Solve for x. Remember to check for extraneous solutions. √(x-3) = √(x+2) + 1. Choices: a. 6 b. No solution c. 7 d. 9

Answer:

20/29

Step-by-step explanation:

SOH CAH TOA

so its opposite/hyp...

20/29

is the answer

Answer:

6.25 kg cement, 7.5 L water

Step-by-step explanation:

2.5 kg cement / 4 kg sand = x kg cement / 10 kg sand

x = 6.25

3 L water / 4 kg sand = y L water / 10 kg sand

y = 7.5

Answer:

[tex]Probability = 51\%[/tex]

Step-by-step explanation:

Given

Radius of inner circle = 5ft

Radius of outer circle = 7ft

Required

Determine the probability that the thumbtack will be placed on the inner circle

We start by calculating the area of both circles;

Inner Circle

[tex]Area = \pi r^2[/tex]

[tex]Area = 3.14 * 5^2[/tex]

[tex]Area = 3.14 * 25[/tex]

[tex]Area = 78.5[/tex]

Outer Circle

[tex]Area = \pi R^2[/tex]

[tex]Area = 3.14 * 7^2[/tex]

[tex]Area = 3.14 * 49[/tex]

[tex]Area = 153.86[/tex]

At this point, the probability can be calculated;

The probability = Area of Inner Circle / Area of Outer Circle

[tex]Probability = \frac{78.5}{153.86}[/tex]

[tex]Probability = 0.51020408163[/tex]

Convert to percentage

[tex]Probability = 0.51020408163 * 100\%[/tex]

[tex]Probability = 51.020408163\%[/tex]

Approximate

[tex]Probability = 51\%[/tex]

Answer:

x = 3.25

Step-by-step explanation:

Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.

PEMDAS =

Parenthesis

Exponents (& Roots)

Multiplication

Division

Addition

Subtraction

...and is the order of operation.

First, subtract 3 from both sides of the equation:

4x + 3 = 16

4x + 3 (-3) = 16 (-3)

4x = 16 -3

4x = 13

Next, dvide 4 from both sides:

(4x)/4 = (13)/4

x = 13/4

x = 3.25

x = 3.25 is your answer.

~

Answer:

x = 3.25

Step-by-step explanation:

4x + 3 = 16

4x + 3 - 3 = 16 - 3

4x = 13

4x/4 = 13/4

x = 3.25

Answer:

Step-by-step explanation:

The average number of runs scored by a Little League team in a game is 5.7. If he chooses five games at random in which his team scored 5 , 9, 4, 11, and 8 runs, their average score of the five games is expressed as shown;

Average score of 5 games = (5+9+4+11+8)/5

Average score of 5 games  = 37/5

Average score of 5 games  = 7.4

Comparing the average score in 5 games to the the average number of runs scored nationally, it can be seen that their difference is 7.4 - 5.7 which is 1.7. Since the difference is quite significant, then it is most likely that his team's scores is different from the national distribution.  

Answer:

803.84yd²

Step-by-step explanation:

Surface Area of A Sphere: [tex]A=4\pi r^2[/tex]

We are given the radius of 8 yards.

Using 3.14 for pi:

[tex]A=4*3.14*8^2\\\\A=4*3.14*64\\\\A=12.56*64\\\\\boxed{A=803.84}[/tex]

The correct answer should be 803.84yd².

Brainilest Appreciated.

Answer:

803.84 yd^2

Step-by-step explanation:

4*3.14*8^2

12.56*64

803.84

brainliest pls

hope i helped

           -ZYLYNN

Answer:

Step-by-step explanation:

Volume of cartoon = 5 cm × 8 cm × 15 cm

= 600 cm³

Volume of milk = 5 cm × 8 cm × 12 cm

= 480 cm³

Space = 600 cm³ - 480 cm³ = 120 cm³

Let depth be ' h '

15 × 5 × h = 480

Multiply the numbers

75h = 480

Divide both sides of the equation by 75

75 h / 75 = 480 / 75

Calculate

h = 6.4 cm

therefore, The depth of the milk is 6.4 cm

Hope this helps...

Best regards!!

Answer:1.0111111111

Step-by-step explanation:

18.2 - 18 = .2-18 =1.0111111

Answer:

[tex]\boxed{x = 30}[/tex]

Step-by-step explanation:

x + 2x + 3x = 180 (Interior angles of a triangle add up to 180 degrees)

=> 6x = 180

Dividing both sides by 6

=> x = 180 / 6

=> x = 30

Answer:

x= 30

Step-by-step explanation:

3x + 2x + x = 180

6x= 180

x = 180/6

:• x = 30

Answer:

11.25

Step-by-step explanation:

12*12/12-3/4

PEMDAS says multiply and divide first

from left to right

144/12 - 3/4

12 -3/4

12 - .75

Then add and subtract

11.25

Answer:

[tex]\frac{45}{4}[/tex]

Step-by-step explanation:

Apply PEDMAS

P - parenthesis

E - exponents

D - division

M - multiplication

A - addition and S - subtraction  

Division is first.

12 × [tex]\frac{12}{12}[/tex] - [tex]\frac{3}{4}[/tex]

12 × 1 - [tex]\frac{3}{4}[/tex]

Followed by multiplication.

12 - [tex]\frac{3}{4}[/tex]

Subtract the numbers next.

[tex]\frac{12}{1} -\frac{3}{4}[/tex]

Make the denominators same by LCM.

[tex]\frac{48}{4} -\frac{3}{4}[/tex]

[tex]\frac{45}{4}[/tex]

Answer:

9

Step-by-step explanation:

The diagram showing the three pieces of paper of three digit in which two of the letters were covered can be seen below.

From the diagram; we have;

243 , 1_7 , _26

Assuming the covered digits are _

The sum is 826.

i.e

243 + 1_7 + _26 = 826

The objective is to determine the sum of the two unknown digits

So; we need to think about what number can we add put in 1_7 to determine the covered digit in  _26

From ; 1_7 , we have the choice to pick from 0 - 9

Assuming the covered digit is 0; let's check if we are right

So; 243 + 107  +  _26 = 826

350 +   _26 = 826

_26 = 826 - 350

_26 = 476

So; the covered digit is in the position of 4 , but it doesn't tally together

i.e 426 is not the same as 476, which makes our assumption to be wrong.

Let consider the covered digit to be 5 for example.

So; 243 + 157  +  _26 = 826

400 +   _26 = 826

_26 = 826 - 400

_26 =  426

The covered digit is in the position of 4

SO;

426 = 426

Here , our assumption is right.

As such , the covered digits are 5 and 4

The sum of the two  covered digits are = 5 + 4 = 9

Answer:

She did not represent the two original factors correctly on the headers.

Step-by-step explanation:

Adi Algebra titles method is based on the field of values. In the given question the representation of of the product is not correct. The two negative titles must be in the top header so the correct sign in incorporated with the variables.

Answer:

A. She used the algebra tiles correctly.

Step-by-step explanation:

She represents each step of the equation with algebra tiles correctly, even if it could be simplified more.

Answer:

  A.  4.40 square units

Step-by-step explanation:

The triangle is isosceles with base angles of 70°. The a.pex angle will be ...

  180° -2(70°) = 40°

The area of a triangle can be computed from two sides and the angle between them as ...

  A = (1/2)ab·sin(γ)

  A = (1/2)(3.7)(3.7)sin(40°) ≈ 4.40 . . .  square units

Answer:

E: all real numbers

Step-by-step explanation:

Answer:

A) SAS postulate

Step-by-step explanation:

Answer:

SAS

Step-by-step explanation:

you know that ST is equal and you also know two equal angles and one other equal side

Answer:

Step-by-step explanation:

[tex]6\: km\: in \:10\: minutes\\First\:lets\:convert\:10\:min\:to\:seconds\\\\1\:minute \:\:\:\:=60\:seconds\\\\10\:minutes = x \:seconds\\\\x = 60\times 10\\x = 600seconds\\\\6km\: = 600\:seconds\\x\:km = 1 \:second\\\\Cross\:Multiply\\600x =6\\\frac{600x}{600} =\frac{6}{600} \\\\x = 1/100\\\\ =0.01km[/tex]

Answer:

the number is -6  (assuming "3 lots of" means 3 times)

Step-by-step explanation:

Let the number be x

1 less than a doubled number

2x-1

5 more than 3 lots of (times???) the number

3x+5

Solve for x

2x-1 = 3x + 5

-x = 5+1

x = -6

Answer:

The rate at which the biomass is increasing when t = 5 is 180.36 g/week

Step-by-step explanation:

Given that :

t = 5 weeks

Population N(t) = 824 guppies

Growth Rate [tex]\dfrac{dN(t)}{dt}= 50 \ guppies /week[/tex]

average mass M(t) = 1.3 g

increase rate of biomass  [tex]\dfrac{dM (t)}{t}[/tex]= 0.14 g/week

Therefore; the rate at which the biomass is increasing when t = 5 is:

[tex]\dfrac{dB(t)}{dt}= M(t) * \dfrac{dN(t)}{dt}+ N(t)* \dfrac{dM (t)}{t}[/tex]

[tex]\dfrac{dB(t)}{dt}=1.3 * 50+ 824* 0.14[/tex]

[tex]\dfrac{dB(t)}{dt}=65+115.36[/tex]

[tex]\mathbf{\dfrac{dB(t)}{dt}=180.36 \ g/week}[/tex]

The rate at which the biomass is increasing when t = 5 is 180.36 g/week

The rate at which the biomass is increasing when t = 5 is 180.36 g/week

Since time = 5 weeks, Population N(t) = 824 guppies, and growth rate = 50 guppies / week, average mass = 1.3g, and the increase rate of biomass is 0.14g/week

So,

[tex]= 1.3\times 50 + 824 \times 0.14[/tex]

= 65 + 115.36

= 180.35 g/weel

Learn more about mass here: https://brainly.com/question/3943429

Answer:

0.8

Step-by-step explanation:

because the template should be axr^n-1

where r is the common ratio

r=0.8

Answer:

0.8

Step-by-step explanation:

Corrected Question:

Complete the proof of the Law of Sines/Cosines.  

Given triangle ABC with altitude segment AD labeled x. Angles ADB and CDA are _____1._____ by the definition of altitudes, making triangle ABD and triangle ACD right triangles. Using the trigonometric ratios sine of B equals x over c and sine of C equals x over b. Multiplying to isolate x in both equations gives x = _____2._____ and x = b ⋅ sinC. We also know that x = x by the reflexive property. By the substitution property, _____3._____. Dividing each side of the equation by bc gives: sine of B over b equals sine of C over c.

Answer:

(1) right angles

(2) c sin B

(3) c sin B = b sin C

Step-by-step explanation:

As shown in the diagram attached to this response,

(i) the given triangle is ABC with altitude segment AD labeled as x,

(ii) side AB is labeled as c, side AC is labeled as b, and

(iii) angles ADB and CDA are right angles by definition of altitudes.

(iv) Therefore, triangle ABD and CDA are right-angled triangles.

(v) Now, using trigonometric ratios, sine of B equals x over c. i.e

sin B = [tex]\frac{x}{c}[/tex]          --------(i)

(vi) Also, sine of C equals x over b. i.e

sin C = [tex]\frac{x}{b}[/tex]         ------------(ii)

(vii) Multiplying to isolate x in both equations gives;

x = c sin B           [from equation (i)]           ------------(iii)

x = b sin C          [from equation (ii)]             -----------(iv)

(viii) We know that x = x by the reflective property. i.e x in equation (iii) is equal to x in equation (iv). By substitution property, this becomes,

c sin B = b sin C           -----------------(v)

(ix) Dividing each side of the equation in equation (v) by bc gives: sine of B over b equals sine of C over c i.e

[tex]\frac{csinB}{bc} = \frac{bsinC}{bc}[/tex]

[tex]\frac{sinB}{b} = \frac{sinC}{c}[/tex]             [This is the sine rule]

Answer:

86.7

Step-by-step explanation:

Answer:

86.7%

Step-by-step explanation:

Correct on Edge2020

Answer:

[tex]f(-1) = 8[/tex]

[tex]f^{-1}(x) = \frac{5}{3} - \frac{x}{3}[/tex]

Step-by-step explanation:

Given

[tex]f(x) = 5 - 3x[/tex]

Required

[tex]f(-1)[/tex] and [tex]f^{-1}(x)[/tex]

Solving for f(-1)

Substitute -1 for x in [tex]f(x) = 5 - 3x[/tex]

[tex]f(-1) = 5 - 3(-1)[/tex]

[tex]f(-1) = 5 + 3[/tex]

[tex]f(-1) = 8[/tex]

Solving for [tex]f^{-1}(x)[/tex]

Let y = f(x)

[tex]y = 5 - 3x[/tex]

Interchange the position of x and y

[tex]x = 5 - 3y[/tex]

Make y the subject of formula (add 3y to both sides)

[tex]3y + x = 5 - 3y + 3y[/tex]

[tex]3y + x = 5[/tex]

Subtract x from both sides

[tex]3y + x - x = 5 - x[/tex]

[tex]3y = 5 - x[/tex]

Divide through by 3

[tex]\frac{3y}{3} = \frac{5}{3} - \frac{x}{3}[/tex]

[tex]y = \frac{5}{3} - \frac{x}{3}[/tex]

Replace y with [tex]f^{-1}(x)[/tex]

[tex]f^{-1}(x) = \frac{5}{3} - \frac{x}{3}[/tex]

Answer:

Line y = −x + 4 intersects the line y = 3x + 3.

Step-by-step explanation:

Please Help! Which description best describes the solution to the following system of equations?

y = −x + 4

y = 3x + 3

Line y = −x + 4 intersects the line y = 3x + 3.

This is the response because the solution to a system of two equations is represented by the intersection of the equations of the two lines/curves.

Lines y = −x + 4 and y = 3x + 3 intersect the x-axis.

Lines y = −x + 4 and y = 3x + 3 intersect the y-axis.

Line y = −x + 4 intersects the origin.

Answer: The answer is D.

Step-by-step explanation: Ok, we start by simplifing the equation to 3√x^2 - 3√x=2. Now, by plugging the possible options in, we can find the answer. You find that -1 is a possible answer for x, so that eliminates E. Since there is no cube root for 2, we elimate A and B. By plugging in C and D, you find that C=6, not C=2. So D must be the answer.

Answer:

a) CD = 41 m

b) 77.32°

c) 1380 square metres

Step-by-step explanation:

We can divide the trapezium as shown in the diagram below.

a) To find CD, we use Pythagoras Rule:

[tex]CD^2 = 9^2 + 40^2[/tex]

[tex]CD^2 = 81 + 1600\\\\CD^2 = 1681\\\\=> CD = 41 m[/tex]

b) To find <BCD, we use trigonometric function SOHCAHTOA:

sin(BCD) = opp / hyp

sin(BCD) = 40 / 41

sin(BCD) = 0.9756

=> <BCD = 77.32°

c) The area of a trapezium is given as:

A = 1/2 (a + b) * h

where h = height = 40 m

a = top length = 30 m

b = bottom length = 39 m

A = 1/2 * (30 + 39) * 40

A = 1/2 * 69 * 40

A = 1380 square metres

Hey there! I'm happy to help!

To find the volume of a cylinder, you multiply the base by the height and then divide by three. The volume of a cone is the same as the volume of a cylinder with the same dimensions divided by three.

So, since a cone's volume is 1/3 of that of a cylinder, we just divide 72 by 3!

72/3=24

Therefore, the volume of the cone is 24 feet cubed.

Have a wonderful day! :D

Answer: its 24.

Step-by-step explanation:

Answer:

N

Step-by-step explanation:

Since this hexagon has six sides, and to end up back at E again we’d need to rotate 360°, this means for every side we cross it’s a 60° turn.

Therefore, [tex]60 \cdot 2 = 120[/tex]° would be two sides.

Since we are moving counter-clockwise, the image for E would be to the left of it.

Two sides/points to the left of E is N, so the image of E for a 120° counterclockwise rotation around the center of this shape would be N.

Hope this helped!

Answer:

28.142m

Step-by-step explanation:

area of rectangle=width x lenght

so; (rotating the formula with what is given)

area of rectangle/width=lenght

197/7=lenght

28.142m =lenght

Answer:

Length is 18 m and width is 11 m

Step-by-step explanation:

So based on the information given length is seven cm more than your width, and since we don’t know the values of these, we can plot this information into a formula that looks like this: (x+7)(x)=198, which is basically how you take the area of the plot of land.

If you multiply your values, you will get a quadratic equation that looks like this x²+7x-198. If you follow the quadratic formula to solve this equation, the positive result you will get for x is 11, this is your width. And since length exceeds by 7, you just add 7 to 11 to find the length, which ends up being 18.

to verify, you can simply multiply these two values