Solve: log4 (5x-3) + log4 (9-x) = 3

The sum of 3/8 and 1/4 is 5/8. Therefore, any expression that sums up to 5/8 will have the same sum as 3/8 + 1/4.

To find the expression that has the same sum as 3/8 + 1/4, we need to first compute the sum of the given fractions. When summing fractions, we need the denominators to be the same. In this case, 8 and 4 could both be divisible by 2, so we need to convert the second fraction to have the denominator of 8:

3/8 + 2/8 = 5/8

Therefore, the expression that will have the same sum as 3/8 + 1/4 is any other expression that also amounts to 5/8. Examples could be 2/8 + 3/8 or even 5/8 + 0.

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To find an expression with the same sum as 3/8 + 1/4, we need to find a common denominator and add the fractions. The expression with the same sum is 5/8.

To find an expression with the same sum as 3/8 + 1/4, we need to find a common denominator.

The least common multiple of 8 and 4 is 8, so we can rewrite 3/8 as 3/8 × 1 = 3/8 × 2/2 = 6/16.

Now we can add 6/16 + 1/4, which equals (6 + 4)/16 = 10/16.

Simplifying this fraction gives us 5/8. Therefore, the expression with the same sum as 3/8 + 1/4 is 5/8.

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Answer:

The domain of the relation is [tex][(5,16,18,21][/tex]

Step-by-step explanation:

we have

[tex][(15,65),(21,70),(18,73),(16,62)][/tex]

Remember that

The domain of the relation are the values of x

The range of the relation are the values of y

therefore

The domain is

[tex][(5,21,18,16][/tex]

order them from lowest to highest ------->  [tex][(5,16,18,21][/tex]

The range is

[tex][65,70,73,62][/tex]

order them from lowest to highest ------->[tex][62,65,70,73][/tex]

Answer:

Step-by-step explanation:

Conversion a mixed number 8 1/6 to a improper fraction: 8 1/6 = 8 1/ 6  = 8 · 6 + 1/ 6 = 48 + 1/ = 49/6 To find a new numerator: a) Multiply the whole number 8 by the denominator 6. Whole number 8 equally 8 * 6/6 = 48/6

b) Add the answer from the previous step 48 to the numerator 1. New numerator is 48 + 1 = 49

c) Write a previous answer (new numerator 49) over the denominator 6.

Eight and one sixth is forty-nine sixths

Conversion a mixed number 1 7/8 to a improper fraction: 1 7/8 = 1 7/8  = 1 · 8 + 7/8  = 8 + 7/8= 15/8 To find a new numerator:

a) Multiply the whole number 1 by the denominator 8. Whole number 1 equally 1 * 8/8 = 8/8 b) Add the answer from previous step 8 to the numerator 7. New numerator is 8 + 7 = 15

c) Write a previous answer (new numerator 15) over the denominator 8. One and seven eighths is fifteen eighthsDivide: 49/6: 15/8= 49/6· 8/15 = 49·\.8/6 · 15 = 392/90= 2 · 196/=2 · 45= 196/45 Dividing two fractions is the same as multiplying the first fraction by the reciprocal value of the second fraction. The first sub-step is to find the reciprocal (reverse the numerator and denominator, reciprocal of 15/8 is 8/15) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. In the following intermediate step, cancel by a common factor of 2 gives 196/ 45. In other words - forty-nine sixths divided by fifteen eighths = one hundred ninety-six forty-fifths.

Answer:

8

Step-by-step explanation:

Note that 2 divides into 8 evenly, yielding the quotient 4.  8 is the LCD.  To combine 3/8 and 11/2, we would rewrite 11/2 as

4·11

------ = 44/8

 4·2

and then combine 44/8 with 3/8.  The sum would be 47/8.

In summary, the LCD of 3/8 and 11/2 is 8; 3/8 stays as is and 11/2 is rewritten by mult. numerator and denominator by 4 each.

Answer:

17 x 5 = 85. It is the right answer, my way of solving it was different but still correct.

Step-by-step explanation:

4 / 20 = 5

5 x 17 = 85.

Answer:

Taylor is 14.

Step-by-step explanation:

Max is 3. Emma is six years older than Max.

3+6=9

Emma is 9. Taylor is five years older than Emma.

9+5=14

Answer:

14 yrs old

Step-by-step explanation:

Surface area of original prism: 113.5 cm

Surface area of enlarged prism: 1816

its pretty simple to find the ratio so you can probably figure that out on your own :) Good luck!

Answer:

.04

Step-by-step explanation:

(5^10)/(5^12)

5 to the tenth power = 5×5×5×5×5×5×5×5×5+5 = 9,765,625

5 to the twelfth power = 5×5×5×5×5×5×5×5×5×5×5×5 = 244,140,625

244,140,625 ÷ 9,765,625 =25

9,765,625 ÷ 244,140,625 =0.04

hope this is what ur looking for :)

6.  Jim's house is 5.1 miles from the mall

7. Jim's house is closer to the mall by 0.3 miles.

8. The total distance of the round trip is 5.7 miles + 5.7 miles = 11.4 miles.

Since Jim's car has 25 miles until it runs out of gas and the round trip is 11.4 miles, Jim would be able to make it from his house to the grocery store and back without stopping for gas.

9. Jim had traveled 5.4 miles / 2 = 2.7 miles when his wife called.

10. The park is within 5 miles of Jim's house.

6. How many miles is Jim's house from the mall?

To find the distance between Jim's house and the mall, we can use the distance formula:

distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

where (x1, y1) and (x2, y2) are the coordinates of the two points.

In this case, the coordinates of Jim's house are (12, 11) and the coordinates of the mall are (7, 10). Plugging these values into the distance formula, we get:

distance = sqrt((7 - 12)^2 + (10 - 11)^2)

distance = sqrt(25 + 1)

distance = sqrt(26)

distance = 5.1 miles (rounded to the nearest tenth)

Therefore, Jim's house is 5.1 miles from the mall

7. Is Jim's house closer to the mall or the bank? How many miles closer is it?

To find which point is closer to Jim's house, we can calculate the distance between Jim's house and each point and compare the results.

The distance between Jim's house and the bank is:

distance = sqrt((14 - 12)^2 + (16 - 11)^2)

distance = sqrt(4 + 25)

distance = sqrt(29)

distance = 5.4 miles (rounded to the nearest tenth)

Therefore, Jim's house is closer to the mall by 0.3 miles.

8. Jim is at his house, and his car has 25 miles until it runs out of gas. Would Jim be able to make it from his house to the grocery store and back without stopping for gas? Explain.

To find out if Jim can make it from his house to the grocery store and back without stopping for gas, we need to calculate the total distance of the round trip.

The distance between Jim's house and the grocery store is:

distance = sqrt((16 - 12)^2 + (15 - 11)^2)

distance = sqrt(16 + 16)

distance = sqrt(32)

distance = 5.7 miles (rounded to the nearest tenth)

Therefore, the total distance of the round trip is 5.7 miles + 5.7 miles = 11.4 miles.

Since Jim's car has 25 miles until it runs out of gas and the round trip is 11.4 miles, Jim would be able to make it from his house to the grocery store and back without stopping for gas.

9. Jim left his house and drove to the bank. On his way back home, Jim's wife called when he was exactly halfway home. How many miles had Jim traveled when his wife called?

To find the distance Jim had traveled when his wife called, we can divide the total distance between Jim's house and the bank by 2.

The distance between Jim's house and the bank is:

distance = sqrt((14 - 12)^2 + (16 - 11)^2)

distance = sqrt(4 + 25)

distance = sqrt(29)

distance = 5.4 miles (rounded to the nearest tenth)

Therefore, Jim had traveled 5.4 miles / 2 = 2.7 miles when his wife called.

10. Jim is hoping that a park will be built within 5 miles of his house. If a park is built at the coordinates (12, 10), does that meet Jim's criteria? Explain.

To find out if the park is within 5 miles of Jim's house, we can calculate the distance between the park and Jim's house.

The distance between the park and Jim's house is:

distance = sqrt((12 - 12)^2 + (10 - 11)^2)

distance = sqrt(1)

distance = 1 mile (rounded to the nearest tenth)

Therefore, the park is within 5 miles of Jim's house.

Step-by-step explanation:

[tex]f(x)=x^3+2x^2-x-2=x^2(x+2)-1(x+2)=(x+2)(x^2-1)\\\\\text{use}\ a^2-b^2=(a-b)(a+b)\\\\f(x)=(x+2)(x-1)(x+1)\\\\\text{The zeros (x-intercepts):}\\\\f(x)=0\iff(x+2)(x-1)(x+1)=0\iff \\x+2=0\ \vee\ x-1=0\ \vee\ x+1=0\\\\x=-2\ \vee\ x=1\ \vee\ x=-1\\\\\text{y-intercept}:\\\text{Put x = 0:}\\\\f(0)=0^3+2(0^2)-0+2=2\to(0,\ 2)[/tex]

Answer:

The number of three-point field goals was [tex]7[/tex]

Step-by-step explanation:

Let

x-----> the number of two-point field goals

y-----> the number of three-point field goals

we know that

[tex]x+y=16[/tex]

[tex]x=16-y[/tex] -----> equation A

[tex]2x+3y=39[/tex] ----> equation B

substitute equation A in equation B and solve for y

[tex]2(16-y)+3y=39[/tex]

[tex]32-2y+3y=39[/tex]

[tex]y=39-32=7[/tex]

Using a system of equations, it is found that Marlene made 7 three-point field goals in the game.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the variables are:

Marlene made 16 field goals, hence:

x + y = 16 -> x = 16 - y

She scored a total of 39 points from field goals, hence:

2x + 3y = 39

2(16 - y) + 3y = 39

32 - 2y + 3y = 39

y = 7

Marlene made 7 three-point field goals in the game.

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Answer:

Area = 30 , Perimeter = 22.31 ⇒ Answer (B)

Step-by-step explanation:

* Lets study the figure

- The length of AE = 5

- The length of DC = 3

- The length of BC = 4

- Tho find the length of DE and AB we must use Pythagoras Theorem

∵ The vertical distance of ED = 3 and the horizontal distance = 2

∴ ED = √(3² + 2²) = √13  

- Similar we will find AB

∵ The vertical distance of AB = 6 and the horizontal distance = 3

∴ AB = √(6² + 3²) = √45

* Now we can find its perimeter

- The perimeter = 5 + 4 + 3 + √13 + √45 = 22.31

* to find the area we will divided it into 2 trapezium

- The first one contains E , D , C with point of intersection

 between the vertical axis with side CB

- The lengths of its 2 parallel bases are 3 , 6 and height 2

- The second one contains E , A , B with  point of intersection

 between the vertical axis with side BC

- The lengths of its 2 parallel bases are 2 , 5 and height 6

∵ Area trapezium = (1/2)(b1 + b2) × h

- The area of 1st one = (1/2)(3 + 6) × 2 = 9 units²

- The area of 2nd one = (1/2)(2 + 5) × 6 = 21 units²

∴ The area of the figure = 9 + 21 = 30 units²

* Area = 30 , Perimeter = 22.31

Answer:

Step-by-step explanation:

Geometric transformations involve taking a preimage and transforming it in some way to produce an image. There are two different categories of transformations:

The rigid transformation, which does not change the shape or size of the preimage.

The non-rigid transformation, which will change the size but not the shape of the preimage.

keep in mind that there's 4 types of transformants!!!

While the term 'transformants' is unclear in geometry, related concepts include various geometric transformations like conformal transformations, contact-transformations, and orthogonal transformations, which alter geometric entities while preserving specific properties such as angles or lengths.

The term transformants in geometry does not have a standard definition and appears to be a typographical error or a confusion with transformations, which are well-defined in geometric contexts. However, based on the provided information, we can discuss various types of geometric transformations that are relevant to the discussion at hand. These transformations include conformal transformations, which preserve angles; contact-transformations introduced by Sophus Lie that deal with the transformation of geometric entities; and orthogonal transformations, which preserve lengths and angles.

Answer:

The third side must be 10:  {3, 10, 10}; {10, 3, 3} is not possible.

Step-by-step explanation:

Everything depends on our understanding of "isosceles."

This term indicates that two sides of a given triangle are equal.

If two sides of an isosceles triangle have lengths of 3 and 10, then:

Either 1)  Two sides have length 10 and the third side has length 3.  This is certainly possible

or

2)  sides have length 3 and the third side has length 10.  This is NOT possible, since 3 + 3 adds up to 6, which is less than 10.

The third length is 10 units and the pair of the side lengths is 3, 10, 10.

In terms of geometry, the triangle is a three-sided polygon with three edges and three vertices. The triangle's interior angles add up to 180°.

We have:

Two sides of an isosceles triangle have lengths of 3 and 10

As we know, in the isosceles triangle two sides are equal in length.

10, 3, 3 is not possible they cannot form a triangle.

So the third length is 10 units.

Thus, the third length is 10 units and the pair of the side lengths is 3, 10, 10.

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Answer:

The answer is D.

Step-by-step explanation:

If you look at the tables, you notice that in table D the distance reaches 50 km as the time reaches 1 hour.

The table that represents the situation is the table d

From the question, we have the following parameters that can be used in our computation:

Rate = 50km/h

The table that shows that the bird travels 50 km each hour will be a table where the distance is directly proportional to the time

The slope of the line is 50, which means that for every hour that the bird flies, it travels an additional 50 kilometers.

Using the above as a guide, we have the following:

The table is table d

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Answer:

The coefficients in increasing order of k are;

1, 4, 6, 4, 1

Step-by-step explanation:

The expansion of (x+y)^4 falls under the category of binomial expansions in which the coefficients are computed using combinations;

For k = 0, the coefficient is;

4 combination 0 = 1

For k = 1, the coefficient is;

4 combination 1 = 4

For k = 2, the coefficient is;

4 combination 2 = 6

For k = 3, the coefficient is;

4 combination 3 = 4

For k = 4, the coefficient is;

4 combination 4 = 1

These values can also be obtained from the Pascal's triangle;

The coefficients always exhibit some degree of symmetry

Answer:

1, 4, 6, 4, 1

Step-by-step explanation:

apex

q = 10p because all of them are multiplied by ten

answer

y/7

step by step explanation

Answer:

The answer is A) Yes, 56 sq. ft

Step-by-step explanation:

You will have to waste 56 sq. ft . The total area of the carpet = 40 x 12=480 sq ft - the area of the room (26 x 12) + (8 x 14) = 424 sq ft.

Using the area of rectangle formula to solve the problem. Then the waste of carpet is 56 ft².

It deals with the size of geometry, region, and density of the different forms both 2D and 3D.

Given

you use 40 linear feet of 12-foot wide carpet to carpet this room.

The room is 26 by 12 and 8 by 14.

The waste carpet after the installation.

We know the area of the formula

Area = Length x width

The area of the carpet will be

area of the carpet = 40 x 12

area of the carpet = 480

The area of the room will be

area of the room = (26 x 12) + (8 x 14)

area of the room = 312 + 112

area of the room = 424

So the waste of carpet will be

waste of carpet = area of carpet -the area of the room

waste of carpet = 480 - 424

waste of carpet = 56

Thus, the waste of carpet is 56 ft².

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The answer to this question is A

Vertical angles are congruent. Option A

Vertical angles are pairs of angles formed by the intersection of two lines or line segments, where the angles are opposite each other and share a common vertex but do not share any sides.

Vertical angles are always congruent, meaning they have equal measures.

For instance, in an "X" shape formed by two intersecting lines, the angles opposite each other at the intersection are vertical angles.

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Answer:

The wholesale price of TV is 0.35 times the retail price of this TV

x = 0.35y

Step-by-step explanation:

Let say x = wholesale price of a TV

Let say y = retail price price of a TV

We can write an equation that represents what is mention in the question

Equation

x = y - 65%y

x = y - 65/100y

x = y - 0.65y

x = 0.35y

Hence, the wholesale price is 0.35 times the retail price

Answer:

12km

Step-by-step explanation:

this really is actually kind of simple so it takes shawn 6 hours to get there at a speed of 2 kilometer per hour so you take the time and you X it by the speed therefor 6 X 2 = 12 and that would be your answer

Answer:

The distance would be 12 kilometers.

Step-by-step explanation:

Since,

[tex]Speed = \frac{Distance}{Time}[/tex]

[tex]\implies Distance = Speed\times time[/tex]

Here,

Speed of Shawn = 2 kilometers per hour,

Time taken by him = 6 hours,

Hence, the distance between Shawn's house and Susan's house

= 2 × 6

= 12 kilometers.

Answer:

3 people

Step-by-step explanation:

The grandma is a mother to her daughter and her daughter is the mother to the granddaughter.

Answer:

448 R50

Step-by-step explanation:

Answer: 448

All you need to do is plug that into a calculator and you’ll get the answer

Answer:

[tex]y + 2 = \frac{2}{3}(x+1)[/tex]

Step-by-step explanation:

Parallel lines are parallel because they never intersect. As such, they have the same slope. The slope of the line y = 2/3x + 7 is 2/3. Substitute m = 2.3 and the point (-1,-2) into the point slope form of a line.

[tex]y -y_1 = m(x-x_1)\\y --2 = \frac{2}{3}(x --1)\\y + 2 = \frac{2}{3}(x+1)\\[/tex]

Answer:

5 feet tall!

Step-by-step explanation: Just divide 1,250 by 250 and that is your height

Answer:

Her model will be 5 foot

Step-by-step explanation:

1 foot = 250 feet

250x5=1,250

Answer:

[tex]\large\boxed{\dfrac{18}{2x-6}=\dfrac{9}{x-3}}[/tex]

Step-by-step explanation:

[tex]\dfrac{18}{2x-6}=\dfrac{18\!\!\!\!\diagup^9}{2\!\!\!\!\diagup_1(x-3)}=\dfrac{9}{x-3}[/tex]

Answer:3980

Step-by-step explanation:

Answer:

Step-by-step explanation:

3980