In the triangles, TR = GE and SR = FE.


Triangles S T R and F G E are shown. Angle S R T is 56 degrees. Angle F E G is 42 degrees. Sides T R and G E are congruent. Sides S R and F E are congruent.

if Line segment G F = 3.2 ft, which is a possible measure of Line segment T S?

Answer:

$60

Step-by-step explanation:

Represent the original price by p.  Then:  

1.00 p = original price

0.20 p = discount

0.80p = price after discount = $48

Solving for p, we divide both sides by 0.80:

        $48

p = ---------- = $60

        0.80

Answer:

[tex]$\[x^2 + 22x + 121\]$[/tex]

Step-by-step explanation:

Given

[tex]$\[x^2 + 22x + \underline{~~~~}.\]$[/tex]

Required

Fill in the gap

Represent the blank with k

[tex]$\[x^2 + 22x + k\]$[/tex]

Solving for k...

To do this, we start by getting the coefficient of x

Coefficient of x = 22

Divide the coefficient by 2

[tex]Result = 22/2[/tex]

[tex]Result = 11[/tex]

Take the square of this result, to give k

[tex]k= 11^2[/tex]

[tex]k= 121[/tex]

Substitute 121 for k

[tex]$\[x^2 + 22x + 121\]$[/tex]

The expression can be factorized as follows;

[tex]x^2 + 11x + 11x + 121[/tex]

[tex]x(x + 11)+11(x+11)[/tex]

[tex](x+11)(x+11)[/tex]

[tex](x+11)^2[/tex]

Hence, the quadratic expression is [tex]$\[x^2 + 22x + 121\]$[/tex]

Answer:

6a+10= 3a+55

6a-3a= 55-10

3a= 45

a= 45/3

a= 15

The answer is (A) 15

Hope this helps^°^

Answer:

A. 15

Step-by-step explanation:

The angles are vertical angles, therefore they are congruent. We can set the two measures equal to each other.

[tex]6a+10=3a+55[/tex]

Now, solve for a. We must get a by itself on one side of the equation.

First, subtract 3a from both sides of the equation.

[tex]6a-3a+10=3a-3a+55[/tex]

[tex](6a-3a)+10=55[/tex]

[tex]3a+10=55[/tex]

Next, subtraction 10 to both sides of the equation. We subtract because 10 is being added to 3a. The inverse of addition is subtraction.

[tex]3a+10-10=55-10[/tex]

[tex]3a=55-10[/tex]

[tex]3a=45[/tex]

3 and a are being multiplied. The inverse of multiplication is division. Divide both sides of the equation by 3

[tex]3a/3=45/3[/tex]

[tex]a=45/3[/tex]

[tex]a=15[/tex]

The value of a is 15 and choice A is correct.

Answer: A.71

Step-by-step explanation: 1.set up the equation

2. 4n-18+n+9=151-5n

3.combine like terms ->  5n-9=151-5n

4.solve for n

5.10n=160

n=16

now you have to plug 16 in for n in order to get the remote exterior angle.

151-5(16)

151-80

71°

The sum of any two interior angle is equal to the third exterior angle. The value of n will be 16°. Then the correct option is B.

A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.

The triangle having the interior angle x and y, and z is the exterior angle of triangle.

m∠x = (4n − 18)°, m∠y = (n + 9)°, and m∠z = (151 − 5n)°

Then the value of n will be

We know that the sum of any two interior angle is equal to the third exterior angle. Then we have

∠x + ∠y = ∠z

4n - 18 + n + 9 = 151 - 5n

10n = 160

n = 16°

Then the correct option is B.

More about the triangle link is given below.

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Answer:

can i see a picture of the number line?

Step-by-step explanation:

Answer:

8/5

Step-by-step explanation:

There are 8 jokers combined, and 5 decks, so the mean is 8/5.

Answer:

[tex] 2w^2(w + 2)(4w - 3) [/tex]

Step-by-step explanation:

[tex] 8w^4 + 10w^3 − 12w^2 = [/tex]

First, factor out the GCF of all terms, 2w^2:

[tex] = 2w^2(4w^2 + 5w - 6) [/tex]

Now we work on the trinomial.

Think of ax^2 + bx + c.

Multiply ac

ac = 4 * (-6) = -24

Now we need two numbers whose product is -24 and whose sum is 5.

They are -3 and 8.

We break up the middle term, 5w, into a sum using these two numbers.

5w = 8x - 3w

[tex] = 2w^2(4w^2 + 8w - 3w - 6) [/tex]

Now we factor by parts. We factor a common factor out of the first two terms, and we factor a common factor out of the last two terms.

[tex] = 2w^2[4w(w + 2) - 3(w + 2)] [/tex]

[tex] = 2w^2(w + 2)(4w - 3) [/tex]

Answer:

In a right triangle, the sine of one acute angle, A, equals the cosine of the other acute angle, B. Since the measures of these acute angles of a right triangle add to 90º, we know these acute angles are complementary. ∠A is the complement of ∠B, and ∠B is the complement of ∠A.

Step-by-step explanation:

===================================================

Explanation:

A graph is a nice addition (and it will likely help us see the vertex directly), but it isn't necessary because we can use the equation given to us. Though I recommend using a graphing calculator to confirm the answer.

The original function is the same as y = 1x^2+8x + (-2). We see that it is in the form y = ax^2+bx+c where

a = 1

b = 8

c = -2

Use the values of 'a' and b to get the value of h, which is the x coordinate of the vertex.

h = -b/(2a)

h = -8/(2*1)

h = -4

The x coordinate of the vertex is x = -4. Plug this into the original equation to get

f(x) = x^2+8x-2

f(-4) = (-4)^2 + 8(-4) - 2

f(-4) = -18

Plugging x = -4 into f(x) leads to y = -18. The point (-4, -18) is on the parabola. Furthermore, this is the vertex (h,k)

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

Alternatively, you can complete the square as shown below

y = x^2 + 8x - 2

y = (x^2 + 8x) - 2

y = (x^2 + 8x + 0) - 2

y = (x^2 + 8x + 16 - 16) - 2

y = (x^2 + 8x + 16) - 16 - 2

y = (x+4)^2 - 18

y = 1(x+4)^2 - 18

y = 1(x-(-4))^2 - 18

The last equation is in the form y = a(x-h)^2 + k with (h,k) = (-4,-18) being the vertex. The 16 is the result of taking half of 8 and squaring that result. We have 16-16 = 0 to make sure that we don't change the equation and keep things balanced. This is the same as adding 16 to both sides. All of this is done so we can end up with the (x+4)^2 perfect square portion.You can expand out (x+4)^2 - 18 and you should get x^2+8x-2 again.

Answer:

D

Step-by-step explanation:

It's a guess because none of them look like the exponential form. However, I think D is probably the answer you want.

On this site it should be written as C = 15^3.

Answer:

[tex]y > 125[/tex]

Step-by-step explanation:

[tex]y + \frac{3}{8} > 16 \\ y > 16 - \frac{3}{8} [/tex]

[tex]y > (16 \times 8) - ( \frac{3}{8} \times 8) [/tex]

[tex]y > 128 - 3[/tex]

[tex]y > 125[/tex]

Answer:

Child ticket = $16.

Step-by-step explanation:

Let adult tickets = a;

child ticket = c.

2a + c = 94 — eq no. 1,

2a + 2c = 110 — eq no. 2,

then,from eq 1,

c = 94 - 2a. —eq no. 3.

Substitute eq 3 into eq 2,

2a + 2(94 - 2a) = 110

2a - 4a = 110 - 188

-2a /-2 = -78 / -2

a = 39.

Substitute value of a into eq 3,

c = 94 - 2(39)

= 94 - 78

c = 16.

Thus, child ticket = $16.

Answer:

Solving 5x + y = 5 and - 3x + 2y = 6 gives (4/13,45/13) Similarly solve other combinations by observing graph to get other coordinates. From the figure we have obtained coordinates of corners as:

Step-by-step explanation:

The Solution for the linear equation is ( 6, -7)

First order equations include linear equations. In the coordinate system, the linear equations are defined for lines. A linear equation in one variable is one in which there is a homogeneous variable of degree 1 (i.e., only one variable). Multiple variables may be present in a linear equation.

Given:

2x + y = 5.......................(1)

and, 3x + 2y = 4....................(2)

Multiply the equation (1) by 2 we get

4x + 2y = 10 ....................(3)

Solving Equation (2) and (3), we get

  3x  +  2y  = 4      

  4x  +  2y  = 10

-         -           -

_____________

    -x = -6

      x= 6

and, y= 5- 2x = 5-2(6) = -7

Hence, the solution is (6, -7)

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Answer: The solution for the system is (2, -7)

Step-by-step explanation:

Ok, here we have linear relationships.

A linear relationship can be written as:

y = a*x + b

where a is the slope and b is the y-axis intercept.

For a line that passes through the points (x1, y1) and (x2, y2), the slope can be written as:

a = (y2 - y1)/(x2 - x1).

In this case, we have two lines:

ya, that passes through:

(-8, -5) and (-3, -6)

Then the slope is:

a = (-6 - (-5))/(-3 - (-8)) = (-6 + 5)/(-3 + 8) = -1/5

now, knowing one of the points like (-3, - 6) we can find the value of b.

y(x) = (-1/5)*x + b

y(-3) = -6 = (-1/5)*-3 + b

-6 = 3/5 + b

b = -6 - 3/5 = -33/5

then the first line is:

ya =  (-1/5)*x  -33/5

For the second line, we know that it passes through the points:

(-8, -15) and (-3, -11)

Then the slope is:

a = (-11 - (-15))/(-3 -(-8)) = (-11 + 15)/(-3 + 8) = 4/5

The our line is:

y(x) = (4/5)*x + b

and for b, we do the same as above, using one of the points, for example (-3, -11)

y(-3) = -11 = (4/5)*-3 + b

b = -11 + 12/5 = -(55 + 12)/5 = -43/5

then:

yb = (4/5)*x - 43/5.

Ok, our system of equations is:

ya = (-1/5)*x  -33/5

yb = (4/5)*x - 43/5.

To solve this, we suppose ya = yb

then:

(-1/5)*x + -33/5 = (4/5)*x - 43/5.

-33/5 + 43/5 = (4/5)*x + (1/5)*x

10/5 = 2 = (4/5 + 1/5)*x = x

2 = x

now we evaluate x = 2 in one of the lines:

ya = (-1/5)*2 -33/5 = -2/5 - 33/5 = -35/5 = -7

Then the lines intersect at the point (2, - 7), which is the solution for the system.

Answer:

h(-5)=22

Step-by-step explanation:

Replace x with -5.

[tex]h(-5) = (-5)2-5(-5) + 7[/tex]

Simplify.

[tex]h(-5)=-10+25+7[/tex]

Simplify.

[tex]h(-5)=22[/tex]

Answer:

x = 18

Step-by-step explanation:

Because the 2 lines are parallel we can use same side interior theorem to find  x

This would mean the equation is 6x + 30 + 2x + 6 = 180

When you solve that this would be 18

Answer:

x = 18

Step-by-step explanation:

→ Utilise the fact that interior angles add up to 180

6x + 30 + 2x + 6 = 180

→ Simplify

8x + 36 = 180

→ Minus 36 from both sides to isolate 8x

8x = 144

→ Divide both sides by 8 to isolate x

x = 18

Answer:C and F are correct

Step-by-step explanation:

got it right on edge

Answer:

[tex]$x=\sqrt{\frac{7(4+\sqrt{15})}{2}} $[/tex]

Step-by-step explanation:

From the way it is written, the [tex]x[/tex] is outside the square root. I will rewrite it as:

[tex]x\sqrt{5} =x\sqrt{3} +\sqrt{7}[/tex]

[tex]x\sqrt{5}-x\sqrt{3}=\sqrt{7}[/tex]

[tex]x(\sqrt{5} - \sqrt{3} )=\sqrt{7}[/tex]

[tex]$x= \frac{\sqrt{7} }{\sqrt{5} - \sqrt{3}} \implies \frac{\sqrt{7}(\sqrt{5} + \sqrt{3}) }{2} $[/tex]

[tex]$x=\frac{1}{2} \sqrt{7} (\sqrt{5} + \sqrt{3} )$[/tex]

[tex]$x=\frac{\sqrt{35}}{2} +\frac{ \sqrt{21}}{2} $[/tex]

[tex]$x=\frac{\sqrt{35}+\sqrt{21}}{2} $[/tex]

Multiply denominator and numerator by 3

[tex]$x=\frac{3\sqrt{35}+3 \sqrt{21}}{6} $[/tex]

Factor [tex]\sqrt{3}[/tex]

[tex]\sqrt{3} (\sqrt{105}+3 \sqrt{7})[/tex]

[tex]$x=\frac{\sqrt{3} (\sqrt{105}+3 \sqrt{7})}{6} $[/tex]

Divide denominator and numerator by [tex]\sqrt{3}[/tex]

[tex]$x=\frac{\sqrt{105}+3 \sqrt{7}}{2\sqrt{3} } $[/tex]

Let's rewrite it again

[tex]$x=\frac{\sqrt{ (\sqrt{105}+3 \sqrt{7})^2}}{\sqrt{12} } $[/tex]

[tex]$x=\sqrt{ \frac{1}{12} \cdot (\sqrt{105}+3 \sqrt{7})^2}$[/tex]

It is already in the form [tex]$\sqrt{\frac{a}{b} } $[/tex]

Expanding the perfect square, we have

[tex]63+42\sqrt{15}+105[/tex]

[tex]$\frac{63}{12} +\frac{42\sqrt{15}}{12} +\frac{105}{12} $[/tex]

[tex]$\frac{21}{4} +\frac{7\sqrt{15}}{2} +\frac{35}{4} $[/tex]

Factor [tex]$\frac{7}{2} $[/tex]

[tex]$\frac{7}{2} (4+\sqrt{15} )$[/tex]

Therefore,

[tex]$x=\sqrt{\frac{7}{2} \left(4+\sqrt{15} \right)} $[/tex]

[tex]$x=\sqrt{\frac{7(4+\sqrt{15})}{2}} $[/tex]

Answer:

c) p = 3/q

Step-by-step explanation:

If 3 is divided by a smaller number "q", then it would result in a larger number "p".

Example:

1. Substitute 3 for "q"

3/3 = 1

q = 3

p = 1

2. Substitute 1 for "q"

3/1 = 3

q = 1

p = 3

When "q" decreased, "p" increased.

Step-by-step explanation:

c) p=3/q

i can confirm after 10.30

Answer:

Heres the graph:

Step-by-step explanation:

Constant is $2 dollars per bag od candy or just 2.

Answer:

2

Step-by-step explanation:

from (0,0) ⇒ (1,2) ⇒ (2,4) ⇒ (3,6)

∴ 2

Answer:

20

Step-by-step explanation:

I believe it's 20 because you multiply 20 . with 60 and 80 and it will give 1200 and 1800.

Answer:

It should be 20

Step-by-step explanation:

The question is asking multiply the serving by __ to find amount of pretzels.

Be careful what is the question is asking.

30*20=600

60*20=1200

90*20=1800

and continue on...

Pls give brainliest

Answer:

Option (B):3

Step-by-step explanation:

S.A of Box J =57ft^2 ; using formula 2(lb+lh+hb)

S.A of BoxF=54Ft^2;using formula (6a^2)

Differenceof S.A of boxes:57-54=3

Answer:

5/8 of the game

Step-by-step explanation:

Half of a quarter is 1/2, and 1 quarter is already done, therefore 1/2, or to simplify it 1/8, plus 2/8, would be 3/8. Now, a quarter is 1/4th of something therefore there must be 4 quarters in a total.so that means that there are 8 halfves  in total , so 8-3=5, so the fractional parts of the game left is 5/8.

The part of the game i.e. left should be [tex]5\div 8[/tex]

Since the half of the quarter is one-half. And, the one quarter is done so one-half is remaining. That means

[tex]= 1\div 8 + 1\\\= 2\div 8[/tex]

Since one-fourth should be of something also there are total 4 quarters that means there are 8 halves.

So, remaining it should be

= 8 -3

= 5

Hence, The part of the game i.e. left should be [tex]5\div 8[/tex]

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Answer:

x=9

Step-by-step explanation:

PQ + QR + RS = PS

2x-6 + 1 + x-4 = 18

Combine like terms

3x -9 = 18

Add 9 to each side

3x-9+9= 18-9

3x = 27

Divide by 3

3x/3 = 27/3

x = 9

Answer:

RS=5

Step-by-step explanation:

solve for x:

2x-6+1+x-4 = 18

combine like terms

3x-9=18

subtract both sides to make x isolated

3x=27

divide by 3 to get x

x=9

RS=x-4

RS=9-4

RS=5

Answer:

1 1/2 miles / hour

Step-by-step explanation:

We want distance / time

3/4 miles

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

1/2 hour

3/4 ÷ 1/2

Copy dot flip

3/4 * 2/1

3/2

1 1/2 miles / hour

Answer:

D

Step-by-step explanation:

Multiple (3/4)  by 2 to find the information for one hour)

6/4 in one hour

3/2 or 1 + 1/2 mi/h

D is the answer

Table Given in the question :

Open = HT 111 = 8

Side = 1111 = 4

Side = HT 111 = 8

Answer:

The probability of landing on the open end is greater.

Step-by-step explanation:

Given the experimental probability distribution :

Open = HT 111 = 8

Side = 1111 = 4

Side = HT 111 = 8

The experimental probability is the ratio of the number of times an event occurs and the total number of trials.

P(A) = number of times A occurs / total number of trials

Where A is defined event.

COMPARING the probabilities of open and closed events

P(open) = 8 / 20 = 2 / 5

P(closed) = 4 / 20 = 1/5

2/5 > 1/5

P(open) > P(closed)

Answer:

a) x greater than or equal to 10

b) x = 9

Step-by-step explanation:

a)

[tex]x + 5 \geqslant 15 \\ x \geqslant 15 - 5 \\ x \geqslant 10[/tex]

b)

[tex]2x < 18 \\ x = \frac{18}{2} \\ x = 9[/tex]

Step-by-step explanation:

yes the f( x) and g( x) is inverse each other.

f(x) = 3x-5

3x-5=0

x=5/3

g(x) = x+5/3

5x/3

x=3/5