We have the coordinates of two points on the line, those are (-6,-8) and (-3,-6).
Using these two points we can find the slope of the line using the following equation:
[tex]m=\frac{-8-(-6)}{-6-(-3)}=\frac{-2}{-3}=\frac{2}{3}[/tex]Use one of these points and the slope in the point slope formula to find the linear function:
[tex]\begin{gathered} y-(-6)=\frac{2}{3}(x-(-3)) \\ y+6=\frac{2}{3}(x+3) \\ y+6=\frac{2}{3}x+2 \\ y=\frac{2}{3}x+2-6 \\ y=\frac{2}{3}x-4 \end{gathered}[/tex]It means that the linear function is:
[tex]f(x)=\frac{2}{3}x-4[/tex]The perimeter of a parallelogram is 72 meters . The width of the parallelogram is 4 meters less than its length. Write an equation that could be used to find the length of the parallelogram.
4L = 64
Explanation: The perimeter of a parallelogram (like most other quadrilaterals) is defined as;
P = 2 (L + W)
Where P is the perimeter, L is the length and W is the width. Note that the width is given as 4 metres less than its length, hence if the length is L then the width shall be L-4. The perimeter can now be expressed as follows:
P = 2 (L + [L-4])
If the perimeter is 72, then
72 = 2 (L + L - 4)
72 = 2 (2L - 4)
By expanding the bracket on the right hand side we now have;
72 = 4L - 8
Add 8 to both sides of the equation
72 + 8 = 4L - 8 + 8
80 = 4L
Therefore the equation is 4L = 80
And the Length is 20 metres.
2x=8 what is the answer
To solve x:
Divide both sides of the equation into 2:
[tex]\begin{gathered} \frac{2}{2}x=\frac{8}{2} \\ \\ x=4 \end{gathered}[/tex]Then, the solution for the given equation is x=4The function C(x) = 10x +3,000 represents the cost to produce a number of items. How many items should beproduced so that the average cost is less than $30?Provide your answer
Given:
The cost function is C(x) = 10x + 3000.
Explanation:
The equation for the average cost is,
[tex]\begin{gathered} A(x)=\frac{C(x)}{x} \\ =\frac{10x+3000}{x} \end{gathered}[/tex]The inequality for x is,
[tex]\frac{10x+3000}{x}<30[/tex]Solve the inequality for x.
[tex]\begin{gathered} \frac{10x+3000}{x}\cdot x<30\cdot x \\ 10x+3000-10x<30x-10 \\ \frac{3000}{20}<\frac{20x}{20} \\ 150So the number of items should be more than 150.
A tortoise is walking in the desert it walks for 5.12 m at a speed of 4 m/min. how many minutes does it walk
1.3 minutes does the tortoise walk.
What is speed- distance formula?Speed, time, and distance relationships
Distance/Time x Speed This reveals how quickly or slowly an object is moving. It gives the amount of time it took to travel a certain distance divided by the distance travelled.Speed is inversely correlated with time and directly correlated with distance. Therefore, as the speed increases, the time required, because Time = Distance / Speed. Distance = Speed X Time.Each Speed, Distance and Time can be expressed in different units:
Time: seconds(s), minutes (min), hours (hr)Distance: (meters (m), kilometers (km), miles, feetSpeed: m/s, km/hrGiven:
distance= 5.2 m
speed= 4 m/ min
Now using
speed= Distance / time
4 = 5.2 / time
time= 5.2/4
time= 1.3 minutes.
Hence, 1.3 minutes does the tortoise walk.
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Define a variable, using let statements, set up an equation, then solve. Mark flew from Boston to Baltimore, then Baltimore to Orlando. the number of people on his first flight was five more than four times the number of people on his second flight. if there were 365 people altogether on the two flights how many were on the flight from Baltimore to Orlando?
First flight = f
second flight = s
Equations
f + s = 365 Equation 1
f = 4s + 5 Equation 2
Solve by substitution
(4s + 5) + s = 365
4s + 5 + s = 365
5s = 365 - 5
5s = 360
s = 360 / 5
s = 72
Find f
f = 4(72) + 5
f = 288 + 5
f = 293
Result
In the flight from Baltimore to Orlando there were 72 people.
A rectangular piece of cardboard that is 10 inches by 14 inches has squares of length x inches on a side cut from each corner. (Assume that 0 < x < 5.) If the flaps of the figure are folded up, an open box is formed. Represent the volume of this box in the form of a polynomial function V(x).
This is an aproximation of the described situation. We are taking 4 squares of side lenght x from each corner.
The dashed lines mark up what would be the base of the box. The blue scrabbled areas will be the sides of the box.
Recall that to calculate the volume of the box, we need to multiply the lenghts of each side of the base and then multiply it by the height of the box. So, to calculate the volume we need to determine the lenght of the dashed lined.
Let us calculate the lenght of the black dashed lines. Notice that the horizontal side has a total lenght of 14. So, since we are taking 2 squares of side x, we have that the lenght of the dashed line plus twice the lenght x, we get the total lenght of the side. That is
[tex]\text{Black dashed line + 2x = 14}[/tex]Then the lenght of the black dashed line is 14-2x.
In the same manner, we can calculate the red dashed lines' lenght. It is 10-2x. Now, our box would be
In the picture, the green line represents the height. Comparing the blue and red lines, we have that the lenght of the green line corresponds to the lenght of the side of the square (x).
So now, we know that the volume of the box is
height * lenght of the base * width of the base = (14-2x)*(10-2x) * (x)
which is a polynomial of the variable x.
Question 5(Multiple Choice Worth 2 points)
(Multi-Step Linear Equations MC)
Find the value of x in the following equation:
3.6(2x + 5) = 7.2x + 18
No solution
Infinite solutions
x = 0
x = 2.3
The Linear equation 3.6(2x + 5) = 7.2x + 18.3 has no solution except when x is put to be zero.
The provided equation is 3.6(2x + 5) = 7.2x + 18.
This is a linear equation in one variable.
We have to solve the equation for x,
We can solve it by simplifying it,
3.6(2x + 5) = 7.2x + 18
7.2x + 18 = 7.2x + 18
7.2x = 7.2x
7.2x - 7.2x = 0
(7.2-7.2)x = 0
(0)x = 0
x =0/0
Hence, there can not be any value of x.
But, if we put x = 0 in the equation,
Then,
3.6(2(0) + 5) = 7.2(0) + 18
18 = 18
So, x = 0 is satisfying the equation.
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The number line is a graph of the
Rational number
Real numbers
Integers
The number line is a graph of the Real numbers.
Rational Number And Real Numbers Integers ?Rational and irrational numbers are the two basic categories for real numbers. All fractions and integers are considered rational numbers. The set of integers consists of all whole numbers and negative integers. All natural numbers and zero are considered whole numbers. The only positive and negative whole numbers and natural numbers that fall under the category of integers are real numbers. Due to rational and irrational numbers, real numbers can incorporate fractions; however, integers cannot. Since integers are a collection of all positive counting numbers, zero, and all negative counting numbers that count from negative infinity to positive infinity, they are all rational numbers. Decimals and fractions are not included in the set.
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a(n)=3n-7 what is the sum of the 1st and 5th terms of sequence
Answer: 4
Step-by-step explanation:
To find the first term you replace n with 1.
a(1) = 3(1) -7
a(1) = -4
Now that you have the first term you must find the fifth term by filling in 5 for n.
a(5) = 3(5) - 7
a(5) = 15 - 7
a(5) = 8
Now that we have both terms simply add them together to find the sum.
-4 + 8 = 4
Slope is 1 and (-2,1) is on the line
Answer:
y = x + 3
Step-by-step explanation:
Write the equation?
Use:
m (slope) = 1
x = -2
y = 1
y=mx + b
1 = 1(-2) +B
1 = -2 + b Add 2 to both sides
3 = b
y = mx + b
y = 1x + 3
y = x + 3
pls help thx i don’t know what to do here options are a)0.3125b)2.2c)6.6d)3.2
Given:
The graph for height and width.
[tex]Height=constant\times width[/tex]Required:
What is the value of the constant in the equation?
Explanation:
From graph, we can evaluate respective values in equation and can get value of constant as:
[tex]\begin{gathered} height=constant\times weight \\ 1.6=constant\times0.5 \\ constant=3.2 \end{gathered}[/tex]Answer:
The value of constant equals 3.2
Find the equation of the line passing through the points (10,8) and (-10,30). Write your answer in the form
The equation of a line in slope-intercept form is given by:
[tex]y=mx+b[/tex]Where m is the slope and b is the y-intercept.
We know two points on the line: (10,8) and (-10,30).
The slope can be found by using the following formula:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]Where (x1,y1) and (x2,y2) are the coordinates of two points on the line. By replacing the known coordinates we obtain:
[tex]m=\frac{30-8}{-10-10}=\frac{22}{-20}=-\frac{11}{10}[/tex]The y-intercept can be found by replacing the slope and one of the points in the slope-intercept formula, and solving for b:
[tex]\begin{gathered} 8=-\frac{11}{10}\cdot10+b \\ 8=-11+b \\ 8+11=b \\ b=19 \end{gathered}[/tex]Thus, the equation of the line is:
[tex]y=-\frac{11}{10}x+19[/tex]How many lines of symmetry does the figure have
○ 8
○ 7
○ 9
○0
Answer:
7
Step-by-step explanation:
First count the sides and draw a line above the shape and you will it's 7
3 1/4 x 2/3 = ??grade. 7th
Given the expression:
[tex]3\cdot\frac{1}{4}\cdot\frac{2}{3}[/tex]Fist step is to express the "whole" as a fraction, for this, divide it by 1
[tex]\frac{3}{1}\cdot\frac{1}{4}\cdot\frac{2}{3}[/tex]Second step, multiply the first two fractions:
[tex]\frac{3}{1}\cdot\frac{1}{4}=\frac{3\cdot1}{1\cdot4}=\frac{3}{4}[/tex]Third step, multiply the result of the first operation by the third fraction:
[tex]\frac{3}{4}\cdot\frac{2}{3}=\frac{3\cdot2}{4\cdot3}=\frac{6}{12}[/tex]Finally simplify the expression, both the numerator and denominator are divisible by 6 so:
[tex]\frac{6\div6}{12\div6}=\frac{1}{2}[/tex]Then the result for the given expression is 1/2
[tex]3\cdot\frac{1}{4}\cdot\frac{2}{3}=\frac{1}{2}[/tex]Please solve math question FAST
Answer:
Solution below.
Step-by-step explanation:
This question tests on the concept of percentages and comparing current and previous values.
Lets analyse the first statement from the question.
Taylor earned 15% more each week in September than in July.
We know that the formula for percentage change:
((Final Value - Initial Value) ÷ Initial Value) × 100
Comparing July and September,
we know that the change is 15% and the Final Value (September) is $207.
So we can substitute values into the formula to find the value for July.
[tex] \frac{207 - july}{july} \times 100 = 15 \\ \frac{207 - july}{july} = \frac{15}{100} \\ 207 - july = 0.15july \\ 1.15july = 207 \\ july = \frac{207}{1.15} \\ = 180[/tex]
Now we know Taylor earned $180 in July, we can use the same formula to find the amount she earned in August. Given Initial Value (July) = $180 and percentage change = 10% (She earns 10% more in August than in July)
[tex] \frac{sep - 180}{180} \times 100 = 10 \\ \frac{sep - 180}{180} = \frac{10}{100} \\ \frac{sep - 180}{180} = 0.1 \\ sep - 180 = 0.1 \times 180 \\ sep - 180 = 18 \\ sep = 18 + 180 \\ = 198[/tex]
Therefore, Taylor earns $198 per week in September.
Hello i did this question on my own because I thought I understood it but it was wrong I got 1/2
Given a number 'a', we have the following general rule for exponent:
[tex]a^{-n}=\frac{1}{a^n}[/tex]in this case, we have:
[tex]3^{-4}=\frac{1}{3^4}=\frac{1}{81}[/tex]What is the last step in this process?
A, Find the difference between partial products
B, Find the sum of partial products
C, The last step is already complete
Answer:
B. Find the sum of partial products.
Step-by-step explanation:
Lookout station A is 12 miles from the fire. Lookout station B is 39 miles from station A. The angle at station A is 52°. Find the distance between Station B and the fire.
Therefore, in order to find out the distance from station b to the fire, we must use the sine formula, as we know that sine is the opposite side divided by the hypotenuse.
We want to find out the opposite side and we already have the hypotenuse that is 12 miles.
So:
[tex]\begin{gathered} \sin52=\text{ }\frac{x}{12} \\ 12(\sin52)=x \\ 12(0.788)=x \\ 9.456=x \end{gathered}[/tex]Therefore, station B i 09.456 miles from the fire.
Write the equation in point-slope form of the line that passes through the given point with the given slope.
(3, 1); m = 2
Answer:m = (y – y1)/ (x – x1)
⇒ y – y1 = m(x – x1)….(i)
Step-by-step explanation:
Find the value of AB.D1312mo8AB = [?]
a basketball player averages 13.5 points per game. there are 22 games in a season. at this rate, how many points would the player score in an entire season
In order to find the total player score, we just need to multiply the average of the player by the number of games in the season. So we have:
[tex]\text{total score}=22\cdot13.5=297[/tex]So the player score in the entire season would be 297.
p= principal amount, 0.12= the interest charged; p+0.12p=224 . write a problem based on the given information
Step 1: Let's review the information given to us to answer the problem correctly:
• p = Principal
,• 0.12 = Interest rate
,• 224 = Future value
Step 2: Let's write a problem based on this information, using the Simple Interest Formula, as follows:
A = P(1 + rt), where:
A = Final amount
P = Principal
r = Annual interest rate
t = Time in years
224 = P (1 + 0.12t)
224 = 1.12Pt
Pt = 224/1.12
Pt = 200
If P = 200, then t = 1
Step 3: Let's interpret the answer and the problem we just wrote.
What is the amount of principal and the time of deposit for a savings account that earns 12% annually, and shows a final balance of $ 224?
Answer: $ 200 and the period of time is 1 year.
4. In 2017, chicken consumption in pounds consumed for 100 randomly selected people hasa mean * = 55.2 pounds and a standard deviation s = 23 pounds. Construct a 90%confidence interval the mean weight of chicken consumption in 2017.
(a)
The given parameters are:
[tex]\begin{gathered} \text{Mean}=\bar{X}=55.2 \\ \text{Standard deviation}=\sigma=23 \\ Sample\text{ size}=n=100 \\ z=1.644854\text{ (90\% confidence ineterval)} \end{gathered}[/tex](b)
The formula to find the margin of error for a 90% confidence interval is given below:
[tex]E=z\times\frac{\sigma}{\sqrt[]{n}}[/tex]Substitute the value from part (a), to get
[tex]\begin{gathered} E=1.644854\times\frac{23}{\sqrt[]{100}} \\ =1.644854\times\frac{23}{10} \\ =3.7832 \end{gathered}[/tex]Thus, the margin of error is 3.7832.
(d)
The given sample's confidence interval is,
[tex]55.2\pm3.7832[/tex]So, the confidence interval is (51.42 to 58.98).
(d)
For 90% confidence interval, the mean weight of chicken consumption is between 51.42 pounds and 58.98 pounds.
help fast please!!!!!!
Answer:
B is correct.
Step-by-step explanation:
[tex] \frac{5.96 \times {10}^{4} }{2.98 \times {10}^{3} } = 2 \times 10 = 20[/tex]
Which of these expressions entered into a graphing calculator willreturn the probability that 45 or fewer heads come up when flipping acoin 100 times?
Prob P = Heads/ flips
. = (n,p,c)
Here n is number of flips
. p is prob of 1 success
. c number of sucess
Then ANSWER IS
OPTION A) binomcdf (100,0.5, 45)
Verizon Wireless charges you a one- time processing fee of $250 plus $75 every month for a cell phone. Sprint charges you a one-time processing fee of $50 plus $100 every month for a cell phone. Write an equation to represent the cost of each company. Then complete the table.
Answer:
8
Step-by-step explanation:
7 A total of 340 gallons of oil is divided between two tanks. If at least half of the oil is pumped into the first tank, which number line represents that possible amount of oil in the second tank? (A 400 100 200 300 B 300 400 200 100 tot 200 300 400 100 O HH 300 400 100 200
Half of 340 gallons is:
[tex]170\text{ gallons.}[/tex]Let x represent the amount of oil in the second tank, we know that at least 170 gallons were pumped into the first tank, therefore, at most the other half is in the second tank:
[tex]x\ge170.[/tex]Answer: The above inequality in the number line is represented as follows:
The ordered pair below is form an inverse variation.find the constant of variation.(8,6)
We have that an inverse variation can be represented by the following equation:
[tex]\begin{gathered} k=xy \\ or \\ y=\frac{k}{x} \end{gathered}[/tex]In this case we have the ordered pair (8,6), then, we have the following constant of variation:
[tex]\begin{gathered} (x,y)=(8,6) \\ \Rightarrow k=(8)(6)=48 \\ k=48 \end{gathered}[/tex]therefore, the constant of variation is k = 48
a dealer paid 720 kina for a radio and sold it so as to gain 37.5%. find the selling price
Cost: 720 kina
Earnings: 37.5%
Then, the selling price should be:
100% + 37.5% = 137.5% of 720 kina
=> 137.5*720/100 = 990 kina
The selling price was 990 kina.
write two numbers that multiply to 54 and add to -21
This is the solution to a 2 degree equation:
[tex]x^2-21x+54=0[/tex]The two numbers that multiply to 54 and add to -21 are the roots of this equation.
We can find the solution of an equation with this form:
[tex]ax^2+bx+c=0[/tex]With this formula:
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]For this problem, a = 1, b = -21 and c = 54:
[tex]x=\frac{21\pm\sqrt[]{(-21)^2-4\cdot1\cdot54}}{2\cdot1}=\frac{21\pm\sqrt[]{441-216}}{2}=\frac{21\pm\sqrt[]{225}}{2}=\frac{21\pm15}{2}[/tex]The two numbers are:
[tex]\begin{gathered} x_1=\frac{21+15}{2}=\frac{36}{2}=18 \\ x_2=\frac{21-15}{2}=\frac{6}{2}=3 \end{gathered}[/tex]The numbers are -18 and -3 (they must be negative so they add up to a negative number)
