Can someone point out in which step I made a mistake in and what the mistake was? (I know the answer is 1,980, but I somehow managed to get 360 using these steps which seem logical, and I don't know where I went wrong).

The factored form of the given trinomial is (x -7)(x +1)

From the question, we are to factor the given trinomials

The given trinomial is

x² + 6x - 7

The trinomial is a quadratic expression. The trinomial/ quadratic expression can be factored as a product of two binomial. When factored, the trinomial will take the form (x + a)(x + b)

Where are a and b are integers.

Factoring the trinomial

x² + 6x - 7

To factor the trinomial, we will find two numbers such that when added, we get the middle term; and when these numbers are multiplied we get the constant term.

The numbers that satisfy this condition are +1x and -7x

x² +x -7x - 7

x (x + 1) -7(x +1)

(x -7)(x +1)

Hence, the factored form of the given trinomial is (x -7)(x +1)

Learn more on Factoring trinomials here: https://brainly.com/question/13875709

#SPJ1

Answer:

48

Step-by-step explanation:

The area of this circle is

[tex]\pi( {4}^{2} ) = 16\pi = 50.27[/tex]

about 50.27 square centimeters. So 48 square centimeters seems reasonable here since 3 is used for π.

Answer:

8

Step-by-step explanation:

I belive what they mean is how many dots thier are i am not complety sure though but just by counting them up i came up with 8.

hope this helped

Answer:

4

Step-by-step explanation:

10 - 6 = 4

The cross-price elasticity of demand between strawberries and whipped cream is (C) -0.5.

Therefore, the cross-price elasticity of demand between strawberries and whipped cream is (C) -0.5.

Know more about cross-price elasticity of demand here:

https://brainly.com/question/25996933

#SPJ4

The complete question is given below:

When strawberry prices increase by 20 percent, the quantity demanded of whipped cream falls by 10 percent. What is the cross-price elasticity of demand between strawberries and whipped cream?

a. -2

b. 2

c. -0.5

d. 0.5

Answer: [tex]x=-5, -3[/tex]

Step-by-step explanation:

[tex]x^2 +8x+15=0\\\\(x+5)(x+3)=0\\\\x=-5, -3[/tex]

To estimate the value for g(10), that means that you have to substitute 10 in every x of g(x), then [tex]$g(x) =x^2-10[/tex] exists g(10) = 90.

The value of g(10), we have to substitute in every x of f(x), the

[tex]f(x) = 2x + 1[/tex] exists f(90) = 181

Therefore, the value of f[g(10)] exists 181.

To estimate the value for g(10), that means that you have to substitute 10 in every x of g(x), then

[tex]$g(x) =x^2-10[/tex]

substitute the value of x = 10

[tex]$g(10) = (10)^2-10[/tex]

simplifying the equation, we get

g(10) = 100 - 10

g(10) = 90

We have the value of g(10), we have to substitute in every x of f(x), then

f(x) = 2x + 1

substitute the value of x = 90

f(90) = 2(90) + 1

simplifying the equation, we get

f(90) = 180 + 1

f(90) = 181

The value of f[g(10)] exists 181.

Therefore, the correct answer is option b) 181.

To learn more about functions refer to:

https://brainly.com/question/27063206

#SPJ4

720 cubic inches of soil will be in the flower box.

Cuboid Definition: Cuboid shaped objects surround us in our day-to-day life. From television sets, books, carton boxes to bricks, mattresses, and shoeboxes, cuboid objects are all around us. In Geometry, a cuboid is a three-dimensional figure with six rectangular faces, twelve edges, and eight vertices.

Volume of Cuboid = Length x Width x Height

∴ The volume of the soil box = 15 x 8 x 8 = 960 inch³

Since 3/4 is occupied by the soil, the volume of the soil becomes

= 3/4 x 960

= 720 inch³

Learn more about Cuboid here :

https://brainly.com/question/19754639

#SPJ1

Answer: 60.

Step-by-step explanation:

Let in a right triangle one of the legs is 25, and the hypotenuse is 65.

Hence, the other leg is:  [tex]\sqrt{65^2-25^2}=\sqrt{4225-625}=\sqrt{3600}=60.[/tex]

It looks like the integral is

[tex]\displaystyle 6 \int yz\cos(x) \, ds[/tex]

With [tex]x=t[/tex], [tex]y=\cos(t)[/tex], and [tex]z=\sin(t)[/tex], the line element is

[tex]ds = \sqrt{\left(\dfrac{dx}{dt}\right)^2 + \left(\dfrac{dy}{dt}\right)^2 + \left(\dfrac{dz}{dt}\right)^2} \, dt = \sqrt2 \, dt[/tex]

and so

[tex]\displaystyle 6 \int yz\cos(x) \, ds = 6\sqrt2 \int_0^\pi \cos^2(t) \sin(t) \, dt[/tex]

Substitute [tex]u = \cos(t)[/tex] and [tex]du=-\sin(t)\,dt[/tex], then

[tex]\displaystyle 6 \int yz\cos(x) \, ds = -6\sqrt2 \int_1^{-1} u^2 \, du = 12\sqrt2 \int_0^1 u^2 \, du = \boxed{4\sqrt2}[/tex]

where in the second-to-last equality, we have

[tex]\displaystyle -\int_1^{-1} = \int_{-1}^1[/tex]

and

[tex]\displaystyle \int_{-1}^1 u^2 \, du = 2 \int_0^1 u^2\,du[/tex]

by symmetry.

Answer:

look above

Step-by-step explanation:

hope it helps

Answer:

x = 6

Step-by-step explanation:

put '3' in where 'y' is :

7x + 2(3) = 48

7x + 6 = 48              subtract 6 from both sides of the equation

7x = 42                 divide both sides by 7

x = 6

Answer:

$64

Step-by-step explanation:

Equation: 50 + 15x = 1010

x = (1010 - 50) ÷ 15 = 64

Since x is the total amount of money deposited in the bank per week, the answer is $64.

The expected value of the random variable is 7

The probability distribution is given as:

x=2,3,4,5,6,7,8,9,10,11,12

Probability =1/36,1/18,1/12,1/9,5/36,1/6,5/36,1/9,1/12,1/18,1/36

The expected value of the random variable is calculated using

E(X) = ∑xP(x)

Using the above formula, we have

E(x) = 2 * 1/36 + 3 * 1/18 + 4 * 1/12 + 5 * 1/9+ 6 * 5/36 + 7 * 1/6 + 8 * 5/36 + 9 * 1/9 + 10 * 1/12 + 11 * 1/18+ 12 * 1/36

Evaluate the sum of products

E(x) = 7

Hence, the expected value of the random variable is 7

Read more about expected value at

https://brainly.com/question/15858152

#SPJ1

The inequality that describes this graph is y ≥ x+5

From the given graph, we have the following highlights:

The first highlight above implies, the inequality can be any of ≥ and ≤

While the second highlight above implies, the inequality is ≥

Hence, the inequality that describes this graph is y ≥ x+5

Read more about inequality at

https://brainly.com/question/24372553

#SPJ1

The value of angle ABT is 40 degrees if PTR is the tangent of a circle option (a) 40° is correct.

It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)

It is given that:

A circle is shown in the picture.

PTR is the tangent of a circle.

AT=PT

Angle APT=20°

Let O is the center of the circle:

Angle BOT = 2 Angle PAT = 40 degrees

BO = TO = r

Angle BOT = Angle TBO = (1/2)(180 - 40) = 70 degrees

RTP is the tangent

OT ⊥ PTR

Angle OTA = 90 - Angle ATR = 50 degrees

Angle ABT = 180 - Angle PAT - Angle BTA

= 180 - 20 -  (170 + 50)

= 40 degrees

Thus, the value of angle ABT is 40 degrees if PTR is the tangent of a circle option (a) 40° is correct.

Learn more about circle here:

brainly.com/question/11833983

#SPJ1

The relation that is a function is:

b. y = 2x² - 3x + 7

A relation is a function if each value of the input is mapped to only one value of the output.

Hence, when both x and y are squared, we have that [tex]x = \pm ay[/tex], hence it is not a function. This is the case for items a and c.

For item d, we have that the relation can be simplified as follows:

x = -y² + 3y

x = y(-y + 3)

The solution above, is associated to two values of y, hence it is also not a function. Then the function is given by:

b. y = 2x² - 3x + 7

In the solution, it can be seen that for each input x, only one value of y can be generated.

More can be learned about relations and functions at brainly.com/question/12463448

#SPJ1

The speed of the moving walkway relative to the airport terminal exists at 1.84 m/s.

Let x be the speed of the walkway.

(2.8 + x) = speed of child moving in direction of the walkway

(2.8 - x) =  speed of child moving against the direction of the walkway

Travel time = distance/speed

Travel time of child moving in direction of walkway = 23/(2.8+x)

Total elapsed time given = 29s

23/(2.8 + x)+ 23 / (2.8-x) = 29

LCD = (2.8 + x)(2.8 - x)

[tex]23(2.8 - x) + 23(2.8 + x) = 29(2.8 + x)(2.8 -x)[/tex]

simplifying the equation, we get

[tex]23*2.8-23x+23*2.8+23x=29(2.8^2-x^2)[/tex]

[tex]23(2.8+2.8)/29=2.8^2-x^2[/tex]

[tex]x^2=(2.8)^2-(23*5.6)/29)=3.4[/tex]

[tex]x=\sqrt{3.4}=1.84m/s[/tex]

Speed of walkway = 1.84 m/s

The speed of the moving walkway relative to the airport terminal exists at 1.84 m/s.

To learn more about Speed refer to:

brainly.com/question/4931057

#SPJ4

Answer:

Matrix B should be subtracted from Matrix A.

Step-by-step explanation:

Answer:

LCM=72

Step-by-step explanation:

l.c.m by prime factorization

a)18,24

factor of 18=2*3*3

factor of 24=2*2*2*3

common and remaining factor=2*3*3*2*2= 72

Answer:

  (b)  96 inches

Step-by-step explanation:

The perimeter of the board is the sum of its four edge lengths.

Each edge of the board is indicated as being 8 squares long. Each square is 3 inches on a side, so the edge of the board is ...

  8 × (3 in) = 24 in . . . . board edge length

The perimeter of the board is 4 times the length of one edge, so is ...

  P =4s = 4(24 in) = 96 in

The perimeter of Edgar's checkerboard is 96 inches.

__

The perimeter of one small square on the board is ...

  P = 4s = 4(3 in) = 12 in

The whole board is a dilation of one square by a factor of 8. Its perimeter will be ...

  P' = (scale factor) × P

  P' = 8×(12 in) = 96 in

The perimeter of Edgar's checkerboard is 96 inches.

Given the percentage taken off and the reduced price, the original price of the item is $142.

Given the data in the question;

The original price of the item is at 100%, if the 20% is taken off. The price is now at 80%.

Hence 80% of the original price will give the reduced price.

Let the original price be represented by x

80% × x = $113.60

We solve for x

80/100 × x = $113.60

80x/100 = $113.60

Cross multiply

80x = $11360

x = $11360/80

x = $142

Given the percentage taken off and the reduced price, the original price of the item is $142.

Learn more about Percentages here: brainly.com/question/24159063

#SPJ1

Answer: 14 cars.

Step-by-step explanation:

A car can be washed with : 100/11 oz.

1 gallon=128 oz.

Hence,

[tex]\displaystyle\\\frac{128}{\frac{100}{11} } =\frac{128*11}{100} =\frac{1408}{100} =14,08\ (cars).[/tex]

The total number of cars that can be washed with 1 gallon of soap if 100oz Can wash 11 cars would be given as 14 cars

To determine how many cars can be washed with 1 gallon of soap, we need to find the ratio between the amount of soap used and the number of cars washed.

Given that 100 oz of soap can wash 11 cars, we can set up the following proportion:

100 oz soap / 11 cars = 1 gallon soap / x cars

I gallon is given as 128 OZ

Such that we have

128 x 100 / 11

= 14.08 cars

Hence the total number of cars would be given as 14 cars

Read more on total number here https://brainly.com/question/25734188

#SPJ2

Answer:

  (c)  x < -5.170

Step-by-step explanation:

The given function is an exponential function with a decay factor of 0.5 and a y-intercept of 0.5^2 = 0.25. It will be larger for more negative x-values.

We know that 2^3 = 8, so (1/2)^-3 = 8. This means the exponent of 0.5 in the given inequality will be more negative than -3:

  x +2 < -3

  x < -5 . . . . . . . . subtract 2

The only answer choice in this range is ...

  x < -5.170

Taking the logarithm of both sides of the inequality, we have ...

  (x +2)log(0.5) > log(9)

  x +2 < log(9)/log(0.5) . . . . . . log(0.5) < 0, so the inequality reverses

  x < log(9)/log(0.5) -2 . . . . . . subtract 2

  x < (0.95424251)/(-0.30103000) -2 = -3.1699250 -2

  x < -5.1699250 ≈ -5.170

[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Let's solve ~

Calculate discriminant :

[tex]\qquad \sf  \dashrightarrow \: 3 {x}^{2} + 6x - 1[/tex]

[tex]\qquad \sf  \dashrightarrow \: discriminant = {b}^{2} - 4ac[/tex]

[tex]\qquad \sf  \dashrightarrow \: d = (6) {}^{2} - (4 \times 3 \times 1)[/tex]

[tex]\qquad \sf  \dashrightarrow \: d = 36 - 12[/tex]

[tex]\qquad \sf  \dashrightarrow \: d = 24[/tex]

[tex]\qquad \sf  \dashrightarrow \: \sqrt {d} = 2 \sqrt{6} [/tex]

Now, let's calculate it's roots ( x - intercepts )

[tex]\qquad \sf  \dashrightarrow \: x = \cfrac{ - b \pm \sqrt{d} }{2a} [/tex]

[tex]\qquad \sf  \dashrightarrow \: x = \cfrac{ - 6\pm 2 \sqrt{6} }{2 \times 3} [/tex]

[tex]\qquad \sf  \dashrightarrow \: x = \cfrac{ - 6\pm 2 \sqrt{6} }{6} [/tex]

So, the intercepts are :

[tex]\qquad \sf  \dashrightarrow \: x = \cfrac{ - 6 - 2 \sqrt{6} }{6} [/tex]

and

[tex]\qquad \sf  \dashrightarrow \: x = \cfrac{ - 6 + 2 \sqrt{6} }{6} [/tex]

Answer:

[tex]\left( \dfrac{ -3 + 2\sqrt{3}}{ 3}, \ 0\right), \ \left(\dfrac{ -3 - 2\sqrt{3}}{ 3}, \ 0\right)[/tex]

Explanation:

Given expression:

f(x) = 3x² + 6x - 1

Use quadratic formula:

[tex]\sf x = \dfrac{ -b \pm \sqrt{b^2 - 4ac}}{2a} \ where \ ax^2 + bx + c = 0[/tex]

Here after finding coefficients:

Applying formula:

[tex]x = \dfrac{ -6 \pm \sqrt{6^2 - 4(3)(-1)}}{2(3)}[/tex]

[tex]x = \dfrac{ -6 \pm \sqrt{48}}{6}[/tex]

[tex]x = \dfrac{ -6 \pm 4\sqrt{3}}{6}[/tex]

[tex]x = \dfrac{ -6 \pm 4\sqrt{3}}{2 \cdot 3}[/tex]

[tex]x = \dfrac{ -3 \pm 2\sqrt{3}}{ 3}[/tex]

[tex]x = \dfrac{ -3 + 2\sqrt{3}}{ 3}, \ \dfrac{ -3 - 2\sqrt{3}}{ 3}[/tex]

Answer:

2280 minutes.

Step-by-step explanation:

Time spent each week in lessons = (Lessons per week)(Time per lesson)

= (6)(38)

= 228 minutes/week

Time spent in a 10-week period:

10 weeks * 228 minutes/week

= 2280 minutes

Use conversion factors to determine the time in the desired units (i.e. Hours, seconds, etc.).

Hope this helps!

Answer:

I don't understand the formatting after the first two equations.

Step-by-step explanation:

See attached graph.

In words (6 + q) - xy is six added to a number subtracted from the product of two numbers

The problem is a algebraic expression

A algebraic expression  a mathematical expression containing one or more variables used to express a word problem

We want to convert the algebraic expression (6 + q) - xy into a word problem.

So, (6 + q) - xy in words is six added to a number subtracted from the product of two numbers

Learn more about algebraic expression here:

https://brainly.com/question/4758002

#SPJ1

Step-by-step explanation:

part 1: 64/125 - 2/3

make the denominator ( bottom number) the same

x/125 and x/3

125×3 and 3×125

x/375 and x/375

whatever we do to the denominator we have to do to the numerator ( top number)

64/125

125 × 3

so

64 ×3

=64×3/125×3

=192/375

2/3

3 × 125

so

2 × 125

=2×125/3×125

=250/375

put together:

192/375 - 250/375

denominator is the same so we can simply take 192 from 250

192 - 250 = -58

= -58/375

part 2: + (256/625)-1/4

-58/375 + (256/625)-1/4

do the same for (256/625)-1/4 as in part 1

then add it to -58/375 by making the denominator the same

part 3: + (7/3)​

make the denominator the same and add

part 4: simplify

divide a number from both the top and bottom till there is nothing you can divide from both