Graphs of Polynomial Functions Gizmo
5 Answer Review
1. What are the degree and leading coefficient of the function y=4x2-3x+7?
A. degree=4 leading coefficient=2
B. degree=2 leading coefficient=4
C. degree=2 leading coefficient=7
D. degree=3 leading coefficient=4
2. What is the lowest degree of the function graphed here? (image is attached to this)
A. 1
B. 2
C. 3
D. 4
3. what is the maximum of x-intercepts that can be found on a graph with equation y=ax5+cx2+f? (the values a, c, and f are real numbers)
A. 2
B. 3
C. 4
D. 5
4. Which polynomial function has a y-intercept of 3?
A. y=2x4+x2-3
B. y=3x2+4
C. y=-4x7-5x+3
D. y=9x3+3x2
5. What is the end behavior of y=-2x13+25x8-3 as x approaches infinity?
a. y=-3
b. y=13
c. y approaches infinity
d. y approaches negative infinity
Answers
QUESTION 1
The given polynomial function is [tex]y=4x^2-3x+7[/tex]
The degree of the polynomial is the exponent on the leading term of the polynomial after the polynomial has been written in descending powers of [tex]x[/tex].
The leading term is [tex]4x^2[/tex] the exponent of [tex]x[/tex] in this term is [tex]2[/tex], hence the degree is 2.
The coefficient of this term is the leading coefficient which is [tex]4[/tex].
The correct answer is B.
QUESTION 2
The function graphed has two x intercepts.
The first x intercept has a multiplicity that is even. The least positive even integer is 2.
The second x intercept has a multiplicity that is odd.
The least positive odd integer is 1.
Therefore the lowest degree is the sum of the two least values which is
[tex]2+1=3[/tex]
The correct answer is C
QUESTION 3
The given polynomial function is [tex]y=ax^5+cx^2+f[/tex], where [tex]a,c[/tex] and [tex]f[/tex] are real numbers.
The x intercepts are the roots of the polynomial and we know the maximum number of real roots a polynomial of degree 5 can have is 5.
The maximum number of the x-intercepts of the polynomial is therefore 5.
The correct answer is D
QUESTION 4
To find the y-intercept, we substitute [tex]x=0[/tex] into each polynomial function.
The first function is [tex]y=2x^4+x^2-3[/tex]
When [tex]x=0[/tex], [tex]y=2(0)^4+(0)^2-3=-3[/tex]
The y-intercept is -3
The second function is [tex]y=3x^2+4[/tex].
When [tex]x=0[/tex], [tex]y=3(0)^2+4=4[/tex].
The y-intercept is 4
The third function is [tex]y=-4x^7-5x+3[/tex], when [tex]x=0[/tex],
[tex]y=-4(0)^7-5(0)+3=3[/tex]
The y-intercept is 3
The fourth function is [tex]y=9x^3+3x^2[/tex]
When [tex]x=0[/tex], [tex]y=9(0)^3+3(0)^2=0[/tex]
The y-intercept is 0
The correct answer is C.
QUESTION 5
The given polynomial function is [tex]y=-2x^{13}+25x^8-3[/tex].
This is already in standard form.
The degree of the polynomial is 13, which is odd.
The graph of the polynomial will rise at one end and fall at the other end.
The leading coefficient is negative, so the graph rises on the left and falls on the right.
Therefore as x approaches infinity, y will be approaching negative infinity.
The correct answer is D
The answers to the questions are as follows:
1. The correct option is B. degree=2 leading coefficient=4.
2. The correct option is c. 3. The lowest degree of the function graphed here is 3.
3.The correct option is D. 5.
4. The correct option is C. [tex]\( y = -4x^7 - 5x + 3 \).[/tex]
5.The correct option is d. [tex]\( y \)[/tex] approaches negative infinity.
1. The degree and leading coefficient of the function [tex]\( y = 4x^2 - 3x + 7 \)[/tex]are:
- Degree = 2
- Leading coefficient = 4
Therefore, the correct option is B. degree=2 leading coefficient=4.
The degree of a polynomial is the highest power of the variable [tex]\( x \)[/tex] that appears in the polynomial with a non-zero coefficient. In the given function, the highest power of [tex]\( x \)[/tex] is 2 (in the term [tex]\( 4x^2 \))[/tex], so the degree is 2. The leading coefficient is the coefficient of the term with the highest power, which is 4 in this case.
2. The function graphed has two x intercepts.
The first x intercept has a multiplicity that is even. The least positive even integer is 2.The second x intercept has a multiplicity that is odd.The least positive odd integer is 1.Therefore the lowest degree is the sum of the two least values which is 2+1=3The correct answer is C
3. The maximum number of x-intercepts that can be found on a graph with the equation [tex]\( y = ax^5 + cx^2 + f \)[/tex] is:
- A. 2
- B. 3
- C. 4
- D. 5
The correct option is D. 5.
The degree of the polynomial [tex]\( y = ax^5 + cx^2 + f \)[/tex] is 5, which means it is a fifth-degree polynomial. The maximum number of x-intercepts (real roots) for a polynomial is equal to its degree, provided that the roots are counted with multiplicity and include complex roots. Since we are looking for the maximum number of x-intercepts, we consider the degree of the polynomial, which is 5.
4. The polynomial function that has a y-intercept of 3 is:
- A. [tex]\( y = 2x^4 + x^2 - 3 \)[/tex]
- B. [tex]\( y = 3x^2 + 4 \)[/tex]
- C. [tex]\( y = -4x^7 - 5x + 3 \)[/tex]
- D. [tex]\( y = 9x^3 + 3x^2 \)[/tex]
The correct option is C. [tex]\( y = -4x^7 - 5x + 3 \).[/tex]
5. The end behavior of the function [tex]\( y = -2x^{13} + 25x^8 - 3 \) as \( x \)[/tex] approaches infinity is:
- a. [tex]\( y = -3 \)[/tex]
- b. [tex]\( y = 13 \)[/tex]
- c. [tex]\( y \)[/tex] approaches infinity
- d. [tex]\( y \)[/tex] approaches negative infinity
The correct option is d. [tex]\( y \)[/tex] approaches negative infinity.
Related Questions
The opening balance of one of Jennies 30-day billing cycles for her credit card was $1220, and it remained that amount for the first 10 days of her billing cycle. She then made a purchase for $470, increasing her balance to $1690, where it remained for the next 10 days. Jennie then made a payment of $350, so her balance for the last 10 days of the cycle was $1340. The APR of Jennies credit card is 33%, QUESTION 1: What is her periodic interest rate? QUESTION 2: How much was Jennie charged in interest for the billing Cycle?
Answers
Answer:
1) 2.71%
2) $38.32
Step-by-step explanation:
Opening balance = $1220
Balance after 10 days (after expense) = $1690
Balance after 10 days(after payment) = $1340
APR = 33%
1) Periodic interest rate = APR × [tex]\frac{No. of days in a billing cycle}{365}[/tex]
= 33%× 30/365
= 2.71%
2) Interest charged for first 10 days = [tex]\frac{1220*2.71*\frac{10}{30} }{100}[/tex]
= $11.02
Interst charged for the next 10 days = [tex]\frac{1690*2.71*\frac{10}{30} }{100}[/tex]
= $15.2
Interest charged for the next 10 days = [tex]\frac{1340*2.71*\frac{10}{30} }{100}[/tex]
= $12.10
Total interest for 30 days = 11.02+15.2+12.10
= $38.32
Write an expression for the sequence of operations described below. add q and 10, then subtract r from the result Do not simplify any part of the expression.
Answers
Answer:
q + 10 - r
Step-by-step explanation:
add q and 10 = q + 10
then subtract r from the result = q + 10 - r
Answer:
(q + 10) - r
Step-by-step explanation:
The given verbal expression is " add q and 10, then subtract r from the results."
Add q and 10 = q + 10
subtract r from the result = (q + 10) - r
So, the final expression is (q + 10) - r
In parallelogram ABCD below, line AC is a diagonal, the measure of angle ABC is 40 degrees, and the measure of angle ACD is 57 degrees. What is the measure of angle CAD
Answers
Answer:
The measure of angle CAD is 83 degrees.
Step-by-step explanation:
Given information: ABCD is a parallelogram, AC is a diagonal, [tex]\angle ABC=40^{\circ}[/tex] and [tex]\angle ACD=57^{\circ}[/tex].
The opposite sides of parallelogram are congruent.
The diagonal AC divides the parallelogram in two congruent triangles.
In triangle ABC and ADC,
[tex]AB\cong CD[/tex] (Opposite sides of parallelogram)
[tex]\angle ABC\cong \angle ADC[/tex] (Opposite angles of parallelogram)
[tex]BC\cong DA[/tex] (Opposite sides of parallelogram)
By SAS postulate,
[tex]\triangle ABC\cong \triangle CDA[/tex]
Since we know that opposite angles of parallelogram are equal, therefore
[tex]\angle ABC\cong \angle ADC[/tex]
[tex]\angle ADC=40^{\circ}[/tex]
According to the angle sum property the sum of interior angles of a triangle is 180 degrees.
[tex]\angle CAD+\angle ACD+\angle ADC=180^{\circ}[/tex]
[tex]\angle CAD+57^{\circ}+40^{\circ}=180^{\circ}[/tex]
[tex]\angle CAD=83^{\circ}[/tex]
Therefore the measure of angle CAD is 83 degrees.
The measurement, y, varies directly with regard to another value, x. If y = 9 and x = 24, find x for y = 25.
Answers
Answer:
x=66.667
Step-by-step explanation:
Basically, if y varies directly with a value x, you get an equation of the form y=kx, where k is a constant. To answer the question, first substitute 9 into y, and 24 into x.
9=24k
k=0.375
k is 0.375, so to get x, substitute 0.375 into k and 25 into y
25=0.375x
x=66.667
And we got it!
Final answer:
To find x when y = 25 in a direct variation where y = 9 when x = 24, first find the constant of proportionality (k = 3/8), then use this constant to solve the equation 25 = (3/8)x which yields x ≈ 66.67.
Explanation:
The student's question concerns direct variation, which is a concept where one variable changes in proportion to another variable. In this particular problem, the measure y varies directly with x. Given that y = 9 when x = 24, we can use this information to establish the constant of proportionality k where y = kx.
First, we solve for k using the initial condition:
9 = k * 24
k = 9/24
k = 3/8
Now that we have the constant of proportionality, we can find x when y = 25 by setting up the equation:
25 = (3/8)x
x = 25 * (8/3)
x = 200/3
x ≈ 66.67
Therefore, when y = 25, the value of x is approximately 66.67.
Look at the parallelogram ABCD shown below: The table below shows the steps to prove that if the quadrilateral ABCD is a parallelogram, then its opposite sides are congruent:
Statement Reasons 1 AB is parallel to DC and AD is parallel to BC Definition of parallelogram 2
angle 1 = angle 2, angle 3 = angle 4 If two parallel lines are cut by a transversal then the _______________ are congruent 3
BD = BD Reflexive Property 4
triangles ADB and CBD are congruent If two angles and the included side of a triangle are congruent to the corresponding angles and side of another triangle then the triangles are congruent by ASA postulate 5
AB = DC, AD = BC Corresponding parts of congruent triangles are congruent
Which choice completes the missing information for reason 2 in the chart?
alternate interior angles
corresponding angles
same-side interior angles
vertical angles
Answers
Answer:
The correct option is 1.
Step-by-step explanation:
Statement Reasons
1. AB is parallel to DC and Definition of parallelogram
AD is parallel to BC
2. angle 1 = angle 2, If two parallel lines are cut by a
angle 3 = angle 4 transversal then the alternate
interior angles are congruent
3. BD = BD Reflexive Property
4. [tex]\triangle ADB\cong \triangle CBD[/tex] ASA postulate
5. AB = DC, AD = BC (CPCTC)
If two angles and the included side of a triangle are congruent to the corresponding angles and side of another triangle then the triangles are congruent by ASA postulate.
According to alternate interior angles theorem, two parallel lines are cut by a transversal then the alternate interior angles are congruent.
Therefore option 1 is correct.
nearest millimeter, a cell phone is 76mm long and 42 mm wide. What is the ratio of the width to the length? The ratio of the width to the length
Answers
Answer:
21:38
Step-by-step explanation:
The answer you get is 42:76, but if you simplify it, it's 21:38 by dividing the ratio by 2.
Enter a rational number that is equivalent to
−20/4
Answers
The rational number equivalent to -20/4 is -5.
Explanation:A rational number equivalent to -20/4 is -5. This can be found by dividing the numerator (which is -20) by the denominator (which is 4). The result of this division is -5. Hence, -5 is the rational number equivalent to -20/4.
The number of tickets sold on Friday at a movie theater was 2,000 more than the number of tickets sold on Tuesday. 1,250 tickets were sold on Tuesday. Which integer represents the number of tickets sold on Friday? A) -2,000 B) -1,250 C) 2,000 D) 3,250
Answers
You can think of this question like the photos attached above.
Also, a friendly reminder (I am sure that you know this already though) that variables cannot be capital letters (only lowercase). I used to make (and still make) this mistake a lot when writing equations, so I just thought that this reminder might be helpful.
Hope this helps! Best of luck!
Answer:
The answer is D)
Step-by-step explanation:
A leaky faucet is losing water and is filling a 8-gallon bucket every 25 hours.At this rate,how many gallons of water will the faucet leak in 13 hours?
Answers
Answer:
Proportion states that the two fractions or ratios are equal.
As per the given statement: A leaky faucet is losing water and is filling a 8-gallon bucket every 25 hours.
Let x represents the number of gallons of water that faucet leak in 13 hours.
then by definition of proportion;
[tex]\frac{8}{25} =\frac{x}{13}[/tex]
By cross multiply we get;
[tex]13 \times 8 = 25x[/tex]
Simplify:
[tex]104 = 25x[/tex]
Divide both sides by 25 we get;
[tex]x = \frac{104}{25}[/tex]
Simplify:
x = 4.16
Therefore, 4.16 number of gallons of water will the faucet leak in 13 hours
2x+6=10 is the same as 6+2x=10 this is an example of which algebraic property
Answers
Answer:
Commutative property of algebra.
Step-by-step explanation:
We have been given two expressions:
2x+6=10
And 6+2x=10
This is the commutative property of algebra
which is: a+b=c implies b+a=c
Here, a=2x ,b=6 and c=10
On Comparing the two equations with general form of commutative property we get the required result.
Cataloged 2/3 of new books in shipment. Is she has cataloged 52 books what is the number of books shipped in total
Answers
Answer:
78 books
Step-by-step explanation:
Use proportion: If 52 is 2/3 of the books then number of books shipped = 52 * the inverse of 2/3 which is 52 * 3/2:-
52 * 3/2
= 156/2
= 78 books
Bryson buys a bag of 64 plastic miniature dinosaurs. Could he distribute them equally into six stroke containers and not have any left over?
Answers
Answer:
Yes he will not have any left over
Step-by-step explanation:
because 64 / 6 = 10.666666..
Jen buys sesame bagels and plain bagels. If the ratio of sesame to plain is 1:3 and Jen bought 2 dozen bagels, what percent of bagels are plain? How many bagels are plain? Suppose each plain bagel has 0.53 gram of salt, and each sesame bagel has 0.65 gram. Use a percent to compare the amount of salt in a plain bagel to that in a sesame bagel.
Answers
Answer:
The number of plain bagels are 18 and it is 75% of the total bagels .
The amount of salt in a plain bagel to that in a sesame bagel is 81.5% .
Step-by-step explanation:
Formula
[tex]Percentage = \frac{Part\ value\times 100}{Total\ value}[/tex]
As given
Jen buys sesame bagels and plain bagels. If the ratio of sesame to plain is 1:3 and Jen bought 2 dozen bagels .
As one dozens contains 12 items .
Thus
Total number of bagels bought by Jen = 2 × 12
= 24
Let us assume that the x be the scalar multiple of sesame bagels and plain bagels .
Number of sesame bagels = 1x
Number of plain bagels = 3x
Than the equation becomes
x + 3x = 24
4x = 24
[tex]x = \frac{24}{4}[/tex]
x = 6
Thus
Number of plain bagels = 3 × 6
= 18
Part value = 18
Total value = 24
Putting all the values in the formula
[tex]Percentage = \frac{18\times 100}{24}[/tex]
[tex]Percentage = \frac{1800}{24}[/tex]
Percentage = 75 %
Therefore the number of plain bagels are 18 and it is 75% of the total bagels .
As given
Suppose each plain bagel has 0.53 gram of salt, and each sesame bagel has 0.65 gram.
Part value = 0.53 grams
Total value = 0.65 grams
Putting all the values in the formula
[tex]Percentage = \frac{0.53\times 100}{0.65}[/tex]
[tex]Percentage = \frac{5300}{65}[/tex]
Percentage = 81.5 %
Therefore the amount of salt in a plain bagel to that in a sesame bagel is 81.5% .
The quantity best expressed as -3.2 is ___ .
The quantity best expressed as +5.1 is ___ .
blank one possible answers
3.2 feet above sea level
a withdrawal of $3.20
a profit of $3.20
blank two possible answers
a debt of $5.10
a withdrawal of $5.10
5.1 feet above sea level
18 points !!!
Answers
✿ The Quantity best expressed as -3.2 is a Withdrawal of $3.20
Because :
[tex]\heartsuit[/tex] The Value which is expressed above sea level should be Positive.
[tex]\heartsuit[/tex] Profit is always a Positive
[tex]\heartsuit[/tex] Withdrawal's are Negative
✿ The Quantity best expressed as +5.1 is 5.1 feet above sea level
Because :
[tex]\heartsuit[/tex] The Value which is expressed above sea level should be Positive.
[tex]\heartsuit[/tex] Debt and Withdrawals are always Negative
Answer:
first part : a withdrawal of 3.20
second part : 5.1 feet above sea level
Step-by-step explanation:
unction f is an exponential function
X -2 | 0 | 2 | 4| 6
F(x) 1/8 | ½| 2 |8 | 32
By what factor does the output value increase as each
input value increases by 1?
Answers
Answer:
4
Step-by-step explanation:
As each x value increases by 1, the output values increase by a factor of 4. This means that each y value can be multiplied by 4 to get the next y value.
1/2(4)=2
2(4)=8
8(4)=32
4 is the factor.
The box which measures 70cm X 36cm X 12cm is to be covered by a canvas. How many meters of canvas of width 80cm would be required to cover 150 such boxes.
Answers
Answer:
142.2 meters.
Step-by-step explanation:
We have been given that a box measures 70 cm X 36 cm X 12 cm is to be covered by a canvas.
Let us find total surface area of box using surface area formula of cuboid.
[tex]\text{Total surface area of cuboid}=2(lb+bh+hl)[/tex], where,
[tex]l[/tex] = Length of cuboid,
[tex]b[/tex] = Breadth of cuboid,
[tex]w[/tex] = Width of cuboid.
[tex]\text{Total surface area of box}=2(70\cdot36+36\cdot 12+12\cdot 70)[/tex]
[tex]\text{Total surface area of box}=2(2520+432+840)[/tex]
[tex]\text{Total surface area of box}=2(3792)[/tex]
[tex]\text{Total surface area of box}=7584[/tex]
Therefore, the total surface area of box will be 7584 square cm.
To find the length of canvas that will cover 150 boxes, we will divide total surface area of 150 such boxes by width of canvass as total surface area of canvas will also be the same.
[tex]\text{Width of canvas* Length of canvass}=\text{Total surface area of 150 boxes}[/tex]
[tex]80\text{ cm}\times\text{ Length of canvass}=150\times 7584\text{cm}^2[/tex]
[tex]\text{ Length of canvass}=\frac{150\times 7584\text{ cm}^2}{80\text{ cm}}[/tex]
[tex]\text{ Length of canvass}=\frac{1137600\text{ cm}^2}{80\text{ cm}}[/tex]
[tex]\text{ Length of canvass}=14220\text{ cm}[/tex]
Let us convert the length of canvas into meters by dividing 14220 by 100 as 1 meter equals to 100 cm.
[tex]\text{ Length of canvass}=\frac{14220\text{ cm}}{100\frac{cm}{m}}[/tex]
[tex]\text{ Length of canvass}=\frac{14220\text{ cm}}{100\frac{cm}{m}}[/tex]
[tex]\text{ Length of canvass}=\frac{14220\text{ cm}}{100}\times\frac{m}{cm}[/tex]
[tex]\text{ Length of canvass}=142.20\text{ m}[/tex]
Therefore, 142.2 meters of canvas of width 80 cm required to cover 150 such boxes.
Determine the first four terms of the sequence in which the nth term is...
Answers
Answer:
1/5, 1/6, 1/7, 1/8
Step-by-step explanation:
The formula for the sequence is (n+3)!/ (n+4)!
The first terms uses n=1
a1 = (1+3)!/ (1+4)! = 4!/5! = (4*3*2*1)/(5*4*3*2*1) = 1/5
The first terms uses n=2
a2 = (2+3)!/ (2+4)! = 5!/6! = (5*4*3*2*1)/(6*5*4*3*2*1) = 1/6
The first terms uses n=3
a3 = (3+3)!/ (3+4)! = 6!/7! = (6*5*4*3*2*1)/(7*6*5*4*3*2*1) = 1/7
The first terms uses n=4
a4 = (4+3)!/ (4+4)! = 7!/8! = (7*6*5*4*3*2*1)/(8*7*6*5*4*3*2*1) = 1/8
Answer:
D. 1/5,1/6,1/7,1/8
What is the solution set for the open sentence, using the given replacement set ? 6x?2=10 ; {1, 2, 3, 4} ?
Answers
Answer:
answer is x=2
Step-by-step explanation: 6x2=12-2=10The solution set for the equation 6x - 2 = 10 using the replacement set {1, 2, 3, 4} is {2}, as 2 is the only number in the set that, when substituted into the equation, satisfies it.
The solution set for the open sentence 6x - 2 = 10 using the given replacement set {1, 2, 3, 4} can be found by solving the equation for x and then checking which numbers in the replacement set satisfy the equation.
Add 2 to both sides of the equation: 6x - 2 + 2 = 10 + 2, which simplifies to 6x = 12.Divide both sides by 6: 6x/6 = 12/6, which simplifies to x = 2.Check if x = 2 is within the replacement set: Since 2 is in the set {1, 2, 3, 4}, x = 2 is the solution that belongs to the replacement set.Therefore, the solution set is {2}.
The longest side of a triangle is six more inches than the shortest side. The third side is twice the length of the shortest side of the perimeter of the triangle is 26 units, what's all three lengths of the triangle?
Answers
Answer:
a=5, b=10, c=11
Step-by-step explanation:
a= shortest side
b= "third" side
c= longest side
Equations:
c=6+a
b=2a
a+b+c=26
so we can see there is a in all of the equations, so we can plug all of them into the equation for the perimeter
a+(2a)+(6+a)=26-->4a=20-->a=5
with a, we can plug that into the equations to get b and c
c=6+a-->6+(5)-->c=11
b=2a-->b=2(5)--> b=10
Identify the values of the variables. Give your answers in simplest radical form. HELP PLEASE!!!
Answers
Answer:
sqrt(15)/2 = g
h = sqrt(5) /2
Step-by-step explanation:
We know that sin 30 = opposite / hypotenuse
sin 30 = h/ sqrt(5)
Multiply by sqrt(5) on each side
sqrt(5) sin 30 = h
sqrt(5) (1/2) = h
h = sqrt(5) /2
cos 30 = adjacent/ hypotenuse
cos 30 = g / sqrt(5)
Multiply each side by sqrt(5)
sqrt(5) cos (30 ) = g
sqrt(5) (sqrt(3)/2) = g
sqrt(15)/2 = g
When the sum of 8 and twice a positive number is subtracted from the square of the? number, 0 results. Find the number.
Answers
Answer:
4
Step-by-step explanation:
The equation is
x^2 - (2x + 8) = 0 where x is the number to be found.
removing the parentheses by distributing the negative:-
x^2 - 2x - 8 = 0
(x - 4)(x +2) = 0
x = 4, -2.
The value of x must be 4 because it is positive.
Simplify (in picture)
Answers
[tex]x^2+2x+1=x^2+x+x+1=x(x+1)+1(x+1)=(x+1)(x+1)\\----------------------\\2x+2=2(x+1)\\----------------------\\\\\dfrac{2x+2}{x^2+2x+1}=\dfrac{2(x+1)}{(x+1)(x+1)}\\\\\text{Canceled}\ (x+1)\\\\=\boxed{\dfrac{2}{x+1}}[/tex]
Sammy buys his clothes at super discounts. On saturday he bought shoes regularly priced at $40 for 25% off, and jacket regularly priced at $100 for 30% off before the sales taxe what was the total price of the items sammy bought .Approximately what percent discount did Sammy get on his total purchases
Answers
Answer:
A. $100
B. 29%
Step-by-step explanation:
A. To find total price of the items Sammy bought we will add the price of shoes and jacket after discount.
Let us find price of shoes after 25% discount.
[tex]\text{Price of shoes after discount}=40-(\frac{25}{100}*40)[/tex]
[tex]\text{Price of shoes after discount}=40-(\frac{1}{4}*40)[/tex]
[tex]\text{Price of shoes after discount}=40-10=30[/tex]
Therefore, price of shoes after discount is $30.
Now let us find price of jacket after 30% discount.
[tex]\text{Price of jacket after discount}=100-(\frac{30}{100}*100)[/tex]
[tex]\text{Price of jacket after discount}=100-30[/tex]
[tex]\text{Price of jacket after discount}=70[/tex]
Therefore, price of jacket after discount is $70.
Now let us add both prices to find the total price of the items.
[tex]\text{Total price of items}=30+70[/tex]
[tex]\text{Total price of items}=100[/tex]
Therefore, the total price of the items bought by Sammy is $100.
B. To find the percent discount which Sammy got on his total purchases, we will use percent change formula.
[tex]\text{Percent change}=\frac{\text{Difference}}{\text{Original value}}\times 100[/tex]
Total price without discount= 100+40=140
[tex]\text{Discount percent}=\frac{140-100}{140}\times 100[/tex]
[tex]\text{Discount percent}=\frac{40}{140}\times 100[/tex]
[tex]\text{Discount percent}=0.2857142857142857\times 100[/tex]
[tex]\text{Discount percent}=28.57142857142857\approx 29[/tex]
Therefore, Sammy got approximately 29% discount on his total purchases.
Answer:
Sammy bought a car and got a discount of 2/5 off the original price of $30,000. How much did Sammy pay for the car after the discount?
Step-by-step explanation:
Felicity the clown inflates two balloons in five minutes. Grumpy a clown ties five balloon animals in 12 minutes. They both work at a steady rate. If Felicity maintain this constant rate, how many balloons could she inflate in one hour ?
Answers
Answer:
24 balloons
Step-by-step explanation:
1 hour= 60 min
60 min/ 5 min= 12 min
12 min* 2 balloons= 24 balloons per hour
What about Grumpy?Don't pay attention to Grumpy, it was just to confuse you. We are talking about how fast Felicity can inflate balloons.Answer:
The correct answer is A
Sorry if this is late but hope it helps however finds it
Mr. Fox's had is students identify the sex of each of their frog's while they performing their dissections. There were a total of 46 groups for which there were 19 females and 27 males identified. He has one more group that needs to complete their dissection, the probability that it will be a male is approximately 59% based on the results of the first 46 groups. This is an example of:
A Experimental Probability
B Can not determine
C Theoretical Probability
D Neither
Answers
Answer:
A Experimental Probability
Step-by-step explanation:
The 59 percent is based on the data from the actual data. The theoretical probability is 50 percent for male and 50% and female.
ANSWER THIS PLEASSSSSSSSSS
17. Write a function rule for the following arithmetic sequence and use it to find the 250th term. Show your work.
−3, 1, 5, 9, ….
Function Rule: Determining 250th term:
Answers
First check the difference between terms:
[tex]\{1-(-3),5-1,9-5,\ldots\}=\{4,4,4,\ldots\}[/tex]
So every term differs by 4. The first term in the sequence is [tex]a_1=-3[/tex]. Recursively, the sequence is given by
[tex]\begin{cases}a_1=-3\\a_n=a_{n-1}+4&\text{for }n>1\end{cases}[/tex]
Then
[tex]a_2=a_1+4[/tex]
[tex]a_3=a_2+4=a_1+4(2)[/tex]
[tex]a_4=a_3+4=a_1+4(3)[/tex]
and so on, with the general rule
[tex]a_n=a_1+4(n-1)\implies a_n=4n-7[/tex]
Then the 250th term of the sequence would be
[tex]a_{250}=4(250)-7=993[/tex]
Mr. Grimm is trying to build a playground set in his backyard. Part of the playground set will have a slide. The ladder is 5 feet tall, and the slide is 7 feet long. What is the distance between the ladder and the bottom of the slide?
Answers
Answer:
~5 feet.
Step-by-step explanation:
assuming that it is a right triangle. if a=5 and c=7 then b the other leg is equal to the square root of c squared minus a squared. which equals about 4.9
[tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]
where a and b are sides of the triangle and c is the hypotenuse.
from my image we can see:
[tex]c = 7 \\ b = 5[/tex]
so plugging these numbers into the Pythagorean theorum gives
[tex] {a}^{2} + {b}^{2} = {c}^{2} \\ {a}^{2} + {5}^{2} = {7}^{2} \\ {a}^{2} + 25 = 49 \\ {a}^{2} = 49 - 25 \\ {a}^{2} = 24 \\ a= \sqrt{24} \\ a \: = 4.90[/tex]
so the length from the ladder to the end of the slide is 4.90 feet.
Is the triangle with side lengths of 18cm, 24cm and 30 cm a right triangle ?
Answers
If a, b and c are the lengths of a right triangle and c is the longest side, then:
[tex]a^2+b^2=c^2[/tex]
We have a = 18cm, b = 24cm and c = 30cm. Substitute and check:
[tex]L_s=18^2+24^2=324+576=900\\\\R_s=30^2=900\\\\L_s=R_s[/tex]
Answer: It's the right triangle.Pls help I'm bad at math v.v
Lines m and n are parallel.
Answers
Answer:
The measure of angle 1 is 55.
Step-by-step explanation:
The top angle= 75 because of the vertical angle theorem
The right angle= 50 because of the alternate exterior angle theorem
75+50=125
There are 180 degrees in a triangle so the angle has to equal 55
What are the factors of m^2-6m+6m-36?