The values of the variables t and k are 33 and 21, respectively.
We are given a system of two equations. The equations are linear in nature. Each equation represents a straight line. We need to find the solution to the system of linear equations. The coordinates of the intersection point of the straight lines are the solution. The equations are given below.
t - k = 12
3t + 2k = 141
We will substitute the value of t from the first equation into the second equation.
t = 12 + k
3t + 2k = 141
3(12 + k) + 2k = 141
36 + 3k + 2k = 141
5k = 105
k = 21
We will substitute the value of k into the first equation to find the value of t.
t = 12 + k
t = 12 + 21
t = 33
Hence, the values of t and k are 33 and 21, respectively.
To learn more about variables, visit :
https://brainly.com/question/22277991
#SPJ1
-6.6 < 1.7 + u Solve the inequality for u.
Simplify your answer as much as possible.
Solving the inequality -6.6 < 1.7 + u for u, the solution is simplified as: u > -8.3 or -8.3 < u.
What is an Inequality?In maths, an inequality is defined as a statement that is used to compare two quantities that are unequal. For example, we can state that 5 is greater than 3 + 1, or 5x is less than 4x + 3x. We can equally state that a given value of a variable can be equal to or greater than a number, and so on.
Basically, we are comparing two unequal quantities when we state inequalities.
Given the inequality, -6.6 < 1.7 + u, we are asked to solve the inequality for u. That is, we need to find the possible value that u represents in the inequality or that would make the inequality true.
Therefore:
-6.6 < 1.7 + u
Subtract 1.7 from both sides
-6.6 - 1.7 < 1.7 + u - 1.7 [subtraction property of equality]
-8.3 < u
It can be rewritten as:
u > -8.3
Learn more about inequality on:
https://brainly.com/question/11613554
#SPJ1
A ubmarine travel 4. 2 km due Eat from it bae and then turn and travel due North for 6. 5 km. How far away i the ubmarine from it bae?
Give your anwer rounded to 1 DP
The Submarine is 7.74 Km away from its base .
In the question ,
it is given that ,
the distance travelled by Submarine from base in East direction = 4.2 Km
let the distance from base to east direction be denoted by AB ,
that means AB = 4.2 Km
the distance travelled by Submarine from East to North direction = 6.5 Km
let the distance from east to north direction be denoted by BC .
that means BC = 6.5 Km
the given situation form a right triangle ,
So , the distance from submarine to its base is the hypotnuse of the right triangle , that is AC .
So By Pythagoras Theorem ,
AC² = AB² + BC²
Substituting the values , we get
AC² = 4.2² + 6.5²
AC² = 17.64 + 42.25
AC² = 59.89
AC = √59.89
AC = 7.7388
AC = 7.74
Therefore , The Submarine is 7.74 Km away from its base .
The given question is incomplete , the complete question is
A Submarine travel 4. 2 km due Eat from it base and then turn and travel due North for 6. 5 km. How far away is the submarine from it base ?
Learn more about Pythagoras Theorem here
https://brainly.com/question/21926466
#SPJ4
An animal shelter wants to track its profit for each animal that is
adopted. Each animal costs $65 dollars to adopt. What is the
equation for the proportional relationship?
The equation for the proportional relationship is y = 65x
The animal shelter wants to track its profit for each animal that is
adopted.
The cost of each animal adoption = $65
Consider the number of animal adoption = x
Consider the total profit from animal adoption = y
From the given the details, we can say that the profit from the animal adoption is directly proportional to the number of animal adoption,
Then the relationship will be
y ∝ x
y = kx
Here the cost of each animal adoption is k = 65
Then the equation will be
y = 65x
Hence, the equation for the proportional relationship is y = 65x
Learn more about proportional relationship here
brainly.com/question/12917806
#SPJ1
Please help me please i beg you can someone tell me if my answer is right or not
Answer:
Absolutely correct. you got the answer
rita and tina each make 11$ an hour
The expressions that represent the total weekly wages of Rita is 11r + 32 and of Tina is 11t.
We are given;
Rita and Tina each make $11 an hour working as cashiers at a supermarket.
Last week, Rita worked r hours while Tina worked t hours.
Rita also worked overtime hours during the week, for which she was paid an extra $32 flat wage.
We need to find the expressions that represent the total weekly wages of both Rita and Tina.
Let us form an algebraic expression for both one by one;
For Rita:
Number of hours Rita worked for = r
Cost per hour = $ 11
The amount for overtime Rita earned = $32
So, the equation expressing the total weekly wage for Rita = 11r + 32.
For Tina :
Number of hours Tina worked for = t
Cost per hour = $ 11
So, the equation expressing the total weekly wage for Tina = 11t.
Thus, the expressions that represent the total weekly wages of Rita is 11r + 32 and of Tina is 11t.
To learn more about algebraic expression visit:
https://brainly.com/question/28884894
#SPJ1
f(x)=x² + 6x + 2; Find f(-6)
Answer: 2
Step-by-step explanation:
if you plug in -6 into x, we get
36 - 36 + 2
the 36s will cancel each other out, leaving us with only 2 as our final answer.
Answer: -70
Step-by-step explanation:
-[tex]6^{2}[/tex] + 6(-6)+2
= -36 - 36 + 2
= - 70
Solve the equation.
x-2/5=2/3-3x-2/6
Answer:
11/48
Step-by-step explanation:
x-2/5=2/3-3x-2/6
collect like terms
x-2/5 + 3x = 2/3 - 2/6
taking LCM on both sides
[(x-2) + 5(3x)]/5 = [2(2) -2]/6
(16x - 2)/5 = 2/6
cross multiply
6(16x - 2) = 5(2)
96x - 12 = 10
96x = 22
therefore; X = 22/96
= 11/48
CHECK:
(11/48 - 2)/5 = 2/3 - 3(11/48) - 2/6
(-85/48)/5 = 2/3 - 11/16 - 2/6
-85/48 × ⅕ = -17/48
-17/48 = -17/48
Answer:
[tex]x=\frac{11}{60}[/tex]
Step-by-step explanation:
Given the equation
[tex]x-\frac{2}{5}=\frac{2}{3}-3x-\frac{2}{6}[/tex]
Lets solve for x.
Simplify the right side of the equation.
Cancel the common factor of 2 and 6 .
Factor 2 out of 2 .
[tex]x-\frac{2}{5}=\frac{2}{3}-3x-\frac{2(1)}{2(3)}[/tex]
[tex]x-\frac{2}{5}=\frac{2}{3}-3x-\frac{1}{3}[/tex]
Combine the numerators over the common denominator.
[tex]x-\frac{2}{5}=-3x-\frac{2-1}{3}[/tex]
[tex]x-\frac{2}{5}=-3x-\frac{1}{3}[/tex]
Move all terms containing x to the left side of the equation.
Add [tex]3x[/tex] to both sides of the equation.
[tex]x-\frac{2}{5}+3x=\frac{1}{3}[/tex]
Add [tex]x[/tex] and [tex]3x[/tex].
[tex]4x-\frac{2}{5}=\frac{1}{3}[/tex]
Move all terms not containing x to the right side of the equation.
Add [tex]\frac{2}{5}[/tex] to both sides of the equation.
[tex]4x=\frac{1}{3}+\frac{2}{5}[/tex]
To write [tex]\frac{1}{3}[/tex] as a fraction with a common denominator, multiply by [tex]\frac{5}{5}[/tex] .
[tex]4x=\frac{1}{3}*\frac{5}{5} +\frac{2}{5}[/tex]
To write [tex]\frac{2}{5}[/tex] as a fraction with a common denominator, multiply by [tex]\frac{3}{3}[/tex]
[tex]4x=\frac{1}{3}*\frac{5}{5} +\frac{2}{5}*\frac{3}{3}[/tex]
Simplify.
Write each expression with a common denominator of 15 , by multiplying each by an appropriate factor of 1 .
[tex]4x=\frac{11}{15}[/tex]
Divide each term in [tex]4x=\frac{11}{15}[/tex] by 4 and simplify.
[tex]x=\frac{11}{60}[/tex]
Graph the line with the given point and slope. the line through (0,0) with slope 6/5
Check the picture below.
What is the value of sin(A)?
Answer: 3/5
Step-by-step explanation:
Once such a triangle is chosen, the sine of the angle is equal to the length of the opposite side, divided by the length of the hypotenuse: The other trigonometric functions of the angle can be defined similarly; for example, the tangent is the ratio between the opposite and adjacent sides. As stated, the values and.
10. (Modeling) Height of a Projectile A projectile is fired vertically upward, and its
height s(t) in feet after t seconds is given by the function defined by
s(t) = -16t² + 800t + 600.
(a) From what height was the projectile fired?
(b) After how many seconds will it reach its maximum height?
(c) What is the maximum height it will reach?
(d) Between what two times (in seconds, to the nearest tenth) will it be more than
5000 ft above the ground?
(e) How long to the nearest tenth of a second will the projectile be in the air?
fuel
The answer is a) 0 height, b) 25 seconds c) 10,600 feet d) 3 times e) (x+1)(x-3)(x+5).
A projectile is fired vertically upward, and its height s(t) in feet after t seconds is given by the function defined by
s(t) = -16t² + 800t + 600.
To find out
(a) From what height was the projectile fired
Given height functions: s(t) = -16t² + 800t + 600
Now,
[tex]s^{'}(t)[/tex] - -32t+800
(b) Now, to find the time it will attain maximum height,
[tex]s^{'}(t)[/tex] = 0
-32t = -800
t = 25 seconds
(c) The maximum height it will reach
= [tex]-16*(25)^{2} + 800*25+600[/tex]
= -10000+20000+600
= 10,600 feet
(d) Between what two times (in seconds, to the nearest tenth) will it be more than 5000 ft above the ground
By putting x = 3
[tex]P(3) = 4*(3)^{3}-50 * (3)^{2}-8*3+6[/tex]
= 108-90-24+6
= 114-114
= 0
Therefore x = 3 is a zero of P(x)
(e) How long to the nearest tenth of a second will the projectile be in the air
Now, factoring,
[tex]f(x) = x^{3}+3x^{2} -13x-15\\ \\= x^{3}+x^{2} +2x^{2}+2x-15x-15\\ \\ = (x+1)(x^{2} +5x-3x-15)\\\\= (x+1)(x(x+5)-3(x+5))\\\\=(x+1)(x-3)(x+5)[/tex]
Hence the answer is a) 0 height, b) 25 seconds c) 10,600 feet d) 3 times e) (x+1)(x-3)(x+5)
To learn more about equations click here https://brainly.com/question/22688504
#SPJ9
What is the sum of the x-values that represent the solution for this system of equations?
1+2x=y
y=4x^2+6x−2
A discount of 25 % is allowed on an article marked at rs 17 500. calculate the discount
.
Answer: 4,375 rs
Step-by-step explanation:
25% × 17,500 = 4,375
Answer:
$4375
Step-by-step explanation:
25 percent *17500 =
(25:100)*17500 =
(25*17500):100 =
437500:100 = 4375
Now we have: 25 percent of 17500 = 4375
growth or decay, and determine the percentage rate of increase or decrease.
y
=
660
(
0.902
)
x
The expression y = 660(0.902)ˣ represents a decay , the rate of decrease is 9.8% .
In the question ,
it is given that ,
the the exponential function is y = 660(0.902)ˣ
we need to determine that , the equation represents a growth or decay .
0.902 is the variable that will determine a growth or decay .
Since, 0.902 is less than 1 , so it represents a decay function .
To find the rate we subtract 0.902 from 1
= 1 - 0.902
= 0.098
= 9.8% decrease rate
Therefore , The expression y = 660(0.902)ˣ represents a decay , the rate of decrease is 9.8% .
The given question is incomplete , the complete question is
Identify if it's Growth or Decay , and determine the percentage rate of increase or decrease , the function is y = 660(0.902)ˣ ?
Learn more about Growth and Decay here
https://brainly.com/question/22392518
#SPJ1
PLSS HELP AASP I NEED THIS LIKE RNN
Answer:
4/6 and 6/9
Put 6 in both the boxes as the both ratios will be equal to 2/3 if 6 is put.
Answer:
[tex] \frac{4}{6} \: and \: \frac{6}{9} [/tex]
Find the 8th term of the geometric sequence 10, -20, 40, ...
Answer:
a₈ = - 1280
Step-by-step explanation:
the nth term of a geometric sequence is
[tex]a_{n}[/tex] = a₁ [tex](r)^{n-1}[/tex]
where a₁ is the first term and r the common ratio
here a₁ = 10 and r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{-20}{10}[/tex] = - 2 , then
a₈ = 10 [tex](-2)^{7}[/tex] = 10 × - 128 = - 1280
The 8th term of geometric sequence is -1280
Step of calculate geometric sequence
This is a geometric sequence. The geometric number sequence is characterized by the presence of a ratio (the ratio between the next term and the previous term). The next term is the product of the previous term with the ratio. Another sequence called arithmetic sequence is characterized by the presence of difference (the difference between the next term and the previous term).
10, -20, 40, ...
We will first analyze the things that can be found in the three numbers in the sequence. The thing to look for is the first term (a) and also the ratio (r). The first term can also be written as U1, where the 2nd term is U2, and the n-th term is Un.
[tex]a = 10[/tex]
[tex]r=\frac{U2}{U1}[/tex]
[tex]r=\frac{-20}{10}[/tex]
[tex]r=2[/tex]
When the first term (U1) and ratio (r) have been obtained, then we can find the 8th term by substitute it in the formula.
[tex]Un=ar^{n-1}[/tex]
With that formula, let's find the 8th term.
[tex]U8=10(-2)^{8-1}[/tex]
[tex]U8=10(-2)^{7}\\U8=10(-128)\\U8=-1280[/tex]
Learn more about geometric sequence here: https://brainly.ph/question/5507726
#SPJ1
The histogram below shows information about the honey produced by some beehives in one year. 400 beehives each produced between 16 kg and 18 kg of honey. Use this information to work out the value of x on the frequency density axis. If your answer is a decimal, give it to 1 d.p.
The value of x on the frequency density axis is 200.
What is frequency?
The frequency of a repeated event is its number of instances per unit of time. In some cases, it is also referred to as temporal frequency or ordinary frequency to underline differences with spatial and angular frequencies, respectively.
What is density?
The mass of a substance per unit of volume is its density. Density is most frequently represented by the symbol, however, the Latin letter D may also be used.
Here, we have
x is about half of the number of beehives producing 16 to 18 kg of honey, for the middle blue bar.
x = half of 400
x = 200
Hence, The value of x on the frequency density axis is 200.
To learn more about the frequency from the given link
https://brainly.com/question/254161
#SPJ9
What is the expression in factored form?
5x² - 7x-6
O
(5x-2)(x-3)
(x + 3)(5x - 2)
O (5x + 3)(x - 2)
O (5x + 3)(x + 2)
Kareem correctly answered 85% of the questions on his last math test. If he missed 6 problems, how many questions were on the test
Answer:
40 questions
Step-by-step explanation:
100-85=15
15/100=6/x
cross multiply
15x=100(6)
15x=600
x=40
there were 40 questions on the test
hopes this helps please mark brainliest
Help thanks with d pls
At point 1, the carrying capacity is both the area is around 5, and therefore it can very well be said that growth rate in Area A is at a much higher pace than that of Area B. And that can subsequently be verified from the succeding graph.
What is Carrying Capacity?
The quantity of humans, other living species, or crops that a place can support without negatively impacting the environment is termed as carrying capacity.
To learn more about Carrying Capacity from the given link
https://brainly.com/question/14645317
#SPJ1
everyday a person uses about 90 liters of water at home 6 gallons is about 23 liters about how many liters of water does a person use at home daily?
The volume in liters a person uses daily is about 90 liters which is equivalent to 23.48 gallons
How to find the amount of water the person uses dailyInformation given in the question
everyday a person uses about 90 liters of water at home
6 gallons is about 23 liters
how many liters of water does a person use at home daily = ?
Volume is a three dimensional calculation, the formula depends on the object. how ever the calculation is usually done by area * height or thickness
the unit for volume can liters, gallons, cubic meters, and so on
The question have it that a person uses about 90 liters of water daily converting this quantity in gallon is done by
= 90 liters * 6 gallons / 23 liters
= 90 * 6 / 23
= 23.48 gallons
Learn more about volume calculation here:
https://brainly.com/question/12410983
#SPJ1
4x-4y=8
5x-3y = 18
Find X
Let's solve your system by substitution.
4x−4y=8 and 5x−3y=18
Step: Solve 4x−4y=8 for x:
4x − 4y = 8
4x − 4y + 4y = 8 + 4y (Add 4y to both sides)
4x = 4y + 8
[tex]\frac{4x}{4} = \frac{4y + 8}{4}[/tex]
x = y + 2
Step: Substitute y + 2 for x in 5x − 3y = 18:
5x − 3y = 18
5(y+2) − 3y = 18
2y + 10 = 18 (Simplify both sides of the equation)
2y + 10 + (−10) = 18 + (−10) (Add -10 to both sides)
2y = 8
y = 4
Step: Substitute 4 for y in x = y + 2:
x = y + 2
x=4+2
x=6 (Simplify both sides of the equation)
Answer:
x = 6 and y =4
A printing company calculates its costs using the function e(x) 0.3²-125x+100 and calculates its revenue using the function (x) -
function is p(x) r(x) - c(x)
Which function represents the company's profit?
A p(x)= 0.7x² + 35x + 190
B
(x) 0.7x² - 285x + 100
CP(x)= -0.7x² + 35x + 190
D p(x)= -0.7x² + 285x - 190
0.4x + 160x The company's profit
Answer:yes
Step-by-step explanation:
yes
I need help for #4 You have to find the slope and I missed a day at school and I am confused on what to do
Math trigonometry non right angle help please
guys please
Answer:
about 21.3 cm²
Step-by-step explanation:
Given a triangle with three sides 6 cm, 8 cm, and 12 cm, and smallest angle 26.4°, you want the area.
Area using sine formulaA = 1/2ab·sin(C)
A = 1/2(12 cm)(8 cm)·sin(26.4°) ≈ 21.34 . . . . square units
Area using Heron's formulaThe semiperimeter is ...
s = (6 +8 +12)/2 = 13
The area is ...
A = √(s(s -a)(s -b)(s -c))
A = √(13·(13 -12)(13 -8)(13 -6)) = √(13·1·5·7) = √455
A ≈ 21.33 . . . . square centimeters
The area of the triangle is about 21.3 cm².
__
Additional comment
The problem with over specifying the dimensions of a geometry problem is that it is often difficult to make them consistent. Here, the area values agree to three significant figures. That is about all we can expect, given the angle precision is 3 significant figures.
Your answer depends on the set of dimensions you choose to use. It will be different yet if you use the Law of Sines to find angle A or B for the Sine Formula, especially if you round the angle value to tenths.
The attachment shows the solution using side lengths only.
Once an antibiotic is given, number of bacteria decreases at a rate of 15% /day. There
were about 15,000 bacteria prior to the treatment. The graph models the number of
bacteria after x days of treatment.
W
What are the key features of the exponential function modeled in terms of this
situation and how can they be interpreted?
Asymptote indicates that as time increases, the number of bacteria approaches 0.
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
Given,
Once an antibiotic is given, number of bacteria decreases at a rate of 15% /day.
There were about 15,000 bacteria prior to the treatment.
The line y = 0 is an asymptote of the graph.
The y-intercept is 15,000.
The y-intercept represents the number of bacteria when treatment began.
The asymptote indicates that as time increases, the number of bacteria approaches 0.
Hence, asymptote indicates that as time increases, the number of bacteria approaches 0.
To learn more on Graph click:
https://brainly.com/question/17267403
#SPJ1
The distance between the school and the park is 6 km. There are 1.6 km in 1 mile.How many miles apart are the school and the park
Answer:
3.7miles
Step-by-step explanation:
divide the length value by 1.6
Uplift occurs at a rate of 0. 1 m per 1,000 years. How much will the uplift change over 1,000,000 years? responses 0. 1 m 0. 1 m 100 m 100 m 1,000 m 1,000 m 1,000,000 m.
As per given information about change in uplift it occurs at the rate of 0.1 m per 1,000 years then change in uplift over 1,000,000 years is equal to 100m.
As given in the question,
Rate of occurring of uplift is equal to 0.1m per 1000 years
Represent the given relation in equality form we get,
Change of uplift in 1000 years = 0.1 m
⇒ 1 year = 0.1 m / 1000
⇒ 1,000, 000 years = ( 0.1 m / 1,000 ) × 1,000, 000
⇒ 1,000, 000 years = ( 1 m / 10,000 ) × 1,000, 000
⇒ 1,000, 000 years = 100 m
Therefore, for given information about change in uplift it occurs at the rate of 0.1 m per 1,000 years then change in uplift over 1,000,000 years is equal to 100m.
Learn more about uplift here
brainly.com/question/6036848
#SPJ4
(a) a box contains 3 red balls, 2 white balls, and 5 black balls. two balls are drawn at random from the box (with replacement of the first before the second is drawn). what is the probability of getting a red ball on the first draw and a white ball on the second? (enter your probability as a fraction.)
Answer:2
Step-by-step explanation:i did it
A telecommunications company will be laying new fiber optic cables underground. One cable will be perpendicular to the road shown, passing through the point ( 7, 2 . At what point will the cable pass through the road?
The point at which this cable would pass through the road shown is at the y-intercept of (0, -17/2).
How to determine an equation and the point on this perpendicular line?Mathematically, the slope of a straight line can be calculated by using this formula;
Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope, m = (y₂ - y₁)/(x₂ - x₁)
By critically observing the road shown in the graph above, the points on the line include the following:
Points (x, y) = (0, -2)
Points (x, y) = (-3, 0)
Substituting the given points into the formula, we have;
Slope, m = (0 + 2)/(-3 - 0)
Slope, m = 2/-3
Slope, m = -2/3.
In Mathematics, a condition that must be met for two lines to be perpendicular is given by:
m₁ × m₂ = -1
-2/3 × m₂ = -1
-2m₂ = -3
m₂ = 3/2
At point (7, 2), a linear equation for the line can be calculated by using the point-slope form:
y - y₁ = m(x - x₁)
Where:
m represents the slope.x and y represent the points.c represents the y-intercept.Substituting the given points into the formula, we have;
y - 2 = 3/2(x - 7)
y - 2 = 3x/2 - 21/2
y = 3x/2 - 21/2 + 2
y = 3x/2 - 17/2
At the y-intercept of (0, -17/2), the cable pass through the road.
Read more on slope here: brainly.com/question/3493733
#SPJ1
If you are tossing a six-sided die, what is the probability of getting either a 1 or a 2 on your first toss and a 1 or a 2 on your second toss?.
A six sided dice is tossed twice. The probability of getting either a 1 or a 2 on your first toss and a 1 or a 2 on your second toss is 1/9 .
A dice has six faces or sides and it is throws twice . When a dice is toss first time,
Total possible outcomes on toss = 6 ={ 1,2,3,4,5,6}
In our first toss we want to get 1 or 2
So, favourable outcomes of getting 1 or 2 = 2
Probability of getting 1 or 2 on first toss= favourable cases /total outcomes = 2/6 = 1/3
For second toss, we want to get a1 or a2 again.
Total possible outcomes = 6
Probability of getting a1 or a2 on second toss= 2/6= 1/3
Now, Multiply these probsbilites togethers and chance of getting 1 or 2 on first and second which is 1/3× 1/3 = 1/9
Hence , probability of getting either a 1 or a 2 on your first toss and a 1 or a 2 on your second toss is 1/9.
To learn more about Probability , refer:
https://brainly.com/question/29312865
#SPJ4