13 is slope of parallel line and -1/13 is slope of perpendicular line.
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
The given points are (7, 3) and (6, −10)
m=-10-3/6-7
m=-13/-1=13
So slope of line is 13
The equation of line is y=13x+b
Now let us find b.
3=13(7)+b
3=91+b
-88=b
y=13x-88
Now we have to find slope of line parallel to y=13x-88.
The slope of parallel line is 13 because in parallel lines slopes will remain same.
-1/13 is the slope of perpendicular line.
Hence , 13 is slope of parallel line and -1/13 is slope of perpendicular line.
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Solve y = x³ for x if y = - 1000.
Answer: x = - 10
Step-by-step explanation:
We will use the equation given, substitute -1,000 in for y, and solve.
y = x³
(1,000) = x³
[tex]\sqrt[3]{ (1,000)} = \sqrt[3]{x^3}[/tex]
- 10 = x
x = - 10
Simplify each radical expression. ⁴√ (-5)⁴ . ³ √-5³ ⁵ √125 ⁶ √729
Each radical expression;
i)⁴√ (-5)⁴ ∛-5³ = 25
ii) ⁵√128 = 2 √2
iii) ⁶√729 = 3
If the following circumstances apply, a radical expression is said to be in standard form:
1. A positive radicand exists.
2. There is the least amount of radical index conceivable.
3. Each radicand factor's exponent is a natural integer lower than the radical index.
4. The radicand has no fractions.
5. A fraction's denominator has no radicals.
i)⁴√ (-5)⁴ ∛-5³
= -5 * -5
= 25
ii) ⁵√128
= ⁵√2 * 2 * 2 * 2 * 2 * 2
= 2 √2
iii) ⁶√729
= ⁶√3 * 3 * 3 * 3 * 3 * 3
= 3
Hence, the radical expressions are 25, 2 √2, 3.
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Need help ASAP this is due in 2 hours snd I procrastinated
Answer:
Step-by-step explanation:
perimeter of given square = 2 x 4 = 8 units
area of given square = 2^2 = 4 units^2
side of dilated square = 2 x 3 = 6 units
perimeter of dilated square = 6 x 4 = 24 units
area of dilated square = 6^2 = 36 units^2
Small square
The perimeter is 8
the area is 4
Big Square
the perimeter is 24
the area is 36
Express535cm in meters
Answer:
5.35
Step-by-step explanation:
Answer:
5.35 meters
Step-by-step explanation:
To find the answer, you divide the length value by 100
Graph the given function by making a table of coordinates.
f(x)=3ˣ
Complete the table of coordinates.
x -2 -1 0 1 2
y __ __ __ __ __
(Type integers or fractions. Simplify your answers.)
The exponential function f(x) = 3ˣ has a function table of values calculated below and a graph attached
Function TableA function table is a visual table with columns and rows that displays the function with regards to the input and output. Younger students will also know function tables as function machines. Every function has a rule that applies and represents the relationships between the input and output.
In the function given;
f(x) = 3ˣ
When x = -2
f(-2) = 1/9
When x = -1
f(-1) = 1/3
When x = 0
f(0) = 1
When x = 1
f(1) = 3
when x = 2
f(2) = 2
The function can be represented in a graph below;
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Which graph represents the solution to negative one half m is greater than or equal to seven elevenths?
number line with closed circle on point negative 14 over 11 and arrow shaded to the right
number line with closed circle on point negative 7 over 22 and arrow shaded to the right
number line with closed circle on point negative 14 over 11 and arrow shaded to the left
number line with closed circle on point negative 7 over 22 and arrow shaded to the left
The solution set to the inequality, -1/2m ≥ 7/11, is: m ≤ -14/11 (see attachment for the graph).
How to Graph the Solution Set to an Inequality?Translating the statement given as an inequality, we have:
-1/2m ≥ 7/11
To find the solution, isolate the variable of m to one side of the inequality:
-1/2m ≥ 7/11
Multiply both sides by -2 then change the sign to
-1/2m(-2) ≥ 7/11(-2)
m ≤ -14/11
Therefore, it means the solution is any value of m that is less than or equal to -14/11.
The graph of the solution is shown in the attachment below.
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Differentiate the function with respect to x. Shot steps
The value of function after differentiation will be;
⇒ dy/dx = 2 / (x log3)
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The function is,
⇒ y = log ₃ 2x²
Now,
Since, The function is,
⇒ y = log ₃ 2x²
Differentiate with respect to x, we get;
⇒ dy/dx = 1 / (2x² log3) × d/dx (2x²)
= 1 / (2x² log3) × 4x
= 2 / (x log3)
Thus, The value of function after differentiation will be;
⇒ dy/dx = 2 / (x log3)
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an image shows a right triangle with a circle cut out of it. the legs that make up the right triangle are both 90meters. the diameter of the circle cut out is 40 meters. all of the triangle is shaded, except where the circle is cut out
Answer:
2794 m^2
Step-by-step explanation:
Area of Triangle - Area of Circle
1/2bh - piR^2
4050 - 1256
= 2794
For a recent algebra exam, Pat studied 1 8/15 hours, Toni studied 1 11/20 hours, and Morgan studied 1 9/16 hours. List the students in order by who studied the most. Top label: Studied MostStudied Most
Answer:
This is just comparing fractions:
Pat: [tex]1\frac{8}{15} =1.53[/tex]Toni: [tex]1\frac{11}{20} =1.55[/tex]Morgan: [tex]1\frac{9}{16} =1.5625[/tex]So, from most to least time spent studying, it would be
MorganToniPat.Can someone help me with this
It takes 8 months for the investment to grow to $6000 if interest was compounded quarterly.
What is compound interest?
The interest charged on a loan as well as deposit is known as compound interest. It is the idea that we use the most frequently on a daily basis. Compound interest is calculated for an amount based on both the principal and cumulative interest. The main distinction between compound as well as simple interest is this.
Given:
Principal amount = $5000
Annual amount interest = 2.6%
Compounded quarterly = 4
Final amount = $7000
Formula:
A = P(1 + r)^4n - 1
A is the quarterly compounded interest.
P would be the principal amount.
r is the quarterly compounded rate of interest.
n is the number of periods.
Solving it:
7000 = 5000 (( 1 + 0.026))^ 4t -1
7/5 = (( 1 + 0.026))^ 4t
7/5 = (1.026)^ 4t -1
ln (7/5) = 4t ln (1.006) - ln 1
t = 7.61 months
t ~ 8months
Hence, it takes 8 months for the investment to grow to $6000 if interest was compounded quarterly.
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Differentiate the function wi respect to x. Shot steps
The differentiation of the given function will be y' = 2xy (log 2).
What is differentiation?The rate of change of a function with respect to the variable is called differentiation. It can be increasing or decreasing.
A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.
The function is given below.
[tex]\rm y = 2^{x^2}[/tex]
Take log on both sides, then we have
log y = x² log 2
Differentiate the function with respect to 'x', then we have
(1/y) y' = (log 2) 2x
y' = 2xy (log 2)
The differentiation of the given function will be y' = 2xy (log 2).
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pls help pls ??????????????????????????????????????????????????????
The probability that a student is in the choir or band or both is 0.911
What is probability?Probability is the likelihood that an event will happen. This can range from an event being impossible to some likelihood to being absolutely certain. In math terms, probability is on a scale from 0 to 1. Zero means the event is impossible, like rolling a seven on a die that only has digits from 1 to 6. One is an event that will happen, it is certain.
Total number of students in the school = 450
number of students in choir = 110
number of students in band = 240
number of students in both = 60
Probability a student chosen at random is in the choir or band or both is
110/450 + 60/450 + 240/450
= 410/450 which is 0.911
In conclusion, the probability of a student being in music, or band or both is 0.911
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Obtain a 98% confidence interval estimating the difference (actual minus sham) in mean shoulder condition score one year after such interventions in the population of patients with persistent shoulder pain. When expressed in the format (lower bound, upper bound), give the numerical values rounded to 1 decimal place (for ex. 1.1, no text).
Enter the margin of error for this confidence interval as a numerical value rounded to one decimal places (for ex. 1.1, no letters or text):
The 98% confidence interval estimating the difference in mean shoulder condition score one year after such interventions in the population of patients with persistent shoulder pain is given by:
(-2.5, 5.1).
What are the mean and the standard error for the distribution of differences?For each sample, the mean and the standard error are given as follows:
Actual: [tex]\mu_A = 39.4, s_A = 1.1[/tex]Sham: [tex]\mu_B = 38.1, s_B = 1.2[/tex]Hence the mean and the standard error of the distribution of differences is given as follows:
Mean: [tex]\overline{x} = \mu_A - \mu_B = 39.4 - 38.1 = 1.3[/tex]Standard Error: [tex]s = \sqrt{s_A^2 + s_B^2} = \sqrt{1.1^2 + 1.2^2} = 1.6[/tex]What is the confidence interval?The bounds of the confidence interval are given by the rule presented as follows:
[tex]\overline{x} \pm ts[/tex]
The critical value, using a t-distribution calculator, for a two-tailed 98% confidence interval, with 72 + 65 - 2 = 135 df, is t = 2.35.
Then the bounds of the interval are:
Lower bound: 1.3 - 2.35 x 1.6 = -2.5.Upper bound: 1.3 + 2.35 x 1.6 = 5.1.Missing InformationThe missing information is given by the image shown at the end of the answer.
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Please help will mark Brainly
Translations do not change the slope of the line, so the original line and the transformed line are always a parallel option (B) is correct.
What is a perpendicular line?Lines that intersect at a right angle are named perpendicular lines. Lines that are always the same distance apart from each other are known as parallel lines.
As we know, parallel lines never intersect.
Parallel lines result from changing the y-intercept while keeping the slope constant.
The original line and the transformed line are always parallel since translations do not alter the slope of the line.
Thus, translations do not change the slope of the line, so the original line and the transformed line are always a parallel option (B) is correct.
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Classify 8x^3+32x^2+x+4.......
Answer:
(x+4)( 8x^{2}+1)
Step-by-step explanation:
:)
Need help ASAP explanation would be appreciated
a)Perimeter of given right angle triangle is 48.
Perimeter of dilated right angle triangle is 192.
b) Area of given figure is 96cm²
Area of figure after dilation is 1536cm².
Define dilation.Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size.
Given,
Triangle given,
Base = 12
hypotenuse = 20
Leg = 16
Dimensions of new triangle after dilatated by scale factor of 4:
Base = 48
hypotenuse = 80
Leg = 64
Area of right angled triangle:
Base × Leg/2
Area of given figure:
12 × 16/2
12 × 8
96
Area of given figure is 96cm²
Area of figure after dilation:
48 × 64/2
24 × 64
1536
Area of figure after dilation is 1536cm².
Perimeter of right angle triangle:
Perimeter of given figure:
12 + 20 + 16
48
Perimeter of given right angle triangle is 48.
Perimeter of dilated figure:
48 + 80 + 64
192
Perimeter of dilated right angle triangle is 192.
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√196b^12 simplest form
The simplest form of the given expression, √196b^12, is 14b⁶
Simplifying an expression to its simplest formFrom the question, we are to simplify the given expression to its simplest form
The given expression is
√196b^12
The given expression can be written as ]
√196 × √b^12
14 × √b^12
From one of the laws of indices, we have that
√x^y = x^(y/2)
Thus, the expression becomes
14 × b^(12/2)
14 × b^6
14 × b⁶
14b⁶
Hence, the simplest form is 14b⁶
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What are the next numbers in the series 1, 2, 3, 0, 1, 2, -1
The next numbers in the series will be 0,1,-2,-1,0,-3,-2,-1........
What is number Series?This refers to a pattern of arranging numbers. In the number series problems, we will have to make the rules that result in the formation of a number series.
From the question:
1, 2, 3, 0, 1, 2, -1
The pattern is:First value plus one, second value plus one, Third value minus three. Then the pattern starts afresh again.
Calculating the pattern we have:1 +1 = 2
2 + 1 = 3
3 -3 =0
0+1 = 1
1 + 1 = 2
2 -3 =-1
-1 + 1 =0
0 + 1 =1
1 - 3 = -2
-2 + 1 = -1
-1 + 1 = 0
0 -3 = -3
-3 + 1 = -2
-2 + 1= -1
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Help me with this maths question please
The sales of raincoats next month is 140.
What is Correlation?A statistical measure known as correlation expresses how closely two variables are related linearly (meaning they change together at a constant rate). By examining how the variables vary in relation to one another, correlation evaluates the association or relationship between two variables. Simultaneous changes in two variables are also described by statistical correlation, which is typically illustrated by linear relationships.
Given:
As, from the figure The type of correlation is Positive correlation.
and, when x= 70 the value of y is 140.
So, the sales of raincoats next month is 140.
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Select the number line that shows the two ooposite numbers have a sum of 0.Select the number line that shows the two ooposite numbers have a sum of 0. PLEASE HELP !!!
The number line that shows the two opposite numbers have a sum of 0 is option B.
What is number line?
A number line is a visual representation of numbers on a straight line. This line is used to compare numbers that are placed at equal intervals on an infinite line that extends on both sides, horizontally or vertically.
The number line that shows the two opposite numbers have a sum of 0.
Here,
A) 0+1=1
B) -3+3=0
C) 0+2=2
D) -5+0=-5
Hence, the number line that shows the two opposite numbers have a sum of 0 is option B.
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1/3x+ 1/3y=–9/5
in standard form
helpp
David has a hose that is 27 ft long. He wants to cut it into two pieces is 3 ft more than 2 times the length of the shorter piece
Answer: The shorter piece is 8 ft and the longer piece is 19 ft.
Step-by-step explanation:
Let x be the shorter piece. We will write an equation that represents the original problem to help us solve.
27 ft = x + (2x + 3)
Now, we will solve this equation.
27 ft = x + (2x + 3)
27 ft = 3x + 3
24 ft = 3x
8 ft = x
The shorter piece is 8 ft long.
Then, we will use substitution for the longer piece.
2x + 3
2(8) + 3
19
The longer piece is 19 ft long.
To do a rough check of our work, 19+8=27 ✓
playerxa
ics Level 1 (FSMO107) (Practice)
12
16
19 20
23 24
<12/24
Last year the animal rescue centre rescued 2520 dogs and cats in the ratio of 3:2.
This year the number of dogs rescued has increased by 15%.
How many dogs have been rescued this year?
Show your calculations and/or workings out in the box on the right hand side.
5 marks
Win
The dogs rescued this year were 1738.
What is ratio?A ratio is a way to show a relationship or compare two numbers of the same kind. We use ratios to compare things of the same type.
Given that, Last year the animal rescue centre rescued 2520 dogs and cats in the ratio of 3:2. This year, the number of dogs rescued has increased by 15%.
Let the number of dogs and cats be x,
3x+2x = 2520
5x = 2520
x = 504
The number of dogs were = 3*504 = 1512
This year, 1512*115/100 = 1738.8
Hence, The dogs rescued this year were 1738.
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Which expressions are equivalent to (18^5)^3/8?
Select all that apply.
Answer:
It is a little hard to read. I cannot read the last choice,. but the two above it are correct
Step-by-step explanation:
When you raise an exponent to an exponent, you multiply the exponents
[tex]18^{\frac{15}{8} }[/tex]
[tex]18^{5x\frac{3}{8} }[/tex]
The population of a town has been decreasing since 1991. The population of the town was 26,700 people in the year 1995. In the year 2003, the population of the town had decreased to 20,300 people.
Find the linear function
P=mt+b that models the town's population, P, as a function of the number of years, t, since 1991.
Find a reasonable domain for the function P
Domain:
Find a reasonable range for the function P
Range:
In what year will the population of the town be 14,700?
Year: ?
The linear function is P=-800(t)+1622700 where P and t are population and years respectively.
Domain of P is (1991, 1992, 1993, ............)
Range of P is (29900, 29100, 298300, .........)
In 2010 there will be 14,700 population
How do you determine a domain's and range's?
How Can I Determine an Equation's Domain and Range? In order to identify the values of the independent variable x and acquire the domain, we simply solve the equation y = f(x). Simply put, x=g(y) will calculate the function's range after we identify g's domain (y).
Given that
In 1995 there will be 26700 population and in 2003 there will be 20300 population
So in above statement we can form 2 linear equations
26700=m(1991)+b
20300=m(2003)+b
by this we can solve for m and b
m = -800
b= 1622700
By this now we can find the year for population of 14700
14700 = -800(t)+1622700
t = 2010
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a.5+6+7....+95
b.5+7+9....+95
The sum of n terms of expression a is 4940 and b is 9405.
a.
5+6+7....+95
d = 6 - 5
d = 1
This expression is in arithmetic progression.
a = 5
n = 95
sum of n terms = n/2(2a+(n-1)d)
= 95/2(2*5+(95-1)1)
= 95/2(10+94)
= 95/2*104
= 95*52
= 4940.
b.
5+7+9....+95
d = 7 - 5
d = 2
This expression is in arithmetic progression.
a = 5
n = 95
sum of n terms = n/2(2a+(n-1)d)
= 95/2(2*5+(95-1)2)
= 95/2(10+94*2)
= 95/2*188+10
= 95/2*198
= 95*99
= 9405.
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Alexander is drawing a map of the Federal Triangle in Washington, D.C. The actual Federal Triangle has a base of 300030003000 feet and height of 120012001200 feet. Alexander needs his drawing to fit on his paper, so he decides to make the base of his triangle 101010 inches.
1. What scale is Alexander using?
2. What is the height of Alexander's triangle in inches?
Alexander is utilizing a scale of 1 inch : 300 feet for his map.
The Alexander's triangle has a height of 4 inches in inches.
How to determine the map's scaleWhen comparing the initial dimensions as used by alexander, the scale of the map may be determined.
The scale is 1 inch: 300 feet since he used 10 inches to symbolize 3000 feet, this is gotten by diving both sides by 10
Using the scale factor 1 inch: 300 feet, the height of 1200 feet would be.
300 feet per inch, then ? inch is 1200 feet
? * 300 = 1200 * 1
? = 1200 / 300
? = 4 inches
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Help! My friend and I can't figure this out!
Answer:
if F = Gm^1(m^2)d^-2 is the formula for this question, the answer to question A. would be: G = 6.67 x 10^17 N KG^2/KM^2
Step-by-step explanation:
Brainliest Please?
Leo deposit at $7671.12 in an account that earned 2.5% interest compounded weekly for 13 years after 13 years how much had Leo earned an interest
The amount that Leo has earned as interest, given the amount that Leo deposited, and the compounding period, is $2, 945.12
How to find the interest earned?First, find the weekly rate on the account:
= Annual rate / Number of weeks in a year
= 2.5 % / 52
= 0.048 %
The number of periods is:
= Number of years x Weeks per year
= 13 x 52
= 676 weeks
The amount that Leo would have earned after 13 years is:
= Deposit x ( 1 + rate) ^ number of periods
= 7, 671.12 x ( 1 + 0.048%) ⁶⁷⁶
= $10, 616.24
The interest earned is:
= Amount earned - Amount deposited
= 10, 616.24 - 7, 671.12
= $2, 945.12
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Evaluate the expression for the given values.2W+2L; W=3 and L=11
Answer:
28
Step-by-step explanation:
W = 3; L = 11
2W + 2L = 2(3) + 2(11) = 6 + 22 = 28
Answer:
28
Step-by-step explanation:
2(3)+2(11)
6+22
28
Hopes this helps please mark beainliest
