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Vesna [10]
2 years ago
10

Solve x: 3x + 99x= 1224 10 pts

Mathematics
2 answers:
Tatiana [17]2 years ago
4 0

\huge\text{Hey there!}

\mathsf{3x + 99x = 1,224}\\\\\large\textbf{COMBINE the LIKE TERMS}\\\\\mathsf{(3x + 99x) = 1,224}\\\mathsf{3x + 99x = 1,224}\\\mathsf{\bold{102x} = 1,224}\\\\\large\textbf{DIVIDE 102 to BOTH SIDES}\\\\\mathsf{\dfrac{102x}{102} = \dfrac{1,224}{102}}\\\\\large\textbf{SIMPLIFY IT!}\\\\\mathsf{x = \dfrac{1,224}{102}}\\\\\mathsf{x = 12}\\\\\\\huge\text{Therefore, your answer should be: \boxed{\mathsf{x = 12}}}\huge\checkmark

\huge\text{Good luck on your assignment \& enjoy your day!}

<h3>~\frak{Amphitrite1040:)}</h3>

Masja [62]2 years ago
3 0
Answer is 12
Reason
Combine like terms
3x + 99 x = 1224
102x = 1224
Now solve for x
Divide both sides by 102
x= 12
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Answer: The GREATEST number of bookmarks that Logan can make = 31.

Step-by-step explanation:

GIven: Total petals = 95

Number of petals required for each bookmark = 3

Number the number of bookmarks can be prepared from 95 petals = 95 ÷ (Petals required of each bookmark)

= 95÷3

=31\dfrac{2}{3}\ \ \ \approx31\text{    [Round to the nearest whole number.]}

i.e. The GREATEST number of bookmarks that Logan can make = 31.

5 0
3 years ago
You want to get from a point A on the straight shore of the beach to a buoy which is 54 meters out in the water from a point B o
anyanavicka [17]

Answer:

x =\dfrac{45 \sqrt{6}}{ 2}

Step-by-step explanation:

From the given information:

The diagrammatic interpretation of what the question is all about can be seen in the diagram attached below.

Now, let V(x) be the time needed for the runner to reach the buoy;

∴ We can say that,

\mathtt{V(x) = \dfrac{70-x}{7}+\dfrac{\sqrt{54^2+x^2}}{5}}

In order to estimate the point along the shore, x meters from B, the runner should  stop running and start swimming if he want to reach the buoy in the least time possible, then we need to differentiate the function of V(x) and relate it to zero.

i.e

The differential of V(x) = V'(x) =0

=\dfrac{d}{dx}\begin {bmatrix} \dfrac{70-x}{7} + \dfrac{\sqrt{54^2+x^2}}{5} \end {bmatrix}= 0

-\dfrac{1}{7}+ \dfrac{1}{5}\times \dfrac{x}{\sqrt{54^2+x^2}}=0

\dfrac{1}{5}\times \dfrac{x}{\sqrt{54^2+x^2}}= \dfrac{1}{7}

\dfrac{5x}{\sqrt{54^2+x^2}}= \dfrac{1}{7}

\dfrac{x}{\sqrt{54^2+x^2}}= \dfrac{1}{\dfrac{7}{5}}

\dfrac{x}{\sqrt{54^2+x^2}}= \dfrac{5}{7}

squaring both sides; we get

\dfrac{x^2}{54^2+x^2}= \dfrac{5^2}{7^2}

\dfrac{x^2}{54^2+x^2}= \dfrac{25}{49}

By cross multiplying; we get

49x^2 = 25(54^2+x^2)

49x^2 = 25 \times 54^2+ 25x^2

49x^2-25x^2 = 25 \times 54^2

24x^2 = 25 \times 54^2

x^2 = \dfrac{25 \times 54^2}{24}

x =\sqrt{ \dfrac{25 \times 54^2}{24}}

x =\dfrac{5 \times 54}{\sqrt{24}}

x =\dfrac{270}{\sqrt{4 \times 6}}

x =\dfrac{45 \times 6}{ 2 \sqrt{ 6}}

x =\dfrac{45 \sqrt{6}}{ 2}

8 0
3 years ago
Anna buys 12 pens and 20 pencils for a total cost of $16. One pen costs $0.40 more than a pencil. What would one pencil and one
vladimir2022 [97]

It is given in the question that

Anna buys 12 pens and 20 pencils for a total cost of $16. One pen costs $0.40 more than a pencil.

Let the cost of pencil is $ x .

Therefore cost of pen is

$(x+0.40)

According to the question

12(x+0.40)+20x =16

Distributing 12 and combining like terms, we will get

12x+4.8+20x=16\\32x = 11.2\\x = 0.35

Therefore cost of pencil is $0.35 and cost of pen is

0.35+0.40=0.75

3 0
3 years ago
Daniela has the same amount of money automatically deposited into a new savings account each week. After 3 weeks, she has $18. A
Burka [1]

Answer:

$6 per week  (ratio 6/1)

Step-by-step explanation:

18/3=6

30/5=6

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100PT AND BRAINLIEST! PLEASE HELP! Use technology to approximate the solution(s) to the system of equations to the nearest tenth
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Answer:

C. (0.9, 0.3)

Explanation:

\rightarrow \sf  \dfrac{1}{4^{x}} = \log(2x)

The above given equation is critical to solve algebraically thus they have mentioned to solve it using a technology - graphing calculator.

<h3><u /></h3><h3><u>When graphed the following equations</u>:</h3>

They meet each other at: (0.9371, 0.2728)   \sf   \underset{ solution }{ \xrightarrow{ \text{ nearest tenth } } }  (0.9, 0.3)

8 0
2 years ago
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