-1/3(x-15) = -4
1st step distribute(multiply) the -1/3 with what is inside parenthesis
-1/3x + 5 = -4
2nd step subtract 5 from both sides of the equation
-1/3x = -9
3rd step divide both sides of the equation by -1/3 to get x
x = -9 / -1/3
x = 27
What are the coordinates of the vertex for f(x) = x2 + 4x + 10?
Answer:
The coordinates of the vertex are [tex] (-2, -6)[/tex]
Step-by-step explanation:
The graph of this function is a parabola that opens up in the Cartesian plane. We can find like this:
[tex]y = (x ^ 2 + 4x +4) +6 = (x + 2) ^ 2 +6[/tex], where, [tex](y - 6) = (x + 2) ^ 2[/tex]
In the canonical equation of the parabola:
[tex](y - k) = (x + h) ^ 2[/tex], with the point (h, k) as the vertex, [tex]h = -2[/tex] and [tex]k = 6[/tex].
Conclusion: the coordinates of the vertex are [tex](-2, -6)[/tex]
a recipe makes a total of 5 cups a serving of pudding is 3/4 cup how many servings of pudding does the recipe make?
To find the number of servings of pudding the recipe makes, divide the total number of cups by the serving size. The recipe makes approximately 6.67 servings of pudding.
Explanation:To find the number of servings of pudding the recipe makes, divide the total number of cups by the serving size. In this case, the recipe makes 5 cups and each serving is 3/4 cup. So, to find the number of servings, divide 5 cups by 3/4 cup: 5 cups ÷ (3/4 cup) = 5 cups × (4/3 cup) = 20/3 servings
Therefore, the recipe makes approximately 6.67 servings of pudding.
Jane can pack 48 shirts into each box. round to the nearest compatible numbers to estimate how many boxes she will need to box 1,453 shirts
Answer: There are 30 boxes for 1453 shirts.
Step-by-step explanation:
Since we have given that
Number of shirts = 48
Number of box for 48 shirts = 1
We need to adjust number of boxes she will need to box 1453 shirts.
So, number of boxes would be
[tex]\dfrac{1453}{48}\\\\=30.27\\\\\approx 30[/tex]
Hence, there are 30 boxes for 1453 shirts.
Let c be parametrized by x = et sin (10t) and y = et cos (10t) for 0 ≤ t ≤ 2. find the length l of
c. l = 2 correct: your answer is correct.
To find the length of the curve c parameterized by given equations, we differentiate these equations with respect to t, find the magnitude of the derivative vector, and integrate this magnitude from t = 0 to t = 2.
Explanation:Finding the Length of Parametrized CurveTo find the length L of a curve c parametrized by x = et sin(10t) and y = et cos(10t) for 0 ≤ t ≤ 2, we use the formula for the arc length of a curve given in parametric form. The formula is L = ∫ |c'(t)| dt, where |c'(t)| represents the magnitude of the derivative of the parametric equations. The integral is evaluated over the given interval of t.
Step-by-step ExplanationFirst, compute the derivatives of the parametric equations: dx/dt and dy/dt.Next, find the magnitude of the velocity vector |c'(t)| = sqrt((dx/dt)^2 + (dy/dt)^2).Finally, integrate |c'(t)| from t = 0 to t = 2.Using this approach, we find that the length L of the curve c over the interval from 0 to 2 is indeed 2, as verified by the calculus of parametric functions.
What are fissures and how are theu created by land subsidence?
Karen is riding her bike at 4 miles per hour she wants to show this on a graph what should she draw
3.1666666667 as a fraction
circle P had a circumference of approximately 75 inches. what is the approximate of the radius ,r? use 3.14 for
Answer:
1) 12in
Step-by-step explanation:
The circumference is 75, so to find the diameter you have to divide 75 by 3.14. You get 24 approximately. Then divide the diameter by 2, so 24/2=12.
3x-2=x
show work and check
a garden table and a bench cost $1,000 combined the cost of a garden table is three times the cost of the bench what is the cost of the bench.
Tammy is at the dentist's office waiting on her appointment. She notices that the 6-inch-long minute hand is rotating around the clock and marking off time like degrees on a unit circle. Part 1: How many radians does the minute hand move from 1:20 to 1:55? (Hint: Find the number of degrees per minute first.)
Answer:
Part 1:
In order to find how many radians the minute hand moves from 1:20 to 1:55, we need to remember that there are 60 minutes in an hour (clock) and there are 360 degrees in the clock since the clock is a circle. After dividing 360 by 60, we find that each minute is equal to 6 degrees. After that, we can subtract the times, which tells us that there are 35 minutes between 1:20 and 1:55. Using this we can just multiply this out, to get 35 times 6, which is equal to 210 degrees. We can get our final answer by converting this into degrees. Since one 1 degree is about 0.0174, we can set up a proportion. After solving, we will get that the minutes hand moves 3.555 radians in total.
Isaac drinks 8 glasses of water each day. He says he will drink 2,920 glasses of water in a year that has 365 days. Is the exact answer reasonable
multiply 365 by 8
365 * 8 = 2920
so yes it is reasonable
How much does mike earn at fresh foods if he works 20 hours ? 40 hourss ? 60 hours ? when mike gets paid 10 per hour
Find x- and y-intercepts. Write ordered pairs representing the points where the line crosses the axes y= 1/2 x− 3/2
The x-intercept would be, (3,0). And the y-intercept would be, (0,-3/2).
One of the angles formed by two intersecting lines is 42°. What is the measure of the other three angles?
Answer:
42, 138, 138
Step-by-step explanation:
The manager of a plant nursery bought 120 lb of soil to use for potting plants. The manager can put 5 lb into each of the small pots and 12 lb into each of the large pots. The manager made a sketch to show the line representing the different combinations of pots that can be used. The x-axis represented the number of small pots and the y-axis represented the number of large pots. The manager labeled only the intercepts.
Which points did the manager label?
(0, 12) and (5, 0)
(0, 10) and (24, 0)
(0, 24) and (10, 0)
(0, 5) and (12, 0)
Three times a first number decreased by a second number is 1. the first number increased by twice the second number is 12. find the numbers.
Final answer:
The first number is 2 and the second number is 5.
Explanation:
Let's represent the first number as x and the second number as y.
According to the problem, we have the following equations:
3x - y = 1 (Equation 1)
x + 2y = 12 (Equation 2)
To solve this system of equations, we can use the method of substitution. We can rearrange Equation 2 to solve for x:
x = 12 - 2y
Now, we substitute this value of x into Equation 1:
3(12 - 2y) - y = 1
Expand and solve for y:
36 - 6y - y = 1
Combine like terms:
-7y = -35
Divide both sides by -7:
y = 5
Now, substitute this value of y back into Equation 2 to find x:
x + 2(5) = 12
x + 10 = 12
Subtract 10 from both sides:
x = 2
Therefore, the first number is 2 and the second number is 5.
What number is the solution of the inequality of 10.6 < b
For a circle of radius 3 feet, find the arc lengths subtended by a central angle of 57 degrees.
Answer: The length of an arc is 2.98 feet.
Step-by-step explanation:
Since we have given that
Radius of a circle = 3 feet
Angle subtended at the centre = 57°
We need to find the length of an arc:
As we know the formula for "Length of an arc":
[tex]Length=\dfrac{\theta}{360^\circ}\times 2\pi r\\\\Length=\dfrac{57}{360}\times 2\times \dfrac{22}{7}\times 3\\\\Length=2.98\ feet[/tex]
Hence, the length of an arc is 2.98 feet.
Will Reward Brainliest!
The average person lives for about 78 years. Does the average person live for at least 1,000,000 minutes? (Hint: There are 365 days in each year, 24 hours in each day, and 60 minutes in each hour.)
Answer:
cool kkdkdkkdkkfkkfkfkd
A pond at a hotel 4,290 gallons of water. The groundskeeper drains the pond at a rate of 78 gallons of water per hour. How long will it take to drain the pond?
divide total gallons by rate:
4290 / 78 = 55 hours
A person standing 20 feet from a street light casts a 10 foot shadow. How many times taller is the streetlight than the person? Assume the triangles are similar.
at a school pep rally, the ratio of students who wore red to those who wore yellow is 7 to 3. There are 300 students at the pep rally, and each student wore either red or yellow. How many more students wore red?
When converted to speeds, which list is in order from slowest to fastest?
17 miles in 2 minutes;
26 miles in 4 minutes;
33 miles in 6 minutes;
60 miles in 8 minutes
17 miles in 2 minutes;
60 miles in 8 minutes;
26 miles in 4 minutes;
33 miles in 6 minutes
33 miles in 6 minutes;
26 miles in 4 minutes;
60 miles in 8 minutes;
17 miles in 2 minutes
60 miles in 8 minutes;
33 miles in 6 minutes;
26 miles in 4 minutes;
17 miles in 2 minutes
When converted to speeds, the list which is in order from slowest to fastest is:
1) 33 miles in 6 minutes
2) 26 miles in 4 minutes
3) 60 miles in 8 minutes
4) 17 miles in 2 minutes
Step-by-step explanation:We know that speed is defined as the ratio of distance and time.
Here we are given distance and time in each of the options and we will check the speed of each and arrange them in increasing order.
1)
33 miles in 6 minutes
The speed is:
[tex]\dfrac{33\ \text{miles}}{6\ \text{minutes}}=5.5\ \text{miles\ per\ minute}[/tex]
2)
26 miles in 4 minutes
The speed is:
[tex]\dfrac{26\ \text{miles}}{4\ \text{minutes}}=6.5\ \text{miles\ per\ minute}[/tex]
3)
60 miles in 8 minutes
The speed is:
[tex]\dfrac{60\ \text{miles}}{8\ \text{minutes}}=7.5\ \text{miles\ per\ minute}[/tex]
4)
17 miles in 2 minutes
The speed is:
[tex]\dfrac{17\ \text{miles}}{2\ \text{minutes}}=8.5\ \text{miles\ per\ minute}[/tex]
Since,
[tex]5.5\ \text{miles\ per\ minute}<6.5\ \text{miles\ per\ minute}<7.5\ \text{miles\ per\ minute}<8.5\ \text{miles\ per\ minute}[/tex]
Hence, the increasing order of speed is:
1→2→3→4
The photography club has 28 members .there are 12 boys in the club . What is the ratio of boys to girls in simplest form?
A TV has a listed price of $607.95 before tax. If the sales tax rate is 8.75% , find the total cost of the TV with sales tax included.
Answer:
$661.15
Step-by-step explanation:
The addition of tax causes the price to be multiplied by (1+0.0875), so the final price is ...
$607.95×1.0875 ≈ $661.15
Solving Equations with Variables on Both Sides
1. (g+4) - 3g = 1 + g
g = 1
g = 4
no solution
identity
2. -6a + 3 = -3(2a - 1)
a=5
a=10
no solution
identity
3. 0.5b + 4 = 2(b+2)
b=0
b=0.5
no solution
identity
4. 8 -(3 + b) = b - 9
7
8
no solution
identity
−2 is less than or equal to w , and 8 is greater than or equal to w Use w only once in your inequality.
In 34 pound of a spice mix, there is 5/6 cup of cinnamon. How much cinnamon does the spice mix contain per pound? a 5/8 cup b 9/10 cup c 1 1/9 cups d 1 3/5 cups
Answer:
c. 1 1/9 cups
Step-by-step explanation:
To find cups per pound, divide cups by pounds.
(5/6 cup)/(3/4 pound) = (5/6)/(3/4) cup/pound
= (5/6)×(4/3) cup/pound . . . . . . . invert the denominator and multiply
= 20/18 cup/pound = 10/9 cup/pound = 1 1/9 cup/pound