We must mix 240 liters of the 51 % solution and 10 liters of the 26 % solutions to produce 250 liters of 50 % solution.
How to prepare a solution by using weighted averages
Herein we have to prepare a solution with fertilizers by mixing two different solutions. The amount needed of the 51 % solution can be found by weighted averages:
(50/100) · (250 L) = (51/100) · x + (26/100) · (250 - x)
50 · 250 = 51 · x + 26 · 250 - 26 · x
24 · 250 = 25 · x
x = 240
We must mix 240 liters of the 51 % solution and 10 liters of the 26 % solutions to produce 250 liters of 50 % solution.
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Rectangle ABCD is graphed in the coordinate plane. The following are the vertices of the rectangle:
A(5,5)
B(7,5)
C(7,-1)
D(5,−1)
Given these coordinates, what is the length of side of BC Rectangle?
Answer:
6 units
Step-by-step explanation:
5--1=6
Annoying me I’ve been at this for hours
Is the graph increasing, decreasing, or constant?
A. Constant
B. Increasing
C. Decreasing
Answer:
C. Decreasing
Step-by-step explanation:
The graph is decreasing because the graphed line read from left to right is slanting down.
Hope this helps!
If not, I am sorry.
Answer:
DecreasingStep-by-step explanation:
Hello
If a graph is constant, it doesn't have any change at all.
If a graph is increasing, it looks like this-:
[tex]\Huge\nearrow[/tex]
If a graph is decreasing, it looks like this-:
[tex]\searrow[/tex]
Since the given graph is most similar to [tex]\searrow[/tex], it's decreasing.
[tex]\pmb{\tt{done~!!}}[/tex]
[tex]\orange\hspace{300pt}\above2[/tex]
Determine whether the geometric series 27 + 18 + 12 + 8 + ... converges or diverges, and identify the sum if it exists.
A geometric sequence goes from one term to the next by always multiplying or dividing by the constant value except 0. The constant number multiplied (or divided) at each stage of a geometric sequence is called the common ratio (r).
A geometric series is the sum of an infinite number of terms of a geometric sequence.
A geometric series is convergers if |r| < 1.
A geometric series is diveres if |r| > 1.
Calculate the common ratio:
[tex]r=\dfrac{18}{27}=\dfrac{18:9}{27:9}=\dfrac{2}{3}\\\\r=\dfrac{12}{18}=\dfrac{12:6}{18:6}=\dfrac{2}{3}\\\\r=\dfrac{8}{12}=\dfrac{8:24}{12:4}=\dfrac{2}{3}[/tex]
[tex]\left|\dfrac{2}{3}\right| < 1[/tex]
The geometric series is converges.Therefore exist the sum.
Formula of a sum of a geometric series:
[tex]S=\dfrac{a_1}{1-r},\qquad|r| < 1[/tex]
Substitute:
[tex]a_1=27,\ r=\dfrac{2}{3}[/tex]
[tex]S=\dfrac{27}{1-\frac{2}{3}}=\dfrac{27}{\frac{1}{3}}=27\cdot\dfrac{3}{1}=81[/tex]
[tex]\huge\boxed{S=81}[/tex]
Rectangle ABCD is graphed in the coordinate plane. The following are the vertices of the rectangle:
A(−7,−5)
B(−7,6)
C(−4,6)
D(−4,−5)
Given these coordinates, what is the length of side CD of this rectangle?
[tex]\huge\boxed{11\ \text{units}}[/tex]
To solve this, we need to find the distance between points C and D.
The distance formula is:
[tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Substitute the values from points [tex]C(x_1, y_1)[/tex] and [tex]D(x_2, y_2)[/tex].
[tex]\sqrt{(-4-(-4))^2+(-5-6)^2}[/tex]
Subtract.
[tex]\sqrt{0^2+(-11)^2}[/tex]
Evaluate the powers.
[tex]\sqrt{0+121}[/tex]
Solve for the final answer.
[tex]\sqrt{121}\\\boxed{11}[/tex]
How do i solve f(x)=log3(x-2)-2
To have solution for f(x)=log3(x-2)-2. x must be x >2 or x ( 2, ∞) .
f(x)=log3(x-2)-2
What are functions?Functions is the relationship between sets of values. e g y=f(x), for every value of x there is its exists in set of y. x is independent variable while Y is dependent variable.
Since,
f(x)=log3(x-2)-2
The above function will goes to infinity when we put x = 2.
So the given function has solution for x > 2.
Thus, the To have solution for f(x)=log3(x-2)-2. x must be x >2 or x ( 2, ∞) .
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100% of x and also 200% of y
Hello !
Answer :
100% of x ⇒ 100/100 × x = 1 × x = x
200% of y ⇒ 200/100 × y = 2 × y = 2y
what is the value of 3ypower zero
Answer:
3
[tex]3 {y}^{0} [/tex]
[tex] = 3 \times 1[/tex]
[tex] = 3[/tex]
If any numbers or constant power is zero then it will be 1
Answer:
3
Step-by-step explanation:
So anything to the power of zero is equal to 1. So you have the equation: [tex]3y^0=3(1)=3[/tex]
If this doesn't make much sense, I sometimes like to use identities to show why this is. So since you're most likely learning exponents, you likely know the identity: [tex]\frac{x^a}{x^b}=x^{a-b}[/tex] well you can use this identity to express the equation: [tex]\frac{x^a}{x^a}=x^{a-a}=x^0[/tex]. and since x^a should equal x^a, and it's being divided by it self, this is equal to 1.
Btw if you didn't understand the identity: [tex]\frac{x^a}{x^b}=x^{a-b}[/tex] I'll try to briefly explain it. The reason this is true, is because you can cancel stuff out if it's being multiplied in the denominator and numerator. For example: [tex]\frac{3a}{3}[/tex]. I can cancel out the 3, because if I multiply 3 by a, and then divide by 3, I'm going to be left with a, because they're inverse to each other. This should hold true for exponents. So you can think of the identity more like: [tex]\frac{x*x*x...\text{a amount of times}}{x*x*x\text{b amount of times}}[/tex] seeing it like this might help understand why you subtract, since you're just cancelling out the x's.
I'll give you a more definitive example to help you grasp it in an example so: [tex]\frac{2^4}{2^2}=\frac{2*2*2*2}{2*2}=\frac{2*2}{1}=2^2[/tex]. See how I canceled out 2 of the 2's, well all I was really doing was subtracting 2 from the degree of the numerator, or in other words I was subtracting the degree of the denominator from the numerator since the bases were the same which is exactly what the identity is doing.
Part 2 - Find the error(s) and solve the problem correctly.
The error is present in second step when cancelling numerator and denominator and the solution of the expression [tex](1+1/x)/(1-1/x^{2} )[/tex] is [tex]x/x-1[/tex].
Given Expression [tex](1+1/x)/(1-1/x^{2} )[/tex] and incorrect solution. and we need to identify the error and solve the expression correctly.
The expression is [tex](1+1/x)/(1-1/x^{2} )[/tex]
In the solution given the second step of cancelling 1's in numerator and denominator is wrong.
The solution which is correct is as under:
[tex](1+1/x)/(1-1/x^{2} )[/tex]
firstly take LCM in numerator and denominator
=[tex](x+1)/x/(x^{2} -1)/x^{2}[/tex]
Now we can write the expression properly.
=[tex](x+1)*x^{2} /(x^{2} -1)*x[/tex]
Power of [tex]x^{2}[/tex] to be deducted from x
=[tex](x+1)*x/(x^{2} -1)[/tex]
Now [tex]x^{2} -1[/tex] can be written as (x+1)(x-1)
=[tex](x+1)*x/(x+1)(x-1)[/tex]
(x+1) will be deducted now from numerator and denominator.
=x/(x-1)
Hence the solution of the given expression is x/(x-1).
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The answer to this question is x/x₋1
Given the expression is 1₊1/x /1₋1/x²
Take the LCM of the denominators
we get, x₊1/x / x²₋1/x²
Now multiply the expression
=x₊1/x × x²/x²₋1
=(x₊1) x²/ x(x²₋1)
(x²₋1) is in the form of (a²₋b²)=(a₊b)(a₋b)
Therefore, (x₊1)x²/x(x₋1)(x₊1)
After cancelling like terms we get the answer as:
x/(x₋1)
Hence we get the simplification answer as x/(x₋1).
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Total area =
Help please thanks
The total area of the given right trapezoidal prism is gotten as; A = 2592 sq.units
How to find the area of a right trapezoidal prism?The formula to find the Surface Area of a Trapezoidal Prism is;
A = h(b + d) +l(a + b + c + d) unit square.
Where;
h = height
b and d are the lengths of the base
a + b + c + d is the perimeter
l is length
Thus;
A = 12(25 + 15) + 32(13 + 25 + 13 + 15)
A = 480 + 2112
A = 2592 units square
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Price of an article is 400 and sold with discount including 13% vat at 339 find discount rate
If (x+ 1) is a factor of the polynomial x³ + px² + x + 6 = 0. Find p.
Answer:
p=4
Step-by-step explanation:
plug x=-1 into the polynomial with the unknown
(-1)³+p(-1)+(-1)+6=0
-1-p-1+6=0
-p+4=0
p=4
Which equation are true
A. 3^4)(3^5)=3^9
B.8^6=1\-6
C
use the quadratic formula to solve the equation : 10x2 +11x=1
Answer:The answers are 0.084 or -1.184
Step-by-step explanation:
The solution is in the attached file
Section 6.1 Add and Subtract Polynomials
Add and Subtract Monomials
In the following exercises, add or subtract the monomials.
594. 12q − (−6q)
Answer:
The simplified form of [tex]12 q-(-6 q) \text { is } 18 q[/tex].
Step-by-step explanation:
[tex]- Given: $12 q-(-6 q)$\\ - Simplify.\\ - The simplified form of $12 q-(-6 q)=(12+6) q$ i.e., $18 q$.[/tex]
Which represents the inverse of the function f(x) = 4x?
• h(x) = x + 4
O h(x) = x-4
O h(x) = =x
h(x) = Lx
Step-by-step explanation:
[tex]f(x) = 4x[/tex]
[tex] \: [/tex]
[tex]y = 4x[/tex]
[tex]4y = x[/tex]
[tex]y = \frac{x}{4} [/tex]
[tex] {f}^{ - 1} (x) = \frac{ x}{4} [/tex]
[tex]h(x) = \frac{x}{4} [/tex]
The answer is D.
What is the rate of change of the linear function represented by the table? StartFraction one Over three EndFraction StartFraction one Over two EndFraction 2 3
The rate of change of the linear function represented by the table is 3
Rate of change of a functionThe rate of change of a function is also known as the slope of a function. The equation for calculating the slope is expressed as:
Slope = y2-y1/x2-x1
using the coordinates from the table (-2, -13) and (-1, -10)
Substitute
Slope = -10-(-13)/-1-(-2)
Slope = -10+13/-1+2
Slope =3
Hence the rate of change of the linear function represented by the table is 3
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Find x A. 212√2 B. 212–√ C. 213√2 D. 7
The value of x in the triangle is (d) 7
How to solve for x?The complete question is in the attached image.
From the attached image of the triangle, we can see that the triangle is a right triangle, and x can be solved using the following sine function
[tex]\sin(45) = \frac{x}{7\sqrt 2}[/tex]
Evaluate sin(45)
[tex]\frac 1{\sqrt 2} = \frac{x}{7\sqrt 2}[/tex]
Solve for x
[tex]x = \frac{7\sqrt 2}{\sqrt 2}[/tex]
Divide
x = 7
Hence, the value of x in the triangle is (d) 7
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need rn!
If a point C is inside AVB, then mAVC + mCVB = ______.
Answer:
Hi sorry if the reply is late! The answer is
OPTION (B)m∠AVC+m∠CVB=m∠AVB
Step-by-step explanation:
Given: It is given that a point C is inside ∠AVB and ∠AVC=39° and ∠CVB=23°.
From the figure, we can see that C is inside ∠AVB, therefore ∠AVB is divided into two parts that is ∠AVC and ∠CVB, thus
m∠AVC+m∠CVB=c
⇒39°+23°=62°
Select the correct answer. two triangles, abc and cde, share a common vertex c on a grid. in triangle abc, side ab is labeled 4x minus 1, side bc is labeled 4, side ac is labeled 5. in triangle cde, side cd is labeled 5, side de is labeled x plus 2, side ce is labeled 4. if geometry symbol represented as small triangle with three sides. abc a geometry symbol represented as small triangle with three sides. dec, what is the value of x? a. x = 8 b. x = 5 c. x = 4 d. x = 1 e. x = 2
The value of x based on the information given in the triangle is D. x = 1.
How to compute the value?From the information given, it stated that the triangles are similar.
In this case, both triangles have side 4 and 5. Therefore, we are to find the last side. This will be:
4x - 1 = x + 2
Collect like terms
4x - x = 2 + 1
3x = 3
x = 3/3
x = 1
Therefore, the correct option is D.
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Answer:
x=1
Step-by-step explanation:
Drag each expression or value to the correct box. Not all tiles will be used.
Luke started a weight-loss program. The first week, he lost x pounds. The second week, he lost pounds less than times the pounds he lost the first week. The third week, he lost 1 pound more than of the pounds he lost the first week.
Liam started a weight-loss program when Luke did. The first week, he lost 1 pound less than times the pounds Luke lost the first week. The second week, he lost 4 pounds less than times the pounds Luke lost the first week. The third week, he lost pound more than times the pounds Luke lost the first week.
Assuming they both lost the same number of pounds over the three weeks, complete the following sentences. Luke started a weight-loss program. The first week, he lost x pounds. The second week, he lost 3/2 pounds less than 3/2 times the pounds he lost the first week. The third week, he lost 1 pound more than 3/4 of the pounds he lost the first week.
Liam started a weight-loss program when Luke did. The first week, he lost 1 pound less than 3/2 times the pounds Luke lost the first week. The second week, he lost 4 pounds less than 5/2 times the pounds Luke lost the first week. The third week, he lost 1/2 pound more than 5/4 times the pounds Luke lost the first week.
Assuming they both lost the same number of pounds over the three weeks, complete the following sentences.
Answer:Liam started a weight-loss program when Luke did. The first week, he lost 1 pound less than 3/2 times the pounds Luke lost the first week. The second week, he lost 4 pounds less than 5/2 times the pounds Luke lost the first week. The third week, he lost 1/2 pound more than 5/4 times the pounds Luke lost the first week.Assuming they both lost the same number of pounds over the three weeks, complete the following sentences.Step-by-step explanation:
See photo, it’s got to do with Pythagoras theorem but I don’t understand. Please help
Answer:
x = 12.0 cm
Step-by-step explanation:
If we draw a line parallel to the 12 cm line right below the line x, a right-angled triangle is formed, with x as the hypotenuse and the shortest side equal to (8 - 7 = ) 1 cm.
∴ x² = 12² + 1²
⇒ x = [tex]\sqrt{12^2 + 1^2}[/tex]
⇒ x = [tex]\sqrt{144 + 1}[/tex]
⇒ x = [tex]\sqrt{145}[/tex]
⇒ x = 12.0 cm [3 s.f.]
Answer:
12.0 cm
Step-by-step explanation:
See attached image for steps. Take the figure and convert it into a rectangle and right triangle by drawing a single line. The Pythagorean Theorem can then be used.
What is the inverse of f(x)= 1/3x + 2?
Answer:
y^-1 = 3x - 6
Step-by-step explanation:
f(x) = 1/3x + 2
The inverse function is where we swap out y for x and x for y. f(x) represents y, so we will be replacing it with x. Then, we solve and get a new equation for the inverse of y.
x = 1/3y + 2 (subtract 2 from both sides)
x - 2 = 1/3y (multiply by 3 on both sides)
y^-1 = 3x - 6
Brainliest, please :)
Answer:
f(x) = 3x- 2
Step-by-step explanation:
The easiest way to find the inverse of a function is to replace y with x and rearrange the equation.
x = 1/3y + 2
-2 -2
______________
x-2 * 3 = 1/3y * 3
y = 3x-2
The function (x) is a transformation of the square root parent function,
f(x)=√. What function is /(x)?
5
-5
f(x)
h(x)
O A. h(x)=√x-2
OB. h(x)=√√T-2
OC. h(r)=√x+2
O D. h(x)=√x+2
Hello,
check for x = 2, we can see h(x) = 0
h(x) = √(x - 2) ⇒ h(2) = √(2 - 2) = √0 = 0 ⇒ ok
h(x) = √x - 2 ⇒ h(2) = √2 - 2 ≠ 0 ⇒ not this answer
h(x) = √x + 2 ⇒ h(2) = √2 + 2 ≠ 0 ⇒ not this answer
h(x) = √(x + 2) ⇒ h(2) = √(2 + 2) = √4 ≠ 0 ⇒ not this answer
So the answer is h(x) = √(x - 2)
The owner of a farm plants apple trees and mango trees in a ratio of 16:6. How many oak trees are planted if 198 mango trees are planted?
Answer:528 apple trees
Step-by-step explanation:Listen 198/6=33 so then just multiply 33x16 that equals 528 hope this helps
HELP HELP HELP
Quick algebra 1 question for 15 points!
Explain the difference between slope-intercept form and point-slope form.
Answer:
slope intercept is used when you are given a point (most likely a y intercept) on the graph and a slope. The point slope is a larger formula that is used when you are given a slope and the coordinates of a point.
Step-by-step explanation:
slope intercept : y=mx+b
point slope : y-y1= m(x-x1)
Part B
Question
Use an online graphing tool to find the equation that best models the data in the table.
Enter the correct equation in standard form. Round parameters to the nearest tenth.
Answer:
y=17.2x²-226.3x+2184.5
Solve a) with Substitution and b) with Elimination (check attached picture)
a) Solve the first equation for [tex]x[/tex].
[tex]x + 3y = 7 \impiles x = 7 - 3y[/tex]
Substitute this into the second equation and solve for [tex]y[/tex].
[tex]2x + 4y = 12 \implies 2(7 - 3y) + 4y = 12 \\\\ \implies 14 - 6y + 4y = 12 \\\\ \implies -2y = -2 \\\\ \implies \boxed{y=1}[/tex]
Solve for [tex]x[/tex].
[tex]x = 7 - 3y \implies x = 7-3\times1 \\\\ \implies \boxed{x = 4}[/tex]
b) Eliminate [tex]y[/tex] by combining the two equations in appropriate parts, namely
[tex]2 (2x - y) + (3x + 2y) = 2\times3 + (-3)[/tex]
and solve for [tex]x[/tex].
[tex]2 (2x - y) + (3x + 2y) = 2\times3 + (-3) \implies 4x - 2y + 3x + 2y = 6 - 3 \\\\ \implies 7x = 3 \\\\ \implies \boxed{x = \dfrac37}[/tex]
Solve for [tex]y[/tex].
[tex]2x - y = 3 \implies 2\times\dfrac37 - y = 3 \\\\ \implies \dfrac67 - y = 3 \\\\ \implies -y = \dfrac{15}7 \\\\ \implies \boxed{y = -\dfrac{15}7}[/tex]
Let f(x)=1/x+x, where is a nonzero number.what is the product of all the values of a, such that f(a)=f(2a)?
The product of all the values of a, such that f(a)=f(2a) is -1/2
Functions and expressionsGiven the function below;
f(x)=1/x + x
f(a) = 1/a + a
f(2a) = 1/2a + 2a
If f(a) = f(2a), hence;
1/a + a = 1/2a + 2a
Collect the like terms
1/a - 1/2a = 2a - a
2-1/2a = a
1/2a = a
Cross multiply
2a² = 1
a² = 1/2
a = ±√1/2
The values of a are √1/2 and -√1/2
Product = -√1/2 * √1/2
Product = -1/2
Hence the product of all the values of a, such that f(a)=f(2a) is -1/2
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A production manager at a wall clock company wants to test their new wall clocks. The designer claims they have a mean life of 14 years with a variance of 25. If the claim is true, in a sample of 50 wall clocks, what is the probability that the mean clock life would differ from the population mean by greater than 1.5 years
The probability that the mean clock life would differ from the population mean by greater than 12.5 years is 98.30%.
Given mean of 14 years, variance of 25 and sample size is 50.
We have to calculate the probability that the mean clock life would differ from the population mean by greater than 1.5 years.
μ=14,
σ=[tex]\sqrt{25}[/tex]=5
n=50
s orσ =5/[tex]\sqrt{50}[/tex]=0.7071.
This is 1 subtracted by the p value of z when X=12.5.
So,
z=X-μ/σ
=12.5-14/0.7071
=-2.12
P value=0.0170
1-0.0170=0.9830
=98.30%
Hence the probability that the mean clock life would differ from the population mean by greater than 1.5 years is 98.30%.
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There is a mistake in question and correct question is as under:
What is the probability that the mean clock life would differ from the population mean by greater than 12.5 years?