Answer:
40/7
Step-by-step explanation:
14x - 71 = 9
14x=80
x=80/14
x=40/7
Directions: Solve for X Round your answer to the nearest tenth. Make sure you calculator
is in degree model
12
Answer:
36.87
Step-by-step explanation:
Using tan inverse of 9 over 12
Answer:
x ≈ 36.9°
Step-by-step explanation:
Using the tangent ratio in the right triangle
tan x = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{9}{12}[/tex] , then
x = [tex]tan^{-1}[/tex] ([tex]\frac{9}{12}[/tex] ) ≈ 36.9° ( to the nearest tenth )
Write an equation to model the given scenario, then solve:
Each year the local country club sponsors a tennis tournament. Play starts with 128 participants. During each
round, half of the players are eliminated. How many players remain after 5 rounds?
Given:
Initial number of participants = 128
During each round, half of the players are eliminated.
To find:
The number of players remain after 5 rounds.
Solution:
It is given that, the initial number of participants is 128 and during each round, half of the players are eliminated.
If half of the players are eliminated, then half of the players are remained.
So, the initial value is 128 and the decay factor is [tex]\dfrac{1}{2}[/tex].
The general exponential decay model is:
[tex]y=a(b)^x[/tex]
Where, a is the initial value and b is the decay factor.
Putting [tex]a=128[/tex] and [tex]b=\dfrac{1}{2}[/tex] in the above model, we get
[tex]y=128\left(\dfrac{1}{2}\right)^x[/tex]
Here, y is the number of remaining players after x rounds.
Substituting [tex]x=5[/tex], we get
[tex]y=128\left(\dfrac{1}{2}\right)^5[/tex]
[tex]y=128\left(\dfrac{1}{32}\right)[/tex]
[tex]y=4[/tex]
Therefore, the required model is [tex]y=128\left(\dfrac{1}{2}\right)^x[/tex] and the number of players remain after 5 rounds is 4.
slope:1/6 point: (24 ,4)
Answer:
y -4 = 1/6(x-24)
y = 1/6x -2
Step-by-step explanation:
We can point slope form
y-y1 = m(x-x1) where m is the slope and (x1,y1) is a point on the line
y -4 = 1/6(x-24)
Or we can write slope intercept form
y = mx+b where m is the slope and b is the y intercept
Substituting the points
4 = 1/6(24)+b
4 = 6+b
4-6 = b
-2 =b
y = 1/6x -2
Answer:
[tex]y = mx + c \\ 4 = (\frac{1}{6} \times 24) + c \\ 4 = 4 + c \\ c = 0 \\ y = \frac{1}{6} x[/tex]
Please help!!!!!!
Which of these are examples of mutually beneficial interactions? Choose all that apply.
A. Ants living in special hollow thoms in a tree rush out and sting plant-eaters.
B. An orchid grows high in a tree to get more sunlight, but it does not affect the tree.
c. Wolves eat the deer that cannot run as fast as the other deer.
D. A bee gets nectar and pollen from the clover flowers in a meadow.
E. A tick bites a dog and drinks the dog's blood.
Answer:
A. The tree provides shelter for the ants, and the ants help the tree to stay alive
The number -2 is a solution to which of the following inequalities?
x + 7 > 5
-3 x < 1
x - 7 < -4
Answer:
The answer is the third one, x - 7 < 4
Step-by-step explanation:
Factor this polynomial expression. 2X2 + 12x + 18
A. 2(x+3)(x+3)
B. 2(x - 3)(x-3)
c. 2(x+3)(x - 3)
D. (2x + 9)(x+2)
[tex]\longrightarrow{\green{A.\:2 \: ( x + 3)(x + 3) }}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]
[tex]2 {x}^{2} + 12x + 18[/tex]
Taking 2 as common factor, we have
[tex] = 2 \: ( {x}^{2} + 6x + 9) \\ = 2 \: ( {x}^{2} + 3x + 3x + 9)[/tex]
Next, we take [tex]x[/tex] as common from first two terms and 3 from last two terms,
[tex] = 2 \: [x(x + 3) + 3(x + 3)][/tex]
Taking the factor [tex](x+3)[/tex] as common,
[tex] = 2 \: ( x + 3)(x + 3)[/tex]
[tex]\red{\large\qquad \qquad \underline{ \pmb{{ \mathbb{ \maltese \: \: Mystique35}}}}}[/tex]
20 POINTS
The function f(x)=45x represents the number of jumping jacks j(x) you can do in x minutes. How many jumpibg jacks can you do in 10 minutes
Answer:
450 jumping jacks
Step-by-step explanation:
f(10) = 45 (10)
45 * 10 is just 450 :)
Answer:
450.
Step-by-step explanation:
f(10) = 45 * 10 = 450 jumping jacks.
Given that a*b = 2a - 3b, then 2*(-3) =
Answer:
2*(-3)= -6
Step-by-step explanation:
I do not see how "a*b=2a-3b" would change the fact 2 times negative 3 is -6
is the ordered pair a solution of the equation?
y= 3x + 4; (4, 16)
Answer: Yes.
Step-by-step explanation: Plug in your values. Does y=16 when x=4? 16 = 3(4) +4, which equals 16, so yes.
HELP ASAP NEED HELP. WILL GIVE BRAINIEST AND 100 POINTS.
Algebra 1
Use the function f(x) = 4x^2 - 7x - 15 to answer the questions.
Part a: completely factor f(x).
Part b: what are the x-intercepts of the graph of f(x)? Show your work.
Part C: describe the end behavior of the graph of f(x). Explain.
Part D: what are the steps you would use to graph f(x)? Justify that you can use the answers obtained in part B and part C to draw the graph.
Answer:
A: [tex]f(x)=(4x+5)(x-3)[/tex]
B: [tex](-\frac{5}{4} , 0)[/tex] and [tex](3, 0)[/tex]
C: They are parallel, which means they have no endpoint.
The actual amount in a 12-ounce container of a certain brand of orange juice is normally distributed with mean μ = 12.34 ounces and standard deviation σ = 0.04 ounce. What percentage of the juice bottles contain between 12.24 and 12.30 ounces of orange juice?
Answer:
15.25%
Step-by-step explanation:
The actual amount in a 12-ounce container of a certain brand of orange juice is normally distributed with mean μ = 12.34 ounces and standard deviation σ = 0.04 ounce. What percentage of the juice bottles contain between 12.24 and 12.30 ounces of orange juice?
We solve using the z score formula
z-score is is z = (x-μ)/σ,
where x is the raw score
μ is the population mean = μ = 12.34 ounces
σ is the population standard deviation = σ = 0.04 ounce
For x = 12.24
z = 12.24 - 12.34/0.04
z = -2.5
Probability value from Z-Table:
P(x = 12.24) = 0.0062097
For x = 12.30
z= 12.30 - 12.34/0.04
z = -1
Probability value from Z-Table:
P(x = 12.30) = 0.15866
Hence, the probability of the juice bottles contain between 12.24 and 12.30 ounces of orange juice
P(x = 12.30) - P(x = 12.24)
= 0.15866 - 0.0062097
= 0.1524503
Therefore, the percentage of the juice bottles contain between 12.24 and 12.30 ounces of orange juice is calculated as:
= 0.1524503 × 100
= 15.24503%
= 15.25%
A rectangle has length 127.3 cm and width 86.5 cm, both correct to 1 decimal place. Calculate the upperbound and the lowerbound for the perimeter of the rectangle. pls answer fast. i need all the workings.
Answer:
Correct to 1dp
127.3 cm = 127.0 cm
86.5 cm = 87.0 cm
Upper limits:
127.0 cm = 127.05 cm
87.0 cm = 87.05 cm
Lower Limits:
127.0 cm = 126.95 cm
87.0 cm = 86.95 cm
upper limit of perimeter of rectangle:
P = 2(l+w)
= 2(127.05 + 87.05)
= 2(214.1)
= 428.2 cm
lower limit of perimeter of rectangle:
P = 2(l+w)
= 2(126.95 + 86.95)
= 2(213.9)
= 427.8 cm
therefore;
[tex]427.8 cm \leqslant perimeter < 428.2cm[/tex]
The upperbound and the lowerbound for the perimeter of the rectangle are;
Upper bound perimeter = 428.2 cm
Lower bound perimeter = 427.8 cm
To get the upper bound and Lower limits for the length and width, we need to first approximate them to 1 decimal place to get;
Length; 127.3 cm ≈ 127 cm
Width; 86.5 cm ≈ 87 cm
Thus;
Upper limit of length = 127.05 cm
Lower limit of length = 126.95 cm
Upper limit of width = 87.05 cm
Lower limit of width = 86.95 cm
Formula for perimeter of rectangle is;
P = 2(length × width)
Thus;
Upper bound perimeter = 2(127.05 + 87.05)
Upper bound perimeter = 428.2 cm
Lower bound perimeter = 2(126.95 + 86.95)
Lower bound perimeter = 427.8 cm
Read more on perimeter of rectangle at; https://brainly.com/question/17297081
Simplify √49 + [√81 - x(9x = 14)]
[tex]\longrightarrow{\green{- 9 {x}^{2} + 14x + 16}}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]
[tex] \sqrt{49} + [ \sqrt{81} - x \: (9x - 14) ] \\ \\ = \sqrt{7 \times 7} + [ \sqrt{9 \times 9} - 9 {x}^{2} + 14x] \\ \\ = \sqrt{( {7})^{2} } + [ \sqrt{ ({9})^{2} } - 9 {x}^{2} + 14x ] \\ \\ (∵ \sqrt{ ({x})^{2} } = x ) \\ \\ = 7 + (9 - 9 {x}^{2} + 14x) \\ \\ = 7 + 9 - 9 {x}^{2} + 14x \\ \\ = - 9 {x}^{2} + 14x + 16[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{♡}}}}}[/tex]
If two lines are intersected by a third line, is the third line necessarily a transversal?
No, The third line does not necessarily be a transversal.
What is Equation of line?
The equation of line with slope 'm' and y intercept at point 'b' is given as;
⇒ y = mx + b
Given that;
Two lines intersected by a third line.
Since, When two lines are parallel to each other and two lines intersected by a third line then, third lines are transversal.
So, Here it is not given two lines are parallel.
Thus, Third line is not necessarily a transversal.
Hence, The third line does not necessarily be a transversal.
Learn more about the transversal visit:
https://brainly.com/question/2141319
#SPJ2
Please HELP WITH THIS !!!
Sam built a ramp to a loading dock. The ramp has a vertical support 2 m from the base of the loading dock and 3m from the base of the ramp. If the vertical support is 1.2 m in height, what is the height of the loading dock?
Answer:
tan angle = x/5.
Step-by-step explanation:
If I understand your description,
tan angle at bottom of ramp = 1.2/3.
Then tan angle = x/5.
Check my thinking.
URGENT HELP NEEDED!!!!!
Find the simple interest earned at the end of 1 year. Show your calculations as best as possible (1 mark) correct answer (1mark) P = $1800 R = 5% T = 1 year
What is the total amount earned at the end of 3 years? P = $2600 R = 12% T = 3 years
1 point
$936
$3 536
$93 600
Both A and B
What principal would give an interest of $36 in 3 years at 3% p.a.? Show your calculations as best as possible (1 mark) correct answer (1mark)
In how many years will $600 double itself at 10% simple interest?
1 point
8 years and 4 months
8 years and 1/3
100 Months
All of the above
Both A and B
In what time will $400 amount to $512 if the simple interest is the calculated at 14% p.a.? Write your answer
Imagine you have a friend who doesn't quite understand what investing money into a bank means. Think of a financial situation and use the following words and numbers to help teach them. (principal $1200, interest earned, interest rate 4%, total amount, term, per anum). This is worth 8 marks.
Answer:
k
Step-by-step explanation:
Which equation can be used to solve a - 5 = 30?A. a = 30 - 5 B. a = 30 + 5 C a = 30 + 5 = 5 D a = 30.5
Which equation can be used to solve a - 5 = 30
answer= a=30+5
HOPE THIS HELPS YOU......
I need help with this quickly, I only have a couple hours left before homework is gone.
last day of school is tomorrow....
please answer quickly..
It only has one x intercept
Step-by-step explanation: when you graph it there is only one point where the line meets the x intercept
Find the y-intercept of the line which passes through (-2,-2) and (2,-4). O A. (0, -3) O B. (-3,0) O C. (0, -6) O D. (-6,0) O E. (0,-5)
9514 1404 393
Answer:
A. (0, -3)
Step-by-step explanation:
Graphing the given points shows you the y-intercept is between them. The x-coordinate of the y-intercept is always 0, so the only viable answer choice is ...
(0, -3)
A rocket is launched from a tower. The height of the rocket, y in feet, is related to the time after launch, x in seconds, by the given equation. Using this equation, find the time that the rocket will hit the ground, to the nearest 100th of second.
y=-16x^2+232x+134
Answer:
Step-by-step explanation:
when it touch the ground,y=0
-16x²+232x+134=0
-16(x²-29/2 x+(-29/4)²-(-29/4)²)=-134
-16(x-29/4)²-16(-861/16)=-134
-16(x-29/4)²+861=-134
-16(x-29/4)²=-134-861
(x-29/4)²=-995/-16=995/16
x-29/4=±√995/4
rejecting negative sign
x=29/4+√995/4=(29+√995)/4≈15.14 second
Derek can carry 65% of his weight in
his backpack while camping. If his
backpack weighs 88.4 pounds, how
much does Derek weigh?
a regular polygon has a perimeter of 40 cm and a apothem of 6 cm. find the polygons area
Answer:
a = 120 cm²
Step-by-step explanation:
n = number of sides
edge length
40/n
divide the polygon into n congruent triangles
a = (1/2)(edge * apothem) * number of triangles
a = (1/2)(40/n)(6) * n
n cancels out
a = (1/2)(40)(6)
a = 120 cm²
how does the graph of g(x)=3(2)^x -5 compare to the graph of g(x)=2^x
Answer:
Step-by-step explanation:
The graph of g(x)=3(2)^x -5 is vertically stretched as compared with that of h(x) = 2^x. Also, the graph of g(x)=3(2)^x -5 has been translated downward by 5 units.
To obtain the graph of g(x)=3(2)^x -5, we start by graphing g(x)= 2^x, whose y-intercept is (0, 1). We then stretch this new graph vertically by a factor of 3; the y-intercept becomes (0, 3). Finally, we translate the entire new graph downward 5 units.
When should a heart rate monitor be used?
Answer:
There are two simple, compelling reasons to use a heart-rate monitor: to train and race at the best pace for you. The table below shows you how to find your perfect paces for: (1) the three most important workouts in any training program; and (2) the four most popular road-race distances.
Step-by-step explanation:
Hope this helps :)
ILL BRAINLIEST YOU IF YOU HELP ME PLEASE
Answer:
B
Step-by-step explanation:
They are alternate interior angles so that means they are equal
4x - 30 = 2x
2x = 30
x = 15
Which statements about the factors of the terms in the expression 12 x + 18 x y minus 24 y are true? Select three options.
The factors common to 12x and 18xy are 1, 2, 3, 6, x, and y.
The factors common to 12x and 18xy are 1, 2, 3, 6, and x.
The factors common to 12x and 24y are 1, 2, 3, 4, 6, and 12.
The GCF of the expression is 6xy.
The GCF of the expression is 6.
Answer:
i think the answer is Options B, C and E holds.
Step-by-step explanation:
this makes options B and C a choice:
Given the expression: 12x+18xy-24y
Factors of 12x=1,2,3,4,6,12 and x
Factors of 18xy=1,2,3,6,9,18,x and y.
Factors of 24y=1,2,3,4,6,8,12,24 and y.
next for E this is why its a choice:
12x+18xy-24y=6(2x+3xy-4y)
Answer:
bce
Step-by-step explanation:
I need help please and thank you!!
Answer:
Option 4
Step-by-step explanation:
2x² + 32 = 0
2x² = -32
x² = -16
sqrt(-16) got no real solution. (no real number multiplied by itself will be negative)
Solve the quadratic equation by using a graphic approach. Round your answer to the hundredths place.
x² - 2x - 4= 0
a. x= 3.24 or x = -1.24
c. x = 4.24 or x = -0.24
b. x = 2.73 or x = -0.73
d. x= 5.24or x = -1.24
Pls explain I’m having a hard time understanding the lesson
Answer:
x = 3.24, x = -1.24
Step-by-step explanation:
The standard form for a quadratic equation is [tex]ax^2+bx+c=0[/tex]. For your equation a = 1, b = -2, c = -4. The quadratic formula you will be using is [tex]x=\frac{-b\pm \sqrt{b^{2} -4ac} }{2a}[/tex].
Plug in a = 1, b = -2, and c = -4 into the formula.
[tex]=\frac{-\left(-2\right)\pm \sqrt{\left(-2\right)^2-4\cdot \:1\cdot \left(-4\right)}}{2\cdot \:1}[/tex]
We'll do the top part first:
[tex]\sqrt{\left(-2\right)^2-4\cdot \:1\cdot \left(-4\right)}[/tex]
Apply rule [tex]- (-a) = a[/tex]
[tex]=\sqrt{\left(-2\right)^2+4\cdot \:1\cdot \:4}[/tex]
Apply exponent rule [tex](-a)^{n} =a^n[/tex] if [tex]n[/tex] is even
[tex](-2)^2=2^2[/tex]
[tex]=\sqrt{2^2+4\cdot \:1\cdot \:4}[/tex]
Multiply the numbers
[tex]=\sqrt{2^2+16}[/tex]
[tex]2^2=4[/tex]
[tex]=\sqrt{4+16}[/tex]
Add
[tex]=\sqrt{20}[/tex]
The prime factorization of 20 is [tex]2^2*5[/tex]
20 divides by 2. 20 = 10 * 2
[tex]=2*10[/tex]
10 divides by 2. 10 = 5 * 2
[tex]=2* \:2*5[/tex]
2 & 5 are prime numbers so you don't need to factor them anymore
[tex]=2*2*5[/tex]
[tex]=2^2*5[/tex]
[tex]=\sqrt{2^2\cdot \:5}[/tex]
Apply radical rule [tex]\sqrt[n]{ab} =\sqrt[n]{a} \sqrt[n]{b}[/tex]
[tex]=\sqrt{5}\sqrt{2^2}[/tex]
Apply radical rule [tex]\sqrt[n]{a^{n} } =a[/tex]; [tex]\sqrt{2^2} =2[/tex]
[tex]=2\sqrt{5}[/tex]
[tex]=\frac{-\left(-2\right)\pm \:2\sqrt{5}}{2\cdot \:1}[/tex]
Because of the [tex]\pm[/tex] you have to separate the solutions so that one is positive and the other is negative.
[tex]x=\frac{-\left(-2\right)+2\sqrt{5}}{2\cdot \:1},\:x=\frac{-\left(-2\right)-2\sqrt{5}}{2\cdot \:1}[/tex]
Positive x:
[tex]\frac{-\left(-2\right)+2\sqrt{5}}{2\cdot \:1}[/tex]
Apply rule [tex]-(-a)=a[/tex]
[tex]=\frac{2+2\sqrt{5}}{2\cdot \:1}[/tex]
Multiply
[tex]=\frac{2+2\sqrt{5}}{2}[/tex]
Factor [tex]2+2\sqrt{5}[/tex] and rewrite it as [tex]=2\cdot \:1+2\sqrt{5}[/tex]. Factor out 2 because it is the common term. [tex]=2\left(1+\sqrt{5}\right)[/tex].
[tex]=\frac{2\left(1+\sqrt{5}\right)}{2}[/tex]
Divide 2 by 2
[tex]x=1+\sqrt{5}[/tex] or [tex]x=3.24[/tex] (You'll probably have to use a calculator for the square root of 5)
^Repeating the process of positive x for negative x in order to get [tex]x=1-\sqrt{5}[/tex] or [tex]x=-1.24[/tex]
How do you perform constructions related to circles? What theorems and explanations can be used to justify these constructions? How do you perform constructions related to circles? What theorems and explanations can be used to justify these constructions?
Answer and explanation:
To construct a circle, draw a line that represents the diameter of the circle. Bisect the line so that it is a perpendicular bisector of the diameter of the circle. Place your compass at the bisection point/midpoint and draw an arc or better still the whole circle.
Theorem: the perpendicular bisector of a chord passes through the center of a circle.
Note: a diameter of a circle is a chord that passes through the center of a circle.
