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.

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:

101 squared not rational

-25 squared is rational

pi or any number times pi is not rational

Step-by-step explanation:

Answer:

-22.5

Step-by-step explanation:

-15- |-7.5|

after taking the absolute value off, -7.5 would become positive 7.5. But then the negative outside the absolute value makes it negative again.

-15-7.5

=-22.5

The simplified expression -15 - |-7.5| is equal to -22.5.

To simplify the expression -15 - |-7.5|, we'll follow these steps:

Evaluate the absolute value: |-7.5|.

The absolute value of a number is its distance from zero on the number line. In this case, |-7.5| is equal to 7.5 because 7.5 units away from zero.

Substitute the absolute value into the expression:

-15 - 7.5.

Perform the subtraction:

-15 - 7.5 = -22.5.

Therefore, the simplified expression -15 - |-7.5| is equal to -22.5.

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Answer:

24 tons

Step-by-step explanation:

My senses point to this is the correct answer.

Answer:

See below

Step-by-step explanation:

5/8 - 1/4 = 3/8ths of L  = 9 tons ......    

3/8 L = 9

L  =  9 * 8/3

  = 24 tons full load

1) [tex]\overline{UT}[/tex]

2) [tex]\overline{UT} \cong \overline{UT}[/tex]

3) [tex]\overline{BT} \cong \overline{EU}[/tex]

4) [tex]\overline{BU} \cong \overline{ET}[/tex]

5) [tex]\triangle UBT \cong \triangle TEU[/tex] by SSS

6) CPCTC

Answer:

To rewrite 1 as 10 to power, you'd write 10^0 (ten to the power of zero).

Any non-zero number with the power of zero equals one. You might be wondering why, so to prove this theorem...

2^1

-----

2^1

Since the numbers are the same on the numerator and denominator, we can agree that the fraction above is equal to 1, yes? It is also equal to...

2^1-1

...because of the quotient rule. And what does 1-1 equal? 0. So you'd get

2^0

This is known as the "zero-exponent rule!"

Hope this helped.

Step-by-step explanation:

Answer:

11. When 3 students are working, they each need to plant 36 trees. So the club must plant 36*3 = 108 trees total. The equation would be t = 108/s, and the constant of proportionality is 108.

12. The constant of proportionality represents the number of trees the club needs to plant regardless of the number of participants.

Answer:

[tex]9 \frac{5}{8} [/tex]

Step-by-step explanation:

[tex]1. \: lcd = 24 \\ 2. \: \frac{2 \times 8}{3 \times 8} + 9 \times \frac{24}{24} - \frac{1}{24} \\ 3. \: \frac{16}{24} + \frac{216}{24} - \frac{1}{24} \\ 4. \: \frac{16 + 216 - 1}{24} \\ 5. \: \frac{231}{24} \\ 6. \: \frac{77}{8} \\ 7. \: 9 \frac{5}{8} [/tex]

Answer: 0.5 < x < 16.5.

Step-by-step explanation: Two sides of triangle: 8.0 units and 8.5 units

Measure of third side = x

According to the triangle's inequality,

Sum of any two sides > third side.    (i)

Difference between the sides < third side.    (ii)

If x is the third side, then

x < 8+8.5   [Using (i)]

i.e. x< 16.5  

Also, x > 8.5-8   [Using (ii)]

i.e. x> 0.5

Hence, Range of possible sizes for side x would be 0.5 < x < 16.5.

The range of possible sizes for side x is,

⇒ 0.5 < x < 16.5

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

Two sides of the triangle are 8.5 and 8.

Now, The range of possible sizes for side x is,

⇒ x < 8.5 + 8

⇒ x < 16.5

⇒ x > 8.5 - 8

⇒ x > 0.5

Thus, The range of possible sizes for side x is,

⇒ 0.5 < x < 16.5

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Answer: 153

Step-by-step explanation:

The maximum number of dots that can be seen from one position is 153 dots.

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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Answer: 4

Step-by-step explanation: 3%12=4

1) [tex]\overline{UP}[/tex]

2) [tex]\overline{UP} \cong \overline{UP}[/tex]

3) [tex]\overline{UR}[/tex]

4) [tex]\overline{PR}[/tex]

5) [tex]\triangle OUP \cong \triangle RUP[/tex] by SSS

6) CPCTC

Answer:

Medunno got the first pic, now i help with the second pic.

Step-by-step explanation:

Draw segment PU (don't forget the line above)

PU ≅  PU  reflexive property

UO≅ UR   given

PO≅ PR  given

△OUP ≅ △RUP   by SSS  congruence postulate

∠O ≅ ∠R  corresponding parts of congruent triangles are congruent.

The size of ∠QTW in degrees is 72°. See the explanation below. This is based on the concept of opposite sides in a quadrilateral.

QSUWY which is a pentagon is regular that mean:

∠QYW = 108°

The quadrilateral QTWY is a cyclic one. This means that we can apply the rule that states that opposites sides must add up to 180°

Thus, ∠QTW =

180 - 108

= 72°

A closed quadrilateral has four sides, four vertices, and four angles. It is a form of polygon.

In order to create it, four non-collinear points are joined. Quadrilaterals always have a total internal angle of 360 degrees.

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Full Question:

See the attached image for missing details.

[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

Answer: #1) 3. The semicircle has twice the area of the circle

#2) 3. 28.26 cm

Step-by-step explanation:

#1) The formula for area of circle is A=πr².

First, plugging in the radius for the circle, A=π(5)², we get an area of about 78.54 inches².

Plugging in the radius for the semicircle, A=π(10)², which is equal to 314.159.... However, since it is a SEMI-circle, we will divide this value by 2 to give us an area of about 157.08 inches².

Comparing the two areas, we see the semicircle has twice the area of the circle as 78.54 x 2 = 157.08.

#2) Again use the area of circle formula, A=πr². The radius is half the diameter, so half of 6cm=3cm, meaning r=3. plug it in.

A= π(3)²

A= 28.27 cm²

Answer:

Step-by-step explanation:

This expression involves the distributive property. In the distributive property, there is a number followed by an equation in parenthesis.

3(n+6)

To simplify it, you have to multiply the first number by each number in the parenthesis, separately:

3(n+6)

3n + 3(6) or 3xn + 3x6 (same thing)

3n+18

Finally, we can check the other 4 choices to double check.

A. 3n+6 (wrong)

B. 2(n+6) + (n+6)=

2xn + 2x6 + n + 6

2n + 12 + n + 6

combine like terms, or all the terms that are the same. start with the Ns, then the numbers:

2n+n + 12+6

3n+18

C. 2(n+6)+n= 2n+2(6) +n = 2n+12+n= 2n+n+12= 3n+12

D.3n+18

E. 2n+2+n+4= 2n+n+2+4= 3n+6

Answer= B and D

hope this helps :))

Answer: 3n+18 bcz of the distributive property

Step-by-step explanation:

b & d

olution

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Let the one's digit be y and tens digit be x,

Number = 10x + y

Then,x=3y⋯(i)

Reversed number = 10y + x

A.t.Q :- (10x+y)−(10y+x)=36 Put x = 3y in eq. (i)

⇒9x−9y=36

⇒x−y=4⋯(ii)

⇒3y−y=4

∴2y=4  x=3y  ∴x=6

y=2

∴ Number = 62

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

The expression  3x²+x+5 is the sum of 3 terms and coefficients are 3 and 1 therefore, Neither Joanna nor Linne is correct.

An algebraic expression is consists of variables, numbers with various mathematical operations,

The given expression is,

3x²+x+5.

According to Joanna, the entire expression is the sum of 4 terms.

and according to Linne the coefficients are 3 and 0.

Since, The expression is the sum of 3 terms:

Square power of x, x and a constant 5.

Also, the coefficient of x² is 3 and coefficient of x is 1.

Therefore, the Joanna and Lienna both are wrong.

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Answer:

awnser B and fbe is 55

Step-by-step explanation:

the entire picture is 180 so cut in half there for 90 ok abfe is 90 so bigger section is always 55 and smaller is 35 ok

If the measure of ∠ABD is 6.2 times greater than the measure of ∠CBD=25° and if ∠ FBE and ∠ EBD are congruent then ∠ FBE =65°.

Given that the measure of ∠ ABD is 6.2 times greater than the measure of ∠ CBD and ∠ FBE and ∠ EBD are congruent.

We are required to find the measure of ∠ CBD and ∠ FBE.

∠ABD=6.2*∠CBD--------1

∠ABD+∠CBD=180°

6.2 ∠CBD+∠CBD=180  (From equation 1)

7.2 ∠CBD=180

∠CBD=180/7.2

∠CBD=25°

∠ABD=6.2*25

=155°

∠ABD=90+∠EBD

155=90+∠EBD

∠EBD=155-90

∠EBD=65°

Because ∠ FBE and ∠ EBD are congruent, ∠ FBE =65°.

Hence if the measure of ∠ABD is 6.2 times greater than the measure of ∠CBD=25° and if ∠ FBE and ∠ EBD are congruent then ∠ FBE =65°.

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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.

Answer:

Step-by-step explanation:

n(U)=100%

n(S)=70%

n(W)=15%

n(S union w compliment)=20%

n(s intersection W)=?

n(u)=n(s)+ n(w)+ n(s union w compliment)- n(s intersection w)

or 100%=70% +15%+ 20% - n( s intersection w)

or 100%= 95%- n(s intersection w)

or 100%-95%=n(s intersection w)

or 5%= n( s intersection w)

now;

n(only w)=n(w)- n(s intersection w)

              =15%- 5%

               =10%

10%of people only like winter season.

i think the question is to find people who only like winter season.

if not then ans is 15% according to question.

a) The illustration of the given information in a Venn diagram is attached.

b) The percentage of people who liked both seasons is 45%.

c) If 180 people liked the summer season only, proportionately, the number of people who liked the winter season only is 300.

The Venn diagram, which shows similarities and contrasts, can be illustrated based on the given percentages.

Percentages are one of the ways to depict proportions, which are the equation of two ratios.

The percentage of survey people who liked the summer season = 60%

The percentage of survey people who liked the winter season = 70%

The percentage of survey people who liked none of the seasons = 15%

The percentage of participants who liked one of the seasons = 85% (100% - 15%)

The total percentage of survey people who liked either summer or winter = 130% (60% + 70%)

b) The percentage of survey people who liked both seasons = 45% (130% - 85%)

The percentage that liked only summer = 15% (60% - 45%)

The percentage that liked only winter = 25% (70% - 45%)

c) 180 people liked summer only

180 = 15%

Proportionately, if 180 = 15% of the people, the total number of people = 1,200 (180/15%)

The number of people who liked winter season only = 300 (1,200 x 25%)

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Answer:

1. Ratio

2. Unit Rate

3. Scale Drawing

4. Similar Figures

5. US Customary System

6. Rate

7. Scale

Step-by-step explanation:

Most of them are just definitions