A triangle has sides with lengths of 19 feet, 59 feet, and 69 feet. Is it a right triangle?

The value of the expression -x³ + 3x² - x + 20 when x = -1 is 23.

Given the expression in the question;

-x³ + 3x² - x + 20

To determine the value of the expression,

First, we substitute -1 for x in the expression:

-( -1 )³ + 3( -1 )² − ( -1 )) + 20

Next, we simplify each term using the order of operations (also known as PEMDAS):

-( -1 )³ = -( -1 ) = 1

(recall that the exponent is evaluated first, then the negative sign is applied)

3( -1 )² = 3(1) = 3

(recall that the exponent is evaluated first)

-( -1 ) = 1

(recall that subtracting a negative is the same as adding a positive)

Now, putting these simplified terms back into the original expression, we get:

1 + 3 + 1 + 20

Finally, we add these terms together to get the final answer:

23

Therefore, the value of the expression is 23.

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Since the distance was measured to the nearest metre, the upper bound for the distance is 101 metres.

1. To calculate the lower bound for Kelly's average speed, we need to divide the lower bound distance by the upper bound time. Since the distance was measured to the nearest metre, the lower bound for the distance is   [tex]99[/tex] Metres.

Since the time was measured to the nearest hundredth of a second, the upper bound for the time is  [tex]10.53[/tex] seconds. Therefore, the lower bound for Kelly's average speed is:

[tex]99/10.53 = 9.411[/tex]  metres per second (to three decimal places)

2. To calculate the upper bound for the perimeter of the regular hexagon, we need to multiply the upper bound length of a side by 6.

Since the length was measured to the nearest millimetre, the upper bound for the length is [tex]3.601 cm[/tex]  (since 3.6005 cm would round up to 3.601 cm). Therefore, the upper bound for the perimeter is:

[tex]6 x\times3.601 = 21.606 cm[/tex]   (to three decimal places)

3. To calculate the upper bound for the area of the rectangle, we need to multiply the upper bounds for the length and width. Since the length is correct to the nearest cm, the upper bound for the length is 35.5 cm (since 34.5 cm would round up to 35 cm).

Since the width is correct to the nearest cm, the upper bound for the width is 26.5 cm (since 25.5 cm would round up to 26 cm). Therefore, the upper bound for the area is:

 [tex]35.5 \times 26.5 = 942.25 cm^2[/tex] (to two decimal places)

4. To calculate the lower bound for Kelly's average speed, we need to divide the upper bound distance by the lower bound time.

Since the time was measured to the nearest hundredth of a second, the lower bound for the time is 10.51 seconds. Therefore, the lower bound

(d) To calculate the lower bound for Kelly's average speed, we need to divide the lower bound of distance by the upper bound of time.

The lower bound of distance is 99.5m (since the measurement was rounded down to the nearest metre).

The upper bound of time is 10.525s (since the measurement was rounded up to the nearest hundredth of a second).

So, the lower bound for Kelly's average speed is:

speed = distance / time [tex]= 99.5 / 10.525 = 9.45260637[/tex] ...

We need to round this to two decimal places to match the precision of the time measurement, giving us:

speed = [tex]9.45 m/s[/tex]

Therefore, the figures on the calculator display are: 99.5 ÷ 10.525 = 9.45260637... ≈ 9.45.

The length of the rectangle is measured as 645 mm correct to the nearest 5 mm. This means that the actual length could be anywhere between 642.5 mm and 647.5 mm (since rounding up or down depends on the decimal value being greater or less than 0.5 respectively).

Similarly, the width of the rectangle is measured as 400 mm correct to the nearest 5 mm. This means that the actual width could be anywhere between 397.5 mm and 402.5 mm.

5. To calculate the lower bound for the area of the rectangle, we need to find the product of the smallest possible length and width.

Smallest possible length [tex]= 642.5 mm[/tex]

Smallest possible width  [tex]= 397.5 mm[/tex]

Area = length x width

Lower bound for area = [tex]642.5 mm x 397.5 mm = 255542.5 mm²[/tex]

Rounding this off to 3 significant figures, we get the final answer as 2.56 x 10^5 mm².

Therefore, the lower bound for the area of the rectangle is [tex]2.56 x 10^5[/tex]  mm².

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Answer:

C.

Step-by-step:

The measure of angle A is congruent to the measure of angle P.

Answer:

50 sweets

Step-by-step explanation:

Let's work through the problem step by step:

The student starts with x sweets.

She gives away 20 sweets to her friends, so she is left with (x - 20) sweets.

One third of the remainder is equal to one fifth of the original number of sweets. In other words, (1/3)(x - 20) = (1/5)x.

To solve for x, we can start by multiplying both sides of the equation by 15 (the least common multiple of 3 and 5) to eliminate the fractions:

5(x - 20) = 3x

5x - 100 = 3x

2x = 100

x = 50

Therefore, the original number of sweets was 50.

Answer:

A

Step-by-step explanation:

Range referes to the smallest and largest values, so the answer you have circles is correct.

Good Job!

Answer: A) Range

Step-by-step explanation:

The range is the difference between the biggest and smallest numbers (or, in this case, folders). If Jack wants to find a notebook that will fit a small and large folder, he will need to find the range.

Answer:

YOU HAVE TO USE THE VECTORS AS WELL MATRIX TO GET THE SOLUTION OF THIS QUESTION

According to the solving Triangle The Value of X in the given figure is 20°

Triangles are three-sided polygons with three vertices. The angles of the triangle are formed by connecting the three sides end to end at a point. The total of the triangle's three angles equals 180 degrees which is called interior angles.

The three angles are given as ∠1=84°, ∠2=41°, ∠3=2x+15°.

Adding three angles

84° + 41° + 2x + 15° = 180° (sum of interior angle is 180°)

140° + 2x = 180°

2x = 180°-140°

2x = 40°

x = 20°

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Answer:

The answer is (f.g)(x) = 12x^2 - 9.

Step-by-step explanation:

To find (f.g)(x), we need to apply the composition of functions formula, which is:

(f.g)(x) = f(g(x))

First, we need to find g(x):

g(x) = 3x^2

Now, we need to plug g(x) into f(x) in place of x:

f(g(x)) = 4(g(x)) - 9

= 4(3x^2) - 9

= 12x^2 - 9

Therefore, (f.g)(x) = 12x^2 - 9.

Hope this helps, I'm sorry if it doesn't! If you need more help, ask me! :]

The ball strikes the grοund after apprοximately 1.07 secοnds.

Time: a measured οr measurable periοd during which an actiοn, prοcess, οr cοnditiοn exists οr cοntinues.

Speed: the rate at which sοmething mοves, οperates, οr happens.

Distance: the amοunt οf space between twο pοints οr οbjects.

We can sοlve this prοblem using the kinematic equatiοns οf mοtiοn. We knοw the initial velοcity (u = 7.30 m/s), the initial height (h = 2.91 m), and we want tο find the time taken fοr the ball tο hit the grοund (t).

Let's use the kinematic equatiοn that relates the final pοsitiοn (s), initial pοsitiοn (h), initial velοcity (u), acceleratiοn (a), and time (t):

[tex]s = h + ut + (1/2)at^2[/tex]

Since the ball is thrοwn vertically dοwnwards, the acceleratiοn is [tex]-9.81 m/s^2[/tex] (negative because it is in the οppοsite directiοn tο the initial velοcity).

At the mοment the ball hits the grοund, its final pοsitiοn s is zerο. Therefοre, we can rewrite the equatiοn as:

[tex]0 = h + ut + (1/2)at^2[/tex]

Solving for t, we get:

[tex]t = [-u\±\sqrt{(u^2 - 2ah)} ] / a[/tex]

We take the positive solution, since time cannot be negative. Substituting the values we get:

[tex]t = [ -7.30 \± \sqrt{((7.30)^2 - 2(-9.81)(2.91))} ] / (-9.81)[/tex]

[tex]t = [ -7.30 \± \sqrt{ (53.25)} ] / (-9.81)[/tex]

t ≈ 1.07 s οr t ≈ 0.31 s

The negative sοlutiοn dοesn't make physical sense in this cοntext, sο we discard it. Therefοre, the ball strikes the grοund after apprοximately 1.07 secοnds.

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The domain and range of given graph is Domain: (-∞, ∞) Range: (0, ∞)

What is Function ?

Function can be defined in which it relates an input to output.

The horizontal axis (x-axis) represents the input values, while the vertical axis (y-axis) represents the output values.

To identify the domain and range of this function from the graph, we can look at the values that the function takes on as well as the values that are excluded.

From the graph, we can see that the function appears to be increasing without bound as the input values increase. This means that the domain of the function is all real numbers or (-∞, ∞).

We can also see that the function appears to be taking on only positive values, and never touches or crosses the x-axis. This means that the range of the function is all positive numbers or (0, ∞).

Therefore, The domain and range of given graph is Domain: (-∞, ∞) Range: (0, ∞)

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The general form of the equation of this quadratic function is f(x) = x² - 2x + 1.

In Mathematics, the standard form of a quadratic equation is represented by the following mathematical equation;

ax² + bx + c = 0

Based on the information provided about this quadratic equation, it comprises the following ordered pairs;

Center (h, k) = (1, 0),

(x, y) = (0, 1).

By substituting the ordered pairs into the standard form of a quadratic equation, we have:

f(x) = a(x - h)² + k

1 = a(0 - 1)² + 0

1 = a

Therefore, the required quadratic equation is given by:

f(x) = 1(x - 1)² + 0

f(x) = (x - 1)(x - 1)

f(x) = x² - x - x + 1

f(x) = x² - 2x + 1

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The inverse functions and the domains and ranges of the inverse functions can be presented as follows;

A. The inverse function of f(x) is; [tex]f^{-1}(x) = \frac{3-x}{7\cdot x}[/tex]

B. f(g(x)) = [tex]\frac{3}{7\times \frac{(3-x)}{7\cdot x} + 1}[/tex] = x

C. The inverse function reverses the effect of the function. The inverse function is therefore;

x [tex]{}[/tex]      y

10[tex]{}[/tex]     5

6[tex]{}[/tex]      8

5[tex]{}[/tex]      9

4[tex]{}[/tex]      13

2) Domain; 10, 6, 5, 4

Range; 5, 8, 9, 13

An inverse function maps the output, or y-value of a function to the input value or x-value of the function.

2. A. f(x) = 3/(7·x + 1)

The inverse function can be found as follows;

Let f(x) = y

y = 3/(7·x + 1)

(7·x + 1) = 3/y

7·x = (3/y) - 1 = (3 - y)/y

x = (3 - y)/(7·y)

Plugging in x = f⁻¹(x), and y = x, to get;

B. g(x) = (3 - x)/(7·x)

f(x) = 3/(7·x + 1)

f(g(x)) = 3/(7 × ((3 - x)/(7·x)) + 1) = 3/(((3 - x)/(x)) + 1) = 3/(3/x - 1 + 1)

3/((3/x - 1 + 1) = 3/(3/x) = 3 × x/3 = x

Therefore; f(g(x)) = 3/(7 × ((3 - x)/(7·x)) + 1) = x

C. The inverse of the function is the function that produces the input of the function from the function's output, therefore, the inverse of the function can be presented as follows;

x [tex]{}[/tex]     y

10[tex]{}[/tex]    5

6[tex]{}[/tex]     8

5[tex]{}[/tex]     9

4[tex]{}[/tex]     13

2) The domain is the set of the possible inputs of the function, and the range is the set of the possible outputs of the function.

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The formula d=b2−4ac when solved for b = ± [tex]\sqrt{d +4ac}[/tex]. Option B

Subject of formula is defined as a variable that is being solved for in an equation.

It is the variable that is made to stand out in an equation. It is the variable that is made to stand alone on one end of the equality sign.

From the information given, we have that;

d=b2−4ac

Now, collect the like terms

d + 4ac = b²

Find the square root of both sides, we have that;

b = [tex]\sqrt{d + 4ac}[/tex]

Insert the plus-minus sign to show the interval, we have;

b = ± [tex]\sqrt{d +4ac}[/tex]

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Answer:

We can use the distance formula to find the distance between the center of the circle (2, -3) and the point (-1, -6), which should be equal to the radius of the circle.

Step-by-step explanation:

Distance = √[(x2 - x1)² + (y2 - y1)²]

Distance = √[(-1 - 2)² + (-6 - (-3))²]

Distance = √[(-3)² + (-3)²]

Distance = √(18)

So the radius of the circle is equal to √(18) or approximately 4.24.

The features of the given function are;

y-intercept at (0,10)

vertical asymptote of x = -4

A function is a relation in which each possible input value leads to exactly one output value. We say “the output is a function of the input.” The input values make up the domain, and the output values make up the range.

The function is given as;

g(x) = f(x + 4) + 8

The domain of a function is a set of all possible input values while the range of a function is defined as a set of all possible output values.

A vertical asymptote of a graph is a vertical line x = a where the graph tends toward positive or negative infinity as the inputs approach a.

Thus, vertical asymptote is x = -4.

The he feat will be at (0, 10)

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Based on the above, the Perimeter of the triangle DEF is 43.3 units

A mathematical statement known as an equation demonstrates the relationship between two or more numbers and variables by utilizing mathematical operations such as addition, reduction, multiplication, division, exponents, and so forth.

Given the triangle DEF. Using trigonometric ratio:

sin(38) = EF / 18EF = 11.1

Also: cos(38) = DF / 18DF = 14.2

The perimeter of triangle

DEF = DE + EF + DF

= 18 + 11.1 + 14.2 = 43.3 units

Hence, the Perimeter is 43.3 units

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The equation would be y = 0.50x + 10.00, and we have drawn the graph for the same.

What is the graph of the equation?

The graph of an equation is a visual representation of the set of all solutions (points) that satisfy the equation.

To find the equation of the line, we use the slope-intercept form of a linear equation, which is:

y = mx + b

where m is the slope of the line and b is the y-intercept (the point where the line crosses the y-axis).

In this case, we are given the slope of the line (0.50) and the y-intercept (10.00), so we can simply substitute these values into the equation:

y = 0.50x + 10.00

This gives us the equation of the line in slope-intercept form. We can use this equation to find the cost of a cab ride for any distance x (in miles) by substituting the value of x into the equation and solving for y (the fare).

Now let's draw the graph of the equation y = 0.50x + 10.00, we get

Hence, the equation would be y = 0.50x + 10.00, and we have drawn the graph for the same.

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]Therefore , the solution of the given problem of deviation comes out to be  the confidence interval contains both positive and negative values.

Statistics uses variance as a gauge of difference. The image of that figure is used to compute the average variance between the collection and the mean. It includes those data points itself into the calculations, unlike many other real measures of variability, by comparing also every figure to the mean.

Here,

Since the population standard deviation is unknown and the sample number is less than 30, we can use a t-distribution to build the confidence interval. The confidence interval's calculation is:

=>CI =  x t /2 × (s/n).

Since we need a 99% confidence range, = 0.01 and /2 = 0.005, and (n-1) = (49-1) = 48 is the number of degrees of freedom.

We discover that t/2 = 2.678 using the t-distribution table with 48 degrees of freedom and 0.005 significance level.

When we enter the numbers, we obtain:

=> CI = 3.1 ± 2.678 * (16.5/√49) = 3.1 ± 7.34

The estimated mean net change in LDL cholesterol following treatment, according to the 99% confidence range, is (4.24, 10.44) mg/dL.

We cannot say with 99% certainty that garlic is effective at lowering cholesterol because the confidence interval contains both positive and negative values.

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Answer:

38°

Step-by-step explanation:

this equal to 38° because angle EGD and angle IGJ are corresponding angles

Answer:

(36 × $7) - $15 = $252 - $15 = $237

The perimeter of the triangle will be 36.

The value of x in the triangle will be 101°.

The value of y will be 3x

It should be noted that the total sum of the angles that are in a triangle is 180°. It should be noted that the triangle is a Equilateral Triangle. In this case, since one of the sides is 12, the perimeter will be:

= 12 + 12 + 12

= 36

The value of x in the triangle will be:

= 180° - (22 + 57)

= 180° - 79°

= 101°.

The value of y will be 3x as vertically opposite angles are equal.

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Answer: An array is a collection of items of same data type stored at contiguous memory locations.

Step-by-step explanation: There you go dude happy to help

In triangles ABC and PQR, the ratio of the measure of side AB and side PQ is 2 : 3 and the ratio of the measure of sides BC and QR is 2 : 3. Thus, AB/PQ = BC/QR. Also, the m∠B = m∠Q. The ratio of two pairs of corresponding sides is congruent and the included angle is equal. Hence, ΔABC  ~ ΔPQR by SAS similarity theorem.

SAS similarity theorem is a theorem in geometry that stands for "Side-Angle-Side Similarity Theorem".

This theorem states that if two triangles have two pairs of corresponding sides that are proportional in length, and the included angles between these sides are congruent (have the same measure), then the two triangles are similar.

We can see that examining the two triangles, it is clear that it is in line with SAS similarity theorem.

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[tex]\dfrac{x^{2} + 10x + 21}{x + 7} = \dfrac{(x+3)(x+7)}{x + 7} = \bf x + 3[/tex]

___

[tex]x^{2} + 10x + 21 = x^{2} + 3x + 7x + 21 = x(x+3)+7(x+3) = (x+3)(x+7)\\[/tex]

Answer:

See below.

Step-by-step explanation:

We're asked to prove that ΔSTV ≅ ΔTUW.

Let's begin by reviewing what was given to us.

Because we already have one side and an angle congruent, we need to prove that another angle or side is congruent.

Our goal is to find a Congruency Postulate to prove that ΔSTV ≅ ΔTUW.

As we can see in the diagram, ∠STV ≅ ∠UTV as they're vertical angles. This is possible because Line Segment SV ≅ & ║ Line Segment TW.

We are now able to prove that ΔSTV ≅ ΔTUW with the Angle-Side-Angle Triangle Congruency Postulate (ASA). We proved, and were given 2 angles, and 1 side.

Summary:

∠STV ≅ ∠UTV | Vertical Angles.

ΔSTV ≅ ΔTUW | ASA.

Answer:

Coefficient, the coefficient is the number before the variable

Step-by-step explanation:

The mathematical word that describes both 2.25 and 6.75 in the expression 2.25x + 6.75x - 5.5 is "coefficients."

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

In this expression,

2.25 and 6.75 are coefficients of the variables x, which means that they multiply the variable x.

The term 5.5 is a constant because it does not contain a variable.

Thus,

The mathematical word that describes both 2.25 and 6.75 in the expression 2.25x + 6.75x - 5.5 is "coefficients."

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Answer:

To find the price of 3 tons of concrete, we need to first figure out how much Trey paid per ton of concrete.

Since Trey paid 42 dollars for 2/3 ton of concrete, we can set up a proportion:

2/3 ton = 42 dollars

1 ton = x dollars

To solve for x, we can cross-multiply:

(2/3) * x = 42 * 1

2x = 126

x = 63

So, Trey paid 63 dollars per ton of concrete.

To find the price of 3 tons of concrete, we can multiply the cost per ton by the number of tons:

3 tons * $63/ton = $189

Therefore, the price of 3 tons of concrete is $189.

Equations that have infinitely many solutions are:

B. 3x+8-x=3+5+2x

D. 5-4x+7= −2 (2x - 6)

An equation has infinitely many solutions when you try to solve the equation and you get a variable or a number equal to itself.

A. 3 (x + 4) = 2x - 7

3x + 12 = 2x - 7

3x -2x = -7 -12

x = -19

B. 3x+8-x=3+5+2x

3x -x - 2x =3 + 5 - 8

0 = 0

This equation has infinitely many solutions.

C. (4x − 8) = 2x − 4 + 12

4x − 2x =  − 4 + 12 + 8

2x = 16

x = 8

D. 5-4x+7= −2 (2x - 6)

5 - 4x + 7 = −4x + 12

-4x + 4x = 12 - 7 - 5

0 = 0

This equation has infinitely many solutions.

E. 4-3x - 8 = 2x + 7 - 5x

-3x - 2x + 5x = 7 + 8 - 4

0 = 11

Therefore, options B and D has infinitely many solutions.

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Note that the graphing form and vertex of each quadratic function are given as follows:


a) for f(x)=x² +6x+15, the graphing form of the quadratic function is f(x) = (x + 3)² + 6. The vertex is (-3, 6).

b) for y= x²-4x+9 the graphing form of the quadratic function is y = (x - 2)² + 5. The vertex is (2, 5).

c) for  f(x)= x² +8x, the graphing form of the quadratic function is f(x) = (x + 4)² - 16. The vertex is (-4, -16).

d) for . y=x² - 4x+9, the graphing form of the quadratic function is y = (x - 2)² + 5. The vertex is (2, 5).

a. To complete the square for the quadratic function f(x)=x² +6x+15, we add and subtract the square of half of the coefficient of x, which is (6/2)² = 9:

f(x) = x² + 6x + 15

= (x² + 6x + 9) + 6

= (x + 3)² + 6

Therefore, the graphing form of the quadratic function is f(x) = (x + 3)² + 6. The vertex is (-3, 6).

b. To complete the square for the quadratic function y= x^2-4x+9, we add and subtract the square of half of the coefficient of x, which is (-4/2)² = 4:

y = x^2 - 4x + 9

= (x^2 - 4x + 4) + 5

= (x - 2)² + 5

Therefore, the graphing form of the quadratic function is y = (x - 2)² + 5. The vertex is (2, 5).

c. To complete the square for the quadratic function f(x)= x² +8x, we add and subtract the square of half of the coefficient of x, which is (8/2)² = 16:

f(x) = x² + 8x

= (x² + 8x + 16) - 16

= (x + 4)² - 16

Therefore, the graphing form of the quadratic function is f(x) = (x + 4)² - 16. The vertex is (-4, -16).

d. To complete the square for the quadratic function y=x² - 4x+9, we add and subtract the square of half of the coefficient of x, which is (-4/2)² = 4:

y = x² - 4x + 9

= (x² - 4x + 4) + 5

= (x - 2)² + 5

Therefore, the graphing form of the quadratic function is y = (x - 2)² + 5. The vertex is (2, 5).

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