Find the missing length given that GH is a midsegment of the trapezoid. Base 42 and midpoint 26

Answer: Coordinates: (1,3) length RS: 3 length RT: 2 ST: 3.6

Step-by-step explanation:

a^2+b^2=c^2

3^2+2^2=c^2

9+4=c^2

13=c^2

3.6=c

The inequality is 100*[tex]3^{t}[/tex]≤ 656100.

The correct option is (B).

A statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.

Given:

From the table attached below:

a=300, r= 900/300 = 3

As, it is GP

Now,

f(t) = [tex]ar^{t-1}[/tex]

f(t) = [tex]300*3^{t-1}[/tex]

f(t) = 300/3 *[tex]3^{t}[/tex]

f(t) = 100*[tex]3^{t}[/tex]

Inequality is used to determine greater than or equal to 656100

100*[tex]3^{t}[/tex]≤ 656100

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as the following pic you can see the answer.

#diameter is 8 so radius is 4

Answer: A=9x^4

Step-by-step explanation:

Hii, do you need to find the area of a square with a side length of 3x^2? Let me help you out! (:

To find the area of a square, you need to square its side length.

Sounds strange, right?

The formula is shown below.

[tex]\LARGE\boldsymbol{A=a^2}[/tex]

Here "A' (capital A) denotes the area

"a" (lower-case a) denotes the side length

The 2 above the a tells us that we need to multiply the side length times itself.

Alright, now it's just a matter of sticking in the known values...

[tex]\sf A=(3x^2)^2[/tex]

Simplify

[tex]\sf A=9x^4[/tex]

Voila! There's our answer, cheers! (;

Hope I helped! Best wishes! (:

Reach far. Aim high. Dream big.

[tex]\underbrace[/tex]

Answer:

c2

Step-by-step explanation:

Given the polynomial f(x)=x³+5x²+2x-8 and f(1)=0.

Factorization is the process of determining the components of a given value or mathematical statement. The integers that are multiplied to create the original number are known as factors. The components of 18 include, for instance, 2, 3, 6, 9, and 18, as well as;

18 = 2 x 9

18 = 2 x 3 x 3

18 = 3 x 6

In a similar way, the factors in the case of polynomials are the polynomials that are multiplied to create the original polynomial. For instance, (x + 2) (x + 3) are the elements of x2 + 5x + 6. The original polynomial is produced when we multiply both x +2 and x +3. We can also locate the polynomials' zeros after factorization. Zeroes in this situation are x = -2 and x = -3.

2. Now, to write f(x) as the product of (x-1) and another factor.

x³+5x²+2x-8 = (x-1)(x²-6x+8).

3. Now, to write f(x) as the product of three linear factors.

x³+5x²+2x-8 = (x-1)(x²-6x+8)= (x-1)(x-4)(x-2)

4. Look at the sketch below.

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Answer:

The second and third equations are correct.  

Step-by-step explanation:

Note that the equations are all the same, with the exception of the math operation (=,>,<,[tex]\leq[/tex], etc.).  Let's do one calculation and then decide which of the statements is true.

The components may be simplified by separating the numbers from the exponents and doing the calculations separately:

(2.06x10^-2)(1.88x10^-1)  becomes (2.06*1.88)*(10^-2 * 10^-1)

Left Side:

(2.06*1.88) = 3.91

(10^-2 * 10^-1) = 10^-3  [The exponents add when multiplying]

(2.06x10^-2)(1.88x10^-1) = 3.91x10^-3

Right side:

(7.69/2.3) = 3.343

(10^-2)/(10^-5) = 10^3  [The bottom exponent is subtracted from the top. ( -2 - (-5)) = 3   ]

(7.69x10^-2)/(2.3x10^-5) = 3.343x10^3

For all equations:

LEFT                    RIGHT

3.91x10^-3       3.343x10^3

We can now answer the question.  Is the left side (3.91x10^-3 )      

A.  <

B.  =>

C.  >, or

D.  =

to the right side (3.343x10^3)

We can drop the 10^-3 to make the comparison simpler, since it is the same on both sides.  Think of it as dividing both sides by 10^3.

                                             Correct?

A.    3.91   <   3.34                NO

B.     3.91 =>  3.34                YES  

C.    3.91  >    3.34, or          YES

D.    3.91  =    3.34                NO

Answer:

Larger percentage of kids

Step-by-step explanation:

Kids: 32/40 = 4/5

Adults: 25/32 = 5/8

4/5 > 5/8

Answer:

The answer is 10/143

Step-by-step explanation:

Answer:

4/8 = y/14

Step-by-step explanation:

These triangles are similar (see 1 sign of similarity of triangles)
Let's rotate the 2nd triangle, we'll see that the ratio of y to 14 is 4/8

If points d and f are on side ab and points e ang g are on side ac then line segment de and fg are parallel.

Given There is a triangle abc.

Parallel lines are those lines that do not meet at any point. If we draw a triangle abc and plot points d and f are marked on side ab and points e and g are marked on side ac then the line segment fg is parallel to de because both the line segments are drawn from the points which are on the sides opposite to each other. We have assumed a simple triangle because no description is given for the triangle.

Hence the line segment fg is parallel to de if drawn points d and f marked on ab and points e and g are marked on ac.

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Answer:D-E is parallel to FG which is parallel to B-C meaning all three are parallel

Step-by-step explanation:

The diameter of the cell model according to the taks content is; 14in.

Volume of paint = 615.44 square inches

π = 3.14

Volume of a sphere = 4πr²

615.44 = 4 × 3.14 × r²

615.44 = 12.56/r²

r² = 615.44 ÷ 12.56

r² = 49

r = 7

Hence, the diameter of the cell is; 2 × r = 2 × 7 = 14in.

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Answer:

B

Step-by-step explanation:

the range of y=|x| is not all real numbers its [0,inf)

sign - ...

Zekrom

Step-by-step explanation:

well you can distribute the sqrt(15x) to the (√3x + √5) and then combine the radicals using the product property of radicals: [tex]\sqrt[n]{a} * \sqrt[n]{b} = \sqrt[n]{ab}[/tex].

[tex](\sqrt{3x} + \sqrt{5})\sqrt{15x} + 2\sqrt{30}\\(\sqrt{3x} * \sqrt{15x}) + (\sqrt{5} * \sqrt{15x}) + 2\sqrt{30}\\\sqrt{45x^2} + \sqrt{75x} + 2\sqrt{30}\\[/tex]

Now we can simplify the radicals using the same property we used to combine them but instead of combining into one radical we'll separate them into two radicals where one of the radicals simplifies into a number without a radical

[tex](\sqrt{9} * \sqrt{x^2} * \sqrt{5}) + (\sqrt{25} * \sqrt{3x}) + 2\sqrt{30}\\3x\sqrt{5} + 5\sqrt{3x} + 2\sqrt{30}[/tex]

Answer:

x = 3

TU = 35

UV = 35

TV = 70

Step-by-step explanation:

As U is the midpoint of TV:

⇒ TU = UV

⇒ 8x + 11 = 12x - 1

⇒ 8x + 11 - 11 = 12x - 1 - 11

⇒ 8x = 12x - 12

⇒ 8x - 12x = 12x - 12 - 12x

⇒ -4x = -12

⇒ -4x ÷ -4 = -12 ÷ -4

⇒ x = 3

Substitute the found value of x into the expression for TU:

⇒ TU = 8x + 11

⇒ TU = 8(3) + 11

⇒ TU = 24 + 11

⇒ TU = 35

Using the transitive property of equality:

As UV = TU and TU = 15 then UV = 35

Using the segment addition postulate:

⇒ TV = TU + UV

⇒ TV = 35 + 35

⇒ TV = 70

Hence

If Bruce can deduct 40% from other interest then the total interest deducted is $2927.

Given Adjusted gross income=$36500, mortgage interest =$2787 and other interest $350.

It is said that 40% of other interest can be deducted by Bruce but it is not said that nothing will be deducted by Bruce from Mortgage interest so we will deduct full of mortgage interest and 40% of other interest. So,

Mortgage interest =$2787

Other interest=$350

Other interest deductable=40%*350

=$140

So the total will be 2787+140 =$2927.

Hence the interest deducted by Bruce is $2927if only 40% of  other interest is deductable.

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Answer:

$2

Step by Step:

Four quarters is one dollar

Four quarters is 8 pennies

Multiply 8 by 25 (25 being the value of the quarters)

25 cents is times four is one dollar

.25x4=1, 25x4=100, 100x.25=25

2x4=8 8x25=200

A pound of pennies is worth $12.5.

In mathematics, multiplication is one of the basic operations where one number is multiplied or added repeatedly to itself as times as that of the other number. Multiplication of two numbers a and b is represented as "a × b", read as a multiplied to b or a times b.

For example 2 multiplied to 4 implies that 2 is added to itself like 4 times (2+2+2+2) or 4 is added to itself 2 times (4+4).

We have from the question,

1 quarter = 2 pennies

Also, it is given that,

A pound of quarters = $25

Since 1 quarters = 2 pennies, we have,

A pound of 2 pennies = $25

A pound of 1 penny = 25 / 2

                                 = 12.5

Hence we have a pound of pennies worth $12.5.

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Step-by-step explanation:

f(x) = y = 64x³ - 1

y + 1 = 64x³

(y + 1)/64 = x³

[tex]x = \sqrt[3]{(y + 1) \div 64} [/tex]

[tex]x = \sqrt[3]{y + 1} \div 4[/tex]

that is the actual inverse function to calculate the original x value for a given y value of the original function.

but to make it a "normal" function, we need to rename the variables (x to y, y to x) :

[tex]y = \sqrt[3]{x + 1} \div 4[/tex]

this is now f^-1(x)

but careful, don't get confused, if dealing together with the original function, this "x" is actually standing for the "y" of the original function ...

Answer:

Should have ended with "at most -15, not "at least -15."

Step-by-step explanation:

[tex]\leq[/tex] -15 means less than or equal to -15

So it can be -15, but also anything less than -15.  The phrase "at most -15, not "at least -15" says exactly that.

1. 5:15 = 1/3
scale factor is 1/3going from bigger to smaller

2. 2/8 = 1/4

14 x 1/4 = 3.5

X = 3.5

Answer:

24 gallons

Step-by-step explanation:

Since the 2 gallons of gas increased the fill ratio from 1/6 to 1/4, we can find how much of the tank the 2 gallons filled by solving the equation 1/4 - 1/6 = 1/12. This means that each gallon of gas is 1/24th of the tank.

Thus, the tank has a fuel capacity of 24 gallons.

Answer:

24

Step-by-step explanation:

Let x be the total fuel capacity of the tank, in gallons.

Then from the given information

x/6 + 2 = x/4,

Multiplying both sides by 12 to remove the fractions, we get

2x + 24 = 3x so x = 24. 

Therefore, the total fuel capacity of the tank is 24 gallons.

Answer

The answer is A. y = x²

Answer:

79°

Step-by-step explanation:

An angle in standard position has it "initial" side glued on to the positive x-axis. The other ray that makes the angle swings around the origin, (0,0) like a hand of a analog clock (but moving backwards) straight up is 90°, straight to the left is 180° straight down is 270°. And all the way back to the start is 360°.

If the angle is 281° it can go 79° more degrees before getting back to the start.

360° - 281° = 79°

Answer:

Step-by-step explanation:

784-263=521

784+521=1305

answer=1305

The expression is 17.

An expression is a sentence with a minimum of two numbers or variables and at least one math operation.

Given:

10+(6-3) 22-4-1

Using the BODMAS rule,

First solve the bracket term

10+ 3 * 22 -4-1

Now, perform multiplication

10+66-4-1

Now, subtraction

10+66-5

=10+61

And lastly addition

=71.

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Answer:

17

Step-by-step explanation:

the answer is 17 :)

The solutions to the trigonometric equation in the desired interval are given as follows:

[tex]\theta = \frac{\pi}{3}, \theta = \frac{5\pi}{3}[/tex]

The trigonometric equation is given by:

[tex]\sqrt{3}\cot{\theta} - 1 = 0[/tex]

Solving it similarly to an equation, we have that:

[tex]\sqrt{3}\cot{\theta} = 1[/tex]

[tex]\cot{\theta} = \frac{1}{\sqrt{3}}[/tex]

Since [tex]\cot{\theta} = \frac{1}{\tan{\theta}}[/tex], we have that the equation is equivalent to:

[tex]\tan{\theta} = \sqrt{3}[/tex]

The tangent is positive in the first and in the fourth quadrant. In the first quadrant, the angle [tex]\theta[/tex] with [tex]\tan{\theta} = \sqrt{3}[/tex] is:

[tex]\theta = \frac{\pi}{3}[/tex]

In the fourth quadrant, the equivalent angle is:

[tex]\theta = 2\pi - \frac{\pi}{3} = \frac{5\pi}{3}[/tex]

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Delete the commas if necessary.

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

Explanation:

There are 6 freshmen total and we want to pick 2 of them, where order doesn't matter. The reason it doesn't matter is because each seat on the committee is the same. No member outranks any other. If the positions were labeled "president", "vice president", "secretary", etc, then the order would matter.

Plug n = 6 and r = 2 into the nCr combination formula below

[tex]n C r = \frac{n!}{r!(n-r)!}\\\\6 C 2 = \frac{6!}{2!*(6-2)!}\\\\6 C 2 = \frac{6!}{2!*4!}\\\\6 C 2 = \frac{6*5*4!}{2!*4!}\\\\ 6 C 2 = \frac{6*5}{2!}\\\\ 6 C 2 = \frac{6*5}{2*1}\\\\ 6 C 2 = \frac{30}{2}\\\\ 6 C 2 = 15\\\\[/tex]

This tells us there are 15 ways to pick the 2 freshmen from a pool of 6 total.

Repeat those steps for the other grade levels.

n = 13 sophomores, r = 5 selections leads to nCr = 13C5 = 1287. This is the number of ways to pick the sophomores.

You would follow the same type of steps shown above to get 1287. Let me know if you need to see these steps.

Similarly, 8C4 = 70 is the number of ways to pick the juniors.

Lastly, 14C3 = 364 is the number of ways to pick the seniors.

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

To recap, we have...

Multiply out those values to get to the final answer.

15*1287*70*364 = 491,891,400

This massive number is a little under 492 million.