Answer:
See below
Step-by-step explanation:
Basically, when you have a product to two factors set equal to 0, you can use the Zero Product Property and make two separate equations, both set equal to 0, to find the roots for each factor:
[tex]2x+10=0\\2x=-10\\x=-5[/tex]
[tex]x-7=0\\x=7[/tex]
Notice that by plugging these roots back into the equation, either factor will be 0, making the whole expression 0:
[tex](2x+10)(x-7)=0\\(2(7)+10)(7-7)=0\\(24)(0)=0\\0=0[/tex]
[tex](2x+10)(x-7)=0\\(2(-5)+10)(-5-7)=0\\(0)(-12)=0\\0=0[/tex]
What is the area of the figure shown?
Check the picture below.
[tex]\textit{area of a circular ring}\\\\ A=\pi (R^2-r^2) ~~ \begin{cases} R=\stackrel{larger}{radius}\\ r=\stackrel{smaller}{radius}\\[-0.5em] \hrulefill\\ R=10.5\\ r=7 \end{cases}\implies \begin{array}{llll} A=\pi (10.5^2 - 7^2)\implies A=61.25\pi \\\\\\ A\approx 192.42~m^2 \end{array}[/tex]
There are 6 swimmers in a race. In how many ways can they finish in first and second place?
-12
-30
-120
-360
Answer:
step 1. 6x2=12 first place way
step 2. 12×2=24
step 3. 24+6=30 second place way
A chocolate bar measures 30 mm wide, 70 mm long, and four and one over two mm high. Will’s Wrapping Company is making a wrapper to cover the chocolate bar. Use the correct net and determine how much paper will be needed to make the wrapper.
Answer:
minimum of 5100 mm^2
Step-by-step explanation:
Surface area 2 * ( 70 * 30 + 70 * 4.5 + 30* 4.5) = 5100 mm^2
At the circus, an acrobat is standing on a platform that is 27 feet from the ground when he sees a peanut on the ground below. How far is the peanut away from the base of the platform if the angle of elevation from the peanut to top of the acrobat's platform is 25°?
Answer:
The peanut is 12.59 feet away from the base of the platform.
Step-by-step explanation:
When solving these equations, we can first start out by noticing that this requires a trigonometry function.
There are three types : cos, sin, and tan. (cosine, sin, and tangent)
Cos is for finding and dealing with the adjacent and the hypotenuse.
Sin is for finding and dealing with the opposite and the hypotenuse.
Tan is for finding and dealing with the opposite and the adjacent.
The opposite is the bottom base, to the peanut.
The adjacent is the height from the bottom base, to the top.
The hypotenuse is the top, to the peanut.
27 feet would be the adjacent.
Since we don't know bottom base to the peanut, we would call this x. (opposite)
*Side note* : The degrees is always in between the adjacent and hypotenuse.
For this, we need the length between the peanut and the bottom base. This would be the adjacent and the opposite. Meaning we're using tangent. The equation for tangent is :
tan (degrees) = opposite/adjacent
So, now we simply put in the data.
tan 25 = x/27
We can now, first get x alone by multipling both sides by 27.
27 * tan 25 = x
Plug this into a scientific calculator :
27 * tan 25
We the answer to be 12.59
The peanut is 12.59 feet away from the base of the platform
I just need an explanation for this. I know the answer is 34 cm, but I don't understand how you get there
Step-by-step explanation:
180 ° - 146°=34°
Where by isosceles triangle is 180
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Answer:
A.
Step-by-step explanation:
Because if she plays for a certain amount of time it would go up. And it she took a break it would be a straight line then go up the same line as the one at the bottom. Thus making your answer A.
23 +42
0-24
О-3/16
O3/16
Step-by-step explanation:
23+42=65
0-24=-24
0-3/16=-3/16= -1875
03/16=0.1875
QUICK ANSWER PLEASE!!
If M(1; -1) is the midpoint of the line segment AB, where A(-4;y)
and B(x; -5), calculate the value of x and y.
Determine which function has the greatest rate of change over the interval [0, 2].
A. c
B. a
C. d
D. b
Answer:
B :a
Step-by-step explanation:
Solve for d.
3(d + 2) = 12
d =
Answer:
d = 2
Step-by-step explanation:
3(d + 2) = 12 ( divide both sides by 3 )
d + 2 = 4 ( subtract 2 from both sides )
d = 2
Answer:
d=2
Step-by-step explanation:
3(d+2)=12
divide both side by 3
d+2 =4
substract 2 from both side
d=2
16.38 divided by 0.06
Answer:
273
Step-by-step explanation:
Answer: 273
Step-by-step explanation: when you divide 16.38 by 0.06 you get 273.
I need help. Find the ratio of the trig function.
Answer:
tanΘ = [tex]\frac{4}{3}[/tex]
Step-by-step explanation:
tanΘ = [tex]\frac{opposite}{adjacent}[/tex]
the opposite side requires to be found.
let the opposite side be x then using Pythagoras' identity in the right triangle
x² + 12² = 20²
x² + 144 = 400 ( subtract 144 from both sides )
x² = 256 ( take square root of both sides )
x = [tex]\sqrt{256}[/tex] = 16
then
tanΘ = [tex]\frac{16}{12}[/tex] = [tex]\frac{4}{3}[/tex]
What number is 90% of
140?
Answer:
126
Step-by-step explanation:
groups, A and B, of size 10. In the simulations, group A always plays the role of the treatment group and group B the role of the control group.
After each simulation, she subtracts the average for group A from the average for group B. The distribution of the differences for all 100 simulations is shown in the histogram.
In the original experiment, the average for the treatment group was 1.6 lower than the average for the control group.
In what percentage of simulations is the average for group A at least 1.6 lower than the average for group B?
The percentage of simulations where the average for group A is at least 1.6 lower than the average for group B is 48%.
Data points where the average for group A is at least 1.6 less than BThe following are the data points from the histogram where the average of group A is at least 1.6 less than average of group B.
At least -1.6 lower implies -1.6, -1.5, -1.4, -1.3, -1.2, -1.1, 0, 1, etc.
the first point = (-1.6 - 1.2) (number of simulation = 1)second point = (-1.2, -0.8) (number of simulation = 8)third point = (-0.8, -0.4) (number of simulation = 16)fourth point = (-0.4, 0) (number of simulation = 23)Outcome of simulations = 1 + 8 + 16 + 23 = 48
Percentage of simulation = outcome/total x 100%
Percentage of simulation = (48 x 100%)/100
Percentage of simulation = 48%
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Mamadou surveyed 500 of the students in the school about their favorite color students could choose between blue and red 390 students said their favorite color was red what percentage of the surveys students said their favorite color was blue
Answer:
22%
Step-by-step explanation:
so 500-390 = 110
110 students said their favorite color was blue.
110/500 = ?/100
110 times 100 = 11000
11000/500 = 22
give brainliest, please!
hope this helps :)
solutia ecuatiei 4x+12= 0 este x =
There are 34 students and five teachers going on a trip if each ticket costs $9.50 how much money do they need to raise
Select all the numbers that are rational
Answer:
-13/3
and the last 2
Step-by-step explanation:
The rational numbers include all the integers, plus all fractions, or terminating decimals and repeating decimals. Every rational number can be written as a fraction a/b, where a and b are integers. For example, 3 can be written as 3/1, -0.175 can be written as -7/40, and 1 1/6 can be written as 7/6.
Find the area of a rectangle with a length of 3 feet and a width of 2 7/8 feet
Answer:
8.625 or 8 5/8
Step-by-step explanation:
to find area you multiply length times width.
first, change 2 7/8 to an improper fraction to make multiplying easier. 2 7/8= 23/8.
then, multiply 3/1 (or 3) by 23/8. multiply across to get 69/8. Simplify the fraction to get 8 5/8 or 8.625.
Jodie started washing her car at 10:15 am she finished at 10:50 am how long did it take jody to wash her car.
Answer:
35 minutes
Step-by-step explanation:
this requires us to find out how long it took and because both times given to figure this out are within the same hour it is easy to figure out in this case, 50 - 15 = 35. This is not as simple with all problems like this but because of the times given in this problem its much easier.
Select the correct answer. which expression is equivalent to the given expression? assume the denominator does not equal zero. a. b. c. d.
The expression that is equivalent to the expression, [tex](\frac{4m^5n^2}{m^2n} )^3[/tex] is the expression, [tex]64m^9n^3[/tex].
What are Equivalent Expressions?If two expressions are equivalent to each other, it means the value of each of them are the same when simplified or evaluated in their simplest form.
Given the expression,
[tex](\frac{4m^5n^2}{m^2n} )^3[/tex]
Evaluate the expression in its simplest form
[tex](\frac{4m^5n^2}{m^2n} )^3 = (4m^3n^1)^3[/tex]
Multiply the exponents in the bracket by the one outside, then find the cube of 4.
[tex]64m^9n^3[/tex]
Therefore, [tex](\frac{4m^5n^2}{m^2n} )^3[/tex] is equivalent to [tex]64m^9n^3[/tex].
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Which is an example of stratified random sampling created from each given population? A. Deciding who should be the president of the senior class by tossing a coin to choose between two candidates. B. C. Surveying members of a political party by calling people listed in the telephone directory whose last names begin with the letter A. D. Surveying subscribers to a magazine by separating the list of subscribers into four age groups and choosing a sample from each group proportional to its size in the population.
Answer:
the answer is D
Step-by-step explanation:
i just did the test
Answer:
D
Step-by-step explanation:
Please help fast-
In △LMN , point E is between points L and M, point F is between points M and N, and EF¯¯¯¯¯∥LN¯¯¯¯¯ .
LE=19 cm , LM=31 cm , and MN=124 cm .
What is MF ?
Enter your answer in the box.
Using the triangle proportionality theorem, the length of segment MF in triangle LMN is: 48 cm.
What is the Triangle Proportionality Theorem?The triangle proportionality theorem states that when a segment intercepts two sides of a triangle and it is parallel to a third side, then it divides the side proportionally.
The diagram of triangle LMN is shown below. Using the triangle proportionality theorem, we have:
MF/MN = ME/ML
Plug in the values
MF/124 = (31 - 19)/31
MF/124 = 12/31
MF = (12 × 124)/31
MF = 48 cm
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Solve this:
Raj is 12m years old. His son was born when he was 9m years old.
(i) Find Raj's age 5 years later.
(ii) Find the sum of their ages in 5 years' time.
Answer:
i = 17 Years old
ii = 25 years
Step-by-step explanation:
i = 12 + 5 =17
ii = his son was born when he was 9, hes 12 now, so his sons 3. In 5 years time his sons 8 and hes 17, 8+17= 25
If the product of 5x+1 and 2x-3 was place in ax2+bx+c form what would the value of a+b+c equal
Answer:
Answer: 10x^2 -13x-3
Foil method
Step-by-step explanation:
I beleive its right.
please help best answer will be brainliest
Answer:
A
Step-by-step explanation:
A fireball
The principal sent a message to 25 students to ask them to
help pick up litter after school. Only 8 of them showed up.
What percentage of the students came to pick up litter?
Answer: 32%
Step-by-step explanation:
100 / 25= 4
4 x 8 = 32%
Which set of real numbers contains 23 and .45?
rational numbers
integers
natural numbers
whole numbers
Answer:
Option A, rational numbers
Step-by-step explanation:
Step 1: Determine which option is correct
Option B and D are automatically ruled out because only one of them is a whole number and the other one is a decimal. Option C doesn't work also because natural numbers are all the whole numbers that are greater than 1. The only option that makes sense is option A which includes whole numbers and decimals.
Answer: Option A, rational numbers
What is the solution to the system of equations?
x-2y = 19
x + 3y = 14
(1.-17) (17.-1)
(-17, 1)
(-1.17)
Answer:
(17,-1)
Step-by-step explanation:
The solution in the image
2x^3-x^2-3x=210
the answer is 5 but I want to know why.
Answer:
[tex]x=5,\frac{-9+\sqrt{255}i }{4} ,\frac{-9-\sqrt{255}i }{4}[/tex]
Step-by-step explanation:
1) Move all terms to one side.
[tex]2x^{3} -x^{2} -3x-210=0[/tex]
2) Factor [tex]2{x}^{3}-{x}^{2}-3x-210[/tex] using Polynomial Division.
1 - Factor the following.
[tex]2x^{3} -x^{2} -3x-210[/tex]
2 - First, find all factors of the constant term 210.
[tex]1,2,3,4,5,6,7,10,14,15,21,30,35,42,70,105,210[/tex]
3) Try each factor above using the Remainder Theorem.
Substitute 1 into x. Since the result is not 0, x-1 is not a factor..
[tex]2*1^{3} -1^{2} -3*1-210=-212[/tex]
Substitute -1 into x. Since the result is not 0, x+1 is not a factor..
[tex]2(-1)^{3} -(-1)^{2} -3*-1-210=-210[/tex]
Substitute 2 into x. Since the result is not 0, x-2 is not a factor..
[tex]2*2^{3} -2^{2} -3*2-210=-204[/tex]
Substitute -2 into x. Since the result is not 0, x+2 is not a factor..
[tex]2{(-2)}^{3}-{(-2)}^{2}-3\times -2-210 = -224[/tex]
Substitute 3 into x. Since the result is not 0, x-3 is not a factor..
[tex]2\times {3}^{3}-{3}^{2}-3\times 3-210 = -174[/tex]
Substitute -3 into x. Since the result is not 0, x+3 is not a factor..
[tex]2{(-3)}^{3}-{(-3)}^{2}-3\times -3-210 = -264[/tex]
Substitute 5 into x. Since the result is 0, x-5 is a factor..
[tex]2\times {5}^{3}-{5}^{2}-3\times 5-210 =0[/tex]
------------------------------------------------------------------------------------------
⇒ [tex]x-5[/tex]
4) Polynomial Division: Divide [tex]2{x}^{3}-{x}^{2}-3x-210[/tex] by [tex]x-5[/tex].
[tex]2x^{2}[/tex] [tex]9x[/tex] [tex]42[/tex]
-------------------------------------------------------------------------
[tex]x-5[/tex] | [tex]2x^{3}[/tex] [tex]-x^{2}[/tex] [tex]-3x[/tex] [tex]-210[/tex]
[tex]2x^{3}[/tex] [tex]-10x^{2}[/tex]
-----------------------------------------------------------------------
[tex]9x^{2}[/tex] [tex]-3x[/tex] [tex]-210[/tex]
--------------------------------------------------------------------------
[tex]42x[/tex] [tex]-210[/tex]
[tex]42x[/tex] [tex]-210[/tex]
-------------------------------------------------------------------------
5) Rewrite the expression using the above.
[tex]2x^2+9x+42[/tex]
[tex](2x^2+9x+42)(x-5)=0[/tex]
3) Solve for [tex]x.[/tex]
[tex]x=5[/tex]
4) Use the Quadratic Formula.
1 - In general, given [tex]a{x}^{2}+bx+c=0[/tex] , there exists two solutions where:
[tex]x=\frac{-b+\sqrt{b^{2} -4ac} }{2a} ,\frac{-b-\sqrt{b^2-4ac} }{2a}[/tex]
2 - In this case, [tex]a=2,b=9[/tex] and [tex]c = 42.[/tex]
[tex]x=\frac{-9+\sqrt{9^2*-4*2*42} }{2*2} ,\frac{-9-\sqrt{9^2-4*2*42} }{2*2}[/tex]
3 - Simplify.
[tex]x=\frac{-9+\sqrt{255}i }{4} ,\frac{-9-\sqrt{255}i }{4}[/tex]
5) Collect all solutions from the previous steps.
[tex]x=5,\frac{-9+\sqrt{255}i }{4} ,\frac{-9-\sqrt{255}i }{4}[/tex]