Quinn used compensation to find the product of 37x4. First, she found 40x4=160. Then she adjusted that product by adding 3 groups of 4 to get her final answer of 172. What did she do incorrectly?
The sum of two numbers is 18 less than twice the first number. their difference is 32 less than twice the second number. find each of the numbers
The problem asks to solve a system of two equations by representing each condition as an equation. By simplifying and substituting, we can find the values of the two unknowns.
Explanation:The question involves solving a system of two equations. Let's denote the first number as x and the second number as y. The given conditions can be represented as follows:
x + y = 2x - 18x - y = 2y - 32To simplify, we can rewrite the equations as:
y = x - 18x = 2y + 32We can substitute equation (1) into equation (2) to get:
x = 2(x - 18) + 32
Solving the equation will give us the value of x and substituting x into equation (1), we will get the value of y.
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Why might algebra tiles not be a good tool to use to factor x2 + 18x + 80? Explain.
Algebra tiles would not be a good tool to use to factor the trinomial because you would need to drag an x-squared tile, 18 x-tiles, and 80 plus tiles. That is a total of 99 tiles. It would take a lot of time to drag that many tiles on the board and there might not be enough space to hold all of them. You would also need to determine how to arrange all those tiles to make a rectangle. Since 80 is a multiple of 10, you might recognize that 10 and 8 are the factors that add to 18, which would give you the values to use in the X method.
please show work along with answer:
[tex] \frac{1 + \tan(x) }{1 + \cot(x) } [/tex]
A zoo has 3 mammals for every 5 reptiles. If the zoo has 72 mammals, how many reptiles does it have? [Type your answer as a number.]
The length of a rectangle is 5 cm more than twice its width. find the largest possible if the perimeter is at most 64 cm
On anne's bicycle, the ratio of pedal turns to rear-wheel turns in second gear is 4 to 7. if her rear wheel turns 875 times per mile,how many times does she turn the pedal in one mile?hint:set up and solve as a propportion to find x.
y=x+2;x=-3 solve each system by graphing step by step
what is the solution to 7ln(x+2.8)=11.2
Strike out bowling balls produces 800 bowling balls per day using 2 workers who each work 8 hours per day. what is strike out's productivity?
what is the equation of the graphed line in point-slope form?
a. y – 1 = (x + 3)
b. y – 1 = (x – 3)
c. y + 1 = (x – 3)
d. y + 1 = (x + 3)
Answer:
[tex]y-1 = \frac{2}{3}(x-3)[/tex]
Step-by-step explanation:
To find the equation of graphed line we pick two points from the line
(3,1) and (-3,-3)
Equation of a line is y=mx+b
where 'm' is the slope and b is the y intercept
slope [tex]m= \frac{y2-y1}{x2-x1} =\frac{1+3}{3+3} = \frac{2}{3}[/tex]
we use point slope formula
y-y1= m(x-x1)
here point(x1,y1) is (3,1) and slope m = 2/3
Plug in all the value
[tex]y-1 = \frac{2}{3} (x-3)[/tex]
Evaluate BC for A = 5, B = -4, and C = 2.
Answer: -8
Step-by-step explanation: Substitute the value of the variable into the expression and then simplify you should get the answer -8
BC= (-4)(2)=-8
How do you solve rearranging equations
Let g(x)=2x and h(x)=x^2+4
(g o h)(0)
Solve for x. x3 = 343 A) 6 B) 7 C) 8 D) 9
The value of x is 7 .
Hence the correct option B .
Given: " x³ = 343
Solve for x,
Rewriting x³ = 343
∛(343) = 7
7³ = 7 × 7 × 7 = 343 .
7³ = 7 × 7 × 7
= 49 * 7
= 343
Therefore correct option is B .
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Alex sells cars at Keith Palmer Ford. He earn$400 a week plus $150 per car he sells. if he earn $1450 last week, how many cars did he sell? brainly
Find the percent change from 48 to 228. Tell whether it is a percent increase or decrease. If necessary, round your answer to the nearest percent.
Which formula gives the coordinates of the midpoint of the segment connecting points (a,
b.and (c, d)?
Answer:
Formula that gives coordinates of the mid point of the segment connecting is [tex](\frac{a+c}{2},\frac{b+d}{2})[/tex]
Step-by-step explanation:
Given point are ( a , b ) and ( c , d )
To find : Coordinates of the mid point of the segment connecting given points.
We know that if point are [tex](x_1,y_1)\:\:and\:\:(x_2,y_2)[/tex]
then coordinate of the midpoints given by [tex](\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]
So, Coordinates of the given points = [tex](\frac{a+c}{2},\frac{b+d}{2})[/tex]
Therefore, Formula that gives coordinates of the mid point of the segment connecting is [tex](\frac{a+c}{2},\frac{b+d}{2})[/tex]
What numbers have the absolute value of 1/2
A 20.0 kg sled is being pulled across a horizontal surface at constant velocity. The pulling force has a magnitude of 80.0N and is directed at an angle of 30.0º above the horizontal. Determine the coefficient of kinetic friction.
The coefficient of kinetic friction is 0.58
To determine the coefficient of kinetic friction [tex](\(\mu_k\))[/tex], we can use the following approach:
1. Identify the horizontal component of the pulling force [tex](\(F_{\text{pull, horizontal}}\))[/tex] and set it equal to the force of kinetic friction [tex](\(f_k\))[/tex].
2. The equation for the horizontal component of the pulling force is:
[tex]\[ F_{\text{pull, horizontal}} = F_{\text{pull}} \cdot \cos(30^\circ) \][/tex]
3. The equation for the force of kinetic friction is:
[tex]\[ f_k = \mu_k \cdot N \][/tex]
4. Since the sled is on a horizontal surface, the normal force [tex](\(N\))[/tex] is equal to the weight of the sled [tex](\(m \cdot g\))[/tex], where m is the mass of the sled and g is the acceleration due to gravity.
Putting these equations together and setting them equal to each other because the sled is moving at constant velocity, we get:
[tex]\[ F_{\text{pull}} \cdot \cos(30^\circ) = \mu_k \cdot m \cdot g \][/tex]
Now, substitute the given values:
[tex]\[ 80 \cdot \cos(30^\circ) = \mu_k \cdot 20 \cdot 9.8 \][/tex]
Solve for [tex]\(\mu_k\)[/tex]:
[tex]\[ \mu_k = \frac{80 \cdot \cos(30^\circ)}{20 \cdot 9.8} \][/tex]
Calculating this expression yields:
[tex]\[ \mu_k \approx 0.58 \][/tex]
So, the calculated coefficient of kinetic friction is approximately 0.58, which matches the provided answer.
Complete question:
A 20 kg sled is being pulled across a horizontal force at a constant velocity the pulling force has a magnitude of 80 N and it's directed at an angle of 30° above the horizontal determine the coefficient of kinetic friction.
What is the perimeter of a polygon with vertices at
(−1, 3) , (−1, 6) , (2, 10) , (5, 6) , and (5, 3) ?
Enter your answer in the box. Do not round any side lengths.
we know that
the perimeter of a polygon is the sum of the length sides
in this problem we have five vertices
so
the polygon has five sides
Let
[tex]A(-1,3)\\B(-1,6)\\C(2,10)\\D(5,6)\\E(5,3)[/tex]
the perimeter is equal to
[tex]P=AB+BC+CD+DE+AE[/tex]
The formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
Step 1
Find the distance AB
[tex]A(-1,3)\\B(-1,6)[/tex]
substitute the values in the formula
[tex]d=\sqrt{(6-3)^{2}+(-1+1)^{2}}[/tex]
[tex]d=\sqrt{(3)^{2}+(0)^{2}}[/tex]
[tex]dAB=3\ units[/tex]
Step 2
Find the distance BC
[tex]B(-1,6)\\C(2,10)[/tex]
substitute the values in the formula
[tex]d=\sqrt{(10-6)^{2}+(2+1)^{2}}[/tex]
[tex]d=\sqrt{(4)^{2}+(3)^{2}}[/tex]
[tex]dBC=5\ units[/tex]
Step 3
Find the distance CD
[tex]C(2,10)\\D(5,6)[/tex]
substitute the values in the formula
[tex]d=\sqrt{(6-10)^{2}+(5-2)^{2}}[/tex]
[tex]d=\sqrt{(-4)^{2}+(3)^{2}}[/tex]
[tex]dCD=5\ units[/tex]
Step 4
Find the distance DE
[tex]D(5,6)\\E(5,3)[/tex]
substitute the values in the formula
[tex]d=\sqrt{(3-6)^{2}+(5-5)^{2}}[/tex]
[tex]d=\sqrt{(-3)^{2}+(0)^{2}}[/tex]
[tex]dDE=3\ units[/tex]
Step 5
Find the distance AE
[tex]A(-1,3)\\E(5,3)[/tex]
substitute the values in the formula
[tex]d=\sqrt{(3-3)^{2}+(5+1)^{2}}[/tex]
[tex]d=\sqrt{(0)^{2}+(6)^{2}}[/tex]
[tex]dAE=6\ units[/tex]
Step 6
Find the perimeter
the perimeter is equal to
[tex]P=AB+BC+CD+DE+AE[/tex]
substitute the values
[tex]P=3+5+5+3+6=22\ units[/tex]
therefore
the answer is
the perimeter of the polygon is [tex]22\ units[/tex]
He box plot shows the total amount of time, in minutes, the students of a class spend reading each day: a box plot is titled daily reading time and labeled time (min). the left most point on the number line is 15 and the right most point is 55. the box is labeled 21 on the left edge and 48 on the right edge. a vertical line is drawn inside the rectangle at the point 37. the whiskers are labeled as 16 and 53 what information is provided by the box plot? the mean for the data the median for the data the number of students who provided information the number of students who read for more than 21.5 minutes
Which expressions are equivalent to ? Check all that apply.
To determine if expressions are equivalent, we simplify them or substitute variables with actual values to see if they yield the same result. We simplify by eliminating terms where possible, grouping like terms, and applying mathematical operations.
Explanation:Without the original mathematical expressions, it's difficult to provide direct answers to your question. Normally, we determine whether expressions are equivalent by simplifying them using algebraic rules or substituting variable with actual values to see if they produce the same results.
For example, the expressions 2(3 + 5) and 6 + 10 are equivalent because they both simplify to 16. We identify equivalent expressions by simplifying which includes eliminating terms where possible, grouping like terms, and applying mathematical operations.
Ultimately, the exact process may vary depending on the complexity and specific form of the expressions in question.
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The expressions equivalent to [tex]$\sqrt[3]{128}^x$[/tex] are (c) [tex]$(4 \sqrt[3]{2})^x$[/tex] and (d) [tex]$\left(4\left(2^{\frac{1}{3}}\right)\right)^x$[/tex] due to their compatible structures with the original expression.
To determine which expressions are equivalent to [tex]$\sqrt[3]{128}^x$[/tex], let's simplify the given expression first:
[tex]\[\sqrt[3]{128}^x = 2^x \times \sqrt[3]{2}^x\][/tex]
Now, let's compare this with the provided options:
a. [tex]$128^{\frac{x}{3}}$[/tex] - Not equivalent.
b. [tex]$128^{\frac{3}{x}}$[/tex] - Not equivalent.
c. [tex]$(4 \sqrt[3]{2})^x$[/tex] - Equivalent, as [tex]$4 = 2^{\frac{3}{2}}$[/tex].
d. [tex]$\left(4\left(2^{\frac{1}{3}}\right)\right)^x$[/tex] - Equivalent, as [tex]$2^{\frac{1}{3}} = \sqrt[3]{2}$[/tex].
e. [tex]$(2 \sqrt[3]{4})^x$[/tex] - Not equivalent.
Therefore, the expressions (c) [tex]$(4 \sqrt[3]{2})^x$[/tex] and (d) [tex]$\left(4\left(2^{\frac{1}{3}}\right)\right)^x$[/tex] are equivalent to [tex]$\sqrt[3]{128}^x$[/tex].
Name the five categories food can be grouped into.
For sets a={1,2,3} and b={a,b,c,d}, find the number of functions from a to b,
which is an equivalent form of the expresion 1800(1.2)?
1800=(1/2)
1800=(5/6)
1800=(6/5)
1800=(2/1)
Answer: Third option is correct.
Step-by-step explanation:
Since we have given that
1800(1.2).
We need to find the equivalent form:
we can rewrite 1.2 as [tex]\dfrac{12}{10}[/tex]
After find the lowest term which is [tex]\dfrac{6}{5}[/tex]
[tex]1800(1.2)\\\\=18000(\dfrac{12}{10})\\\\=18000(\dfrac{6}{5})[/tex]
Hence, it is equivalent to [tex]18000(\dfrac{6}{5})[/tex]
Thus, Third option is correct.
Solve for 8x please
Geoff and Trevor each roll a fair six-sided die. What is the probability that the product of the numbers they roll is even?
The probability that the product of the numbers they roll is even is, 2/3
We have to given that,
Geoff and Trevor each roll a fair six-sided die.
Here, Number of possible outcomes for Geoff,
1, 2, 3, 4, 5, 6
And, Number of outcomes for Trevor,
1, 2, 3, 4, 5, 6
Hence, Possible outcomes for product of the numbers they roll is even are,
2 x 1 = 2
2 x 2 = 4
2 x 3 = 6
2 x 4 = 8
2 x 5 = 10
2 x 6 = 12
3 x 2 = 6
3 x 4 = 12
3 x 6 = 18
4 x 1 = 2
4 x 2 = 8
4 x 3 = 12
4 x 4 = 16
4 x 5 = 20
4 x 6 = 24
5 x 2 = 10
5 x 4 = 20
5 x 6 = 30
6 x 1 = 6
6 x 2 = 12
6 x 3 = 18
6 x 4 = 24
6 x 5 = 30
6 x 6 = 36
Hence, Total possible outcomes = 24
And., Total outcomes = 6x 6 = 36
So, the probability that the product of the numbers they roll is even is,
P = 24 / 36
P = 12/18
P = 2/3
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The ______ is the total area drained by a river and its tributaries.
Which algebraic expression has a term with a coefficient of 3?
the correct answer is option (b) 3x² - 7.
The coefficient is the numerical factor in front of the variable. Let's calculate the coefficient for each option:
a) The coefficient of x in 2x is 2, not 3.
b) The coefficient of x² in 3x² is 3, which matches our requirement.
c) The coefficient of x in 4x is 4, not 3.
d) There is no x term in x³ + 2, so the coefficient for x is 0.
Therefore, the correct answer is option (b) 3x² - 7.
In option (b), the term with the coefficient of 3 is 3x². The coefficient of this term is indeed 3 because it's the number multiplied by x squared. The other terms in the expression do not have a coefficient of 3.
In options (a) and (c), the coefficients for the x terms are 2 and 4, respectively, which do not match the requirement.
Option (d) doesn't have an x term; it only has x raised to the power of 3 (x³), and the coefficient for this term is 0.
So, by process of elimination and calculation, we determine that option (b) is the correct answer with the term 3x² having a coefficient of 3.
complete question
Which algebraic expression has a term with a coefficient of 3?
a) 2x + 5
b) 3x² - 7
c) 4x - 3
d) x³ + 2