Answer:
10 pounds of trial mix that costs $2.45 and 20 pounds of trial mix that costs $2.30
Step-by-step explanation:
[tex]\\\text{Let x pounds of the trial mix that costs \$2.45 per pound, and y pounds of the trial mix}\\\text{that costs \$2.30 per pound are added to get a 30 pounds of trial mix }\\\text{that costs \$2.35 per pound. since the total mixture is 30 pounds, so we get}\\\\x+y=30\ \ \ \ \ \ \ \ \ \ \ \ \ ...... (i)\\\\\text{and the total cost equation is given by}\\\\\$2.45 x + \$2.30 y=\$2.35 (30)\\\\2.45 x + 2.30 y=70.5 \ \ \ \ \ \ \ \ \ \ \ \ \ ...... (ii)\\[/tex]
[tex]\text{now to solve the equation (i) and (ii), we'll substitute }y=30-x \text{ from (i) into (ii)}\\\text{so we get}\\\\2.45x+2.30(30-x)=70.5\\\\2.45x+69-2.30x=70.5\\\\\Rightarrow 2.45x-2.30x=70.5-69\\\\\Rightarrow 0.15x=1.5\\\\\Rightarrow x=\frac{1.5}{0.15}\\\\\Rightarrow x=10\\\\\text{plug this value of x in (i), we get}\\\\y=30-x=30-10=20\\\\\text{so we must add 10 Pounds of trial mix that costs \$ 2.45 and 20 pounds of}\\\text{the trial mix that costs \$2.30}[/tex]
Final answer:
To create a 30-pound trail mix costing $2.35 per pound, mix 20 pounds of $2.45 trail mix with 10 pounds of $2.30 trail mix.
Explanation:
Trail mix costing: $2.45 per pound and $2.30 per pound must be mixed to get a 30-pound mix costing $2.35 per pound.
To calculate:
Let x = pounds of $2.45 mix and y = pounds of $2.30 mix.
Set up the system of equations: x + y = 30 and (2.45x + 2.30y)/30 = 2.35.
Solve the system to find x = 20 pounds of $2.45 mix and y = 10 pounds of $2.30 mix.
Please help!
What is the value of x?
check the picture below.
Please help and show work!!
Answer:
- 2 -2.5 and neither. For the left Panel
A or 40.5 for the right panel
Step-by-step explanation:
Slope AB
Givens
(3,5) (2,7)
y2 = 7y1 = 5x2 = 2x1 = 3Formula
m = (y2 - y1)/(x2 - x1)
Solution
m = (7 - 5)/(2 - 3)m = 2/-1 m= -2Slope CD
Givens
(10,5) (6,15)
y2 = 15y1 = 5x2 = 6x1 = 10Formula
m = (y2 - y1)/(x2 - x1)
Solution
m = (15 - 5)/(6 - 10)m = 10/-4 m= - 2.5What are they?
They are not parallel. m1 must equal m2 exactly. - 2 does not equal - 2.5They are not perpendicular m1 * m2 must = -1 -2 * -2.5= 5 They so not = -1 when multiplied together.Answer: Neither.
Right Panel
The best way to start this is to plot the triangle. I use Desmos for this. See diagram below
The base is between (-6,8) and (3,8)
The 8s are the same for both points. The distance between -6 and 3 is abs(-6) + abs(3) = 9
That is the base of the triangle.
The height is between (-6,17) and (-6,8)
17 - 8 = 9
Notice I did not have to use the absolute values. Why not?
Area = 1/2 * b * hbase = 9height = 9Area = 1/2 * 9 * 9Area = 40.5 AnswerPlease help need answer please
Answer:
There is one solution
Step-by-step explanation:
You can tell by looking at it that 2x and 3x are different. Both are obtained once the brackets have been removed. So you will get just one answer.
2(x -1) = 3(x - 4) Remove the brackets.
2x - 2 = 3x - 12 Subtract 2x from both sides.
2x - 2x - 2 = 3x - 2x - 12 Combine
-2 = x -12 Add 12 to both sides.
-2 + 12 = x -12 +12 Combine
10 = x
Match the following. 1. an angle that measures more than 0° but less than 90° vertical angles 2. two angles that have a common vertex and side but are not overlapping straight angle 3. two angles whose sum is 90° acute angle 4. an angle that measures more than 90° but less than 180° right angle 5. an angle that measures exactly 90° adjacent angles 6. an angle that measures exactly 180° complementary angles 7. two angles whose sum is 180° obtuse angle 8. the point where two line segments, lines, or rays meet to form an angle supplementary angles 9. angles that are opposite from one another at the intersection of two lines; vertical angles are congruent vertex
Answer:
Match the following:
1. An angle that measures more than 0° but less than 90°:
Acute angle.
2. Two angles that have a common vertex and side but are not overlapping:
Adjacent angles.
3. Two angles whose sum is 90°
Complementary angles.
4. An angle that measures more than 90° but less than 180°:
Obtuse angle.
5. An angle that measures exactly 90°:
Right angle.
6. An angle that measures exactly 180°:
Straight angle.
7. Two angles whose sum is 180°:
Supplementary angles.
8. The point where two line segments, lines, or rays meet to form an angle:
Vertex.
9. Angles that are opposite from one another at the intersection of two lines:
Vertical angles.
Step-by-step explanation:
Match the following:
1. An angle that measures more than 0° but less than 90°:
Acute angle.
2. Two angles that have a common vertex and side but are not overlapping:
Adjacent angles.
3. Two angles whose sum is 90°
Complementary angles.
4. An angle that measures more than 90° but less than 180°:
Obtuse angle.
5. An angle that measures exactly 90°:
Right angle.
6. An angle that measures exactly 180°:
Straight angle.
7. Two angles whose sum is 180°:
Supplementary angles.
8. The point where two line segments, lines, or rays meet to form an angle:
Vertex.
9. Angles that are opposite from one another at the intersection of two lines:
Vertical angles.
The terms such as acute angle, adjacent angles, complementary angles, obtuse angle, right angle, straight angle, supplementary angles, vertex, and vertical angles are correctly matched with their respective definitions.
Explanation:The correct matching for the provided terms are as follows:
An angle that measures more than 0° but less than 90° is an acute angle.Two angles that have a common vertex and side but are not overlapping are adjacent angles.Two angles whose sum is 90° are referred to as complementary angles.An angle that measures more than 90° but less than 180° is an obtuse angle.An angle that measures exactly 90° is a right angle.An angle that measures exactly 180° is a straight angle.Two angles whose sum is 180° are supplementary angles.The point where two line segments, lines, or rays meet to form an angle is a vertex.Angles that are opposite from one another at the intersection of two lines; vertical angles are congruent are vertical angles.Learn more about Angles here:https://brainly.com/question/33354646
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Can someone help me please fast!!!!!!!
What happened to Japanese-Americans during this time in WWII?
Answer:
During WWII, 120,000 Japanese-Americans were forced into camps, a government action that still haunts victims and their descendants. ... The roundups began quietly within 48 hours after the Japanese attacked Pearl Harbor, on December 7, 1941. The announced purpose was to protect the West Coast.
hope this helps.
Step-by-step explanation:
Decide whether the function is an exponential growth or exponential decay function, and find the constant percentage rate of growth or decay.
f(x) = 3.6 ⋅ 1.04x
Answer:
Exponential growth; percentage rate of growth is 4%.
Step-by-step explanation:
The function,
[tex]f(x)=3.6.(1.04)^x[/tex]
represents an exponential growth function because the growth factor is greater than 1.
The general form of an exponential growth function is,
[tex]y=a(1+r)^t=(a).(ar)^t[/tex], where 'r' is the percentage rate of growth.
If we compare the given equation with the standard form of the equation we can see that, we have,
[tex]f(x)=3.6(1+0.04)^x[/tex]
Therefore, the percentage rate of growth is = [tex]0.04 \times 100=4\%[/tex] .
A used-droid dealership buys a droid for $2900 and then sells it for $3900. What is the percent increase?
Answer:
The percent increase is 34.48276%
Step-by-step explanation:
we are given
original price =$2900
new price =$3900
now, we can find change in price
change in price = (new price)-(original price)
change in price =3900-2900
change in price =1000
percent increase = (change in price)/(original price) *100
percent increase is
[tex]=\frac{1000}{2900}\times 100[/tex]
[tex]=34.48276[/tex]
What is the x-intercept of the graph below?
-3
-2
2
3
Answer:
-3
Step-by-step explanation:
Which of the following values completes the square or creates a perfect square trinomial for x^2-12x+___
-6
12
36
-36
Answer:
So, 36 completes perfect square
Step-by-step explanation:
we are given
trinomial as
[tex]x^2-12x+......[/tex]
we can square formula
[tex]a^2-2ab+b^2=(a-b)[/tex]
we can see that middle term is 2ab
so, we will factor middle term in 2ab form
[tex]12x=2\times x\times 6[/tex]
We can see that b is 6
so, if we could add 6^2 , then we will get perfect square
[tex]x^2-12x+6^2......[/tex]
[tex]x^2-12x+36......[/tex]
So, we should add 36
so, 36......Answer
Answer: The correct option is
(C) 36.
Step-by-step explanation: We are given to select the value that completes the square or creates a perfect square trinomial for the following incomplete expression :
[tex]E=x^2-12x+?[/tex]
We will be using the following square formula :
[tex]a^2-2ab+b^2=(a-b)^2.[/tex]
Let the required value be represented by c.
We have
[tex]E\\\\=x^2-12x+c\\\\=(x^2-2\times x\times 6+6^2)+c-6^2\\\\=(x-6)^2+c-36.[/tex]
So, for the given expression to be a perfect square trinomial, we must have
[tex]c-36=0\\\\\Rightarrow c=36.[/tex]
Thus, the required value is 36.
Option (C) is CORRECT.
Given x/y=10/4. If y = 18, what is the value of x?
Answer: x = 45
====================================
Work Shown
x/y = 10/4
x/18 = 10/4 ... replace y with 18
x*4 = 18*10 ... cross multiply
4x = 180
4x/4 = 180/4 ... divide both sides by 4
x = 45
Final answer:
By cross-multiplying the given proportion x/y=10/4 with y=18, we determine that the value of x is 45.
Explanation:
To find the value of x given that x/y=10/4 and y = 18, we can use the method of cross-multiplication. This method involves multiplying the numerator of one fraction by the denominator of the other fraction and setting the two products equal to each other. So, we set up the equation:
[tex]\(\frac{x}{y} = \frac{10}{4}\)[/tex]
Let's substitute y with 18:
[tex]\(\frac{x}{18} = \frac{10}{4}\)[/tex]
We then cross-multiply and solve for x:
[tex]4x = 10 \times 18[/tex]
4x = 180
[tex]x = \frac{180}{4}[/tex]
x = 45
Therefore, the value of x is 45 when y is 18.
Can someone plz solve this for me??
Answer:
x=49
Step-by-step explanation:
First multiply 4 on both sides
(4) x/4+7=14(4)
the fours cross out leaving x by itself
x+17=14(4)
x+7=56
subtract 7 on both sides leaving:
x=49
Hi There!
Step-by-step explanation:
Solve: x/4 + 7 = 14 (x/4 = 1/4x)
Simplify: 1/4x + 7 = 14
Subtract 7 to both sides of the equation: 1/4x + 7 - 7 = 14 - 7
Simplify: 1/4x = 7
Multiply 4 to both sides of the equation: 1/4x * 4 = 7 * 4
Answer:
x = 28
Hope This helps :)
Write the equation 2x-3y=6 in slope intercept form
The slope-intercept form:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
We have the equation in standard form.
[tex]2x-3y=6[/tex] subtract 2x from both sides
[tex]-3y=-2x+6[/tex] divide both sides by (-3)
[tex]y=\dfrac{2}{3}x-2[/tex]
What is the slope of the line that passes through the points? (-4,4), (3,2)?
Hi there!
Step-by-step explanation:
[tex]SLOPE=\frac{Y_2-Y_1}{X_2-X_1}=\frac{RISE}{RUN}[/tex]
[tex]\frac{2-4}{3-(-4)}=\frac{-2}{7}[/tex]
Slope is -2/7
Final answer is -2/7.
Hope this helps!
Have a nice day! :)
:D
-Charlie
Thank you! :)
:D
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have the points (-4, 4) and (3, 2). Substitute:
[tex]m=\dfrac{2-4}{3-(-4)}=\dfrac{-2}{3+4}=-\dfrac{2}{7}[/tex]
Answer: The slope is - 2/7.Can someone help please. ITS URGENTTTT. the question is attached
Answer:
7.49
Step-by-step explanation:
1.07x7=7.49
Lucia tried to solve the system below. Lucia’s Work. What error did Lucia make? When Lucia solved for the value of x, she subtracted 2y from both sides. When Lucia solved for the value of y, she treated –2y as 2y. When Lucia solved for the value of x, she added 18 to both sides. When Lucia solved for the value of x, she treated –2(–9) as 18 instead of –18.
Final answer:
The question hints at possible arithmetic or sign operation errors Lucia made while solving a system of equations. Pinpointing her exact mistake involves understanding common errors like incorrect handling of negative numbers or arithmetic operations.
Explanation:
The question involves identifying the mistake Lucia made when solving a system of equations. When solving for the value of x, there are various potential errors one could make, such as incorrect addition, subtraction, or misinterpretation of the operation sign. For instance, treating − 2( − 9) as 18 instead of − 18 is a common mistake due to misunderstanding how to handle double negatives in algebra. Similarly, when solving for the value of y, mistaking − 2y for 2y shifts the equation's balance, leading to incorrect solutions.
Lucia's error could stem from a few different places described in the question, but without the specific steps Lucia took, it's challenging to pinpoint the exact mistake. However, common errors to watch out for when solving for x and y in systems of equations include incorrect operations with negative numbers, improper handling of variables, or erroneous arithmetic operations.
Correctly solving a system of equations requires careful attention to each algebraic step, ensuring that operations on both sides of an equation are correctly applied and that signs are properly managed. Seeking to correct mistakes like treating negative signs improperly or misapplying arithmetic operations is essential for accurate solutions.
which is the slope of the line shown? )
Answer:
slope = [tex]\frac{9}{7}[/tex]
Step-by-step explanation:
to calculate the slope m use the gradient formula
m = ( y₂ - y₁ ) / ( x₂ - x₁ )
with (x₁, y₁ ) = (- 6, - 3) and (x₂, y₂ ) = (1,6) ← 2 points on the line
m = [tex]\frac{6+3}{1+6}[/tex] = [tex]\frac{9}{7}[/tex]
find value of x
pls helpp meeeeeee
[tex]3\times9^{x+1}=27^{x-1}\\\\3\times(3^2)^{x+1}=(3^3)^{x-1}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\3\times3^{2(x+1)}=3^{3(x-1)}\\\\3\times3^{2x+2}=3^{3x-3}\qquad\text{use}\ a^n\times a^m=a^{n+m}\\\\3^{1+2x+2}=3^{3x-3}\\\\3^{2x+3}=3^{3x-3}\iff2x+3=3x-3\qquad\text{subtract 3 from both sides}\\\\2x=3x-6\qquad\text{subtract 3x from both sides}\\\\-x=-6\to\boxed{x=6}[/tex]
Lucy bought a 40-ounce bottle of vegetable oil for $7.69. She used 65% of the vegetable oil in three weeks. For the amount of vegetable oil she used in three weeks the approximate cost was?
To calculate the cost of the vegetable oil used by Lucy in three weeks, we need to determine the cost per ounce and then multiply it by the quantity used. In this case, the approximate cost of the oil used is $5.00.
Explanation:To find out the approximate cost of the amount of vegetable oil Lucy used in three weeks, we first need to figure out how much of the 40-ounce bottle she used. As the question states that she used 65% of it, we can calculate it as follows:
Firstly, to find 65% of 40 ounces, we can multiply 40 by 0.65, which gives us 26 ounces. So, this is the amount of oil Lucy used.Next, we need to find out how much does 26 ounces cost. To do this, we need to calculate the cost per ounce which is $7.69 (cost of the bottle) divided by 40 (the amount of ounces in the bottle). This gives us a cost of about $0.19225 per ounce.Now, to find the cost of 26 ounces of oil, we multiply the cost per ounce ($0.19225) by the amount of ounces used (26). So, $0.19225 * 26 = $4.9985 .So, the approximate cost for the amount of vegetable oil Lucy used in three weeks is $5.00, rounded to the nearest cent.
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To find the approximate cost for the amount of vegetable oil Lucy used in three weeks, calculate 65% of the total cost of the 40-ounce bottle of vegetable oil, and the approximate cost is $4.99.
Explanation:To find the approximate cost for the amount of vegetable oil Lucy used in three weeks, we need to calculate 65% of the total cost of the 40-ounce bottle of vegetable oil.
First, calculate 65% of $7.69: 0.65 x $7.69 = $4.99 (rounded).Therefore, the approximate cost for the amount of vegetable oil Lucy used in three weeks is $4.99.Learn more about cost of vegetable oil here:https://brainly.com/question/29267996
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Please answer in detail
Answer:
[tex]\dfrac{1}{24}[/tex]
Step-by-step explanation:
1. The student is allowed to choose white, blue, green or black Polo shirts. So the student has 4 possibilities to select shirt and the probability of wearing the blue shirt is [tex]\dfrac{1}{4}.[/tex]
2. The student is allowed to choose khaki, black or plaid skirts/pants. So the student has 3 possibilities to select skirt and the probability of wearing the plaid skirt is [tex]\dfrac{1}{3}.[/tex]
3. The student is allowed to choose black or brown shoes. So the student has 2 possibilities to select shoes and the probability of wearing black shoes is [tex]\dfrac{1}{2}.[/tex]
Now use the product rule for probabilities:
[tex]Pr=\dfrac{1}{4}\cdot \dfrac{1}{3}\cdot \dfrac{1}{2}=\dfrac{1}{24}.[/tex]
There were 48 ants on a hill. Then 13 of the ants marched away.how many ants are still on the hill?
Answer: 35
Step-by-step explanation: 48 - 13 = 35
Answer:
35 ants left
Step-by-step explanation:
you start with 48-13then you turn the problem to 40-10=30then subtract 3 from 8 and get 5then you add 30+5 and get 35The amount of time required to download a song from Michael's computer to his music player is the same for each song he downloads. A linear model of this situation contains the values (100, 80) and (212, 169.6), where x represents the number of songs he wants to download to his music player, and y represents the total amount of time, in minutes, it will take him to download the songs. What is the rate of change in this linear model?
A. 1.6 minutes per song
B. 0.4 of a minute per song
C. 0.8 of a minute per song
D. 112 minutes per song
Answer:
The correct answer is A. 1.6
Step-by-step explanation:
1.6x50= 80 minutes per song.
1.6x106= 169.6 minutes per song.
If you don't believe me, then grab yourself a calculator, punch the #'s (above^) in, and you'll get the answer.
Hope this helped ya out! (:
Answer:
ans is C. 0.8 of a minute per song
Step-by-step explanation:
x represents the number of songs he wants to download to his music player,
and y represents the total amount of time, in minutes, it will take him to download the songs.
(100, 80) and (212, 169.6)
subtracting: he DL 212-100=112 songs in 169.6-80=89.6 minutes
so the rate of change = 89.6/112 = 0.8 minute per song
Charlotte bought 16 songs for her MP3 player. Three-fourths of the songs are classical songs. How many of the songs are classical songs?
Divide. Round to the nearest tenth if necessary.
65.2 ÷ 26
Please show procedure.
Final answer:
To divide 65.2 by 26, you perform the division to find that 26 goes into 65.2 exactly 2.5 times. Therefore, the answer, when rounded to the nearest tenth, is 2.5.
Explanation:
To divide 65.2 by 26, start with the division process. Place a decimal point directly above the decimal point in the dividend within the answer area. Since 26 does not go into 6, but goes into 65 twice, write 2 above the 5 in the dividend. Multiply 2 by 26 to get 52, and subtract this from 65, which leaves a remainder of 13. Bring down the 2 from the dividend to get 132.
Now, divide 26 into 132, which goes exactly 5 times. Multiplying 5 by 26 gives 130, subtract this from 132 to get a remainder of 2. Because we are left with no more numbers to bring down and our remainder is less than 26, we stop. The answer to 65.2 divided by 26 when rounded to the nearest tenth is 2.5.
can someone please help me question is hard
Answer: choice A
f(x) = (1/4)x^2, f(x) = -0.5x^2, f(x) = x^2
=======================================================
The coefficient in front of the x^2 term tells us how wide or narrow the parabola will be. It turns out that the further the coefficient value is from 0, in either direction, this will make the parabola more narrow.
Notice how 1/4 = 0.25 which is less than |-0.5| = 0.5 meaning that f(x) = (1/4)x^2 is wider than f(x) = -0.5x^2
Then comparing f(x) = -0.5x^2 to f(x) = 1x^2, we see that 0.5 is smaller than 1, so f(x) = -0.5x^2 is wider than f(x) = 1x^2
That is why the order from widest to narrowest is f(x) = (1/4)x^2, f(x) = -0.5x^2, f(x) = x^2
A graph shown below helps confirm the answer (note the color coding). In figure 1 is the graph of all three functions together. In figure 2, I reflect the second function help show the comparison of why it's the middle-most in terms of how wide it is (it is the orange parabola, which is the reflection of the red parabola)
Find the recursive definition of the following sequence (Remember to define the first term t, the recursive rule to find tn,and the value n will start at.) 1, 6, 36, 216, 1296…..
The answer is composed of the following two equations
[tex]t_1 = 1[/tex] and [tex]t_n = 6*t_{n-1}[/tex]
both of these two equations combine to help form the full recursive definition
=================================================
Further explanation:
The terms are represented by the letter 't' for short. Since we have more than one term, and because we have only so many letters, this means we stick a number onto the 't' to help label multiple terms. We have t1 as the first term, t2 as the second, etc. The numbers are often show as subscripts like so [tex]t_1, t_2, t_3, \ldots[/tex]
The first term of the list of numbers is 1, so [tex]t_1 = 1[/tex] is what we start with to help set up the recursive definition.
Once we have this starting point, we use it to get to the next term which is 6. This value is 6 times the first value. Therefore, the recursive step is [tex]t_n = 6*t_{n-1}[/tex] basically saying "multiply the (n-1)st term by 6 to get the nth term. Translation: "whatever the current term is, multiply by 6 to get the next term".
And this one too!! Thanks in advance
Answer:
20/9 sq.feet
Step-by-step explanation:
The width is 4/3 ft because 1/3 times 4 is 4/3 and the length is 5/3 because 1/3 times 5 is 5/3.
Then to find the area you do length times width.
5/3 ×4/3= 20/9 sq. feet
I hope this helps! :)
Steve just signed a lease to rent a new apartment. His monthly rent will be $800.00, and he will have to pay a one-time nonrefundable security deposit equal to half of the monthly rent. If Steve rents the apartment for x months, which equation can be used to determine T, the total amount Steve will pay to live in the apartment?
7x(x+1.8)=0 please help !
The solutions to the equation 7x(x+1.8)=0 are x = 0 and x = -1.8.
The highest power of the polynomial function is defined as the degree.
The Fundamental Theorem of Algebra asserts that a polynomial has n roots if its degree is n.
The equation is 7x(x+1.8)=0.
To solve this equation, we can use the property that if the product of two factors is equal to zero, then at least one of the factors must be zero.
Therefore, we set each factor equal to zero and solve for x:
7x = 0
x = 0
x + 1.8 = 0
x = -1.8
So, the solutions to the equation 7x(x+1.8)=0 are x = 0 and x = -1.8.
To solve the equation 7x(x+1.8)=0, set each factor equal to zero to find the two possible solutions for x, which are 0 and -1.8.
Explanation:To solve the equation 7x(x+1.8)=0, we need to set each factor equal to zero and solve for x.
Setting 7x=0, we find x=0. Setting x+1.8=0, we subtract 1.8 from both sides to get x=-1.8. Therefore, the solutions to the equation are x=0 and x=-1.8.
SEO Keywords: quadratic equation, solve, factor, solutionsThe given equation is 7x(x+1.8)=0. This is a quadratic equation that can be easily solved by setting each factor equal to zero. Here's how you can find the value(s) of x:
Set 7x equal to zero: 7x = 0 ---> x = 0.Set (x + 1.8) equal to zero: x + 1.8 = 0 ---> x = -1.8.Therefore, the two possible values for x are 0 and -1.8.
66 L : 120 mL
Simplify the ratio