Final answer:
To solve the inequality 10 < -2/3(9+12b), distribute -2/3 inside the parentheses, simplify, and divide by -8, which reverses the inequality. The solution is b < -2.
Explanation:
To solve the inequality 10 < -2/3(9+12b), we must first distribute the -2/3 across the parentheses:
Multiply -2/3 by 9 to get -6.
Multiply -2/3 by 12b to get -8b.
The inequality now looks like this: 10 < -6 - 8b. Next, we simplify by moving the constant term -6 to the left side:
Add 6 to both sides: 10 + 6 < -8b.
Combine like terms: 16 < -8b.
Finally, we divide both sides by -8, remembering that this reverses the inequality symbol:
Divide by -8: -2 > b or b < -2.
Therefore, the solution to the inequality is b < -2.
Dave is helping his grandmother make trail mix. His grandmother asks him to add cup of fruit for every cup of nuts.
To satisfy his grandmother’s request, Dave must mix cups of fruit for a single cup of nuts.
To satisfy his grandmother's request, Dave needs to mix [tex]\( \frac{1}{5} \)[/tex] cup of fruit for every [tex]\( \frac{1}{3} \)[/tex] cup of nuts.
To find out how many cups of fruit Dave needs to mix for a single cup of nuts, we need to find a common denominator for [tex]\( \frac{1}{5} \)[/tex] and [tex]\( \frac{1}{3} \)[/tex], which is 15.
[tex]\[ \frac{1}{5} \times \frac{3}{3} = \frac{3}{15} \][/tex]
[tex]\[ \frac{1}{3} \times \frac{5}{5} = \frac{5}{15} \][/tex]
So, Dave needs to mix [tex]\( \frac{3}{15} \)[/tex] cup of fruit for every [tex]\( \frac{5}{15} \)[/tex] cup of nuts.
Therefore, to satisfy his grandmother's request, Dave must mix [tex]\( \frac{3}{15} \)[/tex] cup of fruit for a single cup of nuts.
The complete Question is given below:
dave is helping his grandmother make trail mix his grandmother asks him to add 1/5 cup of fruit for every 1/3 cup of nuts. To satisfy his grandmother's request, drave must mix ___ cups of fruit for a single cup of nuts
Latoya drove 585 miles in 9 hours.
At the same rate, how many miles would she drive in 5 hours?
585/9 = 65 miles per hour
65 x 5 = 325 miles
she would drive 325 miles in 5 hours
Xavier is two years more than twice as old as Yoko. The sum of their ages is 86. How old is Xavier?
If the directrix of a parabola is the horizontal line y = 3, what is true of the parabola?
a)The focus is at (0, 3), and the equation for the parabola is y2 = 12x.
b)The focus is at (0, –3), and the equation for the parabola is x2 = –12y.
c)The focus is at (3, 0), and the equation for the parabola is x2 = 12y.
d)The focus is at (–3, 0), and the equation for the parabola is y2 = –12x.
Answer: on e2020 it’s b
Step-by-step explanation:
combine like terms
2x+3y+9x-9y-5x+12y
Answer:
6x+6y
Step-by-step explanation:
Hope I get it correct
Find the missing number
how to write 3x2+3y2+12x+18y-15 in general and standard format
What does 5 2/3 - 8 5/6 equal?
5 2/3 = 17/3 = 34/6
8 5/6 = 53/6
34/6 - 53/6 = -19/6 = -3 1/6
which expression gives the distance between the points (4,6)and (7,-3)
Answer:
As shown in the image....
Step-by-step explanation:
This equation follows with the distance formula which is (x2-x1)+(y2-y1) squared.
Mrs. Chin paid a 20 percent tip on the bill for lunch. If the tip amount was $2.75, what was the bill for lunch before the tip was added to it?
need the graphs diagram and answers thanks
y intercept = (0,11)
line of symmetry = x = -3
A mother bottlenose ate about 278 pounds of food in one week. About how much food did she eat in a day?
Miss Nelson works 154 hours each month he works eight months each year how many hours does Miss
Nelson work each year
what is 24 2/3 divided by 1 3/4
Answer:
Step-by-step explanation:
First, you should convert the mixed fractions into an improper fraction.
74/3 divided by 7/4
As you should know, any fraction divided by another is that fraction times the reciprocal of the other fraction.
74/3*4/7
There fore leaving 296/21 as the answer.
Which expression is equivalent to 100 n2 − 1? (10n)2 − (1)2 (10n2)2 − (1)2 (50n)2 − (1)2 (50n2)2 − (1)2
The correct answer is:
(10n)² − (1)²
Explanation:
If we evaluate this expression, we square everything in the first set of parentheses; this means we have 10²n² - 1², or 100n² - 1.
This is the expression we were trying to equal.
Estimate the circumference of the circle to the nearest hundredth. Use 3.14 the diameter is 11
The circumference of a circle with a diameter of 11 using 3.14 for pi is estimated to be 34.54 to the nearest hundredth.
Explanation:To estimate the circumference of a circle to the nearest hundredth, we use the formula C = πd, where C is the circumference and d is the diameter of the circle. Given that the diameter is 11 and we should use 3.14 for π, the calculation is C = 3.14 × 11. Performing the multiplication gives us a result of 34.54, which is the estimated circumference of the circle to the nearest hundredth.
If x = y − 2, simplify the expression x + 6. A. x + 4 B. x − 8 C. y + 4 D. y − 8
What is the value of the number 7 in 43,782
Which of the following sets of numbers could be the side lengths of a right triangle?
3, 4, and 7
9, 40, and 42
8, 15, and 16
20, 21, and 29
the answer is 20,21,29 because
20 times 20 is 400
21 times 21 is 441
and 29 times 29 is 841
the formula to ge tthe answer is a^2 + b^2 = c^2
20^2 + 21^2= 29^2
then plug the rest in
400+441= 841
The difference between the square roots of a number is 30. What is the number?
When measuring board footage for some exotic woods, a carpenter must use 1.25 inches for thickness rather than 1 inch in her calculations. Write 1.25 in expanded form.
Answer: [tex]1.25=1+0.2+0.005[/tex]
Step-by-step explanation:
Given : When measuring board footage for some exotic woods, a carpenter must use 1.25 inches for thickness rather than 1 inch in her calculations.
To write : 1.25 in expanded form.
When we write a decimal number in expanded form, we are showing the place value of each digit.
Now, 1.25 can be written as :
[tex]1.25=1+0.2+0.005[/tex]
Hence, the expanded form of [tex]1.25=1+0.2+0.005[/tex]
How much larger is one cubic foot than one cubic inch
5 less than three times a number is 10
3x-5 =10
add 5 to both sides
3x=15
divide both sides by 3
x=5
check:
3(5)-5 = 15-5 = 10
In a circle an arc 60 centimeters lon subtends an angle of 5 radians. What is the radius of the circle?
Akshat spent 3 hours each day driving to and form work. He opened an office closer to home and now drives 80 minutes to and form work. What is the percent of decrease in his commute time?
3*60 = 180 minutes
80/180 = 0.44
1-0.44 = 0.56
it was a 56% decrease in commute time
Jeremy created a small garden that measured 5 times 7.5 feet how many 10 feet rolls of fencing will he need to completely surround the garden?
If f(x) = 3x + 10x and g(x) = 2x – 4, find (f – g)(x).
Final answer:
To find (f - g)(x), subtract the function g(x) from f(x) by expanding and combining like terms.
Explanation:
To find (f - g)(x), we need to subtract the function g(x) from f(x). The given functions are f(x) = 3x + 10x and g(x) = 2x - 4. Let's subtract g(x) from f(x):
(f - g)(x) = (3x + 10x) - (2x - 4)
Expanding the expression, we get:
(f - g)(x) = 3x + 10x - 2x + 4
Combining like terms, we simplify it to:
(f - g)(x) = 11x + 4
Find the Area.
Triangle: A= 1/2 bh.
area = 1/2 b*h
1/2 *10 *015 =
1/2 * 150 =75
area = 75 square feet
45/100 in simplest form
the three digit number 49x is divisible by 4 with no remainders. if the sum of the digits is divisible by 5 with no remainders, what is the number