The attic floor, ABCD in the model, is a square. The beams that support the roof are the edges of a block (rectangular prism) EFGHKLMN. E is the middle of AT, F is the middle of BT, G is the middle of CT and H is the middle of DT. All the edges of the pyramid in the model have length 12m.

Calculate the area of the attic floor ABCD.

Answer: 46 years

Step-by-step explanation:

Let the father's age be x and the son's age be y, then 3 years ago:

Father = x - 3

son     = y - 3

Then , from the first statement :

x - 3 = 3 ( y - 3 )

x - 3 = 3y - 9

x     = 3y - 9 + 3

x     = 3y - 6 .......................................... equation 1

In five years time

father = x + 5

son = y + 5

Then , from the second statement

x + 5 = 2 ( y + 5 )

x + 5 = 2y + 10

x       = 2y + 10 - 5

x       = 2y + 5 ........................ equation 2

Equating equation 1 and 2 , we have

3y -6 = 2y + 5

add 6 to both sides

3y = 2y + 5 + 6

subtract 2y from both sides

3y - 2y = 11

y = 11

substitute y = 11 into equation 1 to find the value of x

x = 3y - 6

x = 3(11) - 6

x = 33 - 6

x = 27

This means that the father is presently 27 years and the son is presently 11 years.

In four years time

father = 27 + 4 = 31

son = 11 + 4      = 15

sum of their ages in four years time will be

31 + 15 = 46 years

Answer:

46 years

Step-by-step explanation:

Answer:

Step-by-step explanation:

In solving this, we'll make some keen assumptions to solve the question.

We'll represent the father's age with "a"

And represent the sons age as "b"

Lets interpret the question.

3 years ago, (means in the past), we'll subtract.

Therefore:

Father's age = a - 3

Sons age = b - 3

The sentence said, " 3 years ago, father was 3 times the sons age*. Interpreting that becomes:

a - 3 = 3 times (b - 3)

Simplifying that gives :

a - 3 = 3(b - 3)

a - 3 = 3b - 9

a = 3b - 9 + 3

a = 3b - 6 ( FIRST EXPRESSION )

The next line says: In five years time (that's in the future, hence we add) he'll be twice his sons age.

Therefore I become:

Father : a + 5

Son : b + 5

a + 5 = 2(b + 5)

a + 5 = 2b + 10

a = 2b + 5 ( SECOND EXPRESSION)

Equating the first and second equation to solve for "a" - the father's age

3b - 6 = 2b + 5

b = 5 + 6

b = 11 years (Sons age)

Substitute b = 1 in the first expression.

a = 3b - 6

a = 3(11) - 6

a = 33 - 6

a = 27 years (Father's age)

Let resolve, the last sentence:

What will be the sum of their ages in 4 years time. (SINCE IT'S IJ THE FUTURE, WE ADD)

Father's age in four years time: 27 + 4 = 31

Son's age in four years time: 11 + 4 = 15.

The sum of their ages in same four years time becomes:

31 + 15 (years)

46 years

Answer:

B, a cold and nasty winter day

Step-by-step explanation:

.

it said it was wrong for me

The length of the unknown leg is approximately 35.4 inches.

The image shows a right triangle with the following dimensions:

The base of the triangle is 24 inches.

The height of the triangle is 26 inches.

We can use the Pythagorean theorem to solve for the length of the missing leg. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two legs.

Let us call the unknown side "ao".

In this case, we can write the equation as follows:

ao^2 = 24^2 + 26^2

where:

ao is the length of the hypotenuse (unknown)

24 is the length of the base

26 is the length of the height

Simplifying the equation:

ao^2 = 576 + 676

ao^2 = 1252

ao = sqrt(1252)

ao ≈ 35.4 inches

Therefore, the length of the unknown leg is approximately 35.4 inches.

Answer:

2.2

Step-by-step explanation:

It is a 2.2 slope because you just have to divide the depth of water by the time by 2.2 or multiply the time by 2.2 to get the depth of water :)

Answer:

(0,0)&(2,4.4)

(4.4-0)/(2-0)= 4.4/2= 2.2 is the overall slope

Answer:

The irrational conjugate theorem states that if a polynomial equation has a root (a + √b), then we can say that the conjugate of (a + √b), i.e. (a - √b) will also be another root of the polynomial.

Step-by-step explanation:

The irrational conjugate theorem states that if a polynomial equation has a root (a + √b), then we can say that the conjugate of (a + √b), i.e. (a - √b) will also be another root of the polynomial.

For example, if we consider a quadratic equation x² + 6x + 1 = 0, then two of its roots are - 3 + √8 and - 3 - √8 and they are conjugate of each other. (Answer)

The Irrational Conjugate Theorem states that if a complex number is irrational, then its conjugate is also irrational. It is used in mathematics to prove this relationship. The theorem is based on the definition of the conjugate of a complex number, and a proof by contradiction approach can be used to prove it.

The Irrational Conjugate Theorem is used in mathematics to prove that if a complex number is irrational, then its conjugate is also irrational. This theorem is based on the concept of the rational and irrational parts of a complex number. Let's define a complex number as z = a + bi, where a and b are real numbers and i is the imaginary unit. The conjugate of z, denoted by [tex]\bar Z[/tex], is obtained by changing the sign of the imaginary part. So, if z = a + bi, then [tex]\bar Z = a - bi.[/tex] The Irrational Conjugate Theorem states that if a + bi is an irrational complex number, then a - bi (the conjugate) is also irrational.

To prove this theorem, we can use a proof by contradiction approach. Let's assume that a + bi is irrational and a - bi (the conjugate) is rational. We can then use valid reasoning to arrive at contradictory results. For example, we can add a + bi and a - bi to get 2a, which is a rational number. However, this contradicts our initial assumption that a + bi is irrational. Therefore, our assumption must have been false and the theorem is proven.

Answer:

2 students.

Step-by-step explanation:

add together all of the students and then subtract that from 40.

20+15+3 = 38

40-38 = 2

Answer:

3 athdwnts it says

Step-by-step explanation:

Answer:

Explanation:

1. Ratio of campers to counselors in june:

2. Ratio of campers to counselors in july:

3. Equivalent ratios:

Solve for x:

The camp needs approximately 22 counselors in July to maintain the original camper-to-counselor ratio of 12.5:1 that was present in June, when there were 325 campers and 26 counselors.

The question asks how many counselors the camp needs in July to keep an equivalent ratio of campers to counselors from June. In June, the camp had 325 campers and 26 counselors. The ratio of campers to counselors is 325:26, which simplifies to approximately 12.5:1. If 265 campers leave in July and 215 new ones arrive, the total number of campers for July is 325 - 265 + 215 which equals 275. To maintain the same ratio, we divide the number of July campers by the original ratio:

The camp needs approximately 22 counselors in July to maintain the same camper-to-counselor ratio as in June.

Answer:

-12

Step-by-step explanation:

Answer:

Your answer

Step-by-step explanation:

When c=4. Then,

c²-9c+8

= 4²-9c+8

= 4*4-9c+8

= 16-94+8

= 78+8

= -86 ans

Answer:

It’s B

Step-by-step explanation:

Final answer:

The correct statement is that if there is a definite pattern in the residual plot, the least squares regression line is not a good fit. It indicates that potentially another model might better capture the variability in the data. So the correct option is B.

Explanation:

The correct statement about the residual plot for a set of data with a linear regression equation is that if there is a definite pattern in the residual plot, it suggests that the least squares regression line is not a good fit for the data. A good fit would be indicated by residuals that are randomly scattered around the horizontal axis, with no apparent pattern. This is because the residuals, which represent the differences between the observed values and the values predicted by the regression line, should not correlate if the model is appropriate for the data set.

The correct option is B) The least squares regression line is not a good fit as there is a definite pattern in the residual plot. This indicates that the linear model may not be capturing all the variability in the data, and some other models might be more appropriate. Option A is incorrect because a definite pattern in the residuals is a sign of a poor fit. Options C and D are not correct because having the same number of points above and below the line does not necessarily mean the model is a good fit; it's the pattern in the points that matters.

Answer: 4

Step-by-step explanation:

To solve this problem we can use the Pythagorean Theorem to find the length of the other LEG of a right triangle

Pythagorean Theorem can be written as A^2+B^2=C^2

Now we plug in the values. C represents the hypotenuse while A and B represent the legs. We only are given one leg and the hypotenuse so we will be solving for B. (Or A if you swap the legs around)

3^2+b^2=5^2

9+b^2=25

Subtract 9 from both sides:

16=b^2

Now we take the square root of both sides

b=4

The length of the other leg of the triangle is 4 feet.


This is a basic 3-4-5 Triangle. Anytime the hypotenuse of a triangle is 5 and the leg is 3 the other leg will always be 4.

To solve the equation 5(2c + 7) - 3c = 7(c + 5), distribute the values inside the parentheses, combine like terms, and solve for c.

To solve the equation 5(2c + 7) - 3c = 7(c + 5), we will distribute the values inside the parentheses. This gives us 10c + 35 - 3c = 7c + 35. Next, we will combine like terms by subtracting 7c from both sides of the equation and adding 3c to both sides. This simplifies the equation to 10c - 7c = 35. By combining the terms on the left side, we get 3c = 35. Finally, we can solve for c by dividing both sides of the equation by 3, which gives us c = 35/3 or 11.67.

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The actual amount that should be credited is $757.58.

Solution:

Given that,

2% Discount if paid in 10 days.

1% Discount if paid in 15 days, (but greater that 10 days)

Net due in 60 days.

That is,

[tex]\bold{1400\times0.98 = 1372}[/tex] will close the acount on days 1-10

[tex]\bold{1400\times0.99 = 1386}[/tex] will close the acount on days 11-15

And August 8 is Day 15 and falls under the 1% discount rule.

Therefore, we have to divide the partial payment by the complement of the discount rate.

[tex]\bold{\Rightarrow\frac{750}{0.99} = 757.58}[/tex] from the balance, and [tex]\bold{1400.00 - 757.58 = 642.42}[/tex] is due by day 60.

Answer:

2x+2 or 2(x+1)

Step-by-step explanation:

2x-2+4=2x+2

Answer:

Hello! I'm currently doing the test right now on e d g e n u i t y 2/28/2022 and I believe that the right answer is: m<X = 140  and m<Y = 94

Step-by-step explanation: Sorry if I'm wrong.

:)

The pair of measurements that are possible in congruent quadrilaterals are Measure of angle X = 94 degrees and Measure of angle Z = 79 degrees.

Quadrilateral WXYZ is congruent to quadrilateral RSTQ if their corresponding angles are congruent. Let's compare the measurements of the angles in both quadrilaterals:

Therefore, the pair of measurements that are possible in congruent figures are:

Answer:

5/8

Step-by-step explanation:

1/4 = 2/8

2/8 + 3/8 = 5/8

Answer:

5/8

Step-by-step explanation

1/4 has a common denominator as 3/8 and when u find the common denominator add and ur good to go

Answer:

84, 82, 246

Step-by-step explanation:

first multiply by 3 for first term

next term, use previous term minus 2

Answer:

[tex]x=\frac{7}{5}[/tex]

[tex]y=-\frac{22}{5}[/tex]

Step-by-step explanation:

Given:

The given expressions are.

[tex]6x+y=4[/tex]

[tex]x-4y=19[/tex]

We need to find x and y values.

Solution:

Equation 1⇒ [tex]6x+y=4[/tex]

Equation 2⇒ [tex]x-4y=19[/tex]

First solve the equation 1 for y.

[tex]6x+y=4[/tex]

[tex]y = 4-6x[/tex] --------(3)

Substitute [tex]y = 4-6x[/tex] in equation 2.

[tex]x-4(4-6x)=19[/tex]

Simplify.

[tex]x-(4\times 4 - 4\times 6x)=19[/tex]

[tex]x-(16-24x)=19[/tex]

[tex]x-16+24x=19[/tex]

Add 16 both side of the equation.

[tex]25x-16+16=19+16[/tex]

[tex]25x=35[/tex]

[tex]x=\frac{35}{25}[/tex]

Divide Numerator and denominator by 5.

[tex]x=\frac{7}{5}[/tex]

Substitute x value in equation 3 and simplify.

[tex]y=4-6(\frac{7}{5})[/tex]

[tex]y=4-\frac{6\times 7}{5}[/tex]

[tex]y=4-\frac{42}{5}[/tex]

[tex]y=\frac{5\times 4-42}{5}[/tex]

[tex]y=\frac{20-42}{5}[/tex]

[tex]y=-\frac{22}{5}[/tex].

Therefore, the value of [tex]x=\frac{7}{5}[/tex] and [tex]y=-\frac{22}{5}[/tex].

The number of dump truck needed to clear the 40,000 cubic yards is determined as 2,667 trucks.

The rate of dump clearing is determined as follows;

R = 3000 dumps/200 truck

R = 15 dumps/truck

The number of dump truck needed to clear the 40,000 cubic yards is calculated as follows;

N = 40,000/15

N = 2,666.67 trucks

N ≅2,667 trucks

Thus, the number of dump truck needed to clear the 40,000 cubic yards is determined as 2,667 trucks.

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To clear the slide that left 40,000 cubic yards of material on the road, approximately 2,666.67 dump truck loads would be needed.

In the first scenario, a landslide resulted in 3,000 cubic yards of material obstructing the highway. This volume of material requires 200 dump truck loads for removal.

By dividing the total volume (3,000 cubic yards) by the number of loads (200), we can calculate that each dump truck load can carry 15 cubic yards of material.

3,000 / 200 = 15 cubic yards of material.

Now, applying this knowledge to the second scenario, where a landslide left 40,000 cubic yards of material on the road, we can determine the number of dump truck loads needed to clear it.

By dividing the total volume of material (40,000 cubic yards) by the volume each truck load can carry (15 cubic yards), we get the number of dump truck loads required for cleanup.

=> 40,000 / 15 = 2,666.67

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Answer:

First option:  [tex]6*10^{-4}[/tex]

Step-by-step explanation:

The expression is:

 [tex](6.3*10^{-2})(9.9*10^{-3})[/tex]

Scientific Notation (which is also known as "Standard form"), is a way to write numbers. It is very useful to handle very small numbers and very large numbers.

By definition, Scientific Notation has the following form:

[tex]a*10^n[/tex]

Where the coefficient "a" is a number from 1 to 10 without including 10, and the exponent "n" is an Integer.

Given:

[tex](6.3*10^{-2})(9.9*10^{-3})[/tex]

If you want to estimate the result, you can round the coefficients to the nearest whole number. Since the decimal point must be just after the first digit, you know that:

[tex](6*10^{-2})(10*10^{-3})=(6*10^{-2})(1*10^{-2})[/tex]

Now you need to remember the Product of powers properties:

[tex](a^m)(a^n)=a^{(m+n)}[/tex]

Then, solving the multiplication, you get:

[tex]6*10^{-4}[/tex]

Answer:

the answer is a

Step-by-step explanation:

i took the test... 100% i swear

Answer:

$5952

Step-by-step explanation:

The principal of $4800 will become after 24 months at an interest of 12% APR,

[tex]4800(1 + \frac{2 \times 12}{100}) = 5952[/tex] dollars.

Now, the monthly payment is $135.57 for 24 months.

So, the payment by installment is $(135.57 × 24) = $3253.68.

Therefore, the down payment was $(5952 - 3253.68) = $2698.32.

Therefore, the total paid for the motorcycle including the down payment was $5952. (Answer)

Answer:

Infinitely Many Solutions

Step-by-step explanation:

Since it's given that x = 3y + 4 we can use this in second expression

3×(3y+4) = 9y + 12 ➡ 9y + 12 = 9y + 12 add the like terms

9y - 9y = 12-12 ➡ 0 = 0 there's infinitely many solutions for second equation

Same goes for first equation.

Tom and Juanita, starting from the same point and biking in opposite directions for 3 hours, will end up 162 miles apart.

Starting from the same point, Tom and Juanita go biking in opposite directions for 3 hours. From what we know, Tom rides at a speed of 24 mph and Juanita rides at a speed of 30 mph.

When an object moves in one direction, its distance travelled is calculated from the formula distance = speed x time. This is because speed is described as the distance travelled per unit time. In this case, Tom travels 24 miles in 1 hour, so in 3 hours, he will cover 24 mph x 3 hours = 72 miles. Juanita will cover 30 mph x 3 hours = 90 miles.

Because they are moving in opposite directions, these distances add together. So in 3 hours, Tom and Juanita will be 72 miles + 90 miles = 162 miles apart.

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Tom and Juanita will be 162 miles apart after 3 hours of biking in opposite directions at their respective speeds.

To solve this problem, we can use the formula for distance, which is the product of speed and time.

Since Tom and Juanita are riding in opposite directions, their distances from the starting point will add up to the total distance between them after a certain amount of time.

The correct total distance apart should be calculated as follows:

The correct final answer is:

Answer:

$ 322

Step-by-step explanation:

x = his paycheck

x - 1/2x + 55 = 216

1/2x + 55 = 216

1/2x = 216 - 55

1/2x = 161

x = 161 * 2

x = $ 322 <===

Answer: 168/25

Step-by-step explanation:

Convert to a mixed number by placing the numbers to the right of the decimal over 100

. Reduce the fraction. Then, convert the mixed number to an improper fraction by multiplying the denominator by the whole number and adding the numerator to get the new numerator. Place this new numerator over the original denominator.

168/25

Answer:168/25

Step-by-step explanation: The answer for 6.72 as a fraction in simplest form is 168/25. You can solve this using long division method. There are six 25s in 168 which is 150 and the remaining 18 can become the decimal which is 0.72. Or for simplicity, you can use a scientific calculator to evaluate the result of 168/25.

Answers:

1) [tex]cos B=\frac{4}{5}=0.8[/tex]

2) [tex]csc A=\frac{5}{3}=1.66[/tex]

3) [tex]sec B=\frac{5}{4}=1.25[/tex]

4) [tex]tan A=\frac{3}{4}=0.75[/tex]

5) [tex]z=38.65\°[/tex]

Step-by-step explanation:

First exercise:

We have a right triangle with the values of each side an we have to find the following trigonometic functions (taking into account the secant function [tex]sec[/tex] is the inverse of the cosine, the cosecant [tex]csc[/tex] is the inverse of the sine):

1) [tex]cos B=\frac{Adjacent-side}{hypotenuse}[/tex]

[tex]cos B=\frac{4}{5}=0.8[/tex]

2) [tex]csc A=\frac{1}{sin A}[/tex]

[tex]\frac{1}{sin A}=\frac{1}{\frac{5}{3}}[/tex]

Then:

[tex]csc A=\frac{5}{3}=1.66[/tex]

3) [tex]sec B=\frac{1}{cos B}[/tex]

[tex]frac{1}{cos B}=\frac{1}{\frac{4}{5}}[/tex]

Then:

[tex]sec B=\frac{5}{4}=1.25[/tex]

4) [tex]tan A=\frac{opposite-side}{adjacent-side}=\frac{3}{4}[/tex]

Then:

[tex]tan A=\frac{3}{4}=0.75[/tex]

Second exercise:

5) Here, we are given another right triangle and we have to find the measure of the angle [tex]z[/tex].

So, according to the figure, we can use the tangent function:

[tex]tan z=\frac{opposite-side}{adjacent-side}[/tex]

[tex]tan z=\frac{8}{10}[/tex]

Finding the value of [tex]z[/tex]:

[tex]z=tan^{-1}\frac{8}{10}[/tex]

[tex]z=38.65\°[/tex]

[tex]33\frac{1}{3}[/tex] number of messages she can send and receive so the unlimited plan is cheaper than paying for each message

Solution:

Natalie can send or receive a text message for $0.15

Natalie can get an unlimited number for $5

To find: Number of messages she can send and receive so the unlimited plan is cheaper than paying for each message

Let "x" be the number of messages

Cost for sending and receiving message = $ 0.15

Cost for unlimited plan = $ 5

Then, according to given, we frame a inequality as:

The condition is: unlimited plan is cheaper than paying for each message

Therefore,

(number of messages)(Cost for sending and receiving message) is greater than or equal to Cost for unlimited plan

[tex]x \times 0.15\geq 5\\\\0.15x\geq 5\\\\\text{Solve for "x" }\\\\\text{Divide both sides of equation by 0.15 }\\\\\frac{0.15x}{0.15}\geq \frac{5}{0.15}\\\\x\geq 33.33\\\\x\geq 33\frac{1}{3}[/tex]

Thus for [tex]33\frac{1}{3}[/tex] messages ,the unlimited plan is cheaper than paying for each message