problem 1: the longest book toshi had read was 304 pages. she just finished kira-kira by cynthia kadohata, which is 256 pages. how much longer was the longest book toshi read than kira-kira?

Answer:

x = 6

Step-by-step explanation:

AD and EH are equal. Congruent figures are made up of congruent parts.

The inequality to represent the situation is 335 + d ≥ 575; Rhonda must collect at least '240 stamps' in order to reach her goal.

If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true. Such values are called solution to that equation or inequality. Set of such values is called solution set to the considered equation or inequality.

Given that the Stamps Rhonda wants to collect = 575

The Stamps already in collection = 335

Let consider 'd' represents the number of stamps Rhonda needs to achieve her goal.

Thus, the Stamps to collect + Stamps already in collection ≥ 575

d + 335 ≥ 575

d ≥ 575 - 335

d ≥ 240

Hence, The inequality to represent the situation is 335 + d ≥ 575; Rhonda must collect at least '240 stamps' in order to reach her goal.

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Final answer:

To find how many more stamps Rhonda needs to collect to reach her goal, utilize the inequality 335 + d ≥ 575 with d representing the additional stamps needed, resulting in d ≥ 240.

Explanation:

Rhonda's Inequality:

335 + d ≥ 575; d ≥ 240

To determine how many more stamps Rhonda must collect to reach her goal, we set up the inequality 335 + d ≥ 575, where d represents the number of stamps she must collect. By solving this inequality, we find that Rhonda needs to collect at least 240 more stamps to reach her goal.

Answer:

The days will it take them to have the same number of followers is:

Step-by-step explanation:

To solve the proposed exercise, an equation must be made for each one taking into account the information obtained:

Where d is the number of days elapsed. Since you want to identify the day in which they will have the same number of followers, you proceed to match the two equations:

And you clear the variable d (remember that those who are adding to one side of equality, go to the other side to subtract and, if they are subtracting to one side of equality, go to add):

Answer:

D - it uses data entered in certain cells to calculate values for other cells

Step-by-step explanation:

A-p-e-x approved

Answer:

Proof

Step-by-step explanation:

Recall the identity [tex]\sin(a \pm b) = \sin(a)\cos(b) \pm \cos(a)\sin(b)[/tex].

Consider [tex]\sin(a + b) = k\sin(a - b)[/tex]. We firstly apply the above identity to reach

[tex]\sin(a)\cos(b) + \cos(a)\sin(b) = k(\sin(a)\cos(b) - \cos(a)\sin(b))[/tex].

By expanding the bracket on the right we obtain

[tex]\sin(a)\cos(b) + \cos(a)\sin(b) = k\sin(a)\cos(b) - k\cos(a)\sin(b)[/tex] and so

[tex]\cos(a)\sin(b) + k\cos(a)\sin(b) = k\sin(a)\cos(b) - \sin(a)\cos(b)[/tex] and so

[tex](1+k)\cos(a)\sin(b) = (k-1)\sin(a)\cos(b)[/tex] and so

[tex](k+1)\frac{\cos(a)}{\sin(a)}= (k-1)\frac{\cos(b)}{\sin(b)}[/tex] and finally

[tex](k+1)\cot(a)= (k-1)\cot(b)[/tex].

Final answer:

Using the sum and difference identities for sine, we can manipulate the equation sin(a+b) = k sin(a-b) to prove the trigonometric identity (k-1)cotb = (k+1)cota as required.

Explanation:

To solve the given trigonometric identity, we must show that if sin(a+b) = k sin(a-b), then (k-1)cotb = (k+1)cota. First, let's utilize the sum and difference identities for sine:

sin(a+b) = sin(a)cos(b) + cos(a)sin(b)

sin(a-b) = sin(a)cos(b) - cos(a)sin(b)

Substitute these into the original equation:

sin(a)cos(b) + cos(a)sin(b) = k(sin(a)cos(b) - cos(a)sin(b))

Now, distribute the k on the right side and arrange terms:

sin(a)cos(b)(1-k) = cos(a)sin(b)(1+k)

Divide both sides by sin(b)cos(b) to isolate cot(a) and cot(b):

(1-k) cot(b) = (1+k) cot(a)

This proves the identity as required. Notice that the cotangent function is the reciprocal of the tangent function, which is the ratio of sine to cosine.

Answer:

1/6 = 3/18

1/9 = 2/18

Step-by-step explanation:

The common denominator for 6 and 9 is the smallest number that they both go into, which is 18.  We need to multiply 6 by 3 to get 18 and multiply 9 by 2 to get 18

1/6 *3/3 = 3/18

1/9 *2/2 = 2/18

Answer:

the pair would be 3/18 and 2/18

Answer: 12

Explanation: what i did to get that was i did 60 divided by 5 = 12 or u can do 12 times 5 which will give you 60 mins

hope this helps you Good Luck!!!!!!!!

Answer:

b=2A-2a

Step-by-step explanation:

First you subtract a to the other side.

Then you divide by 2.

SO it will be b=2A-2a which is your answer

Answer:

See proof below

Step-by-step explanation:

Consider triangle with midpoints D, E, F of the sides BC, AC and AB, respectively.  If D, E and F are midpoints  of the sides BC, AC and AB, then

Triangle ABC is equilateral triangle, then

If AB=BC=AC, then EA=CE=FA=BF=DC=DB.

By SAS theorem, ΔFAE≅ΔDCE≅ΔEBD.

Congruent triangles have congruent corresponding sides, then

EF=FD=DE. This means that triangle DEF is equilateral.

Final answer:

To find the result of dividing 22.11 by 11, you simply divide 22.11 by 11, yielding an answer of 2.01. This basic division operation demonstrates how to divide a decimal by a whole number.

Explanation:

The question is asking to divide 22.11 by 11. To solve this, you would take the number 22.11 and divide it by 11. Dividing these numbers is straightforward and can be done using long division or a calculator.

Step 1: Place 22.11 under the division bracket and 11 outside of it.

Step 2: Determine how many times 11 fits into 22.11. Since 11 goes into 22 exactly two times, you write 2 above the division bracket, aligned with the last digit of 22.

Step 3: Multiply 2 (the quotient) by 11 (the divisor) to get 22, and subtract this from 22.11, leaving you with a remainder of 0.11.

Step 4: Bring down the next digit (if any), but since we already have no more digits left in 22.11, we look at the remainder. In practical terms for simple school-level math, we can stop here, acknowledging that 11 goes into 22.11 twice without a perfect division due to the decimal.

The actual answer to 22.11 divided by 11 is 2.01.

Answer:

Carol      PLEASE GIVE BRAINLIEST

Step-by-step explanation:

Jon = 6 patients in 1.5 hours

6 ÷ 1.5 = 4 patients per hour

Carol = 10 patients in 2 hours

10 ÷ 2 = 5 patients an hour

Carol sees more patients per hour.

Answer:

The expression equal to 2x^(2)+8 is:

First option (2x-4i)(x+2i)

Step-by-step explanation:

If we multiply

(2x-4i)(x+2i)=(2x)(x)+(2x)(2i)-(4i)(x)-4i(2i)

(2x-4i)(x+2i)=2x^(1+1)+4xi-4xi-8i^(1+1)

Simplifying:

(2x-4i)(x+2i)=2x^2-8i^2

and i^2=-1, then:

(2x-4i)(x+2i)=2x^2-8(-1)

Multiplying:

(2x-4i)(x+2i)=2x^2+8

To find the expression that is equal to 2x^(2) + 8, simplify each option by expanding the multiplication and then compare it to the original expression.

To find the expression that is equal to 2x^(2) + 8, we need to simplify each option by expanding the multiplication and then compare it to the original expression.

Let's simplify each option:

The expression that is equal to 2x^(2)+8 is (2x-4i)(x-2i).

Let the initial savings at first be = x

Given ratio is [tex]\frac{5}{4}[/tex] and after donating $40 to charity, the ratio becomes [tex]\frac{13}{10}[/tex]

Hence, the relation becomes:

[tex]\frac{5x-40}{4x-40}=\frac{13}{10}[/tex]

[tex]10(5x-40)=13(4x-40)[/tex]

= [tex]50x-400=52x-520[/tex]

[tex]-2x=-120[/tex] or

[tex]2x=120[/tex]

[tex]x=60[/tex]

So , Dave's saving at first was 5x = 5*60 = $300

and Sam's saving at first was 4x = 4*60= $240

Answer:

c. 1/4 or 25% or 0.25

Step-by-step explanation:

Answer:

C  1/4

Step-by-step explanation:

When the bases are the same, we can add the exponents

x^a * x^b = x^ (a+b)

4^2 * 4^(-3)

4^(2-3)

4^(-1)

The negative exponent puts it in the denominator

1/4

check the picture below.

make sure your calculator is in Degree mode.

Answer:

2.735

Step-by-step explanation:

:)

Answer:

The null and alternative hypotheses are:

[tex]H_{0}: \mu = 170[/tex]

[tex]H_{a}: \mu >170[/tex]

Under the null hypothesis, the test statistic is:

[tex]z=\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt{n}} }[/tex]

         [tex]=\frac{180-170}{\frac{35}{\sqrt{225}} }[/tex]

         [tex]=\frac{10}{2.33}[/tex]

         [tex]=4.29[/tex]

Now, we have to find the right tailed z critical value at 0.10 significance level. Using the standard normal table, we have:

[tex]z_{critical} = 1.28[/tex]

Since the test statistic is greater than the z critical value, we therefore, reject the null hypothesis and conclude that there is sufficient evidence to support the claim that the university students weigh more than the population.

The type of angle that is not formed by two parallel lines cut by a transversal is complementary angles. So option (d) is correct.

The intersection of two parallel lines by a transversal forms several types of angles:

1. Alternate Interior Angles: These are angles on opposite sides of the transversal and inside the parallel lines. They are congruent.

2. Alternate Exterior Angles: These are angles on opposite sides of the transversal and outside the parallel lines. They are also congruent.

3. Corresponding Angles: These are angles in the same position at each intersection. They are congruent when the parallel lines are cut by a transversal.

4. Complementary Angles: These are angles whose measures sum up to 90 degrees. They can be formed when a transversal intersects parallel lines, but they are not a specific type of angle formed by this intersection.

Therefore, the type of angle that is not formed by two parallel lines cut by a transversal is D) complementary angles. The other options, A) alternate interior angles, B) alternate exterior angles, and C) corresponding angles, are all formed by this intersection.

Answer:

Correct choice is D

Step-by-step explanation:

Consider the quadratic expression [tex]5x^2 + 7x + 2.[/tex]

First, find the discriminant:

[tex]D=7^2-4\cdot 5\cdot 2=49-40=9.[/tex]

Now find the roots of the quadratic expression [tex]5x^2 + 7x + 2:[/tex]

[tex]x_{1,2}=\dfrac{-7\pm \sqrt{9}}{2\cdot 5}=\dfrac{-7\pm 3}{10}=-1,\ -0.4.[/tex]

Then

[tex]5x^2 + 7x + 2=5(x-(-1))(x-(-0.4))=5(x+1)(x+0.4)=(x+1)(5x+2).[/tex]

Answer:

Cost of 11 cans of Dog food is $9.57

Step-by-step explanation:

Cost of 5 cans of dog food = $4.35

So to find out the cost of 11 cans of dog food at the same price, we need to calculate the price of 1 can of dog food.

Calculation for finding out cost of 1 can of dog food

The price $4.35 which is given is the price of 5 cans

So to find the cost of 1 can, we need to divide the given price by 5

5 Cans of dog food = $4.35

1 can of dog food = 4.35 ÷ 5

1 can of dog food = $0.87

Now to find out the price of 11 cans, we will multiply the price of 1 can with 11

Cost of 11 cans = 11 × $0.87

                          = $9.57

Final answer:

The jogger runs a total distance of 224 meters, which includes running along the width and length of the park and taking a shortcut diagonally across the park.

Explanation:

To calculate the total distance the jogger runs, we must add the distances from each leg of the jogger's path. Starting from the southeast corner, the jogger runs the width of the park (28 meters) to the west, and then the length of the park (96 meters) to the north, reaching the northwest corner. The shortcut from the northwest corner directly back to the southeast corner, where her car is parked, is the hypotenuse of the resulting right-angled triangle. To find the length of this hypotenuse, we use the Pythagorean theorem (a² + b² = c²), where the sides of the rectangle serve as 'a' and 'b'.

Let's calculate the hypotenuse:

a = 28 m (width)

b = 96 m (length)

c = √(a² + b²) = √(28² + 96²)

c = √(784 + 9216)

c = √10000

c = 100 m

Now, we sum up all the distances:

28 m (west along the width)

96 m (north along the length)

100 m (shortcut diagonally)

Total distance = 28 m + 96 m + 100 m = 224 meters

Divide 260 and 156 to get 5/3, or 1 2/3. Multiply by 100 to get 166.(6). (6) means repeating forever. For example 1.(3)=1.333333333....

Answer:

Yes

Step-by-step explanation:

Answer:

Switch around "five decreased by twice a number" and the one below it, then I'm pretty sure you're done. (;

Base Case: plug in n = 1 (the smallest positive integer)

If n = 1, then 3n-2 = 3*1-2 = 1. Square this and we see that (3n-2)^2 = 1^2 = 1

On the right hand side, plugging in n = 1 leads to...

n*(6n^2-3n-1)/2 = 1*(6*1^2-3*1-1)/2 = 1

Both sides are 1. So that confirms the base case.

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

Inductive Step: Assume that

1^2 + 4^2 + 7^2 + ... + (3k-2)^2 = k*(6k^2-3k-1)/2

is a true statement for some positive integer k. If we can show the statement leads to the (k+1)th case being true as well, then we will have sufficiently proven the overall statement to be true by induction.

1^2 + 4^2 + 7^2 + ... + (3k-2)^2 = k*(6k^2-3k-1)/2

1^2 + 4^2 + 7^2 + ... + (3k-2)^2 + (3(k+1)-2)^2 = (k+1)*(6(k+1)^2-3(k+1)-1)/2

k*(6k^2-3k-1)/2 + (3(k+1)-2)^2 = (k+1)*(6(k^2+2k+1)-3(k+1)-1)/2

k*(6k^2-3k-1)/2 + (3k+3-2)^2 = (k+1)*(6k^2+12k+6-3k-3-1)/2

k*(6k^2-3k-1)/2 + (3k+1)^2 = (k+1)*(6k^2+9k+2)/2

k*(6k^2-3k-1)/2 + 9k^2+6k+1 = (k+1)*(6k^2+9k+2)/2

(6k^3-3k^2-k)/2 + 2(9k^2+6k+1)/2 = (k*(6k^2+9k+2)+1(6k^2+9k+2))/2

(6k^3-3k^2-k + 2(9k^2+6k+1))/2 = (6k^3+9k^2+2k+6k^2+9k+2)/2

(6k^3-3k^2-k + 18k^2+12k+2)/2 = (6k^3+9k^2+2k+6k^2+9k+2)/2

(6k^3+15k^2+11k+2)/2 = (6k^3+15k^2+11k+2)/2

Both sides simplify to the same expression, so that proves the (k+1)th case immediately follows from the kth case

That wraps up the inductive step. The full induction proof is done at this point.

Answer:  The answer is:  "  [tex]\frac{7}{80}[/tex] " .

_________________________________________________

Step-by-step explanation:

__________________________________________________

Given:  " 8 [tex]\frac{3}{4}[/tex] % "  ;  Convert this to a "fraction" .

__________________________________________________

Start with the:  " 8  [tex]\frac{3}{4}[/tex] "  portion:

Start with the:  " [tex]\frac{3}{4}[/tex] "  portion :

Note:  " [tex]\frac{3}{4}[/tex] " ;

                           =  3/4 ;

                           =  3 ÷ 4 ;  {use calculator} ;

                           =  0.75  .

_________________________________________________

Or;  recognize, from experience, that:  "3/4" = " 0.75 " .

_________________________________________________

Or:  Calculate as follows:

          →  " [tex]\frac{3}{4}[/tex]  = [tex]\frac{?}{100}[/tex] " ;  

          →   Solve for the:  "(?)" value:

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Consider the "denominator" portions:

         →  " 4 * {what value?} = 100 " ;

         →  100/4 = 100 ÷ 4  = 25 ;  

         →  So:  " 4 * {25}  = 100 ;

Now, consider the "numerator" portions:

         →  " 3 * {25}  = "{?}" ;

         →  " 3 * {25}  = " 75 " ;

__________________________________________________

Now, we can rewrite the expression;

           & replace the "{?}" — with:  " 75 " ;  as follows:

__________________________________________________

The original expression:

          →  " [tex]\frac{3}{4}[/tex]  = [tex]\frac{?}{100}[/tex] " ;  

Rewrite as:

          →  " [tex]\frac{3}{4}[/tex]  = [tex]\frac{75}{100}[/tex] " ;  

_______________________________________________

Note:  " [tex]\frac{75}{100}[/tex] "  ;

                       =   75 / 100  =  75 ÷ 100 ;  

          →   Use calculator:   = 0.75 ;

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                               Or:  75 ÷ 100 = ? ;

     →  Note:  when dividing by "100" ; we take the original value, and move that number backward "2 (two) decimal spaces".  We move "backward" because we are "dividing" (not "multiplying") ; and we move 2 (two) decimal spaces because:  " 100" has 2 (two) zeros.

     →  " 75 ÷ 100  =  75.  ÷  100  =  .75  ;

                               →  Write as:  " 0.75.

_______________________________________________

So:  " 8 [tex]\frac{3}{4}[/tex]  "  ;

          =  8  +  [tex]\frac{3}{4}[/tex]  ;

          =   8  + 0.75 ;

         =   8.75  .

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So:  " 8 [tex]\frac{3}{4}[/tex] % " ;  

          =  8.75 % ;

_________________________________________

Note that " % " ;  refers to parts per hundred;  or:  "divided by 100" ;

_______________________________________________

       →  So:   " 8.75 % " ;

                  = 8.75 / 100 = 8.75 ÷ 100 ;  

       →  Use calculator; to get:  " 0.0875 " .

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Or:  " 8.75 ÷ 100 " ;   →  As aforementioned, when dividing by "100" ;

                                   we move the decimal point "backward 2 (two) spaces:

      →   " 8.75 ÷ 100  =  .0875 ;

                          →  Write as:  " 0.0875 " .

_______________________________________________

Now, let us convert this value to a "fraction value" ;

    →  We have:  " 0.0875 ;

We look at the last consecutive non-zero digits:  "875" .

   →  How many decimal spaces backward from "875" ;  specifically, the digit, "5" ;  are there (counting backward; to the actual decimal point)?

  →  0.0875 .  →  The answer is:  "4 (four)" ;  which are: 5, 7, 8, and 0 " .

                               {Refer to digits in "bold font".}.

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So, this value:  " 0.0875 " ;  

          →  is equal to:  " 875 " ÷ { 1 followed by 4 [four] zeros } ;

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                               =  " 875 ÷ 10000 " ;

                               = " 875 ÷ 10,000 " ;

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  Using a calculator:

       " 875 ÷ 10,000 "  = " [tex]\frac{875}{10,000}[/tex] " ;

______________________________________________

                                    = " [tex]\frac{7}{80}[/tex] " .

______________________________________________

The answer is: "  [tex]\frac{7}{80}[/tex] " .

______________________________________________

Hope this is helpful to you!

       Best wishes to you!

______________________________________________

8 3/4% as a fraction in simplest form is 7/80.

In Mathematics and Geometry, a fraction simply refers to a numerical quantity (numeral) which is not expressed as a whole number. This ultimately implies that, a fraction is simply a part of a whole number.

In Mathematics, a percentage is any number that is expressed as a fraction of hundred (100). This ultimately implies that, a percentage indicates the hundredth parts of any given number.

In this exercise and scenario, we would convert the given percentage 8 3/4% into a fraction by dividing as follows;

8 3/4% = 8% + 0.75%

8% + 0.75% = 8.75%

8.75/100

Multiply both sides by 100, we have:

Fraction: 875/10000 = 7/80.

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To prove that △RST ≅ △UVW by ASA (Angle-Side-Angle) congruence, we need to show that angle S is congruent to angle U, side ST is congruent to side VW, and angle R is congruent to angle V.

To prove that △RST ≅ △UVW by ASA (Angle-Side-Angle) congruence, we need to show that angle S is congruent to angle U, side ST is congruent to side VW, and angle R is congruent to angle V.

1. Given that ∠R ≅ ∠U, we have the first angle in both triangles congruent.

2. Given that ST ≅ VW, we have the side opposite to the congruent angles congruent in both triangles.

3. Given that ∠S ≅ ∠V, we have the second angle in both triangles congruent.

Using ASA congruence, we can conclude that △RST ≅ △UVW.

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Final answer:

Triangles △RST and △UVW are congruent by ASA postulate, which states if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

Explanation:

To prove that triangles △RST and △UVW are congruent by the Angle-Side-Angle (ASA) postulate, we first observe the given congruent parts: ∠R ≅ ∠U, ST ≅ VW, and ∠S ≅ ∠V. Now, by the ASA postulate, if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent. We have two pairs of congruent angles: ∠R ≅ ∠U and ∠S ≅ ∠V, and one pair of congruent sides: ST ≅ VW (△RST's side ST is included between ∠R and ∠S, and △UVW's side VW is included between ∠U and ∠V). This satisfies the requirements for the ASA postulate, so we can conclude the triangles are congruent: △RST ≅ △UVW.

Answer:

4.5 seconds.

Step-by-step explanation:

0.75 of a picture will be taken within a second. 6 times 0.75 is 4.5 seconds.

Hope this helps!

Answer:

4.5 secs

Step-by-step explanation:

Answer: there is an app that helps you with this stuff. but are you solving for x or y

Step-by-step explanation:

Answer:

2 lbs  9 oz

Step-by-step explanation:

Lets line up the ounces and pounds and subtract

  5 lb. 10 oz.

− 3 lb. 1 oz.

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

2 lbs  9 oz

The result of subtraction of 5 lb. 10 oz. − 3 lb. 1 oz.  is: 2 lbs  9 oz.

Here, we have,

given that,

5 lb. 10 oz. − 3 lb. 1 oz.

so, we have to subtract them.

Lets line up the ounces and pounds and subtract

 5 lb. 10 oz.

− 3 lb. 1 oz.

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

2 lbs  9 oz

Hence, The result of subtraction of 5 lb. 10 oz. − 3 lb. 1 oz.  is: 2 lbs  9 oz.

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