State the vertex as an ordered pair.


y = -|3x +5|+7

Answers

Answer 1
in plain and short, what value of "x" makes the expression |3x + 5| to 0?

well, we can check by simply setting it to 0 and solving for x.

[tex]\bf 3x+5=0\implies 3x=-5\implies \boxed{x=-\cfrac{5}{3}}\\\\ -------------------------------\\\\ \textit{therefore, the vertex of }y = -|3x+5|\boxed{+7}\textit{ is at }\left(-\frac{5}{3}~,~7 \right)[/tex]

notice, all you do is, get the x-value that makes the expression to 0, and then append the constant outside it as the y-value, and that's the vertex.

Related Questions

Please put down the steps?

Answers

The answer is:  " x = 0, 1 " .
__________________________________________
Explanation:
__________________________________________
Given:
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   " √(x + 1)  − 1 = x "  ;   Solve for "x" ;

First, let us assume that "x ≥ -1 "

Add "1" to EACH SIDE of the equation:

 →  √(x + 1)  − 1  + 1 = x + 1  ; 

to get:  

 →  √(x + 1)  = x + 1 .

Now, "square" EACH side of the equation:

 →  [√(x + 1) ]²  = (x + 1 )² ;

to get: 

   x + 1 = (x + 1)² 

↔  (x + 1)²  = (x + 1) .


Expand the "left-hand side" of the equation:

 → (x + 1)² = (x + 1)(x +1) ;

Note: (a+b)(c+d) = ac +ad + bc + bd ;

As such:  (x + 1)(x + 1) = (x*x) + (x*1) +(1(x) + (1*1) ;
                                   =  x² + 1x + 1x + 1 ; 
                                   =  x²  + 2x  +  1 ;

Now, substitute this "expanded" value, and bring down the "right-hand side" of the equation; and rewrite the equation:
__________________________________________
   " (x + 1)² = (x + 1)(x +1) " ; 

  →  Rewrite as:  " x² + 2x + 1 = x + 1 " ;

 Subtract "x" ;  and subtract "1" ; from EACH SIDE of the equation:

               →   x² + 2x + 1 - x - 1 = x + 1 - x - 1 ; 

to get:    →   x² − x = 0  

Factor out an "x" on the "left-hand side" of the equation:
___________________________________________
         x² − x = x(x − 1) ;

         →  x (x − 1) = 0 ;

We have:  "x" and "(x − 1)" ; when either of these two multiplicands are equal to zero, then the "right-hand side of the equation equals "zero" .

So, one value of "x" is "0" .

The other value for "x" ;

→  x − 1 = 0 ;

Add "1" to each side of the equation:

  → x − 1 + 1 = 0 + 1 ; 

 →  x = 1 ; 
__________________________________
So, the answers:

 " x = 0, 1 " .
_________________________________

Read the following two statements. Then, if possible, use the Law of Detachment to draw a conclusion. If Robbie wants to save money to buy a car, he must get a part-time job. Robbie started a new job yesterday at a grocery store. Robbie wants to save money. Robbie wants to buy a car. not possible If Robbie wants to save money, he must get a part-time job.

Answers

Final answer:

Using the Law of Detachment, we can conclude that Robbie wants to save money because he started a new job and the first condition states that he needs a job to save for a car.

Explanation:

Using the Law of Detachment, we can draw a conclusion from the following two statements:

If Robbie wants to save money to buy a car, he must get a part-time job.Robbie started a new job yesterday at a grocery store.

Since Robbie started a new job, which is assumed to be part-time, we can conclude that Robbie wants to save money, as per the first statement which sets up a condition that needs to be fulfilled in order to save money. The specific intention of buying a car is not directly established, but it's often implied that people save for larger investments or expenses. The Law of Detachment only allows us to conclude propositions that directly follow from the given condition. Therefore, the direct conclusion we can draw here, based on the given statements and the Law of Detachment, is that Robbie wants to save money.

Final answer:

According to the Law of Detachment, Robbie wants to buy a car since he wants to save money and he has started a new job.

Explanation:

The Law of Detachment states that if we have a conditional statement of the form "If p, then q", and we know that p is true, then we can conclude that q is also true. In this case, let's analyze the given statements:

1. If Robbie wants to save money to buy a car, he must get a part-time job.

2. Robbie started a new job yesterday at a grocery store.

From statement 1, we can see that Robbie wanting to save money is the condition (p), and getting a part-time job is the conclusion (q). Since statement 2 confirms that Robbie has started a new job, which satisfies the condition (p), we can use the Law of Detachment to conclude that Robbie wants to save money (q) and therefore Robbie wants to buy a car (q). So, the conclusion is: that Robbie wants to buy a car.

△VAT≅△BDT. What is length of BT?

Enter your answer in the box.

Answers

we know that

If △VAT≅△BDT, then the corresponding sides will be congruent

[tex]VT=BT\\VA=BD\\ AT=DT[/tex]

we have

[tex]VT=6.3\ unit\\VA=3.7\ unit\\AT=4.7\ unit[/tex]

so

[tex]BT=6.3\ unit[/tex]

therefore

the answer is

[tex]BT=6.3\ unit[/tex]

cindy had a party. She invited two guests. Her guests each invited four guests, and then those guests each invited three guests.

Answers

In all there would be 17 guests. Including Cindy.
The total amount of guests would be 18 because the two guests brought four guests which would be 10 and since those guests in invited three guests each then it would lead up to the total of 18.

solve for p if 2|p|=4

Answers

First, isolate the absolute value by dividing both sides by 2.

2|p| = 4

|p| = 2

Now set p = 2, and set p = -2.

Since what was inside the absolute value symbol is just p, the equation is solved.

Answer: p = 2 or p = -2

which statement is equivalent to the inequality 14x-14>7x+7

Answers

14x-14>7x+7

14x - 7x > 7 + 14

7x > 21

x > 21/7

x > 3

Choose the correct answer for the amount of interest earned in the following simple interest problem. A deposit of $4,000 at 6.5% for 270 days

Answers

The formula is
I=prt
I interest earned?
P principle 4000
R interest rate 0.065
T time 270/360days
I=4,000×0.065×(270÷360)
I=195

Note that the interest is ordinary not exact. Ordinary interest assumes that there are 30 days in every month or in other word 360 days a year.

Hope it helps!


Answer:

195.00

Step-by-step explanation:

A scientist is working with 3 meters of gold wire. How long is the wire in millimeters?

Answers

Final answer:

To convert the length of 3 meters of gold wire to millimeters, multiply the length in meters by 1000. The wire is 3000 millimeters long.

Explanation:

The scientist is working with 3 meters of gold wire, and we need to convert this length into millimeters. There are 1000 millimeters in a meter, so to convert meters to millimeters, you multiply the length in meters by 1000.

Conversion formula: Length in millimeters = Length in meters × 1000 mm/m.

Using the formula:

Length in millimeters = 3 m × 1000 mm/m = 3000 millimeters.

Therefore, 3 meters of gold wire is 3000 millimeters long.

To convert meters to millimeters, we can use the conversion factor that 1 meter is equal to 1000 millimeters.

Therefore, to find the length of the wire in millimeters, we multiply the given length in meters by 1000:

3 meters * 1000 millimeters/meter = 3000 millimeters

Final answer:

The length of the gold wire in millimeters is 3000.

Explanation:

To convert meters to millimeters, you need to multiply the measurement by 1000. Since the scientist is working with 3 meters of gold wire, you can calculate the length in millimeters by multiplying 3 by 1000, which equals 3000 millimeters. Therefore, the length of the wire is 3000 millimeters.

Bill, Bob, and Barry are hired to paint signs. In 8 hours Bill can paint 1 sign, Bob can paint 2 signs, and Barry can paint 1 and 1/3 signs. They all come to work the first day, but Barry doesn't like the job and quits after 3 hours. Bob works half an hour longer than Barry and quits. How long will it take Bill to finish 2 signs they were supposed to paint?

Answers

Answer:
Bill will take a total of 5 hours (or 1½ hours additional after Bob quits).

There is a sales tax of $6 on an item that cost $80 before tax. The sales tax on a second item is $11.25. How much does the second item cost before tax?

Answers

The second item's cost before the sake tax would be $17.25

A parabola opens to the left. Which could be the equation of the parabola?
(x – 4)2 = 4(y + 3)
(x – 4)2 = –4(y + 3)
(y – 4)2 = 4(x + 3)
(y – 4)2 = –4(x + 3)

Answers

Answer:

[tex](y - 4)^2 = -4(x + 3)[/tex]

Step-by-step explanation:

When parabola opens the left then it is a horizontal parabola

Vertex form of horizontal parabola is

[tex](y-k)^2= 4p(x-h)[/tex]

where (h,k) is the vertex

When the parabola opens to the right then 4p is positive

when parabola opens to the left then 4p is negative

Now we look at the given equation and check with vertex form of parabola

[tex](y - 4)^2 = -4(x + 3)[/tex]

Here the value of 4p is negative , so parabola opens left

Is 55.56 greater than 55.65? I'm in a hurry so answer quick

Answers

no it is equel hope this helps
 

Factor the polynomial completely 20x -220x squared + 600x

Answers

I first would rearrange the problem

-220x^2 + 20x + 600x

Simplify

-220x^2 + 620x

Find the GCF of the two values

20x(11x + 13)

Hope this helps!

This set of points is on the graph of a function.
{(−3, 9), (−1, 1), (0, 0), (2, 4)}
Which points are on the graph of the inverse?
Select each correct answer.
(0, 0)
(−9, 3)
(4, 2)
(1, −1)

What is the inverse of f(x)=4x+3 ?
f^−1(x)=1/4x−3/4
f^−1(x)=−1/4x+3/4
f^−1(x)=4x−3
f^−1(x)=−4x−3

What is the inverse of the function?
g(x)=−4/3x+2

g^−1(x)=−4/3x−2
g^−1(x)=3/4x+2/3
g^−1(x)=−3/4x+3/2
g^−1(x)=4/3x−2

Which functions are invertible?
Select each correct answer. (has pictures)

A.
B.
C.
D.

What is the inverse of f(x)=x4+7 for x≥0 where function g is the inverse of function f?



g(x)=x+7√4 , x≥−7

g(x)=x√4+7 , x≥0

g(x)=x−7√4,  x≥7

g(x)=x√4−7 , x≥0

Answers

Problem 1)

(-3,9) is one point on the original function, so (9,-3) is on the inverse. We swap x and y. The point (9,-3) isn't listed so we move onto the next.

(-1,1) is on the original so (1,-1) is on the inverse. Again we swap x and y. Choice D matches with this. So D is one of the answers.

Choice A is also an answer since (0,0) swaps to (0,0)

Choice C is also an answer since (2,4) swaps to (4,2)

In summary, the answers are A, C, D

======================================================================
Problem 2)
Replace f(x) with y. Swap x and y. Then solve for y

f(x) = 4x+3
y = 4x+3
x = 4y+3
x-3 = 4y+3-3
x-3 = 4y
4y = x-3
4y/4 = (x-3)/4
y = (x-3)/4
y = x/4-3/4
y = (1/4)x-3/4

which matches with choice A, so choice A is the answer

======================================================================
Problem 3)
Replace g(x) with y. Swap x and y. Then solve for y

g(x) = (-4/3)x + 2
y = (-4/3)x + 2
x = (-4/3)y + 2
x-2 = (-4/3)y + 2-2
x-2 = (-4/3)y
(-3/4)(x-2) = (-3/4)(-4/3)y
(-3/4)(x-2) = y
y = (-3/4)(x-2)
y = (-3/4)x+(-3/4)(-2)
y = (-3/4)x+3/2 ... answer is choice C

======================================================================
Problem 4)

The first two are invertible while the last two are not. The last two fail the horizontal line test so they don't have an inverse.

======================================================================
Problem 5)

It's a bit tricky to determine what the answer choices are saying but I'm assuming they are referring to fourth roots. If so, then we have

f(x) = x^4+7
y = x^4+7
x = y^4+7
x-7 = y^4+7-7
x-7 = y^4
y^4 = x-7
FourthRoot(y^4) = FourthRoot(x-7)
y = FourthRoot(x-7)

which is written as [tex]\sqrt[4]{x-7}[/tex]
Final answer:

The points on the inverse function are (9, -3), (1, -1), (0, 0), and (4, 2). The inverse of f(x)=4x+3 is[tex]f^{-1}(x) = -3 + \frac{1}{4}x[/tex]. The inverse of g(x)=−4/3x+2 is [tex]g^{-1}(x) = \frac{3}{4}x + \frac{2}{3}[/tex] . The inverse of f(x)=x^4+7 for x≥0 is [tex]g(x) = \sqrt{\frac{x-7}{4}}[/tex], for x≥7.

Explanation:

To find the points on the graph of the inverse of the function, simply switch the x and y coordinates. So, the points on the graph of the inverse function would be (9, -3), (1, -1), (0, 0), and (4, 2).

For the inverse of the function f(x)=4x+3, you rearrange the equation to solve for x. That gives [tex]f^{-1}(x) = -3 + \frac{1}{4}x[/tex]Therefore, the correct answer is [tex]f^{-1}(x) = \frac{1}{4}x - \frac{3}{4}[/tex]

The inverse of the function g(x)=−4/3x+2 could be found in the same way, which gives[tex]g^{-1}(x) = \frac{3}{4}x + \frac{2}{3}[/tex]

As for the question regarding invertible functions, without the images it is not possible to provide an answer.

The inverse of the function [tex]f(x)=x^4+7[/tex] for x≥0 is calculated by swapping x and y, and then solving for y. This yields: [tex]g(x) = \sqrt{\frac{x-7}{4}}[/tex], for x≥7.

Learn more about Inverse Functions here:

https://brainly.com/question/17872426

#SPJ2

Sam made 6 identical necklaces, each having beads and a pendant. the total cost of the beads and pendants for all 6 necklaces was $31.80 . if the beads cost $2.70 for each necklace, how much did each pendant cost?

Answers

Since six necklaces all together costs 31.80 to make, I divided 31.80 by 6 and got 5.3. That means that to make one necklace, they'd spend $5.30. The beads alone for 1 necklace cost $2.70, so I subtracted that from the $5.30.

Answer: Each pendant costs $2.60

An oil slick is expanding as a circle. The radius of the circle is increasing at the rate of 20 meters per day. Express the area of the circle as a function of d, the number of days elapsed.

Answers

The circle expands it radius 20m each day. From this description you can get this equation:
r=0+ 20*d
r=20d

The oil slick expands as a circle and the formula for circle area is [tex] \pi [/tex] r^2.  If you insert the first equation into this equation you will got:
circle area = [tex] \pi [/tex] r^2
circle area = [tex] \pi [/tex] (20d)^2
circle area = [tex] \pi [/tex] 400*d^2

Answer:

Step-by-step explanation:

d = number of days since the oil slick started

r = radius in d days = 22d

A(d) = area of oil slick in d days = π(22d)2

A(d) = 484πd2

What is 75% of 400 write evaluate an expression to find the answer.then explain how touse the model to justify the answer?

Answers


75 /100  x 400 =

75 x400/ 100= 

 300

Hey there
I like to do it this way :
100% = 400
1%= 400/100
     = 4
75%= 4 x75
       = 300

Hope this helps :))

~Top

Based on the lines 5 and 6, what is the best meaning of treasure divine? precious item inconsequential object frivolous amulet incredible wealth

Answers

precious item is the answer

the first one if correct

What does it mean for data on a scatter plot to have no association? How does that affect the line of best fit?

Answers

If there isn't any association, or CORRELATION, then you'd have a very difficult time determining a line of best fit since the independent and dependent variables wouldn't have any form of relationship.

For instance, let's say that I was going to plot (x,y) where x represented somebody's first name, and y represented how old they were

Does a person's name determine their age?  Of course not, so there would be no association, or CORRELATION, which means there would not be a way to put in a line of best fit for this.

Hope this helps.

Brian

Answer:

If there isn't any association, or CORRELATION, then you'd have a very difficult time determining a line of best fit since the independent and dependent variables wouldn't have any form of relationship

Step-by-step explanation:

What are the dimensions of the following matrix?
5 -6
0 1
3 5
-1 7

A. 2x4
B.4x2
C.3x2
D.none of these

Answers

B; you do the rows first then columns.

Two people start walking at the same time in the same direction. one person walks at 4 mph and the other person walks at 7 mph. in how many hours will they be 2.25 miles apart?

Answers

3/4 of an hour. 2.25 is 3/4 of 3.

A cube is packed with decorative pebbles. If the cube has a side length of 4 inches, and each pebble weighs on average 0.5 lb per cubic inch, what is the total weight of the pebbles in the cube?

Answers

First we must find the volume of the cube. This is equal to side^3. 4^3=64 cubic inches. Since the pebbles are .5 pounds per cubic inch and we assume it is packed we multiply the volume by .5
This will give 32 pounds

Determine if the lines are parallel, perpendicular, or neither y=5 and y =-1

Answers

The are parallel to each other because the are both straight horizontal lines
 y = 5 and y = -1 is a parallel line .
They both line on the y - axis .
( 0,5 ) and ( 0,-1 ) 

1. In what country did the government debate the merit of teaching students quadratics? 2. What modern technology would not be possible without quadratics? (hint: I have one at my house.) 3. What great ideas did the Babylonians come up with? 4. Why did the Babylonians need to solve quadratic equations?

Answers

i would say number 2 but dont take my word for it 

What is the equation of a line with a slope of -1/2 and passes through the point (6,-6)

Answers

Well I am going to assume you need slope-intercept form. So the equation is y=mx+b. m is slope, b is y intercept. So you just plug it in -6= -1/2(6)+b. -6=-3+b. Now you figure out for b so what does b have to be to make the equation equal. Well -3 so -6=-3+-3, or -6=-6. 

y=-1/2x-3
 
Hope that helped

the shadow of an object varies directly as it height a man 1.8m tall cast a shadow 4.32m long if at the same time a flagpole cast a shadow 12.8m long how it is the flagpole?

Answers

this will help a lot if you know how to do proportions... hope I helped

X^2= 1/100 what does x equal?

Answers

X^2= 1/100
x = 1/10

Because 1/10 * 1/10 = 1/100

if im reading the problem correctly the awnser should be X^1=-1/10 or x ^2= 1/10

How can you distinguish the base of an isosceles triangle from a leg

Answers

In an isosceles triangle the two legs are equal while the base is the different side

The sum of two numbers is 95. If the larger number is increased by twice the smaller number, the result is 120. What is the larger number?

If S = the smaller number and L = the larger number, then which of the following systems of equations represents the word problem?

Answers

S+L=95
2s+L=120 
so it's 120

Answer: correct answer is S + L = 95 and 2S + L = 120

Step-by-step explanation:

Classify the expression 7x3 + 2x2 − 9 as a monomial, binomial, trinomial or polynomial.

Answers

Trinomial is your answer. 
Trinomial my dude / dudette
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