Answer:
x=5
Step-by-step explanation:
Factoring x2 - 2x – 15 we get
(x+3)(x-5) so x+3=0 and x-5=0 or x=-3 and x=5
Answer:
x=5
Step-by-step explanation:
x^2 - 2x – 15 = 0
Factor
What 2 numbers multiply to -15 and add to -2
-5*3 = -15
-5+3 = -2
(x-5) (x+3) = 0
Using the zero product property
(x-5) =0 x+3 =0
x-5+5 =0+5 x+3-3 = 0-3
x=5 x=-3
30 points
An observer is 120 feet from the base of a television tower, which is 150 feet tall. find the angle of depression at the top of the tower. Round to the nearest degree.
Answer:
the angle of depression is 45 degrees
Step-by-step explanation:
120(150)
angle theorem
points postulate
90/2=45
please mark brainliest and give thanks
Is the expression 2f + 4f + 2 – 3 equivalent to 6f – 1?
6f – 1 evaluated at f = 9 is 53.
2f + 4f + 2 – 3 evaluated at f = 9 is also 53.
6f – 1 evaluated at f = 3 is 17.
What is 2f + 4f + 2 – 3 evaluated at f = 3?
iv been stuck for 10 min now
Answer:
Yes it is equivalent.
Step-by-step explanation:
In this case the only thing that you have to do to know if the two expressions are equivalent are put them on opposite sides of the equation like this:
6f-1= 2f+4f+2-3
When you simplify this you´ll end up with the next equation:
6f-1= 6f -1
In this case you can see that both expressions are equivalent because they are the same once you put them on opposite sides of the equation.
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.
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
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
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]
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
The table shows the number of pools sold by the Allied Pool company over a six month period.
Allied Pool Sales
Month
Number of
Pools Sold
Feb.
11
Mar.
10
Apr.
12
May
16
June
15
July
18
According to the above table, what was the average number of pools sold per month during this period? Round to the nearest tenth if necessary.
14.6 pools
13.5 pools
13.7 pools
8 pools
Answer
Average/Mean: 13.7 pools
Step-by-step explanation:
When asked to find the average number of anything, you are trying to find the mean.
The Arithmetic Mean is the average of the numbers: a calculated "central" value of a set of numbers.
To calculate it:
• add up all the numbers,
• then divide by how many numbers there are.
Is 1 half equal to 0.50
What is 8a-16=40
I can’t figure it out and I’m in 9th grade
Hello!
Answer:
[tex]\boxed{A=7}\checkmark[/tex]
The answer should have a positive sign.
Step-by-step explanation:
First, you add by 16 from both sides of an equation.
[tex]8a-16+16=40+16[/tex]
Then, simplify.
[tex]40+16=56[/tex]
[tex]8a=56[/tex]
Therefore, divide by 8 from both sides of an equation.
[tex]\frac{8a}{8}=\frac{56}{8}[/tex]
Finally, you simplify and solve to find the answer.
[tex]56\div 8 =7[/tex]
[tex]\boxed{x=7}[/tex], which is our correct answer.
I hope this helps you!
Have a great day! :)
-Charlie
To solve for a you must isolate it, meaning that a must be the only thing on the left side of the equation.
To do this first add 16 to both sides (what you do on one side you must do to the other). Since 16 is being subtracted, addition (the opposite of subtraction) will cancel it out (make it zero) from the left side and bring it over to the right side.
8a + (- 16 + 16) = 40 + 16
8a + 0 = 56
8a = 56
Next divide 8 to both sides to finish isolating a. Since 8 is being multiplied by a, division (the opposite of multiplication) will cancel 8 out (in this case it will make 8 one) from the left side and bring it over to the right side.
8a/8 = 56/8
1a = 7
a = 7
Check:
8(7) - 16 = 40
56 - 16 = 40
40 = 40
Hope this helped!
~Just a girl in love with Shawn Mendes
What is the slope intercept equation of the line below?
Answer:
B
Step-by-step explanation:
The slope is 2
Y int is -3
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.
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)
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)
Find one value of x that is a solution to the equation:
(3x - 1)2 + 12x – 4= 0
Answer:
⅓, -1⃣ = x
Step-by-step explanation:
Move all terms to the left side and set equal to zero. Then set each factor equal to zero.
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.
what is the equation of a line that contains the points (2,-2) and (0,-2)
A. y=0
B. x=-2
C. y=-2
D.x=O
Answer:
C
Step-by-step explanation:
By observation, and inspecting the 2 given points closely, we can immediately see that both points have y = -2 as common y-ordinates .
This means that the horizontal line y =-2 joins these 2 points.
Answer C is correct.
Answer:
C
Step-by-step explanation:
use slope formula and slope-intercept form Y=mx=b
PLEASE HELP: Choose the function whose graph is given by:
Answer:
The function of the graph is y = 3 cos (4x) ⇒ answer A
Step-by-step explanation:
- If the equation is y = A cos (B x)
* A is the amplitude
- The amplitude is the height from highest to lowest points and
divide the answer by 2
* The period is 2π/B
- The period is the distance from one peak to the next peak
* Lets look to the graph
- The maximum value is 3 and the minimum value is -3
∵ The height from the maximum point to the minimum point is
3 - (-3) = 3 + 3 = 6
∴ The amplitude is 6/2 = 3
∵ A is the amplitude
∴ A = 3
- The distance between two consecutive peaks is π/2
∵ The period is the distance from one peak to the next peak
∴ The period = π/2
∵ The period = 2π/B
∴ 2π/B = π/2 ⇒ divide both sides by π
∴ 2/B = 1/2 ⇒ by using cross multiplication
∴ B = 4
- Lets write the form of the function
∵ y = A cos (Bx)
∵ A = 3 and B = 4
∴ y = 3 cos (4x)
* The function of the graph is y = 3 cos (4x)
Which of the following is the rule for the geometric
sequence 1, 3, 9, 27, ...?
Answer:
Multiply by three for every number 1*3 =3 3*3=9 9*3=27
Step-by-step explanation:
Common ratio of the geometric sequence is 3.
What is a geometric sequence?A geometric sequence is a sequence in which the ratio of two consecutive terms is a fixed ratio.
Given,
Geometric sequence: 1, 3, 9, 27
The ratio of second and first term = 3/1
= 3
Similarly, the ratio of third and second term = 9/3
= 3
Hence, the common ratio of the geometric sequence is 3.
To learn more about geometric sequence visit:
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What is 8 percent of 33.52
Answer:
W =2.6816
Step-by-step explanation:
Is means equals and of means multiply
W = 8% * 33.52
Change to decimal form
W = .08 * 33.52
W =2.6816
the park is 6 miles due west of your house, and the library is 11 miles north of your house. How far is the shortest distance from the park to the library? Round to the nearest half mile.
Answer:
Step-by-step explanation:
Given that the park is 6 miles due west of your house, and the library is 11 miles north of your house.
Thus the park and library forms the legs of a right triangle with shortest distance being the hypotenuse (provided there are no buildings in between)
We can use pythagoren theorem to find the shortest distance i.e. hypotenuse.
Shortest distance^2 =[tex]\sqrt{6^2+11^2} =\sqrt{197}[/tex]
We find that square root is 14.03
Thus shortest distance is 14 miles.
The shortest distance from the park to the library is 12.53 miles.
DistanceIt is the measure of the length between the two points. It is a scalar quantity.
Right-angle triangleIt is a type of triangle in which one angle is 90 degrees and it follows the Pythagoras theorem and we can use the trigonometry function.
Given
The park is 6 miles due west from your house.
And the library is 11 miles north of your house.
To findThe shortest distance from the park to the library.
How to get the shortest distance from the park to the library?Perpendicular P = 11
Bas B = 6
We know the Pythagoras theorem.
H² = P² + B²
H² = 11² + 6²
H² = 121 + 36
H² = 157
H = 12.53
Thus, The shortest distance from the park to the library is 12.53 miles.
More about the distance link is given below.
https://brainly.com/question/989117
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.
Find the equation in slope-intercept form of a line with slope –2 and y-intercept 4.
[tex]\bf y=\stackrel{\stackrel{m}{\downarrow }}{-2}x+\stackrel{\stackrel{y}{\downarrow }}{4}\qquad \impliedby \qquad \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]
The equation of the line in slope-intercept form of a line with slope –2 and y-intercept 4 is y = -2x + 4.
What is the slope?The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}m=(y₂-y₁) / (x₂-x₁)[/tex]
It is given that:
A line with slope –2 and y-intercept 4.
The linear equation in one variable can be made:
As we know,
The standard equation of the line is:
y = mx + c
Here m is the slope and c is the y-intercept.
m = -2
c = 4
y = -2x + 4
Thus, the equation of the line in slope-intercept form of a line with slope –2 and y-intercept 4 is y = -2x + 4.
Learn more about the slope here:
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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
( 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:
Solve the system of equation. 5x+2y=7 and -2x+6y=9. Enter the y-coordinate of the solution.
Answer: [tex]\bold{y=\dfrac{59}{34}}[/tex]
Step-by-step explanation:
5x + 2y = 7 ⇒ 2(5x + 2y = 7) ⇒ 10x + 4y = 14
-2x + 6y = 9 ⇒ 5(-2x + 6y = 9) ⇒ -10x + 30y = 45
34y = 59
÷34 ÷34
y = 59/34
Answer:
y=59/34
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°
Which of the following matrices has the order of 3 x 6?
Answer:
the first one
Step-by-step explanation:
Answer this question thanks
for this question, it ask you to draw out.
j + 6 ≥ 7
j ≥ 7 - 6
j ≥ 1
How to draw it:
1. draw a Solid point on the number"1".
2. draw a small vertical line on the top of the point.
3. draw a long horizontal line to number "1" 's right side, and add an arrow in the end of the line.
First bring 6 to the right side by subtracting 6 to both sides (what you do on one side you must do to the other). Since 6 is being added on the left side, subtraction (the opposite of addition) will cancel it out (make it zero) from the left side and bring it over to the right side.
j + 6 ≥ 7
j + 6 - 6 ≥ 7 - 6
j + 0 ≥ 1
j ≥ 1
For the graph will you have a empty or colored in circle?
If the symbol is ≥ or ≤ then the circle will be colored in. This represents that the number the circle is on is included.
If the symbol is > or < then the circle will be empty. This represents that the number the circle is on is NOT included.
Which direction will the ray go?
If the variable is LESS then the number then the arrow will go to the left of the circle.
If the variable is MORE then the number then the arrow will go to the right of the circle.
In this case your inequality is:
j ≥ 1
aka j is greater then or equal to one
This means that the graph will have an colored circle and the arrow will go to the right of 1. (look at the image below)
Hope this helped!
~Just a girl in love with Shawn Mendes
Sorry I’m really behind
The answer will be 238,900 miles.
If you round off 238, 854 to the nearest hundreds, you get
238,900 in miles.
Hope this helps!!!
Mark Brainliest!!!