Given: △ABC, AB=5√2 m∠A=45°, m∠C=30° Find: BC and AC

Answer:

d ≈ 8.3

Step-by-step explanation:

This is kind of like the pythagorean theorem, but with one extra value.  Thus, [tex]d^2=l^2+w^2+h^2[/tex].

Plug in the values to get:

[tex]d^2=2^2+7^2+4^2\\d^2=4+49+16\\d^2=69\\d=\sqrt{69} \\[/tex]

Thus d ≈ 8.3

Answer:

x = 7

Step-by-step explanation:

7 = 7

It's given

Answer:

[tex]\huge\boxed{slope=\dfrac{1}{2}=0.5}[/tex]

Step-by-step explanation:

The formula of a slope:

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

We have the points

[tex](-5;\ 3)\to x_1=-5;\ y_1=3\\(7;\ 9)\to x_2=7;\ y_2=9[/tex]

Substitute:

[tex]m=\dfrac{9-3}{7-(-5)}=\dfrac{6}{7+5}=\dfrac{6}{12}=\dfrac{6:6}{12:6}=\dfrac{1}{2}[/tex]

Answer:

1/2

Step-by-step explanation:

We can use the slope formula since we have 2 points

m = ( y2-y1)/(x2-x1)

    = (9-3)/( 7 - -5)

    = (9-3) /( 7+5)

   = 6/ 12

  = 1/2

Hey there! I'm happy to help!

Let's set this up as a system of equations, where x is equal to the number of 10 dollar bills and y is equal to the number of 50 dollar bills.

10x+50y=1080

x+y=28

We want to solve for x or y. We can rearrange the second equation to find the value of one of the variables.

x+y=28

Subtract x from both sides.

y=28-x

Now, we have a value for y. So, we could replace the y in the first equation with 28-x and the solve for x.

10x+50(28-x)=1080

We use distributive property to undo the parentheses.

10x+1400-50x=1080

We combine like terms.

-40x+1400=1080

We subtract 1400 from both sides.

-40x=-320

We divide both sides by -40.

x=8

Since there are 28 total bills, this means that there must be 20 50 dollar ones because there are 8 10 dollar bills.

Have a wonderful day! :D

Answer:

x1= -4, x2 = 7

Step-by-step explanation:

Move expression to the left-hand side:

1/4x-3/4-7/x=0

Write all the numerators above a common denominator:

x^2 - 3x - 28 /4x =0

When the quotient of expressions equal 0, the numerator has to be 0

x^2 + 4x - 7x - 28 = 0

x(x+4) - 7(x+4) =0

(x+4) × (x-7) =0

Separate into possible cases:

x+4=0

x-7=0

Answer: -9

Step-by-step explanation:

Answer:

The  99%  confidence interval is

                     [tex]37.167< \= x < 44.833[/tex]

Step-by-step explanation:

From the question we are told that

  The sample size is  [tex]n = 29[/tex]

  The  sample mean is  [tex]\= x =[/tex]$41

  The  sample standard deviation is  [tex]\sigma =[/tex]$8

   The  level of confidence is [tex]C =[/tex]99%

Given that the confidence level id  99% the level of confidence is evaluated as

        [tex]\alpha = 100 - 99[/tex]

        [tex]\alpha = 1[/tex]%

Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table which is  

      [tex]Z_{\frac{\alpha }{2} } = 2.58[/tex]

The reason we are obtaining values for  is because  is the area under the normal distribution curve for both the left and right tail where the 99% interval did not cover while   is the area under the normal distribution curve for just one tail and we need the  value for one tail in order to calculate the confidence interval

Next we evaluate the margin of error which is mathematically represented as

          [tex]MOE = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]

substituting values

         [tex]MOE = 2.58 * \frac{8 }{\sqrt{29} }[/tex]

           [tex]MOE = 3.8328[/tex]

The 99% confidence level is constructed as follows

      [tex]\= x - MOE < \= x < \= x + MOE[/tex]

substituting values

    [tex]41 - 3.8328 < \= x < 41 + 3.8328[/tex]

     [tex]37.167< \= x < 44.833[/tex]

Answer:

Step-by-step explanation:

Given,

Perpendicular ( p ) = 9x

Base ( b ) = 10

Hypotenuse ( h ) = x + 10

Now, let's find the value of x

Using Pythagoras theorem:

[tex] {h}^{2} = {p}^{2} + {b}^{2} [/tex]

Plug the values

[tex] {(x + 10)}^{2} = {(9x)}^{2} + {(10)}^{2} [/tex]

Using [tex] {(a + b)}^{2} = {a}^{2} + 2ab + {b}^{2} [/tex] , expand the expression

[tex] {x}^{2} + 20x + 100 = {(9x)}^{2} + {10}^{2} [/tex]

To raise a product to a power , raise each factor to that power

[tex] {x}^{2} + 20x + 100 = 81 {x}^{2} + {10}^{2} [/tex]

Evaluate the power

[tex] {x}^{2} + 20x + 100 = 81 {x}^{2} + 100[/tex]

Cancel equal terms on both sides of the equation

[tex] {x}^{2} + 20x = 81 {x}^{2} [/tex]

Move x² to R.H.S and change its sign

[tex]20x = 81 {x}^{2} - {x}^{2} [/tex]

Calculate

[tex]20x = 80 {x}^{2} [/tex]

Swap both sides of the equation and cancel both on both sides

[tex]80x = 20[/tex]

Divide both sides of the equation by 80

[tex] \frac{80x}{80} = \frac{20}{80} [/tex]

Calculate

[tex]x = \frac{20}{80} [/tex]

Reduce the numbers with 20

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

The value of X is [tex] \frac{1}{4} [/tex]

Now, let's replace the value of x to find the approximate value of hypotenuse

Hypotenuse = [tex] \frac{1}{4} + 10[/tex]

Write all numerators above the common denominator

[tex] \frac{1 + 40}{4} [/tex]

Add the numbers

[tex] \frac{41}{4} [/tex]

[tex] = 10.25[/tex] inches

Hope this helps..

best regards!!

Answer:

10.25

Step-by-step explanation:

because I said so ya skoozie

Answer:

k ≥ 24

Step-by-step explanation:

ᵏ⁄₄ ≥ 6

Multiply each side by 4

ᵏ⁄₄ *4 ≥ 6*4

k ≥ 24

Answer:

k≥24

Step-by-step explanation:

k/4≥6

Use the multiplication property of equality by multiplying both sides by 4 to get

k≥24

If this is wrong or if I did something wrong, please tell me so I can learn the proper way, I am just treating this like a normal problem

Thank you

Answer:

97 m

Step-by-step explanation:

Perimeter = 2 * (length + width); perimeter = 344, width = 75 (solving for length)

344 = 2(length + 75)

172 = length + 75

length = 97

Answer:

3057.6 cm³

Step-by-step explanation:

You have a cylinder and a rectangular prism.  Solve for the area of each separately.

Cylinder

The formula for volume of a cylinder is V = πr²h.  The radius is 7, and the height is 7.

V = πr²h

V = π(7)²(7)

V = π(49)(7)

V = 343π

V = 1077.57 cm³

Rectangular Prism

The formula for volume of a rectangular prism is V = lwh.  The length is 20, the width is 11, and the height is 9.

V = lwh

V = (20)(11)(9)

V = (220)(9)

V = 1980 cm³

Add the areas of the two shapes.

1077.57 cm³ + 1980 cm³ = 3057.57 cm³

Round to the nearest tenth.

3057.57 cm³ ≈ 3057.6 cm³

Answer:

[tex]\large \boxed{\sf \ \ x = -\dfrac{\sqrt{33}+1}{4} \ \ or \ \ x = \dfrac{\sqrt{33}-1}{4} \ \ }[/tex]

Step-by-step explanation:

Hello, please find below my work.

[tex]2x^2+x-4=0\\\\\text{*** divide by 2 both sides ***}\\\\x^2+\dfrac{1}{2}x-2=0\\\\\text{*** complete the square ***}\\\\x^2+\dfrac{1}{2}x-2=(x+\dfrac{1}{4})^2-\dfrac{1^2}{4^2}-2=0\\\\\text{*** simplify ***}\\\\(x+\dfrac{1}{4})^2-\dfrac{1+16*2}{16}=(x+\dfrac{1}{4})^2-\dfrac{33}{16}=0[/tex]

[tex]\text{*** add } \dfrac{33}{16} \text{ to both sides ***}\\\\(x+\dfrac{1}{4})^2=\dfrac{33}{16}\\\\\text{**** take the root ***}\\\\x+\dfrac{1}{4}=\pm \dfrac{\sqrt{33}}{4}\\\\\text{*** subtract } \dfrac{1}{4} \text{ from both sides ***}\\\\x = -\dfrac{1}{4} -\dfrac{\sqrt{33}}{4} \ \ or \ \ x = -\dfrac{1}{4} +\dfrac{\sqrt{33}}{4}[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

a) Mean = 4.55

   Median = 4.7

   Mode = 1.9

b) S =  2.3952

   CV = 52.64 %

   Range = 6.3

c) Yes, since the average and median values are both over "acceptable" ranges.

Step-by-step explanation:

Explanation is provided in the attached document.

Answer:

Step-by-step explanation:

Can you please include a image?

Thanks!!!

Range is [tex]y\in[-3,+\infty)[/tex].

Hope this helps.

Answer:

(11π/9 )ft/s

Step by step Explanation

Let us denote the height as h ft

But we were told that The diameter of the base of the cone is approximately three times the altitude, then

Let us denote the diameter = 3h ft, and the radius is 3h/2

The volume of the cone is

V = (1/3)π r^2 h

Then if we substitute the values we have

= (1/3)π (9h^2/4)(h) = (3/4)π h^3

dV/dt = (9/4)π h^2 dh/dt

We were given as 22feet and rate of 8 cubic feet per minute

h = 22

dV/dt = 8

8= (9/4)π (22) dh/dt

= 11π/9ft/s

Therefore, the rate is the height of the pile changing when the pile is 22 feet is

11π/9ft/s

Answer:

Step-by-step explanation:

First , let us rewrite the given equation into y= mx+b format

.y= -x +7

Slope is -1

Slope of the line perpendicular to the given equation is -(-1) ie., 1

Let us find the y-intercept by plugging in the values of x,y and slope into the equation y= Mx +b

1 = -1 +b

2 = b

Equation of the line perpendicular to the given equation and passing through (-1,1) is

y=x +2

Answer:

38.68 cm

Step-by-step explanation:

Perimeter of an equilateral triangle : P = 3a

Area of an equilateral triangle : A = [tex]\frac{\sqrt{3} }{4}a^2[/tex]

a = side length

The area is given, solve for a.

[tex]72= \frac{\sqrt{3} }{4}a^2[/tex]

[tex]a = 12.894839[/tex]

The side length is 12.894839 centimeters.

Find the perimeter.

P = 3a

P = 3(12.894839)

P = 38.684517 ≈ 38.68

The perimeter is 38.68 centimeters.

Triangle DAC is congruent to triangle BCA by SAS congruence theorem.

Triangle congruence theorem or triangle congruence criteria help in proving if a triangle is congruent or not. The word congruent means exactly equal in shape and size no matter if we turn it, flip it or rotate it.

Given that, AD = BC and AD || BC.

AD = BC (Given)

AD || BC (Given)

AC = AC (Reflexive property)

∠DAC=∠BCA (Interior alternate angles)

By SAS congruence theorem, ΔDAC≅ΔBCA

By CPCT, AB=CD

Therefore, triangle DAC is congruent to triangle BCA by SAS congruence theorem.

To learn more about the congruent theorem visit:

https://brainly.com/question/24033497.

#SPJ5

Answer:

(a) $7/ticket

(b) 3 cats/dog

(c) 10 ft/sec

(d) 16 cups/gal

Step-by-step explanation:

(a) $35 for 5 tickets

$35/(5 tickets) = $7/ticket

(b) 21 cats and 7 dogs

21 cats/(7 dogs) = 3 cats/dog

(c) 40 ft in 4 seconds

40 ft/(4 sec) = 10 ft/sec

(d) 48 cups for 3 gallons

48 cups/(3 gal) = 16 cups/gal

Answer:  Focus = (-2, 3)

Step-by-step explanation:

[tex]y=-\dfrac{1}{4}x^2-x+3\\\\\rightarrow a=-\dfrac{1}{4},\ b=-1[/tex]

First let's find the vertex. We do that by finding the Axis-Of-Symmetry:

[tex]AOS: x=\dfrac{-b}{2a}\quad =\dfrac{-(-1)}{2(\frac{-1}{4})}=\dfrac{1}{-\frac{1}{2}}=-2[/tex]

Then finding the maximum by inputting x = -2 into the given equation:

[tex]y=-\dfrac{1}{4}(-2)^2-(-2)+3\\\\y=-1+2+3\\\\y=4[/tex]

The vertex is: (-2, 4)

Now let's find p, which is the distance from the vertex to the focus:

[tex]a=\dfrac{1}{4p}\\\\\\-\dfrac{1}{4}=\dfrac{1}{4p}\\\\\\p=-1[/tex]

The vertex is (-2, 4) and p = -1

The focus is (-2, 4 + p) = (-2, 4 - 1) = (-2, 3)

Answer:

50*0.4*45=900cm²

Answer:

[tex]\boxed{Option \ 4}[/tex]

Step-by-step explanation:

∠YVZ = 180 - 52 - 43 - 38   (Angles on a straight line add up to 180 degrees so if we try to find an unknown angle on the straight line, we need too subtract all the other angles from 180 degrees)

=> ∠YUZ = 47 degrees

Step-by-step explanation: In the figure shown, <UVW is a straight angle.

This means it measures 180 degrees.

So to find <YVZ, we add up all the angles and subtract the sum

from 180 to get the answer to this problem.

43 + 52 + 38 gives us a sum of 133.

Now we take 180 - 133 yo get 47.

So m<YVZ is 47 degrees.

Answer:

36.1683

Step-by-step explanation:

45*80.374/100=

Answer:

D (The last choice)

Step-by-step explanation:

We know that rays are lines with a dot on one side and an arrow on the other. WE also know that lines have two arrows on each end. Keeping this in mind, we can identify which line segments and rays and lines.

Answer:

( 2A - kn) /k = m

Step-by-step explanation:

A = k/2(m+n)

Multiply each side by 2/k

2/k *A =2/k * k/2(m+n)

2A /k = m+n

Subtract n from each side

2A /k - n = m+n -n

2A /k - n = m

Getting a common denominator

2A/k - kn/k = m

( 2A - kn) /k = m

Answer:

Step-by-step explanation:

[tex]A=\frac{k(m+n)}{2}\\2A=k(m+n)\\\frac{2A}{k} =m+n\\\frac{2A}{k}-n=m\\2A-kn=km\\\frac{(2A-kn)}{k}=m[/tex]

Answer:

792

Step-by-step explanation:

The first three composite numbers are 4,  6 ,8

so 4^3+6^3+8^3=64+216+512=792

Answer:

8.5cm

Step-by-step explanation:

convert 3.4metres to cm that is by multiplying by 100

3.4×100=340cm

1rep 40

?rep 340

that is 340/40

=8.5cm

Answer:

8.5 cm

Step-by-step explanation:

Scale = 1:40

Length of the room = 3.4 meters

3.4 meters =3.4 X 100 =340 cm

Since 1 unit on the diagram represents 40 units

The length of the diagram

[tex]=\dfrac{340}{40}\\\\=8.5$ cm[/tex]

The length of the room on the diagram is 8.5 cm.

Answer:

C. μ = 3.60

Step-by-step explanation:

Two tables have been attached to this response.

One of the tables contains the given data and distribution with two columns: Houses Sold and Probability

The other table contains the analysis of the data with additional columns: Frequency and Fx

=> The Frequency(F) column is derived from the product of the probability of each item in the Houses sold column and the total number of houses sold (which is 28). For example,

When the number of houses sold = 0

F = P(0) x Total number of houses sold

F = 0.24 x 28 = 6.72

When the number of houses sold = 1

F = P(1) x Total number of houses sold

F = 0.01 x 28 = 0.28

=> The Fx column is found by multiplying the Frequency column by the Houses Sold column. For example,

When the number of houses sold = 0

Fx = F * x

F = 6.72 x 0 = 0

Now to get the mean, μ we use the relation;

μ = ∑Fx / ∑F

Where;

∑Fx = summation of the items in the Fx column = 100.8

∑F = summation of the items in the Frequency column = 28

μ = 100.8 / 28

μ = 3.60

Therefore, the mean of the given probability distribution is 3.60

The mean of the discrete probability distribution is given by:

C. μ = 3.60

The expected value of a discrete distribution is given by the sum of each outcome multiplied by it's respective probability.

In this problem, the table x - P(x) gives each outcome and their respective probabilities, hence, the mean is:

[tex]E(X) = 0(0.24) + 1(0.01) + 2(0.12) + 3(0.16) + 4(0.01) + 5(0.14) + 6(0.11) + 7(0.21) = 3.6[/tex]

Hence option C is correct.

More can be learned about the mean of discrete distributions at https://brainly.com/question/24855677

Answer:

the linear system has two valid solution.

Answer:one solution

Step-by-step explanation:

Answer:

The value of the polynomial function at P(1) and P(-2) is 24 and 0 respectively.

Step-by-step explanation:

We are given with the following polynomial function below;

[tex]\text{P}(x) = 2x^{5} +9x^{4} +9x^{3} +3x^{2}+7x-6[/tex]

Now, we have to calculate the value of P(x) at x = 1 and x = -2.

For this, we will substitute the value of x in the given polynomial and find it's value.

At x = 1;

[tex]\text{P}(1) = 2(1)^{5} +9(1)^{4} +9(1)^{3} +3(1)^{2}+7(1)-6[/tex]

[tex]\text{P}(1) = (2\times 1) +(9\times 1)+(9 \times 1)+(3\times 1)+(7\times 1)-6[/tex]

[tex]\text{P}(1) = 2 +9+9+3+7-6[/tex]

P(1) = 30 - 6

P(1) = 24

At x = -2;

[tex]\text{P}(-2) = 2(-2)^{5} +9(-2)^{4} +9(-2)^{3} +3(-2)^{2}+7(-2)-6[/tex]

[tex]\text{P}(-2) = (2\times -32) +(9\times 16)+(9 \times -8)+(3\times 4)+(7\times -2)-6[/tex]

[tex]\text{P}(-2) = -64 +144-72+12-14-6[/tex]

P(-2) = 156 - 156

P(-2) = 0

Hence, the value of the polynomial function at P(1) and P(-2) is 24 and 0 respectively.