Answer:
[tex]y=\frac{4}{3}x+\frac{38}{3}[/tex]
Step-by-step explanation:
So we want to find an equation of a line passing through (-8,2) with a slope of 4/3.
To do so, we can use the point-slope form. This is:
[tex]y-y_1=m(x-x_1)[/tex]
So, substitute (-8,2) for x₁ and y₁, and let m be 4/3:
[tex]y-2=\frac{4}{3}(x+8)[/tex]
Distribute the right:
[tex]y-2=\frac{4}{3}x+\frac{32}{3}[/tex]
Add 2 to both sides. Note that 2 can be written as 6/3. Thus:
[tex]y=\frac{4}{3}x+\frac{32}{3}+\frac{6}{3}[/tex]
Simplify:
[tex]y=\frac{4}{3}x+\frac{38}{3}[/tex]
And this is our equation :)
Express 4/5 in
a) percentage
b) decimal
c)decimal
Answer:
4/5 = 80/100 = 80%
4/5 = 0.8
The position of an object in circular motion is modeled by the given parametric equations. Describe the path of the object by stating the radius of the circle, the position at time t = 0, the orientation of the motion (clockwise or counterclockwise), and the time t that it takes to complete one revolution around the circle.
x = 4 cos 3t, y = 4 sin 3t
How do you get to that solution?
Answer:
4 units ; counter clockwise ; 2.09 units
Step-by-step explanation:
Given the following :
x = 4 cos 3t
y = 4 sin 3t
The Radius (r) could be obtained using Pythagoras:
R = √(x^2 + y^2)
R = √[(4cos3t)^2 + (4sin3t)^2]
R = √[16cos^(2)3t + 16sin^(2)3t]
Recall : cos^2θ + sin^2θ = 1
Therefore, cos^(2)3t + sin^(2)3t= 1
Where, 3t stands for θ
R = √[16cos^(2)3t + 16sin^(2)3t]
Factorizing:
R = √16[cos^(2)3t + sin^(2)3t)]
R = √16[1]
R = √16
R = 4 units
Position at time t = 0
x = 4 cos 3(0)
x = 4 cos 0
x = 4 * 1 = 4 units
y = 4 sin 3t
y = 4 sin 3(0)
y = 4 * sin 0
y = 0
Position at t = 0;
(x, y) = (4, 0) = counterclockwise
Time taken to complete 1 complete revolution:
2π/3 = 6.2831853 /3 = 2.0943951
= 2.09
A model plane has a scale of 1 in: 6 yd. If
the model plane is 3 in tall then how tall is
the real plane?
Answer:
18 yards
Step-by-step explanation:
Let's set up a proportion using the following setup.
inches / yards = inches / yards
We know the scale is 1 inch to 6 yards.
1 inch / 6 yards = inches / yards
We know the model plane is 3 inches tall, but we don't know how tall the real plane is. Therefore, we can it is 3 inches to x yards.
1 inch / 6 yards= 3 inches / x yards
1 /6= 3/x
Cross multiply. Multiply the numerator of the first fraction by the denominator of the second. Then, multiply the denominator of the first by the numerator of the second.
1*x= 6*3
1x= 6*3
x= 6*3
x=18
x= 18 yards
The real plane is 18 yards.
20 points, I HAVE SCHOOL IN 1 HOUR PLEASE HELP, ONLY 2 QUESTIONS,
1. use distributive property to simplify the expression 7(6x + 1)
2. Simplify the expression 4 + ( 14 + x )
Answer:
[tex]\Huge \boxed{42x+7} \\ \\ \\ \Huge \boxed{x+18}[/tex]
Step-by-step explanation:
Part 1:
[tex]7(6x + 1)[/tex]
Distribute 7 to the terms in the brackets.
[tex]7(6x)+7(1)[/tex]
[tex]42x+7[/tex]
Part 2:
[tex]4+(14+x)[/tex]
Removing brackets.
[tex]4+14+x[/tex]
Combining like terms.
[tex]18+x[/tex]
Select the correct answer.
What are the domain and range of this function?
(x + 3)² - 5
A Domain: (0o,00)
Range (-00,00)
Domain: (-5,00)
Range: (-5,00)
C. Domain: (-0,00)
Range: (-5,00)
D. Domain: (-5,00)
Range: (-00,00)
Reset
Next
Answer:
Domain: [tex](-\infty,\infty)[/tex]
Range: [tex][-5,\infty)[/tex]
C
Step-by-step explanation:
Please refer to the graph.
Recall that the domain is the span of x-values covered by the graph, while the range is the span of y-values covered by the graph.
So we have the equation.
[tex]y=(x+3)^2-5[/tex]
This is a quadratic.
The domain of a quadratic is all real numbers. If you look at the graph, we can also see that the x-values will go on infinitely in both direction.
In interval notation, this is:
[tex](-\infty,\infty)[/tex]
For the range, note that the lowest the parabola goes is y=-5.
Therefore, our range is all values greater than or equal to -5.
In interval notation, this is:
[tex][-5,\infty)[/tex]
Note that we use brackets for the -5 because it is included in our range.
So, our answer is C
Answer:
Step-by-step explanation:
the domain and range of y = (x+3)^2 - 5
Doman: (-∞,∞). {x|x∈R}
Range:{-5,∞),{y|y≥-5}
the solution is C
A Women making $29 an hour gets a 15% raise. How much money will she make after 4 hours of working with the increased hourly pay?
Answer:
$133.40
Step-by-step explanation:
First you have to find 15% of 29 which is 4.35. The way I figured this out was 10% of 29 is 2.9 and 5% of 29 is 1.45 and 2.9 + 1.45 = 4.35.
Then you want to add 4.35 to 29 which equals 33.35, her new hourly pay. Multiply 33.35 by the 4 hours she is working and you end up with $133.40.
Which numbers are factors of 42? Check all that apply.
1
2
3
6
8
Answer:
1, 2, 3, 6
Step-by-step explanation:
Find AB if AC = 6x-2 AB= 2x+12 BC =3x
Answer:
AB = 40 units
Step-by-step explanation:
Given:
AC = 6 x - 2
AB = 2 x + 12
BC = 3 x
Find:
AB
Computation:
Assume, AC is a straight line
So,
AC = AB + BC
6 x - 2 = 2 x + 12 + 3 x
6 x - 5 x = 14
x = 14
AB = 2 x + 12
AB = 2 (14) + 12
AB = 40 units
Miguel runs 7 miles in 60 minutes. At the same rate, how many miles would he run in 24 minutes?
Answer:
We use the rule of three
7 miles ---------------> 60 minutes
So x ------------------> 24 minutes
So x= (24 minutes × 7 miles )/60 minutes .
We simplify by 《minutes》 because it's in the numerator and the denominator .
So x= (24×7 miles )/60
x = 168 miles /60
x=2,8 miles
So Miguel runs 2,8 miles in 24 minutes.
36 1 3 2. 13 = 20
Order of operations
Answer: (36 - 1) ÷ (3 + 2) + 13 = 20
Step-by-step explanation:
PEMDAS rule calls for parenthesis to be solved first, then exponents, then multiplication or division then addition or subtraction depending on which comes first in the equation.
Using the PEMDAS rule the 20 can be gotten to if the equation is expressed as follows;
(36 - 1) ÷ (3 + 2) + 13 = 20
The parenthesis will be solved first;
35 ÷ 5 + 13 = 20
The division will be done first;
7 + 13 = 20
Then the addition;
7 + 13 = 20
Use the commutative law of multiplication to write an expression equivalent to: (5x)y.
Answer:
(5y)x
Step-by-step explanation:
the commutative law of multiplication=ab=ba, a(bc)=c(ab)
(5x)y=(5y)x=5(xy)
A. 3^2+2x8
—————
16-11
B. (32x1/2+6)-(4-1)
C. ((8-10.3)+2^3-5)
Answer:
=3²+2×8
=9+2×8
=9+16
=25
PROVED!!
A survey reported that 40% of people save loose change to pay bills. The margin of error was given as 3.1 percentage points. Which confidence interval corresponds to the given information
Answer:
0.369≤[tex]\mu[/tex]≤0.431Step-by-step explanation:
The confidence interval boundaries is represented mathematically as shown below;
CI = p±E where;
p is the percentage of people surveyed
E is the margin of error
Given parameters
p = 40% = 0.4
E = 3.1% = 0.031
Required
Confidence interval corresponds to the given information.
Substituting the given parameters into the given formula:
CI = p±E
CI = 0.4±0.031
CI = (0.4-0.031, 0.4+0.031)
CI = (0.369, 0.431)
Hence the confidence interval that corresponds with the information is 0.369≤[tex]\mu[/tex]≤0.431.
Thomas’s gross salary in 2017 was $68,000. If he qualifies for an $8,350 exemption when filing his taxes, how much does he owe for the year in federal income taxes? (Section 4.6 and 4.7) (1 point)
Answer: $14,912.5
Step-by-step explanation:
given data:
thomas salary in 2017 = $68,000
exemption = $8,350
solution:
thomas taxable income
= salary in 2017 - tax exemptions
= $68,000 - $8350
= $59,560
federal income tax = 25%
= 0.25 * $59,560
= $14,912.5
thomas Owe’s $14,912.5 in federal Income tax at the end of the year.
According to the National Center for Health Statistics, in 1990, 28% of babies in the United States were born to parents who were not married. Throughout the 1990s, this increased by approximately 0.6% per year. If this trend continues, in which year will 49% of babies be born out of wedlock
Answer:
2029
Step-by-step explanation:
We can write an equation:
0.28+0.006x=0.51
A few things explained:
The constant 0.28 comes from the fact in 1990, 28% of babies were born to parents who were not married. 28%=0.28
0.006 represents 0.6% and x represents the number of years will pass until 49% of babies will be born out of wedlock
0.51 represents 51%. 51% represents the percentage of babies who will be born to parents not married (100% - 49%=51%). You want to use 51% instead of 49% because the right side represents the babies born to parents not married.
We can solve the equation:
0.28+0.006x=0.51
0.006x=0.23
x=38.33
Since you can't have 38.3333 years, we'll say that 39 will pass until 49% of babies are born out of wedlock.
So, we add 39 years to 1990.
1990+39=2029
Hope this helps!
Combine the like terms to create an equivalent expression: \large{-4p+(-2)+2p+3}−4p+(−2)+2p+3
Answer:
-2p+1
Step-by-step explanation:
-4p+2p+(-2)+3
-2p+1
The equivalent expression of the expression {-4p+(-2)+2p+3}−4p+(−2)+2p+3 is -4p+2.
What is expression?An expression is a combination of numbers, variables, function, indeterminants, symbols like addition, multiplication, subtraction and division. It is not usually present in equal to form.
How to create equivalent expression?We have been given one expression {-4p+(-2)+2p+3}−4p+(−2)+2p+3 and we have to find the equivalent expression by solving the expression.
First we need to put appropriate signs by solving brackets and the expression will look like after opening brackets and after opening of brackets the signs may change:
=-4p-2+2p+3-4p-2+2p+3
=-4p+2p-4p+2p-2+3-2+3
=-4p+2
Hence the equivalent expression of {-4p+(-2)+2p+3}−4p+(−2)+2p+3 is -4p+2.
Learn more about expressions at https://brainly.com/question/723406
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15.2, 3,6,11,18, ...
Describe the pattern. Then write the next three numbers
Answer:
27, 38, and 51
Step-by-step explanation:
3, 6, 11, 18, ...
We increase the first number by 3. Then 5. Then 7.
The pattern is that the difference increases by 2.
That means this is a quadratic sequence.
y = x² + 2, where x = 1, 2, 3, etc.
The next three numbers are 27, 38, and 51.
Steve rides his bike at a rate of 1760 feet per minute. What is his rate in miles per hour?
Answer:
The answer is 19.36 miles per hoursStep-by-step explanation:
this problem is a unit conversion problem
In this problem, we are expected to convert from feet/min to miles per hour
given that the rate is 1760 feet per minute
from tables, we are given that
1 foot per minute is 0.011 miles per hour hence
1760 feet per minutes will give x miles per hour
cross multiplying we have
x= 1760*0.011
x= 19.36 miles per hours
Find the value of ab when a=5/12 and b=1/3
Step-by-step explanation:
When two letters are right next to each other, you multiply them. Since a and b are next to each other, we multiply them together.
[tex]A=\frac{5}{12}[/tex]
[tex]B=\frac{1}{3}[/tex]
To multiply fractions, you place them next to each other and multiply across.
[tex]\frac{5}{12}*\frac{1}{3} \\5*1=5\\12*3=36[/tex]
Our final answer: [tex]\frac{5}{36}[/tex] (we cannot simplify it any further)
For 5 days Lydia studied math for a certain amount of time and read for 15 minutes each day Represent the total amount of time Lydia studied and read over the 5-day period.
Since Lydia studied for 5 days
Then it will be 5*15=75 minutes in 5 days
Starting with x = 0.773, express x as a fraction in simplest form.
Answer:
773/1000
Step-by-step explanation:
[tex]x = 0.773 \\ \\ x = \frac{773}{1000} \\ [/tex]
0.000000000009256 scientific method
Answer:
9.256×10^−12
Step-by-step explanation:
to get standard notation we have a number less ten.
since it is a very small number it has a negative exponent
7/9 x 1/2 =
what’s the answer guys
Answer:
0.388
Step-by-step explanation:
7/9 x 1/2 = 0.388
Does anyone know this? Need it ASAP
Answer:
D) P = 80 feet, A = 360 square feet
Step-by-step explanation:
Perimeter=15+20+17+8+20=80 feet
Area=(15*20)+(1/2*8*15)=300+60=360 square feet
At the market, Joey buys 3 avocados for $0.40 each and 5 lemons for $0.40 each. The cashier in training rings up 3 × 0.40 and then 5 × 0.40 to get the total. The experienced cashier says to add the 3 plus 5 in his head and then ring up 8 × 0.40.
What property says that these two totals would be the same?
multiplicative identity
associative property of multiplication
distributive property
commutative property of multiplication
Answer:
Distributive property
Step-by-step explanation:
3*$0.40 + 5*$0.40 = (3+5)*$0.40
Distributive law, in mathematics, the law relating the operations of multiplication and addition, stated symbolically, a(b + c) = ab + acAccording to distributive property multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together.answer is distributive property
Step-by-step explanation:
hope this answer helps :)
$325.50 of 30% what is the price
8-|21 - 13 - 9| -| -4|
Answer:
8-1-4=8-1-4=3
Step-by-step explanation:
Order of operations: solve inside the absolute value first. 21-13-9=8-9=-1. The absolute value of -1 is 1.
write each ratio statement as a fraction and reduce to lowest terms if possible.(i)18 to 24 (ii)5 to 15 (iii)14:42 (iv) 15 cents to 18 cents.
Answer:
i) 3/4
ii) 1/3
iii) 1/3
iv) 5/6 cents
Step-by-step explanation:
Any ratio can be written as a fraction.
For example 3:4 can be writen as 3/4 or 14:42 as 14/42.
After you convert them to fractions you then simplify them by finding their highest common factor (HCF) and then divide both numerator and denominator by the HCF. When you cant simplify the fraction anymore, that is the fraction in its lowest terms.
A school newspaper decides to survey all the students enrolled in a gym class to determine the percentage of these students who are
also on the football team. What is the population of this study?
A. students who take gym class
B. students who take gym class and are on the football team
C. all students in the school
D. students who are on the football team
Answer:
A sudents who take gym class
Step-by-step explanation:
the survey only asks for all the students enrolled in a gym class so they can compare with the data for all the students enrolled in the football team
Answer:
a
Step-by-step explanation:
How much money did she earn?
Answer:
$160, basic multiplication ^^
Step-by-step explanation:
20×8=160
Answer:
$20 x 8
=$160
Multiplication
Hope it helped u if yes mark me BRAINLIEST pzllzllzl