Select the correct answer from each drop-down menu.

Answer:

Step-by-step explanation:

Use pythagorean theorem (a^2+b^2=c^2). The diagonal represents c and the width represents b or a. 8^2+b^2=10^2->64+b^2=100->b^2=36->b=6. So your height would be 6.

La altura del triangulo está dada por el polinomio:

p(x) = a + 4

Recordar que para un triangulo de base B y altura H, el area es

A = B*H/2

En este caso, sabemos que la base es B = (4*a^2 + 6)

Y el area es A = 2a^3 + 8a^2 +3a +12

Entoces la altura será un polinomio tal que:

P(a)*(4*a^2 + 6)/2 = 2a^3 + 8a^2 +3a +12

P(a)*(4*a^2 + 6) = 2*(2a^3 + 8a^2 +3a +12) = 4a^3 + 16a^2 + 6a + 24

Podemos ver que p(a) va a ser un polinomio de grado 1, entonces:

p(a) = (c*a + b)

Reemplazando eso:

(c*a + b)*(4*a^2 + 6) = 4a^3 + 16a^2 + 6a + 24

Expandiendo:

(4c)*a^3 + (6c)*a + (4b)*a^2 + 6*b = 4a^3 + 16a^2 + 6a + 24

Comparando terminos del mismo exponente, podemos ver que:

(4c) = 4

6c = 6

4b = 16

6b = 24

Resolviendo esas ecuaciones para c y b, podemos ver que:

b = 16/4 = 4

c = 4/4 = 1

Entonces la altura del triangulo está dada por el polinomio:

p(x) = a + 4

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The total number of ways in which 4 questions can be answered if the first 2 questions have 3 choices and the last 3 have 4 choices = 144 + 192 = 336

We are given;

Total number of objective questions = 5 questions

Number of choices of first 2 questions = 3 choices

Number of choices of last 3 questions = 4 choices

Number of ways of answering the first 2 questions = 3 * 3 = 9 ways

Number of ways of answering the last 3 questions = 4 * 4 * 4 = 64 ways

Total number of ways of answering the five questions = 9 * 64 = 576 ways

Now, she has to answer only 4 which means it can be either 2 of the first and 2 of the last of 1 of the first and 3 of the last.

Thus, total number of ways of answering 4 questions if it is fist 2 and last 2 = 9 * 16 = 144

Total number of ways of answering 4 questions if 1 of the first and 3 of the last = 3 * 64 = 192

The total number of ways in which they can be answered if the first 2 questions have 3 choices and the last 3 have 4 choices = 144 + 192 = 336

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Using it's concept, the approximate perimeter of pentagon ABCDE is given as follows:

34.4 units.

The perimeter of a figure is given by the sum of the lengths of it's outside dimensions.

In this problem, the vertices are in a coordinate-plane, hence the distances are found using the formula for the distance between two points.

Suppose that we have two points, [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]. The distance between them is given by:

[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

The length of segment AB is:

[tex]AB = \sqrt{(6 - 0)^2+(0 - 7)^2} = 9.2[/tex]

The length of segment BC is:

[tex]BC = \sqrt{(6 - 3)^2+(0 + 4)^2} = 5[/tex]

The length of segment CD is:

[tex]CD = \sqrt{(-3 -3)^2+(-4 + 4)^2} = 6[/tex]

The length of segment DE is:

[tex]DE = \sqrt{(-6 + 3)^2+(0 + 4)^2} = 5[/tex]

The length of segment EA is:

[tex]EA = \sqrt{(-6 +0)^2+(0 - 7)^2} = 9.2[/tex]

Hence the perimeter is:

P = AB + BC + CD + DE + EA = 9.2 + 5 + 6 + 5 + 9.2 = 34.4 units.

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Considering the standard deviation, the data-set has no outliers.

For the given data-set, the mean is:

(35+31+29+34+6+31+32+30)/8 = 28.5.

Hence the standard deviation is:

[tex]S = \sqrt{\frac{(35-28.5)^2+(31-28.5)^2+(29-28.5)^2+(34-28.5)^2+(6-28.5)^2+(31-28.5)^2+(32-28.5)^2+(30-28.5)^2}{8}} = 8.7[/tex]

A measure is said to be an outlier if it is more than 3 standard deviations for the mean. Hence the thresholds are:

Since all values are between 2.4 and 54.6, the data-set has no outliers.

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Minimum: 59

Lower Quartile: 67

Median: 76

Upper Quartile: 86

Maximum: 92

Interquartile Range: 19

Answer: 25 ?

Step-by-step explanation:

Using it's concept, the average rate of change of the function on the interval [6,13] is given by:

[tex]r = \frac{f(13) - f(6)}{7}[/tex]

The average rate of change of a function is given by the change in the output divided by the change in the input. Hence, over an interval [a,b], the rate is given as follows:

[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]

In this problem, we want to find the rate in the interval [6, 13], which is given as follows:

[tex]r = \frac{f(13) - f(6)}{13 - 6} = \frac{f(13) - f(6)}{7}[/tex]

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The value of the functions f(x) and g(x) will be √(4x + 3) and √2. Then the correct option is B.

A statement, principle, or policy that creates the link between two variables is known as a function. Functions are found all across mathematics and are required for the creation of complex relationships.

If (f g)(x) = h(x) such that h(x) = √(8x + 6). Then we have

(f g)(x) = h(x)

f(x) · g(x) = h(x)

Then put the value of h(x), then we have

f(x) · g(x) = √(8x + 6)

f(x) · g(x) = √2(4x + 3)

f(x) · g(x) = √(4x + 3) × √2

Thus, the value of the functions f(x) and g(x) will be √(4x + 3) and √2.

Then the correct option is B.

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Answers:

16 cm²

24 cm²

40 cm²

Step-by-step explanation:

     The area of a rectangle can be found with A = L * W where A is the area, L is the length, and W is the width.

     [1] First shaded area

A = L * W

A = (4 cm) * (12 cm - 5 cm - 3 cm)

A = (4 cm) * (4 cm)

A = 16 cm²

     [2] Second shaded area

A = L * W

A = (2 cm) * (12 cm)

A = 24 cm²

     Lastly, we add them together.

16 cm² + 24 cm² = 40 cm²

[tex]5(1.5)=\boxed{7.5 \text{ yd}}[/tex]

The length of the curved border or arc is 7.5 yards.

the length of the arc = [tex]\theta \times r[/tex]

given that [tex]\theta[/tex] = 1.5 radian

radius = 5 yards

then the length of arc from the above formula

[tex]l = \theta \times r\\l = 1.5 \times 5 = 7.5[/tex] yards

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The graph of the four linear equations is the one we can see below, such that:

Here we have the set of linear equations:

We want to graph these 4 lines on the same coordinate axis.

The line:

y = -3

Is an horizontal line at y = -3

The line:

x = -3

Is a vertical line at x = -3.

And the other two are common linear equations that are graphed in the usual way, then the graph of all the linear equations is the one you can see below.

Where:

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Answer:

Maximum/Minimum Value:  (0,−2)   is a local minima (1/8,8)  is a local maxima

Explanation: Use the derivative to find the maximum and minimum

Answer:

Period = ¹/₄

Step-by-step explanation:

The cosine function is periodic, meaning it repeats forever.

Standard form of a cosine function:

f(x) = A cos(B(x + C)) + D

where:

Given function:

[tex]y=-5 \cos (8 \pi x)+3[/tex]

Comparing the given function with the standard form:

[tex]\implies \sf Period=\dfrac{2 \pi}{B}=\dfrac{2 \pi}{8 \pi}=\dfrac{1}{4}[/tex]

Therefore, the period of the given function is ¹/₄.

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A function, C(x), to model the water used by the car wash on a shorter day will be (B) 3x³ + 4x² - 11x - 8.

To find a function, C(x), to model the water used by the car wash on a shorter day:

Given information -

Now the amount of water is cut from the total water usage so to find out the new model c(x) we need to subtract the decrease in water from the total water usage.

We are trying to find:

Therefore, a function, C(x), to model the water used by the car wash on a shorter day will be (B) 3x³ + 4x² - 11x - 8.

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The correct question is given below:

The water usage at a car wash is modeled by the equation W(x) = 4x3 + 6x2 − 11x + 7, where W is the amount of water in cubic feet and x is the number of hours the car wash is open. The owners of the car wash want to cut back their water usage during a drought and decide to close the car wash early two days a week. The amount of decrease in water used is modeled by D(x) = x3 + 2x2 + 15, where D is the amount of water in cubic feet and x is time in hours.

Write a function, C(x), to model the water used by the car wash on a shorter day

Answer:

[tex]\huge\boxed{\sf x < 4}[/tex]

Step-by-step explanation:

-4x + 7 > x - 13

Subtract x to both sides

-4x - x + 7 > -13

-5x + 7 > -13

Subtract 7 to both sides

-5x > -13 - 7

-5x > -20

Divide -5 to both sides

x < -20/-5

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

Answer:

[tex]x < \bf 4[/tex]

Step-by-step explanation:

[tex]-4x + 7 > x -13[/tex]

We have to make [tex]x[/tex] the subject of the equation:

• Subtract [tex]x[/tex] from both sides:

[tex]-4x - x + 7 > -13[/tex]

⇒ [tex]-5x + 7 > -13[/tex]

• Now subtract 7 from both sides:

[tex]-5x > -13 - 7[/tex]

⇒ [tex]-5x > -20[/tex]

• Next divide both sides by -5, and remember that dividing an inequality by a negative number reverses the inequality symbol:

[tex]x < \frac{-20}{-5}[/tex]

⇒ [tex]x < \frac{20}{5}[/tex]

⇒ [tex]x < \bf 4[/tex]

A rule which describes the transformations that maps ΔJKL to ΔJ"K"L" is: D. translation of -2 units x, 0 units y composition 90 degree rotation about point 0.

A transformation refers to the movement of a point on a cartesian coordinate from its original (initial) position to a new location.

In Geometry, there are different types of transformation and these include the following:

Based on the diagram (see attachment), we can infer and logically deduce that a rule which describes the transformations that maps triangle JKL to triangle J"K"L" is a rotation of 90 degrees about the origin and then translated 2 units left.

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Since the product of the slope is -1, hence the lines are perpendicular

Two lines are known to be parallel if they have the same slope while if two lines are perpendicular if the product of the slope is -1

Given the coordinates of line 1 passing through (0, 6) and (6, 4), the slope is given as;

Slope = 4-6/6-0
Slope = -2/6
Slope = -1/3

Similarly for the coordinate points (-1, -7) and (1, -1).

Slope = -1+7/1+1
Slope of line 2 = 6/2

Slope = 3

Take the product of the slopes

Slope = -1/3 * 3
slope = -1

Since the product of the slope is -1, hence the lines are perpendicular

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Answer:

B.) x + 4y = 7

Step-by-step explanation:

(Step 1) ----------------------------------------------------------------------------------------------

To find the equation, we first need to find the slope using the point-slope form:

y₁ - y₂ = m(x₁ - x₂)

In this form, "m" represents the slope, "x₁" and "y₁" represent the values from the first point, and "x₂" and "y₂" represent the values from the second point.

Point 1: (-1, 2)                     Point 2: (3, 1)

x₁ = -1                                   x₂ = 3

y₁ = 2                                   y₂ = 1

y₁ - y₂ = m(x₁ - x₂)                                  <----- Point-slope form

2 - 1 = m(-1 - 3)                                      <----- Insert values

1 = m(-4)                                                <----- Subtract

-1/4 = m                                               <----- Divide both sides by -4

(Step 2) ---------------------------------------------------------------------------------------------

The given equations are in the slope-intercept form. The general structure looks like this:

y = mx + b

In this form, "m" represents the slope and "b" represents the y-intercept. To find the y-intercept, you can plug the newfound slope and values from one point into the equation.

x = -1

y = 2

m = -1/4

y = mx + b                                              <----- Slope-intercept form

2 = (-1/4)(-1) + b                                       <----- Insert values

2 = 1/4 + b                                              <----- Multiply -1/4 and -1

8/4 = 1/4 + b                                           <----- Make common denominators

7/4 = b                                                    <----- Subtract both sides by 1/4

(Step 3) ---------------------------------------------------------------------------------------------

The equation in slope-intercept form is thus: y = -1/4x + 7/4.

While this equation is accurate, it seems that it must be slightly manipulated. Therefore, we need to alter this equation to look like one of the answer choices. For instance, we can multiply the entire equation by 4 to remove the denominator.

y = -1/4x + 7/4                                         <----- Equation

4y = -x + 7                                               <----- Multiply all terms by 4    

x + 4y = 7                                               <----- Add "x" to both sides

The solution to the system of equations y = 1/2x - 6, x = -4 is x = -4 and y = -8. (x, y) = (-4, -8)

There are different types of equation. Namely;

y = 1/2x - 6

x = -4

y = 1/2x - 6

y = 1/2(-4) - 6

= -4/2 - 6

= -2 - 6

y = -8

Therefore,

The solution to the system of equations y = 1/2x - 6, x = -4 is x = -4 and y = -8. (x, y) = (-4, -8)

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Answer:

ANSWER:  mix 120 ml of 35% acid solution with 60 ml of 65% acid                      solution to obtain 180 ml 0f 45% acid solution

Step-by-step explanation:

If x = number of ml of 35% acid solution and 60 = number of ml of 65% acid solution, then x + 60 = number of ml of the mixture.

Acid content of first ingredient + acid content of second ingredient = acid content of the mixture

So, 0.35x + 0.65(60) = 0.45(x + 60)

    0.35x + 39 = 0.45x + 27

                12 = 0.10x

               120 = x

If the p-value is smaller than the level of significance, then it indicates strong evidence against the null hypothesis, as there is less than a 5% probability the null hypothesis is correct.

In this question,

A p-value is a probability, calculated after running a statistical test on data and it lies between 0 and 1. The p-value only tells you how likely the data you have observed is occurred under the null hypothesis.

One of the most commonly used p-value is 0.05. If the value is greater than 0.05, the null hypothesis is considered to be true. If the calculated p-value turns out to be less than 0.05, the null hypothesis is considered to be false, or nullified (hence the name null hypothesis).

A small p-value (< 0.05 in general) means that the observed results are unusual, assuming that they were due to chance only. Now, the smaller the p-value, the stronger the evidence that should reject the null hypothesis.

Hence we can conclude that if the p-value is smaller than the level of significance, then it indicates strong evidence against the null hypothesis, as there is less than a 5% probability the null hypothesis is correct.

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Step-by-step explanation:

Reduce 13/100 to lowest terms

13

100

is already in the simplest form. It can be written as 0.13 in decimal form (rounded to 6 decimal places).

Steps to simplifying fractions

Find the GCD (or HCF) of numerator and denominator

GCD of 13 and 100 is 1

Divide both the numerator and denominator by the GCD

13 ÷ 1

100 ÷ 1

Reduced fraction:

13

100

Therefore, 13/100 simplified to lowest terms is 13/100.

The mixed number [tex]7\dfrac{13}{100}[/tex] is [tex]\dfrac{713}{100}[/tex] on simplification.

A mixed number is a mathematical representation of a number that consists of a whole number and a fraction. It's called a "mixed number" because it combines both a whole number and a proper fraction. The whole number part represents a whole quantity, while the fractional proportion represents a proportion of a whole.

Mixed numbers are generally employed to represent measures that aren't whole numbers but are still greater than 1. They're particularly useful when dealing with magnitudes, such as lengths or quantities of things, that concern both whole units and fractional parts.

Given that

[tex]7\dfrac{13}{100}[/tex] [tex]= 7 + \dfrac{13}{100}[/tex]

       [tex]= \dfrac{700}{100}+ \dfrac{13}{100}\\= \dfrac{700+13}{100} \\= \dfrac{713}{100}[/tex]

Hence, The mixed number [tex]7\dfrac{13}{100}[/tex] can be simplified as [tex]\dfrac{713}{100}[/tex].

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The area of ​​the figure Magda shaded with side lengths of 1 and √2 centimeter is equal to 1.21 cm².

Mathematically, the area of a triangle can be calculated by using this formula:

Area = 1/2 × b × h

Where:

In order to calculate the area of ​​the figure Magda shaded with side lengths of 1 and √2 centimeter, we would determine the area of ​​each triangle as follows:

For triangle 1, we have:

Area = 1/2 × b × h

Area = 1/2 × 1 × 1

Area = 0.5 cm².

For triangle 2, we have:

Area = 1/2 × b × h

Area = 1/2 × √2 × 1

Area = 0.71 cm².

Total area = Area of triangle 1 + Area of triangle 2

Total area = 0.5 + 0.7

Total area = 1.21 cm².

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Complete Question:

Magda used a 1 cm square grid to draw the shaded figure, using right triangles. 1 cm 3 cm √2 cm 1 cm 1 cm what is the area of ​​the figure Magda shaded?​

Answer:

2.1 litres

Step-by-step explanation:

the 5 part of the ratio refers to 3.5 litres of red paint

divide this amount by 5 to find the value of one part of the ratio

3.5 litres ÷ 5 = 0.7 litres ← value of 1 part of the ratio , then

3 parts = 3 × 0.7 litres = 2.1 litres ← amount of blue paint used

Answer:

The value of

[tex]a {}^{b} - c \: b {}^{c} - a \: c {}^{a} - b \: [/tex]

is

[tex] \frac { 19}{8} [/tex]

Step-by-step explanation:

[tex]a {}^{b} - c \: b {}^{c} - a \: c {}^{a} - b[/tex]

where,

Thus, substitute these values to the given equation to find the values.

[tex]a {}^{b} - c \: b {}^{c} - a \: c {}^{a} - b ... \: substitute \: \\ given \: values \\ (1) {}^{2} - ( - 3)(2) {}^{ - 3} - 1( - 3) {}^{1} - 2 \\ 1 + 3 \: ( \frac{1}{8} ) - 1( - 3) - 2 \\ 1 + \frac{3}{8} + 3 - 2 \\ \frac{11}{8} + 3 - 2 \\ \frac{35}{8} - 2 \\ \frac{19}{8} = 2 \frac{3}{8} [/tex]

Hope it helps

The given statement is false because the triangles may not be identical if their corresponding angles are genuinely different.

Based only on the information given in the diagram, it is guaranteed that PQR~ STU:

Two right triangles, ΔPQR and  ΔSTU—are shown in the illustration with their right angles at ∠P and ∠S, respectively.

It is also demonstrated that TU = 12 units and QR = 6 units.

Because we only provided one set of congruent angles, we are unable to apply the A postulate of similarity to it.

Additionally, since there is only one pair of comparable sides, we are unable to determine whether they are proportionate.

The statement "based purely on the information presented in the diagram, it is assumed that triangle PQR triangle STU" is False because the triangles may not be identical if their corresponding angles are genuinely different.

Hence, The given statement is false.

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Answer:

748.23 in^2.

Step-by-step explanation:

Area = 1/2 * apothem * perimeter

        = 1/2 * 14.7 * 101.8

        =  748.23 in^2.

Answer:

748.23

Step-by-step explanation:

Answer:

1) 9.69

2) 87.36

3) 171.42

4) 18.75

5) 16.29

Step-by-step explanation:

Treat each value's full price as x. then, all of the values are (2/3)x. To get (2/3)x back to x, we must multiply (2/3)x*(3/2)=x. Multiply each of the questions given by 3/2 or 1.5

Answer:

look above

Step-by-step explanation:

hope it helps