the graph of y=f(x) is shown below. find all the values of x where f(x)=1

Answer:

x >= -7  ................(1a)

x >= 3   ...............(2a1)

Step-by-step explanation:

f(x) =  [tex]\sqrt{x+7}-\sqrt{x^2+2x-15}[/tex]  .............(0)

find the domain.

To find the (real) domain, we need to ensure that each term remains a real number.

which means the following conditions must be met

x+7 >= 0  .....................(1)

AND

x^2+2x-15 >= 0 ..........(2)

To satisfy (1),  x >= -7  .....................(1a) by transposition of (1)

To satisfy (2), we need first to find the roots of (2)

factor (2)

(x+5)(x-3) >= 0

This implis

(x+5) >= 0 AND (x-3) >= 0.....................(2a)

OR

(x+5) <= 0 AND (x-3) <= 0 ...................(2b)

(2a) is satisfied with x >= 3   ...............(2a1)

(2b) is satisfied with x <= -5 ................(2b1)

Combine the conditions (1a), (2a1), and (2b1),

x >= -7  ................(1a)

AND

(

x >= 3   ...............(2a1)

OR

x <= -5 ................(2b1)

)

which expands to

(1a) and (2a1)   OR  (1a) and (2b1)

( x >= -7 and x >= 3 )  OR ( x >= -7 and x <= -5 )

Simplifying, we have

x >= 3  OR ( -7 <= x <= -5 )

Referring to attached figure, the domain is indicated in dark (purple), the red-brown and white regions satisfiy only one of the two conditions.

Answer:

-7 is a Negative Number, which is also an integer.

Step-by-step explanation:

Negative numbers are any number less than 0. The greater a negative number is, is the smaller its value.

Answer:

=90

Step-by-step explanation:

because d=32° and b=58°

this is because corresponding  angles are equal

Answer:

Step-by-step explanation:

b+d =90 degree

hope it helps

Answer:

the slope is 5

Step-by-step explanation:

Solve for y

20x -4y = 40

Subtract 20x from each side

20x-20x -4y = -20x +40

-4y = -20x+40

Divide each side by -4

-4y/-4 = -20x/-4 +40/-4

y = 5x -10

This is in slope intercept form  y = mx+b where m is the slope and b is the y intercept

The slope is 5

Solve for y:

20x - 4y = 40

Subtract 20x to both sides

-4y = 40 - 20x

Divide -4 to everything

y = -10 + 5x

Therefore, the slope is 5

Best of Luck!

Hey there! I'm happy to help!

Let's look at our diameters.

[tex]1*10^2^1\\5*10^2^2[/tex]

We want to see how many times greater the diameter of the IC 1101 is than the Milky Way. So, we will divide it's diameter by the diameter of the Milky Way.

[tex]\frac{5*10^2^2}{1*10^2^1} \\[/tex]

We divide the numbers without exponents, giving us 5. Then, we divide the 10s with exponents. When dividing exponents, you subtract the numbers in the exponent to get your result. For example, x³÷x²=x

[tex]\frac{5*10^2^2}{1*10^2^1} = 5*10=50[/tex]

Therefore, your answer is 50.

Have a wonderful day! :D

Answer:

-6723cw

Step by Step:

(-3c * 3w * 5) * 3 - 9c * 6w* 8 - 9c * 9w * 15 - 27c * 6w * 8 - 27c * 9w * 15

Answer:

Camel's shadow is growing at a rate of 8 ft/sec.

Step-by-step explanation:

Given:

Height of camel = 8 ft

Height of streetlight = 20 ft

Speed of camel = 12 ft / sec

To find:

How fast is the camel's shadow growing = ?

Solution:

First of all, have a look at the image attached for the situation as given in the question statement.

PQ be the streetlight.

AB be the camel.

Camel is loping away from the streetlight.

BT will be the shadow of the camel.

We are given that speed of camel = 12 ft / sec

And we know that Speed is the Rate of change of distance w.r. to time.

i.e. as per the image, we are given:

[tex]\dfrac{dx}{dt} = 12 ft /sec[/tex]

And we have to find the value of:

[tex]\dfrac{ds}{dt} = ?[/tex]

(Because s is the shadow length and we have to find the rate of change of shadow's length w.r.to time.)

Here, let us consider the two similar triangles [tex]\triangle TAB\ and\ \triangle TPQ[/tex]as per the image attached:

Ratio of corresponding sides will be same.

[tex]\dfrac{AB}{PQ}=\dfrac{TB}{TQ}\\\Rightarrow \dfrac{8}{20}=\dfrac{s}{s+x}\\\Rightarrow 8s+8x=20s\\\Rightarrow 12s = 8x\\\Rightarrow s = \dfrac{2}{3}x[/tex]

Now, differentiating w.r.to t:

[tex]\dfrac{ds}{dt}=\dfrac{2}{3}\dfrac{dx}{dt}\\\Rightarrow \dfrac{ds}{dt}=\dfrac{2}{3}\times 12\\\Rightarrow \dfrac{ds}{dt}=\bold{8\ ft/sec}[/tex]

Camel's shadow is growing at a rate of 8 ft/sec.

Answer: g(1) is 1.

Step-by-step explanation:

If we are solving for g of 1  then the first equation can't be used to solve for g of 1 because it only works in x is equal to -2.

The same way the second function will not work because x has to equal to -1.

But in the last function which is written as a polynomial it will work for this situation because x is not equal to -2 or -1 so apart from those numbers every number will work the same way 1 will work.    

So plot 1 into the function and solve for it .

g(1) = 1^3 - 1^2 + 1  

g(1)=  1 - 1 + 1

g(1)= 1

Answer:

Below in bold.

Step-by-step explanation:

The  zeroes ( = x-intercepts) are x = -3 and x = -1.

So the x -coordinate of the vertex is between x = -3 and x = -1.

The actual x-coordinate is halfway between these value: at x = -2.

Answer:

x = -3 or x = -1

Step-by-step explanation:

f(x) = (x + 3)(x + 1)

⇒ x = -3 or x = -1

Answer:

-17

Step-by-step explanation:

First thing to do in this equation is to multiply both sides by 22.

This becomes, -5+x=-22

Add 5 to both sides.

x=-17

Answer:

x = -17

Step-by-step explanation:

-5+x

-------- = -1

22

Multiply each side by 22

-5+x

--------  * 22= -1 *22

22

-5 +x = -22

Add 5 to each side

-5+x +5 = -22 +5

x = -17

Answer:

Child ticket = $16.

Step-by-step explanation:

Let adult tickets = a;

child ticket = c.

2a + c = 94 — eq no. 1,

2a + 2c = 110 — eq no. 2,

then,from eq 1,

c = 94 - 2a. —eq no. 3.

Substitute eq 3 into eq 2,

2a + 2(94 - 2a) = 110

2a - 4a = 110 - 188

-2a /-2 = -78 / -2

a = 39.

Substitute value of a into eq 3,

c = 94 - 2(39)

= 94 - 78

c = 16.

Thus, child ticket = $16.

Answer:

11.2$

Step-by-step explanation:

Kristina and Melissa had 32$ at total

● 32$ => 100%

They have spent 35%

Let x be that amount

● x => 35%

●32 => 100

● x => 35

● x = (35×32)/100 = 11.2$

They have spent 11.2$

Answer:

They spent $20.80

Step-by-step explanation:

Since they had $32 and spent 35% of it you would do 32 * 35%

 then you would get 11.2

now that is not the answer because that is just what 35% of 32 is

to get the answer you would then subtract 11.2 from 32 to get 20.8

and since this is a matter of money you would write 20.8 as $20.80.

Answer:

The 16 cases will fit the box as shown.

Step-by-step explanation:

One disk case has the dimensions 14.2 cm by 19.3 cm, with thickness 1.6 cm.

Temporarily ignoring the 14.2 cm and 19.3 cm measurements, we multiply this 1.6 cm thickness by 16, obtaining a total thickness for the stack of cases of 25.6 cm.  

1) The 16 cases, arranged as shown, and measuring 25.6 cm from left to right in this diagram, will fit within the 26 cm horizontal distance shown.

2) The horizontal length of each case is 14.2 cm.  Stacked as shown, the 16 cases will fit within the 15 cm depth of the box.

3) The vertical measurement of each case is 19.3 cm.  The 20 cm vertical measurement of the box can accommodate this 19.3 height within 20 cm.

All indications are that the 16 cases will fit comfortably inside the box.

Answer:

16 discs capacity of the cuboid.

Step-by-step explanation:.

for simplicity...

i would just divide 26cm to 1.6cm = 16 .25

therefore,  16 discs capacity of the cuboid.

Answer:

3.14 units²

Step-by-step explanation:

The key realization here is that this shape is one quarter of a circle.

Therefore, it's area will be [tex]\frac{1}{4}[/tex] of the whole circle's area.

So, let's first find the area as if this were a whole circle.

The formula is [tex]\pi r^2[/tex], and we know that the radius, r, is 2. So:

[tex]\pi\cdot2^2\\\\\pi\cdot4\\\\3.14\cdot4\\\\12.56[/tex]

Now we need to find one fourth of this, we can do this by dividing by 4.

[tex]12.56\div4=3.14[/tex]

Hope this helped!

Answer:

pi units squared

Step-by-step explanation:

(cant find pi sign)

(pi times r^2)/4

4pi/4

pi

Answer:

f(1) = 10.33985 + 18.1294406 i

Step-by-step explanation:

f(1) = 4log2(1-7)

f(1) = 10.33985 + 18.1294406 i

Answer:

[tex]$\[x^2 + 22x + 121\]$[/tex]

Step-by-step explanation:

Given

[tex]$\[x^2 + 22x + \underline{~~~~}.\]$[/tex]

Required

Fill in the gap

Represent the blank with k

[tex]$\[x^2 + 22x + k\]$[/tex]

Solving for k...

To do this, we start by getting the coefficient of x

Coefficient of x = 22

Divide the coefficient by 2

[tex]Result = 22/2[/tex]

[tex]Result = 11[/tex]

Take the square of this result, to give k

[tex]k= 11^2[/tex]

[tex]k= 121[/tex]

Substitute 121 for k

[tex]$\[x^2 + 22x + 121\]$[/tex]

The expression can be factorized as follows;

[tex]x^2 + 11x + 11x + 121[/tex]

[tex]x(x + 11)+11(x+11)[/tex]

[tex](x+11)(x+11)[/tex]

[tex](x+11)^2[/tex]

Hence, the quadratic expression is [tex]$\[x^2 + 22x + 121\]$[/tex]

Answer:

The cost might be or would be$53.00

Answer:

B: The discriminant is equal to zero which means it has one real number solution

Step-by-step explanation:

Hello Again!!

Your right answer will be is B. The discriminant is equal to 0, which means the equation has one real number solution.

For this case we have the following quadratic equation:

2x^2 - 8x + = 0

Where:

a = 2

B = -8

c = 8

The discriminant is given by:

d = b^2 - 4(a)(c)

Substituting the values we have:

d = (-8)^2 - 4(2)(8)

d = 64 - 64

d = 0

So, Your best answer choice is B.

Good Luck!!

•Comments•

Ask if you need help! Because I'm glad to help you.

By ☆Itsbrazts☆

Answer: 15 square Inches

Step-by-step explanation: I believe you should divide 75 and 5(75mi÷5mi=15in) to get 15in.

Answer: 3 square inches.

If the park is 25 square miles, it could be 5×5 miles. If the scale is 1 inch = 5 miles, that would be 1×1 inch or 1 square inch on the map. Since 75 is 3×25, it will be 3×1 square inches on the map.

Step-by-step explanation: Remember that the scale represents linear measurements. For area, you must square the linear "sides" to get the number of actual square units represented by a square unit on the map.

You are told 2/9 = 16

Let total number of batteries = x

So you now have 2/9x = 16

To find x divide both sides by 2/9

X = 72 total batteries

Awnser

72

i dunno how to explain i did it in my head

Answer:

(-2,-1) is where u start

Step-by-step explanation:

Answer:

(-2,-1)

Step-by-step explanation:

The point we ended at is (-3,-1)

We have moved 4 units left so we will add 4 to -3

● -3+4 = 1

We have moved 3 unirs right so we will substract 3 from 1

● 1-3 = -2

So the initial point was (-2,-1)

Answer:

3^6 = 729

Step-by-step explanation:

3 to the power of 5 equals 243. Explain how to use that fact to quickly evaluate 3 to the power of 6  

Symbolically, we have:

3^5 = 243 (given)

Multiplying both sides by 3, we get:

3^6 = 3(243)

If you want to take this further, multiply 3(243):  3^6 = 729

The value of [tex]3^6[/tex] is 729.

Important information:

We need to find the value of [tex]3^6[/tex].

Using the rules of exponents, we get

[tex]3^6=3^{5+1}[/tex]

[tex]3^6=3^{5}*3^{1}[/tex]          [tex][\because a^{m+n}=a^ma^n][/tex]

[tex]3^6=243*3[/tex]

[tex]3^6=729[/tex]

Therefore, the value of [tex]3^6[/tex] is 729.

Find out more about 'Exponents' here:

https://brainly.com/question/14404700

Answer:

Step-by-step explanation:

option A ,  angle B is congruent to angle E { SINCE IT IS AA POSTULATE

Answer:

B=E (b)

Step-by-step explanation:

Step-by-step explanation:

-16t2 + 47t + 3 = 0

-16t2 + 48t - t + 3 = 0

-16t( t - 3) - 1 ( t - 3) = 0

-16t - 1 = 0. t - 3 = 0

-16t = 1 t = 3

t = 1/ - 16.

Answer:

3 hours

Step-by-step explanation:

Speed is the ratio of distance traveled to time taken, it is given as:

Speed = distance / time

An executive drove from his home at an average speed of 35 mph to an airport where a helicopter was waiting. He then took the helicopter and flew to the corporate offices at an average speed of 78 mph. Given that the executive spent the same amount of time in the car as he did the helicopter how long did it take the executive to get to work.

Let the amount of time the executive spent in the car be t hours, therefore the amount of time spent in the helicopter = t hours.

For car:

Speed = distance / time

35 = distance ([tex]d_1[/tex]) / t

[tex]d_1=35t[/tex]

For helicopter:

Speed = distance / time

78 = distance ([tex]d_2[/tex]) / t

[tex]d_2=78t[/tex]

The total distance traveled = 169.5 miles

[tex]d_1+d_2=169.5\\35t+78t=169.5\\113t=169.5\\t=169.5/113\\t=1.5\ hours[/tex]

The time taken for the executive to get to work = time spent on car + time spent on helicopter = 1.5 + 1.5 = 3 hours

Answer:

can i see a picture of the number line?

Step-by-step explanation: