Answer:
-10x - 6y
Step-by-step explanation:
simplify - 2(5x + 3y): - 10x - 6y
-2(5x + 3y)
Apply the distributive law: a(b + c) = ab + ac
-2(5x + 3y) = -2 · 5x - 2· 3y
simplify -2 · 5x - 2· 3y : - 10x - 6y
therefore the answer is: = -10x - 6y
Lucius has at most $80 to spend on clothes. He wants to buy a pair of jeans for $22 and spend the rest on t-shirts. Each T-shirt costs $15. How many shirts can Lucius buy?
Answer:
He can only buy 3 t-shirts
Step-by-step explanation:
80-22= 58
58-(15*3) = 13
This is a one step inequality can you help my find the answer I don't know how to do this X + 7 < 19
Answer:
X<12
Step-by-step explanation:
A pulley is turning at an angular velocity of 14.0 rad per second. How many revolutions is the pulley making each second? (Hint: one revolution equals 2 pi rad)
Answer:
7/π ≈ 2.23 revolutions per second
Step-by-step explanation:
You want the know the angular velocity in revolutions per second of a pulley turning at 14.0 radians per second.
Unit ConversionThe velocity in rad/s can be converted to rev/s using the conversion factor ...
1 rev = 2π rad
The angular velocity is ...
[tex]\dfrac{14\text{ rad}}{\text{s}}\times\dfrac{1\text{ rev}}{2\pi\text{ rad}}=\dfrac{14}{2\pi}\,\dfrac{\text{rev}}{\text{s}}=\boxed{\dfrac{7}{\pi}\text{ rev/s}\approx2.23\text{ rev/s}}[/tex]
At the lake, two companies are giving boat rides. At one booth a boat leaves every 12 minutes and at the
other booth a boat leaves every 18 minutes. In how many minutes will both boats be leaving at the same
time?
A) 6 minutes
B) 24 minutes
C) 36 minutes
C) 72 minutes
Answer:
Step-by-step explanation:B
Maple tree diameters in a forest area are normally distributed with mean 10 inches and standard deviation 2.2 inches. Find the proportion of trees having a diameter greater than 15 inches.
Given:
[tex]\begin{gathered} \mu=10\text{ }inches \\ \sigma=2.2\text{ inches} \end{gathered}[/tex]To find- P(X>15)
Explanation-
We know that a z-score is given by-
[tex]z=\frac{x-\mu}{\sigma}[/tex]where x is the raw score, mu is the mean and sigma is the standard deviation.
Hence, the proportion of trees having a diameter greater than 15 inches will be-
[tex]\begin{gathered} P(x>15)=P(\frac{x-\mu}{\sigma}>\frac{15-\mu}{\sigma}) \\ P(x>15)=P(Z>\frac{15-10}{2.2}) \end{gathered}[/tex]On further solving, we get
[tex]\begin{gathered} P(x\gt15)=P(Z\gt\frac{5}{2.2}) \\ P(x\gt15)=P(Z\gt2.2727) \end{gathered}[/tex]With the help of an online tool, the probability will be
[tex]P(x>15)=0.0115[/tex]Since the significance level is not mentioned, we assumed it is 0.05.
Thus, the proportion of trees having a diameter greater than 15 inches is 0.0115.
The answer is 0.0115.
1)What Miller is adding a room to the back of his house. For the foundation, 12 ft wide, & and 4 ft deep. How many cubic ft of soil have to be Removed?
We need to find the volume, the volume can be found as:
[tex]V=w\cdot l\cdot h[/tex]Where:
w = width = 12ft
l = length = 16ft
h = height = 4ft
so:
[tex]\begin{gathered} V=12\cdot16\cdot4 \\ V=768ft^3 \end{gathered}[/tex]He has to remove 768ft³ of soil
The weight of a bacterium is defined by multiplying the functions of f(x) and g(x). Given f(x) = 6x6 + 8x and g(x) = 2x. Which of the following represents the weight of the bacterium?12x6 + 16x12x7 + 16x2-12x7 - 16x23x5 + 4
Given the following functions:
[tex]\begin{gathered} f(x)=6x^6+8x \\ g(x)=2x \end{gathered}[/tex]The weight of a bacterium is defined by multiplying the functions of f(x) and g(x).
So, the product of the functions will be as follows:
[tex]f(x)*g(x)=(6x^6+8x)*2x[/tex]We will use the distributive property to find the result as follows:
[tex]\begin{gathered} f(x)*g(x)=6x^6*2x+8x*2x \\ f(x)*g(x)=12x^7+16x^2 \end{gathered}[/tex]So, the answer will be 12x⁷+16x²
What is the slope of the line?
Answer: 2
Step-by-step explanation: For every time it goes right 1 it goes up 2
Answer: 2
Step-by-step explanation:
Find two points, and then do rise/run. (0,-3) and (1,-1) are both points, so rise over run is 2/1, so your slope is 2
A school is planning a 4th grade field trip. There are 157 students and 9 teachers in the 4th gradeIf each bus holds 45 people, how many buses does the school need to make the field trip?Which of the following equations can be used to solve this problem?
Given:
A school is planning a 4th grade field trip. There are 157 students and 9 teachers in the 4th grade. Each bus holds 45 people.
Required:
To find the number of buses does the school need to make the field trip.
Final Answer:
There area total
[tex]\begin{gathered} =157+9 \\ =166 \end{gathered}[/tex]166 people.
Let the number of bus be x.
Each bus holds 45 people, therefore
[tex]\begin{gathered} 45x=166 \\ x=\frac{166}{45} \\ x=3.68 \\ x\approx4 \end{gathered}[/tex]Final Answer:
4 buses need to make the field trip.
. Amy's school is selling
tickets to a choral
performance. A senior
citizen's ticket is $6 and a
child's ticket is $15. If they
made $810 dollars and
sold a total of 72 child
and senior citizen tickets,
how many of each ticket
did they sell?
By solving the equation we know that Amy's school sold 30 tickets to seniors and 42 tickets to children.
What are equations?A mathematical statement called an equation includes the symbol "equal to" between two expressions with equal values. Consider the formula 3x + 5 = 15. Different types of equations exist, including linear, quadratic, cubic, and others. Any value of the variable that satisfies the equality, that is, makes the Left Hand Side (LHS) and the Right Hand Side (RHS) of the equation equal, is a solution of the equation. Finding an equation's solution or solution is known as solving the equation.So, let 's' represents seniors and 'c' represents children.
The equation is as follows:
6s + 15c = 810 - 6(s + c = 72)⇒ -6s - 6c = -432 (Cut s)Then,
9c = 378c = 378/9c = 42Then,
s = 72 - 42s = 30Therefore, by solving the equation we know that Amy's school sold 30 tickets to seniors and 42 tickets to children.
Know more about equations here:
https://brainly.com/question/2972832
#SPJ13
A fitness club offers two water aerobics classes. There are currently 40 people in the moming class and
attendance is growing at a rate of 2 people per month. The afternoon class has 22 members and is growing at
a rate of 8 people per month. In how many months will there be the same number of people in each class and
how many people will be in each class?
please help
Answer:
3 months
Step-by-step explanation:
You would set the equations = to each other to identify when they will be the same number of __. The equations to begin with is 40 + 2x and 22 + 8x, you would do 40 + 2x = 22 + 8x and algebraically solve for X, which is the months. so 18 = 6x, x = 3
QUESTION IN SCREENSHOT, FIRST PERSON MARKING BRANLIEST
The equation of a line in slope intercept form parallel to 6x + 5y = 11 and passes through (-2, -8) is y = (-6/5)x - (28/5)
What is an equation?An equation is an expression that can be used to show the relationship between numbers and variables.
The equation of a line in slope intercept form is:
y = mx + b
Where m is the slope and b is the y intercept
Two lines are parallel if they have same slope
Given a line:
6x + 5y = 11
5y = -6x + 11
y = (-6/5)x + (11/5)
The line parallel to 6x + 5y = 11 have a slope of -6/5. The line passes through (-2, -8), hence:
y - (-8) = (-6/5)(x - (-2))
y + 8 = (-6/5)x + 12/5
y = (-6/5)x - (28/5)
Find out more on equation at: https://brainly.com/question/2972832
#SPJ1
Compare the quantities in Column A and Column B Column A Column B The solutions of 4x - 30 2-3x + 12 The solutions (A) The quantity in Column A is greater. (B) The quantity is Column B is greater. (C) The quantities are equal. (D) The relationship cannot be determined from the inform
Column A:
[tex]4x-30\ge-3x+12[/tex]The solution will be as following :
[tex]\begin{gathered} 4x+3x\ge12+30 \\ 7x\ge42 \\ \frac{7x}{7}\ge\frac{42}{7} \\ \\ x\ge6 \end{gathered}[/tex]Column B:
[tex]\frac{1}{2}x+3<-2x-6[/tex]The solution will be as following :
[tex]\begin{gathered} \frac{1}{2}x+2x<-6-3 \\ 2\frac{1}{2}x<-9 \\ \frac{5}{2}x<-9 \\ \\ x<-9\cdot\frac{2}{5} \\ \\ x<-3.6 \end{gathered}[/tex]Compare the quantities in Column A and Column B
so,
[tex]x\ge6\text{ and x < -3.6}[/tex]So, the answer is option A) The quantity in Column A is greater.
Leila deposits the same amount of money into a bank account every month. The table below shows the amount of money in the account after different amounts of time.
To see how money is changing with respect to time, we will observe the time and money value differences between two periods.
At 6 months, there is $467
At 8 months, there is $557
We can see that within a two month increase, the amount of money has also increased.
We can observe the values for 10 and 12 months and see that these months are also asscociated with increased account values.
a)
Correct option: As the time increases the amount of money in the account increases.
Rate of increase:
r = (557-467)/2 =
$45 dollars per month.
We are asked to find the amount of money at time t= 0 months.
Since then, the amount in the account has increased 6 times. It has increased by $270.
b)
Therefore the account started with $197.
Determine the distance between the two points (-1,-9) and (4,-7)What is the midpoint of the line segment joining the pairs of Points.
The distance between two points (x₁,y₁) and (x₂,y₂) is given by the following formula.
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Then, we have:
[tex]\begin{gathered} (x_1,y_1)=(-1,-9) \\ (x_2,y_2)=(4,-7) \end{gathered}[/tex][tex]\begin{gathered} d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\ d=(4-(-1))^2+(-7-(-9))^2 \\ d=(4+1)^2+(-7+9)^2 \\ d=\sqrt{5^2+2^2} \\ d=\sqrt{25+4} \\ d=\sqrt{29} \\ d\approx5.4 \\ \text{ The symbol }\approx\text{ is read 'approximately'.} \end{gathered}[/tex]Finding the midpoint of the line segment joining the pointsThe midpoint of the line segment P(x₁,y₁) to Q(x₂,y₂) is:
[tex]\text{ Midpoint }=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]Then, we have:
[tex]\begin{gathered} \text{ Midpoint }=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}) \\ \text{ Midpoint }=(\frac{-1+4}{2},\frac{-9+(-7)}{2}) \\ \text{ Midpoint }=(\frac{3}{2},\frac{-16}{2}) \\ \text{ Midpoint }=(\frac{3}{2},-8) \end{gathered}[/tex]AnswerThe distance between the given points is √29 units or 5.4 units rounded to the nearest tenth.
The midpoint of the line segment that joins the pairs of points is (3/2,-8).
On a cold day the temperature is a certain change -34.08 over 4.8 hours what was the average change in temperature per hour 
The average change in temperature per hour is -7.1 degree/hour.
What is average rate of change? It is the average amount by which the function changed per unit throughout that time period.Divide the change in y-values by the change in x-values to find the average rate of change. The average rate of change is especially useful for determining changes in measurable values such as average speed or average velocity. Here are some examples of average rates of change: A bus travels at an average speed of 80 kilometers per hour. A lake's fish population grows at a rate of 100 per week. When the voltage in an electrical circuit drops by one volt, the current in the circuit drops by 0.2 amps.Given,
Change in temperature = -34.08 degree
Total time = 4.8 hours
Average change = -34.08 / 4.8
= -7.1 degree/hour
To learn more about average calculation, refer to:
https://brainly.com/question/20118982
#SPJ10
HELPPP please
Which of the following products is irrational?
Answer: B) 7 x π
Step-by-step explanation:
π is irrational since it doesn't have an end(yet)
At a particular restaurant, each slider bas 200 calories and each mini hotdog bas 100calories. A combination meal with mini hotdogs and sliders is shown to have 1200total calories and 4 times as many mini botdogs as there are sliders. Graphically solveagystem of equations in order to determine the number of sliders in the combinationmeal, 2, and the number of mini hotdogs in the combination meal, y.
x: the number of sliders in the combination meal
y: the number of mini hotdogs in the combination meal
Each slider has 200 calories and each mini hotdog has 100 calories. A combination meal with mini hotdogs and sliders is shown to have 1200
total calories, means:
200x + 100y = 1200
The combination meal has 4 times as many mini hotdogs as there are sliders, means:
y = 4x
Suppose the First Bank of Lending offers a CD (Certificate of Deposit) that has a 6.45% interest rate andis compounded quarterly for 3 years. You decide to invest $5500 into this CD.a) Determine how much money you will have at the end of three years.b) Find the APY.
In order to solve this, we have to use the compound interest formula given by the following expression:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Where r is the interest rate, P is the initial amount deposited, n the number of times the period is compounded a year, t the year, and A the final amount.
By replacing 0.0645 (6.45%) for r, 4 for n, 3 for t and 5500 for P into the above equation, we get:
[tex]A=5500(1+\frac{0.0645}{4})^{4\times3}=6663.8978[/tex]Then, after 3 years you will have $6663.9.
In order to determine the APY, we can use the following formula:
[tex]APY=100\times((1+r/n)^n-1)[/tex]Where n is the number of times the interest is compounded a year (4) and r is the rate of interest (0.0645), then we get:
[tex]APY=100\times((1+0.0645\/4)^4-1)=6.61[/tex]Then, the APY equals 6.61%
Find the slope of the line that goes through the points (2,-6) and (11,15).Slope,m=___Enter your answer as an integer or a reduced fraction in the form A/B
Answer:
m = 7/3
Explanation:
The slope of a line that passes through two points (x1, y1) and (x2, y2) can be calculated as
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]So, replacing (x1, y1) = (2, -6) and (x2, y2) = (11, 15), we get:
[tex]m=\frac{15-(-6)}{11-2}=\frac{15+6}{9}=\frac{21}{9}=\frac{7}{3}[/tex]Therefore, the slope is 7/3
daniel picked 7 pounds of strawberry he wants to share the strawberry equally among three of his friends how many pounds of strawberries will each friend receive ?
Diana, this is the solution to the problem:
• Amount of strawberry Daniel picked = 7 pounds
,• Number of friends = 3
• Amount of strawberry that each friend will receive = Amount of strawberry Daniel picked/Number of friends
Replacing by the values we know:
• Amount of strawberry that each friend will receive = 7/3
,• Amount of strawberry that each friend will receive = 2.33 pounds
Systems of equations
The slopes to the linear functions are given as follows:
2. Parallel line: slope of m = -3.
3. Two points: slope of m = -0.06.
What is the slope of a linear function?A linear function is modeled according to the following rule:
y = mx + b.
The coefficient m represents the slope of the linear function, which is the rate of change, given by change in y divided by change in x.
When two functions are parallel, they have the same slope. In item 2, the function is defined as follows:
-7x - 2y = 6.
In slope-intercept format, the function is given by:
2y = -7x - 6
y = -3.5x - 3.
Hence the slope of the parallel line is of -3.
Given two points, the slope is given by change in y divided by change in x. For problem 3, the two points are given as follows:
(-7,0) and (9,-1).
Hence the slope is given by:
m = (-1 - 0)/(9 - (-7)) = -1/16 = -0.06.
More can be learned about linear functions at https://brainly.com/question/24808124
#SPJ1
which number is a solution of the inequality 8 - 1/4 b > 27
The inequality is 8-1/4x>27. The solution of the inequality is b<-76.
Given that,
The inequality is 8-1/4x>27
We must determine how to address the inequity.
Take,
8-1/4x>27
Multiply the inequality's two sides by its lowest common denominator,
4×8-4×1/4b>27×4
Reduce the expression to the lowers term,
4×8-b>4×27
Calculate the product or quotient,
32-b>4×27
Calculate the product or quotient,
32-b>108
Rearrange unknown terms to the left side of the equation,
-b>108-32
Calculate the sum or difference,
-b>76
Divide the inequality's two sides by the variable's coefficient,
b<-76
Therefore, the solution of the inequality is b<-76.
To learn more about inequality visit: https://brainly.com/question/28823603
#SPJ1
Give two systems of equations that would be easier to solve by substitution than by elimination. Then give two systems that would be easier to solve with elimination. Finally, explain how you decide whether to use elimination or substitution to solve a system.
Please don't answer too complicated
Step-by-step explanation:
if the given equations are linear, then no matter which method is used, it depends on pupils ability/habbits, but usually 'by elimination' is easier, then 'by substitution';
in the most cases the 'by substitution' can be used only (systems of non-linear equations).
Example 1. This system can be solved by any method, but 'by elimination' is shorter:
[tex]\left \{ {{x+y=2} \atop {x-y=2}} \right.[/tex]
Example 2. This system can be solved by any method, but 'by substitution' is shorter:
[tex]\left \{ {{2x+y=3} \atop {7x+3y=10}} \right.[/tex]
Simplify the expression by combining the radical terms using the indicated operations(s) Assume all variables are positive.
Answer:
[tex]38x\sqrt[]{34xy}[/tex]Step-by-step Explanation:
Given the below expression;
[tex]8x\sqrt[]{34xy}+3x\sqrt[]{34xy}+9x\sqrt[]{306xy}[/tex]We'll go ahead and simplify the given expression following the below steps;
Step 1: Combine like terms;
[tex]\begin{gathered} (8x\sqrt[]{34xy}+3x\sqrt[]{34xy})+9x\sqrt[]{306xy} \\ 11x\sqrt[]{34xy}+9x\sqrt[]{306xy} \end{gathered}[/tex]Step 2: Split the radicand of the second term as seen below;
[tex]\begin{gathered} 11x\sqrt[]{34xy}+9x\sqrt[]{9\cdot34\cdot xy} \\ =11x\sqrt[]{34xy}+9x(\sqrt[]{9}\cdot\sqrt[]{34xy}) \\ =11x\sqrt[]{34xy}+9x\cdot3\sqrt[]{34xy} \\ =11x\sqrt[]{34xy}+27x\sqrt[]{34xy} \end{gathered}[/tex]
Step 3: Combine like terms;
[tex]\begin{gathered} 11x\sqrt[]{34xy}+27x\sqrt[]{34xy} \\ =38x\sqrt[]{34xy} \end{gathered}[/tex]
Find the value of X.
Answer:
15
Step-by-step explanation:
#10 Round your answer to the nearest to two decimal points
Answer: $108.75
Given:
P = $5000
r = 8.7% = 0.087
t = 3 months
We will use the formula for the simple interest rate to solve for the interest penalty
[tex]I=\text{Prt}[/tex]Substitute the given values to the formula and we will get:
[tex]\begin{gathered} I=\text{Prt} \\ I=(5000)(0.087)(\frac{3}{12}) \\ I=108.75 \end{gathered}[/tex]Therefore, the interest penalty is $108.75
If R(-2,-1) is the midpoint of ST and S(-14,3),find the coordinates of t
Answer
Explanation
Mathematically, if a point R(x, y) divides the coordinates S (x₁, y₁) and T (x₂, y₂) internally in the ratio m:n then point R(x, y) is given as
x = [(mx₂ + nx₁)/(m + n)]
y = [(my₂ + ny₁)/(m + n)]
For this question, we are given that
R (x, y) = R(-2, -1)
S (x₁, y₁) = S (-14, 3)
T (x₂, y₂) = ?
Since it is divided equally into two parts (As per the midpoint), m : n = 1 : 1
x = -2
y = -1
x₁ = -14
y₁ = 3
x₂ = ?
y₂ = ?
m = 1
n = 1
x = [(mx₂ + nx₁)/(m + n)]
-2 = [(1 × x₂) + (1 × -14)]/(1 + 1)
-2 = [x₂ - 14]/2
[tex]\begin{gathered} -2=\frac{x_{2}-14}{2} \\ \text{Cross multiply} \\ x_{2}-14=2\times-2 \\ x_{2}-14=-4 \\ x_{2}=-4+14 \\ x_{2}=10 \end{gathered}[/tex]y = [(my₂ + ny₁)/(m + n)]
-1 = {
i need help with this!
Answer:
19. 7
20. 11
21. -12
22. 15
23. 77
24. −6
Step-by-step explanation:
Simply plug the values of a, b and c into each equation and evaluate using a calculator or manually
A store is selling scooter for $40. You have coupon and purchase it for $15. What percentage was the coupon?
We can solve this problem by applying the rule of three:
[tex]\begin{gathered} 40\text{ dollars ------100\%} \\ 15\text{ dollars ------ x} \end{gathered}[/tex]hence,
[tex]x=\frac{(15)(100)}{40}[/tex]and it yields
[tex]x=\frac{1500}{40}[/tex]which result in x= 37.5. It means that 15 dollars corresponds to 37.5%
