In AABC, mZA = 27°, c = 14, and mZB = 25°. Find a to the nearest tenth.

[tex]\boxed{\sf Slope(m)=\dfrac{y_2-y_1}{x_2-x_1}}[/tex]

[tex]\\ \sf\longmapsto m=\dfrac{7-4}{10-4}[/tex]

[tex]\\ \sf\longmapsto m=\dfrac{3}{6}[/tex]

[tex]\\ \sf\longmapsto m=\dfrac{1}{2}[/tex]

[tex]\\ \sf\longmapsto m\approx0.5[/tex]

Answer:

[tex]m=\frac{1}{2}[/tex]

Step-by-step explanation:

The slope of a line, also known as the change in the line or the ([tex]\frac{rise}{run}[/tex]) can be found using the following formula,

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Where ([tex]x_1,y_1[/tex]) and ([tex]x_2,y_2[/tex]) are points on the line. Substitute the given information into the formula and solve for the slope.

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Points on the line: [tex](4,4)\ \ \ (10, 7)[/tex]

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m=\frac{7-4}{10-4}[/tex]

[tex]m=\frac{3}{6}[/tex]

[tex]m=\frac{1}{2}[/tex]

[tex]m=0.5[/tex]

After completing the square the quadratic equation [tex]3x^{2} -12x-15=0[/tex] is equivalent to [tex](x-2)^2=3^2[/tex].

"It is a polynomial equation with degree two."

"It is a method that is used for converting a quadratic expression of the form [tex]ax^2 + bx + c[/tex] to [tex]a(x - h)^2 + k[/tex] "

For given example,

We have been given a quadratic equation.

[tex]3x^{2} -12x-15=0[/tex]

First we divide above quadratic equation by 3,

[tex]x^{2} -4x-5=0\\\\x^2-4x=5[/tex]                             ................(i)

Now for completing the square first find [tex](\frac{-b}{2a} )[/tex]

[tex]\frac{-b}{2a}\\=\frac{-(-4)}{(2)(1)}\\\\ =\frac{4}{2}\\\\ =2[/tex]

Add [tex](\frac{-b}{2a} )^2[/tex] on both the sides of equation (i),

[tex]x^{2} -4x+4=5+4\\\\(x-2)^2=9\\\\(x-2)^2=3^2[/tex]

Therefore, after completing the square the quadratic equation [tex]3x^{2} -12x-15=0[/tex] is equivalent to [tex](x-2)^2=3^2[/tex].

Learn more about completing the square here:

https://brainly.com/question/4822356

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please mark this answer as brainlist

Answer:

[tex]216\ km^2[/tex]

Step-by-step explanation:

1. Approach

The surface area of a three-dimensional figure is the two-dimensional distance around the figure.  The easiest way to find the surface area of a figure is to find the area of each of its facets, then add up the area to get the total surface area. The given pyramid is composed of four congruent triangles and a square. Find the area of one of the triangles, and then the area of the rectangle. Multiply the area of the triangle by four to account for the fact that there are four congruent triangles. Then add the area of the base to the result, the result attained is the surface area of the prism.

2. Find the area of the triangles

The formula to find the area of a triangle is the following:

[tex]A_t=\frac{b*h}{2}[/tex]

Where (b) represents the base and (h) represents the height of the triangle. Substitute the given values into the formula and solve for the answer.

[tex]A_t=\frac{b*h}{2}[/tex]

[tex]A_t=\frac{9*7.5}{2}[/tex]

[tex]A_t=\frac{67.5}{2}[/tex]

[tex]A_t=33.75[/tex]

3. Find the area of the rectangle

The formula to find the area of a rectangle is the following,

[tex]A_r=b*h[/tex]

Substitute the given values in and solve,

[tex]A_r=b*h[/tex]

[tex]A_r=9*9[/tex]

[tex]A_r=81[/tex]

4. Find the total surface area

Multiply the area of the triangle by four to account for the fact that there are four triangles. Then add its area to the area of the rectangle.

[tex]A_t+A_t+A_t+A_t+A_r=A[/tex]

[tex]4(A_t)+(A_r)=A[/tex]

[tex]4*33.75+81=A[/tex]

[tex]135+81=A[/tex]

[tex]216=A[/tex]

Answer:

0

Step-by-step explanation:

for y= -2*(3^x), as x is greater, the slope is steeper, and since the two graphs don't intercept in the picture we can see, they won't ever intercept because the slop of y=-2x+3 stays the same. as x becomes greater the distance between the two graphs is larger

Answer:

m = [tex]\frac{2q}{3y}[/tex]

Step-by-step explanation:

Given

q = [tex]\frac{3ym}{2}[/tex] ( multiply both sides by 2 to clear the fraction )

2q = 3ym ( isolate m by dividing both sides by 3y )

[tex]\frac{2q}{3y}[/tex] = m

Answer:

C

Step-by-step explanation:

using the theorem of Pythagoras

x = sqrt * 10.2^2 - 9.6^2 *

using the calculator

x = 3.4 units

rounded to 1 decimal place

===========================================================

Explanation:

Label a new point E at the intersection of the diagonals. The goal is to find angle CEB. Notice how angle AED and angle CEB are vertical angles, so angle AED is also x.

Recall that any rectangle has each diagonal that is the same length, and each diagonal cuts each other in half (aka bisect). This must mean segments DE and AE are the same length, and furthermore, triangle AED is isosceles.

Triangle AED being isosceles then tells us that the base angles ADE and DAE are the same measure (both being 55 in this case).

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

To briefly summarize so far, we have these interior angles of triangle ADE

For any triangle, the three angles always add to 180, so,

A+D+E = 180

55+55+x = 180

110+x = 180

x = 180-110

x = 70

Answer:

100000

Step-by-step explanation:

Answer:

6'2

Step-by-step explanation:

9514 1404 393

Answer:

   $40,615.20

Step-by-step explanation:

The amortization formula will tell you Michelle's monthly payment.

  A = P(r/12)/(1 -(1 +r/12)^(-12t)) . . . . loan value P at interest rate r for t years

  A = $124,500(0.059/12)/(1 -(1 +0.059/12)^(-12·10)) ≈ $1375.96

__

The total of Michelle's 120 monthly payments is ...

  12 × $1375.96 = $165,115.20

This amount pays both principal and interest, so the amount of interest she pays is ...

  $165,115.20 -124,500 = $40,615.20

Michelle will pay $40,615.20 in interest over the course of the loan.

__

A calculator or spreadsheet can figure this quickly.

Answer:

Xbar = 20.813

Median = 19.95

5 - number summary :

Minimum = 15.2

Q1 = 19.05; Q2 = 19.95 ; Q3 = 21.95 ; maximum = 29.4

Standard deviation, s = 4.068

Step-by-step explanation:

Given the data:

X : 15.2, 18.8, 19.3, 19.7, 20.2, 21.8, 22.1, 29.4

Ordered data:

15.2, 18.8, 19.3, 19.7, 20.2, 21.8, 22.1, 29.4

The mean (xbar) :

Xbar = Σx / n ; n = sample size = 8

Xbar = 166.8 / 8 = 20.8125

Xbar = 20.813

The median :

1/2 *(n+1)th term

1/2(9) = 4.5

(4 + 5)th term / 2

(19.7 + 20.2) / 2 = 19.95

The five number summary :

Minimum = 15.2

Lower quartile (Q1) = 1/4(9) = 2.25 ; (2nd + 3rd) term / 2

(18.8 + 19.3) / 2 = 19.05

Median (Q2) = 19.95

Upper quartile (Q3) :

3/4(9) = 6.75 = (6th + 7th) / 2

(21.8 + 22.1) / 2 = 21.95

Maximum = 29.4

The standard deviation, s = sqrt[(x - xbar)²/ (n-1)]

Using calculator ;

s = 4.068

Answer:

yall do school right now???and i forgot how to do these sorry

Answer:

18 = 2x-14

or, 2x =18+14

or, 2x =32

or, x=32/2

x=16

2(6x-7)=10

or, 12x-14=10

or, 12x=10+14

or, x=24/12

x=2

Answer:

It's 28 3/4

Step-by-step explanation:

Answer:

Answer is 19.5

Step-by-step explanation:

27-9+(12-5)÷4

27-9+6÷4   [BOD MAS Rule]

27-9+1.5

28.5-9

19.5

Coordinates of point A is (-2 and 1)

Coordinates of point B is (1 and -1)

[tex] \begin{cases}\large\bf\red{ \longrightarrow} \rm \: Distance \: = \: \sqrt{(x_2 - x_1 ) \: + \:(y_2 - y_1 )} \\ \\ \large\bf\red{ \longrightarrow} \rm \:Distance \: = \:\sqrt{(1 - [ - 2]) ^{2} \: + \:( - 1 - 1)^{2} } \\ \\ \large\bf\red{ \longrightarrow} \rm \: Distance \: = \: \sqrt{( - 3) ^{2} \: + \:( - 2) ^{2}} \\ \\ \large\bf\red{ \longrightarrow} \rm \: Distance \: = \: \sqrt{6 \: + \: 4} \\ \\ \large\bf\red{ \longrightarrow} \rm \: Distance \: = \: \sqrt{10} \ \\ \ \\ \large\bf\red{ \longrightarrow} \rm \: Distance \: = \:3.1622 \: \: units \end{cases}[/tex]

Answer:

what's the problem!?......

angle CDT is the opposite angle of ADN

and the segment DF=FN, so AD= AN

and thats why angle FAN= angle FAD

here, Angle FAN =60,

therefore, FAD=60, and AFD = 90 so angle ADN must be 30 degree

and the opposite of ADN is CDT, and the opposite angles are equal.

Hope u got it.

Answer:

(b) 829 seconds

(c) 13.8 minutes

Step-by-step explanation:

(b) 2.48×10⁸/2.99×10⁵ = 829 seconds

(c) 829/60 = 13.8 minutes

Answer:

a) 0

b) 2,3,4,5,6,7

c)3,4,6,7

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

0.0015

hope this helps

Answer:

1/13

Step-by-step explanation:

There are 52 cards in a deck of cards and 13 of them are hears

P(heart) = hearts / total

              = 13/52 = 1/13

[tex]\boxed{\sf (a+b)^2=a^2+b^2+2ab}[/tex]

Now

[tex]\\ \sf\longmapsto x+\dfrac{1}{x}=12[/tex]

[tex]\\ \sf\longmapsto \left(x+\dfrac{1}{x}\right)^2=12^2[/tex]

[tex]\\ \sf\longmapsto x^2+2\times x\times \dfrac{1}{x}+\left(\dfrac{1}{x}\right)^2=144[/tex]

[tex]\\ \sf\longmapsto x^2+\dfrac{1}{x^2}+2=144[/tex]

[tex]\\ \sf\longmapsto x^2+\dfrac{1}{x^2}=144-2=142[/tex]

Answer:

122

Step-by-step explanation:

x+1/x = 12

x + 1 = 12x

x = 1/11

（1/11）² + 1 / （1/11）² = 1/121 +1 /1/121 = 122

Answer:

It will take Sophia 1 hour to run 6 miles.

And 1 1/2 hours for 9 miles.

Step-by-step explanation:

Answer:

see similar to the number of the number

Answer:

Step-by-step explanation:

The hypotenuse is 2 * sqrt(11) because all the sides are equal. 1/2 the base is given as root 11.

x^2 = (2*sqrt(11) )^2 - (sqrt(11) ) ^2

x^2 = 4 * 11 - 11

x^2 = 44 - 11

x^2 = 33

x = sqrt(33)

sqrt(33) = 5.744

sqrt(33) = 5.7 rounded to the nearest 1/10

Answer:

[tex] \frac{2 \sqrt{7} + \sqrt{3}}{3 \sqrt{7} - \sqrt{3} } = \frac{2 \sqrt{7} + \sqrt{3}}{3 \sqrt{7} - \sqrt{3} } . \frac{3 \sqrt{7} + \sqrt{3} }{3 \sqrt{7} + \sqrt{3} } \\ \\ = \frac{(2 \sqrt{7} + 3)(3 \sqrt{7} + \sqrt{3}) }{(3 \sqrt{7} - 3)(3 \sqrt{7} + \sqrt{3} ) } \\ \\ = \frac{(42 + 2 \sqrt{21} + 9 \sqrt{21} + 3 \sqrt{21} )}{63 - 3} \\ \\ = \frac{42 + 2\sqrt{21} + 9 \sqrt{21} + 3 \sqrt{21} }{60} [/tex]

Answer:

Answer:

B) 3

Step-by-step explanation:

4+5+1/3=10/3=3.333~3

Answer:

B) 3

Step-by-step explanation:  

========================================================

Explanation:

At 95% confidence, the z critical value is roughly z = 1.960

The population standard deviation is given to be sigma = 3.7

The error is E = 2 since we want to be within 2 inches of the population mean mu

The min sample size needed is:

n = (z*sigma/E)^2

n = (1.960*3.7/2)^2

n = 13.147876

n = 14

We always round up to the nearest whole number to ensure that we clear the hurdle (otherwise, the sample is too small). It doesn't matter that we're closer to 13 than to 14.

Answer:

Remainder is -53/8

Step-by-step explanation:

the divisor is (2x - 3):

make x the subject:

[tex]2x - 3 = 0 \\ 2x = 3 \\ x = \frac{3}{2} [/tex]

substitute for x in the function:

[tex]f(x) = {x}^{3} - 6 {x}^{2} + 3x - 1 \\ f( \frac{3}{2} ) = {( \frac{3}{2}) }^{3} - 6 {( \frac{3}{2}) }^{2} + 3( \frac{3}{2} ) - 1 \\ \\ f( \frac{3}{2} ) = \frac{ - 53}{8} [/tex]

9514 1404 393

Answer:

  (a)  8 km

Step-by-step explanation:

Let m represent the distance (in kilometers) Michelle has walked. Then Janet walked a distance of (m-2). These distances are at right angles, so the distance between them can be found using the Pythagorean theorem.

  m² +(m -2)² = 10²

  m² +m² -4m +4 = 100

  2m² -4m = 96 . . . . . . subtract 4, collect terms

  m² -2m +1 = 49 . . . . . divide by 2 and add 1

  (m -1)² = 7² . . . . . . .write as squares

  m -1 = 7 . . . . . . positive square root

  m = 8

Michelle walked 8 km.