Answers
Because angle ATN is 70 degrees, then angle ANT is also 70 degrees
The 3 inside angles of a triangle = 180 degrees,
so angle A would = 180 - 70 - 70
Angle A = 180 -70-70 = 40 degrees
Related Questions
A laptop company has discovered their cost and revenue functions for each day: c(x) = 3x2 − 10x + 200 and r(x) = −2x2 + 100x + 50. if they want to make a profit, what is the range of laptops per day that they should produce? round to the nearest number which would generate profit.
Answers
c(x) = 3x2 − 10x + 200
and
r(x)=−2x2 + 100x + 50
Profit is given by:
P(x)=r(x)-c(x)
P(x)=(−2x2 + 100x + 50)-(3x2 − 10x + 200)
P(x)=-5x^2+110x-150
thus:
at maximum profit P'(x)=0
thus:
P'(x)=-10x+110=0
hence:
x=11
thus the number of units required for one to make profit is 11 units
Solve the equation. Check for extraneous solutions
please help!!!
Answers
!4x+3!=9+2x
1) 4x+3=9+2x
Solving for x:
4x+3-3-2x=9+2x-3-2x
2x=6
2x/2=6/2
x=3
Checking for extraneous solution:
!4x+3!=9+2x
x=3→!4(3)+3!=9+2(3)
!12+3!=9+6
!15!=15
15=15 Ok, then x=3 is not a extraneous solution
2) 4x+3=-(9+2x)
Solving for x:
4x+3=-9-2x
4x+3-3+2x=-9-2x-3+2x
6x=-12
6x/6=-12/6
x=-2
Checking for extraneous solution:
!4x+3!=9+2x
x=-2→!4(-2)+3!=9+2(-2)
!-8+3!=9-4
!-5!=5
5=5 Ok, then x=-2 is not a extraneous solution
Answer:
x = -2 or 3
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
Answers
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:
plz help
(4+3.2)×[(9−2)+2.5]
Answers
7.2((9 - 2) + 2.5)
Subtract the numbers in the parenthesis found inside the other parenthesis.
7.2(7 + 2.5)
Add the numbers in the parenthesis.
7.2(9.5)
Now multiply the two numbers together to get your final answer.
68.4
This means the expression (4 + 3.2) × ((9 − 2) + 2.5)is equal to 68.4.
Let me know if you have any further questions.
:)
A tunnel is in the shape of a parabola. The maximum height is 16 m and it is 16 m wide at the base, as shown below.
A parabola opening down with vertex at the origin is graphed on the coordinate plane. The height of the parabola from top to bottom is 16 meters and its width from left to right is 16 meters.
What is the vertical clearance 7 m from the edge of the tunnel?
15.4 m
0.3 m
15.7 m
0.6 m
Answers
Width: w=16
x=w/2→x=16/2→x=8
x=8, y=-16→y=ax^2→-16=a(8)^2→-16=a(64)→-16/64=a(64)/64→-1/4=a→a=-1/4
y=ax^2→y=-(1/4)x^2
7 m from the edge of the tunnel → x=w/2-7=8 m-7 m→x=1 m
x=1→y=-(1/4)x^2=-(1/4)(1)^2=-(1/4)(1)→y=-1/4
Vertical clearance: 16-1/4=16-0.25→Vertical clearance=15.75 m
Please, see the attached file.
Answer: Third option 15.75 m
y -k= 4a (x-h)^2
Solving for this, the vertical clearance 7m forom the edge of the tunnel must be
15.7m
Hope this helps! Goodluck!
Express 0.0037 as a power of 10.
Answers
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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in the box below, enter the value that missing from the table.
Answers
d = v * t
Where,
d: distance
v: speed
t: time
Clearing the time we have:
t = d / v
Rewriting:
t = d * (1 / v)
We look for the value of d:
For t = 1, v = 75 we have:
1 = d * (1/75)
d = 75
Then, v = 15 we have:
t = 75 * (1/15)
t = 5 hours
Answer:
The value that is missing from the table is:
t = 5 hours
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.
Answers
y_2 - y_1/x_2 - x_1
Fill in:
0 - r/0 - r
r/r
1
The answer to this problem is 1.
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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Find the value of the lesser root of x 2-8x+7=0
Answers
[tex] {x}^{2} - 8x + 7 = 0[/tex]
[tex](x - 7)(x - 1)[/tex]
Rule AB = 0, gives A = 0 or B = 0
[tex]x - 7 = 0 \: \: or \: \: x - 1 = 0 \\ x = 7 \: \: \: \: \: \: \: \: \: or \: \: x = 1[/tex]
Therefore, the smallest of both roots is x = 1.
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.
Answers
(158 + 139)/8
297/8 = 37.125
You will need a minimum of 38 chaperones for the 297 students. If there is any remainder(decimal) you will need an extra chaperone so the groups do not exceed 8.
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
Answers
In x second, the plane will have descended by 200*x ft = 200x ft
The altitude of the plane, y after x seconds will be 36000 - 200x. That is,
y= 36000-200x = -200x + 36000.
Therefore, the correct expression representing this situation is D.
y=ax+b
where:
a=slope=rate
b=y-intercept or initial valuegiven:
from the question
a=200 ft per second
b=36000 ft
thus the expression representing the situation will be:
y=200x+36000
where x is time in seconds
thus the answer is:
B. y = 200x + 36000
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
Answers
Simply because polynomials have solutions. 3x2 − 11x + 8 does have 2 solutions.
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
Answers
B) 0.7373
To find the probability that she is correct exactly 3 days, we have
[tex]_5C_3(0.8)^3(1-0.8)^{5-3} \\ \\\frac{5!}{3!2!}(0.8)^3(0.2)^2=0.2048[/tex]
To find the probability that she is right at least 4 of the 5 days, we find the probability she is right 4 days, the probability she is right 5 days, and add them together:
[tex]_5C_4(0.8)^4(1-0.8)^{5-4}+_5C_5(0.8)^5(1-0.8)^{5-5} \\ \\\frac{5!}{4!1!}(0.8)^4(0.2)^1+\frac{5!}{5!0!}(0.8)^5(0.2)^0 \\ \\5(0.8)^4(0.2)+0.8^5=0.4096+0.32768=0.73728\approx0.7373[/tex]
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
Answers
solution:
Gross pay=(salary)+(commissions)
base salary=$1500
commission=4%
monthly sales=$8000
commissions earned in cash
=4/100×8000
=$320
thus
Gross salary=320+1500=$1820
The hypotenuse of a right triangle is 5 m long. The longer leg is 1 m longer than the shorter leg. Find the side lengths of the triangle.
Answers
The Pythagorean theorem is used to determine the lengths of a right triangle's sides. When we know the hypotenuse length and the fact that one leg is 1m longer than the other, we can solve for the lengths to be approximately 3m and 4m.
Explanation:The subject of your question is related to the geometric concept of right triangles and the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be written as: a² + b² = c².
In this problem, we know the hypotenuse = 5m and the longer leg is 1m longer than the shorter leg. Let's denote the shorter leg as 'x' m. Consequently, the longer leg is 'x+1' m. Applying the Pythagorean theorem, we get: (x)² + (x+1)² = 5².
Solving this equation, we find x~3m (shorter leg) and x+1~4m (longer leg). These are the lengths of the sides of your right triangle.
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What is -1 3/5 x -2/3 as a mixed number?
Answers
-8 -2
--- * ----- = 16/15 (an improper fraction), or 1 1/15 (a mixed number)
5 3
1 3/5=8/5x2/3=16/15=1 1/15
Given: ABCD is a trapezoid, AC ⊥ CD AB = CD, AC=the square root of 75 , AB = 5 Find: AABCD
Answers
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.
Answers
We have then that the slope of the line is:
[tex]m = \frac{y2-y1}{x2-x1} [/tex]
Substituting values:
[tex]m = \frac{150-75}{30-15} m = 5[/tex]
Then, the equation of the line is:
[tex]y = 5x [/tex]
Answer:
C) A linear function to model the burned calories, and, 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:
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.
Answers
(x-2)(x+14)
Solve for x
x-2=0
x=2
x+14=0
x=-14
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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What are the coordinates of the image of vertex P after a reflection of rx-axis(x, y)? P'( , )
Answers
Answer: (-7, 4)
Step-by-step explanation:
Express answer in exact form.
A regular hexagon with sides of 3" is inscribed in a circle. Find the area of a segment formed by a side of the hexagon and the circle.
(Hint: remember Corollary 1--the area of an equilateral triangle is 1/4 s2 √3.)
Answers
the regular hexagon can be divided into 6 equilateral triangles
area of one equilateral triangle=s²*√3/4
for s=3 in
area of one equilateral triangle=9*√3/4 in²
area of a circle=pi*r²
in this problem the radius is equal to the side of a regular hexagon
r=3 in
area of the circle=pi*3²-----> 9*pi in²
we divide that area into 6 equal parts------> 9*pi/6----> 3*pi/2 in²
the area of a segment formed by a side of the hexagon and the circle is equal to 1/6 of the area of the circle minus the area of 1 equilateral triangle
so
[ (3/2)*pi in²-(9/4)*√3 in²]
the answer is
[ (3/2)*pi in²-(9/4)*√3 in²]
What is the length of AC?
Answers
[tex]\bf \cfrac{small}{large}\qquad \cfrac{DE}{BA}=\cfrac{EC}{CA}\implies \cfrac{7}{84}=\cfrac{x}{156-x}\implies 1092-7x=84x \\\\\\ 1092=91x\implies \cfrac{1092}{91}=x\implies 12=x\qquad \quad \qquad \boxed{AC=156-12}[/tex]
Find the equation for the line that passes through the point (−4,−2), and that is perpendicular to the line with the equation y−1=34(x+2).
Answers
y−1=34(x+2)
the equation above can be written in the form of y=ax+b, as follows:
y-1=34x+68
y=34x+69
the slope of the line is a=34
the slope of the perpendicular line will be:
m=-1/34
thus the equation of the perpendicular line cutting through (-4,-2) will be:
m(x-x1)=y-y1
thus
-1/34(x-(-4))=y-(-2)
-1/34x-4/34=y+2
y=-1/34x-36/17
Answer: y=-1/34x-36/17
Find the equation for the line that passes through the point (−4,−2), and that is perpendicular to the line with the equation y−1=34(x+2).
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?
Answers
A. -1
For confirmation, check a graph of cos(x) at π/2. It has negative slope at that point.
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?
Answers
volume of the tank=1130 gal
step 1
find the volume of the tank with deep 9 ft
volume of the tank with deep 9 ft=pi*r²*h
r=4/2-----> 2 ft
h=9 ft
volume of the tank with deep 9 ft=pi*2²*9-----> 113.04 ft³
step 2
convert to gal
1 ft³------------------> 7.48052 gal
113.04 ft³--------> x
x=113.04*7.48052-----> x=845.60 gal
the answer is
845.60 gal
alternative method
if the volume of the tank is 1130 gal for ----------> a height of 12 ft
X volume-----------------------------------> 9 ft
x=9*1130/12-----> 847.5 gal
Find the sum or difference: 2.8 - -5.1
Answers
-(-5.1)=5.1
2.8+5.1= 7.9
Is this what you were asking?
2.8 - (-5.1) = 2.8 + (+5.1) = 2.8 + 5.1 = 7.9
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
Answers
In short, the second option is correct. Hope this helps!
Find 2 numbers that have... a product of 49 and a sum of 14
Answers
Two triangles have side lengths 3, 4, 5 and 6, _____, 10, respectively. The triangles are similar to each other.
9
7
8
6.6
Answers
You have to find out happened between triangles
6 / 3 = 2
10 / 5 = 2
They multiplied the first triangle by 2 to get the second
Apply this to find the missing side
4 * 2 = 8
The answer is 8
Hope this helps!
Answer:
The correct option is: 8
Step-by-step explanation:
Suppose, the missing side length in second triangle is [tex]x[/tex]
So, the side lengths of first triangle: [tex]3, 4, 5[/tex]
and the side lengths of second triangle: [tex]6, x, 10[/tex]
As two triangles are similar, that means their corresponding side lengths will be proportional.
So,
[tex]\frac{3}{6}=\frac{4}{x}\\ \\ 3x= 4*6\\ \\ 3x= 24\\ \\ x=\frac{24}{3}=8[/tex]
So, the missing side length in second triangle is 8.
FACTORIZE PLEASE, A LOT OF POINTS
64x^(3)-48x^(2)+12xy^(2)-y^(3)
Answers
=> (4x)³ - 3(4x)²(y) + 3(4x)(y)² - y³
We know the formula: (a - b)³ = a³ - 3a²b + 3ab² - b³
By applying this formula above, we will get
=> (4x - y)³. (Ans)
Hope this helps!
or you can just put it in a smaller form by saying (4x - y)³