42 out of the 84 teachers in a school staff meeting were first-year teachers. What percentage of the teachers in the meeting were first-year teachers? Write your answer using a percent sign (%).

Answer:

Step-by-step explanation:

Step 1 Find the slope

1-3/3-(-3)

-2/6=1/3

m=-1/3

Use the point slope formula

y-1=-1/3(x-3)

y=-1/3x+2

Triangle 1's x value is 8 and LN's length is 14 units. Triangle 2's x value is 8 and IH's length is 11 units. Triangle 3's x value is 9 and CB's length is 23 units. Triangle 4's x value is 11 and its IH length is 11 units.

If the respective sides of two triangles have the same ratio and the corresponding angles are equal, then the triangles are comparable (or proportion). Triangles that are similar will have the same shape but may not be the exact same size. According to the fundamental principles of triangles, two triangles are said to be congruent if their size and shape are the same, but two triangles are said to be similar if their shape is the same but their sizes differ. The proportions of similar triangles are the same.

Here,

Since these are similar triangle,

ME=EN

MN=ME+EN

MN=2ME

this will be same for all the triangles,

1. 2x-9/2x-2=1/2

2(2x-9)=2x-2

4x-18=2x-2

2x=16

x=8

LN=2x-2

LN=14 units

2. 2x-5/x+14=1/2

2(2x-5)=x+14

4x-10=x+14

3x=24

x=8

IH=2x-5

=11 units

3. (x+14)/(x+19)=1/2

2(x+14)=x+19

2x+28=x+19

x=9

CB=x+14

CB=23 units

4. 2x-11/x+11=1/2

2(2x-11)=x+11

4x-22=x+11

3x=33

x=11

IH=2x-11

IH=11 units

In triangle 1, The value of x is 8 and length of LN is 14 units. In triangle 2, The value of x is 8 and length of IH is 11 units. In triangle 3, The value of x is 9 and length of CB is 23 units. In triangle 4, The value of x is 11 and length of IH is 11 units.

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The required answer choice is vertical translation 2 units up and vertical translation 4 units down.

What is translation?

In mathematics, a translation is the movement of a shape to the left or right and/or up or down. The translated shapes appear to be the same size as the original shape, and thus the shapes are congruent. They were simply shifted in one or more directions. There is no change in the shape because it is simply moved from one location to another.

The -2 indicates that you need to translate 2 units up, and the -4 indicates that you need to translate 4 units down.

As a result, the answer is vertical translation 2 units up and vertical translation 4 units down.

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Answer:

y=1/2x-2

Step-by-step explanation:

Answer:

The machine requires at least 9 hours and 45 minutes to complete the hole on schedule.

Step-by-step explanation:

To find this, you can use the formula provided in the previous response:

(required depth - current depth) / digging rate = hours of digging

Plugging in the values from the problem, you get:

(12.5 feet - 4.75 feet) / (3/5 feet per hour) = (7.75 feet) / (3/5 feet per hour)

This simplifies to:

(7.75 feet) / (3/5 feet per hour) = 15.5 hours

Then, to convert this number of hours to hours and minutes, you can divide by the number of minutes in an hour (60 minutes) and round up to the nearest whole number for the number of hours. The remainder will be the number of minutes:

15.5 hours / 60 minutes/hour = 0.258333... hours

Rounding up to the nearest whole number, you get:

0.258333... hours = 1 hour

The remainder is:

15.5 hours - 1 hour = 14.5 hours

14.5 hours / 60 minutes/hour = 0.241666... hours

Rounding up to the nearest whole number, you get:

0.241666... hours = 0 hours

The remainder is:

14.5 hours - 0 hours = 14.5 hours

14.5 hours / 60 minutes/hour = 0.241666... hours

Rounding up to the nearest whole number, you get:

0.241666... hours = 0 hours

The remainder is:

14.5 hours - 0 hours = 14.5 hours

14.5 hours * 60 minutes/hour = 870 minutes

Therefore, the machine requires at least 9 hours and 45 minutes to complete the hole on schedule.

Answer:

2i[tex]\sqrt{6[/tex]

Step-by-step explanation:

So, for right now, ignore the negative. Consider the factors of 24. Both 6 and 4 multiply to 24. This means that [tex]\sqrt{24} = \sqrt{6}[/tex] x [tex]\sqrt{4}[/tex]. [tex]\sqrt{4}[/tex] can simplfy down to just 2. Now let's remember the negative. When taking a negative square root, you need to add an 'I' to the number you take out of the root. So right now you have 2i. Then [tex]\sqrt{6}[/tex] does not have any additional square roots to take out. So your final answer is 2i[tex]\sqrt{6[/tex].

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If an IR signal has a percent transmittance of 45%, then the sample absorbed 55% of the IR light

The percent transmittance of an IR signal = 45%

The equation of percent transmittance is

Percent transmittance = ( I / Io ) × 100

Where Io is the intensity of the IR signal entering the sample

I is the intensity of the IR signal leaving the sample

If the Io = I, then the percent transmittance is 100% that means the sample did not absorb any light and if Io= 0 then the the percent transmittance is 0% then sample absorbed all the light

Here, the percent transmittance is 45%, that mean the 55% of light absorbed by the sample

Therefore, the sample absorbed 55% of the IR light

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The number of children and adults using the swimming pool is x=318, and y=235 respectively.

Given that,

Swimming pool on a certain hot summer day 553 people use the public swimming pool. The daily prices are $1.75 for children and $2.25 for adults. The receipts for admission totaled $1085.25.

Here,
let the number of children be x and the number of adults be y,
According to the conditions,
x + y = 553,  - - - - - - (1)
1.75x + 2.25y = 1085.25 - -- - - - - -(2)
Solving the above equations by substitution of x from 1 in equation 2.
1.75[y - 553] + 2.25y = 1085.25
x = 318
Now,
x = 553 - 318
x = 235

Thus, the number of children and adults using the swimming pool is x=318, and y=235 respectively.

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Answer: -41

Step-by-step explanation:

-7x - 6

-7(5) - 6

-35 - 6

-41

The two points A and B that will be added to produce the complex number -3 + 4i are; -1 + 2i and -2 + 2i.

A complex number is defined as one that has both a real and an imaginary component, whereby both of them are preceded by the letter i which denotes the square root of -1.

Complex numbers are written in the general form; x + iy

Where;

x is the real part.

iy is the imaginary part.

From the graph attached, we can deduce that the two points that were added to obtain the result of -3 + 4i are;

A = -1 + 2i

B = -2 + 2i

Now, let us confirm the sum of the two points A & B;

A + B

= -1 + 2i + -2 + 2i

⇒ -3 + 4i

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Step-by-step explanation:

remember :

when multiplying terms with the same base, we add the exponents.

when dividing terms with the same base, we subtract the exponent of the denominator from the exponent of the numerator.

when putting exponent on exponent, we multiply the exponents.

a negative exponent means 1/...

e.g. 6^-4 = 1/6⁴

1/6^-4 = 1 / 1/6⁴ = 6⁴

so,

1.

(3^-4 × 3²)/3 = 3^-2 × 3^-1 = 3^-3 = 1/3³ = 1/27 =

= 0.037037037...

2.

(4²)^-1 × 4² = 4^-2 × 4² = 4⁰ = 1

3.

(2^-4 / 2^-2)^-1 = (2^-4 × 2²)^-1 = (2^-2)^-1 = 2² = 4

4.

(3^-3)² / (3²)^-1 = 3^-6 / 3^-2 = 3^-6 × 3² = 3^-4 =

= 1/3⁴ = 1/81 = 0.012345679...

Answer:

x = 45

Step-by-step explanation:

Answer:

62.92

Step-by-step explanation:

John has the greater total change in the amount of detergent in their bottle.

Given that, Brenda pours laundry detergent from a bottle into the cap and then into the washing machine.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Every time she fills the cap, the amount of detergent in the bottle changes by -0.26 L. She fills the cap 314 times in all.

Now, the volume of bottle =314×0.26

= 81.64

≈ 82 L

Every time he fills his cap, the amount of detergent in his bottle changes by -0.21 L. He fills his cap 256 times in all.

Here, the volume of bottle =256×0.21

= 53.76

≈ 54 L

Hence, John has the greater total change in the amount of detergent in their bottle.

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Answer:

[tex]\frac{2}{3}[/tex]

Step-by-step explanation:

Slope can be determined by using two points (x1, y1) and (x2, y2) and putting them in rise-over-run format (rise-over-run is equal to slope)

in this case we can use (3, 2) as (x1, y1) and (0, 0) as (x2, y2)

Rise-over-run format is: [tex]\frac{y2 - y1}{x2 - x1}[/tex]

so substitute our number in and you get: [tex]\frac{2-0}{3-0}[/tex]

solve to get: [tex]\frac{2}{3}[/tex]

this is your slope

The range of horn lengths for the middle 99.7% is  (46.5 , 73.5) inches .

In the question ,

it is given that ,

the horn lengths of Texas cattle are Normally Distributed ,

the mean of the horn spread is = 60 inches ,

the standard deviation of horn spread is = 4.5 inches ,

we know that the range for the middle 99.7% is (μ ± 3σ) ,

So , substituting the values in the range formula ,

we get ,

Range = (μ ± 3σ)

= (μ - 3σ , μ + 3σ)

= (60 - 3*4.5 , 60 + 3*4.5)

= (60 - 13.5 , 60 [tex]+[/tex] 13.5)

= (46.5 , 73.5)

Therefore , the range is (46.5 , 73.5) inches .

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Answer: a

Step-by-step explanation:

Answer:

y-10=   1/2(x-2) --- point slope form

Step-by-step explanation:

Point slope form is:

y- y1=m(x-x1)

y1= 10

m= y2-y1/x2-x1

y2= 6

x2= -10

x1= -2

Using point slope form and defining the variables using the given coordinates, the equation can be written.

Answer:

y-6 = -1/3(x-10)

Step-by-step explanation:

Let's use point slope form! The form of this is y-y1 = m(x-x1) where m is the slope.We have points to use, so let's find the slope.

The slope is rise over run, so we take the difference in y and divide it by the difference in x. This gives us [tex](10-6)/(-2-10)[/tex], which simplifies to -1/3. Now we plug in a point, say (-2, 10) for x1 and y1, and -1/3 for the slope, which gives us y-6 = -1/3(x-10)

Another way you could approach this is to plug in both the points to solve for m. Plug in both the y-values(10, 6) for y and y1 and both the x-values(-2, -10) for x and x1.

This gives us [tex]10-6 = m(-2-10)[/tex], which simplifies to [tex]4 = -12m[/tex]. Dividing both sides by -12 gives m = -1/3, which is the slope. Whichever way makes most sense works!

I hope this helps!

If the side lengths of triangle are 2 cm, 8 cm, and x cm then the measure of x can be 9 , the correct option is (b) .

In the question ,

it is given that ,

the side lengths of the triangle are 2 cm, 8 cm, and x cm .

we know that the sum of two sides of triangle is greater than the third side ,

So , x < 8 + 2 ,

x < 10 ,

and the difference of two sides of triangle is less than the third side ,

So , 8 - 2 < x

6 < x .

So , the side length x can be ,  6 < x < 10 .

the options that suits the condition is (b) 9 .

Therefore , the correct option is (b) .

The given question is incomplete , the complete question is

A triangle has side lengths of 2 cm, 8 cm, and x cm. Which measure could be the value of x in centimeters?

(a) 6

(b) 9

(c) 10

(d) 12

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Answer: 25

Step-by-step explanation:

part of a low is anything lower than 1oo

twice of 1/8 = 2/8 = 1/4

Answer:

25%

Step-by-step explanation:

"twice" means two times.

"twice the value of 1/8" is

2 × 1/8

(to multiply a whole number times a fraction, multiply the big number × the top number)

2 × 1/ 8 is 2/8

2/8 is 1/4.

1/4 = .25 = 25%

Since the answer is a percent, change 1/4 to a decimal, .25, change the decimal to a percent.

Or you could change 1/4 to 25/100. Percent means "per hundred" 25/100 is 25%.

Answer:

  C.  x² -8x +16 = 20

Step-by-step explanation:

You want the next step in completing the square after you get x² -8x = 4.

The constant in a perfect square monic trinomial is the square of half the coefficient of the linear term.

The coefficient of x is -8. Half that is -4, and its square is (-4)² = 16. This will be the value added to the equation in the second step.

  x² -8x +16 = 4 +16

  x² -8x +16 = 20

__

Additional comment

A monic polynomial has a leading coefficient of 1. We generally work with monic quadratics when completing the square. We do this by factoring the leading coefficient out of the variable terms.

Answer:

It would have saved 445$

Explanation: because for 4 weeks he saved 35% of 200$ which would be 70 and 70+70+70+70 280$ and the he saved 175$ on the fifth week because 7/8 of 200 is 175 so 280+175 is 445

Step-by-step explanation:

Answer:x>1

Step-by-step explanation:

Answer:

8 years old

Step-by-step explanation:

Make Nick's age = x

Caroline's age = x + 12

Mark's age = x - 4

So,

x + (x + 12) + (x - 4)

Remove brackets:

x + x + 12 + x - 4 = 44

Collect like terms:

3x = 44 - 12 + 4

3x = 36

x = 12 

Mark is 8 yrs old

Nick is 12 yrs old

Caroline is 24 yrs old

Youngest is Mark = 8 years old.

Hope this helps :-)

The ratio shows how many times one value is contained in another value.

The fraction of the bracelets from the total items is 6/13.

The ratio shows how many times one value is contained in another value.

Example:

There are 3 apples and 2 oranges in a basket.

The ratio of apples to oranges is 3:2 or 3/2.

We have,

The ratio of earrings, bracelets, and necklace is 13:24:15.

This means,

Earrings = 13x

Bracelets = 24x

Necklace = 15x

The fraction of the bracelets from the total items.

= 24x / (13x + 24x + 15x)

= 24x / 52x

= 24/52

= 12/26

= 6/13

Thus,

The fraction of the bracelets from the total items is 6/13.

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if h(x) = 2x² - 5x + 7

h(-3) = 2(-3)² - 5(-3) + 7

= 18 + 15 + 7

= 40

Answer:

Here,

Given:

Area of a square- 264 sq. cm

To find:

1. The length ( side)

2.Perimeter.

Solution :

Now,

Let the side of the square be x cm.

according to the formula for finding the area of a square:

Area= side× side

264= x× x

264= x^2

√264= x

16.2481= x

16.25= x

hence,

Length= side= 16.25 cm.

Now,

Perimeter of a square:

= 4× side

= 4× 16.25

= 65

Hence,

perimeter of the square= 65 cm

Step-by-step explanation:

I hope I helped you