Without graphing estimate the x-intercepts of the graph of f(x)=7x^2+9x+1 to the nearest tenth.

The friend lives in a town that is 10° farther north than 40° N. The latitude of that town is 40° +10° = 50° N. When that latitude is reflected across the equator, N changes to S. The new latitude would be c. 50° S.

the two consecutive odd integers that have a product of fifteen are 3 and 5.

The question asks for the two consecutive odd integers whose product is fifteen. To solve this, we can use algebraic methods or observe that the square root of 15 is less than 4, and since 15 is an odd number, we look for odd numbers around 4 that multiply to 15.

Let's define the smaller integer as n. Since the integers are consecutive and odd, the next odd integer after n is n+2. The equation to represent their product is n*(n+2) = 15. Solving for n gives us the integers 3 and 5, since 3*5 = 15.

Therefore, the two consecutive odd integers that have a product of fifteen are 3 and 5.

The third fraction [tex]\frac{10}{80}[/tex] is not equivalent to the other options. The other options,  0.8, 80% and [tex]\frac{24}{30}[/tex] are all equivalent.

In mathematics, a fraction is a composition that represents a part of a whole. Fractions can be written in a few different ways, but the most frequent way is to utilize a numerator and a denominator. The numerator is the number of parts we have, and the denominator is the total number of parts. For illustration, the fraction 1/2 represents one part out of two.

Option 1 is 0.8.

Option 2 is 80% which is in fact equal to [tex]\frac{80}{100}[/tex] .

[tex]\frac{80}{100}[/tex] = [tex]\frac{8}{10}[/tex] = 0.8.

Option 3 is [tex]\frac{24}{30}[/tex] .

[tex]\frac{24}{30}[/tex] = [tex]\frac{8}{10}[/tex] = 0.8.

So, only the third option is not equivalent to the others.

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Answer is Exponential Decay.

Exponential Growth and Decay:

Exponential decay is a process that decreases quantity over time.

Exponential growth is a process that increases quantity over time.

(Given),

[tex]A = 21000(1-0.12)^{t}[/tex]

Let's take,

[tex]B = (1 - 0.12)^{t}[/tex]

As the t increases the B value decreases exponentially. So, the  A = 21000*B also decreases exponentially as t increases.

And the rate of change per time period is (0.12 x 100)% = 12%.

So, It is exponential decay.

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Final answer:

To find the area of the floor not covered by the rug, calculate the total floor area (120 square feet), subtract the rug's area (58.5 square feet), resulting in 61.5 square feet of uncovered floor.

Explanation:

To find the area of the floor that is not covered by the area rug, we first need to calculate the area of the entire floor and then subtract the area of the rug.

The area of the floor is calculated by multiplying its length and width. So for a floor that measures 10 feet by 12 feet, the area is 10 feet × 12 feet = 120 square feet.

The area rug measures 6.5 feet by 9 feet, which means its area is 6.5 feet × 9 feet = 58.5 square feet.

Now, subtract the area of the rug from the area of the entire floor to find the part of the floor not covered by the rug:

120 square feet - 58.5 square feet = 61.5 square feet.

Therefore, the area of the floor not covered by the rug is 61.5 square feet.

ANSWER

[tex]\frac{5( \sqrt{11} + \sqrt{3} )} {8} [/tex]

EXPLANATION

The given rational function is

[tex] \frac{5}{ \sqrt{11} - \sqrt{3}} [/tex]

We need to rationalize the denominator by multiplying both the numerator and the denominator by the conjugate of

[tex] \sqrt{11} - \sqrt{3} [/tex]

which is

[tex]\sqrt{11} + \sqrt{3} [/tex]

When we rationalize we obtain:

[tex] \frac{5( \sqrt{11} + \sqrt{3} )}{(\sqrt{11} - \sqrt{3} )( \sqrt{11} + \sqrt{3} )} [/tex]

The denominator is now a difference of two squares:

[tex](a - b)(a + b) = {a}^{2} - {b}^{2} [/tex]

We apply this property to get

[tex]\frac{5( \sqrt{11} + \sqrt{3} )}{( \sqrt{11}) ^{2} - ( \sqrt{3}) ^{2} )} [/tex]

[tex]\frac{5( \sqrt{11} + \sqrt{3} )}{11 - 3} [/tex]

This simplifies to

[tex]\frac{5( \sqrt{11} + \sqrt{3} )} {8} [/tex]

Or

[tex]\frac{5 } {8}\sqrt{11} + \frac{5 } {8}\sqrt{3} [/tex]

Answer:

B

Step-by-step explanation:

60 miles per hour
Or
60/1

The smaller triangular prism's surface area is calculated by squaring the scale factor of 1/5 (which is 1/25) and then multiplying it by the surface area of the larger prism. The result is 2.4 square centimeters.

The question asks about the surface area of a similar but smaller triangular prism given that the larger prism has a surface area of 60 square centimeters and the scale factor of the smaller prism is 1/5. When the size of an object changes by a scale factor, the surface area changes by the square of that scale factor. For the smaller triangular prism, the surface area will be the square of 1/5, which is 1/25, times the surface area of the larger prism.

To calculate it:

Therefore, the surface area of the similar smaller triangular prism by the given scale factor is 2.4 square centimeters.

Answer: The corresponding segments in the in the figure and the image are :

AB and EF,  

AD and EH,

CD and HG,

BC and FG,

Step-by-step explanation:

Given: Polygon ABCD is the result of a translation of polygon EFGH .

AB is parallel to DC in the pre-image.

We know that a translation is a rigid transformation which produces congruent images such that the corresponding segments have equal lengths.

So from the given statements the corresponding segments in the figure and the image are :

AB and EF,  

AD and EH,

CD and HG,

BC and FG,

Answer: c

Step-by-step explanation: hope this helps