A rectangle has a width of 9 units and a length of 40 units What is the length of the diagonal?

Answer:

[tex]y-3=-5(x-6)[/tex]

Step-by-step explanation:

we know that

The equation of the line into point-slope form is equal to

[tex]y-y1=m(x-x1)[/tex]

we have

[tex]m=-5[/tex]

[tex](x1,y1)=(6,3)[/tex]

substitute

[tex]y-3=-5(x-6)[/tex] ----> equation of the line into point-slope form

Answer:

[tex]\$2,161.1[/tex]

Step-by-step explanation:

we know that    

The compound interest formula is equal to  

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

in this problem we have  

[tex]t=10\ years\\P=\$4,500\\ r=0.04\\n=1[/tex]  

substitute in the formula above  

[tex]A=\$4,500(1+\frac{0.04}{1})^{1*10}[/tex]  

[tex]A=\$4,500(1.04)^{10}[/tex]

[tex]A=\$6,661.10[/tex]    

Find the interest

[tex]I=A-P[/tex]

[tex]I=\$6,661.10-\$4,500=\$2,161.1[/tex]

Answer:

2161.10

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}y=\dfrac{1}{2}x-4&(1)\\y=-2x-9&(2)\end{array}\right\\\\\text{substitute (1) to (2):}\\\\\dfrac{1}{2}x-4=-2x-9\qquad\text{multiply both sides by 2}\\\\x-8=-4x-18\qquad\text{add 8 to both sides}\\\\x=-4x-10\qquad\text{add 4x to both sides}\\\\5x=-10\qquad\text{divide both sides by 5}\\\\x=-2\\\\\text{put it to (2):}\\\\y=-2(-2)-9\\\\y=4-9\\\\y=-5[/tex]

Answer:

C = 8π

Step-by-step explanation:

The circumference (C) of a circle is calculated using

C = πd ← d is the diameter

here d = 8, hence

C = 8π ft ← exact value

For this case we have by definition, that the circumference of a circle is given by:

[tex]C = \pi * d[/tex]

Where:

d: It is the diameter of the circle

We have as data that the diameter of the circle measures:8ft, then, replacing:

[tex]C = \pi * 8[/tex]

Finally, the circumference is [tex]8\pi[/tex]

ANswer:

[tex]8\pi[/tex]

For this case we have that by definition, the distance between two points is given by:

[tex]d = \sqrt {(x_ {2} -x_ {1}) ^ 2+ (y_ {2} -y_ {1}) ^ 2}[/tex]

We have the following points:

[tex](6,5 \sqrt {2})\\(4,3 \sqrt {2})[/tex]

Substituting:

[tex]d = \sqrt {(4-6) ^ 2 + (3 \sqrt {2} -5 \sqrt {2}) ^ 2}\\d = \sqrt {(- 2) ^ 2 + (- 2 \sqrt {2}) ^ 2}\\d = \sqrt {4+ (4 * 2)}\\d = \sqrt {4 + 8}\\d = \sqrt {12}\\d = \sqrt {2 ^ 2 * 3}\\d = 2 \sqrt {3}[/tex]

Answer:

Option C

Answer: Third option.

Step-by-step explanation:

The distance between two points can be calculated with this formula:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Then, given the points [tex](6,5\sqrt{2})[/tex] and [tex](4,3\sqrt{2})[/tex], we can identify that:

[tex]x_2=4\\x_1=6\\y_2=3\sqrt{2}\\y_1=5\sqrt{2}[/tex]

Now we must substitute these values into the formula:

 [tex]d=\sqrt{(4-6)^2+(3\sqrt{2}-5\sqrt{2})^2}[/tex]

We get that the distance between these two points is:

[tex]d=2\sqrt{3}[/tex]

Answer:

5 gallons and 3 quarts

Step-by-step explanation:

There are 4 quarts in a gallon so 23/4=5 gallons and 3 quarts

Answer:

5 gal and 3 qt.

Step-by-step explanation:

For this case, we must build a quotient that, when multiplied by the divisor, eliminates the terms of the dividend until it reaches the remainder.

It must be fulfilled that:

Dividend = Quotient * Divider + Remainder

According to the attached image we have the quotient is:

[tex]x ^ 2-2x-3[/tex]

Answer:

[tex]x ^ 2-2x-3[/tex]

See attached image

Answer:

186

Step-by-step explanation:

Cut it 6+7+11=24×5=120

6+11=66

120+66=186

Answer:  The correct option is (A) 186 sq. units.

Step-by-step explanation:  We are given to find the area of the polygon shown in the figure.

Let us divide the given polygon in two rectangles A and B as shown in the attached figure below.

The dimensions of rectangle A are

length, l = 11 units and breadth, b = 6 units.

So, the area of rectangle A is given by

[tex]AREA_A=l\times b=11\times6=66~\textup{sq. units}.[/tex]

And the dimensions of rectangle B are

length, l' = 7 + 11 + 6 = 24 units  and  breadth, b' = 5 units.

So, the area of rectangle B is given by

[tex]AREA_B=l'\times b'=24\times5=120~\textup{sq. units}.[/tex]

Therefore, the total area of the given polygon is given by

[tex]AREA=AREA_A+AREA_B=66+120=186~\textup{sq. units}.[/tex]

Thus, the required area of the given polygon is 186 sq. units.

Option (A) is CORRECT.

Answer:

The correct answer is second option

3.2

Step-by-step explanation:

It is given that, Coordinates of triangle ABC,

A(0, 1), B(0, 2) and C(3, 2)

ΔABC ≅ ΔDEF

Therefore we can write, AB = DE, BC = EF and AC = DF

To find the measure of DF

DF = AC

(0, 1) C(3, 2)

By using distance formula,

AC = √[(3 - 0)² + ( (2 - 1)²]

 = √(9 + 1) = 3.16≈ 3.2

Answer:

Option B. Chef Andre used more than 3 1/2 cups of flour.

Step-by-step explanation:

we have

[tex]c > 3\frac{1}{2}[/tex]

The solution is all real number greater than [tex]3\frac{1}{2}[/tex]

therefore

Let

c -----> the number of cups

The statement that best represented by the inequality is

Chef Andre used more than 3 1/2 cups of flour

Answer:

The answer is B

Step-by-step explanation:

Answer:

Option C. approaches but does not cross.

Step-by-step explanation:

In Maths, an asymptote is a line that the graph (a drawing that shows two sets of related amounts) of a function (e.g. x=1/x) approaches but does not cross (or intersect). The image below illustrates such concept.

Answer:    C. Approaches but does not cross

Step-by-step explanation:  Basically an asymptote is a line that approaches a given curve which is graph of a function, but it never touches, cross or intersect in any finite. Asymptote can be any line, horizontal, vertical, inclined, which approaches the function graph. Theoretically, according to mathematical principles,  the function graph line is approaching to a asymptote at infinity, and therefore the asymptotes are suitable as the type of guide to complete the graph of the function.

1 pound = 16 ounces.

1 can weighs 8 ounces, so 2 cans weigh 8 +8 = 16 ounces, which is 1 pound.

Multiply total pounds by number of cans per pound:

25 pounds x 2 cans per pound = 50 total cans.

The number of cans each box hold will be 50.

In one pound there is a total of sixteen ounces.

So it means 1 pound = 16 ounces.

Given that the weight of the can is 8 ounces it means in 2 cans there are 16 ounces which are 1 pound.

2 cans = 1 pound

Since, the box can hold only 25 pounds Hence,

25 × 2 = 50 cans so a box can hold up to 50 cans.

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Answer:

There are 18 nickel coins and 27 dime coins

Step-by-step explanation:

Remember that

1 nickel=$0.05

1 dime=$0.10

Let

x ----> the number of nickel coins

y ---> the number of dime coins

we know that

x+y=45

x=45-y -----> equation A

0.05x+0.10y=3.60

Multiply by 100 both sides

5x+10y=360 ----> equation B

Solve the system by substitution

Substitute equation A in equation B and solve for y

5(45-y)+10y=360

225-5y+10y=360

5y=360-225

5y=135

y=27

Find the value of x

x=45-27= 18

therefore

There are 18 nickel coins and 27 dime coins

Answer:

-5,-4,-3

Step-by-step explanation:

Let n be an integer.

The next integer would have to be n+1.

The integer before n would have to be n-1.

So the numbers in order are n-1, n , n+1

The sum of the first 2 equals 3 times the third:

n-1     +     n                      =     3(n+1)

2n-1                                 =      3(n+1)

2n-1=3n+3

Subtract 2n on both sides

    -1=n+3

Subract 3 on both sides

    -4=n

If n=-4

then n-1=-5

and n+1=-3

So the three numbers are -5,-4,-3 .

Answer:

[tex]A=5, B=0,C=3[/tex]

Step-by-step explanation:

The partial fraction decomposition is given as:

[tex]\frac{5x^2+3x+54}{(x+3)(x^2+9)} \equiv \frac{A}{x+3}+\frac{Bx+C}{x^2+9}[/tex]

We collect LCD on the RHS to obtain;

[tex]\frac{5x^2+3x+54}{(x+3)(x^2+9)} \equiv \frac{A(x^2+9)+(x+3)(Bx+C)}{(x+3)(x^2+9)}[/tex]

We expand the parenthesis in the numerator of the fraction on the RHS.

[tex]\frac{5x^2+3x+54}{(x+3)(x^2+9)} \equiv \frac{Ax^2+9A+Bx^2+(3B+C)x+3C}{(x+3)(x^2+9)}[/tex]

This implies that:

[tex]\frac{5x^2+3x+54}{(x+3)(x^2+9)} \equiv \frac{(A+B)x^2+(3B+C)x+3C+9A}{(x+3)(x^2+9)}[/tex]

This is now an identity. Since the denominators are equal, the numerators must also be equal.

[tex]5x^2+3x+54=(A+B)x^2+(3B+C)x+3C+9A[/tex]

We compare coefficients of the quadratic terms to get:

[tex]A+B=5\implies B=5-A...(1)[/tex]

Also the coefficients of the linear terms will give us:

[tex]3B+C=3...(2)[/tex]

The constant terms also gives us;

[tex]3C+9A=54...(3)[/tex]

Put equation (1) in to equations (2) and (3).

[tex]3(5-A)+C=3\implies C=3A-12...(4)[/tex]

[tex]3C+9A=54...(5)[/tex]

Put equation (4) into (5).

[tex]3(3A-12)+9A=54[/tex]

[tex]9A-36+9A=54[/tex]

[tex]9A+9A=54+36[/tex]

[tex]18A=90[/tex]

[tex]A=\frac{90}{18} =5[/tex]

Do backward substitution to get:

[tex]C=3(5)-12=3[/tex]

[tex]B=5-5=0[/tex]

[tex]\therefore A=5, B=0,C=3[/tex]

The constants A, B, and C in the partial fraction decomposition are determined to be A = 5, B = 0, and C = 3.

To find the values of A, B, and C in the partial fraction decomposition of the rational function

Therefore, the number of adul, follow these steps:

Answer:

(3, 1)

Step-by-step explanation:

x = y + 2

y = -2x + 7

y = -2(y +2) +7

y = -2y -4 +7

y + 2y = 3

3y = 3

y = 3/3

y = 1

x = y +2

x = 1 +2

x = 3

The value of x is 1/3 and y is -5/3. using substitution method

solving this we will get the valve of Y if x is given.

CALCULATION:-

Y=x-2 -----(1)

y=-2x+7 ---------(2)

putting the value of y in the equation (2)

x-2= -2x+7

x+2x=7+2

3x=9

x=9/3

x=1/9

putting the value of X in equation(1)

 Y=x-2 -----(1)

y=1/3-2

y=-5/6  

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Answer:

Step-by-step explanation:

The slope-intercept form of an equation of a line:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept → (0, b).

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have the points A(0, -4) → b = -4 and B(6, 2).

Calculate the slope:

[tex]m=\dfrac{2-(-4)}{6-0}=\dfrac{6}{6}=1[/tex]

Put the value of m and of b to the equation:

[tex]y=1x-4[/tex]         add 4 to both sides

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

Answer:

-0.1715

Step-by-step explanation:

Answer:

3y+4x=5

Step-by-step explanation:

step 1

Find the slope

we have

(–7, 11) and (8, –9)

m=(-9-11)/(8+7)

m=-20/15

m=-4/3

step 2

Find the equation of the line into point slope form

we have

m=-4/3

point (-7,11)

substitute

y-11=-(4/3)(x+7) ----> equation of the line into point slope form

Multiply by 3 both sides

3y-33=-4(x+7)

3y-33=-4x-28

3y+4x=33-28

3y+4x=5 -----> equation of the line into standard form

Answer:

I think that the answer is D

Answer:

A: 270 ,':)

Step-by-step explanation:

Answer:

the answer is A:  270

Step-by-step explanation:

Op= 360

AB= 90

Op(360)-AB(90) = 270

Answer:

D. 804.2

Step-by-step explanation:

The area equation is πr^2 so

16^2 = 256

256 × π (or 3.14) = 803.84

which is ≈ 804.2

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UWU have a nice day!

Answer:

Option A and B

Step-by-step explanation:

sides of the triangle have been given as 15, 15.8, 30 units.

angles of the same triangle has been given as 70°, 80°, [180-(70+80)] or 30°.

Here we see all sides and all the angles of the given triangle have different measures ( all the three sides and angles are different )

By the definition of scalene triangle the given triangle will be scalene.

Since all three angles of the triangle are acute angles (less than 90°).

Therefore, Option A and B are correct.

Answer:

[tex]\large\boxed{\log_84a\left(\dfrac{b-4}{c^4}\right)=\log_84+\log_8a+\log_8(b-4)-4\log_8c}[/tex]

Step-by-step explanation:

[tex]\text{Use}\\\\\log_ab^n=n\log_ab\\\\\log_a(bc)=\log_ab+\log_ac\\\\\log_a\left(\dfrac{b}c{}\right)=\log_ab-\log_ac\\\\==============================[/tex]

[tex]\log_84a\left(\dfrac{b-4}{c^4}\right)=\log_84+\log_8a+\log_8\dfrac{b-4}{c^4}\\\\=\log_84+\log_8a+\log_8(b-4)-\log_8c^4\\\\=\log_84+\log_8a+\log_8(b-4)-4\log_8c[/tex]

Answer:

answer is A

Step-by-step explanation:

bc

Answer:

y=4x-3

Brainly is making me reach a word maximum. But that is my answer ^

Answer:

Let's solve for x.

5y=3x+b

Step 1: Flip the equation.

b+3x=5y

Step 2: Add -b to both sides.

b+3x+−b=5y+−b

3x=−b+5y

Step 3: Divide both sides by 3.

Answer:

x=

−1

3

b+

5

3

y

Step-by-step explanation:

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Answer:

f^(−1)(x)= x/6+4

Step-by-step explanation:

interchange the variables and solve for  

y

Inverse of the given function f(x) is f⁻¹(x) = (x/6) + 4.

Given: Function

f(x) = 6x - 24

Let, y = 6x - 24

Now, to find the inverse of the given function we need to interchange the values of x and y and then we will solve for y.

⇒ x = 6y - 24

⇒ 6y = x + 24

Dividing both sides by 6, we get:

⇒ y = (x + 24)/6

⇒ y = (x/6) + 4

We can write it as:

f⁻¹(x) = (x/6) + 4

Therefore, the inverse of f(x) = 6x -24 is f⁻¹(x) = (x/6) + 4.

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Answer:

-2x² + 12x

Step-by-step explanation:

To simplify, distribute the term outside the parenthesis (-2x) to all terms within the parenthesis. Remember to note the sign too:

-2x(x) = -2x²

-2x(-6) = +12x

-2x² + 12x is your answer.

~

Answer:

-2x²+12x

Step-by-step explanation:

Distributive Property:

       ↓

A(B+C)=AB+AC

A= -2x

B= x

C=6

-2xx-(-2x)*6

-2xx+2*6x

Simplify, to find the answer.

-2xx+2*6x

2*6=12

-2x²+12x is the correct answer.

Answer:

a=-2

b=4

c=-3

Step-by-step explanation:

You just compare -2x^2+4x-3=0 to

                              ax^2+bx+c=0

There is really no work here.

For this case we have that by definition, a quadratic equation is of the form:

[tex]ax ^ 2 + bx + c = 0[/tex]

The roots are given by:

[tex]x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2 (a)}[/tex]

We have the following equation:

[tex]-2x ^ 2 + 4x-3 = 0[/tex]

So:

[tex]a = -2\\b = 4\\c = -3[/tex]

Answer:

[tex]a = -2\\b = 4\\c = -3[/tex]

Answer:

[tex]\large\boxed{Q1.\ 80\ cm^3}\\\boxed{Q2.\ 45\ in^3}\\\boxed{Q3.\ 48\ m^3}\\\boxed{Q4.\ A,\ D}\\\boxed{Q5.\ 96\ in^3}[/tex]

Step-by-step explanation:

[tex]\text{The formula of a volume of a rectangular prism:}\\\\V=lwh\\\\l-length\\w-width\\h-height[/tex]

[tex]\bold{Q1}\\\\l=10\ cm,\ w=4\ cm,\ h=2\ cm\\\\V=(10)(4)(2)=80\ cm^3\\\\\bold{Q2.}\\\\l=5\ in,\ w=3\ in,\ h=3\ in\\\\V=(5)(3)(3)=45\ in^3\\\\\bold{Q3.}\\\\l=4\ m,\ w=2\ m,\ h=6\ m\\\\V=(4)(2)(6)=48\ m^3\\\\\bold{Q4.}\\\\V=120\ ft^3\\\\\bold{A:(5)(4)(6)=120}\\B:\ (7)(7)(6)=294\\C:\ (3)(6)(4)=72\\\bold{D:\ (10)(3)(4)=120}\\\\\bold{Q5.}\\\\l=8\ in,\ w=4\ in,\ h=3\ in\\\\V=(8)(4)(3)=96\ in^3[/tex]