If an equilateral triangles sides are 8 inches long, what is the height?
I think it’s 8.48 but i’m not sure.

Two conditions under which we can assume that the sample means follow a normal distribution are as follows:

1). If the sample size is large​ enough, n greater than or equals 30, the sampling distribution is approximately normal regardless of the shape of the population.

2). In order to be considered a normal distribution, a data set (when graphed) must follow a bell-shaped symmetrical curve centered around the mean.

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Answer:

Step-by-step explanation:

Answer:

4.47

Step-by-step explanation:

4^2+b^2=6^2

16+b^2=36

-16. -16

√b^2=√20

b=4.47

Answer:

y=2/3(x-3)^2+1

Step-by-step explanation:

The parent function of a parabola is y=x^2:

The transformation of this graph shows the parabola is shifted to the right 3 and up 1 so we apply that to our equation y=(x-3)^2+1

to solve the stretch factor:

y=a(x-3)^2+1

we can see when x=0 y=7 so we use this set

7=a(0-3)^2+1

7=a(-3)^2+1

-1            -1

6=9a

divide by 9

a=2/3

The solution to the system of equation graphed is (-1, -3)

Given the system of equations graphed on the plane expressed as:

f(x) = 3x

g(x) = 4x + 1

Equate

f(x) = g(x)

3x = 4x + 1

3x - 4x = 1

-x = 1

x = -1

Determine the value of y

y = 3x

y = 3(-1)

y = -3

Hence the solution to the system of equation graphed is (-1, -3)

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The trigonometric function gives the ratio of different sides of a right-angle triangle. The given problems can be solved as given below.

The trigonometric function gives the ratio of different sides of a right-angle triangle.

[tex]\rm Sin \theta=\dfrac{Perpendicular}{Hypotenuse}\\\\\\Cos \theta=\dfrac{Base}{Hypotenuse}\\\\\\Tan \theta=\dfrac{Perpendicular}{Base}\\\\\\Cosec \theta=\dfrac{Hypotenuse}{Perpendicular}\\\\\\Sec \theta=\dfrac{Hypotenuse}{Base}\\\\\\Cot \theta=\dfrac{Base}{Perpendicular}\\\\\\[/tex]

where perpendicular is the side of the triangle which is opposite to the angle, and the hypotenuse is the longest side of the triangle which is opposite to the 90° angle.

1st.) x = 5 /Sin(30°)

x = 10

!) sin(45°) = 4/x

x = 4/sin(45°)

x = 4√2

I) Cos(45°) = √3 / x

x = √3 / Cos(45°)

x = √6

E) Tan(60°) = 3√3 / x

x = 3√3 / 3

W) For isosceles right-triangle, the angle made by the legs and the hypotenuse is always 45°.

x = 45°

N) x² + x² = (7√2)²

x = 7

V) Tan(60°) = 7 / x

x = 7√3/3

K) x² + x² = (9)²

x = 9/√2

Y) Sin(60°) = 7√3/x

x = 14

M) Sin(30°) = x/11

x = 11/2

T) Sin(45°) = x/√10

x = √5

A) x + 2x + 90° = 180°

x = 30°

O) Sin(45°) = √2 / x

x = 2

R) Tan(30°) = x / 4

x = 4/√3 = 4√3 / 3

S) Sin(60°) = x / (10/3)

x = 5√3 / 3

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In the function, the thing that is represented is the area of the walkway along the length of the flower patch.

From the information given, Sam created function A to represent the total area taken up by the flower patch and walkway by multiplying the functions modeling the new total length and width.

Therefore, the thing that is represented is the area of the walkway along the length of the flower patch.

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The easiest way to find the slope of a line given in standard form is to put it into slope-intercept form.

Slope-intercept form: y = mx + b

---m is the slope, b is the y-intercept

10x + 5y = 4

5y = -10x + 4

y = -2x + 4/5

The slope of the line is -2.

Hope this helps!

The compound inequality that represents the given graph is x < -2 or x ≥ 4. The correct option is B. x < -2 or x ≥ 4

From the question, we are to write the compound inequality that represents the given graph

In the graph, we have

x < -2

or

x ≥ 4

Hence, the compound inequality that represents the given graph is x < -2 or x ≥ 4. The correct option is B. x < -2 or x ≥ 4

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Answer: (3,-2)

Step-by-step explanation:

[tex]-3x-7y=5\\15x+6y=33[/tex]

[tex]5(-3x-7y)=5(5)\\-15x-35y=25[/tex]

new system:

[tex]-15x-35y=25\\15x+6y=33[/tex]

add.

[tex]-29y=58\\y=-2[/tex]

plug in -2 for y

[tex]-3x-7(-2)=5\\-3x+14=5\\-3x=-9\\x=3[/tex]

system:

[tex](3,-2)[/tex]

Answer:

(3, - 2 )

Step-by-step explanation:

- 3x - 7y = 5 → (1)

15x + 6y = 33 → (2)

multiplying (1) by 5 and adding to (2) will eliminate x

- 15x - 35y = 25 → (3)

add (2) and (3) term by term to eliminate x

0 - 29y = 58

- 29y = 58 ( divide both sides by - 29 )

y = - 2

substitute y = - 2 into either of the 2 equations and solve for x

substituting into (2)

15x + 6(- 2) = 33

15x - 12 = 33 ( add 12 to both sides )

15x = 45 ( divide both sides by 15 )

x = 3

solution is (3, - 2 )

Answer:

1.875 liters

Step-by-step explanation:

x=1.25×32=3.752=1.875 liters

The statement first, and the statement second are correct because the number of dimes is 34, and the number of quarters is 66

What is a linear equation?

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

We have:

0.1x + 0.25y = 19.9 and

x + y = 100

Let x = number of dimes

y = number of quarters

After solving the above system of equations by substitution method.

[tex]\rm \dfrac{398-5y}{2}+y=100[/tex]

y = 66

[tex]\rm x=\dfrac{398-5\cdot \:66}{2}[/tex]

x = 34

Thus, the statement first, and the statement second are correct because the number of dimes is 34, and the number of quarters is 66

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Answer:

[tex]x^2 - 10x + 25[/tex]

Step-by-step explanation:

Hello!

Expand the square using the Distributive Property.

Distributive x - 5 to each factor

The answer is [tex]x^2 - 10x + 25[/tex].

We can also use a special binomial product formula.

Formula: [tex](a - b)^2 = a^2 - 2ab + b^2[/tex]

We get the same answer both ways.

Answer:

cheeseburger costs $1.25

Step-by-step explanation:

let x be the cost of a cheeseburger and y the cost of chilli and set up 2 simultaneous equations, that is

12x + 4y = 19.4 → (1)

8x + 6y = 16.6 → (2)

multiplying (1) by 6 and (2) by - 4 and adding the result will eliminate y

72x + 24y = 116.4 → (3)

- 32x - 24y = - 66.4 → (4)

add (3) and (4) term by term to eliminate y

40x + 0 = 50

40x = 50 ( divide both sides by 40 )

x = 1.25

the cost of a cheeseburger is $1.25

Answer:

The two numbers are 56 and 23.

Step-by-step explanation:

Let the two numbers be A and B.

We are told that:

A+B = 79, and

2)  3A + 5B = 283

Rearrange the first expression to isolate A:

A = 79-B

Now use this value of B in the second expression:

3A + 5B = 283

3(79-B) + 5B = 283

237-3B + 5B = 283

2B = 46

B = 23

If B=23, we can find A from (1):  

A+B = 79

A+23 = 79

A = 56

CHECK:

Does A+B = 79?

56 + 23 = 79?  YES

Does 3A + 5B = 283?

  3(56) + 5(23) = 283?

 168 + 115 = 283?  YES

Because we can't divide by zero, csc(θ) is undefined when θ = 0°, so the correct option is A.

First, remember that:

[tex]csc(\theta) = 1/sin(\theta)[/tex]

And also remember that we can't divide by zero.

Then the function csc(θ) is undefined for the values of θ such that sin(θ) = 0.

We know that sin(0°) = 0.

Then csc(0°) is undefined. This means that the correct option is the first one.

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Answer:

Hello! The answer is x ≥ [tex]\frac{7}{2}[/tex].

Step-by-step explanation:

To solve this inequality, we have to get x by itself. To do so, we will rearrange the inequality. To do so, we will subtract 6x from both sides and add 3 to both sides:

8x - 3 ≥ 6x + 4

-6x +3  -6x  +3

----------------------

2x ≥ 7

Now, we have to get x by itself and divide both sides by 2 to do so:

2x ≥ 7

--     --

2      2

This leaves us with:

x ≥ [tex]\frac{7}{2}[/tex]

The required solution to the inequality 8x - 3 ≥6x + 4 is x ≥ 3.5.

Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

To solve the inequality, we want to isolate the variable x on one side of the inequality symbol.

8x - 3 ≥ 6x + 4

Subtract 6x from both sides:

2x - 3 ≥ 4

Add 3 to both sides:

2x ≥ 7

Divide both sides by 2:

x ≥ 7/2

Therefore, the solution to the inequality is x ≥ 3.5.

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Using translation concepts, we have that:

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

When the function is translated down, the slope remains constant, while when the function is reflected over the y-axis, the slope is multiplied by -1, hence both lines will have a slope of 3, and since they have the same slope, they are parallel.

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Answer:

[tex]-\frac{1}{\sqrt[3]{3}}[/tex]

Step-by-step explanation:

To do this we can ask ourselves "What number multiplied three times by itself is _____?" In this case we have -27 and 81. We see that -3*-3*-3=-27. We also see that 3*3*3*3=81. This means that [tex]\sqrt[3]{-27}=-3,[/tex] and [tex]\sqrt[3]{81} = 3\sqrt[3]{3}.[/tex]

The fraction we get is [tex]\frac{-3}{3\sqrt[3]{3} }[/tex], and we can simplify to get [tex]-\frac{1}{\sqrt[3]{3}}[/tex].

Answer:

[tex]cotA=\frac{2x}{5}[/tex]

Step-by-step explanation:

Answer:

[tex]\text{cotA} =\frac{2x}{5}[/tex]

Step-by-step explanation:

cotA = (Adjacent side) ÷ (Opposite side)

The measure of the Adjacent side = 2x

The measure of the Opposite side = 5

Then

[tex]\text{cotA} =\frac{2x}{5}[/tex]

The percentage given shows that the amount is decreasing by 8%.

From the information given, the function is f(x) = 9,628(0.92)x. This illustrates that the amount is decreasing by 8% she compared to the previous year. This was computed as:

= 1 - 0.92

= 0.08

= 8%

For part B, the percentage change will be:

= (8,972 - 8,074.80)/8972 × 10

= 10%

Therefore, the account recorded a greater percentage change in amount of money over the previous year is account B as 20% is lore than 8%.

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Answer:

2

Step-by-step explanation:

By the triangle proportionality theorem,

[tex] \frac{12}{2y - 1} = \frac{4y - 4}{1} \\ \\ 12 = (2y - 1)(4y - 4) \\ \\ 12 = 8 {y}^{2} - 12y + 4 \\ \\ 8 {y}^{2} - 12y - 8 =0 \\ \\2 {y}^{2} - 3 y - 2 = 0 \\ \\ (2y + 1)(y - 2) = 0[/tex]

From this, we know that y = -1/2 or 2.

However, as distance must be positive, we disregard the negative case, giving us y = 2.

Answer:

The answer will be the 3rd option, 12.8

Step-by-step explanation:

I'm gonna assume that since you copy and pasted the question, the equation is actually s - 0.2t^2

Now we just need to substitute the values with their respective ones.

20 - 0.2(6)^2

Now we just have to solve :)

20 - 0.2(6)^2

= 12.8

So the answer will be the 3rd option, 12.8

Hope this helped! :D

m∠x+m∠r+m∠y=180° (angles in a triangle add to 180°)

m∠r+m∠s=180° (angles that form a linear pair add to 180°)

m∠x+m∠r+m∠y=m∠r+m∠s (Transitive property of equality)

m∠x+m∠y=m∠s (subtraction property of equality)

m∠s=m∠x+m∠y (symmetric property of equality)

The profit of his investment after 2 years is $8,063.60.

The profit earned is the difference between the amount he earned from the deposit at the bank and the interest paid on the loan.

Total value of the loan in 2 years : 100,000 x (1.042²) = 108,576.40

Total value of the amount deposited in 2 years : 100,000 x (1.08²) = 116,640

Difference = 116,640 - 108,576.40 = $8,063.60

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If the function is vertically stretched by 4, the resulting function will be g(x) = 4(2)^x

Exponential function is written in standard form as y=  ab^x

where

a is the base

x is the exponent

Given the following exponential function f(x) = 2^x. If the function is vertically stretched by 4, the resulting function will be g(x) = 4(2)^x

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Distribute [tex]50[/tex] to every term inside the parentheses.

[tex]50\cdotx^2+50\cdot7x+50\cdot6[/tex]

Simplify with multiplication.

[tex]\huge\boxed{50^2+350x+300}[/tex]

You can't simplify further by adding, so leave the answer as-is.

Answer:

50x^2 + 350x + 300

Step-by-step explanation:

Original Equation:

50(x^2+7x+6)

Distribute 50 to all 3 #'s:

50x^2 + 350x + 300

Answer:

Step-by-step explanation:

ΔABC ≅ ΔDEF

The length AB = 28 and the length of DE = 7. Since these are corresponding sides, we know that DEF= 1/4 (ΔABC)

So, since ΔABC = 160, we know that ΔDEF will be 1/4 of that, meaning that ΔDEF is 40.

ΔDEF = 40cm²

Answer:

10 cm2

Step-by-step explanation:

The ratio per side is 28/7 = 4

When two similar figures have a ratio of 4:1, the difference between their areas is:

[tex](4)^{2} :(1)^{2}[/tex]

[tex]16:1[/tex]

That is, the dimension of the area of the largest figure is 16 times larger than the smallest figure.

So for this case:

the area of the larger figure is

ΔABC = 160 sq.cm

Then the area of the minor figure is:

ΔDEF= 160/16 = 10 sq.cm

Hope this helps

Answer:

It is not a function

Step-by-step explanation:

A function refers to a set of points/lines with this characteristic:

Each Y value has only one corresponding X value.

Meaning one X value cannot have multiple Y Values.

In this case, the X value of 2 has 2 different Y values, making it not a function.