Answer:
x = 2 or x = 1 or x = -1 or x = 3/2 thus from the answers given only A: applies
Step-by-step explanation:
Solve for x over the real numbers:
2 x^4 - 7 x^3 + 4 x^2 + 7 x - 6 = 0
The left hand side factors into a product with four terms:
(x - 2) (x - 1) (x + 1) (2 x - 3) = 0
Split into four equations:
x - 2 = 0 or x - 1 = 0 or x + 1 = 0 or 2 x - 3 = 0
Add 2 to both sides:
x = 2 or x - 1 = 0 or x + 1 = 0 or 2 x - 3 = 0
Add 1 to both sides:
x = 2 or x = 1 or x + 1 = 0 or 2 x - 3 = 0
Subtract 1 from both sides:
x = 2 or x = 1 or x = -1 or 2 x - 3 = 0
Add 3 to both sides:
x = 2 or x = 1 or x = -1 or 2 x = 3
Divide both sides by 2:
Answer: x = 2 or x = 1 or x = -1 or x = 3/2
The width of a rectangle is fixed at 2yd. For what lengths will the area be at least 4 yd ^2?
My second question is: a rectangle has a perimeter of 8ft. The length is 5ft less than two times the width. Fond the length and width.
Answer:
Length of rectangle ≥ 2 yd.
Step-by-step explanation:
Suppose the length of rectangle = X yd.
Given the width of rectangle = 2 yd.
Area ≥ 4 yd²
Length * width ≥ 4 yd²
2X ≥ 4 yd²
X ≥ 2 yd
So, length of rectangle must be at least 2 yd.
****************************************************************************************
Answer:
length = 1 feet and width = 3 feet.
Step-by-step explanation:
Suppose the width of rectangle = X feet.
then length of rectangle = (2X - 5) feet.
Given the perimeter of rectangle = 8 feet.
The formula is Perimeter = 2 * (length + width)
8 = 2 * (2X - 5 + X)
8 = 2 * (3X - 5)
8 = 6X - 10
6X = 8 + 10 = 18
X = 18/6 = 3.
so 2X - 5 = 2(3) - 5 = 6 - 5 = 1.
Hence, length = 1 feet and width = 3 feet.
A 12-ounce bottle of soda costs $3.60. If the unit price remains the same how much would a 20-ounce bottle of soda cost?
A) $3.00
B) $5.50
C) $6.00
D) $6.50
For this, simply set up a proportion. If 12 oz. costs $3.60, then this means $3.60 per oz, or [tex]\frac{3.6}{12}[/tex]. Now letś make a proportion for 20 oz. Itś asking for how much it would cost if the unit price was the same, which means that the two should have a similar ratio. Because we don´t know how much it costs yet, this means x dollars for a 20 oz. bottle, or [tex]\frac{x}{20}[/tex]. I´ve already mentioned that they two are proportional, so write [tex]\frac{3.6}{12} = \frac{x}{20}[/tex].
To solve, cross multiply.
⇒[tex]12*x=3.6*20[/tex]
⇒[tex]12x=72[/tex]
Isolate variable x.
⇒[tex]\frac{12x}{12} = \frac{72}{12}[/tex]
⇒ x = 6: $6.00 for 20 ounces of soda.
Checking your work:
3.6/12 = 0.3
6/20 = 0.3
This means that theyŕe proportional, and that your answer is correct. Hope this was helpful.
In a right triangle the length of a hypotenuse is c and the length of one leg is a. Find the length of the other leg b, if:
c=6, a=5
34 points to the first one who gets it correct
Answer:
b = sqrt(11)
Step-by-step explanation:
Using the Pythagorean theorem
a^2 + b^2 = c^2
and substituting what we know
5^2 + b^2= 6^2
25 + b^2 = 36
Subtract 25 from each side
25-25 + b^2 = 36-25
b^2 = 11
Take the square root of each side.
sqrt(b^2) = sqrt(11)
b = sqrt(11)
We only take the positive because length must be positive.
Use the Pythagorean theorem
[tex]a^2+b^2=c^2[/tex]
a,b - legs
c - hypotenuse
We have c = 6 and a = 5. Substitute:
[tex]5^2+b^2=6^2[/tex]
[tex]25+b^2=36[/tex] subtract 25 from both sides
[tex]b^2=11\to \boxed{b=\sqrt{11}}[/tex]
if i √ 1 what is the value of i 2
Answer:
I is the √-1 so it would be √-2 as your answer
Step-by-step explanation:
If the value of i = [tex]\sqrt{1}[/tex] then value of i² = 1.
What are surds and indices ?When we raise numbers to powers they are either called surds when we raise powers which are greater than zero but less than 1 in fraction from.
We call indices when we raise powers to which are greater than 1.
Indices make the base larger after simplification and surds make the bases smaller after simplification.
According to the given question i = [tex]\sqrt{1}[/tex].
∴ The value of i² is i×i = [tex]\sqrt{1}[/tex] × [tex]\sqrt{1}[/tex] = [tex]1^\frac{1}{2}[/tex] × [tex]1^\frac{1}{2}[/tex] = [tex]1^[\frac{1}{2}+\frac{1}{2}][/tex] = 1¹ = 1.
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You and some friends rent a limousine for a formal reception. The bill for the evening is $65.00. A tax of 7% will be added to your total, and you want to tip the chauffeur for his excellent driving. You decide to leave him a tip that is 20% of the bill before tax is added. How much will be paid in total?
A. 92.00
B.91.00
C. 85.50
D. 82.55
Answer:
D YEET
Step-by-step explanation:
3 pounds of peaches cost $6. how many pounds of peaches could be bought for $24. find the algebraic equation
Answer:
Step-by-step explanation:The algebraic equation is 24/6*3 which will give you 12 pounds
Answer:
Equation
2x = 24
Step-by-step explanation:
3 pounds of peaches cost $6
so each pound = $6/3 = $2
so if you have $24 then $24/ 2 = 12 pounds
Let x = # of pounds of peaches
Equation
2x = 24
Two lawn-mowing services are compared. The monthly cost, y dollars, as compared to the number of times the yard is mowed, x. The monthly cost of Service a is represented by y = 30x+20. The graph of service b costs goes through (0,0) and (5,150). how do these two services differ?
Answer:
Service a charges $30 per mow plus an additional $20 flat fee each month, however, Service b only charges $30 per mow, so Service b would be cheaper.
Step-by-step explanation:
This question is asking you to compare costs using linear equations. In a linear equation, 'x' represents the independent variable, in this case the number of times the yard is mowed, and 'y' represents the dependent variable, or the monthly cost. 30 is the slope, or rate of change, which in this problem is the cost per time the yard is mowed. In the equation for Service a, we can see that it is a charge of $30 per time, however, there is also an additional fee of $20 - which is our y-intercept. However, Service b has two points (0,0) and (5,150). Using these two points, we can find the slope, or rate, by subtracting the 'y' values over the 'x' values, or (150-0)/(5-0), to get 30. Since Service b has the starting point of (0,0), or cost is $0 when there are 0 lawns mowed, then they do not have a flat fee.
The slope of the line below is 2. Write a point-slope equation of the line using the coordinates of the labeled point( 3,10)
Answer:
Point slope form of the line is [tex]y-10=2(x-3)[/tex]
Step-by-step explanation:
The point-slope form of a line is given as:
[tex]y-y_1=m(x-x_1)[/tex]
Where,
[tex]m[/tex] is the slope, and [tex](x_1,y_1)[/tex] is the x point and y point respectivelyThe question tells us the slope is 2, hence [tex]m=2[/tex] and the point given is (3,10) which means [tex]x_1=3[/tex] and [tex]y_1=10[/tex]. Substituting these values into the point slope form of a line gives us:
[tex]y-(10)=2(x-(3))\\y-10=2(x-3)[/tex]
Hence, point slope form of the line is [tex]y-10=2(x-3)[/tex]
Which equation represents a circle that is concentric with the circle shown but has a radius that is twice as large ?
Answer:
the awnser is c
Step-by-step explanation:
the c
Answer:
Its C
Step-by-step explanation:
I got a 100% on the test
how do i prove am + am = AB
Statement 1: AM is the midpoint of AB
Reason 1: Given
=====================================
Statement 2: AM+MB = AB
Reason 2: Segment Addition Postulate
Further explanation: Basically this idea is where you can break up the line segment into smaller pieces, or glue smaller segments to form a larger segment.
=====================================
Statement 3: AM = MB
Reason 3: Definition of midpoint
Further explanation: The midpoint cuts a line segment in half. The two smaller pieces AM and MB are congruent (ie equal in length)
=====================================
Statement 4: AM + AM = AB
Reason 4: Substitution
Further explanation: We replace the MB in statement 2 with AM. This replacement is possible because of the equation AM = MB in statement 3.
This concludes the proof.
2. Dan and Bob went to the carnival. Dan bought 3 ticket refills and a lunch for $10.35. Bob bought 2 ticket refills and the lunch for $8.35. SHOW YOUR WORK (a) Write a system of equations. Use t for tickets and l for lunch. (b) Graph the equations in the system. (c) Use your graph to estimate how much each item cost.
Answer:
Let t represents for ticket and l represents for lunch.
As per the given statement: Dan bought 3 ticket refills and a lunch for $10.35
then, we have
[tex]3t + l = \$10.35[/tex]
Also, it is given that Bob bought 2 ticket refills and the lunch for $8.35.
⇒[tex]2t + l = \$8.35[/tex]
(a)
System of an equations are:
[tex]3t + l = \$10.35[/tex]
[tex]2t + l = \$8.35[/tex]
(b)
Let x-coordinate represents ticket refills and y-coordinates represents lunch
You can see the graph of the given equation as shown below in the attachment.
(c)
To find the cost of each items;
Using graph to estimate the cost of each items;
then;
Cost of ticket refills(t) = $2
and
Cost of lunch(l) = $4.35
Write the expression in complete factored form 3c(c+3)-4(c+3)
3c(c+3)-4(c+3)=3c^2+9c-4c-12=3c^2+5c-12
The expression in complete factored form is (3c - 4)(c + 3)
What is a complete factored form expression ?A complete factored form is a form of expressing a complex polynomial expression as the products of factors of the polynomial. If we equate the complete factored expression with zero, we get the solutions of the polynomial expression.
Solving the given expression in complete factored form -The expression given is [tex]3c(c + 3) - 4(c + 3)[/tex]
Expanding the given expression [tex]3c^{2} + 9c - 4c - 12[/tex]
= [tex]3c^{2} + 5c - 12[/tex]
= [tex]3c^{2} + 9c - 4c - 12[/tex]
= [tex]3c(c + 3) - 4(c + 3)[/tex]
= [tex](3c - 4)(c + 3)[/tex]
Thus the expression in complete factored form is (3c - 4)(c + 3)
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4x=100 the answer on alegebra 1
Answer:
Its C. 25
Step-by-step explanation:
I just divided 100 by 4
4x = 100 divide both sides by 4
x = 25 → c.
--------------------------
5x = 25 divide both sides by 5
x = 5 → c.
---------------------------
3x + 5 = 17 subtract 5 from both sides
3x = 12 divide both sides by 3
x = 4 → a.
--------------------------
3x + 14 = 11 subtract 14 from both sides
3x = -3 divide both sides by 3
x = -1 → b.
The Girls’ Scouts are sponsoring a cookie sale. If their goal is to raise at least $500.00, how many cookies must they sell at $5.50 each in order to meet that goal? Write and solve an inequality.
Answer:
91 boxes
hope it helps
Step-by-step explanation:
you will divide $500.00 by $5.50 to find you how many cookies need to be sold
500 ÷ 5.50 = 90.9
so they need to sell about 91 boxes in order meet their goal
To check your work you can multiply
5.50 x 91 = $500.50
Using the divison operation, the number of cookies that must be sold in other to meet their target is 91
Target amount to be raised = $500Cost per cookie = $5.50The Number of cookies that must be sold to meet their target can be obtained using the divison operation thus :
Target amount ÷ cost per cookieHence,
Number of cookies to be sold = $500 ÷ 5.50 = 90.90 = 91(nearest whole number)
Therefore, the Number of cookies that must be sold to meet their target is 91.
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Using the number 234.58937 what is the sum of the hundreds digit and the hundredths digit? A) 12 B) 11 C) 10 D) 9 E) 8
Answer:
b
Step-by-step explanation:
add 3 and 8 = 11
Jose and Alexia were lab partners in science class. They needed to weigh three samples of rock to the nearest thousandth. The first sample weighed 3.346 grams, the second weighed 2.479 grams, and the third weighed 9.240 grams. How much did the samples weigh altogether? 15.065 g 11.719 g 5.825 g 0.069 g
Answer: 15.065 grams
Step-by-step explanation:
Given: Jose and Alexia needed to weigh three samples of rock to the nearest thousandth.The weight of the first sample = 3.346 grams
The weight of the second sample = 2.479 grams
The weight of the third sample = 9.240 grams
Add all together such that the total weight=[tex]3.346+2.479+9.240[/tex]
⇒The total weight of the samples = 15.065 grams.
Therefore, the samples weigh 15.065 grams altogether.
Help me please he has the high ground
Answer:
line (3)
Step-by-step explanation:
note that [tex]\frac{x}{4}[/tex] + 3 - 3 = - 12 - 3
should then be [tex]\frac{x}{4}[/tex] = - 14 Not - 9
first error occurs in line (3)
Function f is an exponential function.
By what factor does the output value increase as each input value increases by 1?
Answer:
Multiply the output value by 2 for each input value increases by 1
Step-by-step explanation:
Function f is an exponential function
Since it is an exponential function , we find out common ratio of output first
WE divide second term by first term to get common ratio
[tex]\frac{\frac{1}{16}}{\frac{1}{64}}[/tex]
[tex]\frac{1}{16} * \frac{64}{1}= 4[/tex]
Change in output = 4
Now we find change in input
Input increases by 2 so change in input = 2
Factor that increase the output is [tex]\frac{4}{2} = 2[/tex]
Answer:
If the input value increases by 1, the output value increases by 2.Step-by-step explanation:
The given table represents an exponential function, that means that variables show a sequence which have an increasing factor that we can find by division.
If we divide the second values by the first value, we could find the factor of the exponential function.
[tex]\frac{1}{16}\div \frac{1}{64} =\frac{1}{16} \times \frac{64}{1}=4[/tex]
So, [tex]f(x)[/tex] increases by a factor of 2.
Now, using the table we see that [tex]x[/tex] values increases by a difference of [tex]+2[/tex], not a factor.
At the moment, while the input value increases by 2, the output value increases by 4.
This means that if the input value increases by 1, the output value increases by 2.
Therefore, the answer is 2.
a) 120 is what percentage of 30
b) 30 is 120% of what number
c) what number is 30%of 120
WHOEVER GIVES ME THE RIGHT ANSWER AND A STEP BY STEP EXPLANATION GETS POINTS AND BRAINLIST************************************************************************************************
Answer:
a ) 400 percent
b ) n = 25
c) n= 36
Step-by-step explanation:
Is means equals, of means multiply and percents need to be changed to decimals.
a) 120 is what percentage of 30
120 = P * 30
Divide each side by 30
120/30 =P* 30/30
4 = P
Multiply by 100 to give the percentage
4 * 100
400 percent
b) 30 is 120% of what number
30 = 1.2 * n
Divide each side by 1.2
30/1.2 = 1.2n/1.2
25 = n
c) what number is 30%of 120
n = .3 * 120
n =36
Given: m∠1 = 140°, find m∠6.
A) 40°
B) 50°
C) 90°
D) 140°
Answer:
The answer is A
Step-by-step explanation:
When two parallel lines are crossed by another line the angle of 1 will be equal to 4, 5, and 8. The angle 2 will be equal to 3, 6, and 7. Since a straight line has a degree of 180, the subtracted degree of 180-140=40 which would mean 2=40 which 2=6 so 6=40.
Answer:
40°, A
Step-by-step explanation:
What are we going to do to figure out measure 6?
First of all, we know that measure 5 and measure 6 are equal to 180 degrees.
Second of all, we know that measure 1 and measure five are corresponding angles, which means they are congruent. If measure one is 140 degrees, measure 5 would also be 140 degrees.
So we know that measure 5 and measure 6 are equal to 180 degrees. We can now make an equation...
Let x = measure 6
140° + x = 180° x = 40°Armando sang 2/3 of a song in 3/4 minute. What is the rate of his songs per minute?
Answer:
8/9 of a song per minute
Step-by-step explanation:
We want to find the rate, which is songs per minutes
songs/ minute
2/3 / 3/4
We can use copy dot flip
2/3 * 4/3
8/9 songs per minute
Allison is rolling her hula hoop on the playground. The radius of her hula hoop is 35 cm.
Answer:
The hula hoop rolls 879 \text{ cm}879 cm.
Step-by-step explanation:
I hope its bigger so u can seeeeeeeeeee!!!
Answers:
Gabe needs 30 liters of the 50% solution
Gabe needs 30 liters of the 70% solution
Both answers are 30
==================================
Explanation:
We have two beakers, each of which we don't know how much is inside. Let's call this x and y
x = amount of liquid in the first beaker (water+acid)
y = amount of liquid in the second beaker (water+acid)
We're told that the beakers have a 50% solution and a 70% solution of acid. This means that the first beaker has 0.5*x liters of pure acid, and the second beaker has 0.7*y liters of pure acid. In total, there is 0.5x+0.7y liters of pure acid when we combine the two beakers. This is out of x+y = 60 liters total, which we can solve for y to get y = 60-x. We will use y = 60-x later on when it comes to the substitution step
We can divide the total amount of pure acid (0.5x+0.7y liters) over the total amount of solution (x+y = 60) to get the following
(0.5x+0.7y)/(x+y) = (0.5x+0.7y)/60
We want this to be equal to 0.6 because Gabe wants a 60% solution when everything is said and done, so
(0.5x+0.7y)/60 = 0.60
0.5x+0.7y = 0.60*60 .... multiply both sides by 60
0.5x+0.7y = 36
0.5x+0.7( y ) = 36
0.5x+0.7(60-x) = 36 ........ replace y with 60-x (substitution step)
0.5x+0.7(60)+0.7(-x) = 36 .... distribute
0.5x+42-0.7x = 36
-0.2x+42 = 36
-0.2x = 36-42 .... subtract 42 from both sides
-0.2x = -6
x = -6/(-0.2) .... divide both sides by -0.2
x = 30
He needs 30 liters of the 50% solution
Use this x value to find y
y = 60-x
y = 60-30
y = 30
So he needs 30 liters of the 70% solution
Sooo.... I need some help with my math someone plz help
Answer:
The total area of the two triangles is 100 inches²
Step-by-step explanation:
To solve for the area of a triangle we use the formula [tex]\frac{1}{2} bh[/tex]
(or base*height divided by 2)
First I solved for the area of the blue triangle.
The base is 12 inches and the height is 10 inches.
[tex]\frac{1}{2}[/tex] * 12 * 10 equals 60 inches².
For the orange triangle the base is 8 inches and the height is 10 inches.
[tex]\frac{1}{2}[/tex] * 8 * 10 equals 40 inches².
60in² + 40in² = 100in²
cc has 3/4 gallons of chocolate ice cream left from her birthday party .she ate 1/2 of the chocolate ice cream while watching tv .how much ive crea does she have left?
Answer:
3/8 gallons left
Step-by-step explanation:
she has 0.75 of a gallon
she eats 0.5(0.75) while watching TV
multiply 0.5 by 0.75 to get half of 3/4 of a gallon
0.375 of a gallon is what she has left
or 3/8 of a gallon
Mr. Willis is building a new dock at his lake house that will be 35 feet long. If the blueprints show the dock as 16 inches long, what scale was used to create the blueprint?
Answer:
1:26.25
Step-by-step explanation:
Scale = 16 in:35 ft
Convert 35 ft to inches
1 ft = 12 in
35 × 12/1 = 420 in
Scale = 16 in:420 in Divide each term by 16
Scale = 1:26.25
The scale used to create the blueprint for Mr. Willis's dock is 1:26.25, meaning that each inch on the blueprint represents 26.25 inches of the actual dock.
The actual dock is 35 feet long, and there are 12 inches in a foot, so the dock is 35 feet × 12 inches/foot = 420 inches long. The blueprint shows the dock as 16 inches long. Therefore, we use the scale factor formula:
scale factor = blueprint length / actual length
The scale factor is 16 inches / 420 inches, which simplifies to 1/26.25. Thus, the blueprint is drawn at a scale of 1:26.25, meaning that 1 inch on the blueprint represents 26.25 inches in the actual size.
A creative group of students produces a reality television show that features various aspects of college and dorm life. Once the show begins airing on the university's public access cable channel, the function shown below represents the number of weeks that pass until x percent of the campus is watching the show. Compute w(50) to one decimal place, and interpret the result in the context of this problem.
w(x)=(x+125)^1/3
A. It will be about 6 weeks until 50 percent of the campus is watching the show.
B. It will be about 5.7 weeks until 60 percent of the campus is watching the show.
C. It will be about 5.6 weeks until 50 percent of the campus is watching the show.
D. It will be about 5.5 weeks until 50 percent of the campus is watching the show.
Answer:
Option c is correct option
it will be about 5.6 weeks until 50 percent of the campus is watching the show
Step-by-step explanation:
we are given
w(x)=[tex]x+125^{\frac{1}{3} }[/tex]
w(50)=[tex]50+125^{\frac{1}{3} }[/tex]
w(50)=[tex]175^{\frac{1}{3} }[/tex]
w(50)=[tex]\sqrt[3]{175}[/tex]
w(50)=5.59
we have to convert it into one decimal form
5.59=5.6
hence option c is correct option.
Computing w(50) using the provided function yields a value of approximately 5.6, which means it will take about 5.6 weeks for 50 percent of the campus to start watching the student-produced reality show. Thus, the correct answer to the student's question is option (C).
To compute w(50) based on the given function [tex]w(x)=(x+125)^{(1/3)}[/tex], we substitute x with 50:
[tex]w(50) = (50+125)^{(1/3)}[/tex]
Calculate the value inside the parenthesis:
[tex]175^{(1/3)}[/tex]
Taking the cube root of 175 gives us approximately:
5.6
Thus, w(50) ≈ 5.6, and we can interpret this in context by stating:
It will be about 5.6 weeks until 50 percent of the campus is watching the show.
This means the correct answer from the provided options is C. It takes approximately 5.6 weeks for the reality television show produced by the students to reach a viewership of 50 percent of the campus.
plz help undertand this question
Answer:
h=4=30
c=2=60
Hope that help
Which equation could have been used to create this graph
a. y = 4x
b. y = x + 4
c. y = 2x
d.y = x + 2
Answer:
The answer is A
Hoped it helped <3 tell me if I am wrong
Step-by-step explanation:
What’s the answer please
Answer:
Step-by-step explanation:
Answer:
(x, y ) = (5, 4 )
Step-by-step explanation:
given the 2 equations
3x - 2y = 7 → (1)
- 3x + 5y = 5 → (2)
adding the 2 equations term by term will eliminate x
(3x - 3x) + (- 2y + 5y ) = (7 + 5 )
0 + 3y = 12
3y = 12 ( divide both sides by 3 )
y = 4
substitute y = 4 in either of the 2 equations and solve for x
(1 ) : 3x - 8 = 7 ( add 8 to both sides )
3x = 15 ( divide both sides by 3 )
x = 5
solution is (5 , 4 )