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3 years ago

10

A bag contains yellow marbles and blue marbles, 42 in total. The number of yellow marbles is 2 less than 3 times the number of b

lue marbles. How many yellow marbles are there?

2 answers:

lions [1.4K]3 years ago

8 0

Answer:

31 yellow marbles

Step-by-step explanation:

Juliette [100K]3 years ago

4 0

There are 31 yellow marbles. Work is attached.

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It’s worth 10 points if you answer!

Maksim231197 [3]

Answer:

m∠x = 10°

Step-by-step explanation:

Since we are dealing with a <u>right triangle</u> and its two sides and one angle, we can use <u>trigonometry ratios</u>. Remember them all with the acronym SohCahToa.

"o" is for opposite side, "a" is for adjacent side, "h" is for hypotenuse side.

The ratios are:

sinθ = opposite/hypotenuse

cosθ = adjacent/hypotenuse

tanθ = opposite/adjacent

θ means the "angle of reference", or the angle you know or want to find. This determines which side is adjacent (touching) or opposite (not touching). The hypotenuse (longest side) does not change.

In this triangle, θ = x. The sides we know are hypotenuse and opposite. Therefore, we will use the sinθ ratio.

sinθ = opposite/hypotenuse

sinx = CB/AB Substitute the labels in the diagram

sinx = 4/23 Substitute known values (side lengths)

x = sin⁻¹(4/23) Isolate 'x'. Use calculator to solve.

x = 10.015....° Exact answer

x ≈ 10° Round to the nearest degree

Therefore the measure of angle x (m∠x) is 10°.

8 0

3 years ago

Patrick has just finished building a pen for his new dog. The pen is 3 feet wider than it is long. He also built a doghouse to p

zalisa [80]

General Idea:

(i) Assign variable for the unknown that we need to find

(ii) Sketch a diagram to help us visualize the problem

(iii) Write the mathematical equation representing the description given.

(iv) Solve the equation by substitution method. Solving means finding the values of the variables which will make both the equation TRUE

Applying the concept:

Given: x represents the length of the pen and y represents the area of the doghouse

<u>Statement 1: </u>"The pen is 3 feet wider than it is long"

$Length \; of\; the \; pen = x\\ Width \; of\; the\; pen=x+3$

------

<u>Statement 2: "He also built a doghouse to put in the pen which has a perimeter that is equal to the area of its base"</u>

$Area \; of\; the\; Dog \; house=y\\ Perimeter \; of\; Dog\; house=y$

------

<u>Statement 3: "After putting the doghouse in the pen, he calculates that the dog will have 178 square feet of space to run around inside the pen."</u>

$Area \; of \; the\; Pen - Area \;of \;the\;Dog \;House=\;Space\;inside\;Pen\\ \\ x \cdot (x+3)-y=178\\ Distributing \;x\;in\;the\;left\;side\;of\;the\;equation\\ \\ x^2+3x-y=178\Rightarrow\; 1^{st}\; Equation\\$

------

<u>Statement 4: "The perimeter of the pen is 3 times greater than the perimeter of the doghouse."</u>

$Perimeter\; of\; the\; Pen=3\; \cdot \; Perimeter\; of\; the\; Dog\; House\\ \\ 2(x \; + \; x+3)=3 \cdot y\\ Combine\; like\; terms\; inside\; the\; parenthesis\\ \\ 2(2x+3)=3y\\ Distribute\; 2\; in\; the\; left\; side\; of\; the\; equation\\ \\ 4x+6=3y\\ Subtract \; 6\; and \; 3y\; on\; both\; sides\; of\; the\; equation\\ \\ 4x+6-3y-6=3y-3y-6\\ Combine\; like\; terms\\ \\ 4x-3y=-6 \Rightarrow \; \; 2^{nd}\; Equation\\$

Conclusion:

The systems of equations that can be used to determine the length and width of the pen and the area of the doghouse is given in Option B.

$178=x^2+3x-y\\ \\ -6=4x-3y$

8 0

3 years ago

Read 2 more answers

435 L = ______ KL So what do i put in the blank spot ?? i dont know how to do this

docker41 [41]

$1000\ L-1KL\\ 435\ L-x\\ \\1000\cdot x=435\cdot1\cdot \ KL\ /:1000\\ \\x=0.435\ KL$

5 0

2 years ago

Read 2 more answers

federico ha tomado 2/5 de vaso de leche y maria ,4/10de vaso ¿alguno de los dos ha bebido mas leche o han bebido la misma cantid

umka2103 [35]

Answer:

Han bebido la misma cantidad.

Step-by-step explanation:

De la pregunta,

Frederico = 2/5 vaso de leche

María = 4/10 vaso de leche

Simplificando el gozo de la leche para María

= 2/5

Por tanto, podemos decir que:

Sí, han bebido la misma cantidad.

5 0

2 years ago

Tony took a math quiz last week. There were 80 problems on the quiz and Tony answered 70% of them correctly. How many problems d

Nutka1998 [239]

Answer:

56 problems

Step-by-step explanation:

So we already know that the answer is: 56. However, a good help is knowing how to obtain this answer from the data provided.

Tony's quiz had 80 questions

Tony correctly answered 70% of them.

We can always write a percentage amount as a ratio by dividing the amount by 100.

$70\% = \frac{70}{100} = 0.7$ .

This means that for every 100 questions, tony will respond correctly 70.

So, if Toni did a questionnaire of n questions, the amount that will answer correctly is calculated by the following expression:

$C = n*\frac{70}{100}$

If $n = 80$ then:

$C = 80 * \frac{70}{100}\\\\C = 56$

7 0

3 years ago

Read 2 more answers