Each end of a glass prism is a triangle with a height that is 1 inch shorter than twice the base. If the area of the triangle is 60 square inches, how long are the base and height?

Step-by-step explanation:

AC ≅ EF, given

AB ≅ ED, given

∠C ≅ ∠F, right angles are congruent

ΔABC ≅ ΔEDF, SSA congruence

BC ≅ DF, corresponding parts of congruent triangles are congruent

Answer:

n=-4

Step-by-step explanation:

56/-14=n

n=-4

Answer:

[tex]\frac{9}{25}[/tex]

Step-by-step explanation:

Number of red balls = 4

Number of green balls = 6

Total number of balls = 6+4 =10

Probability of drawing a green marble is given as

⇒ [tex]\frac{Number\ of\ green\ balls}{Total\ number\ of\ balls}[/tex]

⇒ [tex]\frac{6}{10}[/tex]

The ball is replaced after drawing.

Probability of drawing a green ball a second time will be:

⇒ [tex]\frac{Number\ of\ green\ balls}{Total\ number\ of\ balls}[/tex]

⇒ [tex]\frac{6}{10}[/tex]

Thus, probability of drawing 2 green balls with replacement can be given as:

⇒  (Probability of drawing a green marble) [tex]\times[/tex] (Probability of drawing a green ball a second time)

⇒ [tex]\frac{6}{10}\times\frac{6}{10}[/tex]

⇒ [tex]\frac{36}{100}[/tex]

Simplifying fraction by dividing numerator and denominator by their GCF.

⇒ [tex]\frac{36\div 4}{100\div 4}[/tex]

⇒ [tex]\frac{9}{25}[/tex] (Answer)

Answer:

B The sum of two constant factors six and three plus a variable

Step-by-step explanation:

The square root of 16 is rational 4.

The ratio of 4 and 7 is rational 0.5714285714285

The product is hence rational.

The product of the square root of 16 and 4/7 (which equals 16/7) is rational.

Rational numbers can be expressed as fractions of integers, while irrational numbers cannot be expressed as fractions and have non-repeating, non-terminating decimal expansions.

The square root of 16 is 4, and 4/7 is a rational number. When you multiply a rational number (4/7) by an integer (4), the result remains rational.

Calculation: √16 * 4/7 = 4 * 4/7

= 16/7

16/7 is the product which is a rational number.

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Answer:

The equation of line is y = 3 x - 1 , i.e option A  .

The rate of change = m = 3

Step-by-step explanation:

Given as :

The points are

([tex]x_1[/tex],[tex]y_1[/tex] ) = (- 2, -7)

([tex]x_2[/tex],[tex]y_2[/tex] ) = (1 , 2)

Let The slope = m

Now, The slope is calculated in points form

So, Slope = [tex]\dfrac{y_2-y_1}{x_2-x_1}[/tex]

I.e m = [tex]\dfrac{2-(-7)}{1-(-2)}[/tex]

or, m = [tex]\dfrac{9}{3}[/tex]

I.e m = 3

So, The slope of points = m = 3

I,e Rate of change = m = 3

Now, the equation of line in slope - point form can be written as

y -[tex]y_1[/tex]  = m ( x -  [tex]x_1[/tex])

where m is the slope of line

i.e y - (-7) = ( 3 ) × ( x - (-2) )

or, y + 7 =  3 × (x + 2)

∴ y + 7 = 3 x + 6

Or, y = 3 x + 6 - 7

Or, y = 3 x - 1

So, The equation of line is y = 3 x - 1

Hence, The equation of line is y = 3 x - 1 , i.e option A  .

And The rate of change = m = 3   Answer

Answer:

I think -4 and 1.25

Step-by-step explanation:

Answer:

A(2.5,36.5)

D(6,36.5)

and

C(6,33)

When multiplying (or dividing) both sides of an inequality by a negative number, the inequality symbol must be reversed/flipped, regardless of how many steps taken when solving the inequality.

If you were to multiply (or divide) by a positive number, then you would not have to reverse/flip the inequality symbol.

The question in the image is incomplete, so I cannot provide a true/false answer, but this information should be what you need to easily choose an answer.

Let me know if you need any clarifications and happy studying~

Answer:

False

Step-by-step explanation:

only flip symbol when dividing by a negative number

(5 - 5)x because it equals -5x+5x which is 0

all the others equal -5x +5

Answer:

(5-5)x

when you distribute the x here it becomes 5x-5x which is 0 this is the only problem that equals 0

Answer:

The arc is 3/10 of the circumference

Step-by-step explanation:

we know that

The complete circumference subtends a central angle of 2π radians

so

using proportion

Find out what fraction of the circumference represent an arc with a central angle of 3pi/5 radians

[tex]\frac{1}{2\pi}=\frac{x}{(3\pi/5)}\\\\x=\frac{(3\pi/5)}{2\pi}\\\\x=\frac{3}{10}[/tex]

Answer:

10-10=10+10 its the same it will increase and decrease the increased level

Answer:

45.72 cm

Step-by-step explanation:

Given: Height of the Chinstrap Penguin= 68.58 cm

           Height of the Emperor penguin= 1.143 meter

Lets calculate the height of Emperor penguin in centimeter.

Remember, 1 meter = 100 centimeter

∴ Converting the unit of height of Emperor penguin.

[tex]1.143\times 100= 114.3\ cm[/tex]

∴ Height of Emperor penguin is 114.3 cm.

Now, comparing the height of Chinstrap penguin and Emperor penguin´s height.

[tex]114.3\ cm - 68.58\ cm= 45.72\ cm[/tex]

∴ The Emperor penguin is 45.72 cm taller than Chinstrap penguin.

Answer:

a) The Inequality representing this problem is [tex]13+2.35x\leq 29.45[/tex].

b) Annie Marie can play maximum of 7 hours.

Step-by-step explanation:

Given:

Entry fee charge of game room = $13

Cost of hourly playtime = $2.35 per hour

Total Money Annie Marie has = $29.45

We need to find number of hours she can play with this amount.

Let number of hours she will play be 'x'.

No we know that Total Money she has should be less than or equal to sum of Entry fee charge of game room and Cost of hourly playtime multiplied by number of hours she can play.

Framing in equation form we get;

[tex]13+2.35x\leq 29.45[/tex]

Hence The Inequality representing this problem is [tex]13+2.35x\leq 29.45[/tex].

On Solving this equation we get;

Subtracting both side by 13 we get;

[tex]13+2.35x-13\leq 29.45-13\\\\2.35x\leq 16.45[/tex]

Now dividing both side by 2.35 using division property of Inequality we get;

[tex]\frac{2.35x}{2.35}\leq \frac{16.45}{2.35}\\\\x\leq 7 \ hrs.[/tex]

Hence Annie Marie can play maximum of 7 hours.

Answer: 1.87500 or 15/8 simplified 1 7/8

Step-by-step explanation:

Answer:

1 7/8

Step-by-step explanation:

So you want to make 2 5/10 into a improper fraction which is 25/10. so 25/10*3/4 you need to do cross cancel but you can't cross cancel so the answer is just going to be 15/8 which is also 1 7/8 hope this helps ;))

Answer:

The minimum is the point (-3,2)

Step-by-step explanation:

we have

[tex]x^{2} +6x+11[/tex]

This is a vertical parabola open upward (because the leading coefficient is positive)

The vertex is a minimum

Convert the equation in vertex form

Complete the square

[tex]f(x)=(x^{2} +6x+3^2)+11-3^2[/tex]

[tex]f(x)=(x^{2} +6x+9)+11-9[/tex]

[tex]f(x)=(x^{2} +6x+9)+2[/tex]

Rewrite as perfect squares

[tex]f(x)=(x+3)^{2}+2[/tex] ----> equation in vertex form

The vertex is the point (-3,2)

therefore

The minimum is the point (-3,2)

Answer:BC=11.77 mi

Step-by-step explanation:

cosα=5.71mi/AC

cos61°=5.71mi/AC

0.485=5.71mi/AC

AC=11.77mi

Answer:

BC=10.28

Step-by-step explanation:

Answer:

The Total number of people were surveyed is 1,350 people.

Step-by-step explanation:

Given as :

The total number of people who preferred walking = 540 people

The percentage of people who preferred walking to running = 40% of the total people

Let The Total number of people were surveyed = n people

Now, According to question

The total number of people who preferred walking = 40% of the total number of people were surveyed

Or, 40% of n = 540

Or, [tex]\dfrac{40}{100}[/tex] × n = 540

Or, n = [tex]\frac{540\times 100}{40}[/tex]

∴ n = 1350

So,Total number of people were surveyed = n = 1350 people

Hence,The Total number of people were surveyed is 1,350 people. Answer

Answer:

False, they are opposite angles

Step-by-step explanation:

Answer:

False

Step-by-step explanation:

this is what i maked on my work

Answer: d = 12

Step-by-step explanation: First isolate d/3 by subtracting 10 from both sides of the equation. That gives you d/3 = 4.

From here, since d is being divided by 5, multiply both sides of the equation by 5 so d = 12.

The expression to represent the sale price, in dollars, of the dress is x - 0.3x dollars

Given that dress that costs "x" dollars is on sale for 30% off

To find: expression to represent the sale price, in dollars, of the dress

Let the original price of dress is "x"

It is on sale for 30% offer. Which means 30 % of "x" is offer price

Sales price means the price of dress after offer

So the sales price is written as original price - offer price

Sales price = original price - offer price

Sales price = x - 30 % of x

On simplification we get,

[tex]\text {Sales price }=x-\frac{30}{100} \times x=x-0.3 x[/tex]

Thus the sales price of dress is x - 0.3x dollars

Answer:

x = 11 m

y = 2 m

Step-by-step explanation:

The given figure is parallelogram, with MP = 21 m, LP = (y + 3) m, NP = (3y – 1) m, and  OP = (2x – 1) m

It is property of parallelogram that, the diagonals bisect each other.

Thus, from above,

MP = OP  and  LP = PN

Thus,

[tex]2x-1 = 21[/tex]

[tex]2x = 22[/tex]

[tex]x = 11[/tex]

and,

[tex]y+3 = 3y-1[/tex]

[tex]2y = 4[/tex]

[tex]y = 2[/tex]

Thus, x = 11 m  and  y = 2 m

Answer:

D. x = 11 m, y = 2 m

Step-by-step explanation:

Answer:

Justin is 1 feet far away from Brandon

Step-by-step explanation:

As shown in the diagram, we let the distance between Justin and Brandon be x

[tex]Speed = \frac{distance}{time} [/tex]

from the question

the total time taken by the ball to reach Brandson=4s

Also the total distance is travelled by the ball=19+x

while the average speed=5ft/s

By substitution we obtain

[tex]5 = \frac{19 + x}{4} [/tex]

[tex] \implies4 \times 5 = 19 + x[/tex]

[tex]\implies20=19 + x[/tex]

[tex]\implies20 - 19 = x[/tex]

x=1 feet

The ball is 39 feet away from Justin. The ball, thrown by Sarah at 5 feet per second away from Justin, reaches Brandon in 4 seconds at a distance of 39 feet from Justin.

We need to understand the direction and speed of Sarah's throw relative to the distance between Sarah, Justin, and Brandon.

Sarah throws the ball away from Justin at a speed of 5 feet per second for 4 seconds. The formula to calculate the distance covered by the ball is:

The ball travels 20 feet away from Sarah. Since Sarah is already 19 feet away from Justin, we need to add this distance to determine how far the ball is from Justin:

Hence, the ball is 39 feet away from Justin when it reaches Brandon.

Answer:The answer is Zero:(0)

Step-by-step explanation:

Answer:

y=0.067825

Step-by-step explanation:

Answer:

Sean earns $7.5 in each hour.

Step-by-step explanation:

Given:

Money earned by Sean = $300

Number of hours worked in a day = 8 hrs

Number of days of work  in a week = 5

We need to find Money earned in each hour.

First we will find Total hours work in a week.

Total hours work in a week is equal to Number of hours worked in a day multiplied by number of days work in a week.

Framing in equation form we get;

Total hours worked in a week = [tex]8\times5 = 40\ hrs[/tex]

Now we will find money earned for each hour.

Money earned each hour will be calculated by Dividing Total Money earned in a week by Total number of hours worked in a week.

Framing in equation form we get;

Money earned each hour = [tex]\frac{300}{40} = \$7.5[/tex]

Hence Sean earns $7.5 in each hour.

Answer:

[tex]\frac{2A}{h} = b[/tex]

Step-by-step explanation:

2A = bh

[tex]\frac{2A}{h} = b[/tex]

so, the required form is : [tex]\frac{2A}{h} = b[/tex]

Answer:

???

Step-by-step explanation:

Answer:

Step-by-step explanation:

2 times x   -------> 2x

The difference between 2 times x and y is 2x - y

The difference between 2 times x and y is less than or equal to 1:

2x - y<= 1

Final answer:

The expressions that correctly represent an 8% increase from T are (1 + 8/100)T, which simplifies to 1.08T, and 1.08T directly. So, choices (A) 1.08T and (C) 1.08T are correct.

Explanation:

The student is asked to determine which expression represents the average temperature last Sunday when it was 8% higher than the temperature two Sundays ago, given as T degrees Celsius. To find 8% of T, the student would multiply T by 0.08. To calculate the total average temperature last Sunday, the student would then add this to T.

The correct expressions that represent this situation are:

Expressions (Choice B) B: T + 8 and (Choice D) D: 1.8T incorrectly represent an absolute increase of 8 degrees and an 80% increase, respectively, not an 8% increase. Expression (Choice E) E: T + 0.08T is equivalent to 1.08T and is also correct.

Therefore, the correct answers are (Choice A) and (Choice C).

Answer:

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

Step-by-step explanation:

The complete question is

Three times the sum of a number and two is less than seven times the number. Find the number

Let

x -----> the number

we know that

The linear equation that represent this problem is

[tex]3(x+2) < 7x[/tex]

Solve for x

Apply distributive property left side

[tex]3x+6 < 7x[/tex]

Subtract 3x both sides

[tex]6 < 7x-3x[/tex]

[tex]6 < 4x[/tex]

Divide by 4 both sides

[tex]\frac{6}{4}< x[/tex]

Simplify

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

Rewrite

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

The perimeter of a triangle with midpoints d, e, and f on each side is twice the sum of segments d, e, and f. However, without specific numerical values for d, e, and f, the exact numerical measurement for the perimeter of triangle ABC cannot be determined.

The question is referring to a specific characteristic of geometry known as the midpoint. The midpoints, in this case d, e, and f, divide each side of the triangle into two equal parts. The side length of ABC is equal to double the sum of segments d, e, and f since they represent the half lengths of the sides.

However, please note that without any additional information or numeric representation, we cannot compute the exact numerical measurement of the perimeter of triangle ABC.

To illustrate, if we were given that the lengths d, e, and f were respectively 5 units, 6 units, and 7 units, we would calculate the perimeter of triangle ABC by adding the lengths of d, e, and f and multiplying the sum by 2.

In such a scenario: Perimeter of ABC = 2 * (d + e + f) = 2 * (5 units + 6 units + 7 units) = 2 * 18 units = 36 units.

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