given f(x) = 3/2x - 5 and g(x) = x^2 + 2x find x (the input) if g(x) = 0 ( the output 0 ) there are 2 answers

Answer: 10.

Step-by-step explanation:

You are given the equation

(ax+b)(ax+c)=4x^2-25

Expand the Left hand side by opening the bracket.

a^2x^2 + axc + abx + bc

a^2x^2 + (axc + abx) + bc = 4x^2 + 0x - 25

From the equation above, we can see that;

a^2x^2 = 4x^2

a^2 = 4

a =  √4

a = 2

Also, axc + abx = 0x

axc = abx

ax will cancel out from both sides

c = b

From the equation, bc = 25

But c = b. Substitute c for b

b^2 = 25

b =  √25

b = 5 = c

b + c is therefore 5 + 5 = 10

Answer:

143 yards squared.

Step-by-step explanation:

According to the diagram, there are 6 sides: two trapezoids, and 4 rectangles.

To find the area of a trapezoid, you need to calculate using the formula shown below.

The height of each trapezoid is 3.5 yards. The b1 of each trapezoid is 3 yards. The b2 of each trapezoid is 7 yards.

So, the area of a single trapezoid is [3.5(3 + 7)] / 2 = (3.5 * 10) / 2 = 35 / 2 = 17.5 yards squared.

The area of two trapezoids will be 17.5 * 2 = 35 yards squared.

To find the area of a rectangle, do base times height.

There are, apparently, three types of rectangles in the diagram. All four rectangles have a width of 6 yards. One rectangle has a length of 3 yards, two rectangles have lengths of 4 yards, and one rectangle has a length of 7 yards.

So, the total areas of the rectangles are: (3 * 6) + 2(4 * 6) + (7 * 6) = 18 + 2 * 24 + 42 = 18 + 48 + 42 = 108 yards squared.

So, the total surface area of the figure is 35 + 108 = 143 yards squared.

Hope this helps!

Answer:

Part 1: Already solved.

Part 2: 1 quesadilla.

Step-by-step explanation:

Part 1: The data points given are 0, 0, 1/4, 1/2, 1/2, 1, 1, 1, 5/4, 2, and 2.

The data are already sorted from least to greatest.

Part 2: To get the interquartile range, we must know the first and third quartiles. To find those, we need to know the median of the data.

There are 11 data points, so we can cross out 5 numbers on the left and cross out 5 numbers on the right. That leaves a median of 1.

Since we know the median is 1, we can find the first quartile by finding the median of the following numbers: 0, 0, 1/4, 1/2, 1/2 (any number less than 1). There are five numbers, so cross out two numbers from the left and cross out two numbers from the right. We are left with a first quartile of 1/4.

Now that we have the first quartile, we need to find the third quartile. Since the median was actually the first "1" in the data set, the third quartile will be the median of the numbers to the right of that "1": 1, 1, 5/4, 2, 2. Cross out the leftmost two numbers, and cross out the rightmost two numbers. We are left with a third quartile of 5/4.

Now that we have both the third and first quartiles, we can find the interquartile range! The IQR is calculated by finding the third quartile minus the first quartile. 5/4 - 1/4 = 4/4 = 1.

So, your interquartile range is 1 quesadilla.

Hope this helps!

Answer:

1

Step-by-step explanation:

On khan

Answer:

240 is the number with a zero and 24 is the number with no zero

Step-by-step explanation:

240 + 24 equals 264 . 240 has a zero take away the zero and you get the second number

Answer:

$118

Step-by-step explanation:

The amount Jordan will have on 1st of the February is $118

The slope or gradient of a line is a number that describes both the direction and the steepness of the line.

Given that, On February 2nd, Jordan is going on a class trip to Washington, D.C. He is saving his weekly allowance to use as spending money while on the trip. Each week, Jordan's parents give him the $8 he earned for the week,

The saving are

In 1st week = $86

In 2nd week = $94

Therefore, we can consider the coordinates as (1, 86) or (2, 94)

We know that, standard equation of a line = y = mx+c

Where, m is the slope,

We have here slope = 8

Finding for c, put x = 1 and y = 86

c = 78

Now finding the amount for 5 weeks, that means x = 5

y = 5x8+78

y = 118

Hence, The amount Jordan will have on 1st of the February is $118

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Answer: 0.20

Step-by-step explanation:

As per given :

P(student enrolled in a math class ) = 65% = 0.65

P( student enrolled in a science class) = 43%= 0.43

P( student enrolled in both ) = 13% = 0.13

Formula of conditional probability :

[tex]P(A|B)=\dfrac{P(A\text{ and }B)}{P(B)}[/tex]

Using the above formula,

The probability that the student is enrolled in a science class given that he is enrolled in maths class :

[tex]P(\text{science}|\text{math})=\dfrac{P(\text{science and maths})}{P(\text{math})}\\\\=\dfrac{0.13}{0.65}\\\\=\dfrac{13}{65}\\\\=\dfrac{1}{5}=0.20[/tex]

Hence, the probability that the student is also enrolled in a science class =  0.20 .

Answer:

8

Step-by-step explanation:

4(HCL)

H=1 mol,CL=1 mol

4(1+1)

4(2)

4x2=8molecules

Answer: 62

Step-by-step explanation:

The surface area of a rectangular prism is 2(wl+hl+hw).

Simply plug in the values to get 62

Answer:

62cm ^2

Step-by-step explanation:

every cube has 6 sides,

2(3*5) + 2(2*3)+ 2(2*5)=

2(15)+2(6)+2(10)=

30+12+20=

62

Answer:

25 units.

Step-by-step explanation:

The first thing we need to do is find the hypotenuse of the triangle with side lengths 12 and 16. 12^2 + 16^2 = 144 + 256 = 400. sqrt(400) = 20. So, the hypotenuse of that triangle is 20 units.

Because the smaller length of the smaller triangle bisects the largest triangle's right angle, the two triangles are similar, with the side length 12 corresponding to the smaller side length of the larger triangle, the side length 16 corresponding to the 20 unit side, and the 20 unit hypotenuse corresponding to x.

Now that we know the triangles are similar, we can construct a proportion...

[tex]\frac{16}{20} =\frac{20}{x}[/tex]

That means that 4/5 = 20/x

1/5 = 5/x

x = 25

Hope this helps!

Answer:

Given that “The amount of money in my wallet is more than $10, but less than $20 " can be written in inequality form as

10 < w <  20   where  " w"  is the amount in the wallet .

1 ) Puzzle : -

Ryan  is eating cookies . His mother ask how many cookies did he have .

He said number of cookies he ate is more than 19 and less than 41 .

We can write it in equality form as  19 < x < 41 where  ' x ' is number of cookies Ryan have .  

2) Puzzle :-

Number of steps a child take in an hour is more than 19 and less than 41 .

Write the situation in inequality form .

19 < p < 41 where  " p " is the number of steps a child take in an hour .

3) Puzzle :-

Mother said to his child : " the number of  coins in your piggy bank is more than 19 and less than 41 .

19 < c < 41  where " c " is number of coins in piggy bank .

Step-by-step explanation:

Answer:

x= 3/2 = 1.5

Step-by-step explanation:

● 5(4x-10)+10x =4(2x-3)+2(x-4)

Simplify the products

● 5*4x-5*10+10x = 4*2x-4*3+2*x-2*4

● 20x-50+10x = 8x-12+2x-8

Add the terms that don't contain x with each other

●20x-50+10x = 8x-20+2x

Add 20 in both sides

●20x-50+20+10x = 8x-20+2x+20

●20x-30+10x = 8x+2x

Add together the terms that contain x

●30x -30 = 10x

Add -10x in both sides

●30x-30-10x = 10x-10x

● 20x -30 = 0

Add 30 in both sides

● 20x-30+30 = 30

● 20x = 30

Divide both sides by 20

●20x/20 = 30/20

● x= 30/20

● x= 3/2

● x= 1.5

Answer:

3/2

Step-by-step explanation:

Answer:

40

Step-by-step explanation:

Answer:

13x+10

Step-by-step explanation:

Answer:

7x+10 cm

Step-by-step explanation:

To find the perimeter add up all the sides

There are 5 sides

3x+5+2x+2x+5

Combine like terms

3x+2x+2x   +5+5

7x+10

The perimeter is 7x+10

Answer:

can you please make the question more clear!

Step-by-step explanation:

i am guessing you are asking if 1/ (2·2) (3+(3.4·5))=

1/ 4+17+3

1/24?

Answer:

xx

Step-by-step explanation:

Answer:

m(-6,2)

Step-by-step explanation:

m=(-8+-4/2,-6+10/2)

=(-12/2,4/2)

=(-6,2)

The coordinates of the midpoint M of CD of the line segment CD with endpoints, C(−8,−6) and D(−4, 10), are (-6,2).

For a line segment, mid-point is the middle point of it which divides the line segment into the two equal parts.

The formula to find the midpoint using the coordinates of the line is,

[tex]m=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)[/tex]

Here, (x1,y1) and (x2,y2) are the coordinates of the endpoints of the line.

The endpoints of CD are C(−8,−6) and D(−4, 10). To find the coordinates of the midpoint M, put the values in the above formula as,

[tex]m=\left(\dfrac{-8+(-4)}{2},\dfrac{-6+10}{2}\right)\\m=\left(\dfrac{-12}{2},\dfrac{4}{2}\right)\\m=\left(-6,2)[/tex]

Thus, the coordinates of the midpoint M of CD of the line segment CD with endpoints, C(−8,−6) and D(−4, 10), are (-6,2).

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Answer:

15 units

Step-by-step explanation:

Distance from the x-axis is measured vertically, so you would look at the second number of the coordinates, the y value. Point Z is 15 units below the x-axis.

Hence, the distance from [tex]Z= (16,-15)[/tex] to the x-axis is [tex]15[/tex] units.

What is the axis?

An axis in mathematics is defined as a line that is used to make or mark measurements.

Here given that,

[tex]Z= (16,-15)[/tex]  which is on the x-axis.

So,

The shortest distance between the coordinate [tex](16,-15)[/tex] and [tex](16,15)[/tex].

Now, applying the distance formula

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Here,

[tex](x_1,y_1)=(16,0)\\(x_2,y_2)=(16,-15)[/tex]

Substituting these values in the formula

[tex]d=\sqrt{(16-16)^2+(-15-0)^2}\\\\d=\sqrt{(0)^2+(-15)^2}\\\\d=\sqrt{0+225}\\\\d=15[/tex]

Hence, the distance from [tex]Z= (16,-15)[/tex] to the x-axis is [tex]15[/tex] units.

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Answer:

Daylilies cost $11 and shrubs cost $11

Step-by-step explanation:

Let's call the cost of daylilies as x and the cost of shrubs as y. We can write:

9x + 4y = 143 -- Equation 1

14x + 4y = 198 -- Equation 2

5x = 55 -- Subtract Equation 1 from Equation 2

x = 11 -- Divide by 5

9 * 11 + 4y = 143 -- Substitute x = 11 into Equation 1

4y = 44 -- Subtract 99

y = 11 -- Divide by 4

Answer:

C; x = 900

Step-by-step explanation:

1. Write out the problem: x/15 = 60

2. Multiply each side by 15 to solve for x. This is because of inverse operations, so if you divide x by 15 you have to multiply 15 to both sides. THis way the 15 cancels out in 15(x/15).

3. Equation then becomes this: x = 15*60

4. Answer: 900

5. Substitute to see if you were right. Ask yourself: Does 900 divided by 15 equal 60. If it does, then you are correct.

Answer:

5/2

Step-by-step explanation:

Step 1: Plug in x

2¹ - 2^-1 + 2⁰

Step 2: Evaluate

2 - 1/2 + 1

3/2 + 1

5/2

Answer:

[tex]\boxed{\frac{5}{2} }[/tex]

Step-by-step explanation:

=> [tex]x - x^{-1} + x^0[/tex]

Rule of exponents [tex]x^0 = 1[/tex]

For x = 2

=> 2 - [tex](2)^{-1}[/tex] + 1

=> 5 / 2

=> [tex]\frac{5}{2}[/tex]

Answer:

300 feet

Step-by-step explanation:

If we were using feet the expression would be 198x, where x is feet per second

Since they are asking in meters we need to convert feet to meters

When you do that you get 60

Now the expression is 60x

When you plug 5 into the equation it is 300

Answer:

13.896 kg

Step-by-step explanation:

You can find the mass of the bar by first finding the volume.

V = BH

where B = area of the base (the trapezium), and

H = height (distance trapezium between bases)

The area of a trapezium is

A = (b1 + b2)h/2

where b1 and b2 are the lengths of the bases of the trapezium (the parallel sides), and

h = the altitude of the trapezium (distance between the bases of the trapezium)

V = (b1 + b2)h/2 * H

V = (12 cm + 6 cm)(5 cm)/2 * 16 cm

V = 720 cm^3

The volume of the bar is 720 cm^3.

Now we use the density and the volume to find the mass.

density = mass/volume

mass = density * volume

mass = 19.3 g/cm^3 * 720 cm^3

mass = 13,896 g

Now we convert grams into kilograms.

1 kg = 1000 g

mass = 13,896 g * (1 kg)/(1000 g)

mass = 13.896 kg

Answer: 1.3896 kg

Answer:

y-intercept is 30

Step-by-step explanation:

Given the model  [tex]y = 10x + 30.[/tex] comparing this model to the equation of a straight lines  we can get the y- intercept

[tex]y = 10x + 30\\\y= mx+c[/tex]

The y- intercept is 30 which is the constant factor and it describes to us about the one-time registration fee of $30.

The y-intercept in this model for the average gym costs is 30.

In a linear equation, the y-intercept can be interpreted as the constant. It is the value that does not change with the number of months a person goes to the gym. The y-intercept can also be referred to as the fixed cost. In this question, the y-intercept is 30.

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Answer:

Using SohCahToa we know it will be opposite over adjacent, opposite being the side across from theta and adjacent being the side next to theta, Using Toa we know it will be opposite over adjacent so the answer will be 6/2sqrt5

If they wants you to simplify more than you cant have a sqrt on the bottom so to fix this you will multiply the top and bottom by sqrt5 leaving you with 6sqrt5/ 2*5 or 6sqrt5/15

hope this helped

Answer:

C. 3^5/5

Step-by-step explanation:

Answer:

805

Step-by-step explanation:

Scaling up by a factor of ten means that you must multiply the original number by 10. Because 10 has one zero, the best way to figure this out is just moving the decimal to the right ONCE (just like there is ONE zero)! This gives us 805.

If you have any other questions about this concept, please comment on my answer!!

Answer: The son is 30 and the mother is 60

Step-by-step explanation:

Mother's age = m

Son's age  = s

m = s + 30

m-15 = 3(s - 15)

m - 15 = 3s - 45

m = 3s - 30

(Substitution)

s + 30 = 3s - 30

2s = 60

s = 30

m = 60

Hope it helps <3

Trick question---

Just kidding I think that 15 years ago his mother was 45

he was 15 and now he is 30 and she is 60.

literally sat here thinking that 30 is ruled out, and 60 would be 20 but then she'd be too old, suddenly it clicked, if you said he'd be half her age now, it'd be to easy, because half her age now would be 30 and it'd give the answer straight away.

You or your teacher has a big percentage of the brain used. I respect.

Answer:

solution,

Angles in a straight line ( linear pair)= 180°

180°-110°=70°

Now,

Sum of angle in triangle= 180°

[tex]70 + x + x + 70 = 180 \\ or \: 70 + 2x + 70 = 180 \\ or \: 140 + 2x = 180 \\ or \: 2x = 180 - 140 \\ or \: 2x = 40 \\ or \: x = \frac{40}{2} \\ x = 20[/tex]

Hope this helps...

Good luck on your assignment...

Answer:

f(x) = |x|

g(x) = |x| - 2

h(x) = |x| + 3

Step-by-step explanation:

All the functions graphed represent the absolute value functions.

Since function g(x) passes through (0, 0) and (1, 1),

Let the equation of a line passing through these points is,

y = mx + b

Slope of the line passing through these points 'm' = [tex]\frac{\text{Rise}}{\text{Run}}=\frac{1-0}{1-0}[/tex]

m = 1

y-intercept of the line 'b' = 0

Therefore, equation of the line will be,

y = x

And the function representing the two lines (both are the mirror images) joining at the origin will be,

f(x) = |x|

When the parent function is shifted 3 units up, the new function will be

h(x) = |x| + 3

When the parent function is shifted 2 units down,

g(x) = |x| - 2

Answer:

D) 1040- EZ Form

Step-by-step explanation:

Hope this helps!