The given system of equation :
x = - 7
-8x - 6y = 14
Substitute the value of x = (-7) in the given system :
-8x - 6y = 14
-8(-7) - 6y = 14
Simplify the equation :
56 - 6y = 14
56 - 14 = 6y
6y = 42
y = 42/6
y = 7
y = 7 & x = (-7)
Answ
Answer:
Step-by-step explanation:
3x - 2y < 10 ) 5x - 3-15 부 다. N
Part 1
we have the inequality
3x-2y < 10
isolate the variable y
-2y< -3x+10
Multipli by -1 both sides
2y > 3x-10
the solution is the shaded area above the dashed line 2y=3x-10
using a graphing tool
see the attached figure
please wait a minute to draw the solution
[tex]5x-3y\leq-15[/tex]isolate the variable y
[tex]\begin{gathered} 5x-3y\leq-15 \\ -3y\leq-5x-15 \\ \text{Multiply by -1 both sides} \\ 3y\ge5x+15 \end{gathered}[/tex]the solution is the shaded area above the solid line 3y=5x+15
using a graphing tool
see the attached figure
Part 7 we have the inequality
Mara bought a bag that contained 16 cups of sugar. She uses two-thirds cup of sugar each time she make a batch of cookies. If the bag now has 10 cups of sugar left, how many batches of cookies has she made?
From a bag of 16 cups of sugar , Mara used 2/3 cups of sugar to make 1 batch of cookies , then number of baches made by 6 cups of sugar is equal to 9 batches.
As given in the question,
Total number of cups of sugar in a bag = 16
Cups of sugar used to make 1 batch of cookies = 2/3
Number of cups of sugar left in a bag = 10
Number of cups of sugar used = 6
2/3 cups of sugar = 1 batch of cookies
1 cup of sugar = 3/2 batch of cookies
6 cups of sugar = [(3/2) × 6 ]
= 9 batches of cookies
Therefore, from a bag of 16 cups of sugar , Mara used 2/3 cups of sugar to make 1 batch of cookies , then number of baches made by 6 cups of sugar is equal to 9 batches.
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raymond bought 5 rolls of toilet paper towels he got 99 4/3 inches of paper towels in all. how many meters of paper towels were on each roll? please help my grades go in tomorrow and i have a lot today that i dont know how and if i dont make a passing grade on my report card i have to quit band
The length of 5 rolls of toilet papers is 99 4/3
So, the length of one roll will be = 99 4/3 ÷ 5 = 20 1/15 inches
During a tropical storm, the temperature decreased from 84° to 63º. Find the percent decrease in temperature during the storm. (a) 33% (b) 25% (c) 40% (d) 75%
To find the percentage of decrease, first, we divide.
[tex]\frac{63}{84}=0.75[/tex]This means 63° represents 75% of 84°. In other words, the temperature decreased by 25%.
Hence, the answer is B.I ONLY need help with the last question help me with special Angles in a circle..GEOMETRY
We want to know the measure of the angle BCD. In this case, we see that it is an inscribed angle, and then its measure is half of the arc it intercepts (in this case BD).
With this in mind,
[tex]m\measuredangle BCD=\frac{1}{2}m\hat{BD}=\frac{1}{2}(130^{\circ})=65^{\circ}[/tex]And then, the angle BCD has 65°.
Steven read a total of 8 books over 4 months. After belonging to the book club for 7 months,how many books will Steven have read in all?
If he reads 8 books over 4 months it means that he reads 2 books per month. So, if we multiply this ratio by the 7 months we would find that he reads 14 books over 7 months.
The answer is 14 books.
I don't need Jimmy wants a game for him and his son Jimmy Jr. The game he wants is $79.93 and he only has $100 in his wallet. he found a discount for 60% off for the game. how much will he save?
Answer:
$47.96
Explanation:
The cost of the game = $79.93
He found a discount for 60% off for the game.
Therefore, the amount he will save will be:
[tex]=60\%\text{ of 79.93}[/tex]We simplify our result:
[tex]\begin{gathered} =\frac{60}{100}\times79.93 \\ =\$47.96 \end{gathered}[/tex]Jimmy will save $47.96.
A high school counselor wants to look at the relationship between GPA and the numberof absences for students in the senior class this year. That data shows a linear patternwith the summary statistics shown below.I answered som of it I just can’t do part D, part E, part F
D.
The slope of a line means the increase in y for each unitary increase in x:
[tex]b=\frac{\Delta y}{\Delta x}[/tex]If the slope is equal to -0.1625, that means if x increases 1 unit, y will decrease by 0.1625 units.
E.
Using x = 3 in the regression equation, we have:
[tex]\begin{gathered} y=a+bx \\ y=3.71-0.16x \\ y=3.71-0.16\cdot3 \\ y=3.71-0.48 \\ y=3.23 \end{gathered}[/tex]So the estimated GPA is 3.23.
F.
If r is the value of the standard deviation, therefore r² is the variance:
[tex]\begin{gathered} r=-0.65 \\ r^2=0.4225 \end{gathered}[/tex]The variance is the average of the squared difference from each point to the mean, and it measures the average of how much each point differs from the mean.
t, Decimal, Fractions a. 100 is what percent of 80? = 125% b. What is 1/20 as a decimal? What is that decimal as a percent? –5%
Explanation
Step 1
a) 100 is what percent of 80?
you can solve this by using a rule of three
Let
x represents the percent
then
[tex]undefined[/tex]The bar graph below shows the number of students at Lindsay's school who were born in various states.Oregon?ColoradoStateUtah -Arizona -New Mexico04812 16 20 24 28 32Number of StudentsThe number of students who were born in Oregon is the same as the number of students from Utah and NewMexico combined.Umantudante at Lindsay's school were born in Oregon?We
Since the number of students who were born in Oregon is the same as the number of students from Utah and New Mexico, add the amount of students from Utah and New Mexico to find the number of students who were born in Oregon.
18 students were born in Utah, and 12 students were born in New Mexico.
Since 18+12=30, then, 30 students were born in Utah and New Mexico combined.
Therefore, the amount of students who were born in Oregon, is:
[tex]30[/tex]Can some one help and explain pls
There, on the hypotenuse, is the longest side. Therefore, 12 might be viewed as C if we consider the Pythagorean theorem, which states that A squared plus B squared equals C squared. The hypotenuse is this. The hypotenuse squared is equal to the C squared.
What is the formula a2 b2 c2 used for?The Pythagorean Theorem describes the relationship among the three sides of a right triangle. In any right triangle, the sum of the areas of the squares formed on the legs of the triangle equals the area of the square formed on the hypotenuse: a2 + b2 = c2.
Consolidate terms multiplied into a single fraction.
i) c + -2/3(2/3c).2
c - 2/3(2/3c).2
c - 2/3 . 2c/3.2
c -4/3 . 2c/3
c + -4.2c / 3.3
c /9.
II)-5u.3(-2)u + -3/5
Add up the numbers.
30uu + -3/5
= 30u² + -3/5
= 3/5(50u² -1).
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Consider the function f(x) =cotx. Which of the following are true? 2 answers
Graphing the function f(x) = cot(x) we have the following
We can observe that the function cot(x) has an asymptote at x = 0, and that it has a period of π.
Jane invested her savings in two investment funds. The $2000 that she invested in Fund A returned a 3% profit. The amount that she invested in Fund B returned a 10% profit. How much did she invest in fund B, if both funds together returned a 8% profit?
Fund A, Jane invested $2000 and has a profit of 3%
Profit at Fund A is :
[tex]\$2000\times0.03=\$60[/tex]at Fund B, let $x be the amount she invested that gives her a profit of 10%
The profit at Fund B is :
[tex]\$x\times0.10=\$0.10x[/tex]It is said that the total amount she invested returned a 8% profit
The total amount she invested is :
[tex]\$2000+\$x[/tex]and the 8% profit of her total investment is :
[tex](2000+x)\times0.08=160+0.08x[/tex]Now we need to equate the sum of her profits from Fund A and Fund B, and this must be equal to the 8% profit.
3% Profit at Fund A = $60
10% Profit at Fund B = $0.10x
8% Profit at both funds together = 160 + 0.08x
[tex]\begin{gathered} 60+0.10x=160+0.08x \\ 0.10x-0.08x=160-60 \\ 0.02x=100 \\ x=\frac{100}{0.02}=5000 \end{gathered}[/tex]Therefore, the amount she invested in Fund B is $5000
system: 3x+2y=6 x-y=-3 find the value for x. find the value for y.
Given a system of equations:
[tex]\begin{gathered} 3x+2y=6 \\ x-y=-3 \end{gathered}[/tex]We have to solve the system of equations.
We can solve this system of equations using the substitution method.
From the second equation, we have x - y = -3, which implies that x = y - 3. Substitute x = y - 3 in the first equation:
[tex]\begin{gathered} 3(y-3)+2y=6 \\ 3y-9+2y=6 \\ 5y=6+9 \\ 5y=15 \\ y=\frac{15}{5} \\ y=3 \end{gathered}[/tex]Now, we have y = 3, put in x = y - 3 to get,
[tex]\begin{gathered} x=3-3 \\ x=0 \end{gathered}[/tex]Thus, the solution of the system of equations is (0, 3).
Paolo noticed that Channel 8 devoted 1/6 hour to news story and Channel 12 devoted 1/8 to the same story. Which channel devoted more time? How much more time?
the channel that devoted more time was channel 8, because since 6<8 then it follows thay 1/6>1/8 (the inequiality changes), channel 8 devoted
[tex]\frac{1}{6}-\frac{1}{8}=\frac{8-6}{6(8)}=\frac{2}{48}=\frac{1}{24}\text{more time}[/tex]3. There are two city buses in Saratoga. Bus A completes its route in 25 minutes. Bus B completes its route in 40 minutes. Both of their routes end at the bus station. If both buses leave the bus station at the same time in the morning, how many minutes will pass before the two buses meet at the train station?
To find the answer, we have to find the LCM of 25 and 40.
To get LCM, we
Write each number as prime factors
take the prime factor that occurs greatest number of time
take the product of those
Thus,
25 = 5 * 5
40 = 2 * 2 * 2 * 5
2 occurs 3 times and 5 occurs 2 times (greatest).
hence,
LCM(25, 40) = 2 * 2 * 2 * 5 * 5 = 200
So,
200 mins will pass before the two buses meet
b. Find a pair of numbers that have a sum of 50 and will produce the largest possible product. Example: +_ = 50 (sum) so _* _ = _ (maximum area) and (enter answers from the sum)
A pair of numbers that have a sum of 50
Let the number is x, so the other number is 50 - x
Let f(x) be the largest product so:
[tex]f(x)=\text{ x(50-x)}[/tex]Simplify the expression :
[tex]\begin{gathered} f(x)=\text{ x(50-x)} \\ f(x)=50x-x^2 \end{gathered}[/tex]Diffrentiate with respect to x
[tex]\begin{gathered} f(x)=\text{ x(50-x)} \\ f(x)=50x-x^2 \\ \text{ Diffrentiate with respect to x} \\ f^{\prime}(x)=50-2x \\ \text{Apply derivative equal to zero:} \\ 50-2x=0 \\ 50=2x \\ x=25 \end{gathered}[/tex]Now for to check for the f(x) is maximum for x = 25
Calculate the second derivative and put x = 25 is the f(x) is negative then the multiplication f(x) is maximum
[tex]\begin{gathered} f^{\prime}(x)=50-2x \\ \text{ Differentiate with respect to x} \\ f^{\prime}^{\prime}(x)=0-2 \\ \text{ Substitute x = 25} \\ f^{\doubleprime}(25)=-2 \\ f^{\doubleprime}(25)<0 \\ \text{Thus the function f(x) is maximum for x = 25} \end{gathered}[/tex]Thus, the first number is 25
Second number is : 50 -x = 50-25 = 25
Numbers are 25, 25
Answer : 25 + 25 =50 (sum)
25 * 25 = 625 (maximum possible product)
Jim began a 156 mile bike trip to build up stamina . Unfortunately his bike chain broke so he finished walking. Th whole trip took 6 hours. If Jim walks at a rate of 5 miles per hour and rides at 33 miles per hour find the amount he spent on the bike.
This diagram represents the problem
We know that distance = speed*time; D=S*t
Total distance: 156 miles
time: 6 h
Speed1: 33 miles/h
Speed2: 5 miles/h
for interval 1:
[tex]\begin{gathered} D_1=S_1\cdot t_1 \\ D_1=33\cdot t_1 \end{gathered}[/tex]for interval 2:
[tex]\begin{gathered} D_2=S_2\cdot t_2 \\ D_2_{}=5\cdot t_2 \end{gathered}[/tex]for the whole trip: -Eq 1. Distance
[tex]\begin{gathered} D=D_1+D_2 \\ D=33\cdot t_1+5\cdot t_2 \\ 156=33\cdot t_1+5\cdot t_2 \end{gathered}[/tex]and also: -Eq 2. Time
[tex]\begin{gathered} t=t_1+t_2 \\ 6=t_1+t_2 \end{gathered}[/tex]Now we have a system of 2 equations with 2 unknowns.
Let's solve it!
[tex]\begin{gathered} 156=33t_1+5t_2 \\ t_1=\frac{156-53t_2}{33} \\ \frac{156-5t_2}{33}+t_2=6 \\ t_2=\frac{3}{2} \\ t_1=\frac{156-5\cdot\frac{3}{2}}{33} \\ t_1=\frac{9}{2} \end{gathered}[/tex]We can see that he spent 4.5 hours riding the bike and 1.5 h walking
graph the line passing through (-6,1) whose slope is m= -6
As given by the question
There are given that the point (-6, 1) and slope (m) is -6.
Now,
To graph, the line, first, finds the equation of the line by using the given point and slope.
Then,
From the formula of point-slope form:
[tex]y-y_1=m(x-x_1)[/tex]Where,
[tex]x_1=-6,y_1=1,\text{ and m=-6}[/tex]Then, put all given values into the above formula:
So,
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-1_{}=-6(x-(-6)_{}) \\ y-1=-6(x+6) \end{gathered}[/tex]Then,
[tex]\begin{gathered} y-1=-6(x+6) \\ y-1=-6x-36 \\ y-1+1=-6x-36+1 \\ y=-6x-35 \end{gathered}[/tex]Then, the graph of the above equation is shown below:
Circumference? (you must include units) Round to the tenthsas needed.
The circumference formula is given by:
[tex]L=2\pi r[/tex]Where r is the radius of the circle. From the problem, we have r = 10.9 ft. Then, using the formula:
[tex]\begin{gathered} L=2\pi\cdot10.9 \\ \\ \therefore L=68.5\text{ ft} \end{gathered}[/tex]The circumference is 68.5 ft
−3x−6+(−1) i need help with this ine
Recall that the order of operations is a rule that tells the correct sequence of steps for evaluating a math expression, this order is: Parentheses, Exponents, Multiplications and Divisions (from left to right), Addition and Subtraction (from left to right).
Simplifying the parentheses in the given expression we get:
[tex]-3\times-6-1.[/tex]Simplifying multiplications in the above result we get:
[tex]18-1.[/tex]Finally, simplifying subtractions in the above result we get:
[tex]17.[/tex]Answer:
[tex]-3\times-6+(-1)=17.[/tex]Last week Forrest cut the grass exactly 3 times. It takes him between 55 and 75 minutes per cut.
CWrite an inequality to model all of the possible amounts of time (t) Forrest could have spent
cutting the lawn last week. Show or explain all your work.
Explanation:
If he mowed the lawn exactly once, then 55 ≤ t ≤ 75 describes all the possible values of t. Basically t is between 55 and 75 inclusive of both endpoints.
Multiply each value by 3
55*3 = 165
75*3 = 225
That's how we end up with 165 ≤ t ≤ 225 to represent the possible span of time values where he mowed the grass three times. His fastest possible time is 165 minutes (2 hr, 45 min) and his slowest possible time is 225 minutes (3 hr, 45 min).
3x + 9 ≤ 30answer the solution
Daphne rolls two 6-sided number cubes. What is the probability that she rollsa sum equal to 3? Use the diagram of the sample space to help you. please help me
From the sample space, there are 2 results equal to 3, and there are 36 total results. Then the probability that she rolls a sum equal to 3 is: 2/36 or 1/18
write an equation of the line that passes through the points in the table x=0,1,2,3 y=10,7,4,1
The line of equation (y + 3x = 10) passes through all the points in the given table.
What are equations?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two expressions 3x + 5 and 14, which are separated by the 'equal' sign.So, the equation will be:
Points:
x=0,1,2,3 y=10,7,4,1We know that when x = 0, then y = 10 and when we will increase x = 1, then y will decrease to y = 7.
The decrease in y is the difference of 3 (10 - 7 = 3)Then, y + 3x = 10 can be the equation.
Lets, 's check:
When x = 0:
y + 3x = 10y = 10 - 3(0)y = 10When x = 1:
y + 3x = 10y = 10 - 3(1)y = 7
When x = 2:
When x = 3:
y + 3x = 10y = 10 - 3(3)y = 1Since all the values of x and y are in proportion now, (y + 3x = 10) is the equation.
Therefore, the line of equation (y + 3x = 10) passes through all the points in the given table.
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The Oakdale Chamber of Commerce compared the local dealerships' vehicle sales.
Dealership
Truck Town
Affordable Cars
Other
0
100
Vehicle sales
200
300
400
500
Number of vehicles
What percent of the vehicles were sold by Truck Town or Affordable Cars?
Write your answer using a percent sign (%).
(Sold / Quantity) * 100 is the formula to get the sales percentage.In other words, it will divide the value before multiplying by 100.You won't need to rewrite the formula for different products.
What is the sales percentage?
Example of a percentage of sales from an image Based on historical and current sales data, the percentage of sales technique is a forecasting tool that generates financial projections.This information includes sales as well as all costs associated with running a firm, such as inventory and cost of goods.The typical business allocates between 1% and 40% of its gross revenue to marketing and advertising.The amount can, however, differ greatly based on a variety of variables, such as your product or service, the market and competition, your profit margin, and the number of years you've been in operation. By dividing the value by the entire value and multiplying the result by 100, one may determine the percentage.The percentage calculation formula is (value/total value)100%.
Determine the ratio of sales to expenses.Examine the balance of each line item on the financial statement of your business and determine its proportion to total sales.To accomplish this, take the following actions:Calculate your period's expenses and total sales.Subtract your costs from your total sales.Add 100 to your result.Vehicle sales = 200+300+400+500
= 1400/100
=14%
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Find the total amount in the compound interest account $2650 is compounded annually at a rate of 11% for 1 year
The compound interest formula is:
[tex]A\text{ = P}(1+i)^t[/tex]where:
A is the final amount including the principal
P is the principal amount
i is the interest rate (as a decimal)
t is time in years
Replacing with P = $2650, i = 0.11, and t = 1, we get:
A = 2650*(1 + 0.11)
A = 2650*1.11
A = $2941.5
11. Natalie budgets $165 for yoga training. She buys a yoga mat for $13.25 and pays $12 per yoga class. Fill in the boxes below to write an inequality to represent the number of classes, c, that Natalie can take and stay within her budget.
She has a budget of $165, so the total cost of the yoga mat and the classes has to be equal or less than $165.
[tex]C\le165[/tex]The cost is equal to the cost of the yoga mat ($13.25) and the cost of the classes ($12*c, being c the number of classes).
We can write this as:
[tex]C=13.25+12c[/tex]We then can combine both equations and get:
[tex]13.25+12c\le165[/tex]That inequality represents that the total expenses of Natalie have to be equal or less than $165.
Answer: 13.25 + 12c <= 165
How many different 3 digit combinations can there be for a combination lock that has a six digit wheel?
The number of 3 digit combinations possible for the six digit wheel combination lock is; 216 combinations.
Combinations and selections.It follows from the task content that the number of possible 3 digit combinations for the six digit wheel as required is to be determined.
The number of possible selections in a given sample space is defined by the combination which defines the situation.
On this note, each digit from the 3 digit combinations could be any of the six digits on the wheel.
Therefore, the number of possible combinations is; 6 × 6 × 6 = 216 combinations.
Ultimately, the number of possible combinations is; 216 combinations.
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Sam rides at a rate of 14.5 miles per 1 hour. If he rides at a constant rate, how many miles would he ride in 1 hour and 15 minutes?
Sam would ride 18.125 miles when hw would ride at the rate of 14.5 miles/hour.
According to the question,
We have the following information:
Speed of Sam = 14.5 miles/hour
Distance to be covered = ?
Time taken to cover the distance = 1 hour and 15 minutes
Now, we will convert the time given in minutes into hour.
We have 15 minutes.
We know that 1 hour is equal to 60 minutes.
So, we will convert 15 minutes into hour:
15/60 hour
0.25 hour
So, the total time taken = (1 + 0.25) hour
Time taken = 1.25 hour
We know that the following formula is used to find the speed:
speed = distance/time
Distance = speed*time
Distance = 14.5*1.25
Distance = 18.125 miles
Hence, the distance covered by Sam in 1 hour and 15 minutes is 18.125 miles.
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