6y-5x=5 and x=2y+7 using substition in linear functions

There were 375 adult tickets sold.

This question involves a concept in basic algebra. Let's denote the number of adult tickets as A and the number student tickets as S. From the problem, we know that the total number of tickets sold is 676, so A+S=676. The problem also tells us that there were 74 fewer student tickets sold than adult tickets, so we know that S=A-74.

We can substitute the value of S from the second equation into the first equation which gives us A+(A-74)=676. By solving this equation we find that A=375, so there were 375 adult tickets sold.

Let's denote the number of adult tickets sold as x. Since there were 74 fewer student tickets sold, the number of student tickets sold is x - 74. The total number of tickets sold is the sum of the adult and student tickets, which is 676.

Therefore, we can write the equation:

x + (x - 74) = 676

Simplifying the equation:

2x - 74 = 676

Adding 74 to both sides:

2x = 750

Dividing by 2:

x = 375

So, 375 adult tickets were sold.

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1/2(4x-5) + 5/2 = 10

Use the distributive property:

2x - 5/2 + 5/2 = 10

Use addition property:

2x = 10

Divide both sides by 2:

x = 10/2

x = 5

Answer:   " 874.33 °  " .

___________________________________

Step-by-step explanation:

15.26 rad * ( 180 degree / [tex]\pi[/tex]  rad )  ;

          =  [ (15.26 * 180) / [tex]\pi[/tex] ]  degrees ;

          =  [ ( 2746.8 ) / [tex]\pi[/tex]  ] degrees.

          =  [ ( 2746.8) / 3.14) ]  degrees  ;

          =  874.3336 degrees;

          →  round to:  " 874.33 degrees ."

____________________________________

Final answer:

To find the degree measure of radian 15.26, multiply 15.26 by 57.3, resulting in 874.798 degrees.

Explanation:

To convert radians to degrees, you can use the conversion factor: 1 radian = 57.3 degrees.

Given that 15.26 radians is the measure:

Multiply 15.26 by 57.3 to get the degree measure.

15.26 radians * 57.3 degrees/radian = 874.798 degrees

Question 1:

Shop A trainers normal price= £85

[tex]\frac{1}{3}[/tex] is off so it becomes [tex]\frac{1}{3}\times85=28.33[/tex]

So price becomes: [tex]85-28.33=56.67[/tex]

Shop B trainers normal price= £80

30% is off so it becomes: [tex]\frac{30}{100}\times80=24[/tex]

So price becomes: [tex]80-24=56[/tex]

So, Shop B has cheaper trainers.

Question 2:

In a sale all items are reduced by = 30%

On the final day the sale price are reduced by = 20%

On the day before the last day of the sale, the price of the sofa was [tex]0.7\times290=203[/tex]

As given, on the last day of the sale, the price was again reduced to 80% of the price the day before, so price becomes: [tex]0.8\times203=162.40[/tex]

Hence the price was £162.40

Final answer:

To use the distributive property to write an expression equivalent to 5×(3+4), distribute the 5 to both the 3 and the 4 and simplify.

Explanation:

To use the distributive property to write an expression equivalent to 5×(3+4), we need to distribute the 5 to both the 3 and the 4. This means we need to multiply 5 by each number inside the parentheses:

5 × 3 = 15

5 × 4 = 20

So, the expression equivalent to 5×(3+4) is 15 + 20, which simplifies to 35.

It is known that 60 minutes equals 1 hour.

Therefore, the first thing we do to solve the problem is to calculate how many hours are equivalent to 96 minutes.

For that we calculate:

[tex]96 minutes * \frac{1 hour}{60minutes}=\frac{96}{60}=1.6hours\\[/tex]

Thus:

96 minutes = 1.6 hours.

1.9 ounces of water are lost every 1.6 hours.

Therefore, in 8 hours the amount of water lost  is:

[tex]\frac{8hours}{1.6hours}*1.9 = 9.5\\[/tex] ounces of water

After 8 hours, 9.5 ounces of water are lost

Therefore, the amount of water left in the tank after 8 hours is:

[tex]80 000-9.5=79990.5[/tex] ounces

the answer is b. to calculate 5% interest you multiply whatever by 0.05, this immediately eliminates any other answer

Answer:

Since discriminant is positive, therefore, the given quadratic equation has two real solutions. Correct answer is the last option.

Step-by-step explanation:

We have been given a quadratic equation and we need to figure out the number of real solutions of the equation.

[tex]2x^{2}+7x-15=0[/tex]

We know that discriminant of a general quadratic equation [tex]ax^{2}+bx+c=0[/tex] is given by [tex]D=b^{2}-4ac[/tex]

For the given quadratic equation [tex]2x^{2}+7x-15=0[/tex], we have [tex]a=2,b=7,c=-15[/tex]. Upon substituting these values in the formula for discriminant, we get:

[tex]D=7^{2}-4(2)(-15)[/tex]

[tex]D=49+120[/tex]

[tex]D=169[/tex]

Since discriminant is a positive number, therefore, the given quadratic equation has two real solutions. Hence, the last option is the correct answer.

Answer:

two real solutions

Step-by-step explanation:

Answer:

So the difference of ages 2 years ago is [tex]B[/tex] years.

Step-by-step explanation:

The difference of age between me and my brother will not change whether we go back in time or forward in time, it will always be the same difference as of now. In this case it is B years. To further prove this we can do a calculation as below,

If I am F years old and brother is [tex]B[/tex] years older, the age of my brother is,

Age of the brother = [tex]F+B[/tex]

Age of me 2 years ago = [tex]F-2[/tex]

Age of my brother 2 years ago  = [tex]F+B-2[/tex]

So the difference of ages 2 years ago can be calculated as,

Age of my brother 2 years ago - Age of me 2 years ago

=[tex]F+B-2[/tex] -  [tex]F-2[/tex]

=[tex]F+B-2-(F-2)[/tex]

=[tex]F+B-2-F+2[/tex]

=[tex]B[/tex]

To find the constant 'a' in the function g(x) = 5x + a, you can substitute the known values into the function. Here, it leads us to the equation 5*4 + a = 31. Solving this equation gives 'a' = 11.

The question gives us the value of g(4) and asks us to find the constant 'a' in the function g(x) = 5x + a.

To solve for 'a', we can substitute the known values into the equation. We know that g(4) = 31, and the function g(x) is defined as 5x + a. Therefore, we replace 'x' with 4 in the function. This gives us 5*4 + a = 31.

Solving this equation, we find that 20 + a = 31. By subtracting 20 from both sides of the equation, we can solve for 'a', giving us 'a' = 31 - 20 = 11.

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Part a)

we know that

to find the equation of the line, I will use the two points that are closest to the line

Let

A(1,14)

B(7,7)

Part b)

Find the slope

we know that

the formula to find the slope between two points is equal to

[tex]m=(y2-y1)/(x2-x1)[/tex]

substitute

[tex]m=(7-14)/(7-1)[/tex]

[tex]m=(-7)/(6)[/tex]

[tex]m=-7/6=-1.167[/tex]

the answer part b) is

the slope is [tex]m=-7/6=-1.167[/tex]

Part c)

we know that

the equation of the line in point slope form is equal to

[tex]y-y1=m(x-x1)[/tex]

use the point B (7,7)

[tex]y-7=(-7/6)*(x-7)[/tex]

therefore

the answer part c) is

[tex]y-7=(-7/6)*(x-7)[/tex]

Part d)

we know that

the equation of the line in slope-intercept for is equal to

[tex]y=mx+b[/tex]

we have

[tex]y-7=(-7/6)*(x-7)[/tex]

[tex]y=(-7/6)x+(49/6)+7[/tex]

[tex]y=(-7/6)x+(91/6)[/tex]

therefore

the answer Part d) is

[tex]y=(-7/6)x+(91/6)[/tex] or [tex]y=-1.167x+15.167[/tex]

Answer:

67.23

Step-by-step explanation:

Please refer to the attachment photo for explanation

Final answer:

The vertical distance between the bird and the fish is 67 2/9 feet.

Explanation:

To calculate the vertical distance between the bird and the fish, we need to add the distance the bird is flying above the sea to the distance the fish is swimming below the sea.

The bird is flying at a height of 43 5/9 feet above the sea, which can be converted to an improper fraction for easier calculation:

43 5/9 = (43×9 + 5)/9 = 392/9 feet

The fish is swimming at 23 2/3 feet below the surface of the sea, which also can be converted to an improper fraction:

23 2/3 = (23×3 + 2)/3 = 71/3 feet

To find the total distance, we add these two fractions:

To add these fractions, we need a common denominator. The lowest common denominator for 9 and 3 is 9.

When we convert the improper fraction back to a mixed number, we get:

So, the vertical distance between the bird and the fish is 67 2/9 feet.

Answer: 747

Step-by-step explanation:

16x9+67x9

First multiply 16 and 9 which is equal to 144

144+67x9

now multiply 67 and 9 which is equal to 603

144+603

Now add 144 and 603 which is equal to 747

So the answer to 16x9+67x9 is 747

use PEMDAS

16 * 9 + 67 * 9 =

144 + 603 =

747

Answer:

XY=8

Step-by-step explanation:

In △XYZ, XY=XZ

It is isosceles triangle whose equal sides are XY=XZ

We are given,  

XY=2a

YZ=3a+1

XZ=5a-12

XY=XZ

So, 2a=5a-12

Solve for a,  

2a-5a=-12

-3a=-12

a=4

Now we put a=4 into XY=2a  

So, XY=2(4)=8

Answer:

1.In △XYZ, XY=XZ.

We have to Find the length of XY of △XYZ if XY=2a, YZ=3a+1, and XZ=5a−12.

Now, X Y=X Z  [given]

→2 a= 5 a-12

Bringing like terms on same side

→2 a-5 a=-12

→-3 a=-12

→a=(-12)÷(-3)

a=4 is correct answer among all the options.

2.In △ABC, m∠A=(4x+7)° and m∠B=(5x−3)°.

What is m∠B?

Ans: as ∠ C not given we can't find ∠B.

The northern hemisphere is experiencing spring at Point B.

Spring is one of the four seasons. It follows winter and is followed by summer. During the spring, in the northern regions of the Northern Hemisphere, the trees become much greener and many plants flower; gradually it gets warmer and the chance of frost decreases.

Astronomical spring starts in the Northern Hemisphere usually on March 20 and ends usually on June 21.

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Answer: point  b

Step-by-step explanation:

ANSWER TO QUESTION 1.

We plot the points:

[tex]P(8,0)[/tex]

[tex]Q(6,2)[/tex]

and

[tex]R(-2,-4)[/tex]

We plot the image triangle also with the points,

[tex]P'(4,0)[/tex]

[tex]Q'(3,1)[/tex]

and

[tex]R(-1,-2)[/tex]

See graph in attachment.

ANSWER TO QUESTION 2.

The scale factor is the ratio of the image length to the object length.

[tex]Scale\: factor=\frac{|P'Q'|}{|PQ|}[/tex].

We need to use the distance formula to determine the two lengths.

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

[tex]|P'Q'|=\sqrt{(3-4)^2+(1-0)^2}[/tex]

[tex]|P'Q'|=\sqrt{(-1)^2+(1)^2}[/tex]

[tex]|P'Q'|=\sqrt{1+1}[/tex]

[tex]|P'Q'|=\sqrt{2}[/tex]

[tex]|PQ|=\sqrt{(6-8)^2+(2-0)^2}[/tex]

[tex]|PQ|=\sqrt{(-2)^2+(2)^2}[/tex]

[tex]|PQ|=\sqrt{4+4}[/tex]

[tex]|PQ|=\sqrt{8}[/tex]

[tex]|PQ|=2\sqrt{2}[/tex]

Therefore the scale factor of the dilation is

[tex]Scale\: factor=\frac{\sqrt{2}}{2\sqrt{2}}[/tex].

[tex]Scale\: factor=\frac{1}{2}[/tex].

ANSWER TO QUESTION 3

For a reflection in the y-axis we negate the x-coordinates. That means we are using the y-axis as our mirror line. The mapping is given as follows:

[tex]P'(4,0)\rightarrow P''(-4,0)[/tex]

[tex]Q'(3,1)\rightarrow Q''(-3,1)[/tex]

and

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

ANSWER TO QUESTION 4

We can see from the diagram that, PQR is bigger than P"Q"R".

The reason is that PQR was reduced by scale factor of half and then reflected in the y-axis to obtain P"Q"R".

Since dilation is not a rigid motion, the two triangles PQR and P''Q''R" are not equal in all respect, therefore they are not congruent.

The equation representing a linear function with a slope of 4 / 5 and a y-intercept of -6 is y = 4 / 5 x - 6.

The equation of a linear function can be written in the form:

y = 4 / 5 x + b

where "m" represents the slope of the line, and "b" represents the y-intercept (the value of y when x is 0).

Given that the slope is 4/5 and the y-intercept is -6, the equation would be:

y = 4 / 5 x - 6

So, the equation representing a linear function with a slope of 4.5 and a y-intercept of -6 is y = 4.5x - 6.

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Complete question is :

Which equation represents a linear function that has a slope of 4/5 and a y-intercept of –6?

y = k / x² ( y varies inversely as the square of x )

y = 1/8 when x = 1:

1/8 = k / 1²

8 k = 1

k = 1/8

For x = 5:

y = 1/8  / 5² = 1/8 : 25 = 1/8 · 1/25 = 1/200

Answer: A ) 1/200

Hope This Helps!!!

Solution is given in image attached.

Not sure exactly what your asking but the numerical form of that would be $322,907.

322,907

3=the hundred thousandth place which in this case is 3

2=the ten thousandth place which in this case is 2

2=the thousandth place which in this case is 2

9=the hundredth place which in this case is 9

0=the tenth place which in this case is 0

7=the ones place which in this case is 7

Hope this helps!

If I understand what you're saying. It would be the absolute value of -37, which is 37. Also, the absolute value of 37 is 37.

The absolue valor of 37 is 37

Answer:

r = y / (4π)  

37.68 = 4 x 3.14 x r  

37.68 = 12.56 r  

so r = 37.68 ÷ 12.56 = 3

Step-by-step explanation:

We want to solve the given equation for r.

We will get:

r = y/(4*π)

The equation for the total amount of  "y" tarn in inches is:

y = 4*π*r

Where π = 3.14159

And r is the radius of the soup can.

We want to solve the given equation for r, this means that we need to isolate r.

To do it, we just need to divide by 4*π in both sides, so we get:

y/(4*π) = 4*π*r/(4*π) = r

Then we got:

r = y/(4*π)

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If you mean standard form its

.000000059

5 pounds= 3.75

12 pounds= x

5x= 12*3.75

5x=45

12 pounds costs $9

Answer:

y = 0.15x+77 is the equation linear connecting total cost y and miles driven x

Step-by-step explanation:

Given that the leasing company charged a flat rental fee for the week, plus a charge for each mile driven.

Let flat rental fee be c and cost per mile driven = m and miles driven = x

Total cost =y

Then y = mx+C is the linear equation.

to find m and c, we use the fact that y =110.30 when x = 222

i.e. 110.30 = c+222x

and similarly 99.05 = c+147x

Subtract to eliminate c

11.25 = 75 x

0.15 =x

Substitute in I equation

110.30 = c+222(0.15)

c = 77

Hence y = 0.15x+77 is the equation linear connecting total cost y and miles driven x

Answer:

y = 0.15x+77

Step-by-step explanation:

i did it

co= same         planar = plane

coplanar means "same plane"

Answer: D

x-intercept: (4,0)

y-intercept: (0,2)

100 can go into 750  7.5 times :)

750 divided by 100 is 7.5 so 100 goes into 750 7.5 times

Answer:

3.2 cm on the map (in centimeters) represents an actual distance of 4 km

Step-by-step explanation:

The scale of a map says 4cm represents 5km

We are supposed to find  what distance on the map (in centimeters) represents an actual distance of 4 km

5 km = 4 cm

1 km = [tex]\frac{4}{5} cm[/tex]

4 km = [tex]\frac{4}{5} \times 4 cm[/tex]

4 km = [tex]3.2 cm[/tex]

Hence 3.2 cm on the map (in centimeters) represents an actual distance of 4 km