Van was asked to add 46 to 37 and round the result to the nearest ten. He figured that since he was going to have to round anyway, he might as well do it before adding the numbers. He rounded 46 to 50 and 37 to 40, thus getting an answer of 50+40=90. This answer is not correct. What is the correct answer?

Answer:

[tex]\large\boxed{-3x+2y\geq7}[/tex]

Step-by-step explanation:

<, > - dotted line

≤, ≥ - solid line

<, ≤ - shaded region below the line

>, ≥ - shaded region above the line

====================================

We have solid line (≤, ≥).

Shaded region is above the line (>, ≥)

Therefore, the inequality sign must be: ≥

Finally, your answer is -3x + 2y ≥ 7.

Check the equation of a line.

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

[tex]y-y_1=m(x-x_1)[/tex]

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

From the graph we ahve the points (3, 8) and (1, 5) - look at the picture.

Substitute:

[tex]m=\dfrac{5-8}{1-3}=\dfrac{-3}{-2}=\dfrac{3}{2}[/tex]

[tex]y-8=\dfrac{3}{2}(x-3)[/tex]

Convert to the standard form [tex]Ax+By=C[/tex]:

[tex]y-8=\dfrac{3}{2}(x-3)[/tex]            multiply both sides by 2

[tex]2y-16=3(x-3)[/tex]           use the distributive property

[tex]2y-16=3x-9[/tex]             subtract 3x from both sides

[tex]-3x+2y-16=-9[/tex]           add 16 to both sides

[tex]-3x+2y=7[/tex]         CORRECT :)

Answer:

The difference between the amount of energy the microwave uses and the amount it puts out is x² + 2x + 8 ⇒ first answer

Step-by-step explanation:

* Lets explain how to solve the problem

- The amount of energy a microwave oven uses is given by the

  function f(x) = 5x + 9

- The amount of energy the microwave puts out is given by the

  function g(x) = − x² + 3x + 1

- x is the amount of time the microwave is turned on in

 both functions

- To find the difference between the amount of energy the

  microwave uses and the amount it puts out we will subtract

  g(x) from f(x)

* Lets do that

∵ f(x) = 5x + 9

∵ g(x) = - x² + 3x + 1

∴ The difference = 5x + 9 - (-x² + 3x + 1) ⇒ multiply the bracket by (-)

- Remember that (-)(-) = (+) and (-)(+) = (-)

∴ The difference = 5x + 9 + x² - 3x - 1 ⇒ Add the like terms

∴ The difference = x² + (5x - 3x) + (9 - 1)

∴ The difference = x² + 2x + 8

* The difference between the amount of energy the microwave uses

  and the amount it puts out is x² + 2x + 8

To find the difference between the energy a microwave uses and the energy it puts out, subtract the output function from the input function using the given equations. The correct answer is [tex]f(x) - g(x) = x^2 + 2x + 8[/tex] that is option A is correct.

The difference between the amount of energy the microwave uses and the amount it puts out can be calculated by subtracting the output function from the input function.

Given:

f(x) = 5x + 9 (energy used by the microwave)

[tex]g(x) = -x^2 + 3x + 1[/tex](energy output by the microwave)

Calculating the difference:

Substitute the values:
[tex]f(x) - g(x) = (5x + 9) - (-x^2 + 3x + 1)[/tex]

Simplify the expression:
[tex]f(x) - g(x) = x^2 + 2x + 8[/tex]

Answer:

see explanation

Step-by-step explanation:

Given

2cosΘ - [tex]\sqrt{2}[/tex] = 0 ( add [tex]\sqrt{2}[/tex] to both sides )

2cosΘ = [tex]\sqrt{2}[/tex] ( divide both sides by 2 )

cosΘ = [tex]\frac{\sqrt{2} }{2}[/tex]

Since cosΘ > 0 then Θ is in first and fourth quadrants, hence

Θ = [tex]cos^{-1}[/tex] ( [tex]\frac{\sqrt{2} }{2}[/tex] ) = [tex]\frac{\pi }{4}[/tex]

OR

Θ = 2π - [tex]\frac{\pi }{4}[/tex] = [tex]\frac{7\pi }{4}[/tex]

solutions are Θ = [tex]\frac{\pi }{4}[/tex], [tex]\frac{7\pi }{4}[/tex]

Answer:

π/4, 7π/4.

Step-by-step explanation:

2 cos O - √2 = 0

2 cos O = √2

cos O  = √2/2

This is an angle in  45-45-90 triangle where  the sides are in the ratio

1:1:√2 where the cosine of 45 degrees = 1 /√2 = √2/2.

In radians it is π/4.

The cosine is also positive in the fourth quadrant so the other solution is

7π/4.

No. Since we cannot factor,

[tex]c^5-49[/tex].

Hope this helps.

r3t40

The correct answer is: b. no [tex]c^5 - 49[/tex] is not a difference of squares

Difference of squares refers to an expression of the form [tex]a^2 - b^2[/tex], which can be factored into [tex](a - b)(a + b)[/tex].

In this case, [tex]c^5 - 49[/tex] cannot be expressed in the form of [tex]a^2 - b^2[/tex] because [tex]c^5[/tex] is not a perfect square (a number raised to the power of 2) since it is c raised to the power of 5. To be a difference of squares, both terms must be perfect squares.

49 on the other is a perfect square of 7 but because of [tex]c^5[/tex] the expression [tex]c^5 - 49[/tex] cannot be converted to the form of [tex]a^2 - b^2[/tex] and is thus not considered a difference of squares.

Thus, The correct answer is: b. no  [tex]c^5 - 49[/tex] is not a difference of squares

Answer:

B)

B)

D)

Step-by-step explanation:

1. [tex]7x^3y+14x^2y^3-7x^2y^2[/tex]

The GCF of all the term of the above polynomial is [tex]7x^2y[/tex] , hence we take it outside and form a bracket

[tex]7x^2y(x+2y^2-y)[/tex]

The polynomial within the bracket can not be factorized further hence this is our final answer. Option (B) is the right answer

2. [tex]5x(x+3)+6(x+3)[/tex]

The GCF of all the term of the above polynomial is [tex](x+3)[/tex] , hence we take it outside and form a bracket

[tex](x+3)(5x+6)[/tex]

The polynomial within the bracket can not be factorized further hence this is our final answer. Option (B) is the right answer

3. [tex]8x^5+2x^4+4x^2[/tex]

The GCF of all the term of the above polynomial is [tex]2x^2[/tex] , hence we take it outside and form a bracket

[tex]2x^2(4x^3+x^2+2)[/tex]

The polynomial within the bracket can not be factorized further hence this is our final answer. Option (D) is the right answer

Answer:

The correct answer is: f(x) = –2/3x – 11

Step-by-step explanation:

We have to convert the line given in point slope form to a form which can be compared by the given options

So,

y+7=-2/3(x+6)

[tex]y=-\frac{2}{3}(x+6)\\ y+7=-\frac{2}{3}x+(6)(-\frac{2}{3}) \\ y+7=-\frac{2}{3}x-4\\y=-\frac{2}{3}x-4-7\\y=-\frac{2}{3}x-11[/tex]

Therefore the correct answer is: f(x) = –2/3x –11 ..

Answer:

Step-by-step explanation:

(x²-6x-3)(7x²-4x+7)= ?

Multiply each term of 2nd bracket with the 1st bracket:

=7x²(x²-6x-3) -4x(x²-6x-3) +7(x²-6x-3)

=7x^4-42x^3-21x^2-4x^3+24x^2+12x+7x^2-42x-21

Now solve the like terms:

=7x^4-46x^3+10x^2-30x-21

Therefore the answer is (x²-6x-3)(7x²-4x+7)=7x^4-46x^3+10x^2-30x-21 ....

Answer:

[tex]w \ne0[/tex]

Step-by-step explanation:

The area of a rectangle is given by:

[tex]Area = L \times \: W[/tex]

In this case, we have the height replacing the length.

[tex]Area=H\times w[/tex]

The area of the rectangle is 70.

[tex]H\times w = 70[/tex]

Dividing through by w gives:

[tex]H = \frac{70}{w} [/tex]

Or to show that H is dependent on w, we write

[tex]H (w)= \frac{70}{w} [/tex]

[tex]w \ne \: 0[/tex]

Domain is the set of all real numbers for which the function is defined.

Therefore the domain is all real numbers except 0.

Answer:

w>0

Step-by-step explanation:

Answer:

a^ (13)

Step-by-step explanation:

We know x^b* x^c = x^ (b+c)

a^8 * a^5 = a^ (8+5) = a^ (13)

Answer:

Step-by-step explanation:

The answer would be A^13, because when multiplying exponents with the same base, you just have to adfd the exponents.

Answer:

[tex]4\ hours[/tex]

Step-by-step explanation:

we know that

1 hour=60 minutes

we know that

To find out how many hours and minutes it will take Michelle to listen to the 5 CDs, add the times for each CD.

so

[tex]2(51)+3(46)=240\ minutes[/tex]

Convert to hours

[tex]240=240/60=4\ hours[/tex]

Answer:

The angular speed is 3,227 rad/min

Step-by-step explanation:

Remember that

1 mile=63,360 inches

step 1

Find the circumference of the wheels

The circumference is equal to

[tex]C=\pi D[/tex]

we have

[tex]D=36\ in[/tex]

substitute

[tex]C=\pi (36)[/tex]

[tex]C=36\pi\ in[/tex]

step 2

we know that

The speed of the wheel is 55 mi/h

Convert to mi/min

55 mi/h=55/60 mi/min

Convert to in/min

(55/60) mi/min=55*63,360/60 in/min= 58,080 in/min

we know that

The circumference of the wheel subtends a central angle of 2π radians

so

using proportion

Find out how much radians are 58,080 inches

[tex]\frac{36\pi }{2\pi }=\frac{58,080}{x} \\\\x=2*58,080/36\\\\x=3,226.67 \ rad[/tex]

therefore

The angular speed is 3,227 rad/min

Final answer:

To calculate the angular speed in radians per minute for a truck with 36-inch diameter wheels traveling at 55 mi/h, convert the diameter to radius in meters, convert the speed to meters per minute, and then use the relationship v = r theta.

Explanation:

To find the angular speed of the wheels in radians per minute, we can use the relationship between linear speed and angular speed, which is given by v = r  * theta, where v is the linear speed, r is the radius of the wheel, and theta is the angular speed.

First, convert the diameter to radius: radius = diameter / 2 = 36 in / 2 = 18 in. Then, convert inches to meters as 1 inch is 0.0254 meters. So, radius in meters = 18 in * 0.0254 m/in = 0.4572 m.

Next, convert the speed from miles per hour to meters per minute:

Convert miles to meters: 1 mile = 1609.34 meters,

Speed in meters per minute: 55 mi/h  * 1609.34 m/mi * 1h/60min = 1,486.86 m/min.

Now we can find the angular speed:  theta = v / r = 1,486.86 m/min / 0.4572 m = 3,252.3 rad/min.

For this case, the first thing to do is define a variable.

We have then:

Then we write the equation that models the problem:

[tex]\frac {2} {3} x = 18[/tex]

From here, we clear the value of x.

We have then:

[tex]x = \frac {3} {2} (18)\\x = 3 * 9\\x = 27[/tex]

Answer:

 the total number of children in the class is:

[tex]x = 27[/tex]

To calculate the total number of children in the fourth-grade class, divide the number of girls by 2 to find one-third of the class, then multiply by 3. The total class size is 27 children.

To find the total number of children in the fourth-grade class, we start by understanding that two-thirds of the children are girls. If there are 18 girls, which is two-thirds of the class, we need to calculate the full class size which constitutes three-thirds (or the whole).

Step 1: Represent two-thirds of the class as 2/3.
Step 2: Equate two-thirds of the class to the number of girls: 2/3 of the class = 18 girls.
Step 3: Find one-third of the class by dividing the number of girls by 2: 18 girls \/ 2 = 9 children.
Step 4: Calculate the full class size (which is three-thirds) by multiplying one-third of the class by 3: 9 children x 3 = 27 children.

Therefore, the total number of children in the fourth-grade class is 27.

The answer is 2+2√3 or 2-2√3

Answer:

[tex]x = 2[/tex]±[tex]\sqrt{12}[/tex]

Step-by-step explanation:

Given the following equation ax^2 + bx + c = 0, the quadratic formula states that the solution to that equation is going to be given by:

[tex]x1 = \frac{-b+\sqrt{b^{2}-4ac } }{2a}[/tex]

[tex]x1 = \frac{-b-\sqrt{b^{2}-4ac } }{2a}[/tex]

In this case, a=1, b=-4 and c=-8. Therefore:

[tex]x1 = \frac{4+\sqrt{(-4)^{2}-4(1)(-8)} }{2}[/tex]

[tex]x1 = \frac{4+\sqrt{48}}{2}[/tex]

[tex]x1 = 2+\sqrt{12}[/tex]

[tex]x2 = \frac{4-\sqrt{(-4)^{2}-4(1)(-8)} }{2}[/tex]

[tex]x2 = \frac{4-\sqrt{48}}{2}[/tex]

[tex]x2 = 2-\sqrt{12}[/tex]

Therefore the solutions are:

[tex]x = 2[/tex]±[tex]\sqrt{12}[/tex]

Answer:

See explanation

Step-by-step explanation:

The given circle has center O.

A, B,C, and D are points on the circumference of the circle.

We want to prove that: [tex]\angle A\cong \angle D[/tex]

We need to join to B and C as shown in the attachment.

Recall that angle subtended by arc BC at the center is twice the angle subtended at the circumference by the same arc.

This implies that:

[tex] \angle O=2\angle A...(1)[/tex]

[tex]\angle O=2\angle D...(2)[/tex]

The LHS of equation (1) and (2) are equal. Therefore the RHS are also equal.

This implies that:

[tex]2\angle A=2\angle D[/tex]

[tex]\therefore \angle A\cong \angle D[/tex]

Answer:

Inscribed angles theorem

Step-by-step explanation:

Just took test on edg2020

Answer:

y = -16

Step-by-step explanation:

f(x)=3/4x+12 (replace f(x) with y)

y =3/4x+12  (rearrange to express x in terms of y)

y - 12=3/4 x

3/4 x = y - 12

3x = 4(y - 12)

x = (4/3)(y - 12)

x = (4/3)y - (4/3)(12)

x = (4/3)y - 16

[tex]f^{-1}[/tex] (y) = (4/3)y - 16

[tex]f^{-1}[/tex] (x) = (4/3)x - 16

comparing to general form

y = mx + b where b is the y-intercept

b = -16

Hence the y-intercept is y = -16

The value of the y-intercept will be given as y = -16

The equation in mathematics is the relationship between the variables and the number and establishes the relationship between the two or more variables.

f (x)  = 3/4x  +  12 (replace f(x) with y)

y     =   3/4x  +  12  (rearrange to express x in terms of y)

y - 12  =  3/4 x

3/4 x  =  y - 12

3x    =   4(y - 12)

x     =  (4/3)(y - 12)

x    =    (4/3)y - (4/3)(12)

x    =    (4/3)y - 16

(y)  =  (4/3)y - 16

(x) =   (4/3)x - 16

Compared to the general form

y = mx + b where b is the y-intercept

b = -16

To know more about equations follow

https://brainly.com/question/2972832

#SPJ2

Answer:

x = -5

Step-by-step explanation:

It just is :)

For this case we must find the value of "x" of the following expression:

[tex]2x-3 + 3x = -28[/tex]

We add similar terms:

[tex]5x-3 = -28[/tex]

We add 3 to both sides of the equation:

[tex]5x = -28 + 3[/tex]

Different signs are subtracted and the sign of the major is placed:

[tex]5x = -25[/tex]

We divide between 5 on both sides of the equation:

[tex]x = \frac {-25} {5}\\x = -5[/tex]

ANswer:

[tex]x = -5[/tex]

CPCTC = corresponding parts of congruent triangles are congruent

BA and CA are corresponding sides for both triangles, namely twins, BA ≅ CA.

Answer: [tex]\overline{BA}\cong\overline{CA}[/tex]

Step-by-step explanation:

Given : [tex]\triangle {BAT}\cong\triangle{CAT}[/tex]

The CPCTC property of congruent triangles says that the corresponding parts of congruent triangles are congruent.

Therefore, the the corresponding angles and sides of [tex]\triangle {BAT}\text{ and }\triangle{CAT}[/tex] are congruent.

i.e. [tex]\angle {BAT}\cong\angle{CAT}[/tex]

[tex]\angle {ATB\cong\angle{ATC}\\\\\[/tex]

[tex]\angle {TBA}\cong\angle{TCA}[/tex]

and

[tex]\overline{BA}\cong\overline{CA}\\\\\overline{AT}\cong\overline{AT}\\\\\overline{TB}\cong\overline{TC}[/tex]

So, from all the options [tex]\overline{BA}\cong\overline{CA}[/tex] is the true option.

Answer:

30

Step-by-step explanation:

Find lowest common multiple of 5 and 6

Multiples of 5                             Multiples of 6

5 × 1 = 5                                       6 × 1 = 6                                      

5 × 2 = 10                                    6  × 2 = 12

5 × 3 = 15                                     6 × 3 = 18

5 × 4 = 20                                    6 × 4 = 24

5 × 5 = 25                                    6 × 5 = 30

5 × 6 = 30

5 × 7 = 35

5 × 2 = 10

5 × 3 = 15

5 × 4 = 20

5 × 5 = 25

5 × 6 = 30

5 × 7 = 35

30 is the lowest number which comes in both lists

It's 30... if your looking at a simple answer, it's 30.

Answer:

$950

Step-by-step explanation:

(500*6*15)/100 = 450 (applying the formula of simple interest)

450 + 500 ( adding the interest to the initial investment or princlple)

= 950 (bank balance after 15 years)

Hope this helps! :)

Answer:

A

Step-by-step explanation:

A:  The student incorrectly divided both sides by 35.  The student should first add 10 to both sides, obtaining 35x = 15, and then divide 15 by 35, obtaining the final answer 3/7.

Answer:

C

Step-by-step explanation:

For the given intervals

( - ∞, - 5) ← use any value < - 5 but not - 5, the parenthesis ) indicates that x is less than - 5 but not equal to - 5

(- 5, - 1) ← - 4, - 3, - 2 can be used but not - 5 or - 1

(- 1, 4) ← 0, 1, 2, 3 can be used but not - 1 or 4

(4, ∞ ) ← use any value > 4 but not 4

Hence

3 can be used in (- 1, 4)

- 6 can be used in (- ∞, - 5)

zero can be used in (- 1, 4)

- 5 cannot be used in any of the given intervals

Answer:

8 pounds of peanuts, 6 pounds of raisins and 6 pounds of chocolate chips

Step-by-step explanation:

Let x be the number of pounds of peanuts and y be the number of pounds of raisins and chocolate chips.

Peanuts cost $2 per pound, then x pounds cost $2x.

Raisins cost $2.50 per pound, then y pounds cost $2.50y.

Chocolate chips cost $4 per pound, then y pounds cost $4y.

In total, x+y+y=20 and those 20 pounds cost

2x+2.50y+4y=20·2.75.

Solve the system of two equations:

[tex]\left \{ {{x+2y=20} \\ \\ \\ \\ \\ \\ \atop {2x+6.5y=55}} \right.[/tex]

From the first equation:

[tex]x=20-2y[/tex]

Substitute x into the second equation:

[tex]2(20-2y)+6.5y=55\\ \\40-4y+6.5y=55\\ \\2.5y=15\\ \\25y=150\\ \\y=6\\ \\x=20-2\cdot 6=8[/tex]

Answer:

$96.75

Step-by-step explanation:

Answer:

16. 5/3

Step-by-step explanation:

let the no of tranquilizer be x

therefore

5/4 + x =18

x= 18-5/4

= 16 5/3

Answer:3, 9, 27, 7, 189

Step-by-step explanation:

The prime factorization of 1323 involves breaking it down into prime factors that multiply together to give the original number, starting with the smallest prime.

The prime factorization of 1323 is the process of breaking down the number into its prime factors, which are numbers that are prime and multiply together to give the original number, 1323. To find the prime factors, we start by dividing the number by the smallest prime number, which is 2. Since 1323 is odd, we move to the next prime number, which is 3. We find that 1323 is divisible by 3, so we can write 1323 as 3 × 441. We continue to take 441 and factor it further, eventually finding the complete prime factorization.

Answer:

Option d. (-2,-5)

Step-by-step explanation:

we know that

The equation of a vertical parabola in vertex form is equal to

[tex]y=a(x-h)^{2} +k[/tex]

where

a is a coefficient

(h,k) is the vertex of the parabola

In this problem we have

[tex]y=x^{2} +4x-1[/tex]

This is the equation of a vertical parabola open up

The vertex is minimum

Convert the equation in vertex form

Group terms that contain the same variable, and move the constant to the opposite side of the equation

[tex]y+1=x^{2} +4x[/tex]

Complete the square. Remember to balance the equation by adding the same constants to each side.

[tex]y+1+4=x^{2} +4x+4[/tex]

[tex]y+5=x^{2}+4x+4[/tex]

Rewrite as perfect squares

[tex]y+5=(x+2)^{2}[/tex]

[tex]y=(x+2)^{2}-5[/tex] -----> equation in vertex form

therefore

The vertex is (-2,-5)

Final answer:

The equation that shows the value on the gift card over time is: Value on gift card = Initial value - Total amount spent.

Explanation:

The equation that shows the value on the gift card over time is: Value on gift card = Initial value - Total amount spent.

Since the initial value of the gift card is $50 and each day a drink costs $3, the equation can be written as: Value on gift card = 50 - 3x, where x represents the number of days.

This equation will give you the value remaining on the gift card after x days of buying a $3 drink.

Answer:

10 inches

Step-by-step explanation:

All the sides are the same.