The vertex angle of an isoceles triangle measures (a+15) ° and one of the base angles measures 7a °. Find a and each angle measure.

Answer: We start with 6 reams of copy paper and 8 teachers.

a) if we distribute the paper equally between all the teachers, then each teacher receive 6/8  (here we are dividing the total number of reams by the number of people that we are are splitting it). but 6/8 is less than one, so we must open the reams in order to split them.

b) If there were twice as many reams of paper, then we will have 2*6 = 12 reams of paper, and if there where half the number of teachers, then we have 8/2 = 4 teachers.

Doing the same procedure as before, we have 12 teams for 4 teachers, then each teacher has 12/4 = 3 reams

before, each teacher received 6/8 reams, and now, each one receive 3.

if we want to know the change, we need to see the difference between these numbers, so 3 - 6/8 =  3*8/8 - 6/8

notice that i am multiplying the 3 by 8/8, this is one, but  this way i can have the same denominator in both numbers.

24/8 - 6/8 = 18/8 = 9/4 = 8/4 + 1/4 = 2 + 1/4

so each teacher receive 2 + 1/4 reams than before.

Check the picture below.

so, bearing in mind that vertical angles are equal, thus ∡AED = ∡BEC, and we know that ∡BEC = 52 = ∡AED, so those two angles added up are 104°.

now, a circle has a total of 360°, if we take away those 104° from the red angles, what's leftover is just 256°, well, the green angles there are also vertical angles and thus twins, so each one will take half of 256°.

∡BEA = 128° = ∡CED.

Answer:

see explanation

Step-by-step explanation:

Multiply through by the lowest common multiple of u, v and f, that is uvf

uvf × [tex]\frac{1}{v}[/tex] + uvf × [tex]\frac{1}{u}[/tex] = uvf × [tex]\frac{1}{f}[/tex], that is

uf + vf = uv ← factor out f on the left side → (1)

f(u + v) = uv ← divide both sides by (u + v)

f = [tex]\frac{uv}{u+v}[/tex]

(b)

Using line (1)

uf + vf = uv ( subtract uv from both sides )

uf + vf - uv = 0 ( subtract uf from both sides )

vf - uv = - uf ← factor out v on the left side

v(f - u) = - uf ← divide both sides by (f - u)

v = - [tex]\frac{uf}{f-u}[/tex]

To solve the given equation, w need to review some rules:

The given equation is :

  ⇒⇒⇒⇒ rule (2)

  ⇒⇒⇒⇒ rule (1) and rule (2)

          ⇒⇒⇒⇒ rule (3)

removing the nature logarithm from both sides

∴ x = 4

So, the correct answer is option (2) ⇒⇒⇒⇒ x = 4

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The solution of the logarithmic equation is x = 4

The power to which a number must be increased in order to obtain another number is known as the logarithm. A power is the opposite of a logarithm. In other words, if we subtract an exponentiation from a number by taking its logarithm

The properties of Logarithm are :

log A + log B = log AB

log A − log B = log A/B

log Aⁿ = n log A

Given data ,

Let the logarithmic equation be represented as A

Now , the value of A is

[tex]ln[e^{ln ( x )} ] + ln[e^{ln (x^{2} )} ] = 2ln(8)[/tex]

On simplifying , we get

The value of ln e = 1

From the laws of logarithm , we get log Aⁿ = n log A

ln ( x ) ln ( e ) + ln ( x )² ln ( e ) = 2 ln ( 8 )

On further simplification , we get

ln ( x ) + ln ( x )² = ln ( 8 )²

From the laws of logarithm , we get log A + log B = log AB

ln ( x )³ = ln ( 64 )

ln ( x )³ = ln ( 4 )³

So , the value of x = 4

Hence , the logarithmic equation is solved

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keeping in mind that perpendicular lines have negative reciprocal slopes, let's find the slopes of these two, if they're indeed perpendicular, they'll be negative reciprocal of each other, meaning one slope will be the same as the other, but negative and upside-down, and thus their product will just be -1.

[tex]\bf (\stackrel{x_1}{-2}~,~\stackrel{y_1}{-1})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{-4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-4}-\stackrel{y1}{(-1)}}}{\underset{run} {\underset{x_2}{1}-\underset{x_1}{(-2)}}}\implies \cfrac{-4+1}{1+2}\implies \cfrac{-3}{3}\implies \boxed{-1} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf (\stackrel{x_1}{5}~,~\stackrel{y_1}{-3})\qquad (\stackrel{x_2}{-2}~,~\stackrel{y_2}{-8}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-8}-\stackrel{y1}{(-3)}}}{\underset{run} {\underset{x_2}{-2}-\underset{x_1}{5}}}\implies \cfrac{-8+3}{-7}\implies \cfrac{-5}{-7}\implies \boxed{\cfrac{5}{7}}[/tex]

well, 5/7 is not the negative reciprocal of -1.

A rectangle with sides 15 and w has perimeter

[tex]2p = 2(15+w) = 2w+30[/tex]

We want this quantity to be at most 50, so it must be less than or equal to 50:

[tex]2w+30\leq 50[/tex]

For the record, this implies that

[tex]2w\leq 20 \iff w \leq 10[/tex]

So, the width can be at most 10.

Answer:

2x+30< 50   ...answer : A

Step-by-step explanation:

the perimeter is :  P = 2(L+W)

let : L= x   given : L=15

P= 2(x+15)

The perimeter of the rectangle is, at most, 50:   P<50

2(x+15) < 50

2x+30< 50   ...answer : A

Answer:

a ) total number of sixth in 5 ribbon will be 6\times 5 = 30

b) length of each sixth will be = 5.97 inches

Step-by-step explanation:

given data:

Number of pieces of ribbon is 5

each piece length 1 yard

total number of cut in one piece of ribbon = 6

a) one piece of ribbon consist of 6 sxiths

therefore total number of sixth in 5 ribbon will be 6\times 5 = 30

b) each ribbon length is 1 yard

so, whole ribbon is divided into 1\6 yard length which is length of individual division

we know that one yard is 36 inches

therefore, in 1/6 yard = 5.97 inches

Answer:

a.  She will have 30 sixths after cutting all the ribbons.

b. 6 inches.

Step-by-step explanation:

a. You know that the lenght of each piece of ribbon is 1 yard.

She cuts each ribbon into sixths, then the lenght of each one of them is:

[tex]\frac{1}{6}\ yd[/tex]

So:

[tex]\frac{6}{6}=1\ yard[/tex]

Since Faye has 5 pieces of ribbon, after cutting all the ribbons she will have:

[tex](5)(\frac{6}{6})=\frac{30}{6}[/tex]

She will have 30 sixths after cutting all the ribbons.

b. You need make the conversion from yards to inches.

Knowing that [tex]1\ yd=36\ in[/tex], you get:

[tex](\frac{1}{6}\ yd)(\frac{36\ in}{1\ yd})=6\ in[/tex]

Answer:

850 rounds up to 900

Step-by-step explanation:

if it's 5 or more it will go up, if it were 840 it'll drop to 800

The required expression would be -2(y+7) represents which is negative two times the sum of y and 7.

Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.

What are Arithmetic operations?

Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions.

We have been given that y represents a number.

To determine the expression for negative two times the sum of y and 7.

As per the given statement,

So the expression would be -2(y+7).

Hence, the required expression would be -2(y+7) represents which is negative two times the sum of y and 7.

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Answer: 5b = 15

Step-by-step explanation:

5b + 2 = 17

     - 2     -2

5b = 15

The two steps are:

step 1  : 5b = 17 - 2

step 2 : b = 15/5

Given,

5b + 2= 17

Now,

The equation given two us is in linear form with one variable .

So,

Simplifying the equation,

5b + 2= 17

Take 2 from LHS to RHS

5b = 17 - 2

5b = 15

b = 15/5

b = 3

Thus the value of b is 3 .

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Answer:36%

Step-by-step explanation:

Answer:

25%

Step-by-step explanation:

3 ribbons/ 12ribbons= 1/12

If You simplify dividing by 3 it becomes =1/4 = 0.25

so.. this is the 25 %

Answer:

x^2-36=0

Step-by-step explanation:

x^2-36=0

(x-6)(x+6)

Answer:

[tex]x^2-36=0[/tex]

Step-by-step explanation:

Solution is 6 and -6. Lets check with each option

[tex]x^2-12x+36=0[/tex]

[tex](x-6)(x-6)=0[/tex]

x-6=0 so x=6

Solutions are 6 and 6. First option does not gives us solution 6 and -6

[tex]x^2+12x-36=0[/tex]. It is not factorable

[tex]x^2+36=0[/tex]. It is not factorable

[tex]x^2-36=0[/tex]

[tex](x+6)(x-6)=0[/tex]

x-6=0 , so x=6

x+6=0, so x=-6

[tex]x^2-36=0[/tex] is the final answer

Answer: 0.58333333333333

Step-by-step explanation: To find the decimal that is equivalent to 7/12, remember that fractions are division problems so we can divide the numerator by the denominator.

Numerator = 7

Denominator = 12

7 ÷ 12 = 0.58333333333333.

Answer:

_

.583

Step-by-step explanation:

In order to convert 7/12 to a decimal you must divide 7/12. The answer won't be a rational number, but will be a repeating decimal. You end up with .583 with 3 repeating. To show that this is repeating, you must put a little bar over the 3 (Because the 3 is the only repeating number) like so:

_

.583

I hope I was helpful!

Answer:

I believe it's D.

Step-by-step explanation:

if you add 237 + 228 you get 455. 455 divide by 2 is 227.5 which doesn't make it even.

Answer: -6

Step-by-step explanation:

When X = - 3, then Y = -6

Slope is 2.

Answer:

When x = -3, then y = -6

Step-by-step explanation:

We need to find out the value of y when x=-3

From the graph we look at the value of y

x is the input of the graph and y is the output .

In x axis the positive numbers on the right side and negative numbers on the left side . In y axis the positive numbers at the top and negative numbers at the bottom.

Given x=-3, Lets find the value of

At x=-3 the graph is at the bottom of x axis

Draw a line down at x=-3 , the line meets the graph at -6

So at x=-3 the value of y is -6

When x = -3, then y = -6

Answer:

the answer is A

Step-by-step explanation:

Answer:

(-1,5)

Step-by-step explanation:

(?,0)

(-1,0)

(5,0)

Answer:

840,000 / 306,000 = 2.7450980392

So, Greenland is about 2 and 3/4 times larger than New Guinea.

Step-by-step explanation:

Greenland, the largest island in the world, is 534,000 square miles larger than New Guinea.

Greenland is 840,000 square miles and New Guinea is 306,000 square miles. To find out how much larger Greenland is than New Guinea, we subtract the area of New Guinea from the area of Greenland:

840,000 - 306,000 = 534,000 square miles

Therefore, Greenland is 534,000 square miles larger than New Guinea.

To determine how much larger Greenland is than New Guinea, one must subtract the size of New Guinea from the size of Greenland. Given that Greenland, the largest island in the world, is 840,000 square miles and New Guinea is 306,000 square miles, you would perform the following calculation:

840,000 - 306,000 = 534,000 square miles

Therefore, Greenland is 534,000 square miles larger than New Guinea.

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Answer:

Option D. 1

Option E. 1/2

Step-by-step explanation:

we know that

Looking at the graph

The domain is the interval ----> [-1,1]

[tex]-1\leq x\leq 1[/tex]

The domain is all real numbers greater than or equal to -1 and less than or equal to 1

The range is the interval ----> [0,1]

[tex]0\leq y\leq 1[/tex]

The range is all real numbers greater than or equal to 0 and less than or equal to 1

therefore

The values that are in the range are

1 and 1/2

Answer:

D.1

E.[tex]\frac{1}{2}[/tex]

Step-by-step explanation:

We have to find the values lie in the range of function in given graph.

Let f(x) be given function

Domain takes along x- axis and range takes along y- axis.

From given graph , we can see that

Domain of function =[-1,1]

It means

[tex]-1\leq x\leq 1[/tex]

Range of function:[0,1]

It means

[tex]0\leq y \leq 1[/tex]

The value of range of given function  from 0 to 1.

Hence, option D and E are correct.

D.1

E.[tex]\frac{1}{2}[/tex]

Answer:

64

Step-by-step explanation:

2 to the power of 3 is 8 and 2 to the power of 4 is 16 and 2 to the power of 1 is 2 and 16 divided by 2 is 8 and 8 times 8 equals 64

Answer:

A. One pound of pistachios plus 1 pound of almonds cost $20

C. Reducing the number of pounds of almonds by 1 results in a total cost of $40.

E. The cost p, in dollars, of 1 pound of pistachios is modeled by 2p + 3(p – 4) = 48.

Step-by-step explanation:

Let

x ----> the cost of one pound pistachios

y ----> the cost of one pound of almonds

we know that

x=y+4 -----> equation A

2x+3y=48 -----> equation B

substitute equation A in equation B and solve for y

2(y+4)+3y=48

2y+8+3y=48

5y=48-8

y=8

Find the value of x

x=8+4 =12

therefore

The cost of one pound pistachios is $12 and the cost of one pound of almonds is $8

Verify all statements

case A) One pound of pistachios plus 1 pound of almonds cost $20.

Is True

x+y=$12+$8=$20

case B) The pistachios cost twice as much per pound as the almonds

Is false

Because

2y=2(8)=$16

$16≠$12

case C)  Reducing the number of pounds of almonds by 1 results in a total cost of $40

Is True

Because

2x+2y=2(12)+2(8)=$40

case D) The cost a, in dollars, of 1 pound of almonds is modeled by 2(a – 4) + 3a = 48.

Is false

The equation will be

2(a + 4) + 3a = 48.

case E) The cost p, in dollars, of 1 pound of pistachios is modeled by 2p + 3(p – 4) = 48

Is true

Because

p=a+4

Solve for a

a=p-4

Answer:

The slope of st is -1/3

Step-by-step explanation:

we know that

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)

[tex]m1*m2=-1[/tex]

we have

[tex]m1=3[/tex]

substitute and solve for m2

[tex](3)*m2=-1[/tex]

[tex]m2=-\frac{1}{3}[/tex]

therefore

The slope of st is -1/3

Answer: 100,335

Step-by-step explanation: Whenever you see the terms "subtract _____ from blank," the numbers in the equation will be reverse. For example, subtract 76 from 100 would be translated as 100-76. This applies here. The equation is 670,630-582,295, which is 100,335

Answer:

(a). $20,000

(b). The estimate will be lower than the actual amount.

Step-by-step explanation:

We have been given that Michael saves $423 dollars a month for college.

(a). We know that 1 year equals 12 months.

4 years = 4*12 months = 48 months.

[tex]\text{Actual amount saved}=\$423\times 48[/tex]

Since we are asked to find the estimated amount of money Michael will save in 4 years, so we will estimate both quantities as:

[tex]423\approx 400\\\\48\approx 50[/tex]

[tex]\text{Actual amount saved}=\$400\times 50[/tex]

[tex]\text{Actual amount saved}=\$20,000[/tex]

Therefore, Michael will save approximately $20,000 in 4 years.

(b).

The estimate will be lower than the actual amount as we rounded $423 down $23 to nearest hundred that is $400 and rounded 48 up 2 to nearest ten that is 40.

Therefore, the estimate will be lower than the actual amount.

Answer:

The answer is y = 11.

Answer: [tex]Range:\{0,2,6,7\}[/tex]

Step-by-step explanation:

By definition:

1) The Domain is the the set of all the input values, which are the x-coordinate of each ordered pair (the first number in each pair).

2)the Range is the set of all output values, which are  the y-coordinate of each ordered pair (the second number in each pair).

 In this case you have the following relation "G":

[tex]G=\{(-1,7),(8,2),(0,0),(6,6)\}[/tex]

Based on the definition shown before, you can conclude that the Domain of G is:

[tex]Domain: \{-1,0,6,8\}[/tex]

And the Range of G is the following:

[tex]Range:\{0,2,6,7\}[/tex]

Answer:

Step-by-step explanation:

It's highly advisable to find and use the LCD in problems like this.

21/32 has the denominator 32; if we multiply numerator and denominator each of 3/4, we get the equivalent fraction 24/32.

Now, compare 21/32 and 24/32.  It's pretty obvious that "21/32 greater than 3/4" is false; 24/32 is greater than 21/32, so 3/4 is greater than 21/32.

Answer:

21, 35 , 49

Step-by-step explanation:

21 = 3 * 7

35 = 5 * 7

49 = 7 * 7

GCF = 7

Answer:

True

Step-by-step explanation:

The base angles of an isosceles triangle are equal.

The sum of the 3 angles in a triangle = 180°, thus

vertex angle = 180° - (55 + 55)° = 180° - 110° = 70°

Answer:

x = - 4

Step-by-step explanation:

Given

2(x - 8) = x + 5x ← distribute left side and simplify right side

2x - 16 = 6x ( subtract 6x from both sides )

- 4x - 16 = 0 ( add 16 to both sides )

- 4x = 16 ( divide both sides by - 4 )

x = - 4

Answer:

He buy 12 eggs from grocery.

Because,

1 dozen of a thing(x) = 12 things(x)

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