Find the sum and the product of the roots of the equation: y^2+41y−371=0

Answer:

7 Children and 18 Adults.

Step-by-step explanation:

Sorry im late but thats the answer ^

There was 7 children attendee and 17 adult attendee.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

A restaurant catered an event for 25 people.

A child’s dinner cost $5 and an adult’s dinner cost $22.

The party cost $431.

let the number of children attendee be x and adult attendee be y.

So, x+ y = 25..............(1)

and, 5x + 22y = 431.......(2)

Solving the Equation (1) and (2) we get

5(25 - y) + 22y= 431

125 - 5y + 22y= 431

17y = 431-125

17y = 306

y = 18

and, x= 25-18 = 7

Hence, there was 7 children attendee and 17 adult attendee.

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Answer:

See Explanation

Step-by-step explanation:

The question didn't specify if letter can be repeated or not;

I'll solve for both;

Given

Number of Letters = 26

Number of squared = 4

If Repetition is allowed;

The four squares can take any of the 26 letters in any order

The first letter can be any of 26; Same with the second, third and fourth letters;

Number of Arrangement = 26 * 26 * 26 * 26

Number of Arrangement = 26⁴

Number of Arrangement = 456976

If Repetition is not allowed;

The first square can be filled with any of the 26 letters;

The second can take any of (26 - 1) letters

The third can take any of (26 - 2) letters

The fourth can take any of (26 - 3) letters

Number of Arrangement = 26 * (26 - 1) * (26 - 2) * (26 - 3)

Number of Arrangement = 26 * 25 * 24 * 23

Number of Arrangement = 358800

Answer:

26!/22!

Step-by-step explanation:

I just took the quiz I got it right

Answer:

yes

Step-by-step explanation:

Answer:

Yes, the heat that flows into the system is used to change the internal energy of the gas and becomes work done by the piston.

Step-by-step explanation:

I took the K12 test :)

Answer:

(a) Because the confidence interval does not include includes 0​, it appears that there is not a significant difference between the mean level of hemoglobin in women and the mean level of hemoglobin in men.

(b) The correct option is (A).

(c) The correct option is (C).

Step-by-step explanation:

The 95% confidence interval for the difference between the two population​ mean hemoglobin level is:

CI = (-1.76 < μ₁ - μ₂ < -1.62)

(a)

The hypothesis to test the equality of the mean hemoglobin level in women and the mean hemoglobin level in​ men is:

H₀: The two population means are equal, i.e. μ₁ = μ₂.

Hₐ: The two population means are not equal, i.e. μ₁ ≠ μ₂.

The (1 - α)% confidence interval can be used to draw conclusion about the hypothesis test.

Decision rule:

If the (1 - α)% confidence interval does not consist of the null value then the null hypothesis will be rejected and vice-versa.

The 95% confidence interval for the difference between the two population​ means is:

CI = (-1.76, -1.62)

The 95% confidence interval does not consist of the null value, i.e. 0.

Thus, the null hypothesis will be rejected.

"Because the confidence interval does not include includes 0​, it appears that there is not a significant difference between the mean level of hemoglobin in women and the mean level of hemoglobin in men."

(b)

The (1 - α)% confidence interval for population parameter implies that there is a (1 - α) probability that the true value of the parameter is included in the interval.

Or, the (1 - α)% confidence interval for the parameter implies that there is (1 - α)% confidence or certainty that the true parameter value is contained in the interval.

So, the 95% confidence interval (-1.76, -1.62) implies that there is a 95% confidence that the above interval actually contains the value of the difference between the two population means, (μ₁ - μ₂).

The correct option is (A).

(c)

Now it is provided that the measures from men is denoted as population  1 and measures from women is denoted as population  2.

The confidence interval for the difference between two mean is:

[tex]CI=(\bar x_{1}-\bar x_{2})\pm MOE[/tex]

According to the information:

[tex]\bar x_{1}=\bar x_{2}\\\\\bar x_{2}=\bar x_{1}[/tex]

So, the new confidence interval will be:

[tex]CI=-(\bar x_{2}-\bar x_{1})\pm MOE[/tex]

Then the confidence interval with measures from men being population

1 and measures from women being population  2 is:

[tex]CI=(1.62<\mu_{1}-\mu_{2}<1.76)[/tex]

The correct option is (C).

Answer:

a) Use a ruler for the measurement.

b) convert to centimetres then use a ruler to draw the unit on the diagram.

c) measure the angle between K and L from K

See explanations below

A complete question related to this found on brainly (ID:15577387) is stated below.

Towns K and L are shown on a map.

a) Work out the actual distance

between towns K and L.

b) A third town, M, is 150 km due

South of town K.

Mark M on the map with X.

c) Measure the bearing of town L

from town K.​

Scale: 1cm represent 50km

Step-by-step explanation:

Scale: 1cm represent 50km

a) To find the actual distance between towns K and L use a ruler to measure the distance between K and L.

Your answer would be in centimetres (cm).

The answer obtained would be multiplied by 50km because from the scale given 1cm represent 50km.

Therefore you'll get the actual distance in km.

b) Here we are told M is 150 km due

South of town K.

Since the length of the initial diagram is in centimeters, we have to find how many centimeters equals 150km.

50km = 1cm

150km = (150km × 1cm)/50km = 150cm/50

150km = 3cm

Now we can represent the distance between K and M on the diagram.

Measure 3cm from K using a ruler in the direction of south (straight line downwards). The distance of M from K would be 3cm on the south of k.

c) Draw a cross on the position of K. Also draw a cross on the position of L. Connect the distance and measure the angle from K to L. The unit would be in degrees.

From the diagram, the angle is greater than 090° but less than 180°

Find attached the diagram.

Answer:

a) 100 km

b) check the photo of my work

c) 117 degrees

Step-by-step explanation:

To get full marks take a look at the photo of my work.

Question (b) use a compass and make sure it’s 3cm aiming down {South} as u can see in the photo, then draw a line aiming {South} with a ruler. On the end of the line you put the (x) point there to get the mark.

Thank you

Answer:

(a) t_n = 3n - 9

(b) t_16 = 39

Step-by-step explanation:

(a)

-3 - (-6) = -3 + 6 = 3

The common difference is 3.

t_1 = -6

t_2 = -6 + 3

t_3 = -6 + 3 + 3

t_4 = -6 + 3 + 3 + 3

t_n = -6 + 3(n - 1)

t_n = -6 + 3n - 3

t_n = -9 + 3n

t_n = 3n - 9

The formula is: t_n = 3n - 9

(b) t_16 = 3(16) - 9 = 48 - 9 = 39

Answer:

an = -6 + 3(n - 1)

a(16) = 39

Step-by-step explanation:

Explicit Formula: an = a1 + d(n - 1)

Our d (common difference) is +3

Our a1 (First term) is -6

To find a(16) (the 16th term), plug in 16 for n.

Answer:

Step-by-step explanation:

Let x represent the number of pennies that Al had​ initially.

He agreed to give six thirteenths of his pennies to Bev. It means that the number of pennies that he gave to Bev is 6/13 × x = 6x/13

if she would give six thirteenths of what she got from Al to Carl, it means that the number of pennies that Carl received is 6/13 × 6x/13 = 36x/169

if Carl in turn would give six thirteenths of what he got from Bev to Dani and Dani received 2376 pennies, it means that

6/13 × 36x/169 = 2376

216x/2179 = 2376

216x = 2376 × 2179

216x = 5220072

x = 5220072/216

x = 24167

AI had 24167 pennies initially

Answer:

It's pretty easy! You can manipulate the numbers to match the equation.

For example,

x + 8y + 6x - 9y = 7x - y

5x + 2x - 2y + y = 7x - y

10x + 7y - 3x - 8y = 7x - y

The other equivalent expressions that are equal to 7x - y​ could be; x + 8y + 6x - 9y = 7x - y, 5x + 2x - 2y + y = 7x - y and 10x + 7y - 3x - 8y = 7x - y

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division. The Numbers constants, variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbol; that can also be used to indicate the logical syntax's order of operations and other features.

We have been given the expression as;

6x + 7y + x-8y = 7x - y

When someone asks to solve an equation, then it usually mean to find the values of the unknowns for which that equation would be true (the equality between expressions should hold true for those values).

The other equivalent expressions that are equal to 7x - y​ could be;

x + 8y + 6x - 9y = 7x - y

5x + 2x - 2y + y = 7x - y

10x + 7y - 3x - 8y = 7x - y

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Answer:

$4,523.40

Step-by-step explanation:

The cell phone cost is $124.65 per month. With 12 months in a year, we multiply $124.65 x 12 to get the answer $1,507.80. Since one year equals $1,507.80, we multiply this answer by 3 for 3 years to get $4,523.40. Thus three years of service with $124.65 a month would equal $4,523.40.

Answer:

x=1.

Step-by-step explanation:

2x + 1 = -x + 4

+x - 1 = +x - 1

3x. = 3

3/3. = x

1. = x

Answer:

5x - 9 = 2x + 23

Step-by-step explanation:

5 times a number is represented by 5x, with x representing the unknown number.  

5x decreased by 9 is (5x - 9) since 9 is being subtracted by 9.  

(5x - 9) is equal to twice the number (2x), increased by 23.  

So, the equation is (2x + 23).  

Therefore, 5x - 9 = 2x + 23

The equation is 5x - 9 = 2x + 23.

The answer is option A.

5 times a number is represented by 5x, with x representing the unknown number.  

5x decreased by 9 is (5x - 9) since 9 is being subtracted by 9.  

(5x - 9) is equal to twice the number (2x), increased by 23.  

So, the equation is (2x + 23).  

Therefore, 5x - 9 = 2x + 23

An equation is a mathematical announcement this is made up of expressions related to the same signal. For instance, 3x – 5 = 16 is an equation. Fixing this equation, we get the price of the variable x as x = 7.

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Answer:

83/5, 16.6, 16 3/5

Step-by-step explanation:

When two secant segments are drawn to a circle from an external point, the product of one secant segment and its external segment equals the product of the other secant segment and its external segment.

6 times 18 = 5(5+x)

The total secant segment is 6+12=18

so one side = 6 times 8.

The line from the circle (but not inside) is 5.

You don't know the entire segment, but you do know that 5 is part of it. Hence 5 times (5+x).

Sorry for the trashy explanation.

Answer:

Step-by-step explanation:

━━━━━━━☆☆━━━━━━━

▹ Answer

(x, y) = (14/5, 87/20)

▹ Step-by-Step Explanation

8x - 4y = -4 - 3x + 4y = 5

8x - 4y = 5

-4 - 3x + 4y = 5

8x - 4y = 5

-3x + 4y = 9

5x = 14

x = 14/5

-3 * 14/5 + 4y = 9

y = 87/20

(x, y) = (14/5, 87/20)

Hope this helps!

- CloutAnswers ❁

Brainliest is greatly appreciated!

━━━━━━━☆☆━━━━━━━

Answer:

11x−8y=−9

Step-by-step explanation:

khan

Answer:

a=1.5b

Step-by-step explanation:

Add 2b on both sides to get 7a=5a+3b

Subtract 5a

2a=3b

divide by 2

a=1.5b

Answer:

Step-by-step explanation:

ε = {x: 2≤ x ≤30}

M = { even numbers} = {2,4,6,8,10,12,14,16,18,20,22,24,26,28,30}

P = { prime numbers} = {2,3,5,7,11,13,17,19,23,29}

T = {odd numbers} = {3, 5, 7, 9, 11,13,15,17,19,21,23,25,27,29}

1. M ∪ P = {2,3,4,5,6,7,8,10,11,12,13,14,16,17,18,19,20,22,23,24,26,28,29,30}

2. M - T =

n(M) - n(T)

15- 14 = 1

3. P(MT)

(MT) = M ∩ T = 0

P ∪ (M ∩ T ) = {2,3,5,7,11,13,17,19,23,29}

4. P' = not a prime number

T' = not odd number = M

P' ∪(M∩T')

P' ∪ {2,4,6,8,10,12,14,16,18,20,22,24,26,28,30}

= {2,4,6,8,9,10,12,14,15,16,18,20,21,22,24,25,26,27,28,30}

Answer:

A.

Step-by-step explanation:

When you multiply the two binomials using distributive property, you get the answer A. I could display the steps since it did not let me.

Hope this helps!!! PLZ MARK BRAINLIEST!!!

Answer:

r=8

Step-by-step explanation:

Using the formula they gave us you could plug in the area (64) and divide it by pi which cancels out the pi so taking the square root of 64 gives you 8FT

Hope this helps :)

Answer:

8 ft

Step-by-step explanation:

[tex] \because \: r = \sqrt{ \frac{Area}{\pi} } \\ \\ \therefore \: r = \sqrt{ \frac{64\pi}{\pi} } \\ \\ \therefore \:r = \sqrt{64} \\ \\ \therefore r = 8 \: ft[/tex]

Hey there! :)

Answer:

(3.5, -1).

Step-by-step explanation:

Use the midpoint formula to solve this problem:

[tex](x_m, y_m) = (\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})[/tex]

Plug in the coordinates given:

[tex](\frac{10-3}{2}, \frac{8-10}{2})[/tex]

Simplify:

[tex](\frac{7}{2}, \frac{-2}{2})[/tex]

Therefore, the coordinates of the mid-point are:

(3.5, -1).

Answer:

The median speed in race A is about 153 miles per hour, and the median speed in race B is about 145 miles per hour.

Step-by-step explanation:

For comparison, we need to analyze and compare both races data which are as follows

For Race A

Maximum range = 170 miles per hour

Minimum  range = 120 miles per hour

First quartile  ≈ 142 miles per hour

Median quartile ≈ 153 miles per hour

It comes from

[tex]= \frac{142\ miles + 165\ miles}{2}[/tex]

= 153 miles

The Third quartile = 165 miles per hour

For Race B

Maximum range  = 165 miles per hour

Minimum range = 125 miles per hour

First quartile  ≈ 139 miles per hour

Median quartile = 145 miles per hour

It comes from

[tex]= \frac{139\ miles + 150\ miles}{2}[/tex]

= 145 miles

The third quartile = 150 miles per hour

Hence, the last option is correct

Answer:

7 1/8

57/8

Hope this helps :)

Answer:

13/3

Step-by-step explanation:

To find the mean of a data set, you must add all the given numbers and then divide the numbers by how many numbers there are.

3+5+4+3+5+6=26/6=4.3333...

When we convert the answer from a decimal to a fraction, we get 13/3.

Hope this helps!!! PLZ MARK BRAINLIEST!!!

Answer:

1

2

6

Step-by-step explanation:

1/2 +1/2 =1

length 1/2 ×4=2

wide 1/2 ×3 =1 1/2

height 1/2×3= 1 1/2

I hope this helps you

Answer:

x=3

Step-by-step explanation:

f(x) = 2^x

Let f(x) =8

8 = 2^x

Rewriting 8 as 2^3

2^3 = 2^x

The bases are the same so the exponents are the same

3=x

Answer:

A. 3

Step-by-step explanation:

y = 2^x

y = 8

Plug y as 8 in the first equation.

8 = 2^x

Make the left side of the equation with a base of 2.

2^3 = 2^x

Cancel bases.

3 = x

Answer:

The amount Sam invested the first year = $2000

The amount Sally invested the last year = $1900

Complete question related to this was found at brainly (ID 4527784):

For three consecutive years, Sam invested some money at the start of the year. The first year, he invested x dollars. The second year, he invested $2,000 less than 5/2 times the amount he invested the first year. The third year, he invested $1,000 more than 1/5 of the amount he invested the first year.

During the same three years, Sally also invested some money at the start of every year. The first year, she invested $1,000 less than 3/2 times the amount Sam invested the first year. The second year, she invested $1,500 less than 2 times the amount Sam invested the first year. The third year, she invested $1,400 more than 1/4 of the amount Sam invested the first year.

If Sam and Sally invested the same total amount at the end of three years, the amount Sam invested the first year is $ and the amount Sally invested the last year is $ .

Step-by-step explanation:

First we would represent the information given with mathematical expressions.

Sam investment for 3 consecutive years:

Year 1 = x dollars

Year 2 = $2,000 less than 5/2 times the amount he invested the first year

Year 2 = (5/2)(x) - 2000

Year 3 = $1,000 more than 1/5 of the amount he invested the first year

Year 3 = (1/5)(x) + 1000

Sally investment for 3 consecutive years:

Year 1 = $1,000 less than 3/2 times the amount Sam invested the first year

Year 1 = (3/2)(x) - 1000

Year 2 = $1,500 less than 2 times the amount Sam invested the first year

Year 2 = 2x - 1500

Year 3 = $1,400 more than 1/4 of the amount Sam invested the first year.

Year 3 = (1/4)(x) + 1400

Since Sam and Sally invested the same total amount at the end of three years, we would equate their sum:

Sum of Sam investment for the 3years = x + (5/2)(x) - 2000 + (1/5)(x) + 1000

= x + 5x/2 -2000 + x/5 + 1000

= (10x+25x+2x)/10 - 1000

= 37x/10 - 1000

Sum of Sally investment for the 3years = (3/2)(x) - 1000 + 2x - 1500 + (1/4)(x) + 1400

= 3x/2 - 1000 + 2x -1500 + x/4 + 1400

= (6x+8x+x)/4 - 1100

= 15x/4 - 1100

37x/10 - 1000 = 15x/4 - 1100

37x/10 - 15x/4 = -100

(148x - 150x)/40 = -100

-2x = -4000

x = 2000

Therefore the amount Sam invested the first year = x = $2000

The amount Sally invested the last year (3rd year) = (1/4)(x) + 1400

(1/4)(2000) + 1400 = 500+1400 = 1900

The amount Sally invested the last year = $1900

Answer:

Point B of 4the quertant

Answer:

A

Step-by-step explanation:

The range refers to the possible y-values.  You can assume that values on the right column are the y-values if it is not specifically expressed.  The right column is the output, or y, column.

Since you have a table, you have to state each number.  Put the numbers in numerical order.  This gives you an answer of

{46, 49, 52, 53, 58, 63, 64, 67}

Answer:

HEY!

your answer is

it would be best to use litres

this is because a litre is 1000 millilitres and a swimming pool is a large amount of water.

Step-by-step explanation:

hope this helps

pls put brainliest

Answer:

B

Step-by-step explanation:

The term 2013 in this context refers to the amount invested.

Mathematically, in finance, we can express the amount to be recouped on an investment, having a particular rate of return over a couple of years using the general formula;

V = P(1+r)^t

Such as in the case of amount obtained in a compound interest formula

Where P is the present value or principal or amount invested

V is the future value

r is the rate of investment

with t being the time taken

Answer:

Answer:

so x=8

Step-by-step explanation:

2x+46=7x+6

subtracting 7x on both sides

2x-7x+46=7x-7x+6

-5x+46=6

subtracting 46 on both sides

-5x+46-46=6-46

-5x=-40

5x=40

x=8

i hope this will help you :)