Answer:
y < x + 7
Step-by-step explanation:
Which of the following statements is true?
a. sin 18° = cos 72°
b. sin 55° = cos 55°
с. sin 72° = cos 18°
d. Bоth a and c.
Answer:
The answer is d.
Step-by-step explanation:
As we know, sin x= cos (90°-x)
sin 18° = cos (90°-18°)
= cos 72°.
Similarly, sin 72°= cos (90°-72°)
= cos 18°
But, sin 55°= cos (90°-55°)
= cos 35°
A rectangular patio is 9 ft by 6 ft. When the length and width are increased by the same amount, the area becomes 88 sq ft. Ginger is using the zero product property to solve the equation (6 + x)(9 + x) = 88. What do her solutions represent?
Area of rectangle is the product of its length and breadth. It is measured in unit squared. When the length and breadth are increased by 2 feet then the area of the given rectangular patio becomes 88 sq ft.
Given-A rectangular patio is 9 ft by 6 ft.
The length of the rectangular patio is 9 ft.
The breadth of the rectangular patio is 6 ft.
What is the area of a rectangle?Area of rectangle is the product of its length and breadth. It is measured in unit squared
The equation is given for the problem is,
[tex](6 + x)(9 + x) = 88[/tex]
On solving the above equation we get,
[tex]x^2+6x+9x+54= 88[/tex]
[tex]x^2+15x+54-88=0[/tex]
[tex]x^2+15x-34=0[/tex]
Find the value of x by using split the middle term method,
[tex]x^2+17x-2x-34=0[/tex]
Using the split the middle term method we get the two factor,
[tex](x+17)(x-2)=0[/tex]
Equate the above equation to zero we get the values of the x are -17 and 2.
Taking positive value of x and keeping it into the given equation we get,
[tex](6 + x)(9 + x) = 88[/tex]
[tex](6 + 2)(9 + 2) = 88[/tex]
[tex]8\times 11=88[/tex]
[tex]88=88[/tex]
Hence When the length and width are increased by 2 feet then the area of the given rectangular patio becomes 88 sq ft.
Learn more about the area of the rectangle here;
https://brainly.com/question/14383947
Ginger is solving for 'x' in a quadratic equation to find the amounts by which the length and width of the original 9 ft by 6 ft patio must be increased to achieve an area of 88 sq ft.
Explanation:The student is working on a quadratic equation derived from the area of a rectangle. The original dimensions of the patio are 9 ft by 6 ft, which, when both the length and width are increased by the same amount 'x', the new area becomes 88 sq ft. Ginger is thus solving the equation (6 + x)(9 + x) = 88 using the zero product property.
By expanding this, we get a quadratic equation in the form of x^2 + 15x + 54 = 88, which can be simplified to x^2 + 15x - 34 = 0. The zeros of this function will give us the values of 'x' where the new dimensions of the patio result in an area of 88 sq ft. Consequently, the solutions 'x' are the amounts by which the length and width of the original patio would need to be increased to reach the new area.
Which of the following is a complex number?
Complex numbers emerge when you take the square root of a negative number, since the imaginary unit [tex]i[/tex] is defined by the relation [tex]i^2=-1[/tex], which implies [tex]\sqrt{-1}=i[/tex]
The only option involving the square root of a negative number is the last one.
Answer:
option D
Step-by-step explanation:
Complex number is a number that has negative under the square root.
Square root (-1) =i is a complex number
square root of a negative number is a complex.
First option does not have any negative number under the square root so it is not a complex.
second option also not have negative number under square root . So it is not a complex
third option have positive 7 under the square root so it is not a complex
Fourth option have -9/5 under the square root . So it is a complex number
A 4000 kg truck is parked on a 7.0° slope. How big is the friction force on the truck?
Answer:
4777.28 N
Step-by-step explanation:
The gravitational force down the slope is given by the formula;
(mass *g * sin θ )
where;
θ is the angle of inclination of the slope
g is the gravitational pull
We plug in the given values into the above expression;
(4,000 x 9.8 x sin 7) = 4777.28 N.
The frictional force must equal to 4777.28 N (pointing up the slope).
Final answer:
To calculate the friction force acting on a 4000 kg truck parked on a slope, the component of the truck's weight acting down the slope is determined and found to be approximately 4780 N. This value represents the maximum static friction force available to prevent the truck from sliding.
Explanation:
The question is asking to calculate the friction force acting on a truck parked on a slope. To find the friction force, first, we need to calculate the component of the truck's weight that is acting down the slope. This can be found with the formula Wparallel = mg sin(θ), where m is the mass of the truck, g is the acceleration due to gravity (9.8 m/s²), and θ is the angle of the slope.
The truck's weight component acting along the slope is:
Wparallel = 4000 kg * 9.8 m/s² * sin(7°) ≈ 4000 kg * 9.8 m/s² * 0.12187 ≈ 4780 N
The friction force will counteract this downhill force to prevent the truck from sliding. Assuming that the friction force equals the downhill component of the truck's weight to keep the truck stationary, the friction force on the truck is approximately 4780 N. However, without the coefficient of friction, this represents the maximum static friction force that could occur before the truck would start to slide down the slope.
What is the length of segment AC?
Answer: 10
Step-by-step explanation:
see attached picture
Answer:
It is 10
Step-by-step explanation:
( g(1) = 14
(g(n) = g(n − 1) – 4
Find an explicit formula for g(n).
g(n) =
Answer:
[tex]g(n)=18-4n[/tex]
Step-by-step explanation:
You are given the function g, for which
[tex]g(1)=14,\\\\g(n)=g(n-1)-4[/tex]
Find some values of this function:
[tex]g(1)=14\\ \\g(2)=g(2-1)-4=g(1)-4=14-4=10\\ \\g(3)=g(3-1)-4=g(2)-4=10-4=6\\ \\g(4)=g(4-1)-4=g(3)-4=6-4=2\\ \\...[/tex]
You can see that ecah next value is 4 less than previous one, so these values form an arithmetic sequence and you have to find the nth term of this sequence. The nth term of arithmetic sequence is
[tex]a_n=a_1+(n-1)d,[/tex]
where
[tex]a_1=g(1)=14\\ \\d=-4[/tex]
So,
[tex]g(n)=a_n=14+(n-1)\cdot (-4)=14-4n+4=18-4n[/tex]
Answer:
18-4n
Step-by-step explanation:
Question 3(Multiple Choice Worth 5 points)
(03.03 LC)
How does the graph of g(x) = (x − 2)3 + 7 compare to the parent function f(x) = x3?
g(x) is shifted 7 units to the right and 2 units up.
g(x) is shifted 2 units to the right and 7 units up.
g(x) is shifted 7 units to the right and 2 units down.
g(x) is shifted 2 units to the left and 7 units up.
Answer: Second option.
Step-by-step explanation:
Below are some transformation for a function f(x):
If [tex]f(x)+k[/tex] then the function is shifted up "k" units.
If [tex]f(x)-k[/tex] then the function is shifted down "k" units.
If [tex]f(x+k)[/tex] then the function is shifted "k" units to the left.
If [tex]f(x-k)[/tex] then the function is shifted "k" units to the right.
Knowing this tranformations and given the parent function [tex]f(x)=x^3[/tex] and the function [tex]g(x) = (x -2)^3 + 7[/tex], we can conclude that the function g(x) is shifted 2 units to the right and 7 units up.
We can observe that this matches with the second option.
Find the surface area of the right prism. Round to the nearest whole number.
Answer:
[tex]\large\boxed{S.A.=96\ cm^2}[/tex]
Step-by-step explanation:
We have:
(1) two trapezoids with bases b₁ = 7cm and b₂ = 5cm and the height h = 4cm
(2) three rectangles 3 cm × 7 cm, 3 cm × 4 cm and 3 cm × 5 cm.
The formula of an area of a trapezoid:
[tex]A=\dfrac{b_1+b_2}{2}\cdot h[/tex]
Substitute:
[tex]A=\dfrac{7+5}{2}\cdot4=24\ cm^2[/tex]
Calculate the areas of the rectangles:
[tex]A_1=(3)(7)=21\ cm^2\\\\A_2=(3)(4)=12\ cm^2\\\\A_3=(3)(5)=15\ cm^2[/tex]
The Surface Area:
[tex]S.A.=(2)(24)+21+12+15=96\ cm^2[/tex]
Plz help plz i need help
Step-by-step explanation:
Remember to follow PEMDAS. PEMDAS = Parenthesis, Exponents (& roots), Multiplication, Division, Addition, Subtraction.
Note the equation:
y = (1/4)x + 1
Plug in a number to x, & solve to get the answer for the variable (y).
In this question, they give you 3 numbers to plug into x: 4, 8, 12. Plug them in:
When x = 4
y = (1/4)(4) + 1
Solve. Simplify. Remember to follow PEMDAS. First, multiply 1/4 with 4:
y = (1/4)(4) + 1
y = (1 * 4)/4 + 1
y = 4/4 + 1
y = 1 + 1
Simplify. Combine the terms:
y = 1 + 1
y = 2
when x = 4, y = 2.
When x = 8
y = (1/4)(8) + 1
Solve. Simplify. Remember to follow PEMDAS. First, multiply 1/4 with 8:
y = (1/4)(8) + 1
y = (1 * 8)/4 + 1
y = 8/4 + 1
y = 2 + 1
y = 3
when x = 8, y = 3.
When x = 12
y = (1/4)(12) + 1
Solve. Simplify. Remember to follow PEMDAS. First, multiply 1/4 with 12:
y = (1/4)(12) + 1
y = (1 * 12)/4 + 1
y = 12/4 + 1
y = 3 + 1
y = 4
when x = 12, y = 4.
~
Evaluate: y( x + x) + 3, where x = 1 and y=3
Answer:
9
Step-by-step explanation:
for the expression y(x+x)+3, we can first simplify:
y(2x)+3
then we can substitute 1 for x and 3 for y:
3(2*1)+3
multiply inside the parenthesis:
3*2+3
multiply 3 and 2:
6+3
add 3:
9
Therefore, this evaluates to 9
y( x + x) + 3, where x = 1 and y=3
Plug 1 in for x and 3 in for y like...
3( 1 + 1) + 3
To evaluate apply the rules of PEMDAS (Parentheses, Exponent, Multiplication, Division, Addition, Subtraction)
Parentheses
3( 1 + 1) + 3
3(2) + 3
Exponent
There are none so go on to the next step
Multiplication
3(2) + 3
6 + 3
Division
There are none so go on to the next step
Addition
6 + 3
9
Hope this helped!
~Just a girl in love with Shawn Mendes
A parachutist’s speed during a free fall reaches 180 miles per hour. What is this speed in feet peer second? At what speed, how many feet will the parachutist fall during 20 seconds of free fall? In your computations, use the fact that 1 mile is equal to 5280 feet. Do not round your answer
Answer:
1. 264 ft/s
2. 5280 feet
Step-by-step explanation:
Changing miles per seconds to feet per hour
If 1 mile= 5280 feet
180 miles=?
[tex](180*5280)/1 = 950400[/tex]
=950400 feet
1 hour= 60×60 seconds = 3600
180 miles/hour = feet/sec = 950400/3600 =264 ft/s
To find the number of feet the parachutist fall during 20 seconds;
Distance= speed × time
=264×20 = 5280 feet
HELP ASAP
The circumference of a circle is 28 pie inches. What is the length of the radius of this circle?
A)14 in.
B)21 in.
C)28 in.
D)56 in.
Answer:A
Step-by-step explanation:
The formula is 2pir, so you divide by the 2, the pin the pi, then you have the radius, r.
At a cost of 200, your club bought 175 frisbees to sell at the pep rally. You plan on selling them for $5 each. What is the domain of the function?
Answer:
Domain: {0, 1, 2, ..., 175}.
Step-by-step explanation:
We are given that a club bought 175 frisbees at a cost of $200 which you plan to sell for $5 each.
We are to find the domain of this function.
Domain is actually the input into a function which is the x value.
Here sales = 5x where x represents the number of frisbees sold.
So the profit will be:
Profit = Sales - Cost = 5x - 200
Here in this case, the domain would be the number of frisbees sold which is between 0 to 175.
To find 45% of 72, multiply 45/100×72.
Study the model: 45/100×72=3,240/100=32.4. Find 35% of 12.
You can also just multiply by the decimal equivalent.
12*.35=4.2
35% of 12 is 4.2
Hope this helps!
Answer:
4.2
Step-by-step explanation:
Find 35% of 12.
To find 35% of 12, you can use the method you demonstrated above by solve
35% = 35/100
of 12 = multiplication.
35/100 × 12
0.35 × 12
= 4.2
OR
35 × 12/100
420/100
= 4.2
Hope this helps!
Thanks.
PLEASE HELP ME PLEASE AS FAST AS POSSIBLE
What is the degree of the following polynomial?
2x5 + x4 + x3 + x - 28
A) 3
B) 4
C) 5
D) 6
Answer:
A)3
Step-by-step explanation:
I need help please hurry
Answer:
9+sqrt(14)
--------------
9+sqrt(14)
Step-by-step explanation:
To get rid of the square root in the denominator, you want to multiply by the conjugate.
Since we have a - sqrt(b) in the denominator
We need to multiply by a + sqrt(b)
What we do the bottom, we do to the top
9+sqrt(14)
--------------
9+sqrt(14)
on Saturday a total of 1292 people went to the movies to see a new show there were four different showings for the new movie and the same number of people attended each showing how many people attended each showing
(25x)° (45x)° (54x)°
what is x?
45x = 25x + 57 + x
45x = 26x + 57
45x - 26x = 57
19x = 57
x = 57/19
x = 3
15 points
The line AB←→ passes through the points A(−3,6) and B(5,−2).
Which equations could be for AB←→ in point-slope form?
MULTIPLE CHOICES
y+2=−4(x−5)
y−6=−(x+3)
y=−x+3
y+2=−(x−5)
y−2=−(x−1)
y+2=x−5
y−6=x+3
y−6=−4(x+3)
y - 6 = -(x + 3) and y + 2 = - (x - 5).
The line AB passes through the points A(-3, 6) and B(5, -2). Find the point-slope form.
First, we have to calculate the slope using the equation m = (y₂ - y₁)/(x₂ - x₁):
x, y
A(-3, 6)
B( 5,-2)
m = [-2 - (6)]/[5 - (-3)] = (-2 - 6)/(5 + 3)
m = -8/8
m= -1
Writing the point-slope form equation as (y - y₁) = m (x - x₁), with A(-3, 6):
y - 6 = -1[(x -(-3)]
y - 6 = - (x + 3)
Writing the point-slope form equation as (y - y₁) = m (x - x₁), with B(5, -2):
y - (-2) = - (x - 5)
y + 2 = - (x - 5)
Given the two Fibonacci numbers below, which number would follow?
(17) - 1597 and F(18) = 2584
Answer:
4181
Step-by-step explanation:
The Fibonacci sequence starts with 0 and 1... then all other terms are obtained by adding the two previous terms.
0, 1, 1, 2, 3, 5, 8, 13, 21, and so on.
So, if you have any two consecutive terms from the sequence, you can easily find the next one by adding them together:
F(19) = F(17) + F(18)
F(19) = 1597 + 2584 = 4181
please help !!!
Use the parabola tool to graph the quadratic function.
f(x)= -2(x+4)^2-3.
Graph the parabola by first plotting its vertex and then plotting a second point on the parabola
[tex]\bf ~~~~~~\textit{parabola vertex form} \\\\ \begin{array}{llll} \stackrel{\textit{we'll use this one}}{y=a(x- h)^2+ k}\\\\ x=a(y- k)^2+ h \end{array} \qquad\qquad vertex~~(\stackrel{}{ h},\stackrel{}{ k}) \\\\[-0.35em] ~\dotfill\\\\ f(x)=-2(x+4)^2-3\implies f(x)=-2[x-(\stackrel{h}{-4})]^2\stackrel{k}{-3}~\hfill \stackrel{vertex}{(-4,-3)}[/tex]
well, to get a second point, we simply pick a random "x" hmmm say x = 1, so then
f( 1 ) = -2( 1 + 4) ² - 3
f( 1 ) = -2(25) - 3
f( 1 ) = -53
so from that we get the point of x = 1, y = -53 ( 1 , -53), so it looks like the picture below.
calculate the missing length on the right triangle. slove for c using the pythagorean theorem. Hint a²+b²=c²
Answer:
C= 10
Step-by-step explanation:
A=8
B=6
C= ?
1. Set up the equation for the Pythagorean theorem and fill in the variables.
8² + 6² = c
64 + 36 = 100
2. Square root 100.
Square root of 100 = 10
Answer = 10
The missing length on the right triangle is 10 in.
What is right triangle?"It is a triangle whose one of the angle measures 90°"
What is hypotenuse?"It is the longest side of the right triangle."
What is Pythagoras theorem?"For a right triangle,
[tex]a^2+b^2=c^2[/tex], where c is the hypotenuse and a, b are other two sides of the right triangle."
For given question,
We have been given a right triangle with a = 8 in. and b = 6 in
We need to find the the value of c.
Using Pythagorean theorem,
[tex]\Rightarrow c^2 = a^2+b^2\\\Rightarrow c^2 = 8^2+6^2\\\Rightarrow c^2 = 64+36\\\Rightarrow c^2 = 100\\\Rightarrow c=10~in[/tex]
Therefore, the missing length on the right triangle is 10 in.
Learn more about the Pythagorean theorem here:
https://brainly.com/question/343682
#SPJ2
if f (x) equals 3 + x / x - 3 what is f (a + 2)?
ANSWER
[tex]f(a + 2) = \frac{a + 5}{a - 1} [/tex]
EXPLANATION
The given function is
[tex]f(x) = \frac{3 + x}{x - 3} [/tex]
To find f(a+2) we substitute x=a+2.
That is wherever we see 'x' we replace it with 'a+2'
[tex]f(a + 2) = \frac{3 + a + 2}{a + 2 - 3} [/tex]
We simplify further to obtain:
[tex]f(a + 2) = \frac{a + 5}{a - 1} [/tex]
This is defined for
[tex]a \ne1[/tex]
The first step in constructing this equilateral triangle is to draw segment AB.
What is the second step?
A. Draw two circles with radius AB.
B. Draw angle CAB.
C. Draw two circles with diameter AB.
D. Draw arc BC.
Answer: draw line segment AB
Step-by-step explanation (A PEX)
The second step in constructing this equilateral triangle is draw two circles with radius AB. Option A is correct.
What is an equilateral triangle?An equilateral triangle is the triangle in which all the three sides are of equal length in measure.
The first step in constructing this equilateral triangle, to draw segment AB. The second step for this has to find out.
Here, the triangle ABC is shown in the given image. As it is known that all the sides of a equilateral triangle are equal. Therefore,
[tex]AB=BC=AC[/tex]
The first circle is co-occur, the second circle completely. This happens when the two circles made with same radius.
Now from the center point of the circle to the boundary of that circle, is called the radius of the circle., Thus, the line segment AB is the radius of the two circles.
Hence, the second step in constructing this equilateral triangle is draw two circles with radius AB. Option A is correct.
Learn more about the equilateral triangle here;
https://brainly.com/question/1099318
Identify the values of a, b, and c in the following quadratic equation.
2x2 + 3x + 7 = 0
a=
b=
c=
Answer:
a= 2, b= 3, c= 7
Step-by-step explanation:
Given the quadratic equation:
2x² + 3x +7 =0Quadratic equation in general form is:
ax² + bx + c = 0Comparing the two above we can get following coefficients:
a= 2
b= 3
c= 7
A= 4
B= 12
C= 9
Theese are correct
Simplify. (-2)-3
A) -8
B)-1/8
C)1/8
D)8
Answer:
B if you mean (-2)^(-3)
Step-by-step explanation:
(-2)-3=-5
But based on the answers I think you meant to write (-2)^(-3)
which means 1/(-2)^3
So we have 1/(-2*-2*-2)=1/-8 or -1/8
Answer:
B. -1/8.
Step-by-step explanation:
I guess you mean (-2)^-3
= 1 / (-2)^3
= 1 / -8
= -1/8.
6x + 3y = -6 2x + y = -2 A. x = 0, y = -2 B. infinite solutions C. x = -1, y = 0 D. no solution
ANSWER
B. infinite solutions
EXPLANATION
We want to solve the equation;
[tex]6x + 3y = - 6...(1)[/tex]
and
[tex]2x + y = - 2...(2)[/tex]
We multiply the second equation by 3 to get:
[tex]6x + 3y = - 6...(3)[/tex]
We now subtract equation (1) and (3).
[tex]6x - 6x + 3y - 3y = - 6 - - 6[/tex]
This implies that
[tex]0 = 0[/tex]
Hence the equation has infinitely many solutions.
What is the slope intercept equation of the line below?
Answer:
B
Step-by-step explanation:
The slope is 2
Y int is -3
How does the graph of g(x) = 3x – 2 compare to the graph of f(x) = 3x?
Answer:
[tex]g(x)= 3x-2[/tex], graph shifted 2 units down.
Step-by-step explanation:
[tex]g(x)= 3x-2[/tex]
g(x) = 3x is a parent function.
When we compare the graph of parent function g(x)= 3x with [tex]g(x)= 3x-2[/tex], negative 2 is added at the end
f(x)---> f(x) + a , the graph will be shifted 'a' units up
f(x)-> f(x) -a , the graph will be shifted 'a' units down
[tex]g(x)= 3x-2[/tex], In this g(x) we have -2 at the end.
So the graph will be shifted 2 units down.
The graph of 3x - 2 is a vertical translation by 2 units down of the function f(x) = 3x
Translation of functions and graphsAccording to the question, we are given the parent function f(x) = 3x, we need to determine the relationship between the parent function and g(x) = 3x - 2
If the function f(x) translate by k units downwards, the resutlting function will be expressed as h(x) - k.
Hence if h(x) = 3x translate by 2 units downwards, the resulting function will be expressed as 3x - 2.
The graph of 3x - 2 is a vertical translation by 2 units down of the function h(x) = 3x
Learn more on translation here: https://brainly.com/question/12861087
What is the slope of the line through (-4.2) and (3,-3)?
Finding the slope using the two points:
The formula for slope is
[tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
In this case...
[tex]y_{2} =-3\\y_{1} =2\\x_{2} =3\\x_{1} =-4[/tex]
^^^Plug these numbers into the formula for slope...
[tex]\frac{-3-2}{3 - (-4)}[/tex]
[tex]\frac{-5}{7}[/tex]
^^^This is your slope
Hope this helped!
~Just a girl in love with Shawn Mendes
Answer:
[tex]-\frac{5}{7}[/tex]
Step-by-step explanation:
Slope formula:
↓
[tex]\frac{Y_2-Y_1}{X_2-X_1}[/tex]
[tex]\frac{(-3)-2}{3-(-4)}=\frac{-5}{7}=-\frac{5}{7}[/tex]
-5/7 is the correct answer.