Solve this (they are all fractions)
6/11=n+7/9
​What does r equal

Answer:

x = ±3

Step-by-step explanation:

x^2 +3 = 12

Subtract 3 from each side

x^2 +3-3 = 12-3

x^2 = 9

Take the square root of each side

sqrt(x^2) =±sqrt(9)

x = ±3

Answer:

[tex]A=\frac{225t^2}{\pi}[/tex] given the circumference is 30t.

Step-by-step explanation:

The circumference of a circle is [tex]C=2\pi r[/tex] and the area of a circle is [tex]A=\pi r^2[/tex] assuming the radius is [tex]r[/tex] for the circle in question.

We are given the circumference of our circle is [tex]2 \pi r=30t[/tex].

If we solve this for r we get: [tex]r=\frac{30t}{2\pi}[/tex].  To get this I just divided both sides by [tex]2\pi[/tex] since this was the thing being multiplied to [tex]r[/tex].

So now the area is [tex]A=\pi r^2=\pi (\frac{30t}{2 \pi})^2[/tex].

Simplifying this:

[tex]A=\pi (\frac{30t}{2 \pi})^2[/tex].

30/2=15 so:

[tex]A=\pi (\frac{15t}{\pi})^2[/tex].

Squaring the numerator and the denominator:

[tex]A=\pi (\frac{(15t)^2}{(\pi)^2}[/tex]

Using law of exponents or seeing that a factor of [tex]\pi[/tex] cancels:

[tex]A=\frac{(15t)^2}{\pi}[/tex]

[tex]A=\frac{15^2t^2}{\pi}[/tex]

[tex]A=\frac{225t^2}{\pi}[/tex]

Answer:

y=5

x=7

Step-by-step explanation:

When given an expression in the form a⁻ᵇ the expression is the same as 1/aᵇ where  a and b are integers.

Solving the question by giving the equivalents of the expression:

Therefore (-j)⁻⁷ is the same as 1/j⁷

The value of x=7

k⁻⁵+m⁻¹⁰=1/k⁵+1/m¹⁰

Therefore the value of y is 5.

Question 1:

For this case we have that by definition of properties of powers it is fulfilled that:

[tex]a ^ {- 1} = \frac {1} {a ^ 1} = \frac {1} {a}[/tex]

So, if we have the following expression:

[tex](-j) ^ {- 7}[/tex]

We can rewrite it as:

[tex]\frac {1} {(- j) ^ 7}[/tex]

So we have to:

[tex]x = 7[/tex]

ANswer:

[tex]x = 7[/tex]

Question 2:

For this case we have that by definition of properties of powers it is fulfilled that:

[tex]a ^ {- 1} = \frac {1} {a ^ 1} = \frac {1} {a}[/tex]

If we have the following expression:

[tex]k^{-5}+m^{-10}[/tex]

We can rewrite it as:

[tex]\frac {1} {k ^ 5} + \frac {1} {m ^ {10}}[/tex]

So we have[tex]y = 5[/tex]

Answer:

[tex]y = 5[/tex]

Answer:

Parallel

Step-by-step explanation:

Instead of putting this and slope intercept form.  I'm going determine the

x-intercept and the y-intercept of both.

The x-intercept can be found by setting y to 0 and solving for x.

The y-intercept can be found by setting x to 0 and solving for y.

So let's look at 3x-2y=5.

x-intercept?

Set y=0.

3x-2(0)=5

3x       =5

 x       =5/3

y=intercept?

Set x=0.

3(0)-2y=5

     -2y=5

        y=-5/2

So we are going to graph (5/3,0) and (0,-5/2) and connect it with a straightedge.

Now for 6y-9x=6.

x-intercept?

Set y=0.

6(0)-9x=6

     -9x=6

        x=-6/9

        x=-2/3

y-intercept?

Set x=0.

6y-9(0)=6

6y        =6

 y        =1

So we are going to graph (-2/3,0) and (0,1) and connect it what a straightedge.

After graphing the lines by hand you can actually do an algebraic check to see if they are parallel (same slopes), perpendicular (opposite reciprocal slopes), or neither.

Let's find the slope by lining up the points and subtracting then putting 2nd difference over 1st difference.

So the points on line 1 are: (5/3,0) and (0,-5/2)

 (5/3 ,  0  )

- (0   ,-5/2)

-----------------

5/3       5/2

The slope is (5/2)/(5/3)=(5/2)*(3/5)=3/2.

The points on line 2 are: (-2/3,0) and (0,1)

 (-2/3 , 0)

- (   0  ,  1)

-----------------

 -2/3      -1

The slope is -1/(-2/3)=-1*(-3/2)=3/2.

The slopes are the same so they are parallel. The line lines are definitely not the same; if you multiply the top equation by -3 you get -9x+6y=-15 which means the equations are not the same.  Also they had different x- and y-intercepts.  So these lines are parallel.

This is what we should see in our picture too.

The lines 3x - 2y = 5 and 6y - 9x = 6 are parallel lines

The lines 3x - 2y = 5 and 6y - 9x = 6 are parallel lines if their their slopes are equal

Lets rewrite the equation to be in slope intercept form: y = mx + b. where m is the slope

3x - 2y = 5

2y = 3x - 5

y = 3x/2 - 5/2. slope is 3/2

6y - 9x = 6

6y = 9x + 6

y = 3x/2 + 1. slope is 3/2

Comparing the equations with equal slope of 3/2, and from the graph shows that they are parallel lines

Learn more about parallel lines

https://brainly.com/question/30097515

#SPJ2

Answer:

a

Step-by-step explanation:

Answer:

The value of y = 4.3

Step-by-step explanation:

It is given that,

5/7 = y/6

To find the value of y

We have, 5/7 = y/6

(5 * 6) = (y * 7)

y * 7 = 5 * 6

y = (5 * 6)/7

 = 30/7

 = 4.29

 ≈ 4.3

Therefore the correct answer, the value of y = 4.3

Answer:

c 5.1

Step-by-step explanation:

The diameter of the circle is 102.

The radius is half of the diameter

r =d/2

r =10.2 /2 =5.1

Answer:

15

Step-by-step explanation:

The formula for factoring a sum of cubes is:

[tex]a^3+b^3=(a+b)(a^2-ab+b^2)[/tex]

We have a=3f and b=5g here.

So a*b in this case is 3f*5g=15fg.

The ? is 15.

The value of the missing coefficient in the factored form of the sum of cubes 27f³ + 125g³ is 15, resulting in the complete factorization being (3f+5g)(9f² -15fg+25g²).

The expression 27f³ + 125g³ can be factored using the sum of cubes formula, which is a³ + b³ = (a + b)(a² - ab + b²).

Given [tex]27f^3+125g^3[/tex], we have [tex]a=3f[/tex] and [tex]b=5g[/tex]

Applying the sum of cubes formula, we get:

[tex]27f ^3+125g ^3 =(3f+5g)((3f) ^2 -(3f)(5g)+(5g)^ 2 )[/tex]

[tex]27f ^3 +125g ^3=(3f+5g)(9f ^2-15fg+25g ^2 )[/tex]

So, the missing coefficient in the factored form is 15.

Therefore, the factored form is,

[tex]27f ^3+125g ^3[/tex] is [tex](3f+5g)(9f^ 2-15fg+25g ^2 )[/tex]

The complete question is:

Find the value of the missing coefficient in the factored form of 27f³ + 125g³ .

27f³ + 125g³ =(3f+5g)(9f² -?fg+25g² )

The value of ? =

Answer:

y=2x-2

Step-by-step explanation:

in slope intercept form we need make in this formula..

y=Mx+c

Answer:

y = 2x - 2

Step-by-step explanation:

Given

y + 6 = 2(x + 2) ← distribute

y + 6 = 2x + 4 ( subtract 6 from both sides )

y = 2x - 2 ← in slope- intercept form

Answer:

The correct answer option is A. 1397.46 ft^2.

Step-by-step explanation:

We are to find the area of the shaded region. For that, we will divide the figure into smaller shapes, find their areas separately and then add them up.

From the given figure, we can see that there are two semi circles )or say one whole circle if we combine them) at the ends while 2 rectangles at the top and bottom.

Radius of circle = [tex]\frac{20+7+7}{2} [/tex] = 17

Area of circle = [tex]\pi r^2 = \pi \times 17^2[/tex] = 907.92 square ft

Area of rectangles = [tex]2(l \times w) = 2(35 \times 7)[/tex] = 490 square ft

Area of shaded region = 907.9 + 490 = 1397.46 ft^2

Answer:

A.) 1,397.46 ft²

Step-by-step explanation:

I got it correct on founders edtell

Answer:

B

Step-by-step explanation:

1/2x < -3

Multiply each side by 2

1/2x *2 < -3*2

x < -6

Since x is less than -6, there is an open circle at -6

Less than means the line goes to the left

Answer:

$3.49

12 quarters,4 dimes,1 nickle, 4 pennies

Step-by-step explanation:

First remember that;

Quarter=25 pennies

Dime=10 pennies

Nickel =4 pennies

I cent =0.01$

Given the amount as $3.50

Assume you use 4 quarters, this means a whole dollar, so it will be;

1 dollar = 4quarters

3 dollars=?

cross multiply

3×4=12 quarters

The remaining $0.49

Here identify 40 cents, which is 40 pennies

But 10 pennies=1 dime

so 40 pennies=?

cross-multiply

(40×1)÷10=4 dimes

and a nickel for 4 pennies.

Answer:

a=1

Step-by-step explanation:

Let's find out!

So we have the point (x,y)=(a,3) is on the equation 5x+y=8.

Let's replace x with a and y with 3. This gives us:

5x+y=8

5a+3=8

Subtract 3 on both sides:

5a    =5

Divide both sides by 5:

a     =5/5

a     =1

So the point has to be (1,3)

Answer:

P(x) is the profit amount from selling tickets.

P(100) = $160

Step By Step Explanation:

First, plug in r(x) and c(x) into the p(x) equation:

p(x) = r(x) - c(x)

p(x) = (10x) - (8x+40)

Then simplify it:

p(x) = 10x - 8x - 40 {just distribute a +1 into the parentheses}

p(x) = 2x - 40 {combine like terms}

Now substitute 100 for x:

p(100) = 2(100) - 40

Then solve:

p(100) = 200 - 40

p(100) = 160

Answer:

The HCF = 3.

Step-by-step explanation:

The prime factors of

234 = 2*3*3*13,

and of 111 = 3*37.

The only common factor is 3.

Answer:

(- 9 × 234 ) + (19 × 111 )

Step-by-step explanation:

Using the division algorithm to find the hcf

If a and b are any positive integers, then there exists unique positive integers q and r such that

a = bq + r → 0 ≤ r ≤ b

If r = 0 then b is a divisor of a

Repeated use of the algorithm allows b to be found

here a = 234 and b = 111

234 = 2 × 111 + 12 → (1)

111 = 9 × 12 + 3 → (2)

12 = 4 × 3 + 0 ← r = 0

Hence hcf = 3

We can now express the hcf (d) as

d = ax + by where x, y are integers

From (2)

3 = 1 × 111 - 9 × 12

From (1)

3 = 1 × 111 - 9( 1 × 234 - 2 × 111)

   = 1 × 111 - 9 × 234 + 18 × 111

   = - 9 × 234 + 19 × 111 ← in required form

with x = - 9 and y = 19

Answer:

Part 1) The measure of angle A is [tex]A=80\°[/tex]

Part 2) The length side of a is equal to [tex]a=10.9\ units[/tex]

Part 3) The length side of b is equal to [tex]b=6.3\ units[/tex]

Step-by-step explanation:

step 1

Find the measure of angle A

we know that

The sum of the internal angles of a triangle must be equal to 180 degrees

so

[tex]A+B+C=180\°[/tex]

substitute the given values

[tex]A+35\°+65\°=180\°[/tex]

[tex]A+100\°=180\°[/tex]

[tex]A=180\°-100\°=80\°[/tex]

step 2

Find the length of side a

Applying the law of sines

[tex]\frac{a}{sin(A)}=\frac{c}{sin(C)}[/tex]

substitute the given values

[tex]\frac{a}{sin(80\°)}=\frac{10}{sin(65\°)}[/tex]

[tex]a=\frac{10}{sin(65\°)}(sin(80\°))[/tex]

[tex]a=10.9\ units[/tex]

step 3

Find the length of side b

Applying the law of sines

[tex]\frac{b}{sin(B)}=\frac{c}{sin(C)}[/tex]

substitute the given values

[tex]\frac{b}{sin(35\°)}=\frac{10}{sin(65\°)}[/tex]

[tex]b=\frac{10}{sin(65\°)}(sin(35\°))[/tex]

[tex]b=6.3\ units[/tex]

Answer:

a=2*n*pi where n is an integer

Step-by-step explanation:

[tex]\frac{\cos^2(a)}{1-\tan(a)}+\frac{\sin^3(a)}{\sin(a)-\cos(a)}[/tex]

The denominators are different here so I'm going to try to make them the same.

I'm going to write everything in terms of sine and cosine.

That means I'm rewriting tan(a) as sin(a)/cos(a)

[tex]\frac{\cos^2(a)}{1-\frac{\sin(a)}{\cos(a)}}+\frac{\sin^3(a)}{\sin(a)-\cos(a)}[/tex]

I'm going to multiply top and bottom of the first fraction by cos(a) to clear the mini-fraction from the bigger fraction.

[tex]\frac{\cos^2(a)}{1-\frac{\sin(a)}{\cos(a)}} \cdot \frac{\cos(a)}}{\cos(a)}+\frac{\sin^3(a)}{\sin(a)-\cos(a)}[/tex]

Distributing and Simplifying:

[tex]\frac{\cos^3(a)}{\cos(a)-\sin(a)}+\frac{\sin^3(a)}{\sin(a)-\cos(a)}[/tex]

Now I see the bottom's aren't quite the same but they are almost... They are actually just the opposite. That is -(cos(a)-sin(a))=-cos(a)+sin(a)=sin(a)-cos(a).

Or -(sin(a)-cos(a))=-sin(a)+cos(a)=cos(a)-sin(a).

So to get the denominators to be the same I'm going to multiply either fraction by -1/-1... I'm going to do this to the second fraction.

[tex]\frac{\cos^3(a)}{\cos(a)-\sin(a)}+\frac{\sin^3(a)}{\sin(a)-\cos(a)} \cdot \frac{-1}{-1}[/tex]

[tex]\frac{\cos^3(a)}{\cos(a)-\sin(a)}+\frac{-\sin^3(a)}{\cos(a)-\sin(a)}[/tex]

The bottoms( the denominators) are the same now.  We can write this as one fraction, now.

[tex]\frac{\cos^3(a)-\sin^3(a)}{\cos(a)-\sin(a)}[/tex]

I don't know if you know but we can factor a difference of cubes.

The numerator is in the form of a^3-b^3.

The formula for factoring that is (a-b)(a^2+ab+b^2).

[tex]\frac{(\cos(a)-\sin(a))(\cos^2(a)+\cos(a)\sin(a)+\sin^2(a)}{\cos(a)-\sin(a)}[/tex]

There is a common factor of cos(a)-sin(a) on top and bottom you can "cancel it".  

So we now have

[tex]\cos^2(a)+\cos(a)\sin(a)+\sin^2(a)[/tex]

We can actually simplify this even more.

[tex]\cos^2(a)+\sin^2(a)=1[/tex] is a Pythagorean Identity.

So we rewrite [tex]\cos^2(a)+\cos(a)\sin(a)+\sin^2(a)[/tex]

as [tex]1+\cos(a)\sin(a)[/tex]

So that is what we get after simplifying left hand side.

So I guess we are trying to solve for a.

[tex]1+\cos(a)\sin(a)=\sin(a)+\cos(a)[/tex]

Subtract sin(a) and cos(a) on both sides.

[tex]\cos(a)\sin(a)-\sin(a)-\cos(a)+1=0[/tex]

This can be factored as

[tex](\sin(a)-1)(\cos(a)-1)=0[/tex]

So we just need to solve the following two equations:

[tex]\sin(a)-1=0 \text{ and } \cos(a)-1=0[/tex]

[tex]\sin(a)=1 \text{ and } cos(a)=1 \text{ I just added one on both sides}[/tex]

Now we just need to think of the y-coordinates on the unit circle that are 1

and the x-coordinates being 1 also (not at the same time of course).

List thinking of the y-coordinates being 1:

a=pi/2 , 5pi/2 , 9pi/2 , ....

List thinking of the x-coordinates being 1:

a=0, 2pi, 4pi,...

So let's come up with a pattern for these because there are infinite number of solutions that continue in this way.

If you notice in the first list the number next to pi is going up by 4 each time.

So for the first list we can say a=(4pi*n+pi)/2 where n is an integer.

The next list the number in front of pi is just even.

So for the second list we can say a=2*n*pi where n is an integer.

So the solutions is a=2*n*pi   ,    a=(4pi*n+pi)/2

We really should make sure if this is okay for our original equation.

We don't have to worry about the second fraction because sin(a)=cos(a) only when a is pi/4 or pi/4+2pi*n OR (pi+pi/4) or (pi+pi/4)+2pi*n.

Now the second fraction we have 1-tan(a) in the denominator, and it is 0 when:

tan(a)=1

sin(a)/cos(a)=1                       =>              sin(a)=cos(a)

So the only thing we have to worry about here since we said sin(a)=cos(a) doesn't hurt our solution is the division by the cos(a).

When is cos(a)=0?

cos(a)=0 when a=pi/2 or any rotations that stop there (+2npi thing) or at 3pi/2 (+2npi)

So the only solutions that work is the a=2*n*pi where n is an integer.

Answer:

[tex]\large\boxed{a=2k\pi\ for\ k\in\mathbb{Z}}[/tex]

Step-by-step explanation:

[tex]\bold{a=x}[/tex]

[tex]\text{The domain:}\\\\1-\tan x\neq0\ \wedge\ \sin x-\cos x\neq0\ \wedge\ x\neq\dfrac{\pi}{2}+k\pi\ (from\ \tan x)\\\\\tan x\neq1\ \wedge\ \sin x\neq\cos x\\\\x\neq\dfrac{\pi}{4}+k\pi\ \wedge\ x\neq\dfrac{\pi}{4}+k\pi\ for\ k\in\mathbb{Z}[/tex]

[tex]\dfrac{\cos^2x}{1-\tan x}+\dfrac{\sin^3x}{\sin x-\cos x}=\sin x+\cos x[/tex]

[tex]\text{Left side of the equation:}[/tex]

[tex]\text{use}\ \tan x=\dfrac{\sin x}{\cos x}\\\\\dfrac{\cos^2x}{1-\tan x}=\dfrac{\cos^2x}{1-\frac{\sin x}{\cos x}}=\dfrac{\cos^2x}{\frac{\cos x}{\cos x}-\frac{\sin x}{\cos x}}=\dfrac{\cos^2x}{\frac{\cos x-\sin x}{\cos x}}=\cos^2x\cdot\dfrac{\cos x}{\cos x-\sin x}\\\\=\dfrac{\cos^3x}{\cos x-\sin x}\\\\\dfrac{\cos^2x}{1-\tan x}+\dfrac{\sin^3x}{\sin x-\cos x}=\dfrac{\cos^3x}{\cos x-\sin x}+\dfrac{\sin^3x}{\sin x-\cos x}\\\\=\dfrac{\cos^3x}{\cos x-\sin x}+\dfrac{\sin^3x}{-(\cos x-\sin x)}[/tex]

[tex]=\dfrac{\cos^3x}{\cos x-\sin x}-\dfrac{\sin^3x}{\cos x-\sin x}\\\\=\dfrac{\cos^3x-\sin^3x}{\cos x-\sin x}\qquad\text{use}\ a^3-b^3=(a-b)(a^2+ab+b^2)\\\\=\dfrac{(\cos x-\sin x)(\cos^2x+\cos x\sin x+\sin^2x)}{\cos x-\sin x}\qquad\text{cancel}\ (\cos x-\sin x)\\\\=\cos^2x+\cos x\sin x+\sin^2x\qquad\text{use}\ \sin^2x+\cos^2x=1\\\\=\cos x\sin x+1[/tex]

[tex]\text{We're back to the equation}[/tex]

[tex]\cos x\sin x+1=\sin x+\cos x\qquad\text{subtract}\ \sin x\ \text{and}\ \cos x\ \text{from both sides}\\\\\cos x\sin x+1-\sin x-\cos x=0\\\\(\cos x\sin x-\sin x)+(1-\cos x)=0\\\\\sin x(\cos x-1)-1(\cos x-1)=0\\\\(\cos x-1)(\sin x-1)=0\iff \cos x-1=0\ or\ \sin x-1=0\\\\\cos x=1\ or\ \sin x=1\\\\x=2k\pi\in D\ or\ x=\dfrac{\pi}{2}+2k\pi\notin D\ for\ k\in\mathbb{Z}[/tex]

Answer:(7,52)

Step-by-step explanation:plug those values into the equation.

52<8(7)+3.

52<59.

D. 103 12/13 or about 104

First sort the data into two sets of points, (1989,2881), (2002, 4232).

Now use the slope equation with your numbers.

(y2-y1)/(x2-x1)

(4232-2881)/(2002-1989)

1351/13=

103 12/13 or about 104

Answer:

d=-4

Step-by-step explanation:

20 = –d + 16

Subtract 16 from each side

20-16 = –d + 16-16

4 = -d

Multiply each side by -1

-1 *4 = -1 * -d

-4 =d

Answer:

c. when all angles are right angles

Step-by-step explanation:

Answer:

y=2

Step-by-step explanation:

8 - y = 9 - 3

Combine like terms

8 - y = 6

Subtract 8 from each side

8-8 - y = 6-8

-y = -2

Multiply each side by -1

-1 * -y = -2 *-1

y =2

Answer:

red: 9/20, 0.45, 45%

White: 15%, 0.15, 3/20

Blue: 0.4, 2/5, 40%

Step-by-step explanation:

For red: you start with 9/20. It’s best to get to a denominator of 10. So divide each number by 2. You would get 4.5/10. Then change to a percent by moving the decimal of the numerator one to the right and changing it to percent. 4.5 -> 45. -> 45%. Then for the decimal, divide 45 by 100. 45/100 = 0.45.

For white: you start with 15%. Divide by 100. 15/100=0.15. Put into a fraction with a denominator of 100. It would be 15/100. Simplify. Each number can be divided by 5, so your fraction would be 3/20.

For blue: you start with 0.4. Turn this into a fraction. Since there is one decimal place, it can have a denominator of 10. The fraction is 4/10, simplified to 2/5. Using the fraction 4/10, the percent would be 40%.

I hope this helps!

Answer:

17.009 in

Step-by-step explanation:

For a normal distribution with mean of 15.2 in and standard deviation of 1.1 inches, we finnd that 5% are excluded when the width of the seats are greater than 17.009 inches.

Therefore, the seat should have a width of 17.009 in.

To accommodate 95% of women based on hip breadth, airline seats should be designed at least 17.015 inches wide, calculated using the given mean of 15.2 inches, a standard deviation of 1.1 inches, and the z-score for the 95th percentile.

To determine the width of airline seats that would accommodate 95% of women, the airline needs to calculate the 95th percentile of women's hip breadths, modeled by a normal distribution.

Using the provided mean of 15.2 inches and a standard deviation of 1.1 inches, we find the z-score that corresponds to the 95th percentile. In normal distribution, the z-score for the 95th percentile is approximately 1.65.

Using the z-score formula Z =(X - μ / Σ, where Z is the z-score, X is the value we seek, μ is the mean, and Σ is the standard deviation, we can set Z to 1.65 and solve for X:

1.65 = (X - 15.2) / 1.1

X = 1.65 * 1.1 + 15.2

X = approx. 1.815 + 15.2

X = approx. 17.015 inches

Therefore, to exclude only the 5% of women with the widest hips, the airline should design seats that are at least 17.015 inches wide.

The function that represents the given scenario is; f(x) = 6(4)ˣ

We know the general formula for this population function is;

f(x) = abˣ

where;

a is initial population

b is the common ratio

x is number of years

We are given;

a = 6

b = 4

Thus;

f(x) = 6(4)ˣ

Read more about exponential function at; https://brainly.com/question/11464095

#SPJ1

Answer:

A, C and E are true.

Step-by-step explanation:

The domain is a set of natural numbers.

The recursive formula is correct:

When x = 1, f(x) = 4 and f(x + 1) = f(2) = 3/2 f(x) = 3/2 * 4 = 6.

It is also true for the other points on the graph.

D is  incorrect.

E is correct exponential growth with the formula  4(3/2)^(x-1).

Answer:

A and C

Step-by-step explanation:

10/3 x 6/5 is 4                                                                                                                      

It can be represented using the formula f(x + 1) = Six-fifths(f(x)) when f(1) = Ten-thirds

It can be represented using the formula f (x) = ten-thirds (six-fifths) Superscript x minus 1. edge 2020-2021

Answer:

27

Step-by-step explanation:

The range is the greatest value subtract the smallest value

greatest value = 50 and smallest value = 23, so

range = 50 - 23 = 27

Answer:

27

Step-by-step explanation:

23,32,37,40,41,41,41,42,43,48,49,49,50.

Range=50-23=27

Answer:

The distance between (-3, 2) and (0,3) is √10.

Step-by-step explanation:

As we go from (-3,2)  to  (0,3), x increases by 3 and y increases by 1.

Think of a triangle with base 3 and height 1.  Use the Pythagorean Theorem to find the length of the hypotenuse, which represents the distance between the points (-3, 2) and (0, 3):

distance = √(3² + 1²) = √10

The distance between (-3, 2) and (0,3) is √10.

For this case we have that by definition, the distance between two points is given by:

[tex]d = \sqrt {(x_ {2} -x_ {1}) ^ 2+ (y_ {2} -y_ {1}) ^ 2}[/tex]

We have the following points:

[tex](x_ {1}, y_ {1}): (- 3,2)\\(x_ {2}, y_ {2}) :( 0,3)[/tex]

Substituting:

[tex]d = \sqrt {(0 - (- 3)) ^ 2+ (3-2) ^ 2}\\d = \sqrt {(3) ^ 2 + (1) ^ 2}\\d = \sqrt {9 + 1}\\d = \sqrt {10}[/tex]

Answer:

The distance between the points is [tex]\sqrt {10}[/tex]

Option C ,

40 degrees

Because angle Z was 70 (isosceles triangle)

Then 180-140=40 degrees

Answer:

x = -4 and x=1

Step-by-step explanation:

The solutions to the equation x^2 +3x -4 = 0 will be given by the points at which the graph intercepts the x-axis.

By looking at the graph, we can clearly see that the graph intercepts the x-axis at x=-4 and x=1.

One of the roots is located between -4 and -3, and the other one between 0 and 1.