Answer:
[tex]\large \boxed{\text{129 g}}[/tex]
Step-by-step explanation:
We can use ratio and proportion to solve this problem.
Let x = the mass of Zn
[tex]\begin{array}{cccl}\dfrac{\text{Zn}}{\text{Cu}} & = & \dfrac{3}{11} & \\\\\dfrac{x}{473} & = & \dfrac{3}{11} & \text{Substituted the mass of Cu}\\\\x & = & \dfrac{3\times473}{11} &\text{Multiplied each side by 473} \\\\ & = &\mathbf{129} & \text{Simplified}\\\end{array}\\\text{The mass of Zn is $\large \boxed{\textbf{129 g}}$}[/tex]
Check:
[tex]\begin{array}{rcl}\dfrac{129}{473} & = &\dfrac{3}{11} \\\\\dfrac{3}{11} & = & \dfrac{3}{11} \\\end{array}[/tex]
OK
7. Bobby buys 10 pounds seafood for $30. It
contains shrimp that sells for $5 per pound and
crawfish that sells $1 a pound. How many of each
kind were purchased in the mixture?
Answer:
5 pounds of shrimp and 5 pounds of crawfish were purchased in the mixture.
Step-by-step explanation:
We are given the following in the question:
Bobby buys 10 pounds seafood for $30.
Let x pounds of shrimp be purchased and y pounds of crawfish.
Thus, we can write,
[tex]x + y =10[/tex]
Cost of shrimp = $5 per pound
Cost of crawfish = $1 per pound
Total money spent = $30
Thus, we can write the equation,
[tex]5x + y = 30[/tex]
Solving the two equation by elimination method,
[tex]5x + y-(x+y) = 30-10\\4x = 20\\x = 5\\y = 10 - x = 10 - 5 = 5[/tex]
Thus, 5 pounds of shrimp and 5 pounds of crawfish were purchased in the mixture.
Pls help!!
y = x + 2
2x - y = -4
Solve the system of equations using substitution.
A) (-2,-4)
B) (-2,0)
C) (-6,-4)
D) (-6,8)
E) (0,-2)
Answer:
B (-2, 0)
Step-by-step explanation:
put the first equation in for y in the second equation - watch the negative
2x - (x +2) = -4
2x - x -2 = -4
x = -2
plug this x back in to find y
y = -2 + 2 = 0
Answer:
B
Step-by-step explanation:
plug in the answers given into both equations to see if the statements true
y=x+2
0=(-2)+2
0=0
2x-y=-4
y=2x+4
0=2(-2)+4
0=0
Add the two expressions.
2x + 6 and 6.2 - 1
Enter your answer in the box.
Answer:
8x + 5
Step-by-step explanation:
By adding
2x + 6 + 6x -1
8x + 5
What is the equation of a circle with center (-7, -3) and radius 2?
Answer:
B = (x + 7)^2 + (y +3)^2 = 4
Step-by-step explanation:
The equation of a circle with center (-7, -3) and radius 2 is (x + 7)² + (y + 3)² = 4.
Explanation:The equation of a circle with a center at point (-7, -3) and a radius of 2 can be written based on the standard form of the circle equation (x - h)² + (y - k)² = r², where (h,k) is the center of the circle and r is the radius.
Plugging in the values given in the question, the equation simplifies to: (x + 7)² + (y + 3)² = 4.
What is the C of a circle that has a radius of 4.5
Step-by-step explanation:
[tex]C = 2\pi \: r \\ = 2 \times 3.14 \times 4.5 \\ = 3.14 \times 9 \\ =28.26 \: units[/tex]
if 1/5 of the remaining blueberries is used to make muffins, how many pounds of blueberries are left in the container
To calculate the remaining blueberries after using 1/5 for muffins, subtract 1/5 from the total, leaving you with 4/5 of the original amount in pounds.
Explanation:To determine how many pounds of blueberries are left after using 1/5 of them to make muffins, we need to perform a subtraction based on the fraction used. Let's assume we start with a certain quantity 'X' pounds of blueberries. After using 1/5 of them, we have 4/5 of 'X' pounds left because we subtract the 1/5 that was used for muffins from the original amount. It's important to convert any measurement units if they are not consistent, as seen when comparing pounds and ounces for other items like yogurt or apples.
The remaining amount of blueberries in the container is [tex]\( \frac{4}{5} \)[/tex] of the initial amount.
To determine how many pounds of blueberries are left in the container, we need to set up the problem and solve it step-by-step.
Let's denote the initial amount of blueberries as [tex]\( x \)[/tex] pounds.
1. Define the amount used for muffins:
If [tex]\( \frac{1}{5} \)[/tex] of the remaining blueberries is used to make muffins, it means that [tex]\( \frac{1}{5} \)[/tex] of the total blueberries is used.
Therefore, the amount of blueberries used for muffins is [tex]\( \frac{1}{5} x \)[/tex].
2. Calculate the remaining blueberries:
The remaining blueberries will be the total amount minus the amount used for muffins.
Thus, the remaining blueberries are:
[tex]\[ x - \frac{1}{5} x \][/tex]
3. Simplify the expression:
[tex]\[ x - \frac{1}{5} x = \frac{5}{5} x - \frac{1}{5} x = \frac{4}{5} x \][/tex]
A jet plane traveling at 550 mph overtakes a propeller plane traveling at 150 mph that had a 3-hour head start. How far from the starting point are the planes?
The planes are 618.75 miles from starting point
Solution:
Let t is the travel time of the jet
Then (t + 3) is the travel time of the propellar
When the jet overtakes the propellar, they will traveled the same distance
Distance is given as:
[tex]Distance = speed \times time[/tex]
Distance equation for JetA jet plane traveling at 550 mph
[tex]Distance\ by\ jet = 550 \times t\\\\Distance\ by\ jet = 550t[/tex]
Distance equation for propellar:propeller plane traveling at 150 mph
[tex]Distance\ by\ propellar = 150 \times (t+3)[/tex]
Equate both distance
[tex]550t = 150(t+3)\\\\550t = 150t + 450\\\\550t - 150t = 450\\\\400t = 450\\\\t = \frac{450}{400}\\\\t = 1.125[/tex]
Find the distance from the starting point[tex]Distance = 550 \times t = 550 \times 1.125\\\\Distance = 618.75[/tex]
Thus they are 618.75 miles from starting point
The distance both planes are from the starting point when the jet overtakes the propeller is 451.125 miles.
Explanation:This question is a math problem involving relative speed and distance traveled. In this case, we are solving for the distance each plane has flown from their respective starting points once the jet plane overtakes the propeller plane.
To start, let's think of the problem in terms of a timeframe. We know the propeller plane had a 3-hour head start. Now, we need to determine how long it took for the jet plane to catch up to the propeller plane. To calculate this, we must find the difference in speed between the two planes (550 mph - 150 mph = 400 mph), and then divide the time difference (3 hours) by the relative speed (400 mph) which equals 0.0075 hours.
Next, we compute the distance covered by the propeller plane in 3.0075 hours (150 mpg * 3.0075 hours = 451.125 miles). Both planes are at this same distance from the starting point when the jet plane overtakes the propeller plane.
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What are the vertex and x-intercepts of the graph of y = (x + 4)(x + 2)? Select
one answer for the vertex and one for the x-intercepts.
O
A. x-intercepts: (4,0), (-2, 0)
O
B. Vertex: (1,3)
O
c. x-intercepts: (-4,0), (-2,0)
O
D. Vertex: (-3,1)
E. Vertex: (-3,-1)
O
F. xintercepts: (-4,0), (2, 0)
Answer:
C. x-intercepts: (-4,0), (-2,0)
E. Vertex: (-3,-1)
Step-by-step explanation:
Part 1) Find the x-intercepts
we have
[tex]y=(x+4)(x+2)[/tex]
This is a vertical parabola written in factored form
[tex]y=(x-x_1)(x-x_2)[/tex]
where
x_1 and X_2 are the roots or x-intercepts
so
[tex]x_1=-4\\x_2=-2[/tex]
Remember that the x-intercepts are the values of x when the value of y is equal to zero
therefore
The x-intercepts are
(-4,0) and (-2,0)
Part 2) Find the vertex
we have
[tex]y=(x+4)(x+2)[/tex]
This is a vertical parabola open upward (the leading coefficient is positive)
The vertex is a minimum
Applying distributive property
[tex]y=x^2+2x+4x+8\\y=x^2+6x+8[/tex]
Convert to vertex form
Complete the square. Remember to balance the equation by adding the same constants to each side.
[tex]y=(x^2+6x+3^2)+8-3^2[/tex]
[tex]y=(x^2+6x+9)-1[/tex]
Rewrite as perfect squares
[tex]y=(x+3)^2-1[/tex] ----> equation in vertex form
[tex]y=(x-h))^2+k[/tex]
where
(h,k) is the vertex
therefore
The vertex is the point (-3,-1)
Answer:
Vertex: (-3,-1) X intercepts: (-4,0), (-2,0)
Step-by-step explanation:
A P E X ;)
What is the graph for the above relationship?
A. 1st Graph
B. 2nd Graph
C. 3rd Graph
D. 4th Graph
How are the two functions f(x) = 0.7(6)x and g(x) = 0.7(6)–x related to each other?
Answer:
The sign of [tex]x[/tex] in [tex]g(x)[/tex] is opposite or negated. This is the only difference between [tex]f(x)[/tex] and [tex]g(x)[/tex], meaning it is a reflection through the y-axis.
Therefore, [tex]g(x)[/tex] will be the reflection of [tex]f(x)[/tex] through the y-axis.
Step-by-step explanation:
Considering the functions
f(x) = 0.7(6)xg(x) = 0.7(6)–xWe know that when we reflect a function through the y-axis, the x-coordinate gets opposite - negated.
Here, the sign of [tex]x[/tex] in [tex]g(x)[/tex] is opposite or negated. This is the only difference between [tex]f(x)[/tex] and [tex]g(x)[/tex], meaning it is a reflection through the y-axis.
Therefore, [tex]g(x)[/tex] will be the reflection of [tex]f(x)[/tex] through the y-axis.
Answer:
The sign of in is opposite or negated. This is the only difference between and , meaning it is a reflection through the y-axis.
Therefore, will be the reflection of through the y-axis.
Step-by-step explanation:
Considering the functions
f(x) = 0.7(6)x
g(x) = 0.7(6)–x
We know that when we reflect a function through the y-axis, the x-coordinate gets opposite - negated.
Here, the sign of in is opposite or negated. This is the only difference between and , meaning it is a reflection through the y-axis.
Therefore, will be the reflection of through the y-axis.
Select the correct answer.
What is the justification for step 3 in the solution process?
10d − 5 = 4d − 15 − 3d
Step 1: 10d − 5 = d − 15
Step 2: 9d − 5 = -15
Step 3: 9d = -10
A.
the subtraction property of equality
B.
the multiplication property of equality
C.
the division property of equality
D.
the addition property of equality
Answer:
D.
the addition property of equality
Step-by-step explanation:
Given the expression in
Step 2: 9d - 5 = -15
The addition property of equality was used to get step 3.
That is
9d - 5 = -15
Move -5 over the equality sign and it becomes +5
9d = -15 + 5
9d = -10
OR add 5 to both sides of the equation as shown below
9d - 5 +5 = -15 + 5
9d = -10 which we have in step 3
The justification for step 3 is the subtraction property of equality, which allows us to subtract the same number from both sides of an equation to maintain its balance.
Explanation:The correct answer is A: the subtraction property of equality.
Here is why: In the step before (step 2), we have 9d - 5 = -15. When we move to step 3, we're solving 9d = -10 which means we added 5 to both sides of the equation. By doing so, we subtract 5 from the left side to get 9d and add 5 to -15 on the right side to get -10. This action is consistent with the subtraction property of equality, which states that you can subtract the same number from both sides of an equation and the equation will still hold true.
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Select True or false for each statement
Answer:
False
True
False
False
Step-by-step explanation:
1. We have to get the sum as follows :
[tex]3\frac{4}{9} + 4\frac{6}{9}[/tex]
= [tex]\frac{31}{9} + \frac{42}{9}[/tex]
= [tex]\frac{31 + 42}{9}[/tex]
= [tex]\frac{73}{9}[/tex]
= [tex]8\frac{1}{9} \neq 7\frac{1}{9}[/tex]
So, this is false.
2. We have to get the sum as follows :
[tex]4\frac{5}{6} + 1\frac{3}{6}[/tex]
= [tex]\frac{29}{6} + \frac{9}{6}[/tex]
= [tex]\frac{29 + 9}{6}[/tex]
= [tex]\frac{38}{6}[/tex]
= [tex]6\frac{2}{6}[/tex]
So, this is true.
3. We have to get the difference as follows :
[tex]4\frac{5}{8} - 2\frac{4}{8}[/tex]
= [tex]\frac{37}{8} - \frac{20}{8}[/tex]
= [tex]\frac{37 - 20}{8}[/tex]
= [tex]\frac{17}{8}[/tex]
= [tex]2\frac{1}{8} \neq 2\frac{3}{8}[/tex]
So, this is false.
4. We have to get the difference as follows :
[tex]7\frac{5}{8} - 4\frac{2}{8}[/tex]
= [tex]\frac{61}{8} - \frac{34}{8}[/tex]
= [tex]\frac{61 - 34}{8}[/tex]
= [tex]\frac{27}{8}[/tex]
= [tex]3\frac{3}{8} \neq 3[/tex]
So, this is also false. (Answer)
Find the first four terms of the arithmetic sequence when a1 =3 and d=2
A. 2,5,8,11
B. 3,5,7,9
C.1,3,5,7
D.3,6,12,24
Answer:
b.
Step-by-step explanation:
Which expression has the same GCF as 15x2 - 21x?
Answer:
12x^2-15x
Step-by-step explanation:
PLATO
The expression 12x²-15x has the same GCF as 15x² - 21x.
What is Expression?An expression is combination of variables, numbers and operators.
The given expression is 15x²-21x
Let us find GCF of the given expression.
The GCF for a polynomial is the largest monomial that divides (is a factor of) each term of the polynomial
15x²-21x
3x(5x-7)
The GCF of 15x²-21x is 3x.
Now GCF of 18x²-24x, 6x(3x-4) is 6x
GCF of 12x²-15x, 3x(4x-4) is 3x
GCF of 15x²-21, 3(5x²-7) is 3
GCF of 12x²-18x, 6x(2x-3) is 6x
Hence, the expression 12x²-15x has the same GCF as 15x² - 21x.
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what is 44/12 as a simplified mixed fraction
3 67/100
3 will stay a whole number so you put that as the whole number. 67 is 67 percent of a whole. so you put it over 100.
Can someone help me please
Answer:
43.7 ft
Step-by-step explanation:
Radius of the semicircular garden is 8.5 ft .
Diameter = 8.5 × 2 = 17 ft
Circumference of the garden = [tex]\frac{1}{2}[/tex] × π × diameter = [tex]\frac{1}{2}[/tex] × π × 17 = 26.7 ft (rounded up to the nearest tenth of a foot)
Distance around the gardent = Circumference + diameter = 26.7 ft + 17 ft = 43.7 ft
Which of the following expressions is equal to - x^2 - 4 ?
A. (-x-2i)(x+2i)
B. (-x - 2i)(x - 2i)
C. (x+2i)(x-2i)
D. (-x+2i)(x-2i)
Final answer:
The expression equal to [tex]-x^2[/tex] - 4 is formed by multiplying two complex conjugates. Option C: (x+2i)(x-2i) correctly expands to [tex]-x^2[/tex] - 4, since the product of the imaginary parts (2i × -2i) equals -4. The correct option is C: (x+2i)(x-2i).
Explanation:
The expression [tex]-x^2[/tex] - 4 can be created by multiplying two complex numbers that, when multiplied, give a negative real part and a positive imaginary part squared. Using the fact that (i)(i) = -1, we can deduce that the product of complex conjugates will give us the desired expression because the imaginary parts will cancel each other out leaving us with a purely real number.
When we multiply two complex conjugates, the general form is (a+bi)(a-bi) = [tex]a^2 - (bi)^2 = a^2 + b^2[/tex], since [tex](bi)^2[/tex] equates to [tex]-b^2[/tex] because [tex]i^2[/tex] = -1. Applying this to our problem, we are looking for 2 numbers whose square equals 4. Since 2i × -2i = -4, we can construct the two factors as (x+2i) and (x-2i), which corresponds to option C: (x+2i)(x-2i).
About how many cubic feet greater is the volume
of the Mega Moving Truck than the 2-bedroom
moving truck?
Mega Moving truck is 632.102 cubic feet greater than 2-bedroom moving truck.
Solution:
Volume of the mega moving truck = length × width × height
[tex]$=22 \frac{1}{4}\times7 \frac{7}{12}\times 8 \frac{5}{12}[/tex]
Convert mixed fraction into improper fraction.
[tex]$= \frac{22\times4+1}{4}\times \frac{7\times12+7}{12}\times \frac{8\times12+5}{12}[/tex]
[tex]$= \frac{89}{4}\times \frac{91}{12}\times \frac{101}{12}[/tex]
Volume of the mega moving truck = 1420.137 cubic ft
Volume of the 2-bedroom moving truck = length × width × height
[tex]$=14 \frac{1}{2}\times7 \frac{7}{12}\times 7\frac{1}{6}[/tex]
Convert mixed fraction into improper fraction.
[tex]$= \frac{14\times2+1}{2}\times \frac{7\times12+7}{12}\times \frac{7\times6+1}{6}[/tex]
[tex]$= \frac{29}{2}\times \frac{91}{12}\times \frac{43}{6}[/tex]
Volume of the 2-bedroom moving truck = 788.035 cubic ft
Difference between them = 1420.137 – 788.035
= 632.102 cubic ft
Hence Mega Moving truck is 632.102 cubic feet greater than 2-bedroom moving truck.
5x-3=21-x please someone answer
Answer:
X=4 Hope it helps Lol
Step-by-step explanation:
5*x-3-(21-x)=0
Step by step solution :
Step 1 :
Pulling out like terms :
1.1 Pull out like factors :
6x - 24 = 6 • (x - 4)
Equation at the end of step 1 :
Step 2 :
Equations which are never true :
2.1 Solve : 6 = 0
This equation has no solution.
A a non-zero constant never equals zero.
Solving a Single Variable Equation :
2.2 Solve : x-4 = 0
Add 4 to both sides of the equation :
x = 4
One solution was found :
x = 4
Answer:
X=4
Step-by-step explanation:
The first thing you would do is to make it so there is only x's on one side. To do this add the x on both sidesThis would make it so you have 6x-3=21Plus the 3 on both sides This would give you 6x=24Do 24÷6 giving you 4X=4please solve 1/4w+5=w/3+10
Answer:
-60
Step-by-step explanation:
1/4w + 5 = w/3 + 10
Collect like terms
1/4 w - 1/3 w = 10 - 5
Find lcm of 4 &3 = 12 and subtract
-1/12 w = 5
Multiply both sides by 12
-w = 5 x 12
-.w = 60
Divide both sides by -1
w = -60
I hope this was helpful, Please mark as brainliest
Elena wrote the equation 5x=25. She wants to multiply 25 by 5 to solve it does this make sense
Answer:
It certainly doesn't make sense. Her equation means
5 times some number is 25.
hope it helps!
How would you graph the solution set of {x}{6}≤ -18?
closed circle on -3 and shaded to the right
closed circle on -3 and shaded to the left
closed circle on -108 and shaded to the right
closed circle on -108 and shaded to the left
Answer:
Step-by-step explanation:
6x ≤ -18.....divide both sides by 6
x ≤ -18 / 6
x ≤ -3
ok...so ur gonna have a closed circle because the inequality contains an equal sign......ur gonna put that closed circle on -3 and shading will go to the left because it is less then
closed circle on -3, shaded to the left <==
Answer:
closed circle on -3 and shaded to the left
Hope it Helped <3
what type of function y<3x+5
Answer:
linear inequality (not a function)
Step-by-step explanation:
The given inequality is linear in the variables x and y. It maps x to an infinite number of possible values for y, so the relation is not a function.
Use the grouping method to factor x3 + x2 + 5x + 5.
A. (x + 1)(x2 + 5)
B. (x2 + 1)(x+5)
C. (x+ 1)(x + 5)
D. x(x + 5)(x + 1)
Answer:
answer is a
Step-by-step explanation:
look at picture
5. Chris pays a fee if her bank balance falls below $10 on the statement
date. Prior to the statement date, her balance was -$3.46. Then, Chris made a deposit, d, in ample time, so she did not have to pay a fee.
a. Write an inequality to represent this situation.
Answer:
d ≥ 13.46
Step-by-step explanation:
Chris has to pay low balance fee if her bank balance falls below $10.
Her balance was -$3.46 before the statement date.
Now, Chris has to deposit a minimum amount of $(3.46 + 10) = $13.46 to her bank account and then only she does not need to pay a fee.
If the deposit amount is d, then the inequality to represent the situation is
d ≥ 13.46 (Answer)
Final answer:
Chris needs to deposit at least $13.46 to prevent a bank fee because her balance was -$3.46. By adding $3.46 to the minimum required balance of $10, we determine the least deposit amount through the inequality d ≥ 13.46.
Explanation:
To solve the situation where Chris avoids a fee by making a deposit, d, we must write an inequality that reflects her balance being above $10 after the deposit. Originally, her balance was -$3.46. Therefore, after deposit d, her new balance must be equal to or greater than $10 to prevent the fee. The inequality representing this situation is:
d - 3.46 ≥ 10
When you add $3.46 to both sides to isolate d, the inequality becomes:
d ≥ 13.46
This inequality indicates that Chris's deposit must be at least $13.46 to avoid the bank fee.
Solve the equation . 3(x+4.5)=36
A box has dimensions of 17inches long , 1.3 feet wide , and 8 inches high . What is the volume of the box?
Answer:
2121.6 cubic inch
Step-by-step explanation:
Length of the box = 17 inches
Width of the box = 1.3 feet = 1.3 * 12 inches = 15.6 inches
Height of the box = 8 inches
Volume of the box is given by the product of its length , width and height.
Hence, Volume = {tex]\[length * width * height\][/tex]
= [tex]\[17 * 15.6 * 8\][/tex]
= 2121.6
Hence the volume of the box is 2121.6 cubic inch
This can also be expressed in cubic feet by dividing it by 1728.
In cubic feet the volume will be 1.23 cubic ft.
Factor each expression (6s + 18t + 3w)
Answer:
3(2s + 6t + w)
Step-by-step explanation:
Since the highest GCF is 3, I divided 6s, 18t, and 3w. This equals to 3(2s + 6t + w)
Answer:
3(2s+6t+w)
Step-by-step explanation:
Solve:
(12 − 4) − (6 ÷ 2) − (2 x 2) =
Answer:
1
Step-by-step explanation:
(12 - 4) - (6 / 2) - (2 * 2)
(8) - (3) - (4)
1
Answer:
1
Step-by-step explanation:
go to google calculator
PLEASE HELP ASAP Which equation BEST models the data shown in the scatterplot below?
A. y=3x+10
B. y=3x+60
C. y=4x+5
D. y=4x+35
Answer:
Option D. y=4x+35
Step-by-step explanation:
From the graph take the points (5,50) and (50,250)
Find the slope
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
substitute the values
[tex]m=\frac{250-50}{50-5}[/tex]
[tex]m=\frac{200}{45}=4.4[/tex]
Find the equation of the line in slope intercept form
[tex]y=mx+b[/tex]
we have
[tex]m=4.4\\point\ (5,50)[/tex]
substitute
[tex]50=4.4(5)+b[/tex]
solve for b
[tex]b=50-22\\b=28[/tex]
substitute
[tex]y=4.4x+28[/tex]
therefore
The equation that BEST models the data is
[tex]y=4x+35[/tex]