Answer:
Parthava had 100 arrows.
Step-by-step explanation:
Let's define N as the number of arrows that Parthava originally has.
He uses one-half of them in defending himself, so he used N/2 arrows
Now he uses four times the square root of the number of arrows, so now he uses:
4*√N
Then he uses 6
Then he uses 3
Then he uses the last one.
If we add all these numbers of arrows that he used, we should get the initial number of arrows that he used, then:
N/2 + 4*√N + 6 + 3 + 1 = N
Now we have an equation that we can try to solve.
First, let's move all the terms to the same side:
N/2 + 4*√N + 6 + 3 + 1 - N = 0
now we can simpify it:
(N/2 - N) + 4*√N + (6 + 3 + 1) = 0
-(1/2)*N + 4*√N + 10 = 0
Now we can define a new variable x = √N
Then we have: x^2 = N
now we can replace these new variables in our equation to get:
-(1/2)*x^2 + 4*x + 10 = 0
Now we just have a quadratic equation.
Remember that for a quadratic equation of the form:
0 = a*x^2 + b*x + c
The solutions were given by:
[tex]x = \frac{-b \pm \sqrt{b^2 - 4*a*c} }{2a}[/tex]
Then in our case, the solutions will be:
[tex]x = \frac{-4 \pm \sqrt{4^2 - 4*(-1/2)*10} }{2*(-1/2)} = \frac{-4 \pm 6 }{-1} = 4 \pm 6[/tex]
So there are two solutions:
x = 4 + 6 = 10
x = 4 - 6 = -2
And remember that x = √N
Then x should be positive, then we take x = 10 as our solution here.
then we can use the equation:
x = 10 = √N
then
10^2 = √N^2 = N
10^2 = 100 = N
Parthava had 100 arrows.
What does x equal in the following equation 3x + 5 = 17 A x = 2 B x = 4 C x = 5
Answer:
see below
Step-by-step explanation:
3x + 5 = 17
Subtract 5 from each side
3x+5-5 = 17-5
3x = 12
Divide each side by 3
3x/3 =12/3
x =4
Answer:
B (x=4)
Step-by-step explanation:
plug it in...
3(4)+5=17
Analyzing the
Predict which statements are true about the intervals of
the continuous function. Check all that apply.
х
f(x)
01
-3
-15
-2
0
f(x) > 0 over the interval (- 3).
f(x) < 0 over the interval [0, 2].
f(x) < 0 over the interval (-1, 1).
f(x) > 0 over the interval (-2, 0).
f(x) > 0 over the interval [2, o).
-1
3
0
0
1
-3
2
0
3
15
Answer:
1 NO
2 YES
3 NO
4 YES
5 ÝE
Step-by-step explanation:
The true statements about the continuous function are:
f(x) ≤ 0 over the interval [0, 2].
f(x) > 0 over the interval (–2, 0).
f(x) ≥ 0 over the interval [2, )
What are the correct intervals of the continuous function?Functions in Math's are used to show relationships between variables.
Next, let us test the given options;
(A) f(x) > 0 over the interval (-∞, 3).
Using the table of f(x), the values in (-∞, 3) are values less than 3; i.e. -3 to 2.
If f(2) = 0, then f(x) > 0 is not true
(B) f(x) ≤ 0 over the interval [0, 2].
The values in [0, 2] are values from 0 to 2; i.e. 0, 1 and 2.
If f(0) = 0, f(1) = -3 and f(2) = 0
Then, f(x) ≤ 0
(c) f(x) < 0 over the interval (−1, 1).
Using the table of f(x), the values in (-1, 1) are values between -1 and 1; i.e. 0
If f(0) = 0, then f(x) < 0 is not true
(d) f(x) > 0 over the interval (–2, 0).
Using the table of f(x), the values in (-2, 0) are values between -2 and 0; i.e. -1
If f(-1) = 3, then f(x) > 0 is true
(e) f(x) ≥ 0 over the interval [2, ∞)
Using the table of f(x), the values in [2, ) are values from 2; i.e. 2 and 3
If f(2) = 0 and f(3) = 15, then f(x) ≥ 0 is true
Finally, the true statements are:
f(x) ≤ 0 over the interval [0, 2].
f(x) > 0 over the interval (–2, 0).
f(x) ≥ 0 over the interval [2, ∞]
Read more about intervals of continuous functions at; https://brainly.com/question/11803482
Select the correct answer.
Which inequality represents all the solutions of 10(3x + 2) > 7(2x − 4)?
A.
x > -4
B.
x < -4
C.
x > -3
D.
x < -3
Answer:
C
Step-by-step explanation:
Given
10(3x + 2) > 7(2x - 4) ← distribute parenthesis on both sides
30x + 20 > 14x - 28 ( subtract 14x from both sides )
16x + 20 > - 28 ( subtract 20 from both sides )
16x > - 48 ( divide both sides by 16 )
x > - 3 → C
5/9+8/9 can someone please help me with this math question? All I know is that you have to add the fractions, Express the sum as a proper fraction or a mixed number.
Answer:
13/9
Step-by-step explanation:
Given
5/9 + 8/9
Both fractions have the same denominator.
Therefore, pick one of the denominator and add the numerators
5/9 + 8/9
= (5+8) / 9
= 13/9
5/9 + 8/9 = 13/9
Will Mark Brainlest Helppp please
Answer:
6
Step-by-step explanation:
how often is that question posted here ?
this means that we need to find the value of x, so that the functional (result) value is 7.
7 = (3x - 4)/2
14 = 3x - 4
18 = 3x
x = 6
21,5=13
7,9=8
36,2=19
1,7=?
find the value of ?
Answer:
4
Step-by-step explanation:
(21 + 5) : 2 = 13
(7 + 9) : 2 = 8
(36 + 2) : 2 = 19
(1 + 7) : 2 = 4
Nêu mệnh đề phủ định của mệnh đề sau và xét tính đúng sai của mệnh đề phủ định: ∀x∈R:x^{2} ≠ 1
Answer:
true
Step-by-step explanation:
[tex]existential \: element \: of \: real \: number \: \binom{o}{o} x {}^{2} = 1[/tex]
HELPPP!!
Rate the following bank accounts from most to least liquid: CD, savings account, checking account, money market
account
a. CD, savings account, checking account, money market account
b. Savings account, checking account, CD, money market account
C. CD, money market account, savings account, checking account
d. Checking account, savings account, money market account, CD
Please select the best answer from the choices provided
OA
OB
О С
OD
Answer:
C
Step-by-step explanation:
There isn’t one
whats the figures and how do I find the area?
Answer:
This is trapezium.
Area of this figure =1/2h(d1-d2)
1/2×5(14-8)
=30/2
=15cm^2
<3 and <6 can be classified as:
a. alternate exterior angles
b. same side interior angles
c. corresponding angles
d. alternate interior angles
Answer: d. alternate interior angles
Note how the two angles are inside, or interior, of the lines L1 and L2. For me, I tend to think of such lines like train tracks. So that takes care of the "interior" portion.
As for the "alternate" portion, we can see that the angles are on either side of the transversal line T.
So that's why angles 3 and 6 are alternate interior angles.
If L1 and L2 are parallel, then angle 3 = angle 6.
Find the equation of the line that is perpendicular to y=1/6x+3
and contains the point (-3,23).
y = [?]x + [?]
Answer:
y = -6x + 6
Step-by-step explanation:
The general equation of a line is
y = mx + b
where m is the slope and b is the y-intercept
The slope in the first equation is 1/6
Mathematically, when two lines are perpendicular, the product of their slopes is -1
1/6 * m2 = -1
m2 = -6
So we have the equation as;
y-y1 = m(x-x1)
y-23 = -6(x + 3)
y = -6x -18 +23
y = -6x + 6
for what value of x does 4^x=(1/8)^x+5?
Use main properties of powers
(a^m)^n=a^{m\cdot n};(am)n=am⋅n;
\dfrac{1}{a^n}=a^{-n}an1=a−n
to simplify given equation.
1.
4^x=(2^2)^x=2^{2x}.4x=(22)x=22x.
2.
\left(\dfrac{1}{8}\right)^{x+5}=\left(\dfrac{1}{2^3}\right)^{x+5}=(2^{-3})^{x+5}=2^{-3x-15}.(81)x+5=(231)x+5=(2−3)x+5=2−3x−15.
3. Then the equation is
2^{2x}=2^{-3x-15}.22x=2−3x−15.
The bases are the same, so equate the powers:
2x=-3x-15,
2x+3x=-15,
5x=-15,
x=-3.
Answer: for x=-3.
Which of the following represents the set of possible rational routes for the polynomial shown below
2x^3+5x^2-8x-10=0
Answer:
The given polynomial is,
2x³+5x²-8x-10=0
all possible roots of a polynomial,
ax³+b²+c x +d=0 ← all possible factors of ration (d/a)
Therefore, eq (1), all possible factors are the factors of ratio (-10/2)
which are, B) { ± 1, 1/2, ± 2, ± 5/2, ±5, ± 10}
OAmalOHopeO
write the equation in standard form. y=4/7x+3
Answer:
4x-7y = -21
Step-by-step explanation:
1. Move 4/7x to the other side
-4/7x+y=-3
2. Multiply both sides by -7
4x-7y=-21
3x-7y=28 is it in standard form
What is the length of leg s of the triangle below?
90°
45
6
172
45
O
A. 72
B. 5
C. 3
O O O O a
D. 6
E. 3.2
F. 36
Answer:
6
Step-by-step explanation:
It's a 45-45-90 triangle, it has two similar sides, since it has two similar angles, which are both 45°
so, side = s = 6
Answered by GAUTHMATH
The length of the leg s of the triangle below is 6.
Option D is the correct answer.
What is the Pythagorean theorem?Pythagorean theorem states that for a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
We can apply this theorem only in a right triangle.
Example:
The hypotenuse side of a triangle with the two sides as 4 cm and 3 cm.
Hypotenuse side = √(4² + 3²) = √(16 + 9) = √25 = 5 cm
We have,
Applying the Pythagorean theorem in the triangle.
√72² = s² + 6²
72 = s² + 36
s² = 72 - 36
s² = 36
s = √36
s = 6
We can also say that,
Opposite angles of equal sides are equal
So,
s = 6.
Thus,
The length of the leg s of the triangle below is 6.
Learn more about the Pythagorean theorem here:
https://brainly.com/question/14930619
#SPJ7
| 3 x - 2 | = 4x + 4
Answer: -2/7
|3x - 2| - 4x = 4
1) (3х - 2) - 4х = 4, if 3x - 2 >= 0
2) -(3x - 2) - 4x = 4, if 3x - 2 < 0
1)
3х - 4х = 4 + 2
-x = 6
x = -6
3х - 2 >= 0
3х >= 2
x >= 2/3 - wrong
2)
-3х + 2 - 4х = 4
-7х = 2
x = -2/7
3x-2<0
3x<2
3(-2/7)<2-right
Can someone please help me with these work rate questions!
Answer:
1/8 rooms per hour
Step-by-step explanation:
We are given that Beatrice can wallpaper 1 room in 8 hours. The work rate is how many rooms Beatrice can wallpaper in one unit of time (in this case, one hour).
Another way of saying 1 room in 8 hours is 1 room/8 hours. We want to find the rate over one hour, so we want to make the denominator ( in hours) equal to 0.
With fractions, we can divide/multiply both the numerator and denominator by the same amount, and still keep the fraction. Therefore, we want to make 8 hours 1 hour by multiplication or division. Since anything divided by itself is equal to 1, we can say that 8/8 is equal to 1. Therefore, we can divide both the numerator and denominator by 8 to get
(1 room/8) = (8 hours / 8)
= (1/8 rooms) / 1 hour
Therefore, the work rate is 1/8 rooms per hour
One-third of a number when subtracted from double of itself is equal to 10. Find the number.
2x−x3=10
X=?
Answer:
number is 6
Step-by-step explanation:
let the number be x , then double the number is 2x and
2x - [tex]\frac{1}{3}[/tex] x = 10 ( multiply through by 3 to clear the fraction )
6x - x = 30
5x = 30 ( divide both sides by 5 )
x = 6
That is the number is 6
10 boys cleared a piece of land for 21 days how many days will it take 7 boys to clear the same land if they work at the same rate
Answer:
it took 7 boys 21 days to clear a piece of land.
The graph is
function because it is symmetrical about the
Answer:
Functions can be symmetrical about the y-axis, which means that if we reflect their graph about the y-axis we will get the same graph. ... These are two types of symmetry we call even and odd functions.
Step-by-step explanation:
John and Pablo caught fish that have the lengths, in centimeters, listed below. 45, 44, 47, 49, 45, 47, 42, 39, 45, 42, 44 Which box-and-whisker plot correctly represents the data?
The options for the box and whisker plots aren't given ; however using technology, a box and whisker plot could be generated from the data.
Answer:
Step-by-step explanation:
Given :
45, 44, 47, 49, 45, 47, 42, 39, 45, 42, 44
Using technology, the box and whisker plot generated for the data is attached below.
The 5 - number summary is also given below :
Minimum: 39
Median: 45
First quartile: 42
Third quartile: 47
Interquartile Range: 5
Maximum: 49
Outliers: none
Answer:
Step-by-step explanation:
juan analyzes the amount of radioactive material remaining in a medical waste container over time. He writes the function f(x)=10(0.98)x to represent the amount of radioactive material that will remain after x hours in the container.
Rounded to the nearest tenth, how much radioactive material will remain after 10 hours?
0.8 units
1.3 units
8.2 units
9.8 units
Answer:
8.2 units
Step-by-step explanation:
For radioactive decay, the amount should decrease over time. Given the function:
f(x) = 10(0.98[tex])^{x}[/tex]
We substitute the time of x = 10 hours:
f(10) = 10(0.98[tex])^{10}[/tex]
f(10) = 8.17
Round 8.17 to 8.2.
Therefore 8.2 units will remain after 10 hours.
Use the diagram. Solve for p.
Answer:
A the first one.
Step-by-step explanation:
Wy = 28
WX = 12
XY = WY - WZ
XY = 28 - 12
XY = 16
4P = 16
P = 16/4
P = 4
In the PQRS triangle PQ=QR, QR side extended to S Show that PQ+RS=QS. -S Q R
pls explain too
Answer:
Step-by-step explanation:
from the picture:
QP = QR
and
QR = RS
so
PQ + RS = QS
Someone please help me find y if you don’t mind Thankyouu so much
Answer:
Step-by-step explanation:
Decreasing rate = 12% = 0.12
y = 2400 * (1- 0.12)^x = 2400*(0.88)^x
x = 8 years
[tex]y = 2400 *(0.88)^{8}\\\\= 2400*0.36\\\\= 863[/tex]
A publishing company expects to sell 5000 copies of a new book from its web site, if the company charges $30 per book. The company expects that 500 more books would be sold for each price reduction of $2. What price would maximize the company's revenue?
Solution :
Let the revenue be = R
Therefore, R = price x quantity
R = (30 - 2x) ( 5000 + 500x)
= [tex]150000 + 5000x - 1000x^2[/tex]
For the maximum revenue,
[tex]$\frac{dR}{dx} = 0$[/tex]
[tex]$-2000x+5000=0$[/tex]
[tex]$x=2.5$[/tex]
[tex]$\frac{d^2R}{dx^2}=-2000<0$[/tex]
At [tex]x=2.5[/tex], the revenue is maximum.
So the price for the maximum company revenue = [tex]$30-2x$[/tex]
[tex]$=30-2(2.5)$[/tex]
= 30 - 5
= 25
Therefore, the price that will maximize the company's revenue is $25.
A walking trail is 1,580.76 feet long. A lake is located 70.62 feet away from the end of the trail. What is the total distance from the start of the trail to the lake? 1,510.14 feet 1,651.38 feet 2,286.96 feet 8,642.76 feet
Answer:[tex]1651.38\ ft[/tex]
Step-by-step explanation:
Given
A walking trail is [tex]1580.76\ ft[/tex] long and a lake is located [tex]70.62\ ft[/tex] away from end of the trail
The distance from the start of the trail to the lake is the sum of the length of the trail and lake
[tex]\Rightarrow 1580.76+70.62\\\Rightarrow 1651.38\ ft[/tex]
Answer:
B
Step-by-step explanation:
[tex]2 \sqrt{75} - \sqrt{108} + 5 \sqrt{48}[/tex]
[tex]\\ \sf\longmapsto 2 \sqrt{75} - \sqrt{108} + 5 \sqrt{48} \\\\ \sf\longmapsto 2 \sqrt{25 \times 3} - \sqrt{36 \times 3} + 5 \sqrt{16 \times 3} \\ \\ \sf\longmapsto 2 \times 5 \sqrt{3} - 6 \sqrt{3} + 5 \times 4 \sqrt{3} \\ \\ \sf\longmapsto 10 \sqrt{3} - 6 \sqrt{3} + 20 \sqrt{3} \\ \\ \sf\longmapsto (10 - 6 + 20) \sqrt{3} \\ \\ \sf\longmapsto 24 \sqrt{3} [/tex]
Answer:
24aprtment3
Step-by-step explanation:
State the domain and range of the graph below:
Answer:
domain [-1, ∞)
range [ -3, ∞)
Step-by-step explanation:
Classify the polynomial and determine its degree.
The polynomial –2x2 – x + 2 is a
with a degree of
.
Answer:
Trinomial, 2
Step-by-step explanation:
Answer:
Trinomial, 2
Step-by-step explanation:
