The base of an isosceles triangle is three times as long as the side of a square. Each leg of the triangle is 1 inch more than twice a side of the square. Find the length of a leg of the triangle if the sum of perimeters is 46 inches.

[tex]\huge\underline{\underline{\boxed{\mathbb {SOLUTION:}}}}[/tex]

▪ [tex]\longrightarrow \sf{10.24}[/tex]

▪ [tex]\longrightarrow \sf{16}[/tex]

We start by obtaining it:

[tex]\longrightarrow \sf{\dfrac{10.24}{16} = 0.64}[/tex]

Therefore, we are asked how many significant figures 0.64 has. The answer is 2. In this case, the significant digits are 6 & 4.

[tex]\huge\underline{\underline{\boxed{\mathbb {ANSWER:}}}}[/tex]

[tex]\large \bm{B. \: 2}[/tex]

Answer:

x = 60°

Step-by-step explanation:

A straight angle is bascially a line with a point marked in it. That is 180°. Supplementary angles add up to 180°. Like the two right angles on the top part of the image are supplementary, as well as the two angles on the bottom part of the image.

120° + x = 180°

x = 60°

Answer:

Sales increase with a decrease in the price.

Step-by-step explanation:

Answer:

Step-by-step explanation:Yikes. Just so we’re all clear—this is not a real SAT question.

So far, Adam’s record is 6 wins/30 games. If he plays x more games, his record will be:

image

You find the minimum x such that the fraction is greater than ½, which would mean he won more than ½ of his games.

Let’s do some math!

image

So if he plays 54 more games, and wins 2/3 of them, he’ll have the same number of wins as losses. Check on that to make sure: He’ll have played 30 + 54 = 84 games, and won 6 + (2/3)54 = 42 of them. Yep, that works.

Now here is where it gets tricky (and why this question is not SAT-caliber). Remember that he’s losing 1/3 of his games. If his 52nd, 53rd, and 54th additional games were win, win, loss, then he would have had, very briefly, a winning record after his 53rd additional game.

His 55th additional game is another chance at a winning record. If he loses that game, then he’ll win the next two, and have a winning record for sure by the 57th additional game. From there, if he continues winning 2/3 of his games, he’ll have a winning record forever.

Answer:

8 or Ryan

Step-by-step explanation:

mean = sum of terms / number of terms so,

6+7+8+9+10/5=8

Answer: x = 60°

Step-by-step explanation:

    We know a circle is equal to 360°, so we can subtract from 360° to find x using vertical angles and other given details.

     Vertical (opposite) angles are equal to each other. This is why, for example, we know AGE and FGC are both 30°.

    See attached for a breakdown of the angles.

360° - 30° - 30° - 90° - 90° = 2x

120° = 2x

60° = x

Answer:

x = 60°

Step-by-step explanation:

Hello!

The sum of angles on a line is 180°.

Given that Angle G is 90°, the other measure on Line DB would also be 90°. The missing angle next to x can be called y.

The Angle y can be calculated by using the Vertical Angles Theorem. The theorem states that if two non-adjacent angles are formed by the intersection of two lines, the measures of the angles are congruent.

This means that the measure of Angle y is 30°, as the 30° angle and y are non-adjacent and are formed by the intersection of lines AC and EF.

We can now solve for x by plugging in 30° for y in the equation.

The value of x is 60°.

Answer:

Explained Below

Step-by-step explanation:

200 people with those email addys might be people you know. While collecting addys randomly is a random sample.

its straight forward

Answer:

See below

Step-by-step explanation:

5% interest = .05  :

8500 x .05 x 150days /365 days/year  = R 174 .66 = interest......

then amount to be paid = 8500+ 174.66 = R 8674.66

Answer:

80, 40, 40

Step-by-step explanation:

The rule is if the number before the tens place is 5 or more round up and if it is 4 or less round down.

I like to look at it without the rule and what makes sense.

82.14:  my choices are 80 or 90.  What number is 82.14 closer to on the number line?  80.

38.5  The choices are 30 and 40.  This number on a number line would be closer to 40

41.3  The choices are 40 and 50.  On a number line this number would be closer to 40.

Answer: H. 12

Step-by-step explanation:

Add all cost of each price of the each fabric once to get $925 (150+275+500). Then, divide 5,550/925 to get 6. Then multiply 1/3 by 6 to get 2. Then multiply 2/3 by 6 to get 4. Then add 2+4+6 to get 12.

Answer:

$0.66 per cup

Step-by-step explanation:

There are 8 cups in 2 quarts, so 5.28/8 is $0.66 per cup.

Answer:

0.66

Step-by-step explanation:

8 cups are in 2 quarts so you going to count 8 cups untill you get 5.28 and then you see how many cents that it is so its 0.66

Answer: The simplest form of ratio 6:15=2×3:5×3=2:5

Step-by-step explanation: So, 2:5 is equivalent to 6:15.

The way that this action is going to affect the mean and the mean and the median value would be decreased than what it was supposed to be.

In a frequency distribution, the mean is the number that is used to represent the average of a group of data. To get the mean, you have to add up the numbers in the data set and divide by the total number in the data set.

The formula is fx/n

When the average of $4800 is removed from the data set, the mean is going to decrease by the number and the value of fx would also decrease. Hence we can conclude that it would cause the value to reduce.

The median is the middle value, it would also cause the median in the data set to be smaller than it was.

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Answer:

It is proved because line segment AC and line segment BD are parallel.

Step-by-step explanation:

I am also trying my best. Please let me know if it’s wrong or you need more help. Have a great day!

The table completing the proof is:

Statements                      Reasons

Draw segments UT       Construction.

[tex]\overline {UT}[/tex] ≅ [tex]\overline {UT}[/tex]                      This is reflexive property.

[tex]\overline{BT}[/tex] ≅ [tex]\overline {EU}[/tex]                                Given

[tex]\overline {BU}[/tex] ≅ [tex]\overline {ET}[/tex]                              Given

ΔUBT ≅ ΔUET                 SAS congruency

∠B ≅ ∠E                               Proof

We have,

From the figure,

Step 1:

Draw segments UT.

Construction.

Step 2:

UT ≅ UT

This is reflexive property.

Step 3:

BT ≅ EU

Given

Step 4:

BU ≅ ET

Given

Step 5:

ΔUBT ≅ ΔUET

This is due to SAS.

Side-Angle-Side (SAS) Congruence.

The two sides and the included angle of one triangle are equal to the corresponding two sides and included angle of another triangle.

Step 6:

∠B ≅ ∠E

Thus,

Statements                      Reasons

Draw segments UT       Construction.

[tex]\overline {UT}[/tex] ≅ [tex]\overline {UT}[/tex]                      This is reflexive property.

[tex]\overline{BT}[/tex] ≅ [tex]\overline {EU}[/tex]                                Given

[tex]\overline {BU}[/tex] ≅ [tex]\overline {ET}[/tex]                              Given

ΔUBT ≅ ΔUET                 SAS congruency

∠B ≅ ∠E                               Proof

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[tex]\begin{array}{ccll} \stackrel{cups}{sugar}&cookies\\ \cline{1-2} \frac{3}{4}&24\\[1em] x&18 \end{array}\implies \cfrac{ ~~ \frac{3}{4} ~~ }{x}~~ = ~~\cfrac{24}{18}\implies \cfrac{ ~~ \frac{3}{4} ~~ }{\frac{x}{1}}~~ = ~~\cfrac{4}{3}\implies \cfrac{3}{4}\cdot \cfrac{1}{x}=\cfrac{4}{3} \\\\\\ \cfrac{3}{4x}=\cfrac{4}{3}\implies 9=16x\implies \cfrac{9}{16}=x[/tex]

now, the fraction is not an improper one, thus we can't quite put it in a mixed format, unless you count 0 as its whole, then I guess we can say is [tex]0\frac{9}{16}=x[/tex]

Answer:

9/16

Step-by-step explanation:

24/6=4

18/6=3

(3/4)x(3/4)=9/16

Polynomials are mathematical expressions made up of many terms.

To simplify a polynomial as much as possible, you must group all the like terms and rearrange them from higher to lower power.

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of any constant term is 0. The derivative of axⁿ it's naxⁿ⁻¹.

Multiply 3 x 3.

Subtract 1 from 3.

Multiply 2 by −12.

Subtract 1 from 2 and subtract 1 from 1.

For any term t, t¹ = t.

For any term t except 0, t⁰=1.

Answer: The solution of the polynomial 3x³ - 12x² - 2x-8 is 9x² - 24x - 2.

Answers:

- DH is correct because a line is connecting the two points D and H as shown in the image, forming a line segment.

- ED is correct because a line is connecting the two points D and E, forming another line segment, as shown in the drawing.

- EH is incorrect because in the drawing shown, there is no line connecting the two points E and H, so there would be no line segment formed between these two points.

- CD is correct because there is another line connecting the two points C and D, forming another line segment in the drawing.

Therefore, lines DH, ED, and CD are all line segments.

Answer:

◘ 12 pears

◘ 3 pineapples

◘ 10 kiwis

Step-by-step explanation:

Let [tex]x[/tex] be the number of pears bought.

Therefore:

• number of pears = [tex]x[/tex]

• number of pineapples = [tex]x - 9[/tex]

• number of kiwis = [tex]x - 2[/tex]

We know that the total cost was $13.50.

This means if she bought [tex]x[/tex] pears at $0.50 each, [tex](x - 9)[/tex] pineapples at $1.50 each, and [tex](x -2)[/tex] kiwis at $0.30 each, the total would be $13.50.

∴  [tex][x \times 0.50] + [(x-9) \times 1.5] + [(x-2) \times 0.3] = 13.50[/tex]

Expanding and multiplying:

⇒ [tex]0.5 x + 1.5x - 13.5 + 0.3x - 0.6 = 13.5[/tex]

Collect like terms:

⇒ [tex]2.3x -14.1 = 13.5[/tex]

Solve for [tex]x[/tex]:

⇒ [tex]2.3x = 13.5 + 14.1[/tex]

⇒ [tex]2.3 x = 27.6[/tex]

⇒ [tex]x = 27.6 \div 2.3[/tex]

⇒ [tex]x = \bf 12[/tex]

Therefore, she bought:

• 12 pears

•  [tex]x - 9[/tex] = 12 - 9 = 3 pineapples

• [tex]x - 2[/tex] = 12 - 2 = 10 kiwis

Marita bought 12 pears, 3 pineapples and 10 kiwis.

Arithmetic operations can also be specified by the subtract, divide, and multiply built-in functions.

Let x the number of pears bought,

y the number of pineapples bought,

z the number of kiwis bought,

Given that, Marita bought 9 more pears than pineapples and 2 fewer kiwis than pears,

y + 9 = x

y = x -9 and

z + 2 = x

z = x - 2

We know that the total cost was $13.50.

This means if she bought  pears at $0.50 each,  pineapples at $1.50 each, and  kiwis at $0.30 each, the total would be $13.50.

∴  0.50x + 1.50y+ 0.30z = 13.50

Substitute the values of y and z in equation,

⇒ 0.50x + 1.50(x -9)+ 0.30(x - 2) = 13.50

Expanding and multiplying terms in equation,

⇒  0.50x + 1.50x -13.50+ 0.30x - 0.60 = 13.50

Rearrange the like terms and apply the arithmetic operation

⇒ 2.3x - 14.1 = 13.50

⇒ 2.3x = 13.50 + 14.1

⇒ 2.3x = 27.6

⇒ x = 27.6/2.3

⇒ x = 12

Therefore, the number of pears bought = 12

So, the number of pineapples bought = 12 - 9 = 3

And the number of kiwis bought = = 12 - 2 = 10

Hence, Marita bought 12 pears, 3 pineapples and 10 kiwis.

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Answer:

4 is the length

Step-by-step explanation:

14 and 4

14 x 14 + 4 x 4 = 212

14 + 4 = 18

Answer:

8 if including the tube and 4 if just counting the roll of toilet paper itself.

Step-by-step explanation:

Well like the question says the diameter of the toilet paper is 12 cm full both including the toilet paper and the tube. But we are also told the tube has a Diameter of 4. Taking this into consideration we both know that the tube will never get smaller but we do know the roll will decrease in size by half so while keeping the diameter of the tube at 4 we evenly remove half of the other 2  and we are left with a diameter of 2 / 4 / 2 in which giving us a total diameter of 8 therefore the diameter now being 8. (pls let me know if im wrong though i doubt i am)

Answer:

C

Step-by-step explanation:

windows arent that big compared to 2 cities, distance between the and moon, or a height of a mountain. so i think C is the only reasonable answer

Answer:B. 80 students like Nepali

 C. 75 students like Social Studies only

Step-by-step explanation: The total of the ratio = the total number of students

 2 + 3 = 5

 5 parts = 200 students

 1 part = 200 ÷ 5 = 40 students

 Therefore,the students who liked Nepali(2 parts) = 2 × 40 = 80

The students who liked Social Studies(3 parts) = 3 × 40 = 120

But since 45 students liked both subjects,then those who liked Social Studies only:

120 - 45 = 75

The answers are a) attached b) 80 and c) 75

A Venn diagram is an illustration that uses circles to show the relationships among things or finite groups of things.

Given that, In a group of 200 students, the ratio of students who like Nepali and Social studies is 2:3. If 45 students like both the subjects and 20 students like none of the subjects,

The total of the ratio = the total number of students

2 + 3 = 5

5 parts = 200 students

1 part = 200 / 5 = 40 students

b) Therefore, the students who liked Nepali(2 parts) = 2 × 40 = 80

c)  The students who liked Social Studies(3 parts) = 3 × 40 = 120

Since, 45 students liked both subjects, then those who liked Social Studies only:

120 - 45 = 75

Hence, The answers are a) attached b) 80 and c) 75

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Answer:

A

Step-by-step explanation:

|-12| = 12

distance from 0 to -12 is 12

and 12 = 12

The ratios of corresponding side lengths are not equal.

Therefore, Figure B is not a scale copy of Figure A.

Here, we have to determine if Figure B is a scale copy of Figure A, we need to compare the corresponding sides of the two triangles and check if the ratios of their side lengths are equal.

Figure A has side lengths: 3.6, 2, and 5.

Figure B has side lengths: 8.9, 4, and 11.3.

Let's check if the ratios of corresponding side lengths are equal:

Ratio of corresponding side lengths of A and B:

3.6 / 8.9 ≈ 0.4045

2 / 4 = 0.5

5 / 11.3 ≈ 0.4425

The ratios of corresponding side lengths are not equal.

Therefore, Figure B is not a scale copy of Figure A.

In order for two triangles to be scale copies of each other, all corresponding side lengths must have the same ratio.

Since the ratios of side lengths in Figure A and Figure B are not equal, they are not scale copies of each other.

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Answer: Alligators

Step-by-step explanation: This entire paper is just about combining like terms.

I won't go too in depth about it since it's self-explanatory, but I'll explain it just a bit. Like terms are two terms that have the same variable. For example, 19 and 24 are like terms since they are both numbers. 15x and 18x are like terms since they are both the same variables. 2y and 5y are like terms since they are both the same variables. However, 3x and 4y are NOT like terms, they do not have the same variable.

Also, variables that have different exponential powers are also not like terms. For example, 5x^2 and 7x are not like terms as one is squares and one is to the 1st power. Similarly, 3x^3 is not the same variable as 2x^4.

When you have 5x and -2x, you subtract 5x and 2x. Thus, the combination would be 3x. When you have -4x - 2x, you would get -6x, and if you have -4x + 2x, you would get -2x.

What you were supposed to do is simplify the equations by combining like terms, and then crossing off the letters that correspond to what you have left in the expression. The remaining letters should spell out a joke.

Attached below I have provided the correct answer.

Hope this helped.

Answer:

1. 3x+5x+14x = 22x

2. 4x+7+11x = 15x+7

3. 10x+8-3x = 7x+8

4. 6x-5+x-11 = 7x-5-11 = 7x-16

5. -8x +19 + 2 - 2x = -10x+19+2 = -10x+21

6. -x+23+4x-34-x = 2x+23-34 = 2x-11

7. 105+27x-68-19x-27+x = 9x+105-68-27 = 9x+10

8. 7x+16-3x+3-2x-2x = 0x+19 = 19

9. -18 + 6 -4x+ 10 - 11x + 2 = -15x

10. 16+4x-12x-28-6x+17+x-1 = -13x +4