Answer:
C. n + n + 1 = 37; n = 18; n + 1 = 19
Step-by-step explanation:
If we let n represent the smaller integer, then the larger one is n+1. Their sum is 37, so you have ...
n + (n+1) = 37
When you subtract 1 and collect terms, you have ...
2n = 36
Dividing by 2 gives you ...
n = 18
Then the larger integer is ...
n+1 = 19
The matching choice is C.
Mrs. Robinson, an insurance agent, earns a salary of $4,800 per year plus a 3% commission on her sales. The average price of a policy she sells is $6,100.
Write an inequality to find how many policies Mrs. Robinson must sell to make an annual income of at least $8,000.
4800+183x<(line under the arrow)=8000
4800+183x=8000
4800+183x>=8000
4800+186>(ine under the arrow)=8000
Answer:
[tex]4800+183x\geq 8000[/tex]
She must sell at least 18 policies to make an annual income of at least $8,000
Step-by-step explanation:
Let [tex]x[/tex] be the number of policies Mrs. Robinson must sell
We know that Mrs. Robins makes 3% on commission for each policy sold. We also know that the average price of a policy is $6,100, so she makes 3% of $6,100 per policy sold. To find the 3% of $6,100 we just need to multiply 3% and $6,100; then dive the result by 100%:
[tex]\frac{3*6,100}{100} =183[/tex]
Now we know that she makes $183 per policy sold. Since [tex]x[/tex] is the number of policies sold, [tex]183x[/tex] is her total commission for selling [tex]x[/tex] policies.
We also know that She makes $4,800 per year, so her total annual income is her salary plus her commissions, in other words:
[tex]4800+183x[/tex]
Finally, we know that she wants to make at least $8,000, so her salary plus her commissions must be greater or equal than $8,000:
[tex]4800+183x\geq 8000[/tex]
Let's solve the inequality:
1. Subtract 4800 from both sides
[tex]4800-4800+183x\geq 8000-4800[/tex]
[tex]183x\geq 3200[/tex]
2. Divide both sides by 183
[tex]\frac{183x}{183} \geq \frac{3200}{183}[/tex]
[tex]x\geq 17.48[/tex]
Since she can't sell a fraction of a policy, we must round the result to the next integer:
[tex]x\geq 18[/tex]
We can conclude that she must sell 18 policies to make an annual income of at least $8,000.
If the distance covered by an object in time t is given by s(t)=t^2+5t , where s(t) is in meters and t is in seconds, what is the distance covered in the interval between 1 second and 5 seconds?
A. 24 meters
B. 30 meters
C. 40 meters
D. 42 meters
E. 44 meters
Answer:
E. 44 meters
Step-by-step explanation:
The function that models the distance covered by the object is
[tex]s(t)=t^2+5t[/tex]
where s(t) is in meters and t is in seconds.
The distance covered by the object after 1 second is
[tex]s(1)=1^2+5(1)=6m[/tex]
The distance covered by the object after 1 second is
[tex]s(1)=5^2+5(5)=50m[/tex]
The distance covered between 1 second and 5 seconds is
50-6=44m
Answer:
person above is right
Step-by-step explanation:
right on plato
if g(x)= 2x -1 then g(4)=
g(4)=2×4_1
8-1
=9
hence the answer is 9
hope it helps you!!!!!!!!!
Answer:
g(4) = 7
Step-by-step explanation:
To evaluate g(4) substitute x = 4 into g(x), that is
g(4) = (2 × 4) - 1 = 8 - 1 = 7
Substitute the value x = -1 into the first equation and solve for y.
{ y= 2x - 1
-2x - y = 5
Answer:
y = -3
Step-by-step explanation:
Following the directions, we have ...
y = 2·(-1) -1 = -2-1 . . . . . . put -1 where x is in the equation
y = -3
I need help on this
Answer:
none of the above
Step-by-step explanation:
The transformation ...
g(x) = k·f(x -a) +b
vertically stretches the function f(x) by a factor of "k", translates it to the right by "a" units and up by "b" units. There won't be any reflection across the x-axis unless the stretch factor (k) is negative.
You have k=2, a=2, b=-2, so the function is stretched by a factor of 2, then translated to the right and down by 2 units each.
_____
The stretch is done first. If it is done last, then the translation factor(s) are also stretched. All the answer choices given in your problem statement list the stretch last, so none is correct. (You are probably expected to choose d.)
A man standing on the roof of a building 64.0 feet high looks down to the building next door. He finds the angle of depression to the roof of that building from the roof of his building to be 34.7°, while the angle of depression from the roof of his building to the bottom of the building next door is 63.3°. How tall is the building next door? (Round your answer to the nearest tenth.)
Answer:
The height of the next door building is 41.7 feet
Step-by-step explanation:
* Lets study the situation in the problem
- The man standing on the roof of a building 64.0 feet high
- The angle of depression to roof of the next door building is 34.7°
- The angle of depression to the bottom of the next door building
is 63.3°
- We need to find the height of the next door building
* Lets consider the height of the man building and the horizontal
distance between the two building formed a right triangle and the
angle of depression is opposite to the side which represented the
height of the building
- Let the horizontal distance between the two buildings called x
# In the triangle
∵ The length of the side opposite to the angle of depression (63.3°)
is 64.0
∵ The length of the horizontal distance is x which is adjacent to the
angle of depression (63.3°)
- Use the trigonometry function tanФ = opposite/adjacent
∴ tan 63.3° = 64.0/x ⇒ use cross multiplication
∴ x (tan 63.3°) = 64 ⇒ divide both sides by (tan 63.3°)
∴ x = 64.0/(tan 63.3°)
∴ x = 32.1886 feet
- Lets use this horizontal distance to find the vertical distance between
the roofs of the two buildings
* Lets consider the height of the vertical distance between the roofs
of the two buildings and the horizontal distance between the two
building formed a right triangle and the
angle of depression is opposite to the side which represented the
vertical distance between the roofs of the two buildings
- Let the vertical distance between the roofs of the two buildings
called y
# In the triangle
∵ The vertical distance between the roofs of the two buildings is y
and opposite to the angle of depression (34.7°)
∵ The horizontal distance x is adjacent to the angle of
depression (34.7°)
∴ tan (34.7°) = y/x
∵ x = 32.1886
∴ tan 34.7° = y/32.1886 ⇒ use the cross multiplication
∴ y = 32.1886 (tan 34.7°)
∴ y = 22.2884 ≅ 22.3 feet
∴ The vertical distance between the roofs of the two
buildings is 22.3 feet
- The height of the next door building is the difference between the
height of the man building and the vertical distance between the
roofs of the two buildings
∴ The height of the next door building = 64.0 - 22.3 = 41.7 feet
Final answer:
This answer explains how to calculate the height of a building using trigonometry based on given angles of depression.
Explanation:
To determine the height of the building next door, we need to use trigonometric functions. Specifically, the tangent of an angle in a right triangle relates the angle to the ratio of the opposite side to the adjacent side.
The total height of the building next door will be H + D.
From the top of the 64.0 feet building, looking down with an angle of depression of 34.7° to the roof of the building next door gives us:
Tan(34.7°) = D/Distance
Similarly, looking down with an angle of depression of 63.3° to the bottom of the building next door gives us:
Tan(63.3°) = (H + D)/Distance
By creating a right triangle for each angle, we can establish the relationships to find the height, which turns out to be around 52.0 feet.
a home building contractor bought 4 2/8 acres for $165,000. What was the cost of each acre? (round to nearest dollar.)
Answer:
$ 38,824
Step-by-step explanation:
Total Area of land that was bought = [tex]4\frac{2}{8}[/tex] acres
Total Cost of this area = $ 165,000
We have to find the cost of 1 acre of land.
Cost of [tex]4\frac{2}{8}[/tex] acres of land = $ 165,000
Dividing both sides by [tex]4\frac{2}{8}[/tex], we get:
Cost of 1 acre of land = $ 165,000 ÷ [tex]4\frac{2}{8}[/tex]
= $ 38,824
Thus the cost of each acre of land is $ 38,824 (rounded to nearest dollar)
Answer: $38,824
Step-by-step explanation:
Convert the mixed number [tex]4\ \frac{2}{8}[/tex] as a decimal number.
Divide the numerator by the denominator and add it to the whole number 4. Then:
[tex]4+0.25=4.25acres[/tex]
Then, knowing that 4.25 acres cost $165,000 , divide this amount by 4.25 acres to find the cost of each acre.
Therefore, you get that the cost of each acre rounded to nearest dollar is:
[tex]cost=\frac{\$165,000}{4.25}\\cost=\$38,824[/tex]
Which of the following formulas could be used to find the perimeter, P, of a regular octagon? P = 6s P = 7s P = 8s P = 9s
Answer: P=8s
Perimeter of octagon=8sides(unit value of side)
Answer:
P=8s
Step-by-step explanation:
we know that
The perimeter of a regular figure is equal to multiply the number of sides by the length of one side
In this problem
A regular octagon has 8 sides
Let
s-----> the length of one side
The perimeter is equal to
P=8s
What is the premieter of this red polygon
Answer:
338 in
Step-by-step explanation:
If each of the measures shown is the measure from the vertex to the point of tangency, then that measure contributes twice to the perimeter (once for each leg from the vertex to a point of tangency).
2(22 in + 27 in + 22 in + 98 in) = 2(169 in) = 338 in
Find the equation of the line that is perpendicular to the line 4x + 2y = 1 and passes through the point (−4, 3).
A) y=2x+5
B) y=2x+2
C) y=1/2x+2
D) y=1/2x+5
Answer:
y=1/2x+5 or d
Step-by-step explanation:
Answer is D
Step-by-step explanation:
HELP PLZ 20 POINTS PLZ DUE TM!!!
Answer:
40 (cm)
Step-by-step explanation:
0. make up a new picture with additional elements (radius of the inscribed circle, it's 'x'; and some elements as shown in the attached picture);
1. the formula of the required perimeter is P=a+b+c, where c- hypotenuse.
2. apply the Pythagorean theorem: a²+b²=c², where c - hypotenuse, then calculate value of 'x' (attention! x>0, the length is positive value !)
3. substitute 'x' into the formula of the required perimeter. The result is 40.
PS. All the details are in the attached picture, answer is marked with red colour.
The equation h(t)=−16t2+19t+110 gives the height of a rock, in feet, t seconds after it is thrown from a cliff.
What is the initial velocity when the rock is thrown?
[tex]\bf ~~~~~~\textit{initial velocity} \\\\ \begin{array}{llll} ~~~~~~\textit{in feet} \\\\ h(t) = -16t^2+v_ot+h_o \end{array} \quad \begin{cases} v_o=\stackrel{}{\textit{initial velocity of the object}}\\\\ h_o=\stackrel{}{\textit{initial height of the object}}\\\\ h=\stackrel{}{\textit{height of the object at "t" seconds}} \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ h(t)=-16t^2+\stackrel{\stackrel{v_o}{\downarrow }}{19}t+110~\hspace{10em}19~\frac{ft}{sec}[/tex]
The initial velocity of the rock when thrown from the cliff is represented by the coefficient of the t term in the quadratic equation, which is 19 feet per second.
The equation h(t) = -16t² + 19t + 110 describes the height of a rock in feet, as a function of time in seconds after it is thrown from a cliff. To find the initial velocity of the rock when it is thrown, we look at the coefficient of the linear term in this equation, which represents the initial velocity in feet per second (since the equation is quadratic and the coefficient of the t2 term corresponds to half the acceleration due to gravity in feet per second squared).
The initial velocity of the rock is given by the coefficient of the t term, which is 19 feet per second.
Which of the following points is a solution of the inequality y < -|x|?
A. (1,-2)
B. (1,-1)
C. (1,0 )
ANSWER
The correct choice is A
EXPLANATION
The given inequality is
y < -|x|
We substitute each point into the inequality to determine which one is a solution.
Option A
-2 < -|1|
-2 < -1.
This statement is true.
Hence (1,-2) is a solution.
Option B.
-1 < -|1|
-1 < -1.
This statement is false.
Option C
0 < -|1|
0 < -1.
This statement is also false.
GEOMETRY!!! 15 PTSSSSS
Answer:
23) option c
JL ≈ 9.3
25) option c
y ≈ 9.6
Step-by-step explanation:
25)Given in the question that,
cos(21°) = 9 / y
y = 9/cos(21°)
y = 9.64
y ≈ 9.6(nearest tenth)
23)Given in the question that the hypotenuse of right angle triangle = 12
To find,
height of the right angle triangle
angle k = 39°
so by using trigonometry identity
cos(39) = opp/hypo
cos(39) = JL / KL
JL = cos(39)(12)
JL = 9.32
JL ≈ 9.3
Answer:
Q 23. Last option 7.6
Q 25 Third option
Step-by-step explanation:
To solve Q 23
From the figure we can write,
Sin 39 = Opposite side/Adjacent side
= JL/KL
= JL/12
JL= 12 * Sin 39
= 12 * 0.629 = 7.55
= 7.6
To solve Q 25
Cos 21 = 9/y
y = 9/Cos 21 = 9/0.9335
= 9.64
= 9.6
Please help
must show work
there are 5 that I'm stuck on
you cannot show too much "work"
basically, you remove what is common to all of the factors, and then put brackets, as it will be multiplied back in, remember that when you multiply exponents with the same base, its same as adding them, so subtract to remove...
you can seperate two of the variables , then factor, then subtract the last one from those two, because it cannot be factored out , as in part2 #2
What is the x-intercept and the y-intercept of the line in the graph
Answer:
x intercept= 3
y=-2
Step-by-step explanation:
the intercept is the point when the line crosses the axis
MATH GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG
Answer:
Option C is correct.
Step-by-step explanation:
The equation used to represent the slop-intercept form is
y= mx + b
where m is the slope
and b is the y-intercept.
So, in the given question y-intercept = (0,8)
b= 8 and
slope =m= 1/2
the equation will be:
y = mx + b
y= (1/2)x + 8
So, Option C is correct.
Use substitution to solve each system of equations.
x – 5y = –3
–7x + 8y = –33
A(2, 7)
B(–5, 1)
C(7, 2)
D(1, –5)
I think it’s C sorry if I’m wrong
For this case we have a system of sos equations with two unknowns:
[tex]x-5y = -3\\-7x + 8y = -33[/tex]
We clear "x" from the first equation:
[tex]x = -3 + 5y[/tex]
We substitute in the second equation:
[tex]-7 (-3 + 5y) + 8y = -33\\21-35y + 8y = -33\\-27y = -33-21\\-27y = -54\\y = \frac {-54} {- 27}\\y = 2[/tex]
We find the value of "x":
[tex]x = -3 + 5 (2)\\x = -3 + 10\\x = 7[/tex]
ANswer:
(7,2)
Option C
Help Please..
Use the point-slope formula to find the equation of a line that goes through point (10, 32)
and has a slope of 3
Answer:
The equation of the line into point slope form is [tex]y-32=3(x-10)[/tex]
Step-by-step explanation:
we know that
The equation of the line into point slope form is equal to
[tex]y-y1=m(x-x1)[/tex]
In this problem we have
[tex]m=3[/tex]
[tex](x1,y1)=(10,32)[/tex]
substitute
[tex]y-32=3(x-10)[/tex] ---> equation of the line into point slope form
[tex]y=3x-30+32[/tex]
[tex]y=3x+2[/tex] ---> equation of the line into slope intercept form
an athlete collected information on different brands of nutrition bars
Answer:
A and C are correct because the farther its is to 1 the stronger it is
Answer:
The answer is A and C
Step-by-step explanation:
Solve the systems of substitution(find out what number x is and what number y is)
y=2x+5
y=3x+11
Answer:
(x, y) = (-6, -7)
Step-by-step explanation:
Substitute for y:
2x +5 = 3x +11 . . . . . use the first expression for y in the second equation
0 = x +6 . . . . . . . . . . subtract 2x+5
-6 = x . . . . . . . . . . . . add -6
y = 2(-6) +5 = -7 . . . .substitute for x
The solution is x = -6, y = -7.
What is the length of the third side of the window frame below?
(Figure is not drawn to scale.)
A picture of a right triangular window frame is shown. The longest side has length labeled as 39 inches. The height of the frame is labeled as 36 inches.
15 inches
27 inches
25 inches
32 inches
Answer:
15 inches
Step-by-step explanation:
The longest side of the right triangular window frame is 39 inches
The height is 36 inches
Let the base of the window frame be x inches
So according to Pythagoras theorem,
x² + 36² = 39²
x² = 39² - 36² = 225
x = [tex]\sqrt{225}[/tex] = 15 inches
The third side of the window frame is therefore equal to 15 inches.
The length of the third side of the window frame will be 15 inches. Then the correct option is A.
What is a Pythagoras theorem?The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.
The Pythagoras theorem formula is given as
H² = P² + B²
The longest side has a length labeled as 39 inches. The height of the frame is labeled as 36 inches.
Let x be the length of the third side of the window frame. Then we have
39² = x² + 36²
x² = 39² - 36²
x² = 1521 - 1296
x² = 225
x = 15 inches
Then the correct option is A.
More about the Pythagoras theorem link is given below.
https://brainly.com/question/343682
#SPJ2
what is the discriminant of the polynomial below 4x^2-20x +25
Answer:
The discriminant D=0
Step-by-step explanation:
For the duadratic polynomial [tex]ax^2+bx+c[/tex] the discriminant is
[tex]D=b^2-4ac.[/tex]
In your case, for the polynomial [tex]4x^2-20x+25,[/tex]
[tex]a=4;[/tex][tex]b=-20;[/tex][tex]c=25;[/tex][tex]D=(-20)^2-4\cdot 4\cdot 25=400-400=0.[/tex]Answer:
The answer is 0 D
A circle with radius r is inscribed into a right triangle. Find the perimeter of the triangle if:the length of the hypotenuse is 24 cm, and r=4 cm;
Answer:
56 cm
Step-by-step explanation:
The tangents from the 90° angle will form a square with the radii that has a side length of 4. If we call the length of the short side of the right triangle "x", then the tangent lengths are ...
on the short side of the triangle: 4, x-4
on the hypotenuse side of the triangle: x-4, 24-(x-4) = 28-x
on the long side of the triangle: 4, 28-x
The perimeter is twice the sum of the unique tangent lengths:
P = 2(4 + (x-4) + (28-x)) = 2·28
P = 56 . . . . . the perimeter is 56 cm.
_____
Using the Pythagorean theorem on side lengths x and 32-x and hypotenuse 24, we find x = 16-4√2 ≈ 10.34, the length of the short side (in cm).
Law of sines: sin(A)/a=sin(B)/b=sin(C)/c How many distinct
Answer:
According to the given question if one of the angle of the triangle is 75 degree and the other two sides are of length 2 and 3 units respectively then option C is correct. Only One triangle can be formed where Angle B will be 40 degree. You can figure it out from the steps mentioned below first of all draw an Arc with the length either 3cm or 2 cm that will be the base of a triangle and then from the ending point again cut an arc then after from the starting point that is the point draw an angle of 75 degree with the help of protactor and extend it to meet the Arc finally you can get the 40 degree.
Hope this helps. Name me brainliest please
*algebra* What is (f−g)(x)?
Answer:
x^3 -6x^2 +18x-10
Step-by-step explanation:
f-g (x) = f(x) -g(x)
f(x) = x^3 -2x^2 +12x-6
g(x) =4x^2 -6x +4
f(x) -g(x) =x^3 -2x^2 +12x-6 - (4x^2 -6x +4)
Distribute the minus sign
x^3 -2x^2 +12x-6 - 4x^2 +6x -4
Combine like terms
x^3 -2x^2- 4x^2 +12x+6x-6 -4
x^3 -6x^2 +18x-10
PLEASE HELP 70 POINTS
4a. An experiment had the following result for 20 flips of a coin: P(Tails) 12/20 P(Heads) = 8/20. If you flip 90 more times, how many would be tails?
4b. Explain how many flips would be tails if you flip 100 more times.
Answer:
4a. About 54 times NOT INCLUDING THE FIRST TRIAL
4b. About 60 times NOT INCLUDING THE FIRST TRIAL
Step-by-step explanation:
I say about because we don't know if it's ALWAYS going to be the same results.
4a. Also 12*4 because it's 20 times so 20*4=80 then you add half of it to become 90 and you get 54
4b. 12*5 because 100/5=20 for the 20 trials of them
What is the point of maximum growth rate? Round to the nearest tenth.
Answer:
(x, f(x)) ≈ (5.5, 4)
Step-by-step explanation:
You can go to the trouble to find the point where the second derivative is zero (the derivative has a maximum), or you can realize the function is symmetrical about y=4, which is where the point of inflection is. The x-value there is ...
4 = 8/(1 +3e^(-0.2x))
1 +3e^(-0.2x) = 8/4 = 2
e^(-0.2x) = 1/3
x = ln(1/3)/-0.2 = 5ln(3) ≈ 5.493 ≈ 5.5
We already know the value of f(x) is 4 there.
The point of maximum growth is about (5.5, 4).
Please help me on this please
Answer:
㏒3(14) = 2.402 ⇒ 3rd answer
Step-by-step explanation:
* Lets revise some rules of the logarithmic functions
- log(a^n) = n log(a)
- log(a) + log(b) = log(ab) ⇒ vice versa
- log(a) - log(b) = log(a/b) ⇒ vice versa
* Lets solve the problem
- We have the value of ㏒3(2) and ㏒3(7)
- We must change the problem to these logarithm to solve
∵ 14 = 2 × 7
∴ We can write ㏒3(14) as ㏒3(2 × 7)
∴ ㏒3(14) = ㏒3(2 × 7)
* Now lets use the rules above
∵ log(ab) = log(a) + log(b)
∴ ㏒3(2 × 7) = ㏒3(2) + ㏒3(7)
∵ ㏒3(2) = 0.631 and ㏒3(7) = 1.771
∴ ㏒3(2 × 7) = 0.631 + 1.771 = 2.402
* ㏒3(14) = 2.402
What is the domain and range of the function shown
Answer:
• domain: x ≥ 0
• range: y ≥ 0
Step-by-step explanation:
The graph shows a ray that starts at the origin and extends to infinity in both the +x and +y directions. The domain (horizontal extent) is [0, ∞), as is the range (vertical extent).