Given:
The system of inequalities
[tex]x\leq 7[/tex]
[tex]x\geq a[/tex]
To find:
The values of a for which the system has at least one solution.
Solution:
We have,
[tex]x\leq 7[/tex] ...(i)
It means all real values of x which are less than or equal to 0.
[tex]x\geq a[/tex] ...(ii)
It means all real values of x which are greater than or equal to a.
Using (i) and (ii), we get
[tex]a\leq x\leq 7[/tex]
The value of x is lies in the interval [a,7].
It means, if the value of a is less than or equal to 7, then system has at least one solution.
But if a is more than 7, then the system of inequalities have to solution.
Therefore, the value of a must be less than or equal to 7.
The sum of two numbers is 10. The larger number is 4
times the smaller number.
The system of equations used to represent this
scenario is y = -x + 10 and y = 4x.
What is the larger number?
04
8
06
08
10
10
Answer:
y = -x + 10 and y = 4x.
4x = -x+10
5x = 10
x=2
largest number = 4x = 4*2 =8
Step-by-step explanation:
Lily and Layla are bakers and were having a contest to see who could bake more cupcakes in 8 hours. Lily can bake 7 cupcakes in 10 minutes. Layla can bake 8 cupcakes in 12 minutes. The next day, Lily sold LaTeX: \frac{2}{3}2 3 of her cupcakes at $1.29 each. Layla sold 75% of her cupcakes at $0.89 each. Who made more money?
Answer:
5.000 and dont say its wrong because whats the point of asking a question you already know?
Step-by-step explanation:
Pls pls pls help ASAP 1,2,3,4 ??
Answer:
draw a circle, cut into 3 equalbparts then shade one part
Step-by-step explanation:
the third one down
hope this helps
Find the remaining side of a 45° – 45° – 90° triangle if the shorter sides are 2/3 each .
Answer:
The length of the longer side is 2√2/3
Step-by-step explanation:
A 45-45-90 triangle is a right-angled triangle.
In fact, since it has two angles equal, it is a right angled isosceles triangle. What we are saying is that two of its sides are equal.
Hence, we have two short sides which are the opposite and the adjacent and a longer side which is the hypotenuse
Thus, to find the length of the longer side, we employ Pythagoras’ theorem and it states that the square of the hypotenuse equals the sum of the squares of the two other sides;
Mathematically, let’s call the longer side x
so x^2 = (2/3)^2 + (2/3)^2
x^2 = 4/9 + 4/9
x^2 = 8/9
x = √(8/9)
x = 2√2/3
Suppose that the x-intercepts of the graph of y=f(x) are -9 and 3. What are the x intercepts of y= f(x+3)
Answer:
the anwser is 6
Step-by-step explanation:
Use the x- intercepts as the x becuase when x=0 it will give you the x- intercept.
therefore, just plug them in.
Olivia needs $104 to buy the bike she wants. She saves $8 a week. Find the number of weeks it would take for Olivia to have enough money to buy the bike.
Answer:
13
Step-by-step explanation:
This is a division problem.
$104/$8 = 13
Answer: 13
The perimeter of a triangle is 32 feet. One side of the triangle is 3 times the second side. The third side is 12 feet longer
than the second side. Find the length of each side.
We have a triangle whose perimeter is 32 feet. Some information regarding the sides of the triangle is given:
GiveN:
One side is 3 times the second side.Third side is 12 feet longer than the second side.As we can see that, two sides of the triangle are defined the second sides. It means First and third side can be expressed in the form of second side.
So let the second side be xThen,
First side = 3xAnd, third side = x + 12We know that, perimeters is the sum of the lengths of all sides of the triangle, So it can be written as:
[tex]3x + x + x + 12 = 32[/tex]
Solving it further,
[tex]5x + 12 = 32[/tex]
Subtracting 12 from both sides,
[tex]5x + 12 - 12 = 32 - 12[/tex]
[tex]5x = 20[/tex]
Dividing 5 from both sides,
[tex] \frac{5x}{5} = \frac{20}{5} [/tex]
[tex]x = 4[/tex]
Then,
First side = 3x = 12 feetSecond side = 4 feetThird side = x + 12 = 16 feetAnd we are done with the answer !!
#CarryOnLearning
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Mrs. Ming invested an amount of money in two accounts for one year. She invested some at 8% interest and the rest at 6% interest. Her total amount invested was $1,500. At the end of the year, she had earned $106.40 in interest. How much had Mrs. Ming invested in the account paying 6%?
Answer: $680
Step-by-step explanation:
Find two consecutive integers whose product is 12.
Answer:
3 and 4
Step-by-step explanation:
The answer is 3 and 4 because consecutive means one more than the previous number. Therefore, 3 + 1 = 4
Also, 3*4 = 12
Hope this helps!
complete the missing number sequence.
1/4, 1/2,___, 1, 11/4
Answer:If the last number is 1¼ then the answer is ¾
Step-by-step explanation:
From one fraction to the other there is a difference of ¼
¼+¼=½
½+½=¾
¾+¼=1
1+¼=1¼
To identify the difference between the fractions you should get the LCM of the denominator which is 4 then you change all the fractions and make them have the same denominator
½ ,²/4 ,_ ,⁴/4 ,⁵/4
Then work with the numerator
1 , 2, _ ,4 , 5,
The dash is to be filled with 3
So your answer is ¾
Hi there! Can someone help with this?
Ali is baking cookies. She bakes 3 dozen sugar cookies, two dozen peanut butter cookies, and four dozen chocolate chip cookies. Ali gives away two dozen sugar cookies, 1.5 dozen peanut butter cookies, and 2.5 dozen chocolate chip cookies. How many total cookies does she keep?
f(x)=2x^7 find the domain and range
Answer:
Domain:
-∞<x<∞, or (-∞,∞) in interval notation
Range:
-∞<f(x)<∞, or (-∞,∞) in interval notation
Step-by-step explanation:
It’s infinite both ways, so:
Domain:
-∞<x<∞, or (-∞,∞) in interval notation
Range:
-∞<f(x)<∞, or (-∞,∞) in interval notation
Help! I need help with question 2 and 3. Thanks.
Answer:
Answer: SW IS 1.5 OKKKKKKKKK
A salesman need to sale 63 items to make it monthly go there are 18 selling days left in the month what is the average number of items you need to sell daily to reach his goal?
Answer:
He needs to sell an average of 3.5 items a day to reach his goal.
Step-by-step explanation:
To find the average he needs to sell, we need to divide the items he needs to sell by the number of days he has left to sell. He has 63 items and needs to sell them within 18 days.
63/18=3.5
He needs to sell an average of 3.5 items a day to reach his goal.
The salesman should sell 3.5 items on a daily average to reach his target when he needs to sell 63 items in 18 selling days.
What is average?The average is defined as the sum total of observations divided by the total number of observations.
How to solve the question?In the question, we are informed that a salesman needs to sell 63 items to make it monthly within 18 selling days left in the month.
We are asked the average number of items he should sell daily to reach his goal.
The average number of items per day can be calculated as the ratio of the total number of items left to the total number of days left.
Therefore, the average number of items per day = 63/18 = 3.5.
Learn more about averages at
https://brainly.com/question/20118982
#SPJ2
What is 4 times of 2 1/2
Answer:
10
Step-by-step explanation:
Change the fraction to a decimal:
2 1/2 = 2 + 1/2 = 2 + 0.5 = 2.5
Multiply:
4 x 2.5 = 10
10 is your answer.
~
You have a part-time job. You earn $7.75 per hour. If you work 20 hours
each week, what is your straight-time pay for each week?
A. $140
B. $145
C. $148
D. $150
E. $152
F. $155
Answer:
F. $155
Step-by-step explanation:
For this problem we simply need to multiply the base hourly pay by the amount of hours worked to find the straight-time pay for each week.
$7.75 * 20 = $155
Thus, your weekly pay will be $155.
Cheers.
Help with this pls ?
Answer:
x = 5
x = 11/2
x = -5/2
x = 3
x = 5/2
Step-by-step explanation:
What is the value of x
Answer:
x =68
Step-by-step explanation:
The sum of the angles of a triangle are 180
37+75+x = 180
Combine like terms
112+x = 180
Subtract 112 from each side
112+x-112=180-112
x =68
Braden biked 10 8/9 miles on Monday. On Tuesday, he biked 3/ 4 as far as Monday. How many total miles did he bike over the two days?
Answer:
19 1/18 miles.
Step-by-step explanation:
For Tuesday's ride we need to multiply 10 8/9 by 3/4.
10 8/9 = (9*10+8) / 9 = 98/9 miles.
98 / 9 * 3/4
= 98/3 * 1/4
49/6
= 8 1/6 miles.
Total miles over 2 days = 10 8/9 + 8 1/6
= 18 + 8/9 + 1/6
= 18 + 48/54 + 9/54
= 18 57/54
= 19 3/54
= 19 1/18 miles.
Ms. Terry's class is hosting a fundraising
challenge. The students in her class are
divided into 4 teams. Each team has an
equal number of students. Do you have
enough information to find how many
students are on each team? Explain.
In being able to find out whether it is possible to know the number of students on each team, there simply isn't enough information to do so.
In order to find out the number of students on each team, the following formula is necessary:
= Number of students in general / Number of teams
The number of teams is 4 so the denominator is present.
We however, do not have the number of students in general so we are unable to find out the number of students in each team.
In conclusion, we do not have enough information to find out the number of students in each team.
Find out more at https://brainly.com/question/15459630.
Rearrange the formula C = 5 9 (F − 32) for F.
Answer:
F = 32 + (C/59)
Step-by-step explanation:
C = 59(F - 32)
C/59 = F - 32
(C/59) + 32 = F
Hence,
F = 32 + (C/59)
Solve for x-
5x-2 = 2x+10
✨__________________________________✨
4 is correct answer
Step-by-step explanation:
[tex]5x - 2 = 2x + 10 \\ 5x - 2x = 10 + 2 \\ 3x = 12 \\ x = \frac{12}{3} \\ x = 4[/tex]
✨__________________________________✨
Written By: A Silent Voice☃️
Solve for the valid solution set: x−3≥2 or x+5≥7
Answer: X ≥ 5 or X ≥ 2
Step-by-step explanation:
Add 3 to both sides for the first equation
x ≥ 5
and subtract 5 from both sides for the second one
x ≥ 2
Write an equation for the description The difference between a number x and 18 is 21.
Answer:
x - 18 = 21
Step-by-step explanation:
In math, the description, "the difference between p and q" is written as ...
p - q
Then the difference between x and 18 is ...
x - 18
When we say that "is 21", we mean it is equal to 21:
x - 18 = 21
(3 + 5i) + (11 -7i) Write answer in standard form a +bi
Answer:
y7987
Step-by-step explanation:
Help ASAP plssssssssssssssssss
Answer:
18
Step-by-step explanation:
(6 - 9)(-2) = 6(-2) - 9(-2) Group of answer choices True False
Answer:
False
Step-by-step explanation:
Given f (x) = 2x + 1 , find x when f (2) = 9
A 4
B 19
C 13
D 9
Answer:
Step-by-step explanation:
2x + 1 = 9
2x = 8
x = 4
answer is A
6.6 as a mixed number
If f(x) = 3x2 + 1 and g(x) = 1 – x, what is the value of (f – g)(2)?
12
14
36
38
Answer: 14
Step-by-step explanation: