Find two number whose sum is 60 such that the sum of the square of one number plus 12 times the other number is a minimum
What is the vertex form, f(x) = a(x − h)2 + k, for a parabola that passes through the point (4, −3) and has (5, 2) as its vertex. What is the standard form of the equation?
Answer:
y = x² - 10x + 27
Step-by-step explanation:
1. What is the median of the following set of numbers?
48.4, 47, 43, 47, 43.6, 41.6, 45, 51.4, 38.6
Hint: Order the numbers from least to greatest first!
A. 48.4 B. 43.6 C. 45
2. Each of the five math teachers are comparing the number of students in their homeroom classes. The number of boys and girls in each teachers’ classes are recorded in the table below.
Hint: Mean is the average.
Which statement best describes the means of the two sets of data?
A. The mean number of girls in 7 times greater than the mean numbers of boys in the homeroom classes.
B. The mean number of girls is the same as the mean number of bboys in the homeroom classes.
C. The mean number of girls is 7 more than the mean number of boys in the homeroom classes.
Answer:b
Step-by-step explanation:divided look around the chart
Circle P is tangent to the x-axis and the y-axis. If the coordinates of the center are (r, r), find the slope of the line through the origin and the center.
The value of slope of the line through the origin and the center is,
⇒ Slope = 1
What is Equation of line?The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
Circle P is tangent to the x-axis and the y-axis.
And, the coordinates of the center are (r, r),
Now, The value of slope of the line through the (0, 0) and the center (r, r) is,
⇒ Slope = (r - 0) / (r - 0)
⇒ Slope = r/r
⇒ Slope = 1
Thus, The value of slope of the line through the origin and the center is,
⇒ Slope = 1
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f(x) = cos(x)
f'(x) = -sin(x)
f'(π/2) = -sin(π/2)
f'(π/2) = -1
My answer to this question is A. -1, but I am posting it here because several students got B. +1 as their answer. Can anyone confirm the answer as A?
Given: ABCD is a trapezoid, AC ⊥ CD AB = CD, AC=the square root of 75 , AB = 5 Find: AABCD
In this attached picture according to the conditions of the problem we have an isosceles trapezoid and since we know that legs are equal (AD=BC=5 cm), we have to calculate bases and height in order to find the area. Working with the triangle BCD, we apply Pythagoras theorem and find that CD = [tex] \sqrt{75+25} [/tex] = 10 cm. Since BDC is a right triangle, applying theorem for the area of triangles, we find that [tex] \frac{1}{2} * BF = \frac{1}{2} * 5 * \sqrt{75} [/tex] and BF= [tex] 0.5\sqrt{75} [/tex]. Since ABCD is an isosceles trapezoid, triangles ADE and BFC are congruent with Angle Side Angle theorem. Then, DE=FC and with the help of Pythagoras theorem, DE=FC=2.5 cm. Then, AB=EF=5 cm and the area of the trapezoid is [tex]A= BF * \frac{AB+CD}{2} = 0.5 \sqrt{75} * \frac{5+10}{2} = 18.75 \sqrt{3} cm^{2} [/tex]
The area of the given trapezoid will be [tex]\frac{75}{4} \sqrt{3}[/tex].
It is given that
In trapezoid ABCD
AE ⊥ CD
AC = √75
AD=BC =5
AB =5
In the triangle ADC
From Pythagoras theorem
AC²+AD²=DC²
(√75)² +5² = DC²
DC=10
Let DE=CF=x (Isosceles trapezoid)
What is isosceles Trapezoid?
Trapezoid in which the base angles are equal and therefore the left and right side lengths are also equal.
AB=EF= DC-2x
5 = DC-2x
x=5/2
AE = [tex]\sqrt({5^{2} } -(5/2)^2)\\\\[/tex]
AE = [tex]\sqrt{75} /2[/tex]
So, the area of the trapezoid ABCD = [tex]\frac{1}{2} *(AB+CD)*AE[/tex]
Area of the trapezoid ABCD = [tex]\frac{1}{2} *(5+10)*\frac{\sqrt{75} }{2}[/tex]
Area of the trapezoid ABCD = [tex]\frac{75}{4} \sqrt{3}[/tex]
Therefore, The area of the given trapezoid ABCD will be [tex]\frac{75}{4} \sqrt{3}[/tex].
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The table shows the calories burned during exercise.
(picture of the table attached)
Which statement is true?
A)The y-intercept of the function is (15, 75).
B)The rate of change is 15 calories burned per minute.
C)A linear function to model the calories burned, y, as a function of time in minutes, x, is y = 5x.
D)An exponential function to model the calories burned, y, as a function of time in minutes, x, is y = 5x.
Answer: C. A linear function to model the calories burned, y, as a function of time in minutes, x, is y = 5x.
Step-by-step explanation:
What is the percent chance a coin lands on heads with 3 tosses?
Consider the equation x^2 + 12x + c = 0. If c = -28, list the steps to solve the equation by completing the square, and give the solution or solutions.
The solutions of the equation x² + 12x - 28 = 0 are x = 2 or x = -14.
What is quadratic equation?A quadratic equation is a second-order polynomial equation in a single variable x , ax²+bx+c=0. with a ≠ 0 .
To solve the equation x² + 12x + c = 0, where c = -28, by completing the square.
Substitute c = -28 into the equation to get x² + 12x - 28 = 0.
x² + 12x = 28
Complete the square by adding the square of half the coefficient of x to both sides of the equation:
x² + 12x + (12/2)² = 28 + (12/2)²
x² + 12x + 36 = 64
(x + 6)² = 64
Take the square root of both sides of the equation.
x + 6 = ±8
x=8-6=2
x=-8-6=-14
Hence, the solutions of the equation x² + 12x - 28 = 0 are x = 2 or x = -14.
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grant is rolling a standard six sided number die eight times. how many outcomes are possible
We have been given that Grant is rolling a standard six sided number die eight times and we have to find the total number of outcomes.
Grant is rolling six sided number die. Hence, we can say that
Number of outcomes if rolled once = 6
Number of outcomes if rolled twice = [tex]6\times 6= 6^2[/tex]
Number of outcomes if rolled thrice= [tex]6\times 6 \times 6= 6^3[/tex]
We can see that if rolled twice then we have exponent 2, when rolled trice then we have an exponent 3.
Hence, if rolled 8 times then we have an exponent 8 on 6.
Therefore, the possible number of outcomes should be [tex]6^8= 1679616[/tex]
Hence, the number of possible outcomes is 1679616
What is the length of AC?
in the box below, enter the value that missing from the table.
help please
Sammy is planning a trip to Nashville. He knows the hotel costs $125 per night and the round trip flight is $159. He has a budget of $900 to spend on his trip. Which of the following inequalities represents his budget to determine how many nights he can stay in Nashville?
125n + 159 ≥ 900
125n + 159 ≤ 900
159n + 125 ≤ 900
159n + 125 ≥ 900
What is the smallest natural number that 2, 10, 14, and 36 will divide evenly?
On Tuesday, Mrs. Myles assigned 7 more problems than she did on Monday. If she assigned x problems on Monday, write an expression to represent how many problems Mrs. Myles assigned on Tuesday
Answer:
Number of problems assigned on Tuesday = x+7
Step-by-step explanation:
Number of problems assigned on Monday = x.
Number of problems assigned on Tuesday is 7 more than that assigned on Monday.
Number of problems assigned on Tuesday = x+7. [In Matha we use + sign for more than]
The expression that will represent the number of problems Mrs. Myles assigned on Tuesday is x+7.
Answer: actually it 7 + x the other way around
Step-by-step explanation:
The local weather person has been accurate in her predictions within 2 degrees temperature forecast 80% of the time. Find the probability that she is accurate...
a) exactly 3 out of the next 5 days
b) at least 4 of the next 5 days
Which of the following shows that polynomials are closed under subtraction when polynomial 5x − 6 is subtracted from 3x2 − 6x + 2?
3x2 − 11x + 8 may or may not be a polynomial
3x2 − 11x + 8 will be a polynomial
3x2 − x + 4 may or may not be a polynomial
3x2 − x + 4 will be a polynomial
Tip: Every 2 after 3x is an exponent.. so it would be 3x^2
There are 158 fourth grade studnets and 139 fifth grade students going on a field trip. There needs to be one caperone for every 8 kids. Explain how to find the number of caperones needed for the trip.
What is -1 3/5 x -2/3 as a mixed number?
Express 0.0037 as a power of 10.
To express 0.0037 as a power of 10, we move the decimal point 3 places to the right, resulting in 3.7 × 10⁻³.
Explanation:To express 0.0037 as a power of 10, we need to count the number of places we have to move the decimal point to get a number between 1 and 10. In this case, we have to move the decimal point 3 places to the right, so the power of 10 is -3.
0.0037 = 3.7 × 10-3
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PLEASE HELP 20 POINTS
Answer:
Step-by-step explanation:
i put a awnser and that person hacked me lol
Find 2 numbers that have... a product of 49 and a sum of 14
A jet plane is descending at a rate of 200 feet per second from an altitude of 36000 feet let x represent the number of seconds of descent and y represent the jet plane’s altitude in feet.
Which expression represents this situation?
A. y = 200x - 36000
B. y = 200x + 36000
C. y = -200x - 36000
D. y = -200x + 36000
Which point best represents the square root of 15?
A. Point A
B. Point B
C. Point C
D. Point D
Find the value of the lesser root of x 2-8x+7=0
Find the approximate circumference of a circle with a radius of 2.6 millimeters. Use = 3.14.
plz help
(4+3.2)×[(9−2)+2.5]
The tank shown is a cylinder with diameter equal to 4 feet and height equal to 12 feet. the tank holds 1130 gallons of rainwater when full. how many gallons of water are in the tank when the depth of the water is 9 feet?
Jack Watkins earns a base salary of $1500 a month, plus a 4% commission on the sales he makes. What is his gross pay of his sales for the month are $8000.
A. 1520
B. 1532
C. 1700
D. 1820
FACTORIZE PLEASE, A LOT OF POINTS
64x^(3)-48x^(2)+12xy^(2)-y^(3)
or you can just put it in a smaller form by saying (4x - y)³