Mathematical
PRACTICE 5 Use Math Tools Sarah buys a pen that costs
$0.75. How much will 2 pens cost?

Answer:

9.8 inches.

Step-by-step explanation:

Progress forward = 18.2 - 13.5 + 5.1

= 4.7 + 5.1

= 9.8 inches.

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:

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

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.

Final answer:

To find out how much was spent on fresh flowers, 10% of the monthly budget of $5,000 was calculated, resulting in $500 spent on fresh flowers.

Explanation:

If the monthly budget for the front of the house is $5,000, and you spent 10% of the budget on fresh flowers, you can calculate the amount spent on fresh flowers by finding 10% of $5,000. To do this, you simply multiply the total budget by the percentage (expressed as a decimal).

To express 10% as a decimal, you divide 10 by 100, which gives 0.10. Next, multiply the monthly budget by this decimal:

0.10 × $5,000 = $500

Therefore, you spent $500 on fresh flowers.

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)

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

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:

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:

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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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:D

Step-by-step explanation:

Your first solution is to look at the 10x^2y in order to get 8 from ten you would need to subtract 2x^something y and there is only one answer with that

Answer:

yes its D.

Step-by-step explanation:

Answer:

X= -0.4545

Step-by-step explanation:

YOU HAVE TO SUBTRACT .2Z FROM .4Z WHICH GETS YOU .2 ON THE RIGHT SIDE

THAT WOULD MEAN YOU HAVE TO CLEAR OUT THE SEVEN BY ADDING IT ON BOTH SIDES GETTING -1

THEN YOU WOULD HAVE -1=.2Z

THEN DIVIDE BY .2 GETTING YOU A TOTAL OF -0.4545 WHEN YOU FINISH DIVIDING

Answer:

(3,2)

Step-by-step explanation:

The coordinates of the point P on the given graph is (-1,5).

So, when we translate point P on the graph by 4 units to the right its x-coordinate will change to (- 1 + 4) = 3.

Again, when we translate point P on the graph by 3 units down then its y-coordinate will change to (5 - 3) = 2.

Therefore, the new coordinates of the point P will be (3,2) (Answer)

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

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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Uncle Drew averaged 5.6 points per minute during that 5-minute game.

To find the average number of points Uncle Drew scored per minute during the 5-minute game, we divide the total number of points scored by the number of minutes played.

Given that Uncle Drew scored 28 points in 5 minutes, we divide 28 by 5:

[tex]\[ \text{Average points per minute} = \frac{28}{5} \]\[ \text{Average points per minute} = 5.6 \][/tex]

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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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:

Andre is taller.

Step-by-step explanation:

I assume Andre's height is 1.7 m.

Let's convert Andre's height to cm.

1 m = 100 cm

1.7 m = 1.7 * 1 m = 1.7 * 100 cm = 170 cm

Andre is 170 cm tall. Diego is 165 cm tall.

Since 170 cm > 165 cm, Andre is taller.

1.7 m = 170 cm

170 cm > 165 cm

Andre > Diego

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:

d15?

Step-by-step explanation:

Answer:

Neil had a better free throw rate.

Step-by-step explanation:

This is because Neil Shot less, but made more.

I hope this helps you!

Final answer:

Neil had a better free throw percentage at approximately 62.87% compared to Avid's 60.07% by calculating the number of successful throws divided by the total attempts and multiplying by 100.

Explanation:

The question involves comparing the free throw rates of two basketball players to determine who had a better free throw percentage. To find the free throw percentage, we divide the number of successful free throws by the total number of attempts and then multiply by 100.

For Neil:

(215 free throws ÷ 342 attempts) × 100 = ~62.87%

For Avid:

(358 free throws ÷ 596 attempts) × 100 = ~60.07%

Neil had a better free throw percentage than Avid as 62.87% is higher than 60.07%.

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.

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:

A) 3x-5=25

I'll try my best on the others

B) x+y^2=18

C)x•6/5=x+4 ????

D).5+x=2-4???

That's all I know :/

Step-by-step explanation:

yeah I'm not sure lol

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

This was a year ago and no one answered I hope you did find the answer

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!