determine whether the point (1,5) is a solution to the system of equations g(x)=3x+2 f(x)=|x-1|+1. Explain your reasoning.

Answer:

3/10

Step-by-step explanation:

Find the LCM of 5 and 2.

LCM = 10

[tex]\frac{4}{5} - \frac{1}{2} = \frac{8 - 5}{10} = \frac{3}{10}[/tex]

Answer:

[tex]\frac{3}{10}[/tex]

Step-by-step explanation:

5 = 5 × 1

2 = 2 × 1

LCM = 2 × 5

10

[tex]\frac{2(4)}{2(5)} -\frac{5(1)}{5(2)}[/tex]

[tex]\frac{8}{10} -\frac{5}{10}[/tex]

[tex]\frac{3}{10}[/tex]

Answer:

First side is: 12cm

Second side is: 36cm

Third side is: 16cm

Step-by-step explanation:

Let x represent the shorter side

Then 3x represents the second side, and

x + 4 represents the third side.

Perimeter of three sides:

P = x + 3x + (x + 4)

Perimeter is 64, so

64 = x + 3x + (x + 4)

64 = 5x + 4

60 = 5x

12 = x

First side is x: 12cm

Second side is 3x: 3(12) = 36cm

Third side is x + 4: 12 + 4 = 16cm

Answer:

1: B. 2: 6n^6+9n^5+4n^2-4n. 3: D. 4: 6b^2-15b-9. 5: 48x^2-4x-4

Step-by-step explanation:

1.

A trinomial is a polynomial with three terms. The expression 7v^2 +2v +2 has 3 terms.

2.

A polynomial in standard form has its powers listed from highest power to lowest power. The terms are 6n^6, 4n^2, 9n^5, and -4n. Remove the bottom numbers to find 6, 2, 5, and 1. Next, put them in order. 6, 5, 3, 1. Then, re-add the bottom numbers. 6n^6+9n^5+4n^2-4n.

3. A sixth degree polynomial is one with a sixth degree power. So, the answer is either C or D. Next, let's look at the terms. The expression here has 4 terms. So, the answer is D.

4 and 5:

To solve expressions in this form, (a+b)(c+d), turn the expression into an equivalent one, ac+ad+bc+bd. Plug in the numbers (with a negative mark if its -a or a-b) into that expression to get your answer.

4 simplifies out into 6b^2+3b-18b-9, which can be simplified into 6b^2-15b-9

5 simplifies out into 48x^2+12x-16x-4, which can be simplified into 48x^2-4x-4.

Answer:

Probably "Median"

The mode doesn't really make sense,

and "mean" would probably be skewed by people who get divorced quickly

I would suggest "Median" the number of years that 1/2 of the couples are above and 1/2 below  

Step-by-step explanation:

Answer:

-2 and 19

Step-by-step explanation:

Answer:

19 and -2

Step-by-step explanation:

19 * -2 = -38

19 + -2 = 17

Hope this helps

Step-by-step explanation:

4*1 = 4

this indicates multiplication

8/9 = 0.88888888888 which when simplified would go back to 8/9 or .889

8 "over" 9 indicates division!

Answer:

Decimal expansion of 1/5 = 0.2

Answer:12

Step-by-step explanation:cumquat

9514 1404 393

Answer:

  yes

Step-by-step explanation:

By the "rule of 72", the amount will be doubled in 72/I years, where I is the annual interest rate in percent. That is, it can be estimated to take 72/4 = 18 years to double the $240 investment to $480. It would take another 18 years to double it again to $960. So, to achieve a balance of $1500 will be expected to take more than 36 years. The only reasonable answer choice is the one you have selected.

__

The exact solution is ...

  log (1500/240)/log(1 +0.04) ≈ 46.72 years ≈ 47 years.

Answer:

63.69 meters

Step-by-step explanation:

the total perimeter of two identical semi-circular = 100+100 = 200m

d = p/π = 200/3.14 = 63.69

Answer:

2- x=16/3 or 5.3

4- x=8

Step-by-step explanation:

yeah

Answer:

1. An Experimental

2. Dependent

3. Independent

Step-by-step explanation:

Considering the description of how the research was carried out, it can be concluded that This study is an example of AN EXPERIMENTAL study. This because the researcher is trying to study the effectiveness of a new drug for lowering cholesterol

The difference in cholesterol level is the DEPENDENT variable. This is because the difference in cholesterol level is what the researcher wants to determine.

The treatment with a drug or placebo is the INDEPENDENT variable. This is because this is what the researcher manipulates to determine the difference in cholesterol level which is the dependent variable in this experimental study.

Answer:

T T → T

Step-by-step explanation:

Given :

p = 10 > 7

q = 10 > 5

Evaluating if the statements are true :

p = 10 > 7, This is TRUE, Because 10 is truly greater Than 7

q = 10 > 5, This is TRUE, Because 10 is truly greater Than 5

The statements are both True statements :

p = True ; q = True

True and True = True

T & T = T

T T → T

Answer:

x2 + 7x + 12 = 0

Step-by-step explanation:

(x + 4) (x + 3)

x + 4 = 0 or x + 3 = 0

x = - 4 or x = - 3

Answer:

15^18/(15^3)=15^15

Step-by-step explanation:

rule for quotients of similar bases with different exponents is:

(a^c)/(a^b)=a^(c-b)  

15^18/(15^3)=15^15

Step-by-step explanation:

the answer is in the above image

Answer:

150 mL

Step-by-step explanation:

270 - 120 = 150

Hope this helps!

Answer:

30

Step-by-step explanation:

There are 14 data points on the plot

The median is the middle value, which is between the 7th and 8th data points

Since it is even, we find the average of the 7th and 8th data points

Add the 7th and 8Th data points values and divide by 2

( 30+30)/2 = 60/2 = 30

The median is 30

Answer:

30

Step-by-step explanation:

Middle numbers are 30 and 30 so you add them and then divide by two:

[tex]\frac{30 + 30}{2}[/tex] = [tex]\frac{60}{2}[/tex]= 30

Answer:

desmos(dot)com/calculator/gv8jsoui4w

Step-by-step explanation:

Create a table of appropriate x values e.g. x = 2 and substitute into y=3x which will be y=3*2 meaning y=6 at the point x=2. Repeat with different x values until you have enough points to draw a straight line.

Answer:

First term is 15

Step-by-step explanation:

Given data:

[tex]a_{7} =3\\d=-2[/tex]

Now,

[tex]a+6d=3.....(1)\\a_{n} =a+(n-1)d\\\\\\From equation (1)\\a+6(-2)=3\\a-12=3\\a=12+3\\a=15[/tex]

Therefore first term a =15

Correct option is (c)

Answer:

(-8,-8)

Step-by-step explanation:

Coordinates of a midpoint:

The coordinates of the midpoint of a segment is given by the mean of the coordinates of the endpoints.

In this question:

Endpoints (-16,0) and (0,-16).

x-coordinate:

[tex]\frac{-16+0}{2} = -8[/tex]

y-coordinate:

[tex]\frac{0-16}{2} = -8[/tex]

Then:

(-8,-8)

Answer:

The third choice

Step-by-step explanation:

a relation is a function if an input has at most one output for a given input

Choices 1, 2 and 4 are not functions as they have two different outputs for the same input. (See the red ovals)

Answer:

b) 27,000

Step-by-step explanation:

3 × 10 × 10 × 10 × 9 = 27000

'3' because the first digit can only be 3,6, or 9

'9' because the last digit cannot be zero, leaving only 9 options

[tex]\huge\bold{Given:}[/tex]

Length of the perpendicular "[tex]a[/tex]" = 5.

Length of the hypotenuse "[tex]c[/tex]" = 12.

[tex]\huge\bold{To\:find:}[/tex]

The length of the missing side ''[tex]b[/tex]".

[tex]\large\mathfrak{{\pmb{\underline{\orange{Solution}}{\orange{:}}}}}[/tex]

The length of the missing side (base) "[tex]b[/tex]" is [tex]\boxed{√119}[/tex].

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]

Using Pythagoras theorem, we have

[tex]({perpendicular})^{2} + ({base})^{2} = ({hypotenuse})^{2} \\ \\⇢ {a}^{2} + {b}^{2} = {c}^{2} \\\\ ⇢ {5}^{2} + {b}^{2} = {12}^{2} \\ \\⇢25 + {b}^{2} = 144 \\ \\⇢ {b}^{2} = 144 - 25 \\ \\⇢ {b}^{2} = 119 \\ \\⇢b = \sqrt{119} [/tex]

[tex]\sf\blue{Therefore,\:the\:length\:of\:the\:missing\:side\:"b"\:is\:√119.}[/tex]

[tex]\huge\bold{To\:verify :}[/tex]

[tex] {5}^{2} + { \sqrt{119} }^{2} = {12}^{2} \\\\ ⇝25 + 119 = 144 \\ \\⇝144 = 144 \\ \\⇝L.H.S.=R. H. S[/tex]

Hence verified. ✔

[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{♡}}}}}[/tex]

Answer:

A

Step-by-step explanation:

to find the inverse, there are two steps

1-interchange x and y

2-solve for y

so y=x+1/x

interchange to get x=y+1/y

and solving for y we multiply both sides by y to get xy=y+1

subtract both sides by y yielding xy-y=1

factor out y to get y(x-1)=1

then divide to get y=1/x-1

Answer:

D

Step-by-step explanation:

The mode is the value that appears most often in the number set for this set the most common numbers are 2, 5, and 6.

Answer:

d

Step-by-step explanation:

all show up 2 times

Answer:

Option B

Step-by-step explanation:

Equation of the function is,

[tex]g(x)=\sqrt{x-1}+2[/tex]

Parent function of the given function 'g' is,

[tex]h(x)=\sqrt{x}[/tex]

By translating the parent function 'h' n=by 1 unit horizontally left and 2 units upwards we get the function 'g'.

That means function 'g' starts from a point (1, 2).

Range of the function 'g' will be all the values of y ≥ 2.

Option B is the answer.

Answer:

Range of the function 'g' will be all the values of y ≥ 2.

Step-by-step explanation:

Answer:

The measure of the first angle is 50°.

Step-by-step explanation:

Let the three angles be a, b, and c.

The measure of the first angle is twice the measure of the second angle. In other words:

[tex]a=2b[/tex]

The measure of the third angle is 80° more than the measure of the second angle. In other words:

[tex]c=b+80[/tex]

And since the interior angles of a triangle must equal 180°:

[tex]a+b+c=180[/tex]

Substitute a and c:

[tex](2b)+b+(b+80)=180[/tex]

Combine like terms:

[tex]4b+80=180[/tex]

Subtract 80 from both sides:

[tex]4b=100[/tex]

And divide both sides by four:

[tex]b=25^\circ[/tex]

So, the measure of the second angle is 25°.

Since the measure of the first is twice the second, the measure of the first angle is 50°.

(And since the measure of the third is 80° than the second, the measure of the third angle is 105°.)

Answer:

y + 7 = -13/6(x-8)

and

y + 1 = -13/6(x+5)

Step-by-step explanation:

1. Find the slope using [tex]m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}[/tex].

-5-8/-1+7 = -13/6

2. Plug the slope into the point-slope form, [tex]y-y_{1}=m\left(x-x_{1}\right)[/tex].

y - y1 = -13/6(x-x1)

3. Plug in one of the points to get the answer.

y + 7 = -13/6(x-8)

y + 1 = -13/6(x+5)