What value of c makes x2 − 12x + c a perfect square trinomial? −36 −24 24 36

Answer: The correct option is  A.

Explanation:

The given function is,

[tex]f(x)=\frac{2}{5}(10)^x[/tex]

If a function is reflect across the x-axis, then the x-coordinate remains the same but the sign of y coordinate change.

[tex](x,y)\rightarrow(x,-y)[/tex]

[tex]g(x)=-f(x)[/tex]

[tex]g(x)=-\frac{2}{5}(10)^x[/tex]

The graph of f(x) and g(x) in shown in below figure.

Therefore option A is correct.

Final answer:

Approximately 71 pounds of macadamia nuts and 31 pounds of almonds were sold, after solving the system of equations p + n = 102 and 1.00p + 5.93n = 452.03.

Explanation:

To determine the amount of almonds and macadamia nuts sold, we need to solve the given system of equations:

Let's start by solving the first equation for p:

p = 102 - n

Now, substitute p in the second equation:

1.00(102 - n) + 5.93n = 452.03

Next, distribute and combine like terms:

102 - n + 5.93n = 452.03

4.93n = 350.03

n ≈ 71.041 (macadamia nuts)

Using n to find p:

p = 102 - 71.041 ≈ 30.959 (almonds)

Therefore, approximately 71 pounds of macadamia nuts and 31 pounds of almonds were sold.

Answer:

The answer to the question: Which professionals most directly use geometry in their work?

b. Astronomers

Step-by-step explanation:

The astronomers are the professionals most directly use geometry in their work in this list options, some examples of the geometric in this profession are:

Orbits of planets around stars or orbits of satellites around planets  behave like ellipses or hyperbolas; geometry is also used to find coordinates of celestial objects

The frog jumped approximately 16.18 feet horizontally. The maximum height it jumped was approximately 4.65 feet.

The function y = -0.017x^2 + 0.55x models the frog's jump, it represents a parabola where the highest point, the vertex, means the highest point the frog reached, and where it hits the x-axis indicates the horizontal distance the frog jumped. We can find the distance of the frog's jump by setting y to 0 and solving the equation for x, whereas, the maximum height of the frog's jump will be determined by the vertex of the parabola.

For a function in the form y = ax^2 + bx + c, the x-value of the vertex, which is the maximum height in this context, can be found by using the formula -b/2a.

Substituting the given values from the equation, -b/2a = -0.55/(-2*-0.017) = 16.18 feet approximately.

Substitute x = 16.18 feet into the given function to find the maximum height the frog jumped: y = -0.017*(16.18)^2 + 0.55*16.18 = 4.65 feet approximately.

So, the frog jumped approximately 16.18 feet horizontally and the maximum height it jumped was approximately 4.65 feet.

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The frog jumped approximately 32.35 feet in distance and reached a maximum height of about 4.71 feet. We found this by setting the quadratic function to zero and solving for the horizontal distance, and by calculating the vertex of the parabola for the maximum height of the jump.

The function y = -0.017x^2 + 0.55x models the height y, in feet, of your pet frog's jump, where x is the horizontal distance, in feet, from the start of the jump. To determine how far the frog jumped, we look for the value of x when y equals zero, which represents when the frog lands back on the ground. To find this, we set the equation equal to zero and solve for x:

0 = -0.017x^2 + 0.55x

This is a quadratic equation in the form of ax^2 + bx + c = 0, where a = -0.017, b = 0.55, and c = 0. We can solve this by factoring or using the quadratic formula. The solutions to this equation represent the starting point (x=0) and the landing point of the jump. Ignoring the x=0 solution, we find that the frog lands at approximately x = 32.35 feet (after rounding to the nearest hundredth).

To determine how high the frog went, we need to find the vertex of the parabola because this represents the highest point of the jump. The x-coordinate of the vertex is given by -b/(2a), so we calculate:

x = -0.55 / (2 * -0.017) = 16.18 (rounded to the nearest hundredth)

We plug this value into the original equation to find the height:

y = -0.017(16.18)^2 + 0.55(16.18) = approximately 4.71 feet (after rounding to the nearest hundredth)

Therefore, the frog jumped approximately 32.35 feet in distance and reached a maximum height of about 4.71 feet.

Answer:

-3

Step-by-step explanation:

The slope of a line is the ratio of the vertical distance and horizontal distance between two points on a line.

Note that zero is tangible if the line is horizontal, and undefined if it is vertical.

Slope = ∆y / ∆x

Coordinates given: (-1,8) and (3,-4)?

Slope = -4 - 8 / 3 - (-1)

Slope = -12 / 4

= - 3

Answer:

5/11

Step-by-step explanation:

5/11 is the equivalent number because its the fraction of the repeating decimal ^^

Answer:

[tex]4 = y \\ 4 = x[/tex]

Step-by-step explanation:

The isosceles triangle containing the side of y + 12 is congruent to 3x² - 32 [base angles are congruent], and if you look closer, they are also equivalent to all three sides of the equilateral triangle adjacent to the isosceles triangle. So, we will be working with alot gadgets here, if you know what I mean. Anyway, this is how we start out:

[tex]5y - 4 = y + 12[/tex]

-5y - 5y

___________________

-4 = -4y + 12

-12 - 12

____________

-16 = -4y

___ ___

-4 -4

4 = y [Plug this back into both equations to get the value of 16.]

Next, you will set 3x² - 32 equal to 16:

[tex]16 = 3{x}^{2} - 32[/tex]

+32 + 32

_________________

48 = 3x²

__ ___

3 3

16 = x²

4 = x [In this case, we want the NON-NEGATIVE root because inputting a -4 for x will not give us identical answers.]

I am joyous to assist you anytime.

The equation 770 x 6 = 77 x 6 x 100 is false.

To determine if the equation 770 x 6 = 77 x 6 x 100 is true or false, let's evaluate both sides of the equation.

On the left side:

770 x 6 = 4,620

On the right side:

77 x 6 x 100 = 46,200

Since 4,620 is not equal to 46,200, the equation 770 x 6 = 77 x 6 x 100 is false.

To learn more on Equation:

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The selling price is $25.2.

If the selling price is greater than the cost price, then the difference between the selling price and cost price is called profit.

If the selling price is less than the cost price, then the difference between the selling price and cost price is called loss.

Given

The cost of the skirt is $18

Profit is 40%

The selling price of the skirt.

The selling price is given by

selling price = cost price + profit

Profit is given by

[tex]\begin{aligned} \rm Profit\ percent\ &= \rm \dfrac{Profit}{cost\ price} *100\\40 &= \rm \dfrac{Profit}{18} *100\\\rm profit &= 7.2 \end{aligned}[/tex]

Then the selling price = 18 + 7.2 =  $25.2.

Thus, the selling price is $25.2.

More about the profit and loss link is given below.

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Answer:

9.3+b=14.5

Step-by-step explanation:

Answer:

Refer the attached graph.    

Step-by-step explanation:

Given : On each coordinate plane,the parent function [tex]f(x)=|x|[/tex] is represented by a dash line translation is represented by a solid line.

To find : Which graph represents the the translation [tex]g(x)=|x+2|[/tex] as a solid line?

Solution :

The parent function [tex]f(x)=|x|[/tex]

with the vertex (0,0)

And the graph of  [tex]g(x)=|x+2|[/tex]

with the vertex (-2,0)

The graph of g(x) is the translation of f(x)

The parent function is translated towards left.

Transformation to the left,

f(x)→f(x+b) , the graph of f(x) is shifted towards left by b unit.

Same as the graph f(x) is shifted towards left by 2 unit and form graph of g(x).

We plot the graph of both the equations in which translation is shown.

Refer the attached graph below.

Answer:

Start with x+y=10 and x-y=4

Add the equations to eliminate y:

   x+y=10 

 + x-y=4 

  2x =14 

So now solve for x:

   2x=14    (Divide each side by 2 to get x by itself)

    x=7 

Now you have solved for x, but you still need to solve for y:

  x+y=10

 7+y=10    (Subtract 7 from both sides to get y by itself)

   y=3 

Now you have both x and y but to check it, just plug it into the original equations:

   x+y=10 ---->  7+3=10   (That's correct)

    x-y=4 ---->  7-3=4   (That's correct) 

Step-by-step explanation:

After estimating and calculating, we find that 6.51326 is greater than the square root of 39, which is approximately 6.245.

To compare 6.51326 and the square root of 39, we first need to calculate the square root of 39 to see how it measures up against 6.51326. Since the exact square root of 39 is not easily found without a calculator, we can estimate it by finding the nearest perfect squares that surround 39.

36 and 49 are the nearest perfect squares to 39, and their square roots are 6 and 7, respectively. Since 39 is closer to 36 than to 49, we can estimate the square root of 39 to be slightly more than 6. Therefore, without performing the exact calculation, we can intuit that the square root of 39 will be between 6 and 7, but closer to 6.

Doing the exact calculation or using a calculator, we find that the square root of 39 is approximately 6.245, which means that 6.51326 is greater than the square root of 39.

Final answer:

The sum of -4 and 3 is -1 because we subtract the smaller number from the larger and keep the sign of the larger absolute value number. The sum of -3 and 5 is positive 2 for the same reason.

Explanation:

The question seems to be asking about the rules for adding numbers with different signs. When adding -4 and 3, which have opposite signs, you subtract the smaller number from the larger number, and the sign of the answer is the same as the sign of the larger absolute value number.

So the sum is -1, because 4 is larger than 3, and the sign is negative. In contrast, when adding -3 and 5, you also subtract the smaller number from the larger, but since 5 is greater than 3, the sum is 2, and it has a positive sign because 5 has a positive sign.

Examples demonstrate the rules of addition:

These basic rules ensure clarity in arithmetic operations and provide a foundation for more complex math problems. The 'complaints' likely refer to the unexpected results when dealing with negative numbers, which can seem counterintuitive but follow consistent mathematical rules.