Question # 4
1) Brett is 18 years younger than Mark. Carl is 10 years younger
than Mark. The sum of the ages of Brett, Mark, and Carl is 212
How old are each of the 3 men? EXPLAIN: ​

Answer:

32000 sh.

Step-by-step explanation:

100%+6%=106%

106%=33920

100%=?

100×33920=3392000

3392000÷106

32000 sh.

Answer:

d15?

Step-by-step explanation:

Answer:

The value of angle of elevation is 44.4°  .

Step-by-step explanation:

Given as :

The measure of the rope of hot air balloon = 100 m

The height of balloon above the ground = 70 m

Let The angle of elevation = Ф

Now, According to question

Sin angle = [tex]\dfrac{\textrm Perpendicular}{\textrm Hypotenuse}[/tex]

Or, SinФ =  [tex]\dfrac{\textrm Height of baoolon above ground}{\textrm measure of rope}[/tex]

Or, SinФ = [tex]\frac{70}{100}[/tex]

Or, SinФ = [tex]\frac{7}{10}[/tex]

∴ Ф = [tex]Sin^{-1}[/tex]([tex]\frac{7}{10}[/tex])

I.e Ф = 44.4°

Hence The value of angle of elevation is 44.4°  . Answer

Draw the situation.

Apply sinθ  [tex]= \frac{opposite}{hypotenuse}[/tex]

sinθ [tex]=\frac{70}{100}[/tex]

θ = [tex]sin^{-1}[/tex][tex](\frac{70}{100} )[/tex]

θ = 44.4°

Answer:

9.8 inches.

Step-by-step explanation:

Progress forward = 18.2 - 13.5 + 5.1

= 4.7 + 5.1

= 9.8 inches.

Option C: y = 80x is the right answer

Step-by-step explanation:

Varying directly means that the increase/decrease in one quantity will cause increase/decrease in other quantity.

If y varies directly with x it is given by::

y ∝ x

When the proportionality symbol is removed, a proportionality constant is introduced

y = kx

If x = 1/2 and y = 40

then

[tex]40 = k * \frac{1}{2}\\k = 40*2\\k = 80[/tex]

Putting the value of k, we get

y = 80x

Hence,

Option C: y = 80x is the right answer

Keywords: Proportion

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Answer:

2y-1

Step-by-step explanation:

1/2(4y-2)=2y-1

Answer:

[tex]\large\boxed{(x+2)(3x-1)-(x+4)(x-7)=2x^2+8x+26}[/tex]

Step-by-step explanation:

[tex](x+2)(3x-1)-(x+4)(x-7)\\\\\text{Use FOIL:}\ (a+b)(c+d)=ac+ad+bc+bd\\\\(x+2)(3x-1)=(x)(3x)+(x)(-1)+(2)(3x)+(2)(-1)\\\\=3x^2-x+6x-2=3x^2+(-x+6x)-2=3x^2+5x-2\\\\(x+4)(x-7)=(x)(x)+(x)(-7)+(4)(x)+(4)(-7)\\\\=x^2-7x+4x-28=x^2+(-7x+4x)-28=x^2-3x-28\\\\(x+2)(3x-1)-(x+4)(x-7)=(3x^2+5x-2)-(x^2-3x-28)\\\\=3x^2+5x-2-x^2-(-3x)-(-28)=3x^2+5x-2-x^2+3x+28\\\\=(3x^2-x^2)+(5x+3x)+(-2+28)\\\\=2x^2+8x+26[/tex]

Answer:

2x^2 +8x +26

Step-by-step explanation:

I think you're supposed to simplify this:

So what you do is: you must have learmt about FOIL

which means First, Outside, Inside, Last.

So, this is how to do it using FOIL:

(3x^2 -x+6x-2) - ( x^2-7x+4x-28)

Now simplify, combine like terms wherever you can,

(3x^2 +5x -2) - ( x^2 -3x -28)

Note: multiply the subtraction sign otherwise you will end up making a mistake,

3x^2 +5x -2 - x^2 +3x+28

3x^2 -x^2 +5x+3x-2+28

2x^2 +8x +26 Answer

Hope this helps!

Please mark brainliest if you think I helped! Would really appreciate!

Note: Some of these steps can be eliminated, i showed everything for the purpose of making things clear for you!

Answer:

The answer would be Option 3: 43.25

Step-by-step explanation:

Triangles angles all added together add up to 180 degrees.

So first we subtract 93.5 from 180. This gives us 86.5. The we divide this by 2 to get 43.25.

Hope this helped!

Final answer:

To find the probability that the product of two standard dice is prime or ends in a 5, we need to count the favorable outcomes and divide it by the total number of possible outcomes. The probability is 1/4 or 0.25.

Explanation:

To find the probability that the product of two standard dice is prime or ends in a 5, we need to count the favorable outcomes and divide it by the total number of possible outcomes.

To have a prime product, the possible combinations are: (2,2), (2,3), (2,5), (3,2), (3,3), (3,5), (5,2), (5,3), (5,5)

To have a product that ends in 5, the possible combinations are: (1,5), (2,5), (3,5), (4,5), (5,5), (6,5).

The total number of favorable outcomes is 9.

When two dice are rolled, there are 36 total possible outcomes (6 possible outcomes for the first die multiplied by 6 possible outcomes for the second die).

Therefore, the probability that the product is prime or ends in a 5 is 9/36, which simplifies to 1/4 or 0.25.

Answer:

A) y=-3/2x+5/2

Step-by-step explanation:

y=mx+b

6x+4y=10

4y=10-6x

4y=-6x+10

y=-6/4x+10/4

simplify

y=-3/2x+5/2

The equation 6x + 4y = 10 written in slope-intercept form is y = -3/2x + 5/2.

The equation Y = mx + b exists in the slope-intercept form of the equation of a straight line. In the equation y = mx + b, m exists the slope of the line and b exists the intercept. X and y describe the distance of the line from the x-axis and y-axis, respectively. The value of b exists equivalent to y when x = 0, and m indicates how steep the line exists.

Let the equation be, 6x + 4y = 10

Simplifying the above equation we get

4y = 10 - 6x

4y = -6x + 10

y=-6/4x + 10/4

simplify

y = -3/2x + 5/2.

Therefore, the correct answer is option A. y= -3/2x + 5/2.

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Answer:

Step-by-step explanation:

450000000000

Answer:

125,000

47,829,690,000,000‬

Step-by-step explanation:

minus the exponents ( when dividing)

r^9- r^3

answer:

r^6

Which expression is equivalent to [tex]r^9/r^3[/tex] ?  The correct answer is b) [tex]r^6[/tex].

To simplify the expression [tex]r^9/r^3[/tex], we need to apply the rule of exponents. When dividing two terms with the same base, you can subtract the exponents.

In this case, both [tex]r^9[/tex] and [tex]r^3[/tex] have the same base 'r', so we subtract the exponent of [tex]r^3[/tex] from the exponent of [tex]r^9[/tex].

[tex]r^9/r^3[/tex] = [tex]r^{9-3}[/tex] = [tex]r^6[/tex].

In this problem, we are given the expression [tex]r^9/r^3[/tex] and we need to find an equivalent expression for it. To do that, let's understand the rules of exponents.

In general, when you have a term raised to a certain power and you divide it by the same term raised to a different power, you can simplify it by subtracting the exponents. For example, [tex]a^m / a^n = a^{m-n}[/tex].

Now, looking at our expression, [tex]r^9/r^3[/tex], we notice that both terms have the same base 'r'. According to the rule mentioned above, we can simplify the expression by subtracting the exponent of r3 from the exponent of [tex]r^9[/tex].

[tex]r^9/r^3[/tex] = [tex]r^{9-3}[/tex] = [tex]r^6[/tex].

So, the expression [tex]r^9/r^3[/tex] is equivalent to [tex]r^6[/tex]. This means that when you have a term raised to the power of 9 and you divide it by the same term raised to the power of 3, the result is the term raised to the power of 6.

In conclusion, the correct answer is b) [tex]r^6[/tex], as it represents the equivalent expression to [tex]r^9/r^3[/tex] after applying the rules of exponents.

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Answer:

HL

Step-by-step explanation:

HL- If the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and one leg of another right triangle, then the triangles are congruent.

The theorem which verifies that ΔGHI is congruent to ΔUVW is LL.

Two or more triangles are said to be congruent if and only if sides and angles of one triangle is equal to the corresponding sides and angles of another triangle.

Given are two triangles.

ΔGHI and ΔUVW.

Given that ∠G = ∠U = 90°.

So the triangles are right angled triangles.

The hypotenuse of the triangles are HI and VW.

Also given that, the legs of the triangles are equal.

Leg - Leg (LL) congruence theorem states that if the legs of a right triangles are equal to the legs of another right triangles, then the triangles are congruent.

Hence the theorem used is LL theorem.

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Answer:

3069

Step-by-step explanation:

q=6/3=2

s10=3(2^10-1)÷(2-1)=3×(1024-1)=

3069

Li incorrectly added 64 and 17 to get 71, but the correct sum is 81 pages. This mistake was likely due to adding the tens place incorrectly.

Li made a mistake in her addition. When adding 64 and 17, she erroneously stated that the sum was 71 pages. To clarify what Li did wrong, we can simply add the two numbers together properly.

Start by adding the ones place: 4 (from 64) + 7 (from 17) equals 11. Write down 1 and carry over the 1 to the tens place.

Next, add the tens place: 6 (from 64) + 1 (from 17) + 1 (carried over) equals 8.

Combine the numbers in the tens and ones place to get 81.

Therefore, the correct sum of 64 and 17 is 81 pages. This is how many pages Li read in all.

Answer

y=-\frac{11}{13}x+\frac{8}{13}

Step-by-step explanation:

Answer:

y = -(11/13)x + (8/13)  

Step-by-step explanation:

recall slope intercept form of a linear equation takes the general form:

y = mx + b

In this case, simply rearrange the given equation such that it looks like the general equation above.

11x+13y=8  (subtract 11x from both sides)

13y = -11x + 8  (divide both sides by 13)

y = -(11/13)x + (8/13)    (answer)

The value of the expression 5w - (w/x) when w=6 and x=2 is 27.

The original expression given with the variables w and x is: 5w - (w/x). The question asks us to evaluate this expression when w=6 and x=2. So, we simply substitute w with 6 and x with 2 into the expression:

5*6 - (6/2) = 30 - 3 = 27

Therefore, the value of the expression 5w - (w/x) when w=6 and x=2 is 27.

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To obtain y - x from x - y, add 2y - 2x to x - y which simplifies to y - x.

To transform x - y into y - x, we need to add something that effectively swaps x and y while also changing the sign of both variables. This is a classic example of using the property that A - B is the same as A + (-B). Applying this to our expression, if we add 2y to x - y, we'll get x + y. But, we need y - x, not x + y. So, we need to subtract x twice. Once to cancel out the original x, and a second time to create the negative x in the desired expression. Essentially, we add -2x to our new expression, x + y. So, the final answer is (x - y) + 2y - 2x, which simplifies to y - x.

The total cost y of a corporate team-building event can be expressed by the equation y = 1 + 1x, where x represents the number of attendees. This equation includes both the fixed and variable costs.

To determine the cost y of a corporate team-building event based on the number of attendees x, we need to include both the initial fixed cost and the variable cost per attendee.

The fixed cost of the event is $1, and the variable cost per attendee is also $1. The total cost can be expressed using the following equation:

y = 1 + 1x

Here:

For example, if there are 5 attendees, the total cost would be calculated as:

y = 1 + 1(5) = 1 + 5 = 6 dollars

Answer:

x=2000

Step-by-step explanation:

The conditions state, being x, N, M positive integers:

[tex]x-64=N^2[/tex]         [1]

[tex]x+25=M^2[/tex]       [2]

Subtracting the [1] from [2]

[tex]89=M^2-N^2=(M-N)(M+N)[/tex]

Since 89 has no other prime factors except 1 and itself, we can write

[tex](M-N)(M+N)=(1)(89)[/tex]

[tex]M+N=89[/tex]

[tex]M-N=1[/tex]

This system of equations results in [tex]M=45, N=44[/tex]

Replacing in [1] or [2] results

[tex]x=2000[/tex]

Proof:

[tex]2000-64=1936 =44^2[/tex]

[tex]2000+25=2025=45^2[/tex]

Answer: False

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

Replace every x with -3. Then simplify the left side.

(x-5)(x-7) < 0

(-3-5)(-3-7) < 0

(-8)*(-10) < 0

80 < 0 ... this statement is false, 80 is not smaller than 0

----

(x-5)(x-7) < 0  is false when x = -3

Answer:

2nd & 3rd choice

just took it and it was right

Answer:

B and C

B:The data is best represented by a quadratic model.

C:If the price is $5 per unit, the expected profit is approximately $4,686.

Step-by-step explanation:

I took it and got it right

Answer:

Brett  is 62 years old, Carl is 70 years old and Mark is 80 years old.

Step-by-step explanation:

let the age of Brett be x years.

thus the age of Mark is (x+18) years .

{as it is given that Brett is 18 years younger than Mark}

∴ Age of Carl is (x+8) years .

Now the sum of ages,

3x+26=212 (given)

3x=186

∴x=62

thus , the age of Brett is 62 years , the age of mark is (x+18)= 80 years and the age of Carl is (x+8)= 70 years

Answer:

(3x + 5)(x - 4)

Step-by-step explanation:

Given

x(3x + 5) - 4(3x + 5) ← factor out (3x + 5) from each term

= (3x + 5)(x - 4) ← in factored form

Answer:

The sell price of the truck rental after applying the coupon of 20 % is       $ 120  .

Step-by-step explanation:

Given as :

The regular rented price for the truck = $ 150

The discount as off coupon = 20 %

Let The sell price for truck after discount = x

So , Discount % = [tex]\dfrac{\textrm market price - \textrm Selling price}{\textrm market price}[/tex]

Or, 20 % = [tex]\dfrac{\textrm 150 - \textrm x}{\textrm 150}[/tex]

Or, [tex]\dfrac{x}{150}[/tex] = 1 -  [tex]\dfrac{20}{100}[/tex]

Or,  [tex]\dfrac{x}{150}[/tex] = [tex]\dfrac{100 - 20}{100}[/tex]

or,  [tex]\dfrac{x}{150}[/tex] = [tex]\dfrac{80}{100}[/tex]

∴ x = [tex]\frac{80\times 150}{100}[/tex]

I.e x = 8 × 15

Or, x = 120

Hence the sell price of the truck rental after applying the coupon of 20 % is $ 120  . Answer

Answer:

the % is 80% and the price $120

Step-by-step explanation:

The number of different ways by which can three diamonds and two non-diamonds be dealt from the standard deck of cards is 2543112.

There are total 52 cards in a deck of card.

Five cards are dealt from a standard deck of cards. In this, three diamonds and two non-diamonds are dealt.

In a standard deck of cards, there are total 13 diamonds and 39 non-diamond cards. By the rule of product, the ways can be found out as, when the arrangement does not matter,

[tex]x=\;^{13}C_3\times\;^{39}C_2\\x={13\times12\times11}\times {39\times38}\\x=2543112[/tex]

Thus, the number of different ways by which can three diamonds and two non-diamonds be dealt from the standard deck of cards is 2543112.

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Answer:

She read 3/4 of a book each month.

Step-by-step explanation:

In order to find this, you divide the amount of books read by the amount of months. When doing this, you get 3/4. If you wanted to check, you can multiply this number of 4 to find the number of books she read. When you do this, you get three, which is correct.

Answer:

MOP = DAB

Step-by-step explanation:

the sides have to be matched up as well. the side with only one dash (MO) has to correspond with the side with one dash from the other triangle (DA). Thus, the letters in the sequence (MOP) have to match up in the same order (DAB)

The correct congruency statement with regards to the congruence of the triangles is the fourth statement

The details of the steps by which the congruence statement can be found can be presented as follows;

The marks on the segment indicates;

PO is congruent to BA

MO is congruent to DA

PM is congruent to BD

Therefore, the triangle MOP is congruent to the triangle DAB

The order in which the markings on the triangles are located can also be used to find the correct congruence statement

The name of the triangle MOP indicates that the vertice of the triangle between the segment with three marklings, III, and the segment with one marking, I, is considered first, which is the vertice M and D on each triangle

The next mentioned vertice is the vertice between the segment with one marking and the segment with two markings, which is the vertice O and A on each triangle

The third considered vertice is the third vertice on both triangles, which corresponds to the vertice P and B on each triangle

The congruency statement is therefore ΔMOP ≅ ΔDAB

Answer:

Biker will catch the cyclist after 2 hr and 40 min.

Step-by-step explanation:

Given:

Speed of Bicyclist = 20 km/h

Travelling time = 4 hrs

∴ Distance = Speed × Time = [tex]20\times4=80 \ km[/tex]

Also he rest for 1 hr.

So we can say that, after 5 hrs Bicyclist is 80 km ahead when the biker Started.

Now Biker rate is given 50 km/h

And Bicyclist rate is 20 km/h

So, for each hour, biker advances 50 - 20 = 30 kilometers

now bicyclist distance is 80 km

and biker advances 30 per hour.

Therefore to catch up bicyclist at 80 km i.e time taken to reach 80 km with 30 km rate per hour.

Time = [tex]\frac{80}{30}=2 \frac{2}{3} h[/tex]

Hence, Biker will catch the cyclist after 2 hr and 40 min.

Answer:

2 hours

Step-by-step explanation:

the biker leaves when the first biker stops not after the break is over