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3 years ago

One integer is 5 more than another integer. Their sum is -13. What are the two integers?

Mathematics

1 answer:

Goshia [24]3 years ago

8 0

Answer:

-4 and -9

Step-by-step explanation:

Let us use variables.

Let x = 5 + y

and x + y = -13

Now we can solve this problem.

x + y = -13

(5 + y) + y = -13

5 + 2y = -13

2y = -13 - 5

2y = -18

y = -9

x = 5 + -9

x = -4

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A ball is thrown upward with an initial velocity of 60 mph. it is thrown from a height of 5 feet. what is the maximum height it

natima [27]

Answer:

h = 61.25 m

Step-by-step explanation:

It is given that,

The initial velocity of the ball, v = 60 m/s

It is thrown from a height of 5 feet, $h_o=5\ ft$

We need to find the maximum height it reaches. The height reached by the projectile as a function of time t is given by :

$h=-16t^2+vt+h_0$

Putting all the values,

$h=-16t^2+60t+5$ .....(1)

For maximum height, put

$\dfrac{dh}{dt}=0\\\\\dfrac{-16t^2+60t+5}{dt}=0\\\\-32t+60=0\\\\t=\dfrac{-60}{-32}\\\\t=1.875\ s$

Put t = 1.875 in equation (1)

$h=-16(1.875)^2+60(1.875)+5\\\\h=61.25\ m$

So, the maximum height reached by the ball is 61.25 m.

8 0

3 years ago

Find the value of the variables please please help me out I will mark you the brainly! Please please

RSB [31]

Answer:

m = 54

Step-by-step explanation:

The secant- secant angle 20° is half the difference of the intercepted arcs, that is

$\frac{1}{2}$ (160 - 2m - 12) = 20° ( multiply both sides by 2 to clear the fraction )

- 2m + 148 = 40° ( subtract 148 from both sides )

- 2m = - 108 ( divide both sides by - 2 )

m = 54

4 0

2 years ago

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Overnight rain has left 8 gallons of water in Juan's boat. Juan secures a small container and begins scooping the water out at a

GuDViN [60]

Answer:

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Step-by-step explanation:

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3 years ago

Find the area of the region enclosed by the graphs of the functions

Vaselesa [24]

Answer:

$\displaystyle A = \frac{8}{21}$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

Multiplication Property of Equality
Division Property of Equality
Addition Property of Equality
Subtraction Property of Equality

Algebra I

Terms/Coefficients
Functions
Function Notation
Graphing
Solving systems of equations

Calculus

Area - Integrals

Integration Rule [Reverse Power Rule]: $\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C$

Integration Rule [Fundamental Theorem of Calculus 1]: $\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)$

Integration Property [Addition/Subtraction]: $\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx$

Area of a Region Formula: $\displaystyle A = \int\limits^b_a {[f(x) - g(x)]} \, dx$

Step-by-step explanation:

*Note:

Remember that for the Area of a Region, it is top function minus bottom function.

Step 1: Define

f(x) = x²

g(x) = x⁶

Bounded (Partitioned) by x-axis

Step 2: Identify Bounds of Integration

Find where the functions intersect (x-values) to determine the bounds of integration.

Simply graph the functions to see where the functions intersect (See Graph Attachment).

Interval: [-1, 1]

Lower bound: -1

Upper Bound: 1

Step 3: Find Area of Region

Integration

Substitute in variables [Area of a Region Formula]: $\displaystyle A = \int\limits^1_{-1} {[x^2 - x^6]} \, dx$
[Area] Rewrite [Integration Property - Subtraction]: $\displaystyle A = \int\limits^1_{-1} {x^2} \, dx - \int\limits^1_{-1} {x^6} \, dx$
[Area] Integrate [Integration Rule - Reverse Power Rule]: $\displaystyle A = \frac{x^3}{3} \bigg| \limit^1_{-1} - \frac{x^7}{7} \bigg| \limit^1_{-1}$
[Area] Evaluate [Integration Rule - FTC 1]: $\displaystyle A = \frac{2}{3} - \frac{2}{7}$
[Area] Subtract: $\displaystyle A = \frac{8}{21}$