Step-by-step explanation:
the area of a triangle is
baseline × height / 2
so, in our case we know this is 10 :
(x+3)(x-1)/2 = 10
(x+3)(x-1) = 20
x² - x + 3x - 3 = 20
x² + 2x - 23 = 0
that is exactly the provided equation. so, yes, x satisfies it.
the general solution to a quadratic equation is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
a = 1
b = 2
c = -23
x = (-2 ± sqrt(2² - 4×1×-23))/(2×1) =
= (-2 ± sqrt(4 + 92))/2 = (-2 ± sqrt(96))/2 =
= (-2 ± sqrt(16×6))/2 = (-2 ± 4×sqrt(6))/2 =
= -1 ± 2×sqrt(6)
x1 = -1 + 2×sqrt(6) = 3.898979486... ≈ 4
or using sqrt(6) ≈ 2.45
= -1 + 2×2.45 = -1 + 4.9 = 3.9 ≈ 4
x2 = -1 - 2×sqrt(6) = -5.898979486... ≈ -6
or using sqrt(6) ≈ 2.45
= -1 - 2×2.45 = -1 - 4.9 = -5.9 ≈ -6
x2 would give us negative lengths for the triangle, which does not make sense.
so, x = 4 is our solution.
and that makes the height x-1 = 4-1 = 3 units.
Need help asap, will give brainliest
26. Each weekday, 3,200,000 people in Massachusetts
commute to work. Of the total commuters, 403,200 take
public transportation. What percentage of commuters take
public transportation?
Answer: 12.6%
Step-by-step explanation:
403,200/3,200,000 = 0.126
0.126 = 12.6%
What is 8,-6 over the x-axis 90 degrees
Answer:
(6,8)
Step-by-step explanation:
The rule for 90 degree rotation is (x,y)=(-y,x)
So the answer is (6,8)
A cooler is filled with different juices. There are 6 bottles of juice:
1 orange juice, 2 apple juice, 2 cranberry juice, and 1 grape juice.
What is the probability of randomly choosing 1 orange juice and then 1 apple juice
without replacing the first juice?
Answer:
1/15
Step-by-step explanation:
Total = 6 bottles
1 orange and apple
Without replacement:
P(orange and apple) = 1/6 x 1/5 = 1/15
Answer: Probability = 1/15
PLEASE HELP WILL GIVE BRAINLEST! What is the amplitude of the function graphed below?
Answer:
[tex]2\pi[/tex]
That's it
how to solve x-3y=1 4x+5y=4 using elimination
Answer:
X=1, Y=0
Step-by-step explanation:
Solve for X and Y using a2 +b2 = c2
distance between points (-4,4) and (4,-2)
Answer:
10 units
Step-by-step explanation:
calculate the distance using the distance formula
d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = (- 4, 4 ) and (x₂, y₂ ) = (4, - 2 )
d = [tex]\sqrt{(4-(-4))^2+(-2-4)^2}[/tex]
= [tex]\sqrt{(4+4)^2+(-6)^2}[/tex]
= [tex]\sqrt{8^2+36}[/tex]
= [tex]\sqrt{64+36}[/tex]
= [tex]\sqrt{100}[/tex]
= 10
What is the slope of the line shown below?
A. -1/3
B. 1/3
C. 3
D. -3
Answer:
C. 3
Step-by-step explanation:
Using the slope formula
Answer:
C. 3
Step-by-step explanation:
8 - 2/ 4 - 2 = 6/2 = 3
...................................................
complete the statement, and find the value of x in the diagram.
help please!
Answer:
Also the quadrilateral shown is a rhombus
Step-by-step explanation:
Which is the completely factored form of 12x4 39x3 9x2? 3x2(x – 3)(4x – 1) 3x2(x 3)(4x 1) 3x(x 3)(4x 1) 3x(x – 3)(4x 1)
The completely factored expression of 12x⁴ + 39x³ + 9x² is 3x²(4x + 1)(x + 3)
How to factor the expression?The polynomial expression is given as;
12x⁴ + 39x³ + 9x²
Factor out 3x² from the expression
3x²(4x² + 13x + 3)
Expand
3x²(4x² + 12x + x + 3)
Factorize the expression
3x² * 4x(x + 3) + 1(x + 3)
Factor out x + 3
3x²(4x + 1)(x + 3)
Hence, the completely factored expression of 12x⁴ + 39x³ + 9x² is 3x²(4x + 1)(x + 3)
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A printer can print 12 pages in 9 seconds. What is the closest estimate of the
number of pages it can print in one minute?
120
100
45
72
Answer:
72 is the closest.The printer will primt 80 pages in one minute
Answer:
72
Step-by-step explanation:
12 pgs in 9 sec
*[tex]\frac{20}{3}[/tex] *[tex]\frac{20}{3}[/tex]
≈80 pgs in 60 sec
Hope this helps!!!
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Each exterior angle of a regular decagon has a measure of (3x + 6)°. What is the value of x?
Which the is the correct answer?
To solve this problem, we need to use combination which is statistical tool to determine the number of ways an event may occur. The combination to select a 5 a side team from 12 students is 792.
CombinationThis a mathematical technique that is used to determine the number of possible arrangements in a collection of items where the way they're arranged does not matter.
Data;
Number of Students = 12Team = 5The combination for this would be
[tex]C = ^1^2C_5 = 792[/tex]
The combination to select a 5 a side team from 12 students is 792.
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V-125 - 5 X 32
[tex]3 \sqrt{ - 125} - 5 \times {3}^{2} [/tex]
Simplify the following and show all your workings
Answer:
Because of the order of operations, we start the equation backwards because exponents are what we prioritize here.
[tex]3^2 = 9\\\\9 * 5 = 45\\\\\sqrt{-125} = -11.1803399\\\\45 - -11.1803399 = 56.1803399\\\\56.1803399 * 3 = \boxed{168.54}[/tex] Result rounded to 2 DP
A box has a width of 5 centimeters and a height of 6 centimeters. If the volume is 150 cubic centimeters, what is the length of the box?
A) 5 centimeters
B) 4 centimeters
C) 7 centimeters
D) 3 centimeters
Answer: A. 5
Step-by-step explanation:
Answer:
A) 5 cm.
Step-by-step explanation:
Volume = length * width * height
150 = length * 5 * 6
Length = 150 / (5*6)
= 150/30
= 5.
Please help quick 30 points
Evaluate 5 x + (-2 x2 ) for x = 3.
Answer:
I'd say 11 but could also be 30
For a project in his Geometry class, Fwam uses a mirror on the ground to measure the height of his school building. He walks a distance of 7.15 meters from the building, then places a mirror flat on the ground, marked with an X at the center. He then walks 2.45 more meters past the mirror, so that when he turns around and looks down at the mirror, he can see the top of the school clearly marked in the X. His partner measures the distance from his eyes to the ground to be 1.55 meters. How tall is the school
Answer:
2106 m
Step-by-step explanation:
IF COREY HAD 100 TOKENS AND HE GIVES SOME TO HIS FRIENDS! HE HAS 4 LEFT OVER! HOW MANY DID HE GIVE EACH OF HIS FRIENDS!?
Answer:
he gave away 96 but depends how many friends he gave them to.
Step-by-step explanation:
This year, you owed $6,414.95 in federal income tax. if you are taxed at a net rate of 17%, what was your taxable income for this year? a. $109,054 b. $26,792 c. $44,867 d. $37,735
Using proportions, it is found that your taxable income for this year is given by:
d. $37,735
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
In this problem, we have that $6,414.95 is 17% of his taxable income, hence it is given by:
T = 6414.95/0.17 = $37,735.
Which means that option D is correct.
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Answer:D
Step-by-step explanation:
bc its D
A is directly proportional to B.
When A = 12, B = 3
Find the value of A when B=5
Answer:
a= 20
Step-by-step explanation:
12/3
a/5
60 = 3a
a = 60/3 = 20
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar. David invested $230 in a savings account that offers a 3% return on the investment. The value of David's investment will be at least $415 after a period of years. Hint: Use the formula A = P(1 + r)t, where A is the amount after t years, P is the amount invested, r is the rate of interest, and t is the time period. Use a calculator to compute the answer, and round it off to the nearest year.
The value of David's investment will be at least $415 after a period of 20 years
Compound interestThe formula for calculating the compound interest is expressed as:
A = p(1+r)^t
Given the following parameters
A = $415P = $230r = 3% = 0.03Substitute
415 = 230(1+0.03)^t
415/230 = 1.03^t
1.8043 = 1.03^t
t = ln(1.8043)/ln1.03
t = 20 years
The value of David's investment will be at least $415 after a period of 20 years
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What are the domain and range of f (x) = log (x minus 1) + 2?
domain: x > 1; range: y > 2
domain: x > 1; range: all real numbers
domain: all real numbers; range: y > 1
domain: all real numbers; range: all real numbers
Answer:
domain: x > 1; range: all real numbers
Step-by-step explanation:
Given function: [tex]f(x)=\log(x-1)+2[/tex]
Logarithms are not defined for zero or negative numbers.
[tex]\implies (x-1) > 0 \implies x > 1[/tex]
Therefore:
domain (input values): [tex]x > 1[/tex]range (output values): all real numbersAnswer:
B on edge
Step-by-step explanation:
Just took the test :)
Need help as asap emergency
Answer:
$1346.4
Step-by-step explanation:
First find the rectangle portions area with lxwxh, which is 8x6x8. That equalls 384.
Then find the triangles, which is bxh, which is 6x8. That equals 144.
Add those two to get 528.
Then multiply the total area by 2.55 which will get you 1346.4
a bicyclist rides 25 miles every 2 hours during race which equation represents the relationship between the number of miles and the number of hours of the bicyclist rides? let x represent the number of hours and let y represent the number of miles?
Answer:
y=12.5x
Step-by-step explanation:
-3(v+1)-3
What is the answer I really need help
Answer:
=-3v-6
Step-by-step explanation:
Distribute:
=(−3)(v)+(−3)(1)+−3
=−3v+(−3)+(−3)
Combine like terms:
=(−3v)+(−3+(−3))
=−3v+−6
=-3v-6
Hope this helps, this was easy!
Please can anybody help me with this:
Show that (x − 9)(x − 1) ≡ x^2 − 10x + 9
We will expand the factored form of (x − 9)(x − 1) into the same form as x² − 10x + 9 to show they are equal.
Distribute and multipy out:
(x − 9)(x − 1)
x * x = x²
x * -1 = -x
x * -9 = -9x
-9 * -1 = 9
Add together:
x² + -x + -9x + 9
x² − 10x + 9
Use the Reflexive property:
x² − 10x + 9 = x² − 10x + 9 ✓
PLS help
Jaime rode her bike 5 miles north to the park to meet a friend. Then they rode east to the library. If Jaime's house is 13 miles from the library, about how far is the library from the park?
please
that is the solution
Answer:8 miles
Step-by-step explanation:
1.4x10 -2 in standard form
Answer:
12
Step-by-step explanation:
1.4x10 is moving the decimal point one spot to the left, so it would be 14., which is just simply 14. Finally, 14-2=12 which is the answer.
If you answer this I SWEAR OMM I WILL LOVE YOU FOR FREAKING EVER
Answer:
5/24 square mm
Step-by-step explanation:
A = lw
A = 5/8 x 1/3
A = 5/24
What is the horizontal asymptote of j (x) = startfraction 14 x cubed 45 over 2 x cubed x 9 endfraction y = 1 y = 5 y = 7 y = 12
The horizontal asymptotes the the point where the horizontal line cutes the y-axis. The horizontal asymptotes of the function is y =7
Horizontal asymptotes of a functionThe horizontal asymptotes the the point where the horizontal line cutes the y-axis,
Given the function
j(x) = 14x³+45/2x³+9
Since the powers of both numerator and denominator is the same, we will take the ratio of their coefficient as shown
y = 14/2
y = 7
Hence the horizontal asymptotes of the function is y =7
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