true or false : the equation below is too complicated to use the isolate the radical then square both sides

True Or False : The Equation Below Is Too Complicated To Use The Isolate The Radical Then Square Both

Answers

Answer 1

The equation is [tex]\frac{\sqrt{x+3} }{\sqrt{x+1} }=3[/tex] is not true.

Given that,

The radical must first be isolated before both sides of the following equation may be squared.

The equation is [tex]\frac{\sqrt{x+3} }{\sqrt{x+1} }=3[/tex]

We have to say the equation is true or false.

The result of multiplying an integer by itself is known as the square root of the number. The radical sign represents the square root. As an illustration, √16 = 4. The radical symbol is also known as the root symbol or surds.

Take Left hand side.

[tex]\frac{\sqrt{x+3} }{\sqrt{x+1} }[/tex]

Root is

[tex]\sqrt{\frac{x+3}{x+1}}[/tex]

The right hand side is 3

The left hand side ≠ right hand side.

Therefore, The equation is [tex]\frac{\sqrt{x+3} }{\sqrt{x+1} }=3[/tex] is not true.

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Related Questions

The probability that it is Tuesday and Robert is absent is 0.04.There are 5 school working days in a week and the probabilitythat it is Tuesday is 0.5. What is the probability that Robert isabsent given that today is Tuesday?

Answers

The probability is 8%.

From the question, we have

The probability that it is Tuesday and Robert is absent is 0.04.

P(Tuesday and  absent) = 0.04

P(Tuesday) =0.5

P(absent/Tuesday) =0.04/0.5 = 0.08

=0.08*100%

=8%

Multiplication:

Finding the product of two or more numbers in mathematics is done by multiplying the numbers. It is one of the fundamental operations in mathematics that we perform on a daily basis. Multiplication tables are the main use that is obvious. In mathematics, the repeated addition of one number in relation to another is represented by the multiplication of two numbers. These figures can be fractions, integers, whole numbers, natural numbers, etc. When m is multiplied by n, either m is added to itself 'n' times or the other way around.

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Please help answer questions one through fiveApply the transformation (a to c) on ABC to get an image

Answers

Answer:

d) area of the pre- image will be less than the new image

e) it is

Explanation:

Given:

Triangle ABC on a coordinate plane

To find:

the transformation on the original image

We need to state the vertices of the triangle ABC:

A = (-1, 2)

B = (-2, 1)

C = (0, 0)

a) dilation by a scale factor of 4

[tex]\begin{gathered} (x,\text{ y\rparen }\rightarrow\text{ \lparen4x, 4y\rparen} \\ A=\text{ \lparen4\lparen-1\rparen, 4\lparen2\rparen\rparen = \lparen-4, 8\rparen} \\ B\text{ = \lparen4\lparen-2\rparen, 4\lparen1\rparen\rparen = \lparen-8, 4\rparen} \\ C=\text{ \lparen4\lparen0\rparen, 4\lparen0\rparen\rparen = \lparen0, 0\rparen} \end{gathered}[/tex]

b) reflect over the x axis:

[tex]\begin{gathered} (x,\text{ y\rparen }\rightarrow\text{ \lparen x, -y\rparen} \\ We\text{ will negate all the y values of the vertices above while keeping x coordinate constant} \\ A\text{ = \lparen-4, -8\rparen} \\ B\text{ = \lparen-8, -4\rparen} \\ C=\text{ \lparen0, -0\rparen = \lparen0, 0\rparen} \end{gathered}[/tex]

c) dilate by 1/2

[tex]\begin{gathered} (x,\text{ y\rparen }\rightarrow(\frac{1}{2}x,\text{ }\frac{1}{2}y) \\ We\text{ will multiply the coordinates above by 1/2 in both the x and y coordinates} \\ A^{\prime}\text{ = \lparen}\frac{1}{2}(-4),\text{ }\frac{1}{2}(-8))\text{ = \lparen-2, -4\rparen} \\ B^{\prime}\text{ = \lparen}\frac{1}{2}(-8),\text{ }\frac{1}{2}(-4))\text{ = \lparen-4, -2\rparen} \\ C^{\prime}\text{ = \lparen}\frac{1}{2}(0),\text{ }\frac{1}{2}(0))\text{ = \lparen0, 0\rparen} \\ \\ Image\text{ of ABC: A' \lparen-2, -4\rparen, B' \lparen-4, -2\rparen and C' = \lparen0, 0\rparen} \end{gathered}[/tex]

d) To determine if the area of the pre-image is greater or less than, we will plot the coordinates of both triangles:

Since the triangle of the Image is greater than the triangle of the pre-image (original figure), then the area of the pre- image will be less than the new image

e) For two triangles to be congruent, the sides and angles for both triangles will be equal

For two triangles to be similar, the ratio of their corresponding sides will be equal

The image A'B'C' is a scaled triangle of ABC. This mean the sides can't be equal but the ratio fo their corresponding sides will be equal.

Hence, it is simlar

What is the value of the algebraic expression if x = 1/2, y = -1, and z = 2?Here is the algebraic expression: 6x(y to second power z)

Answers

The value of the algebraic expression if x = 1/2, y = -1, and z = 2 is 6.

The given expression is [tex]6xy^{2}z[/tex] and we need to evaluate its value when  x = 1/2, y = -1, and z = 2

Simply assign the values of each variable to the variables in the algebraic expression and evaluate the result to get the value of the expression. What we do is:

[tex]6xy^{2}z\\\\=6 * \frac{1}{2}*(-1)^{2} *2 \\\\=6 * \frac{1}{2}*1 *2\\\\=6[/tex]

The algebraic expression's value would be 6, then. In an algebraic expression, the variables are denoted by letters, in this case x, y, and z; the coefficients are denoted by numbers, such as 6, and the exponents are, in this case, 2, as in the expression above. Expressions frequently include several terms made up of those components.

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Hello! Use interval notation to indicate all real numbers between −3 and 5 , including −3 but not including 5.

Answers

Given:

The real numbers given as -3 and 5

Required:

We need to indicate all real numbers between −3 and 5 , including −3 but not including 5

Explanation:

Use [ to include the number and use ) to not include the number

So here we want to include -3 so use [ with -3 and we do not want to incluse 5 so use ) with 5

There is a rule that we need to start with small number and here the small number is -3 among -3 and 5

FInal answer:

[-3,5)

Using the image below. Write the equation of the line fully simplified slope-intercept form. NO SPACES BETWEEN TERMS * just letting you know the answer is not y=-5x+2 or y=6x+2

Answers

The slope-intercept form is

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

m is the slope

b is the y-intercept

The rule of the slope of a line that passes through points (x1, y1) and (x2, y2) is

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

From the given graph, the line passes through points (1, -4) and (0, 2)

Let (x1, y1) = (1, -4) and (x2, y2) = (0, 2)

[tex]\begin{gathered} m=\frac{2-(-4)}{0-1} \\ m=\frac{2+4}{-1} \\ m=\frac{6}{-1} \\ m=-6 \end{gathered}[/tex]

Substitute the value of m in the form of the equation

[tex]y=-6x+b[/tex]

Since the line intersects the y-axis at point (0, 2)

Then the y-intercept is 2

Then b = 2

The equation of the line is

[tex]y=-6x+2[/tex]

convert 15.7cm of the circumference to inches

Answers

Answer: We have to convert 15.7cm into inches, the steps for the conversion are as follows:

[tex]\begin{gathered} 1in=2.54cm\rightarrow\frac{1\imaginaryI n}{2.54cm}=1 \\ \\ \frac{15.7cm}{1}\times\frac{1in}{2.54cm}=\frac{15.7}{2.54}in \\ \\ =6.18in \end{gathered}[/tex]

Therefore the answer is 6.18in.

2) The next day they go to Melties. Al buys a cone with 3.6 oz of frozen yogurt for $4.47, and Beth buys a cone with 4.8 oz of frozen yogurt for $5.01. Find how much Melties charges per ounce of frozen yogurt and how much they charge for the cone.

Answers

2) The next day they go to Melties. Al buys a cone with 3.6 oz of frozen yogurt for $4.47, and Beth buys a cone with 4.8 oz of frozen yogurt for $5.01. Find how much Melties charges per ounce of frozen yogurt and how much they charge for the cone.​

Let

x ------> the number of ounces of frozen yogurt

y ------> the total charge

we have the ordered pairs

(3.6,4.47) and (4.8,5.01)

step 1

Find the slope pr unit rate

m=(5.01-4.47)/(4.8-3.6)

m=$0.45 per ounce

step 2

Find the equation in point slope form

y-y1=m(x-x1)

we have

m=0.45

(x1,y1)=(3.6,4.47)

substitute

y-4.47=0.45(x-3.6)

convert to slope intercept form

y-4.47=0.45x-1.62

y=0.45x+2.85

In this problem, the y-intercept or initial value correspond to the charge for the cone

so

$2.85

When oil was spilled out in the middle of a lake, it spread out on the surface of the water in a circular pattern. The radius of the circular pattern increased at a rate of 4 feet per minute.((() = 4tft/min)Find the radius and area of the circular pattern of oil 5 minutes after the oil starts to spread.

Answers

The radius of the circle increases by 4 feet per minute. When 1 minute has passed, the radius is 4 feet, and when 5 minutes have passed, the radius will be 5 times that:

[tex]4\times5=20[/tex]

The radius of the circle after 5 minutes is 20 feet.

To find the area, we use the formula for the area of a circle:

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

Using the radius of 20 feet:

[tex]r=20ft[/tex]

And substituting it into the formula for the area:

[tex]\begin{gathered} A=\pi(20ft)^2 \\ A=\pi(400ft^2) \end{gathered}[/tex]

Using:

[tex]\pi=3.1416[/tex]

We get the are of the circular pattern:

[tex]\begin{gathered} A=(3.1416)(400ft^2) \\ A=1,256.64ft^2 \end{gathered}[/tex]

Answer:

[tex]\begin{gathered} r=20ft \\ A=1,256.64ft^2 \end{gathered}[/tex]

a card is drawn at random from a standard deck. Determine whether the events are mutually exclusive or not mutually exclusive. Then find each probability. P(jack or 4)

Answers

Mutually exclusive events:

Two events are mutually exclusive if they cannot occur at the same time.

There are 52 cards in a deck of cards.

n(s)=52.

Let A be event of getting jack.

n(A)=4.

So, Probability of getting jack is,

Let B be event of getting 4

n(B)=4.

So, Probability of getting 4 is,

[tex]\begin{gathered} P(B)=\frac{n(B)}{n(s)} \\ =\frac{4}{52} \end{gathered}[/tex]

These two events do not occur at same time.

Therefore the events are mutually exclusive.

[tex]P(A\cap B)=0[/tex]

To find the probability of getting jack or 4

[tex]P(\text{A }\cup\text{B)}=P(A)+P(B)-P(A\cap B)[/tex]

hence,

[tex]\begin{gathered} P(\text{A }\cup\text{B)}=\frac{4}{52}+\frac{4}{52}-0 \\ =\frac{8}{52} \\ =\frac{2}{13} \end{gathered}[/tex]

The probability of getting jack or 4 is,

[tex]\frac{2}{13}[/tex]

Ryan is 6 feet tall. At a certain time of day, he casts a shadow that is 12 feet long. At the same time, a tree casts ashadow that is 28 feet long. What is the height of the tree?

Answers

First, notice that Ryan and its shadow form a right triangle with the following measures:

and with the tree, we have the following triangle:

since both triangles are similar, we can write the following proportions:

[tex]\frac{x}{6}=\frac{28}{12}[/tex]

where 'x' represent the height of the tree. Solving for 'x', we get:

[tex]\begin{gathered} \frac{x}{6}=\frac{28}{12} \\ \Rightarrow x=\frac{28}{12}\cdot6=\frac{28\cdot6}{12}=\frac{168}{12}=14 \\ x=14ft \end{gathered}[/tex]

therefore, the height of the tree is 14 feet

Hi I really do need help with this question. You don’t have to show work but it says we have to explain our answer.

Answers

The Solution:

Pattern A: start with 1 and add 3.

[tex]1,\text{ 4, 7, 10, 13}[/tex]

Pattern B: Start with 1 and add 4.

[tex]1,\text{ 5, 9, 13, 17}[/tex]

Comparing the two patterns, we have that:

Recall:

Median means the middle number.

The median of pattern A is 7 while that of pattern B is 9.

Thus, the median of pattern B is more than the median of pattern A by 2.

Writing an equation of an… Given the foci and major axis length

Answers

We need to find the equation of the ellipse given the foci and major axis.

The equation is given by:

[tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1[/tex]

We have the foci points at (2,4) and (2,-6). The distance is 10 units, then the center is equal to half value c=5.

If the length of the major axis is 12.

Major axis length = 2a

Then

12 = 2a

a=12/2

a=6

To find b, we have the next equation:

[tex]\begin{gathered} b^2=a^2-c^2 \\ Replacing \\ b^2=6^2-5^2 \\ b^2=36-25 \\ b^2=11 \\ Solve\text{ for b} \\ b=\sqrt[]{11} \end{gathered}[/tex]

Now, the center c is given by the point (2,-1). This point is in the middle of both foci points

Finally, we can replace on the ellipse equation:

[tex]\begin{gathered} \frac{(x-h)^{2}}{a^{2}}+\frac{(y-k)^{2}}{b^{2}}=1 \\ Replacing,\text{ the result is} \\ \frac{(x-2)^2}{6^2}+\frac{(y-(-1))^2}{(\sqrt[]{11})^2}=1 \end{gathered}[/tex]

Jameson downloaded one digital song for $1.25, two digital songs for $2.50, and 5 digital songs for $6.25. solve the equation to find the cost to download 20 digital songs

Answers

The cost of downloading 20 digital songs = 20 x 1.25

You want to invest $1000 in an account and plan to leave it there for 12 years. There are three options for investing your money.Account A pays 14% interest per year, compounded annually.Account B pays 13.6% interest per year, compounded monthly.Account C pays 13% interest per year, compounded daily.

Answers

[tex]\begin{gathered} Investment\text{ = \$}1000 \\ Account\text{ A} \\ i=14\text{ \%=0.14} \\ t=12\text{ years} \\ C=1000(1+0.14)^{12} \\ C=4871.9 \\ \text{After 12 years, youll have \$4871,9} \\ \text{Account B} \\ i=13.6\text{\%=0.136},\text{ monthly},\text{ hence} \\ i=\frac{0.136}{12}\approx0.0113 \\ t=\text{ 12 years}\cdot\frac{12month}{year}=144\text{ months} \\ C=1000(1+0.0113)^{144} \\ C=5043.37 \\ \text{After 12 years, youll have \$5}043.37 \\ \text{Account C} \\ i=13\text{\%=0.13, da}ily,\text{ hence} \\ i=\frac{0.13}{365}\approx0.00036 \\ t=12\text{ years}\cdot\frac{365\text{ days}}{years}=4380 \\ C=1000(1+0.00036)^{4380} \\ C=4838.07 \\ \text{After 12 years, youll have \$4838.07} \end{gathered}[/tex]

If you randomly select a card from a well-shuffled standard deck of 52 cards, determine the probabilitythat the card you select is not a 6.a) Write your answer as a reduced fraction.b) Write your answer as a decimal, rounded to the nearest thousandth.c) Write your answer as a percent. Round to the nearest tenth of a percent as needed.

Answers

Answer:

The probability that a card selected at random is not a 6 is:

a. 12/13

b. 0.923

c. 92.3

Explanation:

There are 4 6's in a well-shuffled deck of cards.

The probability that a card selected at random is not a 6 is:

1 - (The probability that it is a 6)

= 1 - 4/52

= 12/13

b. As a decimal, we have 0.923

c. As a percentage, we have 92.3%

I’m getting 57.14 inches for perimeter and 114.29 for area, am I correct? Have struggled a little

Answers

Part 1

Find out the perimeter

The perimeter of the figure is given by

[tex]\begin{gathered} P=\pi(8)+8+8 \\ P=16+8\pi \\ P=41.13\text{ in} \end{gathered}[/tex]The perimeter is 41.13 inches

part 2

Find out the area

The area is given by

[tex]\begin{gathered} A=\pi(4^2)+8^2 \\ A=16\pi+64 \\ A=114.27\text{ in2} \end{gathered}[/tex]The area is 114.27 square inches

Determine the initial investment, PV, for a future value of 6500 dollars if the nominal rate of interest is 5.9 percent compounded quarterly for 12 years? FV = PV(1 + r/n) ^ntPv = ________ (Be sure to give 2 decimal places of accuracy.)

Answers

Answer: PV = 3218.69

Explanation:

The formula for calculating compound interest is expressed as

FV = PV(1 + r/n) ^nt

Where

FV is the future value

PV is the initial value

r is the interest rate

n is the number of compounding periods in a year

t is the number of years

From the information given,

FV = 6500

r = 5.9% = 5.9/100 = 0.059

n = 4 because it was compounded quarterly

t = 12

By substituting these values into the formula,

6500 = PV(1 + 0.059/4)^4 * 12

6500 = PV(1.01475)^48

PV = 6500/(1.01475)^48

PV = 3218.69

how can we determine key words to find what kind of sign to use

Answers

The problem says there are:

2 neighbors with birds

10 neighbors with cats

8 neighbors with dogs.

As each neighbor owns only one pet, the total number of neighbors is then:

2+10+8=20

The percentage of the neighbors that own dogs is the number of neighbors with dogs, divided by the total number of neighbors, then:

[tex]\frac{8}{20}\times100=\frac{4}{10}\times100\text{ \%=0.4x100\%=40\%}[/tex]

Then the 40% of the neighborhood pet owners have dogs.

What is the volume of the prism shown by the net?

Answers

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data

length = 1/2 yd

width = 1/4 yd

height = 1/6 yd

Volume = ?

Step 02:

Volume = l * w * h

[tex]V\text{ = }\frac{1}{2}yd\cdot\frac{1}{4}yd\cdot\frac{1}{6}yd=\frac{1}{48}yd^3[/tex]

The answer is:

The volume of the right rectangular prism is 1 / 48 yd³ .

Suppose that tan(x)csc(x)=1/f(x).Write f(x) in terms of sin(x) and cos(x).f(x)=

Answers

Trigonometry

We are given the equation:

[tex]\tan (x)\csc (x)=\frac{1}{f(x)}[/tex]

It's required to write f(x) in terms of the sine and cosine functions.

Taking the reciprocal of both sides of the equation:

[tex]f(x)=\frac{1}{\tan (x)\csc (x)}[/tex]

Recall:

[tex]\begin{gathered} \tan (x)=\frac{\sin (x)}{\cos (x)} \\ \text{csc(x)}=\frac{1}{\sin (x)} \end{gathered}[/tex]

Substituting:

[tex]f(x)=\frac{1}{\frac{\sin(x)}{\cos(x)}\frac{1}{\sin (x)}}[/tex]

Simplifying:

[tex]f(x)=\frac{1}{\frac{1}{\cos(x)}}=\cos (x)[/tex]

Thus:

f(x)= cos(x)

Round 58,300 to the nearest ten thousand 

Answers

ok

Rounding to the nearest 10000 the result is

60,000

Answer:

60,000

Step-by-step explanation:

The 5 is in the ten-thousands place.

Make all digits right of the 5 into a zero.

You get 50,000.

Since 8 (in the thousands place) is greater than 5, the ten-thousands place goes uo 1 to 6.

Answer: 60,000

Which is the better buy? 36-fluid-ounce carton of apple juice for $8.28 6-cup carton of apple juice for $5.76

Answers

In this case, what we must do is calculate the price per unit each one:

[tex]\begin{gathered} 1\text{cup}=8ounce \\ \frac{8.28}{36}=0.23 \\ \frac{5.76}{6\cdot8}=0.12 \end{gathered}[/tex]

therefore, the second purchase is better because it cost $0.12 per ounce, otheriwse the other purchase compares that they are $0.23 per ounce

12) Alyssa draws a rectangle that is 2/3 of ameter long and 3/5 of a meter wide. What isthe area of this rectangle?

Answers

A=LW

L=2/3

W=3/5

A= (2/3)(3/5)

A=2/5 or 0.4

pls help me with this one & the ones after it !!!

Answers

In the given triangle,

line IF is parallel to line HG,

By the basic proportionality theorem,

[tex]\begin{gathered} \frac{JI}{IH}=\frac{FJ}{FG} \\ \frac{25}{20}=\frac{FJ}{28} \\ \frac{25\cdot28}{20}=FJ \\ FJ=35 \end{gathered}[/tex]

Answer: FJ=35

Which should figure could be formed from the net shown?

Answers

Answer

The solid figure that could be formed from the net show is a square pyramid

Explanation

The figure shown has been opened from the vertex, v, when closed, a square base of side 5 in with perpendicular height 7 in is formed. Hence, the solid figure that could be formed from the net shown is a Square pyramid

What is 73 / 6? I need a whole number, not 12.1666667 with a remainder if there is one!

/= divided by

Answers

It should be 12. you have to round it to a whole number. not sure though.

Answer:

12

Step-by-step explanation:

12.1666667 rounded:

12.1666667 You rounded to the nearest one's place. The 2 in the ones place rounds down to 2 or stays the same because the digit to the right in the tenth place is 1.

12 When the digit to the right is less than 5 we round toward 0.

12.1666667 was rounded down toward zero to 12

how do you solve 15w-4=41

Answers

In order to solve this equation for w, we can do the following steps:

[tex]\begin{gathered} 15w-4=41 \\ 1.\text{ Add +4 to both sides of the equation:} \\ 15w-4+4=41+4 \\ 15w=45 \\ 2.\text{ Divide both sides of the equation by 15:} \\ \frac{15w}{15}=\frac{45}{15} \\ w=3 \end{gathered}[/tex]

So we have that the value of w is 3.

Graph f(x)=log1/2 (x)

Answers

The coordinate are (0.8,0)

Answer:

Step-by-step explanation:

6 in. SA = 2ten2 + 2trh (Use 3.14 for a.) Find the surface area of a cylinder with a height of 8 inches and base diameter of 6 inches. square inches 8 in. Do NOT round your answer.

Answers

207.24 in²

1) Gathering the data

height: 8"

Base Diameter: 6" then a Radius: 3 for D=2R

2) Let's find the Surface Area from this Cylinder by plugging into that the given data:

[tex]\begin{gathered} SA=2\pi\cdot r^2+2\pi rh \\ S_A=2(3.14)\cdot(3)^2+2\cdot3.14\cdot3\cdot8 \\ S_A=207.24in^2 \end{gathered}[/tex]

3) Hence, the answer is 207.24 in²

a rectangle is drawn so the width is 71 inches longer than the height if the rectangles diagonal measurement is 85 inches find the heightround to 1 decimal place______inches

Answers

Let's first conceptualize the given details by drawing a rectangle with the given details being reflected.

Where,

x = Height of the rectangle

x + 71 = The ratio of the width of the rectangle with respect to the height.

Cutting the rectangle in half along the diagonal line makes a right triangle,

Thus, we can use the Pythagorean Theorem to be able to determine the height of the rectangle. We get,

[tex]\text{ a}^2+b^2=c^2\text{ }\rightarrow(x+71)^2+(x)^2=(81)^2_{}[/tex][tex]\text{ x}^2+142x+5041+x^2\text{ = 6561}[/tex][tex]\text{ 2x}^2\text{ + 142x + 5041 - 6561 = 0}[/tex][tex](\frac{1}{2})\text{ (2x}^2\text{ + 142x - }1520)\text{ = 0}[/tex][tex]\text{ x}^2\text{ + 71x - 760 = 0}[/tex][tex]\text{ (x +}\frac{71+\sqrt[]{8081}}{2})(x\text{ + }\frac{71\text{ - }\sqrt[]{8081}}{2})=\text{ 0}[/tex]

There are two possible height of the rectangle,

[tex]x_1\text{ = }\frac{-71-\sqrt[]{8081}}{2}\text{ = -80.45 in.}[/tex][tex]\text{ x}_2\text{ = }\frac{-71\text{ + }\sqrt[]{8081}}{2\text{ }}=9.45\text{ in.}[/tex]

9.45 = 9.5 in. is the most probable height of the rectangle because a dimension must never be negative, thus, let's adopt 9.5 in. as the height.

The width must be = x + 71 = 9.5 + 71 = 80.5 in.

Other Questions
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