A 210-N mass is suspended from a horizontal beam by two cables that make angles of 29 degrees and 53 degrees with the beam. Find, using vectors, the tension in the cables.

Answer:

x=−2 in the formula for F(x) . Therefore, F(−2)=3(−2)2+1=3(4)+1=13 .

Considering the given quadratic function, we have that:

The equation of a quadratic function, of vertex (h,k), is given by:

y = a(x - h)² + k

In which a is the leading coefficient.

In this problem, the function is given by:

g(x) = -5(x - 3)²

Hence h = 3, k = 0, and the vertex is (3,0).

They are the values of x for which g(x) = 0, hence:

-5(x - 3)² = 0

(x - 3)² = 0

Applying the root to both sides:

x - 3 = 0.

x = 3.

The x-intercept is (3,0).

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Answer:

9 cm

Step-by-step explanation:

Formula :

Area (parallelogram) = Base × Height

=========================================================

Given :

⇒ Area = 153 cm²

⇒ Height = 17 cm

===========================================================

Solving :

⇒ 153 cm² = 17 cm × Base

⇒ Base = 153/17

⇒ Base = 9 cm

Answer:

Base = 9 cm

Step-by-step explanation:

Given dimensions:

To Find:

Solution:

This question is a bit tricky.Usually,the height and the base are given. We'll use the formula of area of parallelogram , then substitute/plug the values of height and area of parallelogram, with the exception of base as it's not given.

So recall the formulae of area of parallelogram:

[tex] \rm \: Area_{(Parallelogram)} = b \cdot{h}[/tex]

Plug/substitute the values of area of parallelogram & height:

[tex]\rm \: 153 \: cm ^2 =b \cdot17 \: cm[/tex]

We created an equation.Solve it now.

[tex] \implies \rm \cfrac{153 \: cm^2}{17 cm} = base[/tex]

[tex] \implies \rm9 \; cm = \: base[/tex]

[tex] \implies \rm \: Base = 9\; cm[/tex]

Yes! We're done!

Hence,the base is 9 cm of the parallelogram.

[tex] \rule{225pt}{2pt}[/tex]

The mean absolute deviation, rounded to the nearest hundredth, is: 11.67 calories.

To find the mean absolute deviation, find the mean of the data then find the average distance of each data point from the mean.

Given the data, 61, 42, 52, 27, 35, 23:

Mean = (61 + 42 + 52 + 27 + 35 + 23)/6

Mean = 240/6

Mean = 40

Mean absolute deviation = [(61 - 40) + ( 42 - 40) + ( 52 - 40) + ( 27 - 40) + ( 35 - 40) + ( 23 - 40) 6 = (21) + (2) + (12) + (13) + (5) + (17)] / 6 = 70/6

Mean Absolute Deviation = 11.67 calories.

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The closest to x the distance between the two poles is gotten as; x = 75 ft

From the Brainly link attached, we can see the diagram and we can say that;

We are given a right angled triangle with;

A known angle of; θ = 20°

Length of the hypotenuse = 80

Now, we want to find the length of the base x. Thus, we will use trigonometric ratio to get;

cos θ = x/hypotenuse

Thus;

cos 20 = x/80

x = 80 cos 20

x = 75.17 ft ≈ 75 ft

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Answer:

C: y = 8x^2 + 10.

Step-by-step explanation:

It looks close to being a parabola so I think it is probably a function in x^2.

Try 8x^2 + 10

Checking against the plot

When x = 5 , y = 8(5)^2 + 10 = 210 , and on graph its 200

Calculating y for other values:

When x = 7, y = 8(7)^2 + 10 = 402, and on graph y =  400.

When x = 11, y = 978 , and on graph  =  1000.

When x = 17, y = 2322, and on graph y = about 2350.

The zero of the linear function is -2

This is the point where the line of the equation crosses the x-axis

From the attached figure, the line cross the graph at:

x = -2

Hence, the zero of the function is -2

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[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$45000\\ r=rate\to 6.3\%\to \frac{6.3}{100}\dotfill &0.063\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &5 \end{cases} \\\\\\ A=45000\left(1+\frac{0.063}{12}\right)^{12\cdot 5}\implies A=45000(1.00525)^{60}\implies A\approx 61611[/tex]

Answer:

42 degrees.

Step-by-step explanation:

70 = 3x + 33 + 5x + 13

70 = 8x + 46

8x = 24

x = 3

m∠ABC = 9 + 33 = 42 degrees.

Answer:

how many are of each number

Step-by-step explanation:

because it just shows the range, and the average, and the quarters, you can't really tell how many of the "item" of associated with each number

Answer:

[tex] {f}^{ - 1}(x) = 2x + 8[/tex]

Step-by-step explanation:

[tex]f(x) = \frac{x}{2} - 4 \\ \\ y = \frac{x}{2} - 4 \\ \\ y = \frac{x - 8}{2} \\ \\ x = 2y + 8 \\ \\ {f}^{ - 1} (x) = 2x + 8[/tex]

Answer: 75TT

(When you answer in terms of pi, don’t multiply pi but leave it in your answer)

Step-by-step explanation:

assuming the grain pile is a pyramid, V=1/3 TT r^2

(1/3) (TT) (15^2). Remember radius is 1/2 of diameter

(1/3) (225) TT

Answer 75TT

Answer:

4

Step-by-step explanation:

16/4

Answer: [tex]35^{\circ}[/tex]

Step-by-step explanation:

[tex]m\angle BIG=90^{\circ}[/tex] since the lines are perpendicular, meaning that [tex]m\angle HIG=90-30-25=\boxed{35^{\circ}}[/tex]

The coordinate of point P so that P partitions segment AB in the part-to-whole ratio of 1 to 5 is [tex](-\frac{22}3, \frac{23}6)[/tex]

The given parameters are:

A = (-9,3)

B = (1, 8)

m : n = 1 : 5

The coordinate of point P is then calculated using:

[tex]P = \frac{1}{m + n} (mx_2+nx_1,my_2+ny_1)[/tex]

Substitute known values

[tex]P = \frac{1}{1 + 5} (1 * 1 + 5 * -9, 1 * 8 + 5 * 3)[/tex]

Evaluate

[tex]P = \frac{1}{6} (-44, 23)[/tex]

Evaluate the product

[tex]P = (-\frac{22}3, \frac{23}6)[/tex]

Hence, the coordinate of point P is [tex](-\frac{22}3, \frac{23}6)[/tex]

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Answer:

Step-by-step explanation:

In this numbers:

14.63

85.62

The two numbers where the digit 6 has a value of 0.6 are 14.63 and 85.62.

To determine in which two numbers the digit 6 has a value of 0.6, we need to examine the place value of 6 in each number.

Let's go through each number:

1. 16.7: The digit 6 is in the tens place, so its value is 6 * 10 = 60 (not 0.6).

2. 61.28: The digit 6 is in the ones place, so its value is 6 (not 0.6).

3. 14.63: The digit 6 is in the tenths place, so its value is 6 * 0.1 = 0.6.

4. 28.16: The digit 6 is in the hundredths place, so its value is 6 * 0.01 = 0.06.

5. 96.77: The digit 6 is in the tens place, so its value is 6 * 10 = 60 (not 0.6).

6. 85.62: The digit 6 is in the tenths place, so its value is 6 * 0.1 = 0.6.

The two numbers where the digit 6 has a value of 0.6 are 14.63 and 85.62.

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A function assigns the value of each element of one set to the other specific element of another set. The correct option is B.

A function assigns the value of each element of one set to the other specific element of another set.

The interval of the function for which the given graph is constant is when the value of x is less than -2 and when the value is greater than -4. Therefore, we can write this interval as -4< x < -2.

Hence, the correct option is B.

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The surface area of the composite figure is 144 square cm after calculating separately.

When a triangle is, stretch it out to produce a stack of triangles, one on top of the other. A triangular prism is the name given to this novel 3D object.

We have a composite figure made up of a triangular prism and a cuboid

First we calculate the surface area of the triangular prism:

= 2(area of one triangle) + area of three rectangles

= 2[(1/2)6×4] + 3×5 + 3×5

= 24 + 15 + 15

= 54 square cm

Surface area of rectangle(with three faces) = 2(4×3 + 4×6) + 3×6

= 2(12 + 24) + 18

= 72 + 18 = 90 square cm

Total surface area of figure = 54+ 90 = 144 square cm

Thus, the surface area of the composite figure is 144 square cm after calculating separately.

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A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely.

The correct option is A.

A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely.

The slope of the parallel line is always equal. Given the slope of the green line is -3/7, also, it is parallel to the red line. Therefore, the slope of the red line is -3/7.

Hence, the correct option is A.

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The most appropriate way to report a length measured by using this yardstick is to write the measurement in decimals (0.25) rather than in fraction (¼).

Measurement is a process through which the size, dimensions, or other physical quantities of magnitude that are associated with an object is taken, especially for use in a scientific research and experiment.

In Mathematics, a yardstick refers to a graduated measuring stick that has its length equal to one yard.

In this scenario, the most appropriate way to report a length measured by using this yardstick is to write the measurement in terms of decimals (0.25), so as to make easy approximations of the distance possible.

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The interior angles sum to 180°, so the missing angle has measure

180° - 106° - 12° = 62°

Use the law of sines to find RS:

sin(106°)/RS = sin(62°)/34   ⇒   RS = 34 sin(106°)/sin(62°) ≈ 37

Answer:

no because it just reaches one class, not the student body

Step-by-step explanation:

Answer:

Step-by-step explanation:

Similar = proportional

solve with an equation

12 : 9 = 4 : x

x = 4 * 9 : 12

x = 3

Answer:

1/2

Step-by-step explanation:

to solve this equation you must find the greatest common factor or gcf to make the denominators the same

that happens to be 6

so

-4 5/6 + 5 2/6

then you add

you can break them up at add them like this

(-4 + 5) + (-5/6 + 2/6)

1 + -3/6

-3/6 is also -1/2

1 + -1/2

1/2

that is your answer

The (g-f)(x) is option D: - x² - 6x + 5.

Terms are added or subtracted to make a polynomial. They're composed of variables and constants all in multiplication.

Given;

f(x) = x²+2x-4

g(x) = -4x+1,

Then the subtraction of the two function;

g(x) - f(x)

= -4x+1 - (x²+2x-4 )

= -4x+1 - x²- 2x + 4

= - x² - 6x + 5

Hence, the correct option is D: - x² - 6x + 5.

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(i) Both are boys = 0.3575757576, (ii) Both are girls = 0.1575757576 and (iii) one boy and one girl = 0.48484848 are the probabilities.

The Probability in mathematics is the possibility of an event in time. In simple words, how many times that incident is happening in any given time interval.

Given:

A class consists of 60 boys and 40 girls.

To find the probability if two students are chosen at random:

The probability is ¹⁰⁰C₂.

(i) Both are boys,

The probability is ⁶⁰C₂ ÷ ¹⁰⁰C₂.

⁶⁰C₂ ÷ ¹⁰⁰C₂ = 60! / {2! x (60-2)!} ÷ 100! / {2! x (100-2)!}

⁶⁰C₂ ÷ ¹⁰⁰C₂ = 30 x 59 / 50 x 99

⁶⁰C₂ ÷ ¹⁰⁰C₂ =0.3575757576

(ii) Both are girls,

The probability is ⁴⁰C₂ ÷ ¹⁰⁰C₂.

⁴⁰C₂ ÷ ¹⁰⁰C₂ = 40! / {2! x (40-2)!} ÷ 100! / {2! x (100-2)!}

⁴⁰C₂ ÷ ¹⁰⁰C₂ = 20 x 39 / 50 x 99

⁴⁰C₂ ÷ ¹⁰⁰C₂ =0.1575757576

(iii) one boy and one girl,

The probability is ⁴⁰C₁ ×  ⁶⁰C₁  ÷ ¹⁰⁰C₂.

⁴⁰C₁ ×  ⁶⁰C₁  ÷ ¹⁰⁰C₂ =

40! / {1! x (40-1)!}x 60! / {1! x (60-1)!} ÷ 100! / {2! x (100-2)!}

⁴⁰C₁ ×  ⁶⁰C₁  ÷ ¹⁰⁰C₂ = 40x60 / 50 x 99

⁴⁰C₁ ×  ⁶⁰C₁  ÷ ¹⁰⁰C₂=0.48484848

Therefore, the probabilities are (i) Both are boys = 0.3575757576, (ii) Both are girls = 0.1575757576 and (iii) one boy and one girl = 0.48484848

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The step of Talia that's incorrect is: C. step 3 because the slope ratio she calculated is incorrect.

The slope of a line (m) = rise/run = change in y / change in x.

Calculating the slope using two points on the line, (2, 5) and (1, 3), we should have:

Slope (m) = (5 - 3)/(2 - 1)

Slope (m) = (2)/(1)

Slope (m) = 2

This shows that the ratio of the slope calculated by Talia was wrong. The step that is incorrect is: C. Step 3

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The equation that represents the relationship between the number of liters, x, and the number of liquid pints, y is y = 2.11x

The attached table of values represents the missing piece in the question.

Start by calculating the rate of change using:

m = (y2 - y1)/(x2 - x1)

This gives

m = (14.77 - 10.55)/(7- 5)

Evaluate

m = 2.11

The equation is then calculated using:

y = m(x - x1) + y1

This gives

y = 2.11(x - 5) + 10.55

Evaluate

y = 2.11x - 10.55 + 10.55

y = 2.11x

Hence, the equation that represents the relationship between the number of liters, x, and the number of liquid pints, y is y = 2.11x

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