The sum of two numbers is 10. The larger number is 4 times the smaller number. What are the two numbers?

Let x = the smaller number.

Let y = the larger number.

Which two equations represent the system for this word problem?

Equation 1:
Equation 2:

First we find the slope of the line 2x−3y+8=0 by placing it into slope intercept form:

2x−3y+8=0

⇒−3y=−2x−8

⇒3y=2x+8

⇒y=  

3

2

​

x+  

3

8

​

Therefore, the slope of the line is m=  

3

2

​

.

Now since the equation of the line with slope m passing through a point (x  

1

​

,y  

1

​

) is

y−y  

1

​

=m(x−x  

1

​

)

Here the point is (2,3) and slope is m=  

3

2

​

, therefore, the equation of the line is:

y−3=  

3

2

​

(x−2)

⇒3(y−3)=2(x−2)

⇒3y−9=2x−4

⇒2x−3y=−9+4

⇒2x−3y=−5

Hence, the equation of the line is 2x−3y=−5.

Answer:

y=2/3x-11/3

Step-by-step explanation:

Hi there!

We are given the equation 2x-3y=9 and we want to write an equation that is parallel to it and that passes through (4,-1)

Parallel lines have the same slopes

So we need to first find the slope of 2x-3y=9

We can do this by converting the equation of the line from standard form (ax+by=c where a, b, and c are integers) to slope-intercept form (y=mx+b, where m is the slope and b is the y intercept)

To do this, we need to isolate y on one side

2x-3y=9

subtract 2x from both sides

-3y=-2x+9

divide both sides by -3

y=2/3x-3

as 2/3 is in the place where m is, 2/3 is the slope of the line

It's also the slope of the line parallel to it that passes through (4,-1).

Here's the equation of that line so far:

y=2/3x+b

now we need to find b

as the line will pass through the point (4,-1), we can  4 as x and -1 as y in order to solve for b

-1=2/3(4)+b

multiply

-1=8/3+b

subtract 8/3 to both sides

-11/3=b

Substitute -11/3 as b into the equation

y=2/3x-11/3

There's the equation

Hope this helps!

Answer:

his dad was cutting the grass for 1 hour and 4 minutes i hope this helps

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

the area of the triangle is  18 square units

Answer:

strong, negative;

decreased

Step-by-step explanation:

A correlation coefficient that is close to 1, shows a strong association.

If the correlation coefficient is negative, it implies a negative association, meaning as one variable increases, the other decreases.

A positive correlation coefficient shows a positive association between two variables. This implies that as one variable increases, the other increases, or as one decreases, the other decreases as well.

In the case given, we are given that the correlation coefficient obtained is -0.76. This therefore shows a negative association. Also, the value is closer to 1.

This implies that there is a STRONG, NEGATIVE association association between x and y. This is because as the temperature (x) of the day increases across days, the number of customers who patronized the store DECREASED.

Answer:

x^2+2xy+y^2

Step-by-step explanation:

(x + y)(x + y)

FOIL

first x*x = x^2

Outer x*y = xy

inner: y*x = xy

last y*y = y^2

add together

x^2+xy+xy+y^2

Combine like terms

x^2+2xy+y^2

Answer:

[tex]x^{2}[/tex] + 2xy + [tex]y^{2}[/tex]

Step-by-step explanation:

(x + y)(x + y)

= (x + y)(x + y)

=(x)(x) + (x)(y) + (y)(x) + (y)(y)

= [tex]x^{2}[/tex] + xy + xy + [tex]y^{2}[/tex]

= [tex]x^{2}[/tex] + 2xy + [tex]y^{2}[/tex]

Hope this helps, please mark brainliest. :)

Probability of getting tails when weighted coin is flipped is 2/5

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes for an event. For an experiment with 'n'  outcomes, the number of favorable outcomes can be denoted by x.

The probability of an event can be calculated by simply dividing the  number of favorable outcomes by the total number of possible outcomes using the probability formula. The value of the probability that an event will occur can range from 0 to 1. This is because the preferred number of outcomes can never exceed the total number of outcomes. Also, the resulting favorable number is never negative.

Given,

Chance of getting heads on the weighted coin = 60%

Probability of getting heads = 60/100

Probability of getting heads = 3/5

Probability of getting tails = 1 - 3/5

Probability of getting tails = 2/5

Hence, 2/5 is the probability of getting tails on flipping the weighted coin.

Learn more about probability here:

https://brainly.com/question/30034780

#SPJ7

Answer:

Option D

Step-by-step explanation:

By using geometric mean theorem in the given right triangle ABC,

[tex]\frac{AD}{BD}= \frac{BD}{DC}[/tex]

BD² = AD × DC

h² = (AC - CD) × DC

h² = (25 - 16) × 16

h² = 9 × 16

h = [tex]\sqrt{144}[/tex]

h = 12

Therefore, measure of side h = 12 units.

Option D will be the correct option.

Answer:

12 is correct via a p e x

Hello,

a) photo attached

b) When y = 1, x ≈ 0.5

Verification through calculation :

We have :

y = 4x - 1

⇔ 1 = 4x - 1

⇔ 4x = 2

⇔ x = 2/4 = 0.5

This is just !

:-)

Answer:

0.7208 = 72.08% probability that this whole shipment will be accepted.

Step-by-step explanation:

For each tablet, there are only two possible outcomes. Either it meets the required specifications, or it does not. The probability of a tablet meeting the required specifications is independent of any other tablet, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

4% rate of defects

This means that [tex]p = 0.04[/tex]

26 tablets

This means that [tex]n = 26[/tex]

What is the probability that this whole shipment will be accepted?

Probability that at most one tablet does not meet the specifications, which is:

[tex]P(X \leq 1) = P(X = 0) + P(X = 1)[/tex]

Thus

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{26,0}.(0.04)^{0}.(0.96)^{26} = 0.3460[/tex]

[tex]P(X = 1) = C_{26,1}.(0.04)^{1}.(0.96)^{25} = 0.3748[/tex]

Then

[tex]P(X \leq 1) = P(X = 0) + P(X = 1) = 0.3460 + 0.3748 = 0.7208[/tex]

0.7208 = 72.08% probability that this whole shipment will be accepted.

Answer:

35 mm.

Step-by-step explanation:

That would be (26 + 44)/2

= 70/2

= 35 mm.

Answer:

You would choose Merry Berry Fruit Punch.

Step-by-step explanation:

We need to see the ration of fruit to water. To do this we need to divide the concentrate by the water.

Tropic Fresh Fruit Punch: 10/22 or 5/11

Merry Berry Fruit Punch: 6/13

We see that Tropic Fresh Fruit Punch has a ratio of 5/11 while Merry Berry Fruit Punch has a ratio of 6/13. When we have a common denominater, we can see the difference easier.

Tropic Fresh Fruit Punch: 65/143

Merry Berry Fruit Punch: 66/143

Answer:

The area will be 2 times the old area.

Step-by-step explanation:

When you double something, that means you multiply it by 2, therefor it will be 2 times the old area.

Answer:

option 3

Step-by-step explanation:

Length = 5 m, Base = 3 m

Area = Length x Base

       = 5 x 3

       = 15 m²

Base is double = 2 x 3 = 6 m

Length remains same = 5m

New Area = Length x Base

               = 5 x 6

               = 30 m²

The new Area is increase by 2 times the old Area .

Answer:

5 hours

divide 25 by 5 you get 5

Answer:

1 solution.

Step-by-step explanation:

So we can split this into to equations:

-19x+91=-19x+91−19x+91

And

-19x+91−19x+91=−19x+91

Then simplify them to:

19x=91

And

19x=91

The equations are identical, so we only need to solve one.

X = 91/19

X = 4.789

I believe this is right.

Answer:

24

Step-by-step explanation:

x + (1/4)x + (1/3)x = 38

multiply both sides by 12 to clear the fractions

12x + 3x + 4x = 456

19x = 456

Divide both sides by 19

x = 24

Answer:

24

Step-by-step explanation:

x+1/4x+1/3x=38

x+7/12x=38

19/12x=38

x=38*12/19=24

Answer:

8x³ - 25x² - 3x + 18

Step-by-step explanation:

(2x + 3)(4x²- 5x + 6)

multiply 2x by each of the three terms in the second expression to get:

8x³ - 10x² + 12x

now multiply 3 by each of the three terms in the second expression to get:

12x² - 15x + 18

Combine 'like terms': -10x² + (-15x²) = -25x²

Combine 'like terms':  12x + (-15x) = -3x

Put all terms in decreasing exponent order:

8x³ - 25x² - 3x + 18

Answer:

x = - 11

y = 3

Step-by-step explanation:

5x + 6y = - 37

x = - 11

5( - 11) + 6y = - 37

- 55 + 6y = - 37

- 55 + 55 + 6y = - 37 + 55

6y = 18

6y ÷ 6 = 18 ÷ 6

y = 3

Step-by-step explanation:

[tex](1) \: \: \sqrt[3]{5} \times \sqrt[3]{ \frac{2}{5} } \times \frac{ \sqrt[3]{64} }{ \sqrt[3]{3} } \times \frac{ \sqrt[6]{9} }{ \sqrt[3]{2} } [/tex]

Note that the 1st two factors can be combined:

[tex] \sqrt[3]{5} \times \sqrt[3]{ \frac{2}{5} } = \sqrt[3]{5 \times \frac{2}{5} } = \sqrt[3]{2} [/tex]

We also know that the numerator in the 3rd factor can be rewritten as

[tex] \sqrt[3]{64} = 4[/tex]

And the numerator in the 4th term can be rewritten as

[tex] \sqrt[6]{9} =({( {3})^{2} })^{ \frac{1}{6} } = \sqrt[3]{3} [/tex]

So let's rewrite expression #1

[tex] \sqrt[3]{2} \times \frac{4}{ \sqrt[3]{3} } \times \frac{ \sqrt[3]{3} }{ \sqrt[3]{2} } [/tex]

Notice that all the radical terms cancel out except for 4 therefore,

[tex]\sqrt[3]{5} \times \sqrt[3]{ \frac{2}{5} } \times \frac{ \sqrt[3]{64} }{ \sqrt[3]{3} } \times \frac{ \sqrt[6]{9} }{ \sqrt[3]{2} } = 4[/tex]

Answer:

Step-by-step explanation:

stuck under the bed??

lemme jus quickly pull you back....lol

Answer:

The range of the following relation is(-5,2,-4)

Answer:

B

Step-by-step explanation:

When x=1, we will use the second equation

-(1)+1 = 0

Answer:(first term)

a=27(4th term)

T4= a x r^3 = 64

substituting a as 27 in T4

27 x r^3 = 64

r^3 = 64/27

r=4/3

so; a=27, r=4/3

using the general formula of geometric progression,

a x r^n-1

substitute:.

27 x 4/3^n-1

= 27(4/3)^n-1

Answer: (C) HOPE THIS HELPS!

Answer:

Part A;

$79

Part B;

The amount Stella would have saved in 'w' weeks = 15 + 8·w

Step-by-step explanation:

Part A

The amount of money Stella already has = $15

The amount she can save per week = $8

The total amount of money, 'A', Stella would have after 8 weeks is given as follows;

A = The amount Stella already has + The amount she can save per week × The number of weeks of savings

Therefore;

A = 15 + 8 × 8 = 79

The amount Stella would have after 8 weeks, A = $79

Part B

The expression that represents the amount of money Stella would have saved in w weeks is given as follows;

A = The initial amount Stella has + The amount she can save per week × w (number of weeks)

∴ A = 15 + 8·w.

Answer:

3/10

Step-by-step explanation:

=1/2 *3/5

= 1*3/2*5

= 3/10

hope it helps

Answer:

make Y the subject in eqn........ 1

y + 7 = 2x

y = 2x - 7...........eqn 3

put y = 2x - 7 into eqn 2

x² - xy + 3y² = 15

x² - x(2x - 7) + 3(2x - 7)(2x - 7) = 15

x² - 2x² + 7x + 3(4x² + 14x -14x + 21) = 15

x² - 2x² + 7x + 12x² + 42x - 42x + 63 = 15

x² - 2x² + 7x + 12x² + 63 = 15

x² - 2x² + 12x² + 7x + 63 = 15

11x² + 7x + 63 - 15 = 0

11x² + 7x + 48 = 0

11x² + 7x = - 48

11x²/11 + 7x/11 = - 48/11

x² + 7x

Answer:

DPB

Step-by-step explanation:

Verticle angles are congruent

m∠APC = m∠DPB

Answer:

Two lines that pass through the point (4, 8) are y = 3·x - 4 and y = -5·x + 28

Step-by-step explanation:

The equation of two lines that passes through the point (4, 8) are found using the general form of a straight line equation, y = m·x + c, where;

m = The slope of the line

c = The y-intercept

Therefore, two distinct line pass through a given point if they have a different slope, m, and a different y-intercept, c, as follows;

Fot the given point, the x-value = 4, and the y-value = 8, we get;

8 = m₁·4 + c₁...Line 1 and

8 = m₂·4 + c₂...Line 2

m₁ ≠ m₂

If we set m₁ = 3, for line 1, we get;

8 = 3 × 4 + c₁ = 8 = 12 + c₁

∴ c₁ = 8 - 12 = -4

c₁ = -4

The equation for Line 1 for all x and y-values, where, m₁ = 3, c₁ = -4, becomes;

y = 3·x - 4

The equation for Line 2 where m₂ = -5 for example, we have;

8 = -5 × 4 + c₂

∴ c₂ = 8  + 5 × 4 = 28

c₂ = 28

The general form for the equation for Line 2 becomes;

y = -5·x + 28

Therefore;

The equation of the two formed lines that pass through the point (4, 8) are;

y = 3·x - 4 and y = -5·x + 28

Answer:

49.87%

Step-by-step explanation:

We solve using z score formula

z = (x-μ)/σ, where

x is the raw score

μ is the population mean = 70%

σ is the population standard deviation = 8%

a) For x = 70%

z = 70% - 70%/8%

z = 0

Probability value from Z-Table:

P(x = 70) = 0.5

b) For x = 70%

z = 94% - 70%/8%

z = 3

Probability value from Z-Table:

P(x = 94) = 0.99865

The probability of students that receive between a 70% and 94%

P(x = 94) - P(x = 70)

0.99865 - 0.5

0.49865

Therefore, the percentage of students that receive between a 70% and 94% is

0.49865 × 100

= 49.865%

Approximately = 49.87%