of 0.698 is what will occupy the fraction brackets.
- 0.698 can be rewritten as:
[tex]0.698=\frac{698}{1000}[/tex]- Let us simplify this fraction as follows:
[tex]\begin{gathered} \frac{698}{1000}=\frac{349\times2}{500\times2} \\ \\ 2\text{ crosses out.} \\ \\ =\frac{349}{500} \end{gathered}[/tex]- Thus, the answer is
Pablo Is choosing at random from a bag of colored marbles. The probability he will choose a red marble is1/9What are the odds in favor of him choosing a redmarble?
Given:
[tex]\text{The probability to choose a red marble=}\frac{1}{9}[/tex]The odds in favour of Pablo chosing a re marble is 1 : 8
Given the definitions of f(a) and g(x) below, find the value of (19)( 1),f (x) = x2 + 3x – 11g(x) = 3a + 6
The given functions are,
[tex]\begin{gathered} f(x)=x^2+3x-11_{} \\ g(x)=3x+6 \end{gathered}[/tex]Fog can be determined as,
[tex]\begin{gathered} \text{fog}=f(g(x)) \\ =f(3x+6) \\ =(3x+6)^2+3(3x+6)-11 \\ =9x^2+36+36x+9x+18-11 \\ =9x^2+45x+43 \end{gathered}[/tex]The value of fog(-1) can be determined as,
[tex]\begin{gathered} \text{fog}(-1)=9(-1)^2+45(-1)+43 \\ =9-45+43 \\ =7 \end{gathered}[/tex]Thus, the requried value is 7.
how can you use the vertical line test and the horizontal line test to determine whether a graph represents a function and whether the graph is invertible?
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
vertical line test = ?
horizontal line test = ?
Step 02:
vertical line test ===> function
any vertical line intersect the graph at only one point
horizontal line test ===> invertible
any horizontal line intersect the graph at only one point
graph:
horizontal line test = red
vertical line test = brown
That is the full solution.
Which expression is equivalent to (6 – 3x) + 9x ? 1 A. 8x + 2 B. 8x + 3 C. 10x-2 D. 10x - 6
Given to solve the expression:
[tex]\frac{1}{3}(6-3x)+9x[/tex]step 1: Expand the bracket by multiplying each term by the factor outside
[tex]\begin{gathered} (\frac{1}{3}\times6)-(\frac{1}{3}\times3x)+9x \\ 2-x+9x \end{gathered}[/tex]step 2: Simplify the expression obtained in step 1
[tex]\begin{gathered} 2-x+9x\text{ } \\ =2+8x \\ =8x+2 \\ \\ \text{The answer is \lbrack{}Option }A\rbrack \end{gathered}[/tex]9. If L 1 equals 120 then what is the measure of its supplement <2=
Supplementary angles are angles whose addition sums up to 180 degrees.
Therefore, if angle 1 measures 120, then its supplement which is angle 2, must mean both add up to 180.
Hence, you have
Angle 1 + Angle 2 = 180
120 + Angle 2 = 180
Subtract 120 from both sides of the equation
Angle 2 = 180 - 120
Angle 2 = 60 degrees
By definiton, two angles are complimentary angles if they both add up to 90 degrees. Hence if angle L5 equals 50 degrees, then its compliment would be derived as 90 - 50 which equals 40. The compliment of angle L5 which is 50 degrees, equals 40 degrees.
omg i lost my tutor in the middle of math i need another one btw in fith grade not in middle school yet
by definition the division of fractions can be found by
[tex]\frac{\frac{a}{b}}{\frac{c}{d}}=\frac{b\cdot c}{a\cdot d}[/tex]According to this
[tex]\frac{\frac{6}{10}}{\frac{1}{5}}=\frac{6\cdot5}{10\cdot1}=\frac{30}{10}=3[/tex]What is the measure of ?ХvO A. 46°42°42"38°NуvO B. 42°O C. 40°O D. 38°
The value Z is denoted as the center of the circle. Therefore, arc UV and arc XY should be the same .
[tex]undefined[/tex]Answer: A. 42°
Step-by-step explanation:
Hope this helps :)
Write the equation of the line with x-intercept -2 and y-intercept -1 in slope-intercept form
The x-intercept of -2 gives us an idea that point (-2,0) if found along the line. The y-intercept of -1, tells us that point (0,-1), this also tells us that b = -1.
Now that we have two points, we can solve for slope m
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \text{Given two points} \\ (-2,0)\rightarrow(x_1,y_1) \\ (0,-1)\rightarrow(x_2,y_2) \\ \\ \text{Substitute} \\ m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{-1-0}{0-(-2)} \\ m=-\frac{1}{2} \end{gathered}[/tex]Now that we have both m and b. Substitute these values to the slope intercept form
[tex]\begin{gathered} \text{Slope intercept form is} \\ y=mx+b \\ \text{where} \\ m\text{ is the slope} \\ b\text{ is the y-intercept} \\ \\ \text{Substitute the values from before and we get} \\ y=-\frac{1}{2}x-1 \end{gathered}[/tex]help meeeeeeeeee pleaseee !!!!!
The values of the functions evaluated are:
a. (f + g)(x) = 9x + 1
b. (f + g)(x) = -7x + 1
c. (f * g)(x) = 8x² - 55x - 72
d. (f/g)(x) = (x - 8)/(8x + 9)
How to Evaluate Functions?To evaluate a function expression, we are to input the given value of x and solve by combining like terms and simplifying to find the value of the given function expression.
Given the functions:
f(x) = x - 8
g(x) = 8x + 9
a. Find (f + g)(x): This implies that we are to add the two functions f(x) and g(x) together.
(f + g)(x) = x - 8 + 8x + 9
(f + g)(x) = 9x + 1
b. Find (f - g)(x): This implies that we are to subtract g(x) from f(x).
(f - g)(x) = x - 8 - 8x + 9
(f + g)(x) = -7x + 1
c. Find (f * g)(x): This implies that we are to multiply the functions, g(x) and f(x) together.
(f * g)(x) = (x - 8) * (8x + 9)
(f * g)(x) = 8x² - 55x - 72
d. Find (f/g)(x): This implies that we are to find the quotient of the functions, f(x) and g(x).
(f/g)(x) = (x - 8)/(8x + 9)
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How do I solve this and what is the answer
Answer:
157.5°
Explanation:
To convert from radians to degrees, multiply the angle in radians by 180/π.
Therefore, 7π/8 radians in degrees will be:
[tex]\begin{gathered} \frac{7\pi}{8}\text{ radians=}\frac{7\pi}{8}\times\frac{180}{\pi} \\ =\frac{7}{8}\times180 \\ =157.5\degree \end{gathered}[/tex]PLEASE HURRY ASAP
Determine which integer in the solution set will make the equation true.
4s − 14 = −6
S: {−1, 0, 1, 2}
The solution of the equation is s=2.
Linear FunctionAn equation can be represented by a linear function. The standard form for the linear equation is: y= mx+b , for example, y=7x+1. Where:
m= the slope. It can be calculated for Δy/Δx .
b= the constant term that represents the y-intercept.
For the given example: m=7and b=1.
For solving this question you should replace x for the given values ( −1, 0, 1, 2) in the equation 4s − 14 = −6. If you obtain -6, the value of s is a solution.
For s= -1 -> 4*(-1)-14= -4 -14= -20. Therefore, s=-1 is not the solution.
For s= 0 -> 4*(0)-14= 0 -14= -14. Therefore, s=0 is not the solution.
For s= 1 -> 4*(1)-14= 4 -14= -10. Therefore, s= 1 is not the solution.
For s= 2 -> 4*(2)-14= 8 -14= -6. Therefore, s=2 is the solution.
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What is the largestNumber of these wooden Els that can be packed in a box that is 2 cm x 4 cm x 6 cm
The largest number of the wooden Els with it's total surface area that can be packed in the 2cm×4cm×6cm box is 2 wooden Els.
Total Surface Area of Solid ShapesIn finding the total surface area of a solid cuboid, add the areas of all 6 faces. We can also label the length (l), width (w), and height (h) and use the formula, SA=2(lw+lh+hw), to find the surface area.
For the box, l=2cm, w=4cm and h=6cm
total surface area of box=2(2×6+2×4+6×4) cm square units
total surface area of box=2(44) cm square units
total surface area of box=88cm square units
For the top cuboid of the wooden El, l=3cm, w=1cm and h=2cm
total surface area of top El cuboid=22cm square units
For the bottom cuboid of the wooden El, l=1cm, w=1cm and h=2cm
total surface area of bottom El cuboid=10cm square units
total surface area of the El=32cm square units
(88cm²/32cm²)=2.75
This implies that only two(2) whole Els with total surface area of 32cm² can be packed in the box.
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Use the Rational Zeros Theorem to find all the real zeros of the polynomial function. Use the zeros to factor f over the real numbers. Hint solve this problem using P and Q's and synthetic division f(x) = x^3 + 2x^2 - 5x - 6A -3, -1, 2; f(x) = (x + 3)(x + 1)(x - 2)B-1; f(x) = (x + 1)(x2 + x - 6)C-3; f(x) = (x + 3)(x2 - x - 2)D-2, 1, 3; f(x) = (x + 2)(x - 1)(x - 3)
Since all coefficients are integers, we can apply the rational zeros theorem.
The trailing coefficient is -6 with the following factors (possible values for p):
[tex]p\colon\pm1,\pm2,\pm3,\pm6[/tex]The leading coefficient is 1, with factors:
[tex]q=\pm1[/tex]Therefore, all the possible values of p/q are:
[tex]\frac{p}{q}\colon\pm\frac{1}{1},\pm\frac{2}{1},\pm\frac{3}{1},\pm\frac{6}{1}[/tex]Simplifying, the possible rational roots are:
[tex]\pm1,\pm2,\pm3,\pm6[/tex]Next, we have to check if they are roots of the polynomials by synthetic division, in which the remainder should be equal to 0.
0. Dividing ,f (x), by ,x−1,. Remainder = ,-8, ,+1, is ,NOT ,a root.
,1. Dividing ,f (x), by x+,1,. Remainder = 0, ,-1, ,IS ,a root.
,2. Dividing ,f (x), by x-2. Remainder = 0, ,+2, ,IS ,a root.
,3. Dividing ,f (x), by ,x+2,. Remainder = ,4, ,-2, is ,NOT ,a root.
,4. Dividing ,f (x), by ,x−3,. Remainder = 24,, ,+3, is ,NOT ,a root.
,5. Dividing ,f (x), by ,x+3,. Remainder = 0,, ,-3, IS ,a root.
,6. Dividing ,f (x), by ,x−6,. Remainder = 252,, ,+6, is ,NOT ,a root.
,7. Dividing ,f (x), by ,x+6,. Remainder = -120,, ,-6, is ,NOT ,a root.
Actual rational roots: A. -3, -1, 2; f(x) = (x + 3)(x + 1)(x - 2)
Hello, I need some assistance with this homework question please for precalculusHW Q1
To transform a function about the y axis
f(x) becomes f(-x)
y = sqrt( x) +2
To transform replace x with -x
y = sqrt(-x) +2
The 2 is a vertical translation up 2
Is (6, –21) a solution to the equation y = –5x − –9?
Answer:
Explanation:
Given the equation:
[tex]y=-5x-(-9)[/tex]When x=6:
The relation between the number of batteries (n) and the maximum height reached by the drone (h) in feet (ft) is given. Complete the table and check the correct box(es) given below.
We use the equation: h = 100(n + 2), so:
For n = 1:
[tex]h=100(1+2)=100(3)=300[/tex]For n = 3:
[tex]h=100(3+2)=100(5)=500[/tex]We can see that this is the correct equation. Therefore, given h we find n:
For h = 700
[tex]\begin{gathered} 700=100(n+2) \\ \frac{700}{100}=\frac{100}{100}(n+2) \\ 7=n+2 \\ 7-2=n+2-2 \\ n=5 \end{gathered}[/tex]For h = 900
[tex]\begin{gathered} 900=100(n+2) \\ \frac{900}{100}=\frac{100}{100}(n+2) \\ 9=n+2 \\ 9-2=n+2-2 \\ n=7 \end{gathered}[/tex]Answer:
(n): 1 3 5 7
(h): 300 500 700 900
Correct equation: h = 100(n + 2)
select all of the following equations which represent a function?
To verify that something is a function, we use the horizontal line rule. That is, if the horizontal line passes through two points, then the graph is not a function, like this:
Then the circles and the ellipses are not functions. Then the functions in the problem would be:
1, 3 and 6.
HELP PLEASEEEEE!!!!!!
The solutions of the indices are;
1) 2^7
2) 3^-4
3) 3^4
4) 2^4
What is the power?We know that in this case, we would have to apply the laws of indices and the particular law that we are to apply in each case is dependent on the nature of the problem that have been posed. Let us recall that we are asked to ensure that we express the answer or the solution to the problem as a single power.
1) 64 * 256/128
2^6 * 2^8/2^7
2^6 + 8 - 7 = 2^7
2) 3^4/3^3 * 3^5
3^4 - (3 + 5) = 3^-4
3) 3^9/ (3^4)^1/2 * 3^3
3^9/ 3^2 * 3^3
3^9 - (2 + 3)
3^4
4) (2^3)^4 * 2^4 ÷ 32/ 2 * 64
2^12 * 2^4 ÷ 2^5/2^1 * 2^6
2^12 + 4 -5/2^1 + 6
2^16 -5/2^7
2^11/2^7
2^11 - 7
2^4
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A train travels at 100 mph any equation can be written that compares the time with the distance to find the domain and range
ok
speed = distance / time
time = distance/speed
[tex]\text{ time = }\frac{dis\tan ce\text{ }}{speed}[/tex][tex]\text{ time = }\frac{dis\tan ce\text{ }}{100}[/tex]or
[tex]\text{ distance = 100 x time}[/tex]Substitute the given values into the given formula and alone the unknown variable if necessary round to one decimal place
c = 15
Explanation:The perimter, P = 37
The side lengths of the triangle are:
a = 10, b = 12, c = ?
The perimeter of the triangle is given by the formula:
P = a + b + c
Substitute a = 10, b = 12, and P = 37 into the formula P = a + b + c and solve for c
37 = 10 + 12 + c
37 = 22 + c
c = 37 - 22
c = 15
In the diagram shown, ray CD is perpendicular to ray CE. If the measure of DCF is 115then what is the measure of ECF?
m∠FCE =25º
1) Since the measure of ∠DCF = 115º and ∠DCE = 90º then by the Angle Addition postulate we can state that
∠DCF = ∠DCE +∠FCE Plugging into that the given values
115º = 90º + ∠FCE Subtracting 90º from both sides
115-90=∠FCE
25º =∠FCE
2) Then the measure of ∠FCE is 25º
Which of the following is an equation of a line that is parallel to y = 4x - 5 and has a y-intercept of (0, 7)?
Answer:
Step-by-step explanation:
To start your equation is in the format y=mx+b.
For a line to be parallel it must have the same slope (m) so we know 4 must remain the same. x & y will not change since they represent the variables. y=4x (so far) then the point (0,7) as stated is the y intercept. 0 is the x value and 7 is the y we need to add 7 to our equation.
final equation y=4x+7
mrs smith took her 3 kids and 3 of thejr friends to the Strawberry field. how many kids are there?
Mrs.Smith took : her 3 kids + 3 of their friends = 3 + ( 3x 3 ) = 12 kids
Answer:
There are 3 kids, and 3 friends.
3 + 3 = 6
there are a total of 6 kids.
Marcy baked 132 cookies . She is packaging boxes of eight cookies to give as a gift to he friends how many boxes will she make .
She will make 16 boxes.
To answer this question we simply have to divide the number of cookies (132) by the number of cookies that each box can contain.
Mathematically speaking:
[tex]132/8\text{ }[/tex][tex]16.5[/tex]Since we can´t have half boxes, we have to round the number to 16.
16 boxes.
Jordan plotted the graph below to show the relationship between the temperature of his city and the number of cups of hot chocolate he sold daily:A scatter plot is shown with the title Jordans Hot Chocolate Sales. The x axis is labeled High Temperature and the y axis is labeled Cups of Hot Chocolate Sold. Data points are located at 20 and 20, 30 and 18, 40 and 20, 35 and 15, 50 and 20, 45 and 20, 60 and 14, 65 and 18, 80 and 10, 70 and 8, 40 and 2.Part A: In your own words, describe the relationship between the temperature of the city and the number of cups of hot chocolate sold. (2 points)Part B: Describe how you can make the line of best fit. Write the approximate slope and y-intercept of the line of best fit. Show your work, including the points that you use to calculate the slope and y-intercept. (3 points)
A.
Overall it has a relation that there are more sold cups when the temperature is lower. On the other hand, based on the 40 degrees part, that have to different values of two different days, we can say is not the only factor.
B.
The best lineal approach is the line created with the points at 20 and 80 degrees. First the slope:
[tex]m=\frac{y1-y2}{x1-x2}=\frac{20-10}{20-80}=\frac{10}{-60}=-\frac{1}{6}[/tex]Now the intercept with y axis, b:
[tex]\begin{gathered} y=mx+b \\ 20=20(-\frac{1}{6})+b \\ 20+\frac{20}{6}=b=23.33=\frac{70}{3} \end{gathered}[/tex]The final line formula is:
[tex]y=-\frac{x}{6}+\frac{70}{3}[/tex]Write the ordered pair with no spaces (x,y) of point C for j(x).
This problem is about functions.
In this case, we don't have function j(x) defined in order to find its ordered pairs.
However, assuming that function j(x) is a function of f(x), we can deduct that points C is
[tex]C(0,0)[/tex]Solve system of equations using the method of substitution. Identify wether the system represents parallel, coincident, or parallel lines.5x+2y=167.5x+3y=24
Given
5x+2y=16 ---(1)
7.5x+3y=24 ----(2)
Find
1) value of x and y
2) Type of system
Explanation
From equation (1)
[tex]\begin{gathered} 5x+2y=16 \\ 5x=16-2y \\ x=\frac{16-2y}{5} \end{gathered}[/tex]Putting this value of x in equation 2
[tex]\begin{gathered} 7.5x+3y=24 \\ 7.5(\frac{16-2y}{5})+3y=24 \\ 1.5(16-2y)+3y=24 \\ 24-3y+3y=24 \end{gathered}[/tex]From here we cannot find the values of x and y as 3y and -3y will cancel each other. Hence there is not a particular solution
Checking the type of system
From these equations we get
[tex]\frac{a1}{a2}=\frac{b1}{b2}=\frac{c1}{c2}[/tex]Therefore the lines are coincident to each other
Therefore the lines have infinte solutions
Final Answer
Therefore the lines have infinte solutions
The lines are coincident to each other