The sum of 3 consecutive integers is 270. what is the second number in the sequence

to find the vertical height

 multiply the tangent of the angle by the horizontal distance

 so tan(12) x 5 = 1.0628

 rounded to nearest hundredth = 1.06 miles

The number of candies Bob left by subtraction will be 7.

To subtract in mathematics is to take something away from a group or a number of objects.

The group's total number of items decreases or becomes lower when we subtract from it.

In other meaning, subtraction is a mathematical operation such that two values are going to subtract and give a resultant value.

As per the given,

Total number of candies = 36

Number of candies Bob ate = 29

Left out = 36 - 29 = 7

Hence "The number of candies Bob left by subtraction will be 7".

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Answer:

[tex]\frac{11}{8}[/tex] [tex]\text{gallons}[/tex]

Step-by-step explanation:

Given: In [tex]1\frac{1}{2}[/tex] hour, a lawnmower uses [tex]2\frac{1}{16}[/tex] gallon of fuel.

To Find: How many gallons of fuel did the lawnmower use each hour.

Solution:

Number of hour lawnmower used [tex]=1\frac{1}{2}[/tex] [tex]\text{hour}[/tex]

                                                         [tex]\frac{3}{2}[/tex] [tex]\text{hour}[/tex]

Fuel consumed by lawnmower   [tex]=2\frac{1}{16}[/tex] [tex]\text{gallon}[/tex]

                                                      [tex]\frac{33}{16}[/tex] [tex]\text{gallon}[/tex]

Fuel used by lawnmower each hour [tex]=\frac{\text{Total fuel used}}{\text{Total time taken}}[/tex]

                                                            [tex]=\frac{\frac{33}{16}}{\frac{3}{2}}[/tex]

                                                            [tex]=\frac{11}{8}[/tex] [tex]\text{gallon}[/tex]

Hence the fuel consumed by lawnmower each hour is [tex]=\frac{11}{8}[/tex] [tex]\text{gallon}[/tex]

The length of one leg of the large right triangle in terms of x is; B. x√2 units

The smaller triangles ABD and BDC are isosceles triangles. Thus;

AD = BD = x

DC = BD = x

The hypotenuse AC is equal to;

AC = AD + DC

AC = x + x

AC = 2x

Using Pythagoras theorem;

AC² = AB² + BC²

AC² = 2AB²

AB = AC/√2

AB = 2x/√2

Rationalizing the denominator, we have;

AB = x√2

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Less than or equal to X :)

The greatest integer function is defined so that it produces the greatest integer less than or equal to x

A relation is a function if it has only One y-value for each x-value.

The greatest integer function, denoted by [x], produces the greatest integer less than or equal to x.

Let us consider a example to understand better

[3.8] = 3, [-2.4] = -3, [0] = 0, and [-7] = -7.

The function f(x) = [[x]] applies the greatest integer function twice to x

so f(x) produces the greatest integer less than or equal to the greatest integer less than or equal to x.

Hence, the greatest integer function is defined so that it produces the greatest integer less than or equal to x

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The diagonals are perpendicular because the product of their slope is -1, and their midpoint is same (2,2). Hence, it is proved that the diagonals of the given square are perpendicular bisectors of each other.

Given information:

The square with vertices P (0,4), Q (4,4), R (0,0) and S (4,0).

It is required to prove that the diagonals of the given square are perpendicular bisectors.

First, calculate the slope of the diagonals.

The slope of diagonal PS will be,

[tex]m = \dfrac{0-4}{4-0}\\m = -1[/tex]

So, the slope of diagonal PS is -1.

The slope of diagonal QR will be,

[tex]m' = \dfrac{0-4}{0-4}\\m' = 1[/tex]

So, the slope of diagonal QR is 1.

From the slope of the diagonals, the diagonals are perpendicular because the product of slope is -1.

Now, it is required to find the mid-point of the diagonals.

The midpoint of PS will be,

[tex](x,y)=(\dfrac{0+4}{2},\dfrac{4+0}{2})=(2,2)[/tex]

Midpoint of QR will be,

[tex](x,y)=(\dfrac{4+0}{2},\dfrac{4+0}{2})=(2,2)[/tex]

So, the midpoint of both the diagonals is also same.

Therefore, it can be said that the diagonals are perpendicular because the product of their slope is -1, and their midpoint is same (2,2). Hence, it is proved that the diagonals of the given square are perpendicular bisectors of each other.

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Answer:

-1, 1, (2,2), (2,2), and perpendicular and share the same midpoint

Step-by-step explanation:

Answer:

the answer is 66 feet per second.

The value of ac for the quadratic expression 9x^2 - 16 is -144. The value of b is 0, as it represents the coefficient of x, which is absent in the expression. Therefore, we do not need two numbers that multiply to ac and add to b; the expression is factored using the difference of squares as (3x + 4)(3x - 4).

The polynomial 9x2 − 16 is a quadratic expression that can be factored using the difference of squares method. To answer the questions:

Answer: C.   B=117°.

Step-by-step explanation:

We know that if a pair of angle are supplementary then their sum is added up to 180 degrees.

Given : angle A and angle B are supplementary angles.

i.e [tex]\angle{A}+\angle{B}=180^{\circ}[/tex]

Also, angle A = 63°

i.e  [tex]63^{\circ}+\angle{B}=180^{\circ}[/tex]

i.e  [tex]\angle{B}=180^{\circ}-63^{\circ}[/tex]

i.e  [tex]\angl{B}=117^{\circ}[/tex]

Hence, the measure of angleB is 117°.

C- it translates the graph up 1 unit.

Answer:

C

Step-by-step explanation:

[tex]y=log_5(x)+1[/tex]

Here parent function is [tex]y=log_5(x)[/tex]

If any number is added or subtracted at the end of parent function then we we move up or down

when we compare   [tex]y=log_5(x)+1[/tex] with parent function , +1 is added at the end.

So the graph will be translated 1 unit up

Answer : C: It translates the graph up 1 unit