The function h(x) is a transformation of the square root parent function,
f(t) = t. What function is H(x)?

Answer:

[tex]A=\frac{\sqrt{3}}{4}a^2[/tex]

Step-by-step explanation:

Since an equilateral has all of the sides equal, we can find the height of triangle using: [tex]a^2+b^2=c^2[/tex]. I attached a diagram which should explain how I got the dimensions of the three sides. Using the information from the diagram we get the equation:

[tex]h^2+(\frac{a}{2})^2=a^2[/tex]

Subtract a^2 from both sides

[tex]h^2=a^2-(\frac{a}{2})^2[/tex]

Take the square root of both sides

[tex]h = \sqrt{a^2-(\frac{a}{2})^2}[/tex]

If you know the area of a triangle, it's: [tex]\frac{1}{2}bh[/tex]. In this case the base=a, and the height is what we defined above. Using this we get:

[tex]A = \frac{a}{2}*\sqrt{a^2-(\frac{a}{2})^2}[/tex]

We can distribute the exponent over the division to get:
[tex]A = \frac{a}{2}*\sqrt{a^2-(\frac{a^2}{4})[/tex]

Now we can rewrite a^2 as 4a^2/4

[tex]A = \frac{a}{2}*\sqrt{\frac{4a^2}{4}-(\frac{a^2}{4})[/tex]

Now add the two fractions:

[tex]A = \frac{a}{2}*\sqrt{\frac{3a^2}{4}[/tex]

We can distribute the square root the division just like how we distributed the exponent 2, since the square root can be expressed as an exponent (1/2)

[tex]A = \frac{a}{2}*\frac{\sqrt{3a^2}}{\sqrt{4}}[/tex]

There's a radical identity that states: [tex]\sqrt[n]{a} * \sqrt[n]{b} = \sqrt[n]{a*b}[/tex]. We can use this to rewrite one radical as multiple radicals to simplify it:

[tex]A = \frac{a}{2}*\frac{\sqrt{a^2}*\sqrt{3}}{2}[/tex]

Simplify:

[tex]A = \frac{a}{2}*\frac{a*\sqrt{3}}{2}[/tex]

Now multiply the two fractions

[tex]A = \frac{a^2*\sqrt{3}}{4}[/tex]

This is the formula for the area of an equilateral triangle, but it is also often written as:
[tex]A=\frac{\sqrt{3}}{4}a^2[/tex]

Answer:

222 [ft²].

Step-by-step explanation:

1. the required area can be calculated according to the formula:

A=0.5*b*c*sin(A);

2. after substitution of b=32; c=19 and sin(A)≈0.7313537:

A=0.5*32*19*0.7313537=222.3315248 [ft²].

The given expression is undefined when x = 5 OR x = -5

From the question, we are to determine the value of x for which the given expression is undefined

The given expression is

x-4/3x²-75

An expression is undefined when the denominator equals zero

Thus, the expression is undefined when

3x² - 75 = 0

Now, we will determine the values of x in the equation above

3x² - 75 = 0

3x²  = 75

x² = 75/3

x² = 25

x = ±√25

x = ±5

Hence, the given expression is undefined when x = 5 OR x = -5

Learn more on Undefined expression here: https://brainly.com/question/19815575

#SPJ1

a) The equation of axis is the middle y-coordinate, which is y = -1.5.

b) The period is the amount of time it takes for the graph to repeat, which is 6.

c) The amplitude is the vertical distance from an extreme point to the midpoint, which is 3.

d) This is a cosine graph since when x=0, y is not equal to 0.

La solución del sistema de ecuaciones es igual a (x, y) = (308/47, 42/47).

Los sistemas de ecuaciones basadas en entidades algebraicas se resuelven mediante procedimientos algebraicos. Grosso modo, el método de resolución por igualación consiste en despejar una variable en dos ecuaciones del sistema para eliminarla y reducir el número de ecuaciones lineales y el número de variables.

A continuación, presentamos una aplicación del método de eliminación:

[tex]\frac{3\cdot x}{2\cdot y} = 11[/tex]

[tex]x = \frac{22\cdot y}{3}[/tex]

[tex]x + \frac{y}{2} = 7[/tex]

[tex]x = 7 - \frac{y}{2}[/tex]

[tex]\frac{22\cdot y}{3} = 7 - \frac{y}{2}[/tex]

[tex]\frac{47\cdot y}{6} = 7[/tex]

y = 42/47

[tex]x = 7 - \frac{y}{2}[/tex]

x = 308/47

La solución del sistema de ecuaciones es igual a (x, y) = (308/47, 42/47).

Para aprender más sobre los sistemas de ecuaciones: https://brainly.com/question/15811265

#SPJ1

Answer: 3

Step-by-step explanation:

[tex]\frac{3-0}{1-0}=3[/tex]

Answer:

80 square units

Step-by-step explanation:

These are rectangles and triangles.

The formula to get the area of a rectangle is its length multiplied by its width.

The formula to get the area triangle is its base multiplied by its height, then divided by 2.

The 3 rectangles all share the width of 6 units, so we can combine the 3 rectangles and consider it as 1 large rectangle.

The lengths of the rectangles are 2, 8, and 2 units.

We can add them together to get a total height of 12 units.

So, the formula to get the area of this rectangle is:
[tex]6\times12= A[/tex]

By solving this, we get:
A = 72 square units

There are 4 triangles remaining.

The base and height of all the triangles are 2 units.

So, by plugging these values into the triangle area formula, as mentioned from the beginning, we get:

[tex](2\times2)\div2=A[/tex]

So, the area of 1 triangle is 2 square units.

But since there are 4 triangles with the same bases and heights, we will multiply the area of 1 triangle by 4.

So, [tex]4 \times 2 = A[/tex]

This means the area of all the triangles together is 8 square units.

By adding the area of the triangles and rectangles together, we will get the answer.

[tex]72+8 = A[/tex]

So, the total area of this box is 80 square units.

Considering the Central Limit Theorem, we have that:

a) The probability cannot be calculated, as the underlying distribution is not normal and the sample size is less than 30.

b) The probability can be calculated, as the sample size is greater than 30.

It states that the sampling distribution of sample means of size n is approximately normal has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex], as long as the underlying distribution is normal or the sample size is greater than 30.

In this problem, the underlying distribution is skewed right, that is, not normal, hence:

More can be learned about the Central Limit Theorem at https://brainly.com/question/16695444

#SPJ1

The solution to the given polynomial in their degree are:

2a + 4a³ - 5a² - 1

= 4a³ - 5a² + 2a - 1

The leading coefficient is 4a³

4z - 2z² - 5z⁴

= -5z⁴ - 2z² + 4z

The leading coefficient is -5z⁴

(-3d² - 8 + 2d) + (4d - 12 + d²)

= -3d² - 8 + 2d + 4d - 12 + d²

= -2d² + 6d - 20

(y + 5) + (2y + 4y² - 2)

= y + 5 + 2y + 4y² - 2

= 4y² + 3y + 3

Learn more about polynomial:

https://brainly.com/question/4142886

#SPJ1

Answer:

For an exact answer the width would be the square root of 1011 and the length would be 1.5x the square root of 1011.

Step-by-step explanation:

A = lw

1516.5 = w(1.5)w

1516.5 = 1.5w^2  Divide both sides by 1.5

1011 = w^2  Take the square root of each side

Square root of 1011 = w.

We are looking for the graph of [tex]y=\sqrt{-x}[/tex]. which is shown in the attached image.

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Equation:}[/tex]

[tex]\mathsf{8,903 = e^{5x}}}[/tex]

[tex]\huge\textbf{Simplify:}[/tex]

[tex]\mathsf{8,903 = e^{5x}}}[/tex]

[tex]\mathsf{e^{5x} = 8,903}}[/tex]

[tex]\huge\textbf{Solve for the exponent:}[/tex]

[tex]\large\textsf{We get: }\downarrow\\\\\mathsf{2.718282^{5x}=8903}[/tex]

[tex]\huge\textbf{Take the logarithm from both sides:}[/tex]

[tex]\mathsf{log(2.718282^{5x}) = log(8,903x)}[/tex]

[tex]\large\textsf{We get:}\\\\\mathsf{5x \times log(2.718282)=log(8903)}[/tex]

[tex]\huge\textbf{Simplify it:}[/tex]

[tex]\mathsf{5x = \dfrac{log(8903)}{log(2.718282)}}[/tex]

[tex]\large\textsf{We get: }\\\\\mathsf{5x = 9.094143}[/tex]

[tex]\huge\textbf{Divide 5 to both sides:}[/tex]

[tex]\mathsf{\dfrac{5x}{5} = \dfrac{9.094143}{5}}[/tex]

[tex]\huge\textbf{Simplify it:}[/tex]

[tex]\mathsf{x= \dfrac{9.094143}{5}}[/tex]

[tex]\mathsf{x = 1.818829}[/tex]

[tex]\mathsf{x \approx 2}[/tex]

[tex]\huge\textbf{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{\mathsf{x =}\frak{\ 1.818829}}\huge\checkmark[/tex]

[tex]\large\textbf{Or if you're estimating your answer}\downarrow[/tex]

[tex]\huge\boxed{\mathsf{x \approx }\frak{\ 2}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

The blue curve of the image attached below represents the graph of the function f(x) = 3 · x².

In this question we have a power function formed by the product of a primitive function g(x) = x² and vertical dilation h(x) = 3, then:

f(x) = h(x) · g(x)

f(x) = 3 · x²

Now we proceed to graph both the primitive function and the transformed function with a graphing tool. Please notice that the primitive function is the red curve.

The statement presents typing mistakes. Correct form is shown below:

Show a graph for the following: f(x) = 3 · x².

To learn more on power functions: https://brainly.com/question/12431044

#SPJ1

Answer:

15

Step-by-step explanation:

cost of 20 mobile set=300

cost of 1 mobile set

=cost of mobile set/number of mobile set

=300/20

=15

The cost of each mobile set is ₹1,50,000.

Unit rate can be defined as the ratio between two measurements with the second term as 1. It is considered to be different from a rate, in which a certain number of units of the first quantity is compared to one unit of the second quantity.

Given that, a shopkeeper sold 20 mobile sets of same brand for ₹3,000,000.

The selling price of each mobile set​ = Total cost of mobile sets/Number of mobile sets

= 3,000,000/20

= ₹1,50,000

Therefore, the cost of each mobile set is ₹1,50,000.

To learn more about the unit rate visit:

https://brainly.com/question/11258929.

#SPJ2

Answer:

I think its 19.75

There does not appear to be a linear relationship between the high school girls' height and their IQ scores.

The complete question is added as an attachment

To plot the scatter plot, we make use of the following representations:

Next, we enter the values in a graphing calculator.

From the summary on the graphing calculator, we can conclude that the scatter plot is (c)

To determine the sample correlation coefficient, we make use of the following representations:

Next, we enter the values in a graphing calculator.

From the graphing calculator, we have the following summary:

X Values

Y Values

X and Y Combined

R Calculation

r = ∑((X - My)(Y - Mx)) / √((SSx)(SSy))

r = -19.25 / √((107.875)(813.5))

r = -0.065

Hence, the sample correlation coefficient is -0.065

In (b), we have:

r = -0.065

This means that there is a negative correlation

i.e. There does not appear to be a linear relationship between the high school girls' height and their IQ scores.

To do this, we have:

Number of pairs, n = 8

Significance level =0.01

Using a graphing calculator;

At 0.01 significance level, the critical correlation coefficient is 0.7887

0.7887 is greater than 0.01

This means that we accept the null hypothesis.

Read more about correlation at:

https://brainly.com/question/17237825

#SPJ1

(a) The truth about Karen's sales is that Karen had sales lower in value than about 74% of the salespeople. So, the correct option is D.

(b) The truth about Karen's and Brian's sales is that both Karen and Brian had lower sales in value than the median. So, the correct option is D.

Given that department stores rank their 1,000,000 salespeople by the monetary value of their sales. Karen's sales are at the 26th percentile and brian's sales are at the 33rd percentile.

A percentile is a measure used in statistics that indicates the value below which a certain percentage of observations in a group of observations falls.

(a)  Karen had sales lower in value than about 74% of the salespeople because the 26% percentile represents his relative position among all the employees in terms of sales.

(b) Both Karen and Brian had sales lower in value than the median because the Median represents the 50th percentile. Since Karen's sales are at the 26th percentile and Brian's sales are at the 33rd percentile it implies their sales are less than the median value.

Hence, the truth about Karen's sales is  Karen had sales lower in value than about 74% of the salespeople, and true about Karen's and Brian's sales is both Karen and Brian had lower sales in value than the median.

Learn more about percentile from here brainly.com/question/6616587

#SPJ1

Answer:

a.

2 / 3 + 5 / 6 - 1 / 2a.

2 / 3 + 5 / 6 - 1 / 2

= 0,66... + 0,833... - 0,5

= 1,5 - 0,5

= 1

Step-by-step explanation:

sorry I only know the letter A hope I helped anyway

The endpoints of the sides of the quadrilateral are; (1, 4), (2, 1), (5, 1), (4, 4)

To get the endpoints of the quadrilateral that has 2 sides with negative slope, we will use the formula for slope;

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

Option A; Coordinates are (–4, –4), (–4, –1), (–1, –4), (–1, –1). Slopes are;

m1 = (-1 + 4)/(-4 + 4) = undefined

m2 = (-4 + 1)/(-1 + 4) = -1

m3 = (-1 + 4)/(-1 + 1) = undefined

m4 = (-4 + 1)/(-4 + 1) = 1

No two slopes are negative and this is not correct.

Option B; Coordinates are (–2, –4), (–1, –1), (1, –1), (2, –4). Slopes are;

m1 = (-1 + 4)/(-1 + 2) = 3

m2 = (-1 + 1)/(1 + 1) = 0

m3 = (-4 + 1)/(2 - 1) = -3

m4 = (-4 + 4)/(-2 - 2) = 0

No two slopes are negative and this is not correct.

Option C; Coordinates are (1, 1), (2, 4), (5, 4), (4, 1). Slopes are;

m1 = (4 - 1)/(2 - 1) = 3

m2 = (4 - 4)/(5 - 2) = 0

m3 = (1 - 4)/(4 - 5) = 3

m4 = (1 - 1)/(1 - 4) = 0

No two slopes are negative and this is not correct.

Option D; Coordinates are (1, 4), (2, 1), (5, 1), (4, 4). Slopes are;

m1 = (1 - 4)/(2 - 1) = -3

m2 = (1 - 1)/(5 - 2) = -0

m3 = (4 - 1)/(4 - 5) = -3

m4 = (4 - 4)/(1 - 4) = -0

Two slopes are negative and this is correct.

Read more about Slope of Quadrilateral Sides at; https://brainly.com/question/2823280

#SPJ1

The simplified form of the given expression [tex]\frac{x^2-4x-21}{4(x+3)}[/tex] is [tex]\frac{x-7}{4}[/tex].

The steps to simplify a fractional expression are:

The given expression is [tex]\frac{x^2-4x-21}{4(x+3)}[/tex]

Factorizing the numerator:

x² - 4x - 21 = x² - 7x + 3x - 21

                 = x(x - 7) + 3(x - 7)

                 = (x - 7)(x + 3)

Then,

[tex]\frac{x^2-4x-21}{4(x+3)}[/tex] = [tex]\frac{(x-7)(x+3)}{4(x+3)}[/tex]

common factor (x + 3) is canceled out from both the numerator and the denominator

So,

[tex]\frac{x^2-4x-21}{4(x+3)}[/tex] = [tex]\frac{x-7}{4}[/tex]

Therefore, the simplified expression is [tex]\frac{x-7}{4}[/tex].

Learn more about simplifying an expression here:

https://brainly.com/question/13742517

#SPJ1

Answer:x-3/4

Step-by-step explanation:

(x-3)(x+7)/4(x+7)

=x-3/4

At x=0

At x=5

At x=10

Answer:

x = [tex]6\sqrt{3}[/tex] i

Step-by-step explanation:

We can write the following equation according to Euclidian Theorem to find the value of x:

[tex]x^{2}[/tex] = 12*9 multiply 9 and 12

[tex]x^{2}[/tex] = 108 find the root of both sides

x = [tex]6\sqrt{3}[/tex] is the value of x

Answer: 48m2 + 56m

Step-by-step explanation:

Answer:

Answer B

Step-by-step explanation:

Answer:

[tex]R^{-1}[/tex]={(2,1), (3,2), (9,3), (5,4)}

Step-by-step explanation:

Solution Given:

To find the inverse we need to exchange Domain to Range and vice-versa.

so

[tex]R^{-1}[/tex]={(2,1), (3,2), (9,3), (5,4)}

Answer:

As x increases, y increases along the entire graph.

Answer:

Step-by-step explanation:

First find the percentage of the ones that pass that study

.93 *(88)=88.84%

next find the ones that pass that did not study

.09*(100-88)=1.08

sum these to get the total passing percentage

88.84+1.08=82.92%

The probability is 82.9 per 100 or .8292 for student

E is the answer

The values of f⁻¹(f(6.022)) is 6.022 and f⁻¹(10) + f(-6) is 4

As  a general rule;

f⁻¹(f(x)) = x

This means that:

f⁻¹(f(6.022)) = 6.022

Also, we have:

f⁻¹(10) + f(-6)

From the table of values, we have:

f⁻¹(10) = -6 and f(-6) =10

So, we have:

f⁻¹(10) + f(-6) = -6 + 10

Evaluate

f⁻¹(10) + f(-6) = 4

Hence, the values of f⁻¹(f(6.022)) is 6.022 and f⁻¹(10) + f(-6) is 4

Read more about inverse functions at:

https://brainly.com/question/2541698

#SPJ1

If each collection consists of at most 3 books on each subject, the number of collection that can be made of 3 English, 4 Economics, and 5 Business Mathematics books are 40.

A combination, as a mathematical technique, determines the number of possible arrangements in a collection of items.

In the combination, the order of the selection does not matter.

The implication is that in combinations, one can select the items in any order, unlike permutations, where the order of selection matters.

English books on shelf = 3

Economics books on shelf = 4

Business Mathematics books on shelf = 5

Collections to be made = 3 books on each subject

The solution can be set up as a combination problem, as follows:

3 C 3 x 4 C 3 x 5 C 3

3! / 3! (3 – 3)! The solution is 1.

4! / 3! (4 – 3)! The solution is 4.

5! / 3! (5 – 3)! The solution is 10.

1 x 4 x 10

= 40

Thus, if each collection consists of at most 3 books on each subject, the number of collections that can be made of 3 English, 4 Economics, and 5 Business Mathematics books is 40.

Learn more about combinations and permutations at https://brainly.com/question/4658834

#SPJ1

[tex] \huge{↬ \boxed{ \sf{ \pink{A\green{n \blue{s \color{yellow}w \red{e \orange{r}}}}}}}}[/tex]

[tex] \leadsto[/tex]According to Angle sum property of a triangle , sum of the interior angles of a triangle is 180°.

➱ ∠SPR + ∠QPR = 180° [Linear pair]

➱ 135° + ∠QPR = 180°

➱ ∠QPR = 180° - 135°

➱ ∠QPR = 45°.....(i)

➱ ∠PQT + ∠PQR = 180° [Linear pair]

➱ 110° + ∠PQR = 180°

➱ ∠PQR = 180° - 110°

➱ ∠PQR = 70°.....(ii)

➛ ∠PQR + ∠QPR + ∠PRQ = 180° [Angle sum property of a triangle]

➱ 70°+ 45° + ∠PRQ = 180° [from (i) and (ii)]

➱ ∠PRQ = 180° - 115°

➥ ∠PRQ = 65°

hope it's help u!! :D