Mark incorrectly solved the inequality -4(5/2+3/2x) > 8. His work is shown. Which step shows an error based on the inequality ONLY from the previous step? Help please!!
Answers
Answer : The incorrect step is, (A) step 1: -10 + 6x > 8
Step-by-step explanation :
The given expression is:
[tex]-4(\frac{5}{2}+\frac{3}{2}x)>8[/tex]
Now solving this expression step by step.
First -4 distributed over parentheses.
[tex](-4\times \frac{5}{2})+(-4\times \frac{3}{2}x)>8[/tex]
Now solving bracket term, we get:
[tex]-10-6x>8[/tex]
Now taking like terms together, we get:
[tex]-6x>8+10[/tex]
[tex]-6x>18[/tex]
[tex]-x>3[/tex]
Now multiplying this expression by (-1), we get:
[tex]x>-3[/tex]
Thus, the incorrect step is, (A) step 1: -10 + 6x > 8
Answer:
A. Step 1: -10 + 6x > 8
Step-by-step explanation:
The correct way:
Step 1: Multiply both sides by [tex]-1[/tex] (reverse the inequality)
[tex]\left(-4\left(\frac{5}{2}+\frac{3}{2}x\right)\right)\left(-1\right)<8\left(-1\right)[/tex]
Step 2: Simplify
[tex]4\left(\frac{5}{2}+\frac{3}{2}x\right)<-8[/tex]
Step 3: Divide both sides by 4
[tex]\frac{4\left(\frac{5}{2}+\frac{3}{2}x\right)}{4}<\frac{-8}{4}[/tex]
Step 4: Simplify
[tex]\frac{5}{2}+\frac{3}{2}x<-2[/tex]
Step 5: Subtract [tex]\frac{5}{2}[/tex] from both sides
[tex]\frac{5}{2}+\frac{3}{2}x-\frac{5}{2}<-2-\frac{5}{2}[/tex]
Step 6: Simplify
[tex]\frac{3}{2}x<-\frac{9}{2}[/tex]
Step 7: Multiply both sides by 2
[tex]2\cdot \frac{3}{2}x<2\left(-\frac{9}{2}\right)[/tex]
Step 8: Simplify
[tex]3x<-9[/tex]
Step 9: Divide both sides by 3
[tex]\frac{3x}{3}<\frac{-9}{3}[/tex]
Step 10: Simplify
[tex]x<-3[/tex]
Related Questions
Using inductive reasoning, determine the next two terms in each sequence. -3, 5, -7, 9, , A, C, F, J, , Blank 1: Blank 2: Blank 3: Blank 4:
Answers
Answer:
A = -11
C = 13
F = -15
J = 17
Step-by-step explanation:
Inductive reasoning is the use of observations to draw a conclusion.
The sequence of numbers in this problem is:
-3, 5, -7, 9, ...
A pattern is observed and that pattern is:
(n + 1) th term = |nth term| + 2 (with alternating negative signs)
for instance if (n+1)th term = 2nd term; nth term = 1st term
2nd term = |1st term| + 2
2nd term = |-3| + 2 = 5 (no negative sign since previous term had negative)
-3rd term = |5| + 2 = -7 (negative sign because the previous term was positive)
4th term = |-7| + 2 = 9 (no negative sign since previous term had negative)
-5th term (A)= |9| + 2 = - 11 (negative sign because the previous term was positive)
6th term (C) = |-11| + 2 = 13 (no negative sign since previous term had negative)
if you use the same sequence for F and J, you will get:
F = -15
J = 17
you should try them out to see if you will get the same solution.
A group of boys went on a camping trip. They spent the night in 5 tents and 4 cabins. There were 9 boys in each tent and 7 boys in each cabin. How many boys went on the trip?
Answers
Answer:
Step-by-step explanation:
In a tent, there are nine boys.
There were five tents.
5 tents containing 9 boys can equal 45 boys.
(5 x 9 = 45)
In a cabin, there are seven boys.
There were four cabins.
4 cabins containing 7 boys can equal 28 boys.
(4 x 7 = 28)
Now, to find all the boys, add the numbers together.
28 boys with 45 boys will equal 73 boys.
Please check my answer for no one, not even me is right.
Good luck :)
Max drove 460 miles in 8 hours at a constant speed. How long would it take him to drive 661.25 miles at that speeds?
Answers
Answer:
106
Step-by-step explanation:
Sksjwisjsjsoansnsan just to get points so give it a thanks thing ty
Answer:
x=11.5hours
Step-by-step explanation:
661.25miles÷57.5mph=11.5hours
Can someone help me with part a?
Answers
Answer:
[tex]F(x)=\left\{\begin{array}{cl}15(40-x)&\text{if $0<x<40$}\\0&\text{if $40\le x\le65$}\\15(x-65)&\text{if $x>65$}\end{array}\right.[/tex]
Step-by-step explanation:
(a) For x below 40, the number of miles per hour below 40 is (40-x). Then the fine for that speed is 15(40 -x).
For x between limits, the fine is zero.
For x above 65, the number of miles per hour above 65 is (x-65). Then the fine for that speed is 15(x -65).
[tex]F(x)=\left\{\begin{array}{cl}15(40-x)&\text{if $0<x<40$}\\0&\text{if $40\le x\le65$}\\15(x-65)&\text{if $x>65$}\end{array}\right.[/tex]
Is 7,548,123 rational or irrational
Answers
Answer:
irrational number
Step-by-step explanation:
Answer:
I'm pretty sure its rational.
Step-by-step explanation:
Rational, I'm pretty sure is like above negative numbers. Irrational is like negative numbers, and yeah...I could be wrong. But I'm sure its rational.
Solve for c .
A(c+b)=d
answer choices are in the pic
Answers
Answer:
A(c+b)=d.
Ac+Ab=d.
Ac=d-Ab.
Divide through by A.
c=d-ab/a.
Option A.
Steps to solve:
a(c + b) = d
~Distribute
ac + ab = d
~Subtract ab to both sides
ac = d - ab
~Divide a to both sides
c = d-ab/a (Option 1)
Best of Luck!
side length of 216 cubic yards
Answers
Answer:
6 yards
Step-by-step explanation:
a³ = 216
a = ∛ 216
= 6 yards
Answer:
6 yards
Step-by-step explanation:
The volume of a cube can be found using the following formula.
[tex]v= s^3[/tex]
We know the volume is 216 cubic yards, so we can substitute 216 yd³ in for v.
[tex]216 yd^3=s^3[/tex]
We want to find the side length. Therefore, we must isolate the variable, s, on one side of the equation.
s is being cubed. The inverse of cubed is the cube root. Take the cube root of both sides of the equation.
[tex]\sqrt[3]{216 yd^3}=\sqrt[3]{s^3}[/tex]
[tex]\sqrt[3]{216yd^3}=s[/tex]
[tex]6yd=6[/tex]
The side length of the cube is 6 yards.
what is the sum of the arithmetic series: s10 = -20, d = 4, a1 =?
Answers
Answer:
first term a1 is -40.
Step-by-step explanation:
in an arithmetic series,
sum of first term terms (S10) = -20
Common difference (d) = 4
first term (a)= ?
number of terms (n)= 10
now,
S10 =( n÷2) [a1 +(n-1) d]
or, -20 = (10÷2) [a1 + (10-1) 4]
or, -20 = 5 ( a1 + 36)
or, -4 = a1 + 36
or, a1 = -40
[tex]\blue\star[/tex]s10 = -20
[tex]\blue\star[/tex]n = 10
[tex]\blue\star[/tex] an = -20
[tex] \green\star[/tex] solution
[tex] \green\star[/tex]s10 = n\2 [a+(n-1)d]
[tex] \green\star[/tex]-20 = 10a2[a+(10-1)4]
[tex] \green\star[/tex]-4 = a +36
[tex] \green\star[/tex]a1 = -40
[tex]\small\boxed{a = -40}[/tex]
Hope it helps.
Hope it helps
a garden is in the shape of a rhombus whose each side is 15 and it's one of two diagonal each 24 find the area of Garden
Answers
Answer:
Hey there!
A=[tex]0.5p\sqrt{4a^2-p^2}[/tex]
A=216
Hope this helps :)
What is the slope of
3y = -4x + 6
Answers
Answer:
Hey there!
3y=-4x+6
y=-4/3x+2
Thus, the slope is -4/3.
Hope this helps :)
Answer:
the slope is -4/3
Step-by-step explanation:
3y = -4x + 6
y=-4/3 x +6/3
y=-4/3 x+2
the slope is -4/3
Elliott put 7 cups of tea in to a jar. How many more cups of tea does he need to fill up the jar? Capacity: 4 quarts (1 quart = 4 cups)
Answers
Answer:
9 cups
Step-by-step explanation:
1 quart= 4 cups
4 quart= ? cups (crisscross)
4 quart=16 cups
16-7= 9 cups
Average Weight Animal At Birth (g) Adult Female(g) Adult Male (g) Hamster 2 120 110 Guinea pig 65 800 1,030 Rat 7 265 470 On average, a hamster at birth weighs 2 3 the weight of a gerbil at birth. Enter and solve an equation to find the average weight of a gerbil at birth. Let g represent your variable. The equation is . The average weight of a gerbil at birth is g.
Answers
Answer:
The answer is below
Step-by-step explanation:
An equation is a mathematical statement that shows the equality between two expressions.
From the table, the average weight of the hamster at birth is 2 grams. The average weight of gerbil at birth is 2/3 of that of hamster. Let g represents the weight of the gerbil at birth, hence the weight can be gotten by solving the equation:
2/3 of hamster weight at birth = Average weight of gerbil at birth
2/3 × 2 grams = g
g = 2/3 × 2 grams = 4/3 grams = 1.33 grams
The average weight of gerbil at birth = 1.33 grams
f(x)=x2-x find f (3)
Answers
Answer:
f(3) =6
Step-by-step explanation:
[tex]f(x) =x^2 -x\\\\f(3) = ?\\\\f(3) = (3)^2 -3\\f(3) = 9-3\\f(3) =6[/tex]
Answer:
[tex]\huge \boxed{\sf{f(3)=6}}[/tex]
Step-by-step explanation:
[tex]\sf f(x)=x^2-x[/tex]
For f(3), the input or x value is 3.
[tex]\sf f(3)=3^2-3[/tex]
Evaluate the expression.
[tex]\sf f(3)=9-3[/tex]
[tex]\sf f(3)=6[/tex]
point w is on line segment VX. Given vx=4x, vw=3x and wx=5 determine the numerical length of vx
Answers
Answer:
Numerical length of VX = 20
Step-by-step explanation:
Given that VX is a line segment which has a point W on it.
Kindly refer to the attached diagram for the given points.
We are also given the following dimensions:
[tex]VX=4x\\VW=3x\ and \\WX=5[/tex]
To find:
Numerical length of VX = ?
Solution:
As we can clearly see from the attached diagram:
[tex]VX = VW + WX[/tex]
Putting the given values:
[tex]4x=3x+5[/tex]
Now, let us solve for [tex]x[/tex] and then will put the value of [tex]x[/tex] back to find the numerical value of VX.
[tex]\Rightarrow 4x-3x=5\\\Rightarrow x =5[/tex]
Now,
[tex]VX = 4 \times x = 4\times 5 =\bold{20}[/tex]
Therefore, numerical value of VX is 20.
What is the difference between 6^ and ^ 6 ?
Answers
what is: −6 − (−4)? i need to know
Answers
Answer:
-2
Step-by-step explanation:
-6-(-4)
-6+4
-2
Answer:
-2
Step-by-step explanation:
Make it simpler: -6 + 4-6 + 4 = -2Why:
When you subtract a negative, it automatically becomes a positive. That's why when we were making it simpler above, we canceled out the two minus signs (subtractions sign and negative sign) to make a positive 4. That's why we added a positive instead of subtracting a negative.A negative plus a positive will get bigger. That's why -6 + 4 = -2. The -2 is larger than -6 when you look at it on a number line. It's closer to 0 and the positives.Which properties can be used to solve 7y − 15 = −29? Select all that apply.
Answers
Answer:
addition property of equality
inverse property of multiplication
Step-by-step explanation:
7y − 15 = −29
Add 15 to each side using the addition property of equality
7y -15+15 = -29+15
7y = -14
Divide each side by 7 using the inverse property of multiplication
7y/7 = -14/7
y =2
Answer:
[tex]\Large \boxed{\mathrm{Addition \ Property \ of \ Equality}} \\\\\\ \Large \boxed{\mathrm{Inverse \ Property \ of \ Multiplication}}[/tex]
Step-by-step explanation:
[tex]\sf 7y-15=-29[/tex]
Using the additive property of equality, we add 15 to both sides of the equation.
[tex]\sf 7y-15+15=-29+15[/tex]
[tex]\sf 7y=-14[/tex]
Using the inverse property of multiplication, we divide both sides of the equation by 7.
[tex]\displaystyle \sf \frac{7y}{7} =\frac{-14}{7}[/tex]
[tex]\sf y = -2[/tex]
- = 0.393 as a fraction?
Answers
Answer:
The answer is 393/1000
Step-by-step explanation:
Answer:
131/333 is the correct answer
Step-by-step explanation:
i Find a rational number between -1/2 and 3/4 ?
Answers
Answer:
5/8
Step-by-step explanation:
Find the rational number half way between 1/2 and 3/4
First add 1/2 and 3/4
1/2 + 3/4 = 2/4 + 3/4 = 5/4
Next, divide this sum by 2
5/4 divided by 2/1 = 5/4 * 1/2 = 5/8
5/8 is half from 1/2 and 3/4
1/2 < 5/8 > 3/4
POLYNOMIALS
1. Find a quadratic polynomial whose zeroes are 3 and -5
Answers
Answer:
y = x² + 2x - 15
Step-by-step explanation:
Given the zeros are x = 3 and x = - 5 then the factors are (x - 3) and (x + 5)
The polynomial is then the product of its factors, thus
y = (x - 3)(x + 5) ← expand using FOIL
y = x² + 2x - 15
Explicit equation:
Recursive:
y = 3x + 7
now = previous term + 3
50
term #
1
2
value
10
13
...
Find the value of the 50th term.
Explanation:
Answers
Answer:
50th term = 157
Step-by-step explanation:
Explicit equation for the given table is,
y = 3x + 7
And recursive formula is,
Now = previous + 3
To find the 50th term explicit formula should be used because it will be very difficult to find all 50 terms with the use of recursive formula.
From explicit formula,
y = 3x + 7
y = 3(50) + 7
= 157
Therefore, 50th term of the given table will be 157.
Help please 45³+78-64
Answers
Answer:
91267
Step-by-step explanation:
Please help me whoever does it first will get brainliest!!! a) Write a ratio of girls to boys in three ways b) Write an equivalent ratio to the one you wrote in part a. c) Write the ratio of boys to girls in simplest form
Answers
Answer:
see below (I hope this helps!)
Step-by-step explanation:
a) There are 20 girls and 16 boys so three different ways to write the ratio could be 20:16, 20 / 16 or, in verbal form, 20 to 16.
b) An equivalent ratio to 20:16 is 10:8, all we do to get this is divide the ratio by 2.
c) Since there are 16 boys and 20 girls, the ratio is 16:20 which simplifies to 4:5.
How many oranges equal 6 cups of juice?
Answers
Answer:
1/3
Because 1/3 if divide into two, it'll be 0.5/3 but if the question says that the answer have to be in whole number, that means it must be 1/6.
Answer:12
Step-by-step explanation:
because it will take 2 to make a cup
What type of number is 0.25726?
A) Rational, specifically an integer
B) Rational, not an integer
C) Irrational
Answers
Answer:
B. Rational, not an integer
4) Given that x is an integar
find the three greatest value
of x which satisfies the lines
inequality 7x < 2x - 13
Answers
Answer:
The three greatest are -3, -4, -5
Step-by-step explanation:
7x < 2x - 13
Subtract 2x from each side
7x-2x < 2x-2x - 13
5x < -13
Divide by 5
5x/5 < - 13/5
x < - 2 3/5
Since x is an integer
-3 is the largest integer that fits the inequality
The three greatest are -3, -4, -5
write the polynomial the product and sum of whose zeroes are -9/2 and-3/2
Answers
Answer:
y = 2x² + 3x - 9
Step-by-step explanation:
Given αβ = - [tex]\frac{9}{2}[/tex] = [tex]\frac{c}{a}[/tex]
and α + β = - [tex]\frac{3}{2}[/tex] = - [tex]\frac{b}{a}[/tex]
Then a = 2, b = 3 and c = - 9, thus
y = 2x² + 3x - 9
Find the volume of a box with a height that is 4 inches less than the
length and a width equal to the length. Let x represent the length of the
box. (Formula for volume of a rectangular prism: V equals L times W
times H where L is length, W is width, H is height of the rectangular
prism)
Answers
Answer:
Volume of the box = x^3 - 4x^2
Step-by-step explanation:
V = L × W × H
Where,
V = volume of the rectangular prism
L= Length
W = Width
H = Height
volume of the rectangular prism = length × width × height
Length = x
Width= length = x
Height = x - 4
V = L × W × H
= x * x * (x - 4)
= x^2 (x - 4)
= x^3 - 4x^2
V = x^3 - 4x^2
Volume of the box = x^3 - 4x^2
?
3k12 + 23k4 – 18k? _71
Answers
Answer:
Step-by-step explanation:
Something
1.414 is an ? for the square root of 2
Answers
Answer:
1.999396
Step-by-step explanation:
square of 1.414=1.999396
square root of 1.999396=1.414