Answers
1. Solve s in the second equation:
[tex]\begin{gathered} -s-5t=-2 \\ -s=-2+5t \\ s=-(-2+5t) \\ s=2-5t \end{gathered}[/tex]2. Substitute the s in the first equation by the value you get in the previous step:
[tex]-6(2-5t)+3t=-45[/tex]3. Solve t:
[tex]\begin{gathered} -12+30t+3t=-45 \\ -12+33t=-45 \\ 33t=-45+12 \\ 33t=-33 \\ t=\frac{-33}{33} \\ \\ t=-1 \end{gathered}[/tex]4. Use the value of t to solve s:
[tex]\begin{gathered} s=2-5t \\ s=2-5(-1) \\ s=2+5 \\ s=7 \end{gathered}[/tex]Then, the solution of the given system of equations is s=7t= -1Related Questions
Question 3(Multiple Choice Worth 1 points)
(03.01 LC)
Rewrite the radical expression as an expression with a rational exponent.
the cube root of five to the seventh power
x21
x4
five to the seven thirds power
five to the three sevenths power
Answers
The representation of the radical expression; the cube root of five to the seventh power as an expression with a rational exponent is; five to the seven thirds power.
Which rational exponent expression is equivalent to the radical expression; ³√5⁷?It follows from the task content that the radical expression given; ³√5⁷ is to be expressed as a rational exponent expression.
Recall that the converse of the rational exponent law of indices is such that; ³√x = (x)^⅓.
Hence, it follows that the expression given;
³√5⁷ = (5⁷)^⅓.
Also, it follows from the power of power law of indices that the expression above can be written as;
5^(7/3).
Ultimately, the equivalent rational exponent expression is; five to the seven thirds power; 5^(7/3).
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the admission fee at an amusement park is $3.50 for children and 13.00 for adults. on a certain day, 240 people entered the park, and the admission fees collected totaled $1,980.00. how many children and how many adults were admitted?
Answers
120 children and 120 adults were admitted to the amusement park if the admission fee collected was $1980.00
The number of children and adults that entered the park can be calculated using linear equations.
Considering x to be the number of adults and y to be the number of children;
As 240 people entered the park, therefore;
x + y = 240
As the fee for children is $3.50 and for adults is $13, therefore;
13x + 3.50y = 1980
Determining the value of y in the first equation;
x + y = 240
y = 240 - x
Putting this value of y in the second equation;
13x + 3.50y = 1980
13x + 3.50(240 - x) = 1980
13x + 840 - 3.50x = 1980
9.5x = 1980 - 840
9.5x = 1140
x = 1140 / 9.5
x = 120
To determine the value of y, we Substitute this value of x in the first equation;
y = 240 - x
y = 240 - 120
y = 120
Hence, 120 children and 120 adults entered the park if the admission fee for children was $3.50 and for adults was $13.00
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no joking around and no links
NASA launches a rocket at t = 0 seconds. Its height, in meters above sea-level, as a function of time is given by 4.9t² + 142t+ 346. h(t) Assuming that the rocket will splash down into the ocean, at what time does splashdown occur?
A.The rocket splashes down after seconds. Round your answer to the nearest second.
B.How high above sea-level does the rocket get at its peak? The rocket peaks at meters above sea-level. Round your answer to the nearest meter.
Answers
a. The rocket splashes down after 31.23 seconds.
b. The rocket is 1374.7 meters above sea level.
NASA launches a rocket at t=0 seconds.
Its height, in meters above sea-level, as a function of time is given by
h(t)=-4.9t²+142t+346.
Assuming that the rocket will splash down into the ocean, at what time does splashdown occur?
When splash down occurs, h(t) = 0, therefore
-4.9t²+142t+346 = 0
find t using the quadratic formula; a=4.9, b=142, c=346
t = -142 ± √(142)² - 4(-4.9)(346) / 2(-4.9)
t = -142 ± 164.15 / -9.8
t = -142+164.15/-9.8 , -142-164.15/-9.8
t = 22.15/-9.8 , -306.15/-9.8
t = -2.26 , 31.23
time cannot be negative so t = 31.23
The rocket splashes down after 35.8229 seconds.
The max occurs on the axis of symmetry, use x=-b/(2a) to find it
t = -142/2(-4.9)
t = 142/9.8
t = 14.48 sec
replace t with 17.2449 in the equation
h(t) = -4.9(14.48)² + 142(14.48) + 346
= 1374.7 m
The rocket peaks at 1374.7 meters above sea-level.
Hence we get the answers.
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A large gym with hundreds of members offers yoga classes. Members are free to take these
classes at no charge, but not all members are interested, and some never take advantage of the
yoga classes. Non-members can also take these classes, but they must pay a fee for each class.
A manager at the gym is curious about overall satisfaction with these yoga classes, so they
survey a large random sample of anyone who has taken a yoga class at the gym in the past year.
They find that 78% of those surveyed are "very satisfied" with the yoga classes.
For which population is 78% a legitimate estimate of the percent of people that are "very
satisfied" with the yoga classes?
Choose 1 answer:
only those surveyed
All members who have taken a yoga class at the gym in the past year, but not non-
members
All non-members who have taken a yoga class at the gym in the past year, but not
members
anyone who has taken a yoga class at the gym in the past year but not before that
anyone who has ever taken a yoga class at the gym
Answers
The population for which 78% is a legitimate estimate of the percent of people that are 'very satisfied" with the yoga classes is C. anyone who has taken a yoga class at the gym in the past year but not before that.
What is an estimate?An estimate is a rough calculation that may not be based on real figures or it may be based on rounded-off or appropriated facts and figures.
Estimates enable the decision-maker to make a quick guess or decision that cannot wait for all the facts to be collected.
Thus, the population of interest for the estimate includes members and non-members who have participated.
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Answer:
D
Step-by-step explanation:
name a pair of vertical angles.
Answers
Answer:
The vertical angles are
1 and 3
2 and 4
LaTanya buys 6 yards of blue fabric and 9 yards of green fabric. The blue fabric costs $2 more per yard than the green fabric. She pays a total of $57. What would be the combined cost of 1 yard of blue fabric and yard of green fabric?
Answers
The price of 1 yard of blue fabric and 1 yard of green fabric is obtained by solving the system of linear equations and it is $8
Let
x = price of blue fabric per yard
y = price of green fabric per yard
"The blue fabric costs $2 more per yard than the green fabric" means:
x = y + 2 (Equation 1)
" LaTanya buys 6 yards of blue fabric and 9 yards of green fabric and pays $57" means:
6x + 9y = 57 (Equation 2)
Substitute equation 1 into equation 2:
6x + 9y = 57
6 (y + 2) + 9y = 57
6y + 12 + 9y = 57
15 y = 45
y = 3
Substitute y = 3 into equation 1
x = 3 + 2 = 5
Hence, the price of blue fabric is $5 per yard while the green fabric is $3 per yard.
The price of 1 yard of blue fabric and 1 yard of green fabric = x + y = 3 + 5 = $8
Complete question:
LaTanya buys 6 yards of blue fabric and 9 yards of green fabric. The blue fabric costs $2 more per yard than the green fabric. She pays a total of $57. What would be the combined cost of 1 yard of blue fabric and 1 yard of green fabric?
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Elon sat on the dock with his fishing rod, when suddenly he felt the rod being pulled down! He reeled in his catch, causing it to ascend at a constant rate of 0.10.10, point, 1 meters per second. When it reached the water's surface after 353535 seconds, Elon found it was only an old shoe... Graph the relationship between the shoe's altitude (in meters relative to the water's surface) and time (in seconds).
Answers
The relationship between the shoe's altitude (in meters relative to the water's surface) and time (in seconds) has been plotted in the graph shown below.
The equation of a straight line.Mathematically, the standard form of the equation of a straight line is given by;
y = mx + c
Where:
x represents the time measured in secondsy represents the position relative to water surface and measured in meters.m represents the slope.c represents the intercept or initial altitude of the shoe.Next, we would determine the initial altitude as follows:
y = mx + c
0 = (0.1 × 35) + c
0 = 3.5 + c
c = -3.5
Substituting the given points into the formula, we have;
y = 0.1x - 3.5
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Complete Question:
Elon sat on the dock with his fishing rod, when suddenly he felt the rod being pulled down! He reeled in his catch, causing it to ascend at a constant rate of 0.1 meters per second. When it reached the water's surface after 35 seconds, Elon found it was only an old shoe...
Graph the relationship between the shoe's altitude (in meters relative to the water's surface) and time (in seconds).
Find the equation of the line that contains the given point and is parallel to the given line. Write the equation in slope-intercept form, if possible. (1.-3): y=-2
Answers
The equation of the line is y = -3x + 8.
What exactly is slope?
The slope of a line, or angle between it and the horizontal, is stated numerically. The slope of a line, ray, or line segment in analytical geometry is the ratio of its vertical to horizontal distance between any two locations ("slope equals rise over run").
Given,
x1 = 1
y1 = 5
m = -3
From,
y-y1 = m(x-x1) (x-x1) (x-x1)
y - 5 = -3(x - 1) (x - 1) (x - 1)
y-5 = -3x + 3
y = -3x + 8
As a result, the equation for the line is y = -3x + 8.
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EASY! SHAPES! (points, brainliest, stars)
Answers
how many packages of diapers can you buy with 40$ if one packages cost 8$. this is a one step equation
Answers
In order to determine how many packages of diapers you can buy, it is only necessary to divide the total money you have, between the price of each package.
You have:
available money = 40$
package cost = 8$
Then, you calculate the quotient between available money and package cost:
[tex]\frac{40}{8}=5[/tex]Hence, you can buy 5 packages of diapers with 40$
a random sample of size is selected from a population with . a. what is the expected value of (to decimals)? b. what is the standard error of (to decimals)? c. show the sampling distribution of . (to decimals) (to decimals) d. what does the sampling distribution of show? - select your answer -
Answers
a. The expected value is 0.40
b. The standard error is 0.0024
Given that:
Sample size, n=100
Population proportion, p=0.40
a) The expected value of the sample proportion is defined as:
E(^p)=p
now,
E(^p)=0.40
b) The standard error of the sample proportion is defined as:
SE(^p) = √p(1-p)/n
SE(^p) = √0.40(1-0.40)/100
SE(^p) = 0.0024
c) The sampling distribution of the sample proportion is normally distributed with the expected value of the sample proportion of 0.40.
Therefore,
E(^p) = 0.40
d) The central limit theorem states that the sample statistic (sample proportion) tends to the population parameter (population proportion) as the sample size tends to infinity (OR n→∞).
^P~N(p, p(-p)/n) as n→∞
Hence we get the required answers.
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Please help and provide a real step by step explanation
What is the equation of the line that passes through Point (3, -4) and has a Slope of 0.
Answers
Step-by-step explanation:
the slope of a line is the ratio (y coordinate change / x coordinate change) when going from one point on the line to another.
a slope = 0 means that the y coordinate change is always 0, so y does not change anywhere on the line.
that makes y a constant c, and x can be any value completely independent of y.
the line is the summary of all points that have c as their y coordinate.
so, the general equation for such a line is simply
y = c
what is c ?
as we have one point on the line, remember the statement above : the line is the summary of all points that have c as their y coordinate.
that means (3, -4) must have the same y coordinate.
so, c = -4.
the equation of the line is therefore
y = -4
2. Write in standard form: one hundred dollars and fourteen cents
Answers
Answer:
$100.14
Step-by-step explanation:
convert to a number
Plot each exact point on the coordinate grid. A line will connect the points.
Select at least two points and connect the points with a line
Answers
For the given line, the graph is given below -
What are graphs?In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way. The relationships between two or more items are frequently represented by the points on a graph.
For the given line,
y = 1/4x + 2
the coordinates will be -
for x = 4, y = 3
(4,3)
for x = 8, y = 4
(8,4)
for x = 0, y = 2
(0,2)
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Choose the point-slope form of the equation below that represents the line that passes through the point (6, -3) and has a slope of 1/2OPTIONS: A.) y-6 = 1/2(x+3)B.) y = 1/2x - 6C.) y+3 = 1/2(x-6)D.) y-2y = 12
Answers
ANSWER
B) y = 1/2x - 6
EXPLANATION
We have that the line passes through (6 -3) and has a slope of 1/2.
To find the point-slope form of the equation, we have to use the formula:
[tex]y-y_1=m(x-x_1)[/tex]where m = slope = 1/2
(x1, y1) = (6, -3)
So, we have:
y - (-3) = 1/2 (x - 6)
y + 3 = 1/2 x - (1/2 * 6)
y + 3 = 1/2 x - 3
=> y = 1/2x - 3 - 3
y = 1/2x - 6
The answer is Option B
If benzene has a density of 0.8787 g/mL, what is the volume of 131.8 g of benzene?
Answers
The benzene has a volume value of 149.99 mL
How to determine the volume of the benzene?From the question, the given parameters are
Density of benzene = 0.8787 g/mL
Mass of benzene = 131.8 g
The volume of the benzene is then calculated using
Density = Mass/Volume
Make Volume the subject of the formula
So, we have
Volume = Mass/Density
Substitute the known values in the above equation
So, we have the following equation
Volume = 131.8/0.8787
Evaluate the quotients in the equation
Volume = 149.99
Hence, the volume of the benzene is 149.99 mL
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A football team scored a total of 50 points in one game. They scored 14 times. The scoring
was made up of touchdowns (6 points each), field goals (3 points each), and PATS (1 point
each). They had 3 more touchdowns than field goals. How many of each type of score did the
team have?
Answers
Answer:
Touchdowns: 6
Field goals: 3
PATS: 5
Step-by-step explanation:
6*6 = 36
3*3 = 9
5*1 = 5
9+5+36 = 50 points
6+3+5 = 14 scored times
Answers:
6 touchdowns (TD)
3 field goals (FG)
5 points after touchdown (PAT)
===============================================
Explanation:
Acronyms used in football
PAT = point after touchdownTD = touchdownFG = field goalDefine the following variables
x = number of TDsy = number of FGsz = number of PATs"They had 3 more touchdowns than field goals", so,
TD = FG + 3
x = y + 3
They scored 14 times which means we can say
x+y+z = 14
Let's look at the point breakdown per type of score
TDs give 6 points each. Scoring x of them gives 6x pointsFGs give 3 points each. Scoring y of them gives 3y pointsPATs give 1 point each. Scoring z of them gives 1z pointsThen we can add up those expressions to get us to 6x+3y+1z = 50 points total. This is the same as saying 6x+3y+z = 50.
--------------------------
Here's our system of equations
x = y+3
x+y+z = 14
6x+3y+z = 50
Let's replace each x with y+3 in the second equation. Then solve for z.
x+y+z = 14
y+3+y+z = 14
2y+z = 14-3
2y+z = 11
z = 11-2y
Now replace every x with y+3 in the third original equation
6x+3y+z = 50
6(y+3)+3y+z = 50
6y+18+3y+z = 50
9y+z = 50-18
9y+z = 32
Then plug in z = 11-2y and solve for y
9y+z = 32
9y+11-2y = 32
7y+11 = 32
7y = 32-11
7y = 21
y = 21/7
y = 3 is the number of FGs scored
Use this to find z
z = 11-2y
z = 11-2(3)
z = 11-6
z = 5 is the number of PATs scored
Now let's find x
x = y+3
x = 3+3
x = 6 is the number of TDs scored
--------------------------
Checking the answers:
x+y+z = 6+3+5 = 9+5 = 14 times they scored
6x+3y+z = 6*6+3*3+5 = 36+9+5 = 50 points scored
There are 3 more TDs than FGs since x = y+3 leads to 6 = 3+3 which is a true statement.
All three original equations we set up for the system of equations are true. Therefore, the final answers are confirmed.
Find the area of the rectangle.
1 1/2 yd
58/ 8 yd
Answers
Answer:
[tex]\sf Area = 10\dfrac{7}{8} \yd^2[/tex]
Step-by-step explanation:
Area of rectangle:Area = length *breadth
Convert the mixed fraction to improper fraction.
[tex]\sf 1\dfrac{1}{2}=\dfrac{3}{2} \ yd[/tex]
[tex]\sf area = \dfrac{3}{2}*\dfrac{58}{8}\\\\[/tex]
[tex]\sf = \dfrac{3*29}{8}\\\\=\dfrac{87}{8}\\\\= 10\dfrac{7}{8} \ yd^2[/tex]
help pls!! i have sparx and i literally dont understand
Answers
Ezzzzzzzzzzzzzzzzzzzzzzzzzzz
Answer:
3 and 2
Step-by-step explanation:
the scale factor is the ratio of corresponding sides, image to original
shape on left
consider the length of the horizontal sides
P = 2 and Q = 6 , then
scale factor = [tex]\frac{6}{2}[/tex] = 3
shape on right
consider the length of the horizontal sides
R = 2 and T = 4 , then
scale factor = [tex]\frac{4}{2}[/tex] = 2
Can someone please help me
Answers
Answer:
Y=-3x+7
Step-by-step explanation:
it hit the y axis at 7
And it is going down by 3
The table below shows the average price of a Miami Marlins baseball ticket between 2006 and 2021.
The equation y=1.67x−3338.5 models this relationship, where x is the year and y is the average ticket price.
Use the model to predict the ticket price for a Miami Marlins baseball ticket in 2030.
$=
Answers
By evaluating the equation in x = 2030, we can estimate the price to be $51.60.
How to use the model?We know that the equation:
y = 1.67*x - 3338.5
Models the relationship between the year, x, and the average ticket price of a Miami Marlins baseball ticket.
We know that this relationship works for the years 2006 to 2021, but can be used to estimate the price for years after and before that.
if we use x = 2030, we will get:
y = 1.67*2030 - 3338.5 = 51.6
This will be the price, in dollars, of a game in the year 2030.
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Which is NOT a step when solving an equation using the distributive property?
Use the properties of equality to solve.
Check your work.
Solve for the variable using only the addition property of equality.
Distribute through the parentheses.
Answers
Answer:
use the property’s of equality to solve
Step-by-step explanation:
Use the properties of equality to solve, is not a step when we are solving an equation using distributive property.
Distributive property:- In general,
distribute means to divide something or give a share or part of something. According to this 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.
ex:- a(b+c)=ab+ac
a(b-c)=ab-ac ,also valid true for division
(b+c)/a = b/a + c/a
Steps involved while solving equations
1. If you see parenthesis, with more than one term inside, then distribute first.
2. Rewrite your equations with like terms together. Take the sign in front of each term.
3. Combine like terms.
4. Continue solving to get the answer.
Thus, Use the properties of equality to solve, is not a step involved in solving equation using distributive property.
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Curtis has a part time job working for a video game store. He is paid a wage of $8 per hour plus 2% commission of his total sales each week. Write a linear equation that represents his weekly salary S.
Let H = Hours Worked
Let C = Commission earned on total sales
Answers
The linear equation which can be used to represents Curtis weekly salary is S = 8H + 0.02C
Linear equation that represents weekly salaryCurtis wage per hour = $8Percentage commission = 2%H = Hours WorkedC = Commission earned on total salesS = weekly salaryWeekly salary = Curtis wage per hour(Hours Worked) + Percentage commission(Commission earned on total sales)
S = 8(H) + 2%(C)
S = 8H + 0.02(C)
S = 8H + 0.02C
So therefore, Curtis linear equation for his weekly salary is S = 8H + 0.02C
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The difference of two numbers is 16. The greater number is 4 times the smaller
number minus 5. Find the numbers.
Answers
After using the linear equation - The smaller number is 7, and the greater number will be 23.
what is the substitution method?
Mathematicians frequently use the substitution method to resolve an equation system. With this method, you solve the equation for the first variable first, and then plug the answer into the second equation.
what is a linear equation in two variables?
When an equation is written in the form axe + by + c=0 and the coefficients of x and y, i.e., a and b, respectively, are not equal to zero and the greater of the two numbers is four times the smaller number minus 5, that equation is said to be linear in two variables.
Let's assume that "x" is the smaller number, making "4x-5" the greater number. The requirement that the difference between the two numbers be 16 is also included.
thus,
4x - 5 - x = 16
3x -5 = 16
3x = 16 +5
3x =21
x = 21/3
x = 7
for the second number
4x-5
=4(7)-5
=28-5
=23
hence the smaller number is 7, and the greater number will be 23.
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uestion 14 (2 points)
3
What is the equation of a line that passes through point (3,-5) and is perpendicular to y = -x+5?
Enter your answer with no spaces.
A/
Answers
A line that passes through point (3,-5) and is perpendicular to y = -x+5 has the equation y = x - 8.
What is a straight line equation?A straight line has an equation of y=mx + c, where m is the gradient and c is the constant, also known as the y-intercept, at which the line crosses the y-axis.
How do you determine the line's equation?In order to put the equation in y-intercept (y = mx + b) form and determine the equation of a graphed line, first determine the slope and y-intercept.
It is given that a line's equation passes through point (3,-5) and is perpendicular to y = -x+5.
Slope of given line = -1
Slope of line perpendicular to the given line = Negative of the reciprocal of the slope of a given line = 1
We have the slope and point (3,-5) of the required line. So, we can find the constant of this equation.
y = mx + c
-5 = 1(3) + c
c = -5 - 3
c = -8
Substituting c = -8 and m = 1 to get the equation of required line.
y = mx + c
y = x - 8
As a result, the equation of a line passing through point (3,-5) and perpendicular to y = -x+5 is y = x - 8.
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Noah wants to sign up for a streaming service. Company A charges a one-time fee of $10 and a costs $6 per month. Company B charges a one-time fee of $20 and costs $3 per month. If x represents the number of months using the service and y represents the total cost of the service, which system of equations represent this situation?
Answers
6x+10=y
For company B
3x+20=y
11. Find the area of the shaded region. Each square is 1 cm wide.
Answers
Answer:[tex]26cm^{2}[/tex]
Step-by-step explanation: To do this you have to dissect the shapes into singular shapes.
First, you do the parallelogram at the bottom. 4×2
Then the middle rectangle. 3×4
Then the triangle at the top. 4×3÷2
Area= [tex]26m^{2}[/tex]
Simplify 0.4i−i.
For those of you who have this question the answer is actually -0.6i
Have A Great Day Ya'll
Answers
Answer:-0.9.45
Step-by-step explanation:
-0945
Answer: -0.6i
Step-by-step explanation:
[tex]0.4i-i=\\\\i(0.4-1)=\\\\i(-0.6)=\\\\-0.6i[/tex]
Nan has 3/8 pound of blueberries. if she put equal portions of blueberries into 6 bags, how many pounds of blueberries are in each bag?
Answers
In order to find how many pounds are in each bag, we just need to divide the total amount of blueberries by the number of bags.
So we have:
[tex]\frac{\frac{3}{8}}{6}=\frac{3}{8}\cdot\frac{1}{6}=\frac{3}{48}=\frac{1}{16}[/tex]So in each bag there are 1/16 pounds of blueberry.
12. Write the equation of a line that is perpendicular to y = -x - 6 that goes through
the point (3,-8).
Answers
Answer:
y = x - 11
Step-by-step explanation: