Consider 4(2x + 3) = 2(4x + 6) after each
side of the equation is simplified.
Why does the equation have infinitely many
solutions?

Answer:

one gadget costs $15.80

Step-by-step explanation:

Let w = cost of one widget

Let g = cost of one gadget

Given:

⇒ 5w + 3g = 109.9

Given:

⇒ w + 4g = 75.7

Rewrite  w + 4g = 75.7  to make w the subject:

⇒ w = 75.7 - 4g

Substitute into  5w + 3g = 109.9  and solve for g:

⇒ 5(75.7 - 4g) + 3g = 109.9

⇒ 378.5 - 20g + 3g = 109.9

⇒ 378.5 - 109.9 = 20g - 3g

⇒ 268.6 = 17g

⇒ g = 15.8

Therefore, one gadget costs $15.80

To find the cost of one widget, substitute the found value for g into
w = 75.7 - 4g and solve for w:

⇒ w = 75.7 - 4(15.8)

⇒ w = 75.7 - 63.2

⇒ w = 12.5

Therefore, one widget costs $12.50

Answer:The quadratic model obtained using a quadratic regression solver with Coefficient rounded to the nearest hundredth is :y = - 15.57x² + 179.32x + 0.20height = yx = time                          Using the model obtained;The height, to the nearest foot, at a time, x = 6.4 seconds.y = - 15.57x² + 179.32x + 0.20y = - 15.57(6.4^2) + 179.32(6.4) + 0.20y = 510.1008y = 510

Step-by-step explanation:

Answer:  Reduce the expression, if possible, by cancelling the common factors

25223.52941176

Hoped this helped :)

Answer:

1. 32

2. 47

3. See explanation for number 3 below

Step-by-step explanation:

All you have to do is simply add 17 to however old Titus is. So if he's 15 years old, you just simply have to do 15+17, which is 32. For number 3, I'm assuming that they just want an explanation for how you do this process, in which case, this explanation is the answer to number 3. If that's not what they're looking for in number 3, then I'm sorry. But I'm pretty sure that's what they want there.

Answer:

C

Step-by-step explanation:

To find A you have to divide 3/5 by 4 so that would not work.

To find B you have to subtract 1/4 from 3/5 and that doesn't match the problem.

To find C you do divide 3/5 by 1/4 which matches the problem.

And lastly for D you would divide 1/4 by 3/5 which is the opposite of what the question is asking for.

Answer:

Step-by-step explanation:

4x + y = 8

x + 3y = 8

[tex]Here, \dfrac{a_{1}}{a_{2}}=\dfrac{4}{1}\\\\\\\dfrac{b_{1}}{b_{2}}=\dfrac{1}{3}\\\\\\\dfrac{a_{1}}{a_{2}} \neq \dfrac{b_{1}}{b_{2}}[/tex]

So, this system of equations is consistent and independent.

-4x + 6y = -2

2x - 3y = 1

[tex]\dfrac{a_{1}}{a_2}}=\dfrac{-4}{2}=\dfrac{-2}{1}\\\\\\\dfrac{b_{1}}{b_{2}}=\dfrac{6}{-3}=\dfrac{-2}{1}\\\\\\\dfrac{c_{1}}{c_{2}}=\dfrac{-2}{1}\\\\\\\dfrac{a_{1}}{a_{2}}=\dfrac{b_{1}}{b_{2}}=\dfrac{c_{1}}{c_{2}}[/tex]

So, the system of linear equations are consistent and dependent.

5x -2y = 4

5x - 2y = 6

[tex]\dfrac{a_{1}}{a_{2}}=\dfrac{5}{5}=1\\\\\\\dfrac{b_{1}}{b_{2}}=\dfrac{-2}{-2}=1\\\\\\\dfrac{c_{1}}{c_{2}}=\dfrac{4}{6}=\dfrac{2}{3}\\\\\\ \dfrac{a_{1}}{a_{2}}=\dfrac{b_{1}}{b_{2}} \neq \dfrac{c_{1}}{c_{2}}[/tex]

This system of equations is inconsistent.

Let's assume that all hours she worked were the first 35 hours of the week.

She would've made £22.80 x 35 = £798

So, she would've made 981.54 - 798 = 183.54 less than the actual amount

She is paid 15% more per hour after the first 35 hours -> She will get £26.22 per hour.

So, she work for 183.54 : 26.22 = 7(hours) after the first 35 hours

So in total, she worked for 35 + 7 = 42(hours).

Answer:

42 hours

We know she works at least 35 hours, so 35x22.80=798. This is her base pay without any extra hours.

981.54-798 =183.54. This is the amount she earnt for working extra hours. if we divide this by the rate she earns for extra hours (22.80x1.15=26.22), 184.54/26.22=7, we know she worked an additional 7 hours.

and 35 plus 7 = 42 :)

Answer:

the decimal is 1.75 and  The percentage is 175%

Step-by-step explanation:

Answer:

1.75 = 1 3/4

Step-by-step explanation:

1 3/4 = 1.75

Answer:

=

Step-by-step explanation:

-1.75 is the same as -1 3/4

Answer: The bottom three: [tex]\frac{48}{-17}[/tex], [tex]\frac{-48}{17}[/tex], and -2 [tex]\frac{14}{17}[/tex]

Step-by-step explanation:

     The first option is not because the numerator and denominator are flipped.

     The second option is not because this one is positive while the one given is negative.

     The third option is equivalent.

     The fourth option is equivalent.

     The fifth option is equivalent because - 48 / 17 = -2 [tex]\frac{14}{17}[/tex] when turned into a mixed number.

Answer:

[tex]\frac{48}{-17}, \frac{-48}{17}, -2\frac{14}{17}[/tex] (the last 3 options)

Step-by-step explanation:
As long as the negative is in either the numerator or the denominator (if it is in both then it is positive because the negatives cancel out), the entire fraction will be negative, so both [tex]\frac{48}{-17}[/tex] and [tex]\frac{-48}{17}[/tex] work as answers. The last option is just a simplified version of the fraction.

Answer:

3

Step-by-step explanation:

29 - 8 = 21

21 / 7 = 3

Therefore, the answer is 3

Answer:

wouldnt it be 3? cause 3*7=21 then add 8 thats 29

Step-by-step explanation:

Answer:

86 degrees

Step-by-step explanation:

The angles of a triangle all add up to 180.

x is 45 degrees

y is 49 degrees

49 + 45 = 94

180 - 94 = 86

The last angle of the triangle is 86 degrees. Since z is on the opposite side of it, it is equal to 86

Answer:

11

Step-by-step explanation:

if half of it is 22, then a whole life is 44 days. 1/4 of 44 days is 11 days so its A

Answer:

the answer is A (11 days)

Step-by-step explanation:

Hope this helps you!

Use the slope formula and pick any two points  to find the slope.

m= Y2- Y1/x2-x1

I picked the points (1,8) (3,14).

14-8/3-1= 6/2= 3

Hope this helps .

I think it's like 0.88, but I believe that's it rounded up.

Using a t-distribution, with 20 degrees of freedom, the critical t-value that corresponds to 95% confidence is t = 2.0860.

It is found with the help of a calculator, having two inputs:

Hence, using a calculator, with 20 degrees of freedom, the critical t-value that corresponds to 95% confidence is t = 2.0860.

More can be learned about the t-distribution at https://brainly.com/question/16162795

I really don't know I'm not big on school subjects

Answer:

D

Step-by-step explanation:

1/2 hour -> 1/3 pool

multiply this by 2

1 hour -> 2/3 pool

so D 2/3 pool

The fraction of the pool that would be filled per hour at the given rate is: D. 2/3 of the pool.

A constant rate can be described as a quantity that changes steadlity over time.

The rate that the pool gets filled is given as:

1/2 hr = 1/3 of the water that would be filled in the pool

1 hr would be: 1/3 × 2 = 2/3

Therefore, the fraction of the pool that would be filled per hour at the given rate is: D. 2/3 of the pool.

Learn more about rate on:

https://brainly.com/question/25184007

Answer:

[tex]m\angle L = 100^{\circ}[/tex].

[tex]m\angle J = 80^{\circ}[/tex].

[tex]m\angle M = 100^{\circ}[/tex].

Step-by-step explanation:

Since segment [tex]JM[/tex] is parallel to segment [tex]KL[/tex], quadrilateral [tex]JKLM[/tex] is a trapezoid.

Segment [tex]JK[/tex] and segment [tex]LM[/tex] (the two legs of this trapezoid) are equal in length. Hence, trapezoid [tex]JKLM[/tex] would be an isoscele trapezoid. By symmetry, [tex]m\angle L = m \angle K = 100^{\circ}[/tex].

Line [tex]JK[/tex] traverses line [tex]JM[/tex] and line [tex]KL[/tex]. [tex]\angle J[/tex] and [tex]\angle K[/tex] are a pair of consecutive interior angles as they are both between [tex]JM\![/tex] and [tex]KL\![/tex] and are on the same side of the traversal, [tex]JK\![/tex].

Since line [tex]JM[/tex] is parallel to line [tex]KL[/tex], any pair of consecutive interior angles between these two lines would add up to [tex]180^{\circ}[/tex] (supplementary angles.) Thus, [tex]\angle J[/tex] and [tex]\angle K[/tex] are supplementary angles; [tex]m\angle J + m\angle K = 180^{\circ}[/tex].

Since [tex]m\angle K = 100^{\circ}[/tex], [tex]m\angle J = 180^{\circ} - m\angle K = 180^{\circ} - 100^{\circ} = 80^{\circ}[/tex].

Answer:

For two different equations:

(3x+9)

x = -3

(4x+3)

x = -3/4

Finding x using both equations:

plug x = -3 into the other equation

4(-3) + 3 = -9

x = -9

plug x = -3/4 into the other equation

3(-4/3) + 9 = 27/4

x = 27/4

Set the equations equal to each other:

3x+9=4x+3

3x-4x = 3-9

-x = -3

x=3

PLEASE RATE!! I hope this helps!!

If you have any questions comment below

Answer:

C) 390

Step-by-step explanation:

Area of Blue:

18 × 25 = 450 in

Area of White:

6 × 10 = 60 in

450 - 60 = 390

Therefore, 390 sq in is the correct answer.

Answer:

The simplified expression of (4-5r+8s)(5r-9) is

40r s-25r^2-72s+65r-36

(hope this helped)

The simplified expression of (4-5r+8s)(5r-9) is [tex]65r - 25r^2 + 9r + 40rs - 72s.[/tex]

The simplified expression of (4-5r+8s)(5r-9) step by step.

Understanding how to simplify expressions can be incredibly useful in algebra and will make solving equations much easier. By using the distributive property, we can multiply the terms inside the parentheses and then combine like terms to get the simplified expression.

To simplify the expression (4-5r+8s)(5r-9), we'll use the distributive property, also known as the FOIL method (First, Outer, Inner, Last). This property allows us to multiply each term in the first parentheses by each term in the second parentheses.

1. First, we multiply the term "4" in the first parentheses by each term in the second parentheses:

4 * 5r = 20r

4 * (-9) = -36

2. Next, we move to the second term in the first parentheses, "-5r," and multiply it by each term in the second parentheses:

-5r * 5r = -25r²

-5r * (-9) = 45r

3. Lastly, we move to the third term in the first parentheses, "8s," and multiply it by each term in the second parentheses:

8s * 5r = 40rs

8s * (-9) = -72s

Now, we have all the resulting terms:

20r - 36 - 25r² + 45r + 40rs - 72s.

To simplify further, we combine like terms. Like terms have the same variable(s) raised to the same power:

20r + 45r = 65r

-36 + 45r = 9r

So, the simplified expression is:

65r - 25r² + 9r + 40rs - 72s.

In mathematical terms, we applied the distributive property to multiply each term in the first parentheses by each term in the second parentheses. Then, we combined like terms to obtain the final simplified expression, 65r - 25r² + 9r + 40rs - 72s.

To know more about Algebra here

https://brainly.com/question/29074939

#SPJ2

Answer:

11

Step-by-step explanation:

If you count the total values

it equals 11

Answer:

b) one quarter hour

Step-by-step explanation:

every section is worth 5 minutes, there are three sections, which equals 15 minutes, 15 minutes is a one-quarter hour. hope this helps :)

Answer:

B

Step-by-step explanation:

it Is one quarter of an hour because they are exactly 15 minutes

Answer:

Step-by-step explanation:

[tex]d=2\sqrt{\frac{A}{\pi}} =2\sqrt{\frac{616}{\pi} }[/tex]≈[tex]28.00563cm[/tex]

rounding 28.00563 to 28.

So hence, your answer is 28cm

-------------------------------------------------------------------------------------------------------------The beautiful thing about learning is that no one can take it away from you!

B.B.King

Thanks!

Have a great day!

~ms115~

Answer:

28

Step-by-step explanation:

area of a circle

[tex]\pi{r}^{2} [/tex]

616=3•142×r×r

616/3•142=r^2

196=r^2

r=√196

r=14

d=2r

d=2×14

d=28

Answer:

so how do i find the earea

Step-by-step explanation:

Answer:

No

Step-by-step explanation:

→ Substitute the x value into the equation

-9 × 1 + 1

→ Simplify

-8

→ Compare to given y value

0 ≠ -8

Answer:

no

when you substite the values you don't get the same values

Answer:

A(11:15)

Step-by-step explanation:

3+3 is 6

then Is 6+2 so is 8 then ir repeats ats 3 Like 3 6 8 and then 11

Answer:

24 Letters and 4 Postcards

Step-by-step explanation:

We have to set up a system of equations, since we have two unknown variables. Lets say postcards is the variable "x" and letters is the variable "y".

Our first equation will be the money spent: 0.33x + 0.49y = 13.08, this comes from knowing that it costs 0.33 dollars to mail a postcard and 0.49 dollars to send a letter.

The second equation is the total sent: x + y =28.

Now we need to solve for a single variable, let's do y (or letters). If we subtract y from both sides we get: x = 28 - y.

We can plug that into our first equatino to get: 0.33(28 - y) + 0.49y = 13.08.

If we multiply things out we get: 9.24 - 0.33y + 0.49y = 13.08, and now we have like terms. 9.24 + 0.16y = 13.08.

Subtract 9.24 from both sides to get: 0.16y = 3.84

Divide both sides by 0.16 to get: y = 24.

Now we can plug this into x + y = 28 to see that x= 4.

You could make sure this is correct by solving for x instead of y and do the same process.

Hope this helps.