Find the range of the following set of data.
13. 11, 4,5,6, 9, 10, 12, 15, 16​

Answer:

Step-by-step explanation:

What he did at the end of the given equations is solve for x in x + 8y= 21

x = 21 - 8y                Substitute that result in the top equation.

7(21 - 8y) + 5y = 14  is the correct step To continue Remove the brackets

147 - 56y + 5y = 14   Combine

147 - 51y = 14             Add 51y to both sides.

147 = 51y + 14            Subtract 14 from both sides.

133 = 51y                   divide by 51

y = 2.61 rounded.

The incorrect step is underlined and italicized.

Answer:

Texting speed

Step-by-step explanation:

It's the dependent variable

Answer:

B

Step-by-step explanation:

I has the most numbers varied and has bigger numbers which means it can't be the time which is either 1 2 or 3. The number of words will almost never be the answer!

Answer:

4800 miles

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]\text{For}\ f(x)=a^{(x+h)}+k\\\\\text{always}\ a>0\\\\\text{If}\ a>1,\ \text{then the function is  increasing}\\\\\text{If}\ 0<a<1,\ \text{then the function is decreasing}\\\\<-h,\ k>-\text{translation vector}\\\\============================[/tex]

[tex]\text{From the graph:}\\\\\text{the function is decreased}\to 0<a<1\\\\h<0\\\\k>0[/tex]

The correct answer is: Option: C

              C.  0<a<1

We are given a graph of a exponential function as:

             [tex]f(x)=a^{x+h}+k[/tex]

We know that the function is a exponential decay function if: 0<a<1

and it represents a exponential growth function if: a>1

Hence, by looking at the graph we observe that the graph is continuously decreasing with increasing values of x.

This means that the graph is a graph of exponential decay function.

Hence, we get:   0<a<1

Answer:

True.

Step-by-step explanation:

It is because it is in the form [tex]a^2x^2+2abx+b^2[/tex] and this equals [tex](ax+b)^2[/tex].

Why it is in that form:  well comparing  [tex]a^2x^2+2abx+b^2[/tex], we have [tex]a=1, b=1[/tex]. Testing, plug in those values:

[tex](1)^2x^2+2(1)(1)x+(1)^2[/tex]

[tex]1x^2+2x+1[/tex]

[tex]x^2+2x+1[/tex].

This has the squared form of [tex](x+1)^2[/tex].

Test if you like:

[tex](x+1)^2[/tex]

[tex](x+1)(x+1)[/tex]

Use foil to expand:

First: x(x)=x^2

Outer: x(1)=x

Inner: 1(x)=x

Last: 1(1)=1

---------------Add together

[tex]x^2+2x+1[/tex]

It does indeed equal.

[tex]34+3\cdot5=34+15=49[/tex]

Hope this helps.

r3t40

Answer:

[tex]\huge \boxed{49}\checkmark[/tex]

Step-by-step explanation:

Order of operations

PEMDAS

Parenthesis

Exponent

Multiply

Divide

Add

Subtract

Do multiply first.

[tex]\displaystyle 34+3\times5[/tex]

[tex]\displaystyle 3\times5=15[/tex]

Add from left to right to find the answer.

[tex]\displaystyle 34+15=49[/tex]

[tex]\huge \boxed{49}[/tex], which is our answer.

Hope this helps!

Answer:

The approximate value of arc cos(0.87) is 29.54°

Step-by-step explanation:

we know that

The arc cosine of x is defined as the inverse cosine function of x

so

if y=cos(x)

then

arc cos (y)=x

In this problem we have

y=0.67

so

x=arc cos(0.87)

using a calculator

x=29.54°

So, the approximate value of arccos(0.67) is about 0.84108 radians.

To approximate arccos(0.67) using a calculator, we find it to be approximately 0.84108 radians. This value represents the angle whose cosine is 0.67. Arccos, or inverse cosine, returns the angle in radians between 0 and π (approximately 3.14159) whose cosine is the input value. In this case, 0.67 is the cosine of the angle 0.84108 radians. This angle is commonly used in trigonometric calculations, such as determining the angle of a vector or solving geometric problems involving cosine functions.Let's use a calculator to find the approximate value of arccos(0.67).

Using a calculator:

[tex]arccos(0.67) \approx 0.84108 radians[/tex]

Answer:

The average rate of speed = 53.8 mph

Step-by-step explanation:

Sharon drove 188.3 miles.

She was driving for 3 1/2 hours = 7/2 = 3.5hours

To find the average speed simply divide the miles she drove by driving hours:

188.3/3.5

53.8 mph.

Therefore the average rate of speed = 53.8 mph....

Answer:

110.5 units²

Step-by-step explanation:

The area (A) of a rhombus is calculated as

A = [tex]\frac{1}{2}[/tex] product of diagonals, that is

A = 0. 5 × MK × JL = 0.5 × 13 × 17 = 110.5

The area of the rhombus will be 110.5 square units.

The area of the rhombus can be calculated by half of the product of its two diagonals.

Here given,

JKLM is a rhombus.

The length of its diagonals will be MK=13

JL=17

The diagonal MK and JL intersect each other by 90° at point O.

Now the rhombus is divided by 4 right-angled triangle,

Area of the rhombus will be 4 times of the right-angled triangle ΔMJO

Area of the rhombus= 4*Area of right-angled triangle ΔMJO

=4*(1/2)*MO*JO

= 4*(1/2)*(MK/2)(JL/2)

=(1/2)*MK*JL

=(1/2)*the product of its two diagonals

=(1/2)*13*17

=110.5 Square unit

Therefore the area of the rhombus will be 110.5 square units.

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Answer:

Part 1) The measure of arc AB is 50°

Part 2) The measure of angle AOB is 50°

Part 3) The measure of angle BDA is 25°

Step-by-step explanation:

step 1

Find the measure of arc AB

we know that

arc AD+arc BD+arc AB=360° -----> by complete circle

substitute the given values

212°+98°+arc AB=360°

310°+arc AB=360°

arc AB=360°-310°=50°

step 2

Find the measure of angle AOB

we know that

The measure of angle AOB is the same that the measure of arc AB by central angle

so

m∠AOB=arc AB=50°

step 3

Find the measure of angle BDA

we know that

The inscribed angle measures half that of the arc comprising

so

m∠BDA=(1/2)[arc AB]

we have

arc AB=50°

substitute

m∠BDA=(1/2)[50°]=25°

The arc of a circle is defined as the part or segment of the circumference of a circle.

The measure of arc AB is 50 degrees.

An angle of a circle is an angle that is formed between the radii, chords, or tangents of a circle.

The measure of angle AOB is 50 degrees.

The measure of angle BDA is 25 degrees.

The measure of arc AB is

The measure of angle AOB is

The measure of angle BDA is

The arc of a circle is defined as the part or segment of the circumference of a circle.

An angle of a circle is an angle that is formed between the radii, chords, or tangents of a circle.

1. The measure of arc AB is,

[tex]\rm Arc \ AD+Arc \ BD+Arc \ AB=360\\\\212+98+Arc\ AB=360\\\\310+Arc \ AB=360\\\\ Arc \ AB=360-310\\\\ Arc\ AB = 50[/tex]

The measure of arc AB is 50 degrees.

2. The measure of angle AOB is,

[tex]\rm m\angle \ AOB=Arc \ AB=50 degrees[/tex]

The measure of angle AOB is 50 degrees.

3. The measure of angle BDA is,

[tex]\rm m \angle BDA=\dfrac{1}{2}\times Arc AB\\\\ m \angle BDA=\dfrac{1}{2}\times 50\\\\ m \angle BDA = 25[/tex]

The measure of angle BDA is 25 degrees.

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[tex]\bf y-0=\cfrac{1}{4}(x-3)\implies y=\cfrac{1}{4}(x-3)\implies \stackrel{\textit{distributing}}{y=\cfrac{1}{4}x-\cfrac{3}{4}}[/tex]

For this case we have that by definition, the equation of a line in the slope-intersection form is given by:

[tex]y = mx + b[/tex]

Where:

m: It's the slope

b: It is the cut-off point with the y axis

According to the data we have to:

[tex]m = \frac {1} {4}[/tex]

Then, the equation is of the form:

[tex]y = \frac {1} {4} x + b[/tex]

We substitute point (3.0):

[tex]0 = \frac {1} {4} (3) + b\\b = - \frac {3} {4}[/tex]

Finally, the equation is:

[tex]y = \frac {1} {4} x- \frac {3} {4}[/tex]

Answer:

Option B

Reflection is the correct answer

A reflection would be the single transformation required to map one congruent triangle onto the other in this scenario, with the line AD serving as the line of reflection.

The single transformation required to map one congruent triangle onto the other is a translation.

In the context of two congruent triangles, when point M is the midpoint of AD, the single transformation to map one triangle onto the other would be a reflection. Imagine the line segment AD as the mirror or line of reflection. Because M is the midpoint, both halves of the line segment would mirror each other exactly, corresponding to the two congruent triangles. This means the triangle on one side of the line AD can be reflected over the line AD to coincide exactly with the triangle on the other side.

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The circumcenter O, formed by the intersection of the perpendicular bisectors of sides AB and BC, is equidistant from all vertices, with OA = OB = OC. Here option B is correct.

In a triangle, the circumcenter is the point where the perpendicular bisectors of its sides intersect. In this case, the circumcenter O is formed by the intersection of the perpendicular bisector of side AB and the perpendicular bisector of side BC.

The circumcenter is equidistant from all three vertices, making OA, OB, and OC equal, and these distances represent the radius of the circumcircle.

This line not only bisects side AB but also intersects with the perpendicular bisector of side BC at the circumcenter O. The equality of OA, OB, and OC ensures that the circumcircle passes through all three vertices of the triangle, making it a significant point in the context of the triangle's geometry. Here option B is correct.

Answer:

Hi there!

The answer to this question is: C. -3/2

Step-by-step explanation:

You first find the slope of the equation using the change of y over the change of x formula. You should get 2/3. Then it asks its perpendicular that is simply the negative reciprocal of the original slope. All you do is flip the fraction and make it negative, your final answer should be -3/2

Answer:

C

Step-by-step explanation:

Calculate the slope m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 3, - 1 ) and (x₂, y₂ ) = (3, 3)

m = [tex]\frac{3+1}{3+3}[/tex] = [tex]\frac{4}{6}[/tex] = [tex]\frac{2}{3}[/tex]

Given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{2}{3} }[/tex] = - [tex]\frac{3}{2}[/tex] → C

Answer:

Step-by-step explanation:

Later on in the course, I hope you are told that answers should not rely on diagrams.

Since you have to answer the question somehow, the answer (directly) is BCA. Since this is an appearance question (that's what the answer looks like), you can only state the answer, There really (in this case) is no what to offer a proof).

Answer:

[tex]x1=-5+\sqrt{2} \\x2=-5-\sqrt{2}[/tex]

Step-by-step explanation:

First we need to simplify your equation by grouping coefficients:

[tex]x^{2} +10x+23=0[/tex]

Now, there are two valid values for your variable, wich are determined by the following expressions:

[tex]x=\frac{-b+\sqrt{b^{2}-4ac } }{2a} \\\\x=\frac{-b-\sqrt{b^{2}-4ac } }{2a}[/tex]

We will call those expression as (eq1) and (eq2) in their respective order

In both scenarios the following is derived from your grouped equation.

[tex]a=1\\b=10\\c=23[/tex]

[tex]x1=\frac{-10+\sqrt{10^{2}-4*1*23 } }{2*1}\\x2=\frac{-10-\sqrt{10^{2}-4*1*23 } }{2*1}[/tex]

[tex]x1=\frac{-10+\sqrt{8 } }{2}\\\\x2=\frac{-10-\sqrt{8} }{2}[/tex]

We can simplify these expressions a little more by doing the following

[tex]x1=\frac{-10+2 \sqrt{2 } }{2}\\\\x2=\frac{-10-2\sqrt{2} }{2}[/tex]

The result is

[tex]x1=-5+\sqrt{2} \\x2=-5-\sqrt{2}[/tex]

We can not simplify these expresions anymore

Answer:

Step-by-step explanation:

Good idea to review quadratic functions and the quadratic formula.

Quadratics have three coefficients:  ax² + bx + c, and the "discriminant" is defined as b²-4ac.  Please review these rules:

1) if the discriminant is +, the quadratic equation has two real, unequal roots.

2) if the disc. is 0, the equation has two real, equal root.

3) If the disc. is - , the equation has two complex roots.

Here a = 1, b  = -3 and c = 4.  Therefore the discriminant is (-3)²-4(1)(4), or

-7.  Rule 3) applies:  the equation has two complex roots, but no real ones.  Thus we know that the graph does not cross the x-axis.

Graphing the given quadratic, x² - 3x + 4, using a dashed "line," is helpful.  As you can see in the illustration of this graph, the graph neither touches nor crosses the x-axis.  Thus, y = x² - 3x + 4 is greater than 0 for all x.  The answer:  All real numbers.

[tex]\bf \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{8}{ h},\stackrel{4}{ k})\qquad \qquad radius=\stackrel{4}{ r} \\\\[-0.35em] ~\dotfill\\\\ (x-8)^2+(y-4)^2=4^2\implies (x-8)^2+(y-4)^2=16[/tex]

Answer:

wht are da choices

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

First, find the slope using the slope formula.  The slope is 3.

Now plug in any of the x and y values and the value of the slope into the slope-intercept form equation to solve for b.

9=3(3)+b, solve for b

b=0, Now convert the equation y=3x into slope-intercept form.

y-9=3(x-3) This is the equation of the line, the plant will be about 36 cm tall after 12 months.

Answer:

B. A(w)=w∧2+4w

Step-by-step explanation:

Let the width of the rectangle be w.

The length is  4 feet longer than the width= w+4

Area of a rectangle= length× width

A=L×W

=(w+4)×w

Opening the brackets gives the:

A=w²+4w

Therefore the expression for the area in terms of width is A(w)=w∧2+4w

Answer:

1/4

Step-by-step explanation:

Slope of a line can be found if given two points by using the formula [tex]\frac{y_2-y_1}{x_2-x_1}[/tex] where [tex](x_1,y_1) \text{ and } (x_2,y_2)[/tex] are points on the line.

However, I like to line up the points vertically and subtract then put 2nd difference over 1st difference.

Like this:

(   3   ,   3   )

-(  -1   ,    2  )

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

   4          1

So the slope is 1/4.

Answer:

The slope is 1/4.

Step-by-step explanation:

To find the slope, you'd need to use formula of slope. The slope is y2-y1/x2-x1=rise/run.

y2=3

y1=2

x2=3

x1=(-1)

3-2/3-(-1)

3-2/3+1

3-2=1

3+1=4

Therefore, the slope is 1/4, which is our answer.

I hope this helps!

Answer:

[tex]5x^2 y^2[/tex]

Step-by-step explanation:

We need to use the properties shown below to solve this:

1. [tex]\sqrt[n]{x^a} =x^{\frac{a}{n}}[/tex]

2. [tex]\sqrt{x}\sqrt{x}  =x[/tex]

3.  [tex]\sqrt{x} \sqrt{y}=\sqrt{x*y}[/tex]

Area of a triangle is given by  1/2 * base * height, so we do that and simplify:

[tex]A=\frac{1}{2}(\sqrt{5x^3} )(2\sqrt{5xy^4} )\\A=\frac{1}{2}(5x^3)^{\frac{1}{2}}*2*(5xy^4)^{\frac{1}{2}}\\A=\sqrt{5}x^{\frac{3}{2}}*\sqrt{5}\sqrt{x} }  y^2\\A=\sqrt{5} \sqrt{5}x^{\frac{3}{2}} x^{\frac{1}{2}}y^2\\A=5*x^2y^2\\A=5x^2 y^2[/tex]

Answer:

So first blank=6

Second blank=0

Third blank=-5

Fourth blank=6

Step-by-step explanation:

It is a horizontal line so the equation is just going to be

[tex]y=\text{ whatever y-coordinate they gave you in that one point}[/tex].

So it will be [tex]y=6[/tex]

We are going to do the point-slope form too as I requested.

Point-slope form is [tex]y-y_1=m(x-x_1)[/tex].

We have m=0 since you said the slope was 0 and since it said your have a horizontal line (which means the slope slope or m is 0).

You also that it contains the point [tex](-5,6)=(x_1,y_1)[/tex].

So our line in point-slope form is [tex]y-6=0(x-(-5))[/tex].

Using the law of Tangents:

Tan(angle) = Opposite leg / Adjacent leg.

Using the provided information:

Tangent (61) = BC / 5.7

Solve for BC:

BC = 5.7 x tangent(61)

BC = 10.3 miles ( rounded to the nearest tenth).

The distance from point B to point C is 10.3 mi (to the nearest tenth).

If we have a right angle triangle,

Then, tanθ = Opposite side/ Adjacent side

Here in the right angle triangle ABC,

Adjacent side = AB = 5.7 mi

θ = 61°

We have to find the BC.

∴  tanθ = Opposite side/ Adjacent side

⇒ tanθ = BC/AB

⇒ tan61°= BC/5.7

⇒ BC = 5.7×tan61°

⇒ BC = 10.283 = 10.3 (to the nearest tenth)

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Answer:

x = 2.9.

Step-by-step explanation:

14.3 - 0.4x = 2.6x + 5.6​

14.3 - 5.6 = 2.6x + 0.4x

8.7 = 3x

x = 8.7 / 3 = 2.9 (answer).

Answer:

x=2.9

Step-by-step explanation:

14.3 -0.4x = 2.6x + 5.6​

Add .4x to each side

14.3 -0.4x+.4x = 2.6x+.4x + 5.6​

14.3 = 3x+5.6

Subtract 5.6 from each side

14.3 - 5.6 = 3x - 5.6

8.7 =3x

Divide each side by 3

8.7/3 = 3x/3

2.9=x

[tex]\bf ~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$500\\ r=rate\to 2\%\to \frac{2}{100}\dotfill &0.02\\ t=years\dotfill &3 \end{cases} \\\\\\ I=(500)(0.02)(3)\implies I=30~\hfill \stackrel{\textit{total amount in the account}}{500+30\implies 530}[/tex]

Answer:

The answer is C; (5, 1).

Step-by-step explanation:

2(5) - 1 = 9

10 - 1 = 9

9 = 9

9 = 9 is a true statement so the answer is C.

Answer:

AH

Step-by-step explanation:

we know that

A cube has 6 faces and on each face there are two diagonals joining nonadjacent vertices and there are 4 diagonals through the interior of the cube. Thus in total there are 6×2+4=16 diagonals in a cube.

In this cube, the diagonals through the interior of the cube are

AH, CF, DE and BG  

therefore

The answer is AH

Answer:

The correct answer is first option. AH

Step-by-step explanation:

From the figure we can see a cube ABCDEFGH.

In a cube thee are 4 interior diagonals

To find the diagonal of the cube

AH, BG, CF   and DE

There are 4 interior diagonals.

The given options contain only one interior diagonal.

Therefore the correct answer is first option. AH

Answer:

-3

explanation:

since the line crosses the y-axis on the point -3

Answer:

c = - 3

Step-by-step explanation:

The y- intercept is the point on the y- axis where the line crosses.

The line crosses the y- axis at (0, - 3), hence y- intercept = - 3

Answer:

122.2 in^2.

Step-by-step explanation:

WE can divide a regular octagon into 8 triangles with height ( = the apotherm) = 6.5 and  base = 4.7.

The area of each triangle is 1/2 * 4.7 *6.5 so #the area of the octagon

= 8 * 1/2 * 4.7 * 6.5

= 122.2 in^2.

For this case we have by definition, that the area of an octagon is given by:

[tex]A = \frac {p * a} {2}[/tex]

Where:

p: perimeter

a: apothem

We have that the perimeter is given by the sum of the sides of the octagon:

[tex]p = 8 * 4.7 = 37.6 \ in\\a = 6.5 \ in[/tex]

Substituting:

[tex]A = \frac {37.6 * 6.5} {2} = 122.2[/tex]

So, the area of the octagon is[tex]122.2 \ in ^ 2[/tex]

Answer:

[tex]122.2 \ in ^ 2[/tex]