Amy and Stephanie were playing a number game. Amy picked a number and told Stephanie that if she added 9 to the number and multiplied the sum by 3, it would equal 12. Which equation could Stephanie use to find the number, x?

Answer:

The equation of line whose x-intercept is 5 and whose y-intercept is 3

is given as    5 y + 3x = 15.

Step-by-step explanation:

Here, the given x - intercept  = 5.

⇒ The point on the given equation is (x,0)  = (5,0)

And, the y- intercept is given as 3

⇒ The point on the given equation  is (0,y)  = (0,3)

So, the two points given on the equation of line is A(5,0) and B(0,3)

Now, the slope of the line equation [tex]m = \frac{y_2 - y_2}{x_2-x_1}[/tex]

So, here the slope of line AB  is [tex]m = \frac{3- 0}{0-5}  = -\frac{3}{5}[/tex]

Now by POINT SLOPE FORMULA:

The equation of a line with point (x0,y0) and slope m is given as:

(y- y0) = m (x-x0)

⇒The equation of line AB is given as

[tex]( y - 0) =  -\frac{3}{5} (x -5)\\\implies 5 y = -3x + 15\\\implies 5 y + 3x = 15[/tex]

Hence, the equation of line AB is given as 5 y + 3x = 15.

Answer: 3.75 gallons

Step-by-step explanation:

8 fl oz x 60 (minutes)=480 fl oz

480 fl oz ÷ 128=3.75 gallons

Water flow rate is defined as the volume of the fluid passing by some location. The water leaking from the pipe per hour is 3.75 gallons

A pipe is leaking at the rate of 8 fluid ounces per minute.

Water flow rate is defined as the volume of the fluid passing by some location.

As the flow rate is 8 fluid ounces per minute. In a hour there is total 60 minutes. Thus the flow rate of the pipe in fluid ounces per hour is,

[tex]Q=8\times60[/tex]

[tex]Q=480[/tex]

A fluid ounces is the unit of the measurement of the liquid. There is total 128 fluid ounces in a gallons. Thus the flow rate of the water in gallon can be calculated by dividing the 480 by 128. Thus the flow rate of pipe in gallons per hour is,

[tex]Q=\dfrac{480}{128}[/tex]

[tex]Q=3.75[/tex]

Hence the water leaking from the pipe per hour is 3.75 gallons.

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Answer: [tex]H_0: p=0.30[/tex]

[tex]H_a: p <0.30[/tex]

Step-by-step explanation:

Definition:

Null Hypothesis : It is a statement about the population parameter that contains = , ≤ and ≥ signs.

Alternative hypothesis : It is also a statement about the population parameter against the null hypothesis that contains ≠  , < and > signs.

For the given situation.

Let [tex]\mu[/tex] be the population proportion of treated patients are uninsured.

A hospital director is told that 30% of the treated patients are uninsured.

Then, Null Hypothesis : [tex]H_0: p=0.30[/tex]

The director wants to test the claim that the percentage of uninsured patients is less than  the expected percentage.

i.e. Alternative hypothesis : [tex]H_a: p <0.30[/tex]

Hence, the set of hypothesis :

[tex]H_0: p=0.30[/tex]

[tex]H_a: p <0.30[/tex]

Answer:

Part 1:

Jose's Banquet Hall: 50g+100

Palace of Aaron: 45g+200

Part 2:

20 guests

Step-by-step explanation:

Part 1:

$50 per guest plus $100 fee

50g+100

$45 per guest plus $200 fee

45+200

Part 2:

$50(20)+$100=$1100

$45(20)+$200=$1100

Answer:

II. [tex]\displaystyle 20\:wedding\:guests[/tex]

I. [tex]\displaystyle 100 + 50g = 200 + 45g[/tex]

Step-by-step explanation:

100 + 50g = 200 + 45g

- 200 - 50g - 200 - 50g

___________________

[tex]\displaystyle \frac{-100}{-5} = \frac{-5g}{-5} \\ \\ 20 = g[/tex]

So, at twenty wedding guests, the cost will balance for both venues.

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Answer:

2 dozen eggs are 24 eggs

Answer:

First situation matches to F(x) = 23(1.17)^x.

Second is 17x + 23 .

Third is 13x - 270.

Last one is 27(1.13)^x.

Step-by-step explanation:

Answer:

46% × 2.3 =

(46 ÷ 100) × 2.3 =

(46 × 2.3) ÷ 100 =

105.8 ÷ 100 =

1.058 ≈

1.06;

Answer:

D) 2

Step-by-step explanation:

5x + 7 [tex]\leq[/tex] 8x -3 +2x

5x + 7 [tex]\leq[/tex] 10x - 3

7 + 3 [tex]\leq[/tex] 10x - 5x

10 [tex]\leq[/tex] 5x

2[tex]\leq[/tex] x

x[tex]\geq[/tex]2

Answer:

x=65/14

Step-by-step explanation:

(x-10)/(x-4)=50/-6

-50/6=-25/3

(x-10)/(x-4)=-25/3

x-10=-25/3(x-4)

x-10=-25/3x+100/3

x-(-25/3x)=100/3+10

x+25/3x=130/3

28/3x=130/3

x=(130/3)/(28/3)

x=(130/3)(3/28)

x=130/28

x=65/14

Answer:

Domain- [-4,∞)  ; Range-  [-2,∞)

Step-by-step explanation:

[tex]y=\sqrt{x+4} -2[/tex]

For Domain, we need to find the range of value for x,

As the value for x+4 should be positive or 0 because it is under the square root bracket sign.

[tex]x+4\geq 0[/tex]

[tex]x\geq -4[/tex]

x ∈ [-4,∞)

For the range of values, we need to find all the possible value of y

As the value given by the square root will always be greater than equal to 0.

[tex]\sqrt{x+4}\geq 0[/tex]

[tex]\sqrt{x+4} -2\geq -2[/tex]

Therefore ,

y ∈ [-2,∞)

Answer:

x=0, y=2. (0, 2).

Step-by-step explanation:

3x+2y=4

8x-3y=-6

---------------

3(3x+2y)=3(4)

2(8x-3y)=2(-6)

-----------------------

9x+6y=12

16x-6y=-12

----------------

25x=0

x=0/25

x=0

3(0)+2y=4

0+2y=4

2y=4-0

2y=4

y=4/2

y=2

The solution of the systems of equations by substitution will be;

⇒ x = 0, y = 2

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The system of equation are,

⇒ 3x + 2y = 4

⇒ 8x - 3y = -6

Now,

Since, The system of equation are,

⇒ 3x + 2y = 4  ..(i)

⇒ 8x - 3y = -6  ..(ii)

Find the value of x from (i) as;

⇒ 3x + 2y = 4

⇒ 3x = 4 - 2y

⇒ x = 1/3 (4 - 2y)

Substitute above value in (ii), we get;

⇒ 8x - 3y = -6

⇒ 8 × 1/3 (4 - 2y) - 3y = -6

⇒ 32/3 - 16y/3 - 3y = - 6

⇒ 32/3 + 6 = 25y/3

⇒ 50/3 = 25y/3

⇒ 50 = 25y

⇒ y = 2

And, From (i),

⇒ 3x + 2y = 4

⇒ 3x + 2 × 2 = 4

⇒ 3x  = 4 - 4

⇒ x = 0

Thus, The solution of the systems of equations by substitution are;

⇒ x = 0, y = 2

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Answer:

The numerator is the first number in a division problem (dividend). The denominator is the second number in a division problem (divisor).

Answer:

Divisor

Step-by-step explanation:

The denominator is the divisor. This is the split apart quantity.

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Answer:

23

Step-by-step explanation:

Note there is a constant difference between consecutive terms

- 1 - (- 4) = - 1 + 4 = 3

2 - (- 1) = 2 + 1 = 3

5 - 2 = 3

This indicates that the sequence is arithmetic with n th term

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = - 4 and d = 3, thus

[tex]a_{10}[/tex] = - 4 + (9 × 3) = - 4 + 27 = 23

Answer:

4th month

Step-by-step explanation:

As this graph shows the evolution of your collection over time, and not the number of key chains you collected in each month, you need to look for the month with the highest increase.

According to the graph on the first month you collected 4 key chains. After the 2nd month you had 6 key chains, so, you collected:

keys on 2nd month - keys on 1st month = 6-4 = 2 keys

In month 3 you went from 6 to 10 key chains, so you collected

keys on 3rd month - keys on 2nd month = 10-6 = 4 keys

On the next, month 4, you had 16, so you collected

keys on 4th month - keys on 3rd month = 16-10 = 6 keys

Finally, on the last month you had 18, having collected:

keys on 5th month - keys on 4th month = 18-16 = 2 keys

So, the month you most collected was the 4th, with 6 key chains. All the others months collected less keys (2 on the 2nd, 4 on the 3rd and 2 on the 5th).

I hope it is understandable.

Based on the graph, the month in which you collected the most key chains is May which is 4th month.

To determine this, we can look at the slope of the line between each pair of points. The slope of a line represents the rate of change, so a steeper slope indicates that the change is happening more quickly.

The slope of the line between the points for April and May is the steepest, which means that the number of key chains increased at the fastest rate during that month. Therefore, we can conclude that you collected the most key chains in May.

Here is a table of the slopes between each pair of points on the graph:

Month Previous Month Slope

May April 2.5

April March 2

March February 1.5

February January 1

As you can see, the slope between April and May is the highest, which indicates that you collected the most key chains during that month.

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The correct answer is (a) a sheet of wet cardboard, which becomes limp when moistened as the material loses its rigidity and strength, unlike the other items listed which maintain their form and firmness.

Among the options provided, a sheet of wet cardboard is most likely to feel limp. When cardboard absorbs water, the material becomes weak and loses its rigidity, making it bend or flop easily. The other materials listed, such as a sheet of ice, a sleeping child, and a sheet of plywood, retain their form and rigidity better when they are not altered by external factors like moisture.

A sheet of ice remains solid until it melts, a sleeping child is not an inanimate object and doesn't become limp simply because they are asleep, and a sheet of plywood is a construction material designed to remain sturdy even when faced with various environmental conditions. Therefore, (a) a sheet of wet cardboard is the correct answer as it is the one that could be expected to feel limp when wet.

Answer:

7 and 8 would work

Step-by-step explanation:

just insert them as w and they have to be greater than 20. I hope this helps.

Answer:

7 and 8

Step-by-step explanation:

Solving the inequality

5w - 10 > 20 ( add 10 to both sides )

5w > 30 ( divide both sides by 5 )

w > 6

The only values from the solution set greater than 6 are

7 and 8

Answer:

[tex]\large\boxed{A.\ y^3}[/tex]

Step-by-step explanation:

[tex]\text{Use}\ \dfrac{a^m}{a^n}=a^{m-n}\\\\\dfrac{y^{10}}{y^7}=y^{10-7}=y^3[/tex]

[tex]\text{Other method:}[/tex]

[tex]\text{We know:}\ a^n=\underbrace{a\cdot a\cdot a\cdot...\cdot a}_{n}\\\\y^{10}=\underbrace{y\cdot y\cdot y\cdot y\cdot y\cdot y\cdot y\cdot y\cdot y\cdot y}_{10}\\\\y^7=\underbrace{y\cdot y\cdot y\cdot y\cdot y\cdot y\cdot y}_7}[/tex]

[tex]\dfrac{y^{10}}{y^7}=\dfrac{y\!\!\!\!\diagup\cdot y\!\!\!\!\diagup\cdot y\!\!\!\!\diagup\cdot y\!\!\!\!\diagup\cdot y\!\!\!\!\diagup\cdot y\!\!\!\!\diagup\cdot y\!\!\!\!\diagup\cdot y\cdot y\cdot y}{y\!\!\!\!\diagup\cdot y\!\!\!\!\diagup\cdot y\!\!\!\!\diagup\cdot y\!\!\!\!\diagup\cdot y\!\!\!\!\diagup\cdot y\!\!\!\!\diagup\cdot y\!\!\!\!\diagup}=y\cdot y\cdot y=y^3[/tex]

Answer:

1.) 24

2.) 70°

Step-by-step explanation:

1.) 12*2=24

2.) 180°-110°=70°

Answer:

first proof should be cpctc, second proof is the triangle sum theorem

Answer:

[tex]f(x) = -2x^2 + 7x + 9[/tex]

Step-by-step explanation:

[tex]f(x) = ax^2 + bx + c\\f(0) = 9 => c = 9;\\f(2) = 15 = 4a + 2b + 9 <=> 2a + b  = 3\\f(3) = 9a + 3b + 9 = 12 <=> 3a + b = 1\\Subtract the second equation from the first:\\-a = 2 => a = -2; b = 7; c = 9\\f(x) = -2x^2 + 7x + 9[/tex]

To find a quadratic function, substitute each given coordinate into the equation and solve the resulting system of equations.

To find a quadratic function, we need to use the form y = ax^2 + bx + c. From the given set of values, we can substitute each coordinate (x, y) into the equation to get three different equations. So:

Now we have a system of equations that we can solve simultaneously. Solving the second and third equations using any appropriate method, we find that a = -1 and b = 5.

Therefore, the quadratic function that includes the given set of values is y = -x^2 + 5x + 9.

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Answer:

hnjmmm

Step-by-step explanation:

m,,\

l;'

Answer:

x = 2[tex]\sqrt{10}[/tex]

Step-by-step explanation:

Given that y varies inversely as the square of x then the equation relating them is

y = [tex]\frac{k}{x^2}[/tex] ← k is the constant of variation

To find k use the condition y = 2 when x = 4

k = yx² = 2 × 4² = 2 × 16 = 32

y = [tex]\frac{32}{x^2}[/tex] ← equation of variation

When y = [tex]\frac{4}{5}[/tex], then

[tex]\frac{4}{5}[/tex] = [tex]\frac{32}{x^2}[/tex] ( cross- multiply )

4x² = 160 ( divide both sides by 4 )

x² = 40 ( take the square root of both sides )

x = [tex]\sqrt{40}[/tex] = [tex]\sqrt{4(10)}[/tex] = 2[tex]\sqrt{10}[/tex]

Answer:

231

Step-by-step explanation:

Given

[tex]\frac{4}{77}=\frac{12}{x}[/tex]

Cross Multiply

[tex]x \times 4=12\times 77\\x=\frac{12\times 77}{4} \\x= 3\times 77\\x= 231[/tex]

Therefore x=231

Answer:

Step-by-step explanation:

The formula of an area of a square:

[tex]A=s^2[/tex]

s - side of a square

We have

[tex]A=1yd^2[/tex]

Therefore

[tex]s^2=1yd^2\to s=\sqrt{1yd^2}=1yd[/tex]

Answer:

A) The second day

B) 9/16 inches

Step-by-step explanation:

A) Elsa reached farther on the second day because -1/16 > -5/8

B) To calculate this we must first put both fractions above the same denominator. We can then subtract the smaller one from the bigger one:

-1/16 - (-10/16) = 9/16

Elsa reached 9/16 inches farther on the second day then she did on the first.

Final answer:

Elsa reached farther on the second day than the third day during her flexibility tests. She reached 9/16 inches farther on the second day compared to the third day.

Explanation:

Elsa is taking physical fitness tests in her strength training class where she tracks her progress by comparing her flexibility results to the baseline (first day). A negative value indicates she did not reach as far as the baseline.

A. On the second day, Elsa's flexibility test result was recorded as - 1/16 inches, and on the third day, it was -5/8 inches. Since -1/16 is greater than -5/8 (closer to zero), it means Elsa reached farther on the second day than the third day.

B. To find out by how much Elsa reached farther on the second day compared to the third day, we calculate the difference between the two measurements: (-1/16) - (-5/8) = 5/8 - 1/16. We must find a common denominator to subtract these fractions, which is 16. So we have (10/16) - (1/16) = 9/16 inches. Therefore, Elsa reached 9/16 inches farther on the second day compared to the third day.

First find x and y.

Solve system of equations by elimination.

  3x-y=3

+(-x+y=3)

---------------

2x=6

x=3

Now plug in x into one of the equations to find y.

-3+y=3

y=6

xy=3x6=18

Final answer:

The product of xy, given the system of equations 3x - y = 3 and -x + y = 3, is 18. This is found by first solving for x and y using the elimination method and then multiplying the obtained values.

Explanation:

To find the product of xy, we need to solve the system of equations given by 3x - y = 3 and -x + y = 3. Here we'll use the elimination method. Adding both equations together, we eliminate y:

3x - y + (-x + y) = 3 + 3

Which simplifies to:

2x = 6

Dividing both sides by 2, we get:

x = 3

To find y, we substitute x back into one of the original equations, for example, the second equation -x + y = 3:

-(3) + y = 3

-3 + y = 3

Adding 3 to both sides gives us:

y = 6

Now we can find the product of xy:

xy = 3 * 6

xy = 18

Therefore, the product of xy is 18.

Answer:

165150 is the sum of the multiples of 3 between 100 and 1000.

Step-by-step explanation:

We need to find the sum of multiples of 3 between 100 and 1000.

First we will find the Total number of multiples of 3 between 100 and 1000.

Let a be the first multiple and l be the last multiple of 3

100 is not the multiple of 3.

101 is not the multiple of 3.

102 is the multiple of 3.

Hence first term a = 102

Similarly.

1000 is not a multiple of 3

999 is a multiple of 3

hence last term l = 999

Also d is the common difference.

hence d = 3.

Now by using Arithmetic progression formula we get;

[tex]T_n(l) =a+(n-1)d\\ 999=102+(n-1)3\\999-102=(n-1)3\\897=(n-1)3\\\frac{897}{3}=n-1\\\\n-1=299\\n=299+1\\n=300[/tex]

Hence there are 300 multiples of 3 between 100 and 1000

Now n=300, a=102, l = 999

Hence to find the sum of all the multiples we use the Sum of n terms in AP  formula;

Sum of n term [tex]S_n= \frac{n}{2}(a+l)[/tex]

[tex]S_{300}= \frac{300}{2}(102+999)\\\\S_{300}= 150(102+999)\\S_{300}= 150\times 1101\\S_{300}= 165150[/tex]

Hence,165150 is the sum of the multiples of 3 between 100 and 1000.

Answer:

The number of marbles does Tommy will get is 18 .

Step-by-step explanation:

Given as :

The total number of  marbles share between Tommy and Robbie = 48

The marbles were distributed between then in the ratio 3 : 5

Let the number of marbles does Tommy have = 3 x

The number of marbles does Robbie have = 5 x

Now,

According to question

The total number of  marbles share between Tommy and Robbie = 48

Or,  the number of marbles does Tommy have + The number of marbles does Robbie have = 48

Or, 3 x + 5 x = 48

Or, 8 x = 48

∴  x = [tex]\frac{48}{8}[/tex]

I.e  x = 6

So, the number of marbles does Tommy have = 3 × 6 =18

The number of marbles does Robbie have = 5 × 6 = 30

Hence the number of marbles does Tommy will get is 18 . Answer

Answer: collision zone

Step-by-step explanation:As a result of this collision, the sedimentary rocks which were settled in the large-scale depression in the Earth's crust called Tethys were folded and formed the Himalayas.

C collision zone

The Himalayas are the world's highest mountains, straddling the Indian and Eurasian plates. The Himalayas were formed by a collision zone.

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