The product of two consecutive integers is 420. An equation is written in standard form to solve for the smaller integer by factoring. What is the constant of the quadratic function in this equation?

Answers

Answer 1
Let the smaller integer be x.
The larger integer is x + 1.

x(x + 1) = 420

x^2 + x = 420

x^2 + x - 420 = 0

The constant is -420.

Related Questions

Find the amount paid for the loan.

$2400 at 10.5% for 5 years

Answers

Final answer:

$3,919.24

Explanation:

To calculate the total amount paid for a loan of $2,400 at an interest rate of 10.5% over 5 years, we will assume the interest compounds annually for simplicity. The formula to find the future value of a loan including interest is P(1 + r)^n, where P is the principal amount ($2,400), r is the annual interest rate (10.5% or 0.105), and n is the number of years (5).

Plugging the numbers into the formula gives us $2,400(1 + 0.105)^5. Calculating this gives us approximately $3,919.24. Therefore, the total amount paid for the loan over 5 years would be $3,919.24.

To find the amount paid on a $2400 loan at 10.5% interest for 5 years, calculate the simple interest and add it to the principal. The total interest is $1260, bringing the total repayment amount to $3660 over 5 years.

To find the amount paid for the loan of $2400 at 10.5% interest for 5 years, one would typically use the formula for the compound interest or an installment payment plan depending on whether the loan is paid off in a lump sum at the end of the term or through regular payments over the term. However, you have not specified the method of repayment (lump sum or installments), so let's consider a simple interest scenario which is often used for short-term loans.

The simple interest can be calculated as:

I = PRT

Where:


 I = Interest
 P = Principal amount ($2400)
 R = Annual interest rate (10.5% or 0.105 in decimal)
 T = Time in years (5)

Using the formula:

I = $2400 × 0.105 × 5 = $1260

Therefore, the total interest paid over 5 years is $1260. To find the total amount paid for the loan, add the interest to the principal:

Total Amount Paid = Principal + Interest

Total Amount Paid = $2400 + $1260 = $3660

The borrower would have to pay a total of $3660 after 5 years.

Help! Halfway there. Two square pyramids have the same volume. For the first pyramid, the side length of the base is 16 in and the height is 28. On the 2nd pyramid the height is 112. What is the side length of the base of the 2nd pyramid?,

Answers

Given:

h = height 
s = slant height
a = side length
e = lateral edge length
r = a/2 
V = volume
L = lateral surface area
B = base surface area 
A = total surface area

Pyramid 1. 

h = 28 m
s = 29.1204 m
a = 16 m
e = 30.1993 m
r = 8 m
V = 2389.33 m³
L = 931.854 m2
B = 256 m²
A = 1187.85 m²
Pyramid 2 

h = 112 m
s = 112.071 m
a = 7.99999 m
e = 112.143 m
r = 3.999995 m
V = 2389.33 m³
L = 1793.14 m²
B = 63.9999 m²
A = 1857.14 m²

In your notebook, set up the following addition using a vertical format and find the sum of the given polynomials.

7b + 3, -4b + 5 and -3+2

A.) 10b + 2

B.) 10

C.) 0

D.) b - 8

Please explain.

Answers

Terms containing b are added; terms not containing b are added. The sum of the b terms is 0, because 7-4-3 = 0. That leaves only the constant 3+5+2=10.

Selection B properly describes the sum.

Answer:

Terms containing b are added; terms not containing b are added. The sum of the b terms is 0, because 7-4-3 = 0. That leaves only the constant 3+5+2=10.

Selection B properly describes the sum.

Step-by-step explanation:

PLEASE PLEASE PLEASE PLEASE HELP ME!

suppose ruth ann has 3 routes she can travel between the school to the library and 5 routes from the library to her home. how many routes are there from ruth anns school to her home with a stop at the library.
a. 9
b. 60
c. 15
d. 25

Answers

To find the answer, multiply the number of routes because it gives the number of permutations (choices) you can take. 
There are 3 routes between school and the library.
 There are 5 routes from the library to her home. 
 Therefore, there are 3 x 5 = 15 total routes

Simplify by using fractional exponents.[tex] \sqrt[3]{ x^{2} } [/tex]

Answers

The given expression is:

[tex] \sqrt[3]{ x^{2} } [/tex]

Converting radical sign to fractional exponent:

[tex] ( x^{2} )^{ \frac{1}{3} } [/tex]

Simplifying the expression, we get:

[tex] \sqrt[3]{ x^{2} } = x^{ \frac{2}{3} } [/tex]

A club has members from three grades. It has 36 members from sixth grade, 24 members from seventh grade, and 30 members from eighth grade. What is the ratio of the club's seventh graders to eighth graders?

Answers

There are 24 seventh graders and 30 eight graders, therefore the ratio would be 24/30.

Answer:

the correct answer is 4/5!

have a great day!

10 POINTS + BRAINLIEST ANSWER

The scatterplot below shows the distances and times spent traveling for 22 trips by a driver. What is the time, in hours, of the trip represented by the data point farthest from the line of best fit (not shown)

A. 4

B. 6

C. 8

D. 10

Answers

A AAAAAAAAAAAAAAaaAaaaaaa

A recipe for punch says to use 4 1/2 of lemonade for each cup of ginger ale. If you use 1 2/5 cups of ginger ale, how much lemonade should you use?

Answers

4 1/2 x 1 2/5 = 6.3 (6 3/10) cups

simplify: 27k^5m^8/(4k^3)(9m^2)

Answers

The answer to your question is 3k^2m^6/4

Write a pair of integers whose sum gives
(a) a negative integer (b) zero
(c) an integer smaller than both the integers. (d) an
integer smaller than only one of the integers.
(e) an integer greater than both the integers,

Answers

The pairs below satisfy the five questions. A) -2 & 1. -2 + 1 = -1 B) -2 & 2. -2 + 2 = 0 C) -1 & - 2. -1+ -2 = -3 D) -3 & 1. -3 + 1 = -2 E) 1 & 2. 1 + 2 = 3.

Answer:

The pairs below satisfy the five questions. A) -2 & 1. -2 + 1 = -1 B) -2 & 2. -2 + 2 = 0 C) -1 & - 2. -1+ -2 = -3 D) -3 & 1. -3 + 1 = -2 E) 1 & 2. 1 + 2 = 3.

Step-by-step explanation:

hope this helps have an amazing day

Compare the fraction by using the symbol < , <, or =. a. 4⁄9 _____ 5⁄9 b. 4⁄5 _____ 8⁄10 c. 7⁄12 _____ 7⁄15 d. 3⁄4 _____ 6⁄7

Answers

A. 4/9 < 5/9

B. 4/5 = 8/10

C. 7/12 > 7/15

D. 3/4 < 6/7

Final answer:

To compare fractions, evaluate if they are equal or if one is greater by comparing the numerators and denominators.

a. 4/9 < 5/9

b. 4/5 = 8/10

c.7/12 > 7/15

d.3⁄4 < 6⁄7

Explanation:

In fractions, to compare two fractions, check if the fractions are equal, or if one is greater than the other by comparing the numerators and denominators.

a. 4/9 vs. 5/9: 4/9 < 5/9 since 5 is greater than 4.

b. 4/5 vs. 8/10: 4/5 = 8/10 since they are both equivalent fractions.

c. 7/12 vs. 7/15: 7/12 > 7/15 since 12 is greater than 15.

d. 3/4 vs. 6/7: 3⁄4 < 6⁄7 because converting to decimals, 3⁄4 is 0.75 and 6⁄7 is approximately 0.857, making 6⁄7 larger.

the function f(x)=2^x and g(x)=f(x)+k. if k=2, what can be concluded about the graph?

the graph of g(x) is shifted vertically...

2 units to the left of the graph of f(x)...

Answers

Translations are transformations that change the position of the graph of a function. The general shape of the graph of a function is moved up, down, to the right or to the left. The translations are considered rigid transformations.
 Suppose that k> 0
 To graph y = f (x) + k, move the graph of k units up.
 To graph y = f (x) -k, move the graph of k units down.
 We have then:
 f (x) = 2 ^ x
 g (x) = f (x) + k
 if k = 2
 then,
 the graph of g (x) is shifted vertically 2 units up

 Answer:
 
the graph of g (x) is shifted vertically 2 units up

Answer:

Its shifted verticlly 2 and to the left 2.

Step-by-step explanation:

Its verticlly because when it says 2^x its going up if it said -2^x it would go down.

It goes left because it is 2^x=? so if you put it on  the other side its negative which makes it to the left.

What is the rule for the reflection?
Will mark brainliest!

Answers

When a point is reflected the y coordinate generally tends to stay the same while the x coordinate is the opposite generally leaning towards the negatives. The line y= -x is equal to (-y, -x)

Answer:

Option C is correct.

[tex]r_{y=x} (x, y) \rightarrow (y, x)[/tex]

Step-by-step explanation:

From the given figure:

Coordinate of Triangle ABC are:

A(-2, 1), B(-3, 4) and C(-4, 1)

And

Coordinate of Triangle A'B'C' are:

A'(1, -2), B'(4, -3) and C'(1, -4)

The rule of reflection across the line:

[tex]r_{y=x} (x, y) \rightarrow (y, x)[/tex]

then;

Apply the given rule of reflection on coordinate of triangle ABC

[tex]A(-2, 1) \rightarrow (1, -2) =A'[/tex]

[tex]B(-3, 4) \rightarrow (4, -3) =B'[/tex]

[tex]C(-4, 1) \rightarrow (1, -4) =C'[/tex]

Therefore, the rule of reflection used here is [tex]r_{y=x} (x, y) \rightarrow (y, x)[/tex]

Using a directrix of y = −2 and a focus of (2, 6), what quadratic function is created?

Answers

I believe your answer is: (x-2)^2 = 16(y-2). Hope this helps!!
Hello,

directrix y=-2
focus (2,6)

y=1/(2(6-(-2)) * (x-2)²+(6+(-2))/2
or y=(x-2)²/16+2

A person at ground level measures the angle of elevation to the top of a building to be 74°. If at this point the person is 34 feet away from the base of the building, then how tall is the building?

Please round to the tenths place.
Please show work/steps and provide units with your answer.

Answers

Start by drawing a diagram. 
Mark a line going from the base of the building to the person 34 feet.
Draw another line from the person to the top of the building. Label the angle between the two lines as 74o

Tan(74) = o / a
Tan(74) = o/34
o = 34*Tan (74)
o = 34 * 3.49
o = 118.6

The building is 118.6 feet tall. 

What would a monthly payment be on a purchase of $12000 car at 4.9% for 5 years?

Answers

Answer: it's 225.41 but your answer helped!

Step-by-step explanation:

The monthly payment will be $249

Firstly, we will  calculate the simple interest which will be:

= PRT/100

where,

P = principal = $12000

R = rate = 4.9%

T = time = 5 years

Simple Interest = PRT/100

= ($12000 × 4.9 × 5)/100

= $294000/100

= $2940

Then the total amount to be repaid will be: = Principal + Interest

= $12000 + $2940

= $14940

We'll convert 5 years to months and this will be: = (5 × 12) = 60 months.

The monthly payment will then be:

= $14940/60

= $249

In conclusion, the monthly payment will be $249

Read related link on:

https://brainly.com/question/18860244

barb is making a bead necklace. she strings 1 white bead, then 3 blue beaads, then 1 white bead, and so on. write the numbers for the first eight beads that are white. what is a rule for the pattern.,

Answers

the numbers of first 8 beads which are white are 1,5,9,13,17,21,25,29 think of it as an arithmetic progression here the first term will be 1 cause white was first bead then after 3 blue beads another white added soits position is fifth now the difference would come out as 5-1=4 so now position of next white bead could be predicted by nth term formula of an AP which a+(n-1)d here a is first term which in this case is one and d is difference which here is 4 So nth bead position is 1+(n-1)4

The formula for the area of a triangle is A = 1/2bh, where b is the length of the base and h is the height. The equation solved for h is h =2a/b The formula for the area of a triangle is A = bh, where b is the length of the base and h is the height. The equation solved for h is h = . Find the height of a triangle that has an area of 30 square units and a base measuring

12 units. 3 units 5 units 8 units 9 units

Answers

the height is 5 units, if you want an explanation just say so ^^

the answer is 5 units i know this because i just took a test with this question

Hi guys can you help me factor these two equations?

5x^2-13x-6

4x^4 – 28x^3 + 48x^2

please show your work on both of them, and thank you so much!
(Edit I have to repost this question bc i really need it answered. I'm offering more points now!

Answers

Problem # 1

Not Factored: (5x^2 - 13x - 6)
Factored: (5x + 2 )(x - 3)

There is no real "work" to be shown for this, you can see that
1) Seperating 5x^2 into 5x and x will get you the equation in the form:
 (5x     ) (x      )  = 5x^2 +

2) To complete this factor you need to guess which two numbers will add together to give you - 13x and multiply to form -6 (from the original unfactored equation). The numbers that will do this are 2 and 3

3) You can plug in negative or positives of those numbers to make sure they give you the exact results you need.

For example testing -2 and 3 you will get: (5x - 2) (x + 3 ) = 5(x^2) - 2x + 15x - 6 = 5x^2 +13x - 6.  This is NOT the same as the unfactored equation. So you know -2 and 3 is the wrong choice. Choosing 2 and -3 will give you the answer instead.

As i said, there's no actual "work" to show this, you have to make guesses and try to factor it.

-------------------------------------------------------------------------------------------------
Problem # 2

Not Factored: 4x^4 - 28x^3 + 48x^2
Factored: 4x^2 (x^2 - 7x + 12) =
                4x^2 (x  - 3) (x - 4)

To solve this, you factor out the 4x^2 from the entire equation. Then you can further factor the quadratic equation by seperating x^2 into (x    )(x    ) and guessing for which numbers will add to -7x and multiply to 12

Perform the indicated operation. then estimate to see whether the proposed results is reasonable. 11.58 + 11.9 + 9.2
32.68
22.68
33.68
31.68 Preform the indicated operation. Then estimate to see whether the proposed result is reasonable.
93.8 - 6.48
87.32
97.44
87.42
94.34
Preform the indicated operation. Then choose the best answer. 27.7 x 1.9 5.363
52.63
53.62
5.263 Choose the best estimate. 64.1 ÷ 97
641
6.41
0.641
6410 Use estimation to determine whether the result is reasonable or not. 108.93 x 32.6 Result: 355.112 Is it reasonable or not?

Answers

Answers: See below

These problems are best done by rounding to easy numbers, then picking the closest value. Below I gave an example of how to round them and then picked the best answer.

1) 12 + 12 + 10 = 34     So 33.68 is the closest.

2) 94 - 6 = 88    So 87.42 is the closest.

3) 28 x 2 = 56   So 53.62 is the closest.

4) 60 / 100 = 0.6    So 0.641 is the closest.

5)  100 x 30 = 3000    So 355.12 is not reasonable.

Which equations are true for x = –2 and x = 2? Check all that apply.

x2 – 4 = 0
x2 = –4
3x2 + 12 = 0
4x2 = 16
2(x – 2)2 = 0

Answers

equation 1
equation 4

Answer:

x2 – 4 = 0

4x2 = 16

Step-by-step explanation:

A is an acute angle in a right triangle, Given that Sin A= 7/25, what is the ratio for Cos A? Enter your answer in the box as a fraction in simplest form.

Answers

Find the adjacent side of the triangle ... 
7² + x² = 25²
x² = 25² - 7²
x² = 576
x = 24 
The adjacent side of the triangle is 24

Given that sin A = [tex] \frac{7}{25} [/tex]
Since sin A = [tex] \frac{o}{h} [/tex]
We can conclude that o = 7 and h = 25

cos A = [tex] \frac{a}{h} [/tex]
cos A = [tex] \frac{24}{25} [/tex]
[tex] \sin \theta = \dfrac{opp}{hyp} [/tex]

[tex] \sin A = \dfrac{7}{25} = \dfrac{opp}{hyp} [/tex]

[tex] a^2 + b^2 = c^2 [/tex]

[tex] a^2 + 7^2 = 25^2 [/tex]

[tex] a^2 = 625 - 49 [/tex]

[tex] a = \sqrt{576} [/tex]

[tex] a = 24 [/tex]

[tex] adj = a = 24 [/tex]

[tex] \cos A = \dfrac{adj}{hyp} [/tex]

[tex] \cos A = \dfrac{24}{25} [/tex]

What is the measure of ∠XBC?

1. m∠XBC = m∠BAC + m∠BCA

2. 3p – 6 = p + 4 + 84

3. 3p – 6 = p + 88

4. 2p – 6 = 88

5. 2p = 94

m∠XBC =

Answers

we Know that
m∠ABC=180-[(p+4)+84]--------> 180-[p+88]=92-p
m∠ABC=(92-p)°    equation 1
and
m∠ABC+(3p-6)=180----------m∠ABC=180+6-3p
 m∠ABC=186-3p   equation 2
(1)=(2)
(92-p)=186-3p-----------> 186-92=-p+3p--------------> 2p=94

p=47°
therefore
m∠XBC=(3p-6)°---------->(3*47-6)=135°

the answer is 
m∠XBC=135°

The measure of an exterior angle of triangle is equal to the sum of measures of two interior angles of triangle that are not supplementary with this exterior angles.

In the case of this question this fact sounds as

m∠XBC = m∠BAC + m∠BCA (option 1).

Now if

m∠XBC=(3p-6)°m∠BAC=(p+4)°m∠BCA=84°,

then

3p-6=p+4+84 (option 2),

3p-6=p+88 (option 3),

3p-p-6=p-p+88,

2p-6=88 (option 4),

2p-6+6=88+6,

2p=94 (option 5),

p=47.

Then m∠XBC=(3p-6)°=(3·47-6)°=135°.

Answer: m∠XBC=135°.

On a map, 2 inches represents 60 miles. What part of an inch represents 12 miles? Please show how you get you answer.

A. 1/10in.

B. 1/5in.

C. 2/5in.

D. 1/2in.

Answers

c: 2/5 inches is your answer 

if 2 inches are 60 miles then 12 miles is a fifth of 2 inches.

Which equation is true for the value b = 2? 2b + 24 = 30 3b − 2 = 4 b + 4 = 8 2b − 3 = 0

Answers

The correct answer is 3b-2=4

Hope this helps.

Answer:

3(b – 2) = 24

Step-by-step explanation:

sav meh pl0x ty fam

Mean: 42
Median: 38
Range: 52
Mean Deviation: 11.23

Shift 1
18
25
56
42
29
38
54
47
35
30

Shift 2
23
19
50
49
67
34
30
59
40
33

Shift 3
19
22
24
40
45
29
33
29
39
59

Shift 4
21
23
25
40
35
19
70
40
22
23

The summary statistics for all of the workers at a steel factory are shown. Four sample groups were taken from each of the four shifts. For which sample group is the mean closest to the population mean?
A) Shift 1
B) Shift 2
C) Shift 3
D) Shift 4

Answers

Given that the summary of the population is:
Mean: 42 
Median: 38 
Range: 52 
Mean Deviation: 11.23

To obtain the sample that is closest to the mean we shall proceed as follows:
Shift 1:
18,25,56,42,29,38,54,47,35,30
The mean of the sample is:
(18+25+56+42+29+38+54+47+35+30)/10
=374/10
=37.4

Shift 2:
23, 19, 50, 49, 67,34,30,59,40, 33
The mean is:
(23+19+50+49+67+34+30+59+40+33)/10
=404/10
=40.4

Shift 3:
Shift 3
19, 22, 24, 40, 45, 29, 33, 29, 39, 59
The mean of the values
(19+22+24+40+45+29+33+29+39+59)/10
=339/10
=33.9

Shift 4:
21, 23, 25, 40, 35, 19, 70, 40, 22, 23
The mean of the values is:
(21+23+25+40+35+19+70+40+22+23)/10
=318/10
=31.8

From the calculations, the sample that has mean that is close to population mean is Shift 2

Mr. sam's swimming pool is in the shape of a parallelogram, as shown. what is the area of his swimming pool? 189 ft² 234 ft² 279 ft² 585 ft² parallelogram a b c d with side a d parallel to side b c and side a b is parallel to side d
c. point e is on side a
b. a e is 5 feet. dc is 26 feet. a dotted segment d e runs from point d to the opposite side a b and is perpendicular to side a
b. d e is 9 feet.

Answers

Hi there! i see that this answer has been up for 6 days! i was looking for the answer as well! so i found out that the answer would be 234!! hope this helps!

Answer: 234
Your answer should be 234 I had it on my test and got a A   

Answer:234

Panel 1 is the answer choice

Panel 2 is the question

Answers

D is the midpoint of A and B
A = (0,s)
B = (r,0)

Add up the x coordinates to get 0+r = r. Then cut that in half to get r/2
Similarly, do the same for the y coordinates: s+0 = s ---> s/2

So the location of point D is (r/2, s/2)

Answer: Choice C



Which of these is the algebraic expression for the verbal expression "twelve times the difference of a number and four?"

12 ⋅ x − 4
x − 4 ⋅ 12
4(x − 12)
12(x − 4)
Question 2(Multiple Choice Worth 3 points)
(06.02)

Which of these is the algebraic expression for "some number to the power of 5?"

5x
x5
5x
x + 5
Question 3(Multiple Choice Worth 3 points)
(06.02)

Translate the algebraic expression shown below into a verbal expression.

Fraction with variable x in numerator and 10 in the denominator.

The sum of ten and some number
The quotient of some number and ten
The product of some number and ten
The difference of ten and some number
Question 4(Multiple Choice Worth 3 points)
(06.02)

Which of these is the algebraic expression for "eight less than some number?"

8 − b
b − 8
Fraction 8 over b
Fraction b over 8
Question 5(Multiple Choice Worth 4 points)
(06.02)

Which verbal expression best describes the algebraic expression 4x ÷ 6?

The sum of four and some number divided by six
The quotient of four times some number and six
The product of some number and six divided by four
The quotient of four and some number times six
Question 6(Multiple Choice Worth 3 points)
(06.02)

Which of these is the algebraic expression for "seven more than the product of three and some number?"

7 + 3 + x
3 + 10 ÷ x
3x + 7
3 + 7x

Answers

1. 12(x − 4)
2. x5
3. The quotient of some number and ten
4. b − 8
5. The quotient of four times some number and six
6. 3x + 7

1. x and -4 are multiplied by 12
2 raided to this 5th power is an exponent
3 quotient means division
4 less than means subtraction
5 division means quotient, list numerator first then the denominator
6 product of is multiplication and more is an addition.

I am just going to answer the first  one

1. 12(x - 4)

You are paying 11% interest on a credit card balance of $2,000. Which of the following best estimates the interest you are paying each month?

a) $11.00
b) $13.33
c) $15.33
d) $18.33
Will fan and medal,

Answers

answer is very simple. first you divide 11 by 12 (12 months in a year). you get .9166. next divide 2000 by 100 and multiply by .9166 to get D.) 18.33. i hope this helps.
$2000*11/100=$220 for the whole year
$220/12 (months in a year)=$18.33
d) $18.33
Other Questions
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