Which algebraic expression represents “the difference of fifty-four and seven times a number”?

The unknown number is 46.

A word problem is a verbal description of a problem situation. It consists of few sentences describing a 'real-life' scenario where a problem needs to be solved by way of a mathematical calculation.

For the given situation,

Let the number be x.

The sum of 74 and four times a number is 258,

⇒ [tex]74+4x=258[/tex]

⇒ [tex]4x=258-74[/tex]

⇒ [tex]x=\frac{184}{4}[/tex]

⇒ [tex]x=46[/tex]

Hence we can conclude that the unknown number is 46.

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To be able to solve clearly this problem, the best thing to do is to plot the graph (see attached pic). From the graph we can see that the points form a trapezoid.

The base is formed by the segment connecting point A and point B.

While the two heights: shorter one by the segment connecting points A and D, and the longer one by the segment connecting points B and C.

The formula for area of trapezoid is given as:

A = b (h1 + h2) / 2

Where,

b = base of the trapezoid  = 3 – (-4) = 7

h1 = shorter height = 2 – (-2) = 4

h2 = longer height = 2 – (-5) = 7

Therefore the area is:

A = 7 (4 + 7) / 2

A = 77 / 2

A = 38.5 

The answer is 38.5. I took this exam and I chose 38.5 and got it right, I hope this helps!

Amount of juice that cup B will hold than cup A when both are completely full is A: 18.8 cubic inches.  therefore, Option A: 18.8 cubic inches.

Amount of juice hold by Cup B which is in the shape of a cylinder having width 2 inches that is radius 1 inches and height 7 inches

πr^2h = π × 1^2 ×7 = 7π  cubic inches

Amount of juice hold by cup A which is in the shape of a cone having width 2 inches that is radius 1 inches and height 3 inches

1/3 × π × r^2 h

1/3 × π × 1^2 × 3  =  πcubic inches

Amount of juice that cup B will hold than cup A when both are completely full  = 7π - π = 6π cubic inches

= 6 × 3.14

= 18.84 cubic inches

Option A: 18.8 cubic inches

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Question

Look at the cups shown below (please note that images are not drawn to scale):

A cone is shown with width 2 inches and height 3 inches, and a cylinder is shown with width 2 inches and height 7 inches.

How many more cubic inches of juice will cup B hold than cup A when both are completely full? Round your answer to the nearest tenth.

18.8 cubic inches

21.9 cubic inches

25.1 cubic inches

32.6 cubic inches

we have

[tex] 2x + 5y = 10 [/tex]

we know that

the formula to calculate the slope is equal to

[tex] m=\frac{(y2-y1)}{(x2-x1)} [/tex]

Let

[tex] A( 5,0)\\B( 0,2) [/tex]

Step [tex] 1 [/tex]

Find the slope AB

[tex] mAB=\frac{(2-0)}{(0-5)} \\ \\ mAB=-\frac{2}{5} [/tex]

therefore

the answer is the option B

[tex] -\frac{2}{5} [/tex]

the graph in the attached figure

To determine the length of the hypotenuse in a triangle with an angle measure of 92 degrees and a side length of 10 inches, we can use the sine ratio. Calculating the value of Sin(92 degrees) and dividing 10 by that value, we find that the hypotenuse is approximately 10.001525 inches.

A triangle brace with an angle measure of 92 degrees and a side length of 10 inches opposite this angle, and a base length of 12 inches adjacent to the given angle. To determine which of the given statements is correct, we need to use trigonometric ratios. We can use the sine ratio in this case.

The sine of an angle is equal to the length of the side opposite the angle divided by the length of the hypotenuse. In this case, the angle measure is 92 degrees and the side opposite is 10 inches. Let's calculate:

Sin(92 degrees) = Opposite/Hypotenuse

Sin(92 degrees) = 10/Hypotenuse

To solve for the hypotenuse, we can rearrange the equation:

Hypotenuse = 10/Sin(92 degrees)

Using a calculator, we can evaluate Sin(92 degrees) and then divide 10 by that value to find the hypotenuse:

Hypotenuse = 10/0.9998477 = 10.001525 inches (approximately)

Based on this calculation, the correct statement would be that the hypotenuse is approximately 10.001525 inches.

Answer:

Factors of 60 are:

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60

The value of f(-1) from the table given is 0

Table of functions are used to find the relationship between variables. The variables x and y can be written as coordinate (x, y)

In order to determine f(-1), we need the value of f(x) at the point where x is 1. From the table, the value of f(-1) is 0

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The constant term will be the product of -p and -q.

A trinomial is an algebraic expression that has three non-zero terms and has more than one variable in the expression.

Given that the factors of a trinomial are (x - p) and (x - q) we need to determine the constant term of the trinomial:

We know that a trinomial in its factors form can be written as,

x² + (α+β)x + αβ, where α and β are factors.

So, here the constant term of the trinomial will be (-p) × (-q) = pq.

Hence the constant term will be the product of -p and -q.

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3^2/3 means squaring the number 3 to get 9, and then taking the cube root of 9, which is approximately 2.08008.

To calculate 3^2/3, we are dealing with an exponential expression where 3 is the base and 2/3 is the exponent. The exponent 2/3 means we must first square the base, which is 3, giving us 3 squared: 32 = 9. Next, we take the cube root (denominator of the fraction exponent) of this result since the exponent is 2/3, meaning the cube root of 9.

To find the cube root of 9, we look for a number which, when multiplied by itself three times, equals 9. Unfortunately, 9 is not a perfect cube, but using estimation or a calculator, we can find that the cube root of 9 is approximately 2.08008. Therefore, the exact expression for 32/3 remains (9)1/3 and the approximate decimal value is 2.08008.

there are 3600 seconds per hour

5280 feet per mile

1 foot per second = 3600/5280 = 0.681818 Miles per Hour

 60 seconds per minute

 so 1500/60 = 25 feet per second

25 x 0.681818 = 17.05 miles per hour

Using the combination formula, it is found that it would be possible to elect 27,405 different leadership committees.

The order in which the students are selected to the committee is not important, which means that the combination formula is used to solve this question.

Combination formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

In this problem, 4 students are chosen from a set of 30, thus:

[tex]C_{30,4} = \frac{30!}{4!26!} = 27405[/tex]

It would be possible to elect 27,405 different leadership committees.

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If two triangles are similar then the corresponding sides are in proportion. Thus,

AB / AU = BC / UV = AC / AV

AB / (20x+108) = 703 / 444

Where AB is equivalent to:

AB = AU + UB

AB = 20x + 108 + 273

AB = 20x + 381

Therefore going back to the first equation:

(20x + 381) / (20x + 108) = 703/444

444 (20x + 381) = 703 (20x + 108)

8880x + 169164 = 14060x + 75924

14060x - 8880x = 169164 – 75924

5180 x = 93240

x = 93240 / 5180

x = 18          (ANSWER)

The correct value of x is [tex]\(\frac{1}{20}\)[/tex].

To solve for x, we need to use the properties of similar triangles. The sides of similar triangles are proportional. Given that triangles AU V and ABC are similar, we can set up the following proportion:

[tex]\[\frac{AU}{AB} = \frac{UV}{BC} = \frac{AV}{AC}\][/tex]

We are given the lengths of the sides as follows:

- (AU = 20x + 108)

- (UB = 273) (which is part of AB, since (AB = AU + UB)

- (BC = 703)

- (UV = 444)

- (AV = 372)

- (AC = 589)

Using the proportion involving the sides AU, UB, UV, and BC, we have:

[tex]\[\frac{AU}{UB} = \frac{UV}{BC}\][/tex]

Substituting the given values, we get:

[tex]\[\frac{20x + 108}{273} = \frac{444}{703}\][/tex]

Cross-multiplying to solve for x, we have:

[tex]\[(20x + 108) \cdot 703 = 444 \cdot 273\][/tex]

Expanding both sides gives us:

[tex]\[14060x + 76184 = 121172\][/tex]

Subtract (76184) from both sides to isolate the term with x:

[tex]\[14060x = 121172 - 76184\] \[14060x = 49888\][/tex]

[tex]\[x = \frac{49888}{14060}\][/tex]

Simplifying the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 20, we get:

[tex]\[x = \frac{2494.4}{703}\][/tex]

Since (2494.4) is very close to (2496), and \(2496\) divided by (703) is (3.55), which is (20) times (0.1775), we can see that:

[tex]\[x = \frac{1}{20}\][/tex]

Therefore, the value of x is [tex]\(\frac{1}{20}\)[/tex].

The probability helps us to know the chances of an event occurring. The theoretical probability that they have three dogs or three cats is 0.25.

The probability helps us to know the chances of an event occurring.

[tex]\rm{Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]

As it is given that the pet can either be a dog or a cat, therefore,

The probability that all the three pets are dogs is:

[tex]\rm P(X= 3\ dogs) = \dfrac{1}{2}\times \dfrac{1}{2}\times \dfrac{1}{2} = \dfrac{1}{8}[/tex]

The probability that all the three pets are cats is:

[tex]\rm P(X= 3\ Cats) = \dfrac{1}{2}\times \dfrac{1}{2}\times \dfrac{1}{2} = \dfrac{1}{8}[/tex]

Now, we need to calculate the probability that all three pets are either dogs or cats, therefore, the probability can be written as,

[tex]\rm P(3\ Dogs\ or\ 3\ Cats) = P(X = 3\ dogs) + P(X = 3\ cats)[/tex]

                                [tex]= \dfrac{1}{8}+\dfrac{1}{8}\\\\=\dfrac{2}{8}\\\\ = \dfrac{1}{4} = 0.25[/tex]

Hence, the theoretical probability that they have three dogs or three cats is 0.25.

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Answer:

(-4,-1) satisfies the given system of inequalities

Step-by-step explanation:

[tex]2x+y<-5[/tex]

[tex]-x+y>0[/tex]

To find out the solution we check with each option

(4,1) , x=4 and y=1 (Plug in x and y values in the given inequalities)

[tex]2(4)+1<-5[/tex]

[tex]9<-5[/tex] False

(-4,-1) , x=-4 and y=-1 (Plug in x and y values in the given inequalities)

[tex]2(-4)-1<-5[/tex]

[tex]-9<-5[/tex] True

Now plug it in second inequality

[tex]-(-4)-1>0[/tex]

[tex]3>0[/tex] True

(-8,-21) , x=-8 and y=-21 (Plug in x and y values in the given inequalities)

[tex]2(-8)-21<-5[/tex]

[tex]-37<-5[/tex] True

Now plug it in second inequality

[tex]-(-8)-21>0[/tex]

[tex]-13>0[/tex] False

(8,11) , x=8 and y=-11(Plug in x and y values in the given inequalities)

[tex]2(8)+11<-5[/tex]

[tex]-9<-5[/tex] false