Answer:
x = -5.
Step-by-step explanation:
The solutions of the equation is when the two functions intersect. That is at (-5, 5.5), so where x = -5.
Hope this helps!
Answer:
x = -5
Step-by-step explanation:
f(x) = g(x) has more than one solution, because they intersect at two points.
The question asks for one solution of f(x) = g(x).
One point where they intersect is at (-5, 5.5), as shown in the graph.
(x , y)
x = -5, y = 5.5
which of the binomials below is a factor of this trinomial? x^2 + 5x - 36 A. x - 5 B. x - 9 C. x + 9 D. x^2 + 5
===============================================
Explanation:
Think of two numbers that multiply to -36 and also add to 5. Put another way: think of two factors of -36 that add to 5.
Those two numbers are 9 and -4 since
9 times -4 = -36
9 plus -4 = 5
So we have x^2 + 5x - 36 factor into (x+9)(x-4)
x+9 is one factor
x-4 is the other factor
-------
Alternatively, you can use a graphing tool to locate the x intercepts, and that will in turn lead to the factorization. Or you could use the quadratic formula to get the job done. Completing the square is yet another tool to use. So there are multiple approaches.
A circle has a radius of sqrt 45 units and is centered at (-2.4, -4.8) Write the equation of the circle
Answer:
( x+ 2.4) ^2 + ( y+4.8) ^2 = 45
Step-by-step explanation:
The equation of a circle can be written as
( x-h) ^2 + ( y-k) ^2 = r^2
Where ( h,k) is the center and r is the radius
( x-- 2.4) ^2 + ( y--4.8) ^2 = (sqrt45)^2
( x+ 2.4) ^2 + ( y+4.8) ^2 = 45
compare -1/6 and -2/3
Answer:
-1/6=-0.166
-2/3=-0.66
Step-by-step explanation:
-by looking carefully you will notice that . which number is greater and smaller.
Answer:
-1/6 is greater than -2/3
Step-by-step explanation:
Jennifer invested $302 in a simple interest account. The account earns 3.3%/year how much will Jennifer have in her account in 10 months??
Answer: $310.31
Step-by-step explanation:
Invested amount (P) = $302
Interest rate (r) = 3.3% per year
Period = 10 months
Recall, simple interest formula :
A = P(1 + rt) where ; A = final amount
Interest = 3.3% = 3.3/ 100 = 0.033
A = $302 ( 1 + 0.033(10/12))
A = $302 (1 + 0.033(0.8333333))
A = $302 ( 1 + 0.0275)
A = $302 ( 1. 0275)
A = $310.305
A = $310.31
ASAP! PLEASE help me with this question! I am really stuckk...
Answer:
8 pi cm^2
Step-by-step explanation:
To answer this question, what we need firstly is the name of the cross section that results from slicing a sphere into half.
The cross section that results is called a hemisphere, which is half the size of the sphere.
But before we can calculate the area of the new cross section, we will need the radius of the original shape.
This is obtainable from the volume of the shape.
Mathematically;
Volume of a sphere = 4/3 * pi * r^3
32/3 * pi = 4/3 * pi * r^3
We can take off pi/3 from both sides so we are left with;
32 = 4r^3
Divide through by 4
r^3 = 8
r is the cube root of 8 = 2 cm
Now we find the area of the hemisphere
Mathematically, the area of a hemisphere is 2 * pi * r^2
using the value of r = 2 cm given above, we have
Hemisphere area = 2 * pi * 2^2 = 8pi cm^2
Please help me with
Answer:
[tex]\boxed{\frac{1}{2} }[/tex]
Step-by-step explanation:
Let the assistants be x
Condition:
Ratio is also "division"
So,
[tex]\frac{x}{players} = \frac{1}{6}[/tex]
=> Where players = 36
=> [tex]\frac{x}{36} = \frac{1}{6}[/tex]
Multiplying both sides by 36
=> x = 6
So,
Assistants = 6
Ratio of coaches to assistants = 3 : 6
=> 1 : 2
In Fraction form
=> [tex]\frac{1}{2}[/tex]
F) 1/2
Because no. of players= 36
Since ratio of team assistant to players is 1:6
Let no of assistant be X
X/36 = 1/6
X= 6
No of assistant= 6
Ratio of coach to assistant= 3/6=1/6
= 1:6
Find the values for which the statement is true and mark them on the number line: |x|=x
Answer:
x ≥ 0
Step-by-step explanation:
The absolute value of something will always be the same number if the number is positive. Therefore, the values of x which make this true are x ≥ 0.
? Given: All US area codes are three-digit numbers that use the numerals 0 to 9. Step 2: How many area-codes are possible if the first digit can't be zero and no digit can be repeated? Use your keyboard and the keypad to enter your answer. Then click Done.
Explanation:
For the first slot, we have 9 digits to choose from (1 through 9).
Whatever we pick for the first choice, we have 9 choices left for the second slot. Say we picked 2 for the first slot. That means we have {0,1,X,3,4,5,6,7,8,9} to choose from. I used X to indicate we can't pick that digit any more. You'll see there are 9 items in that list.
Then for the third slot, we had 8 choices to pick from
Overall we have 9*9*8 = 81*8 = 648 different area codes possible where the first digit cannot be zero.
Can an absolute value function also be a polynomial function? Why or why not?
Answer:
For this case a polynomial is defined with the following expression:
[tex] p(x) =\sum_{i=1}^n a_i x^i[/tex]For all x on the domain considered and n is finite
And by definition the absolute value function is defined as:
[tex] |x|= x, x \geq 0[/tex]
[tex] |x| =-x , x<0[/tex]
If we use the function [tex] f(x) =|x|[/tex] we see that is impossible to obtain the general expression of a polynomial since we can't obtain the form |x| and since we don't satisfy the definition the answer would be:
An absolute value function CANNOT be considered as a polynomial function
Step-by-step explanation:
For this case a polynomial is defined with the following expression:
[tex] p(x) =\sum_{i=1}^n a_i x^i[/tex]For all x on the domain considered and n is finite
And by definition the absolute value function is defined as:
[tex] |x|= x, x \geq 0[/tex]
[tex] |x| =-x , x<0[/tex]
If we use the function [tex] f(x) =|x|[/tex] we see that is impossible to obtain the general expression of a polynomial since we can't obtain the form |x| and since we don't satisfy the definition the answer would be:
An absolute value function CANNOT be considered as a polynomial function
Solve by the quadratic formula: 3x^2 - 4x + 1 = 0
Answer:
x = 1/3 and x = 1.
Step-by-step explanation:
3x^2 - 4x + 1 = 0
(3x - 1)(x - 1) = 0
The solutions are when either 3x - 1 = 0 or x - 1 = 0.
3x - 1 = 0
3x = 1
x = 1/3
x - 1 = 0
x = 1
So, x = 1/3 and x = 1.
Hope this helps!
The freezing point of water is
0
∘
C
0
∘
C0, degrees, start text, C, end text. Scientists use positive numbers to show temperatures above the freezing point of water and negative numbers to show temperatures below the freezing point of water.
Jess stores her bacteria samples at
4
∘
C
4
∘
C4, degrees, start text, C, end text.
What does
4
∘
C
4
∘
C4, degrees, start text, C, end text mean in this situation?
Step-by-step explanation:
the freezing point of water is 0⁰c...
0⁰c is as positive value but this is also considered as also in negative so it is not fixed but after a experiment it shows that 0⁰c ⁷
Answer:
Mia's iced coffee is 4^\circ\text{C}4
∘
C4, degrees, start text, C, end text below the freezing point of water.
Step-by-step explanation:
What is the slope of the line?
3(y - 1) = 2x + 2
Answer:
The slope is 2/3
Answer:
2/3
Step-by-step explanation:
This is written in point slope form
y - y1 = m(x-x1)
3(y - 1) = 2x + 2
Divide each side by 3
(y - 1) = 1/3(2x + 2)
Factor out a 2
(y - 1) = 2/3(x - -1)
The slope is 2/3
Find mQPR. If mQPS=40,mRPS=8x+7,mQPR=9x+16
Which statement about this figure is true? Pls give an explanation
Answer:
The correct option is;
It has no reflectional symmetry
Step-by-step explanation:
Reflectional symmetry is one such that a line can be drawn across a shape or figure and the shape or figure on either side of the line is the equivalent of the reflection image obtained from a mirror
Lines of reflectional symmetry can be found in squares, circles, and triangles
The characteristics of the object that has line of reflection symmetry remains the same across the line of symmetry
Two dimensional objects have lines of symmetry while three dimensional objects have planes of symmetry.
what is the expression in radical form (2m^2n)^3/2
Answer:
sqrt[(2m^2n)^3]
Step-by-step explanation:
So let's break down the exponent. The top number represents the number of times the term is repeated. The bottom number represents the root to be taken of the final product. With this in mind, let's rewrite this expression.
(2m^2n)^3/2
= [(2m^2n)^3]^1/2
Notice we have 3 of the (2m^2n) terms, but they are all under the 2nd root (aka a square root).
So now, we'll rewrite this into the radical form.
sqrt[(2m^2n)^3]
I hope this helps.
Cheers.
How much did Angelo pay for his online purchase
Answer:
Step-by-step explanation:
please include a picture of the question! :)
if 1 gallon of water is added to 6 quarts of a mixture of alcohol and water that is 50% alcohol, what percent alcohol is the resulting mixture?
Will mark brainlist
Answer:
The percentage of alcohol in the resulting mixture is 30%
Step-by-step explanation:
The equation given are;
Volume of added water = 1 gallon = 3.79 litres = 4 quarts
Volume of mixture of alcohol = 6 quarts = 5.68 litres
Concentration of the alcohol in 6 quarts = 50%
Given that the mixture of alcohol and water is 50% alcohol and 50% water, we have;
Volume of 100% alcohol in 5.68 liters = 0.5× 5.68 = 2.84 litres = 3 quartz
Total volume of the final solution = 5.68 + 3.78 = 9.46 litres = 10 quarts
Percentage by volume of 100% alcohol in total volume of the resultant solution = 3 quarts/((4 + 6) quarts) × 100 = 3/10 × 100 = 30%
The percentage of alcohol in the resulting mixture = 30%.
Band uniforms cost 45 dollars each how many can i buy for 1000 dollars
Answer:
22
Step-by-step explanation:
Answer:
22 band uniforms
Step-by-step explanation:
Each band uniform costs $45, and you have $1000. We want to find how many band uniforms you can purchase.
Therefore, we can divide 1000 (total money) by 45 (cost of one band uniform)
1000/45
Divide
22.2222222
0.2222... , or a part, of a uniform cannot be purchased, so we must round down to the nearest whole number.
22
22 band uniforms can be purchased.
A box contains 5 blue, 4 red, and 3 yellow marbles. Two marbles are randomly drawn and not replaced. What is the probability of drawing a blue then a red marble?
Answer:
5/33
Step-by-step explanation:
5/12 * 4/11 = 20/132 = 10/66 = 5/33
Please can someone help it will mean the world
Answer:
The solution is (2,5)
Step-by-step explanation:
The solution to the system of equations is where to the two graphs intersect
The two lines intersect at x=2 and y = 5
The solution is (2,5)
Answer:
Hey there!
The solution for a system of equations (simultaneous equations), is where the two lines intersect.
We see that the lines intersect at (2,5), making (2,5) the solution to the system of equations.
Let me know if this helps :)
x: 13, 17, 21, 25 y: 0, 6, 12, 18 is the relationship linear, exponential or neither
━━━━━━━☆☆━━━━━━━
▹ Answer
Linear
▹ Step-by-Step Explanation
As x increases by 4, y increases by 6.
13 + 4 = 17
17 + 4 = 21
21 + 4 = 25
0 + 6 = 6
6 + 6 = 12
12 + 6 = 18
Hope this helps!
CloutAnswers ❁
Brainliest is greatly appreciated!
━━━━━━━☆☆━━━━━━━
[tex]\mathfrak{\huge{\pink{\underline{\underline{AnSwEr:-}}}}}[/tex]
Actually Welcome to the Concept of the GRAPHS AND FUNCTIONS.
This here, from the graph we can see that it's a EXPONENTIAL GROWTH.
Thus the relationship is Exponential.
Real solution in this system of equations
BRAINLIEST WILL BE GIVEN
Answer:
A
Step-by-step explanation:
Firstly we find the x value. x-7=0; x=7
Secondly we introduce x value in 1st ecuation. So
(7-3)^2 +(y+1)^2=16, 16+y^2+2y+1=16,
Consider this ecuation: y^2+2y+1=0
y1=( -b+Δ)/ 2a, y2= (-b-√Δ)/2a, Δ=√b^2-4ac=√4-4=0
y1,2= -2/2= -1
1 Real solution x=7 and y= -1.
Two factory plants are making TV panels. Yesterday, Plant A produced 5000 fewer panels than Plant B did. Five percent of the panels from Plant A and 2% of the panels from Plant B were defective. How many panels did Plant B produce, if the two plants together produced 450 defective panels
Answer:
10,000 panels
Step-by-step explanation:
A TV panel is being produced by two factory plants
Plant A produced 5000 fewer panels than plant B
Let a represent the number of panels produced by plant A and b represent the number of panels produced by plant B
a= b-5000............equation 1
5% of the panels from plant A were defective
= 5/100
= 0.05
2% of the panels from plant B were defective
= 2/100
= 0.02
The total defective panels of both plants is 450
0.05a + 0.02b= 450..............equation 2
Substitute b-5000 for a in equation 2
0.05(b-5000) + 0.02b= 450
0.05b - 250 + 0.02b= 450
Collect the like terms
0.05b+0.02b= 450+250
0.07b= 700
Divide both side by the coefficient of b which is 0.07
0.07 b/0.07= 700/0.07
b= 10,000
Hence plant B produced 10,000 panels
If an object is propelled upward from a height of 72 feet at an initial velocity of 90 feet per second, then its height h after t seconds is given by the equation h = − 16 t 2 + 90 t + 72 . After how many seconds does the object hit the ground?
Answer:
6.34 seconds.
Step-by-step explanation:
The object will hit the ground when h = 0.
-16t^2 + 90t + 72 = 0
8t^2 - 45t - 36 = 0
We can then use the quadratic formula to solve.
[please ignore the A-hat; that is a bug]
[tex]\frac{45±\sqrt{45^2 - 4 * 8 * -36} }{2 * 8}[/tex]
= [tex]\frac{45±\sqrt{2025 + 1152} }{16}[/tex]
= [tex]\frac{45±\sqrt{3177} }{16}[/tex]
= [tex]\frac{45±56.36488268}{16}[/tex]
(45 - 56.36488268) / 16 = -0.7103051678
(45 + 56.36488268) / 16 = 6.335305168
Since the time cannot be negative, the object will hit the ground after about 6.34 seconds.
Hope this helps!
Pam works as an office administrator. She spends $7500 of her income on personal expenses each year. If this represents 18% of her salary, how much money does Pam earn in one year? Round your answer to the nearest whole dollar.
Answer: Pam earns $41,667 in one year.
Step-by-step explanation:
Hi, to answer this question we have to write an equation:
Pam's salary (x) multiplied by the percentage represented by expenses (18%) in decimal form (divided by 100) must be equal to $7500.
Mathematically speaking:
x (18/100) = 7500
Solving for x:
x (0.18) = 7500
x = 7500/0.18
x = 41,667
Pam earns $41,667 in one year.
Feel free to ask for more if needed or if you did not understand something.
Simplify csc θ + cot θ
Answer:
csc θ + cot θ
From trigonometric identities
[tex] \csc(θ) = \frac{1}{ \sin(θ) } [/tex]
And
[tex] \cot(θ) = \frac{ \cos(θ) }{ \sin(θ) } [/tex]
So we have
[tex] \frac{1}{ \sin(θ) } + \frac{ \cos(θ) }{ \sin(θ) } [/tex]
Find the LCM
The LCM is sin θ
So we have
[tex] \frac{1}{ \sin(θ) } + \frac{ \cos(θ) }{ \sin(θ) } = \frac{1 + \cos(θ) }{ \sin(θ) } [/tex]
And
[tex] \frac{1 + \cos(θ) }{ \sin(θ) } = \cot( \frac{θ}{2} ) [/tex]
So we have the final answer as
[tex] \cot( \frac{θ}{2} ) [/tex]
Hope this helps you
the scale on the map is 1 cm represents 40 km . the actual straight line distance between 2 cities is about 320 km what is the map distance between these 2 cities
Answer:
8cm
Step-by-step explanation:
the ratio of cm to km is 1 cm on the map equals 40 km. or 1/40 so you have to find what is x/320 using the ratio of 1/40 you gt that x equals 8
Alicia Keys's new album As I Am is climbing the charts, and the manager of Tip Top Tunes expects to sell a lot of copies. Because she has limited shelf space, she can't put out all her copies of the CD at once. On Monday morning, she stocked the display with 40 copies. By the end of the day, some of the copies had been sold. On Tuesday morning, she counted the number of copies left and then added that many more to the shelf. In other words, she doubled the number that was left in the display. At the end of the day, she discovered that she had sold the exact same number of copies as had been sold on Monday. On Wednesday morning, the manager decided to triple the number of copies that had been left in the case after Tuesday. Amazingly, she sold the same number of copies on Wednesday as she had on each of the first two days! But this time, at the end of the day the display case was empty. How many copies of the As I Am CD did she sell each day?
Answer:
About 4.44
Step-by-step explanation:
Let x represent the unknown amount of CD's sold each day. Thus, the linear equation is formed:
40-x = 2x + 3 (2x) Next collect like terms by adding x to both sides.
40-x+x= x + 2x + 3 (2x)
40 = 3x + 3 (2x)
40 = 3x + 6x
40= 9x
40/9 = 9x/9
x= 4.44
Note: 2x represents doubling up the sales amount, which was left.
3x represents tripling the sales amount left.
What is the value of discontinuity of x^2+8x+4/x^2-x-6? Choices:
Answer:
-2
Step-by-step explanation:
Hello,
First of all, let's check the denominator.
[tex]x^2-x-6 \ \ \text{ *** How to factorise it ...? ***}\\\\\text{*** The product of the roots is -6=-2*3 and their sum is 1 ***}\\\\x^2-x-6=x^2-3x+2x-6=x(x-3)+2(x-3)=(x+2)(x-3)[/tex]
Now, let's see the numerator.
[tex]x^2+8x+4 \ \text{ *** -2 is not a zero as ***}\\\\(-2)^2+8*(-2)+4=4-16+8=-4\\\\\text{*** 3 is not a zero as ***}\\\\3^2+8*3+4=9+24+4=37\\[/tex]
So we cannot factorise the numerator with (x+2) or (x-3)
Then, -2 and 3 are the the discontinuities of the expression.
There is only -2 in the list, this is the correct answer.
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
A twelve-foot ladder is leaning against a wall. If the ladder reaches ft high on the wall, what is the angle the ladder forms with the ground to the nearest degree?*
This question is incomplete.
Complete Question
A twelve-foot ladder is leaning against a wall. If the ladder reaches eight ft high on the wall, what is the angle the ladder forms with the ground to the nearest degree?*
Answer:
42°
Step-by-step explanation:
From the question, the diagram that is formed is a right angle triangle.
To solve for this, we would be using the trigonometric function of Sine.
sin θ = Opposite side/ Hypotenuse
From the question, we are told that:
12 foot ladder is leaning against a wall = Hypotenuse
The ladder reaches 8ft high on the wall = Opposite side.
Hence,
sin θ = 8ft/12ft
θ = arc sin (8ft/12ft)
= 41.810314896
Approximately to the nearest degree
θ = 42°
Therefore, the angle the ladder forms with the ground to the nearest degree is 42°