MATHEMATICS HIGH SCHOOL

9 more than the product of 51 and a number t

Answers

Answer 1

Answer: 51t + 9 should be the mathematical rewrite of this

Answer 2

Answer:

Final answer:

The phrase '9 more than the product of 51 and a number t' translates to the mathematical expression 51t + 9.

Explanation:

The question is asking for an expression representing '9 more than the product of 51 and a number t'. In mathematical terms, this can be expressed as: 51t + 9 .The key step here is understanding that 'the product of 51 and a number t' refers to multiplication: 51 multiplied by t (which can be written as 51t). Then, '9 more than' this product means simply adding 9 to that solution. So, the entire translating phrase becomes 51t + 9, which is the equivalent mathematical expression.

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Meg started her trip with 11 1/2 gallons of gas in her car's tank. She bought an additional 6 4/5 gallons on her trip and arrived back home with 3 3/10 gallons left. How much gas did she use on the trip?

Answers

Answer:

Hence, the amount of gas she used on the trip is:

15 gallons.

Step-by-step explanation:

Meg started her trip with 11 1/2 gallons of gas in her car's tank.

i.e. we can represent the mixed fraction 11 1/2 in fraction as:

$11(1)/(2)=(23)/(2)gallons$

She bought an additional 6 4/5 gallons on her trip.

i.e. we can represent the mixed fraction 6 4/5 in fraction as:

$6(4)/(5)=(34)/(5)gallons$

Hence, the amount of gas filled in tank:

$=(23)/(2)+(34)/(5)\n\n=(23* 5+34* 2)/(10)\n\n=(115+68)/(10)\n\n=(183)/(10)gallons$

now after coming back home the amount of gas left in the car tank is:

3 3/10 gallons ; which could be represented in fraction as:

$3(3)/(10)=(33)/(10)$

Amount of gas used in the trip is:

=Amount of gas filled-gas remaining

$=(183)/(10)-(33)/(10)\n\n=(183-33)/(10)\n\n=(150)/(10)\n\n=15gallons$

Hence, the amount of gas she used on the trip is:

15 gallons.

Meg used 15 gallons. First you find the lowest common denominator to add 11 1/2 and 6 4/5, which is 10. What you do to the bottom you have to do to the top. You multiply 2 and 5, which gives you 10. 1 times 5 is 5... 11 5/10. 2 times 5 is 10, 4 times 2 is 8... 6 8/10. Add 11 5/10 and 6 8/10 and it gives you 18 3/10. To find out how much she used subtract the total amount she bought and how much she returned home with. The fractions cancel out since 3/10 minus 3/10 equals 0. You're just left with 18 minus 3, which is 15.

What are the coordinates of the point on the directed line segment from (−7,−5) to (8,−10) that partitions the segment into a ratio of 3 to 2?

Answers

let's say P(−7,−5) and Q(8,−10) gets partitioned on a 3 : 2 ratio from P to Q by point R, so

$\textit{internal division of a line segment using ratios} \n\n\n P(-7,-5)\qquad Q(8,-10)\qquad \qquad \stackrel{\textit{ratio from P to Q}}{3:2} \n\n\n \cfrac{P\underline{R}}{\underline{R} Q} = \cfrac{3}{2}\implies \cfrac{P}{Q} = \cfrac{3}{2}\implies 2P=3Q\implies 2(-7,-5)=3(8,-10)$

$(\stackrel{x}{-14}~~,~~ \stackrel{y}{-10})=(\stackrel{x}{24}~~,~~ \stackrel{y}{-30}) \implies R=\underset{\textit{sum of the ratios}}{\left( \cfrac{\stackrel{\textit{sum of x's}}{-14 +24}}{3+2}~~,~~\cfrac{\stackrel{\textit{sum of y's}}{-10 -30}}{3+2} \right)} \n\n\n R=\left( \cfrac{ 10 }{ 5 }~~,~~\cfrac{ -40}{ 5 } \right)\implies R=(2~~,~-8)$

The area of a circular cake plate is 1520 cm ².Find the diameter to the nearest cm

Answers

Answer: 44 cm

Step-by-step explanation:

area of circle = πr²

1520 cm² = πr²

r is approximately 22 cm (21.996159369...)

so D (diameter) would be 44

Darnelle drew this figure and the accompanying equations. w + x + y = 180 y + z = 180Which equation must also be true?
A
w + z = 180
B
y – x = w
C
w + x + z = 180
D
w + x = z

Answers

Answer:

The correct option is D w + x = z

Step-by-step explanation:

Consider the provided equations.

$y + z = 180$

Solve the equation for y.

$y= 180-z$

Now substitute the vlaue of y in $w + x + y = 180$

$w + x + 180-z = 180$

Subtract 180 from both sides.

$w + x + 180-180-z = 180-180$

$w + x -z = 0$

Add z to both sides.

$w + x -z+z = z$

$w + x= z$

Hence, the correct option is D w + x = z

180=w+x+y and 180=y+z so

w+x+y=z+y so subtract y from both sides

w+x=z

A ship is traveling around the outside rim of an island surveying a good place to land. If it is 10 miles from a lighthouse at the center of the island and 45° from due north, how far has the ship traveled from the most northern tip of the island to the nearest tenth?

Answers

The correct answer for the question that is being presented above is this one: "C. 7.9 miles."

Area of the circle = pi * r^2
= pi * 100
= 314.15927.

It's traveled 45/360 = 1/8 of the circumference

Here are the following choices:
A. 0.8 miles
B. 4.5 miles
C. 7.9 miles
D. 12.5 miles

Step-by-step explanation:

Read the answer above/ below mine, I just wanted to point out that to solve this problem you use the circumference formula! The circumference of a circle is 2pi(r). r= radius= 10 (because 10 mi). Plug this into a calculator by typing: (20*pi) [division symbol] 8 =, and then it will give you 7.85..., but remember to round up to 7.9.

Kim, Kyle and Katie contribute the same amount to their fathers gift. Their older sister contributes $12. how much does Kate contribute is the total is $30.

Answers

The total cost was $30.00. The oldest sister contributed $12.00 leaving $18.00. The other two sisters divided this and it was $9.00 each

it's would be $6.00 dollars each because 30-12=18 then divide 18 by 3 and you get 6

Other Questions

The graphs of f(x) and g(x) are shown below:If f(x) = (x + 7)^2, which of the following is g(x) based on the translation? g(x) = (x + 9)^2 g(x) = (x + 5)^2 g(x) = (x − 9)^2 g(x) = (x − 5)^2

X = {(2, 3), (2, 4), (2, 5), (2, 6)} is x a function and why? no, each ordered pair in this list has the same first element. yes, no two ordered pairs in this list has the same second element. yes, there is more than one ordered pair in this list. no, there is a limited number of ordered pairs in this list.

What is the basic unit of weight in the metric system

Students who work ____ or more hours per week have average lower GPAs than students who work ____ or fewer hours per week.