what is the gradient of the line y=3x+7

Answer:  2, 6

Step-by-step explanation:

Triangle Inequality Theorem states that the sum of two sides must be GREATER than the third side.

RS + ST > RT    and     RS + RT > ST     and     ST + RT > RS

2x + 4x > 12                  2x + 12 > 4x                  4x + 12  > 2x

       6x > 12                          12 > 2x                          12  > -2x

         x > 2                            6 > x                             -6 < x

         2 < x                             x < 6                             invalid

Answer:  2 < x < 6      

Graph:     O----------------------O

                2                          6

 Note: -6 is invalid because you cannot have a negative length.                     

Answer:

A

d = 2

Step-by-step explanation:

Formula

l = a + (n - 1)d

Givens

n = 10

a = - 5

l = 13

Solution

13 = - 5 + (10 - 1)d       Substitute

13+5 = -5+5 + 9d       Add 5 to both sides

18 = 9d                      Divide by 9

18/9 = 9/d

d = 2

Answer:

x=-9

Step-by-step explanation:

2x+6+5x=6x-3

7x+6=6x-3

7x-6x=-3-6

x=-9

Answer:

x= -9

Step-by-step explanation:

2(x+3)+5x=3(2x-1)

2x+6+5x=6x-3

7x+6=6x-3

7x-6x= -3-6

x= -9

Multiply 25 total students by 40% to find thew number that like science:

25 x 0.40 = 10

10 students like science.

You are told 15 students like math.

More students like math.

Answer:

see attachments

Step-by-step explanation:

Answer:

12/13

Step-by-step explanation:

The probability of not drawing an ace is =

1 minus the probability of drawing an ace.

there are 4 aces in a deck

hence the probability of not drawing an ace =

1 - [tex]\frac{4}{52}[/tex]

= 48/52 = 12/13

The required probability of not drawing an ace would be 12/13.

Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.

You draw a card from a standard deck of 52 playing cards.

The probability of not drawing an ace is P(E)

There are 4 aces in a deck

So the number of favorable outcomes n(E)= 4

And the total number of outcomes n(S) = 52

Thus, the probability of drawing an ace = n(E)/n(S) = 4 / 52

The probability of not drawing an ace will be:

⇒ P(E) = 1 - n(E)/n(S)

⇒ P(E) = 1 - 4 / 52

⇒ P(E) = 48/52

⇒ P(E) = 12/13

Therefore, the required probability of not drawing an ace would be 12/13.

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Resolviendo un sistema de ecuaciones, veremos que el número de dos cifras es 97.

¿Como encontrar el sistema de ecuaciones?

Podemos escribir un número de dos cifras como:

a*10 + b

Donde a y b son dos numeros de una cifra.

Entonces podemos escribir las restricciones:

"Si un número de dos cifras se disminuye en 17 y esta diferencia se divide por la suma de sus cifras, el cociente es 5"

((a*10 + b) - 17)/(a + b) = 5

"si el número disminuido en 2 se divide por la cifra de las unidades disminuida en 2, el cociente es 19"

(a*10 + b - 2)/(b - 2) = 19

Entonces tenemos un sistema de ecuaciones, que vamos a escribir como:

a*10 + b - 17 = (a + b)*5

a*10 + b - 2 = 19*(b - 2)

Donde pase los denominadores a la derecha, así es más simple de leer.

Para resolver esto, primero debemos simplificar ambas ecuaciones, vamos a obtener:

a*10 + b - 17 = a*5 + b*5

a*10 + b - 2 = 19*b - 38

Moviendo los terminos con variables a la izquierda y los constantes a la derecha:

a*10 + b - a*5 - b*5 = 17

a*10 + b - 19*b = -38 + 2

Terminamos de simplificar:

a*5 - b*4 = 17

a*10 - b*18 = -36

Ahora debemos aislar una de las variables en una de las ecuaciones, vamos a aislar a en le primera:

a = (17 + b*4)/5

Ahora reemplazamos esto en la otra ecuación y resolvemos para b:

10*(17 + b*4)/5 - b*18 = -36

2*(17 + b*4) - b*18 = -36

34 + b*8 - b*18 = -36

34 - b*10 = -36

-b*10 = -34 - 36 = -70

b = -70/-10 = 7

Para encontrar el valor de a usamos la ecuación:

a = (17 + b*4)/5 = (17 + 7*4)/5 = 9

Entonces podemos concluir que el número es 97.

Sí quieres aprender más sobre sistemas de ecuaciones, puedes leer:

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Answer:

x=2

Step-by-step explanation:

3x+2=8

Subtract 2 from both sides

3x=6

Divide 3 from both sides

x=2

Answer:

2. 13

Step-by-step explanation:

The least number of classes need for all of the students to be registered in a class is 13 since you want all of the stuednts to be registered so no one should be left out. If we do 12*12 (12 students in each class and there are 12 classes), that would only let 144 students take the swimming classes and 8 students would be left out. We don't want that though since we want all of the students to be registered. So let's go to 12*13 (12 students in each class and  there are 13 classes), that would let 156 students take the swimming class. 156>152 so therefore, 13 classes would allow for all 152 students to be registered and it is the least number of classes needed for all the students to be registered in a class (plus you would have 4 seats left for anyone who wants to register in the future but the remainder doesn't matter).  

Answer:

Macy’s

Step-by-step explanation:

let’s find the cost of each shirt

JCPenny’s: 14.99 x 0.80 = $11.99

                   11.99 x 1.06 = $12.70

                   The final cost of the JCPenny shirt is $12.70

Macy’s: 17.99 x 0.65 = $11.69

             11.69 x 1.07 = $12.51

             The final cost of the Macy’s shirt is $12.51

$12.51 is less than $12.70

So, the Macy’s shirt is the better deal :)

Answer:

The value of x is 13.5 units.

Step-by-step explanation:

You can also apply this formula :

[tex] \frac{a}{ \sin(A) } = \frac{b}{ \sin(B)} = \frac{c}{ \sin(C) } [/tex]

So for this question :

[tex] \frac{x}{ \sin(34) } = \frac{11}{ \sin(27) } [/tex]

[tex]x = \frac{11}{ \sin(27) } \times \sin(34) [/tex]

[tex]x = 13.5 \: units \: (near.tenth)[/tex]

Answer:

x ≈ - 5.32, x ≈ 1.32

Step-by-step explanation:

Given

x² + 4x - 7 = 0 ( add 7 to both sides )

x² + 4x = 7

To complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(2)x + 4 = 7 + 4

(x + 2)² = 11 ( take the square root of both sides )

x + 2 = ± [tex]\sqrt{11}[/tex] ( subtract 2 from both sides )

x = - 2 ± [tex]\sqrt{11}[/tex]

Thus

x = - 2 - [tex]\sqrt{11}[/tex] ≈ - 5.32 ( to 2 dec. places )

x = - 2 + [tex]\sqrt{11}[/tex] ≈ 1.32 ( to 2 dec. places )

Answer:

Step-by-step explanation:

x+y≥ 10

2x+3y≤24

Answer:

x+y≥ 10

2x+3y≤24

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

[tex]y=(2x-3)/5[/tex]

[tex]5y=2x-3[/tex]

[tex](5y+3)/2=x[/tex]

[tex](5x+3)/2=y[/tex]

[tex]f^{-1}(x)=(5x+3)/2[/tex]

Answer:

b^2 + 2b <= 168

Step-by-step explanation:

The base is b.

The height, h, is 4 in. greater than twice the base, so the height is 2b + 4.

The area of a triangle is bh/2. We replace h with the expression for height.

A = bh/2 = b(2b + 4)/2 = (2b^2 + 4b)/2 = b^2 + 2b

The area is b^2 + 2b.

The area is no more than 168 in.^2, so it is less than equal to 168 in.^2.

b^2 + 2b <= 168

("<=" means "less than or equal to")

Since you don't show the choices, choose an inequality that is equivalent to the one just above.

Answer:

Look up how  to find volume and you'll get the answer right away

Step-by-step explanation:

Answer:

s = 1.17, -23.17

Step-by-step explanation:

s^2 + 22s = 27

Take the coefficient of s

22

Divide by 2

22/2 =11

Square it

11^2 =121

Add this to both sides

s^2 + 22s+121 = 27+121

s^2 + 22s+121  = 148

(s+11)^2 = 148

Take the square root of each side

sqrt((s+11)^2) = ±sqrt(148)

s+11 =  ±sqrt(148)

Subtract 11 from each side

s+11-11 = -11  ±sqrt(148)

s =  -11  ±sqrt(148)

s = -11 + sqrt(148) = 1.1655

   - 11 - sqrt(148)=-23.166

Rounding to the nearest hundredth

s = 1.17, -23.17

Answer:

5

Step-by-step explanation:

in math we can write as this

[tex] \frac{4}{x + 7} = \frac{3}{x + 4} [/tex]

4(x+4)= 3(x+7)

4x + 16 = 3x + 21

4x - 3x = 21 - 16

x = 5

Answer:

x=5

Step-by-step explanation:

You can approach this question in many different ways, but i'm gonna look at it algebraically, since it's the quickest and works pretty much all the time.

First, you want to convert the words they've given you and make it into a less confusing equation.

They told us that 4 divided by (x+7) = 3 divided by (x+4), which is the same as:

[tex]\frac{4}{x+7}[/tex] = [tex]\frac{3}{x+4}[/tex]

Now, we can multiply both sides by (x+7), which gives me:

4 = [tex]\frac{3(x+7)}{x+4}[/tex]

Now we can multiply both sides by (x+4), to get rid of the fractions:

4(x+4) = 3(x+7)

Then expand the brackets:

4x + 16 = 3x + 21

Move the x to one side and numbers to another side:

4x - 3x = 21 - 16

x = 5

Hope that helped : )

Answer:

Check photo

Step-by-step explanation:

Answer:

121

Step-by-step explanation:

5x-54=3x+16

5x-3x=16+54

2x=70

x=35

-------

mAB= 5x-54= 5*35-54= 175-54= 121

360÷20 = 18sides

U divide 360 by 20 because angles at the center add up to 360°

The given polygon will have 18 sides in total.

Given information:

The diagram shows part of a regular polygon.

The sides of this polygon subtend angles of 20° at the center of the polygon.

Let the polygon has n number of sides.

Now, the polygon is regular. So, its each side will be equal and it will make equal angle with the center.

The sum of angles made by all the sides will be equal to 360 degrees.

So, the number of sides n can be calculated as,

[tex]20\times n=360\\n=\dfrac{360}{20}\\n=18[/tex]

Therefore, the given polygon will have 18 sides in total.

For more details, refer to the link:

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Answer:

(3,3)

Step-by-step explanation:

x + y - 6= 0

x- y = 0

Add the two equations together

x + y - 6= 0

x- y = 0

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

2x - 6 = 0

Add 6 to each side

2x-6+6 = 0

2x = 6

Divide by 2

2x/2 = 6/2

x = 3

Now find y

x-y = 0

3 - y = 0

y = 3

Answer:

Step-by-step explanation:

y=6-x first equation

y=x for the second

Answer:

- 8/5

Step-by-step explanation:

A line has x-intercept -8 and y-intercept 5.

It means the line has passes through:

Slope as per slope formula:

Perpendicular lines have slopes negative reciprocal to each other

So the slope of the perpendicular line is:

Answer:

see below

Step-by-step explanation:

4. If ∠AYX = 25.5° that means that ∠XYZ = 25.5 * 2 = 51° because YA is the angle bisector.

5. If ∠XYZ = 64°, ∠AYZ = 64 / 2 = 32°.

6. You can construct ∠P and PQ by using a protractor. I'm not sure how to attach an image so I'll just tell you the answer I got for c which is about 3 cm.

Answer:

513333.33 cubic yards

Solution:

[tex]\frac{1}{2} bh[/tex]

[tex]\frac{1}{2} (110)(140)[/tex]

[tex]=7700[/tex]

[tex]V = 1/3AH[/tex]

[tex]V = 1/3(7700)(200)[/tex]

[tex]V=513333.33[/tex]

Answer:

simplified expression for √x^2+6x+9 if x≥3

is x+3

Step-by-step explanation:

[tex]\sqrt{x^2+6x+9} \\=>\sqrt{x^2+3x+3x+9} \\=>\sqrt{x(x+3)+3(x+3)} \\=>\sqrt{(x+3)(x+3)} \\=>\sqrt{(x+3)^2}\\=>(x+3) \ or -(x+3)[/tex]

but given that x≥3

then we have to negate solution -(x+3)\

Then simplified expression for √x^2+6x+9 if x≥3

is x+3

Answer:

1.(1,-2)

2.option 2

3. B

Step-by-step explanation:

y=2x-4

y=-x-1

2x-4=-x-1

3x=3

x=1

y=-1-1=-2

2.

slope is negative and y-intercept=6 (abve x-axis)

so option B

3.

slope is same

so same price to order 150 t-shirts

B

Answer:

D

Step-by-step explanation:

B needs to be 0 or else there is an extra constant term which makes the equation non proportional

Answer:

y = -319/20| x = 377/20

Step-by-step explanation:

/| 7/2-x-y-(3/5) = 0| -11*x-(13*y) = 0

We try to solve the equation: 7/2-x-y-(3/5) = 0

29/10-x-y = 0 // - 29/10-x

-y = -(29/10-x) // * -1

y = 29/10-x

We insert the solution into one of the initial equations of our system of equations

We get a system of equations:

/| -(13*(29/10-x))-11*x = 0| y = 29/10-x

-1*13*(29/10-x)-11*x = 0

2*x-377/10 = 0

2*x-377/10 = 0 // + 377/10

2*x = 377/10 // : 2

x = 377/10/2

x = 377/20

We insert the solution into one of the initial equations of our system of equations

For y = 29/10-x:  

y = 29/10-377/20

y = -319/20

We get a system of equations:

/| y = -319/20| x = 377/20

Answer: the  answer is -0.04 ,1 ,-0.04 ,loss of 0.04 gallons of fuel for every 1 mile

Step-by-step explanation:

From the given table we can noticed that the fuel remaining (gallons) decreases as distance (miles).

It is clear that the distance increases by 1 mile for each next row and the remaining fuel is changed for each next row

The change in fuel remaining from one row to the next in the table is -0.04 gallons.

1) The change in fuel remaining from one row to the next in the table is -0.04 gallons.

2) The change in distance from one row to the next in the table is 1 mile.

3) The slope of the line that runs through the points given in the table is -0.04.

4) The slope is -0.04 it means the remaining fuel decreases by 0.04 gallons in each mile.

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

Now,

From the given table we can noticed that the fuel remaining (gallons) decreases as distance (miles).

Hence, It is clear that the distance increases by 1 mile for each next row and the remaining fuel is changed for each next row is,

⇒ 13.46 - 13.50

⇒ - 0.04

Thus, The change in fuel remaining from one row to the next in the table is -0.04 gallons.

And, The change in distance from one row to the next in the table is 1 mile.

Hence, The slope is the rate of change of remaining fuel with respect to change in distance is,

⇒ m = - 0.04/1

⇒ m = - 0.04

Thus, The slope of the line that runs through the points given in the table is -0.04.

And, The slope indicates a Change in the fuel remaining in each mile. The slope is -0.04 it means the remaining fuel decreases by 0.04 gallons in each mile.

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