Mary and tom were buying a present for their mother on mothers day. mary spent $12 and tom spent $28 if they wanted to share the cost equally, how much money does mary owe tom?

take 63 and divide it by 2.

63÷2= 31.5

so they each had $31.5

Answer:

The answer to your question is about 5.5 hours.

Step-by-step explanation:

The equation is y = 35(3x)

Data

# of bacteria = 550 = y

time = ? h

    Then    550 = 35(3x)                         substitution

                 550 = 105x                           simplifying

                x = 5.23 h.

To find the interest rate that will cause Pablo's money to double in approximately 44 years, we can use the rule of 72. The interest rate is approximately 1.64%.

To find the interest rate that will cause Pablo's money to double in approximately 44 years, we can use the rule of 72. The rule of 72 states that dividing 72 by the interest rate will give you the approximate number of years it takes for money to double. In this case, we need to find the interest rate that makes the money double in 44 years. So, we divide 72 by 44 to get the interest rate.

Interest rate = 72 / 44 ≈ 1.6363636363636363

Therefore, the interest rate that will cause Pablo's money to double in approximately 44 years is approximately 1.64%.

Answer:

B. y = (x-2)(x-6)

Step-by-step explanation:

The quadratic function y = x²- 8x + 12 can be factored into intercept form as y = (x - 2)(x - 6), which corresponds to option (b).

The function given is y = x² - 8x + 12. To write this function in intercept form, we need to factor it as the product of two binomials, each representing its intersections with the x-axis where y=0.

To do this, we look for two numbers that multiply to give the constant term (12) and add up to give the coefficient of the middle term (-8). These two numbers are -2 and -6.

Thus, the factored intercept form is y = (x - 2)(x - 6). This corresponds to answer choice (b).

For this case what we must do is observe the cut points of the function with the x axis.

The cut points with the horizontal axis are:

(-4, 0)

(-2, 0)

(6, 0)

Therefore, the intersections with the axis are:

x = -4

x = -2

x = 6

Answer:

The apparent x-intercept (s) of the function graphed are:

-4, -2, and 6

Answer:

The vertex is (3,-16)  and axis of symmetry is 3

Step-by-step explanation:

The vertex of a quadratic equation [tex]f(x)=ax^{2}+bx+c[/tex] is calculated as [tex](\frac{-b}{2a},f(\frac{-b}{2a}))[/tex]

and the axis of symmetry is  [tex]\frac{-b}{2a}[/tex]

Compare equation [tex]y=x^{2}-6x-7[/tex] with [tex]f(x)=ax^{2}+bx+c[/tex]

Where a= 1 and b = -6

so, [tex]x=\frac{-b}{2a}=\frac{-(-6)}{2}[/tex]

      [tex]x=3[/tex]

Now, put the value of x=3 in [tex]y=x^{2}-6x-7[/tex]

[tex]y=(3)^{2}-6(3)-7[/tex]

[tex]y=9-18-7[/tex]

[tex]y=-16[/tex]

Therefore, the vertex is (3,-16)  and axis of symmetry is 3

Answer:

$909.50

Step-by-step explanation:

$850 x 7% = $59.50 (tax amount)

850 x (1+ 0.07) = $909.50

To simplify the expression (3.2b+0.8)+1.9b, combine like terms by adding the coefficients. The simplified expression is 5.1b + 0.8.

To simplify the expression (3.2b+0.8)+1.9b, we can combine like terms by adding the coefficients. The variable b remains unchanged. So, we have:

(3.2b + 1.9b) + 0.8

Combine the coefficients: 3.2 + 1.9 = 5.1

The simplified expression is therefore 5.1b + 0.8.

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Zero Solutions

Since the two lines have equal slopes and different intercepts

The system of equations has no solution.

First, let's rewrite the second equation in slope-intercept form:

2y = 5x + 8

y = (5/2)x + 4

Now we can see that both equations have the same slope (5/2), but different y-intercepts (2 and 4). Since the slopes are the same, the lines are parallel and will never intersect. Therefore, this system of equations has no solution.

Final answer:

To find the measures of the angles with a ratio of 2:9:1, represent the angles as 2x, 9x, and x, set up the equation 2x + 9x + x = 180, solve for x, and then use x to calculate each angle. The measures of the angles are 30 degrees, 135 degrees, and 15 degrees.

Explanation:

To find the measures of the angles in a triangle with a given ratio, we apply the fact that the sum of the angles in a triangle is always 180 degrees. If we have the ratio of 2:9:1, we can represent the angles as 2x, 9x, and x, respectively. Since the angles must add up to 180 degrees, we can write the equation 2x + 9x + x = 180, which simplifies to 12x = 180.

Divide both sides of the equation by 12 to find the value of x: x = 180 / 12 = 15 degrees. Now, we can find each angle by multiplying x by the respective ratio number:

The first angle is 2x, which equals 2(15) = 30 degrees.

The second angle is 9x, which equals 9(15) = 135 degrees.

The third angle is 1x, which equals 1(15) = 15 degrees.

Therefore, the measures of the angles in the triangle are 30 degrees, 135 degrees, and 15 degrees.

To calculate the height of the radio tower, trigonometry is used to first determine the building height and then the total height including the tower. Subtracting the building height from the total height gives the height of just the radio tower.

To determine the height of the radio tower, we must first use trigonometry to find the height of the building. We use the tangent of the angle and the distance from the surveyor to the building:

After calculating the height of the building, we use the same approach to find the total height to the top of the radio tower:

Finally, to find the height of the radio tower alone, we subtract the height of the building from the total height.

Height of Radio Tower = Total Height - Height of Building

By following these steps, we can calculate the height of the radio tower.

Answer:  The correct option is (B) 60.

Step-by-step explanation:  Given that the line BD is parallel ti the line XY.

We are to find the value of x.

We know that

if two parallel lines are cut by a transversal, then the measures of the alternate interior angles are equal.

In the given figure, BD is parallel to XY and they are cut by a transversal.

So, the angles with measures x° and 60° are alternate interior angles.

Therefore, we must have

[tex]x^\circ=60^\circ\\\\\Rightarrow x=60.[/tex]

Thus, the value of x is 60.

Option (B) is CORRECT.

Answer:

Sample Response: Squaring and square root are inverses, so one should "undo" the other. That is, squaring the square root of a number results in the number. Using the power of a power rule, you multiply the exponents. Since a number to the first power is itself, the product of the exponents must equal 1. This means that the power of the square root must be the reciprocal of 2, or one half.

Answer:25 %

Step-by-step explanation: there are 4 parts and 1 of those is girls 1 divided by 4 is 0.25, which is 25%

The percent of the class that is girls is 75%

Given the ratio of  boys to girls in Mrs. Ronilo's math class is 3 to 1, the total ratio will be:

The percent of the class that is girls = 3/4 * 100

The percent of the class that is girls = 75%

Hence the percent of the class that is girls is 75%

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Answer: A. All equilateral triangles can be mapped onto each other using dilations.

Step-by-step explanation:

We know that all equilateral triangles are similar to each but not congruent because they all have same measure of corresponding angles 60° but do not have same side-lengths.

So, equilateral triangles can be mapped onto each other using dilation because they maps similar shapes (sometimes congruent) where as rigid transformations always map congruent shapes so we cannot map all equilateral triangles by using  rigid transformations.

Answer:

[tex]3x^2y\sqrt{2\cdot y}[/tex]

Step-by-step explanation:

We have been given an radical expression. We are asked to simplify our given expression.

[tex]\sqrt{18x^4y^3}[/tex]

We can rewrite terms of our given function as:

[tex]\sqrt{18\cdot x^4\cdot y^3}[/tex]

[tex]\sqrt{2\cdot 9\cdot x^4}\cdot y^2\cdot y}[/tex]

[tex]\sqrt{2\cdot 3^2\cdot (x^2)^2\cdot y^2\cdot y}[/tex]

Using radical rule [tex]\sqrt[n]{a^n}=a[/tex], we will get:

[tex]3x^2y\sqrt{2\cdot y}[/tex]

Therefore, the simplified form of our given expression would be [tex]3x^2y\sqrt{2\cdot y}[/tex].

Answer:

[tex]\frac{4}{229}+\frac{30i}{229}[/tex]

Step-by-step explanation:

Answer:

SXF ~= GXT

Step-by-step explanation:

SX corresponds to GX,

XF corresponds to XT,

so SF corresponds to GT.