A five pound bag of apples costs $3.45. What is the unit cost of apples

If [tex]\theta[/tex] falls in quadrant IV, then we know [tex]\sin\theta<0[/tex] and [tex]\cos\theta>0[/tex]. By definition of cosecant,

[tex]\csc\theta=\dfrac1{\sin\theta}[/tex]

so we also know that [tex]\csc\theta<0[/tex]. Recall that

[tex]\cot^2\theta+1=\csc^2\theta[/tex]

which means

[tex]\csc\theta=-\sqrt{\cot^2\theta+1}=-\dfrac{\sqrt{10}}3[/tex]

[tex]\implies\sin\theta=-\dfrac3{\sqrt{10}}[/tex]

By definition of cotangent,

[tex]\cot\theta=\dfrac{\cos\theta}{\sin\theta}\implies\cos\theta=\dfrac1{\sqrt{10}}[/tex]

[tex]\implies\sec\theta=\sqrt{10}[/tex]

We also immediately know that

[tex]\tan\theta=-\dfrac{21}7[/tex]

The listed answers are unsimplified relative to the ones we've come up with here, but with some manipulation we find

[tex]\sin\theta=-\dfrac3{\sqrt{10}}=-\dfrac{7\cdot3}{7\sqrt{10}}=-\dfrac{21}{\sqrt{490}}[/tex]

[tex]\cos\theta=\dfrac1{\sqrt{10}}=\dfrac7{7\sqrt{10}}=\dfrac7{\sqrt{490}}[/tex]

[tex]\csc\theta=\dfrac1{\sin\theta}=-\dfrac{\sqrt{490}}{21}[/tex]

[tex]\sec\theta=\dfrac1{\cos\theta}=\dfrac{\sqrt{490}}7[/tex]

[tex]\tan\theta=\dfrac1{\cot\theta}=-\dfrac{21}7[/tex]

so that the third option is correct.

7 Pounds Equals 112.0000oz.

Have A Great Day!

Answer:

1947

Step-by-step explanation:

This is the answer

ANSWER

3

EXPLANATION

The given polynomial is

[tex] {a}^{2} + b - cd[/tex]

The terms of the polynomial are:

First term:

[tex] {a}^{2} [/tex]

Second term:

[tex]b[/tex]

Third term:

[tex] - cd[/tex]

Therefore the given polynomial has 3 terms.

Answer:

Two solutions were found :

x = 6

x = 0

Step-by-step explanation:

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "x2"   was replaced by   "x^2".  

Step by step solution :

Step  1  :

Equation at the end of step  1  :

 32x2 -  54x  = 0  

Step  2  :

Step  3  :

Pulling out like terms :

3.1     Pull out like factors :

  9x2 - 54x  =   9x • (x - 6)  

Equation at the end of step  3  :

 9x • (x - 6)  = 0  

Step  4  :

Theory - Roots of a product :

4.1    A product of several terms equals zero.  

When a product of two or more terms equals zero, then at least one of the terms must be zero.  

We shall now solve each term = 0 separately  

In other words, we are going to solve as many equations as there are terms in the product  

Any solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation :

4.2      Solve  :    9x = 0  

Divide both sides of the equation by 9:

                    x = 0  

Solving a Single Variable Equation :

4.3      Solve  :    x-6 = 0  

Add  6  to both sides of the equation :  

                     x = 6

Answer:

x = 6...... x = 0

Step-by-step explanation:

a p e x.

Step-by-step explanation:

Answer:

4+3 squared 3 equals 9.19 and 4-3 squared 3 equals -1.19

Step-by-step explanation:

Answer:

The simplified form is 1 over the quantity x plus 2 times the quantity

x minus 5 ⇒ 1/(x+2)(x-5) ⇒ last answer

Step-by-step explanation:

* Lets write the product of the two fraction

∵ [tex]\frac{x+4}{x^{2}-3x-10} *\frac{x-3}{x^{2}+x-12}[/tex]

- At first factorize the denominators

# x² - 3x - 10

∵ x² = x × x ⇒ 1st term in the 1st bracket and 1st term in the

  2nd bracket

∵ -10 = 2 × -5 ⇒ 2nd term in the 1st bracket and 2nd term in the

  2nd bracket

∵ x × - 5 = -5x ⇒ ext-reams

∵ x × 2 = 2x ⇒ means

∵ 2x + -5x = -3x ⇒ middle term

∴ x² - 3x - 10 = (x + 2)(x - 5)

# x² + x - 12

∵ x² = x × x ⇒ 1st term in the 1st bracket and 1st term in the

  2nd bracket

∵ -12 = -3 × 4 ⇒ 2nd term in the 1st bracket and 2nd term in the

  2nd bracket

∵ x × 4 = 4x ⇒ ext-reams

∵ x × -3 = -3x ⇒ means

∵ 4x + -3x = x ⇒ middle term

∴ x² + x - 12 = (x - 3)(x + 4)

* Lets write the fractions after factorization

∴ [tex]\frac{x+4}{(x+2)(x-5)}*\frac{x-3}{(x-3)(x+4)}[/tex]

- lets simplify the fractions by cancel (x - 3) up with (x - 3) down

 and cancel(x + 4) up with (x + 4) down

∴ [tex]\frac{1}{(x+2)(x-5)}*1=\frac{1}{(x+2)(x-5)}[/tex]

* The simplified form is 1 over the quantity x plus 2 times the

  quantity x minus 5

Answer:

(x,y)=(85/562, -20/281)

Step-by-step explanation:

4x+2y=-6.5y=-30x+5

{4x+2y=-30x+5

{-6.5y=-30x+5 simplify the expression

{34x+2y=5

{300x-65y=50 multiply

{2210x+130y=325

{600x-1307=100 eliminate on evariable by adding the equations

2810x=425 divide both sides by 2810

x=85/562 substitute the value of x into the equation

34*85/562+2y=5 solve the equation

y=-20/281 a possible solution

(x,y)=(85/562,-20/281) check the solution

4*85/562+2*(-20/281)=-6.5*(-20/281)=-30*85/562+5 simplify the expression

130/281=130/281=130/281 the orderred pair is a solution

Answer:D

Step-by-step explanation:

In corresponding angles formed by parallel lines intersected by a transversal line, the angles are equal. So, if the measure of angle 6 is 21°, the measure of corresponding angle 4 will also be 21°.

The subject of this question is geometry, specifically dealing with parallel lines and the angles formed when a line intersects them. In the given diagram, we are told that lines a and b are parallel (represented as a || b). Therefore, we can use the properties of parallel lines to find the measure of angle 4. When a line intersects two parallel lines, it forms corresponding angles which are equal. Since we know the measure of angle 6, which is 21°, and angle 4 and 6 are corresponding angles, therefore the measure of angle 4 is also 21°. So, the answer is A) 21°.

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Answer:

0.267949192 8s the value of tan 195°

Answer:

Step-by-step explanation:

[tex]a_1=-24\\a_2=-24+10=-14\\a_3=-14+10=-4\\a_4=-4+10=6\\\\\text{Add the common difference d = 10 to the previous term.}\\\\a_5=a_4+10\to a_5=6+10=16\\a_6=a_5+10\to a_6=16+10=26\\a_7=a_6+10\to a_7=26+10=36\\\vdots[/tex]

Answer:

Jimmy and Jane

Step-by-step explanation:

They have used Pythagoras to find the length of BC. Moe is wrong because she wrote ( 1 - 4 ) ² but it's meant to be ( 4 - 1 ) ² and Alice is wrong because she forget to square 3,4 and x

The probability of grabbing a diet soda and a snack bag of Cheetos is 42%.

The question is asking to find the probability of selecting a diet soda and a bag of Cheetos at a party. To calculate this probability, we need to look at the total number of each item and determine how many favorable outcomes there are based on the selections made.

Answer:

The correct answer is A:-3a^3+2a

For this case we must find the quotient of [tex]21a^3-14a[/tex] between -7:

That is to say:

[tex]\frac {21a ^ 3-14a} {- 7} =\\\frac {21a ^ 3} {- 7} + \frac {-14a} {- 7}[/tex]

We know that:

[tex]\frac {21} {7} = 3\\\frac {14} {7} = 2\\\frac {+} {-} = -[/tex]

Finally:

[tex]-3a ^ 3 + (2a) =\\-3a ^ 3 + 2a[/tex]

Answer:

[tex]-3a ^ 3 + 2a[/tex]

Option A

The answer is the first option

[tex]\frac{3^{2}(-2)^{6}}{5^{4}}[/tex]

Quick tips to help you the next time

Multiply the exponents

Add the exponents

Answer:

the first person is right but...

Step-by-step explanation:

you should censor out your name!! Safety!

Answer:

it would be 3 tons and 80 ibs

hope that helps...if i am wrong, i am sorry :-)

Step-by-step explanation:

The mouse's overall displacement or the magnitude of the resultant vector after moving through the maze is 17.7 m, calculated based on principles of vectors in physics and using the Pythagorean theorem.

To find the magnitude of the resultant vector, indicating the mouse's displacement after traversing through the maze, we can use the principles of vectors in physics. The mouse goes through three separate displacement vectors, one of 10 m (right), another of 5 m (downward), and the last one of 7 m (right) again.

We can consider these displacements as components of two dimensions: X (horizontal) and Y (vertical). We sum the horizontal (rightward) displacements and vertical (downward) displacements separately. The horizontal displacement is 10 m + 7 m = 17 m (rightward). The vertical displacement is 5 m (downward).

To find the magnitude of the resultant displacement, we apply the Pythagorean theorem. The magnitude is the square root of the sum of the squares of the horizontal and the vertical displacement, so sqrt((17 m)^2 + (5 m)^2) = 17.7 m (rounded to the nearest tenth).

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Answer:

11 ≤ n

Explanation:

[tex] \frac{66}{6} = 11[/tex]

More than indicates the minimum value, so you use the greater than or equal to.

The above answer is written in reverse, which the exact same result.

I am joyous to assist you anytime.

The answer is:

The correct option is the first option,

[tex]{x|x<8}[/tex]

To solve the problem, we need to remember that the way to solve inequalities is almost the same that solving normal equations.

So, we are given the inequality, we have:

[tex]3(x-2)<18[/tex]

Now, solving we have:

[tex]3(x-2)<18\\\\(x-2)<\frac{18}{3} \\\\x-2<6\\\\x<6+2\\\\x<8[/tex]

Hence, we have that solution to the inequality is:

[tex]x<8[/tex]

So, the correct option is the first option,

[tex]{x|x<8}[/tex]

Have a nice day!

Answer:

[tex]\large\boxed{\{x\ |\ x<8\}}[/tex]

Step-by-step explanation:

[tex]3(x-2)<18\qquad\text{use the distributive porperty}\ a(b+c)=ab+ac\\\\(3)(x)+(3)(-2)<18\\\\3x-6<18\qquad\text{add 6 to both sides}\\\\3x-6+6<18+6\\\\3x<24\qquad\text{divide both sides by 3}\\\\\dfrac{3x}{3}<\dfrac{24}{3}\\\\x<8}[/tex]

Answer:

b=-.5

Step-by-step explanation:

The value of b in the equation 12 - b = 12.5 is determined by subtracting 12 from both sides and then multiplying by -1, resulting in b = -0.5.

The student is asking to solve for b in the equation 12 - b = 12.5. To find the value of b, you need to isolate the variable on one side of the equation. This is done by subtracting 12 from both sides, resulting in -b = 12.5 - 12, which simplifies to -b = 0.5. To get b by itself and not -b, you multiply both sides of the equation by -1, giving b = -0.5.

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Answer:

approx area of circ.=254.34

area of triangl=40.5

shaed region=173.34

just add sq. units

Step-by-step explanation:

areas of the triangle are 9*9=81

r=9

a=pi*r^2

=3.14*81

=254.34

254.34-81=173.34

Answer:

Part 1) [tex]x=-0.07[/tex]

Part 2) [tex]y=2.48[/tex]

Step-by-step explanation:

Part 1) we have

[tex]15^{-9x} =6[/tex]

Solve for x

Apply log both sides

[tex]log(15^{-9x})=log(6)[/tex]

[tex]-x*(9log(15))=log(6)[/tex]

[tex]x=-log(6)/(9log(15))[/tex]

[tex]x=-0.07[/tex]

Part 2) we have

[tex]e^{y}=12[/tex]

Apply ln both sides

[tex]ln(e^{y})=ln(12)[/tex]

[tex]y*ln(e)=ln(12)[/tex]

Remember that

[tex]ln(e)=1[/tex]

[tex]y=ln(12)[/tex]

[tex]y=2.48[/tex]

Answer with explanation:

The two equations which we have to solve for x and y and the way of finding it's solution is

   [tex]1.\rightarrow 15^{-9x}=6\\\\\text{Taking log on both sides}\\\\\rightarrow -9x \log 15=\log 6\\\\\rightarrow x \log 15^{-9}=\log 6\\\\\rightarrow x=\frac{\log 6}{\log 15^{-9}}}\\\\\rightarrow x=\log_{15^{-9}} 6\\\\2.\rightarrow e^y=12\\\\\text{Taking log on both sides}\\\\\rightarrow y \log e=\log 12\\\\\rightarrow y= \log 12[/tex]

Answer:

B. Plane and Line

Step-by-step explanation:

Answer:

I think is 1/6 the answer

Formula for slope is:

[tex]\frac{y_{2} -y_{1}}{x_{2}-x_{1}}[/tex]

In this case...

[tex]y_{2} =8\\y_{1} =7\\x_{2} =-4\\x_{1} =2[/tex]

so...

[tex]\frac{8-7}{-4-2}[/tex]

[tex]\frac{1}{-6}[/tex]

[tex]\frac{-1}{6}[/tex] <---------------------------the slope of the line

Hope this helped!

~Just a girl in love with Shawn Mendes

Looks like your figure is missing...

Could you repost it with the figure next time?

Someone will solve it for sure.

Regards;

Leukonov.

[tex]\bf (2x^2-11x-9)-(14x^2+8x-4)\implies (2x^2-11x-9)-14x^2-8x-4 \\\\\\ 2x^2-14x^2-11x-8x-9-4\implies -12x^2-19x-5~~\checkmark \\\\[-0.35em] ~\dotfill\\\\ 2(x-1)-3(4x^2+7x+1)\implies 2x-2-12x^2-21x-3 \\\\\\ -12x^2+2x-21x-2-3\implies -12x^2-19x-5~~\checkmark \\\\[-0.35em] ~\dotfill\\\\ 3(x-5)-2(6x^2+9x+5)\implies 3x-15-12x^2-18x-10 \\\\\\ -12x^2+3x-18x-15-10\implies -12x^2-15x-25~~\bigotimes \\\\[-0.35em] ~\dotfill\\\\ (4x^2-13x-7)-(16x^2+9x-5)\implies 4x^2-13x-7-16x^2-9x+5[/tex]

[tex]\bf 4x^2-16x^2-13x-9x-7+5\implies -12x^2-22x-2~~\bigotimes \\\\[-0.35em] ~\dotfill\\\\ (-16x^2+10x-3)+(4x^2-29x-2)\implies -16x^2+10x-3+4x^2-29x-2 \\\\\\ -16x^2+4x^2+10x-29x-3-2\implies -12x^2-19x-5~~\checkmark \\\\[-0.35em] ~\dotfill\\\\ (-15x^2+9x-10)+(3x^2-10x-5)\implies -15x^2+9x-10+3x^2-10x-5 \\\\\\ -15x^2+3x^2+9x-10x-10-5\implies -12x^2-x-15~~\bigotimes[/tex]

Answer:

3.8 cm

Step-by-step explanation:

The arc length formula is s = r·Ф, where Ф is the central angle in radians.

Here, s = (2 cm)(1.9 rad) = 3.8 cm

The length of the arc intercepted by a central angle of 1.9 radians in a circle with a radius of 2 cm is 3.8 cm, calculated by multiplying the radius (2 cm) by the angle in radians (1.9).

A circle has a radius of 2 cm and we need to find the length (s) of the arc intercepted by a central angle of 1.9 radians. The formula to find the arc length 's' for a circle is s = r * Θ, where 'r' is the radius and 'Θ' is the central angle in radians. We have 'r' = 2 cm and 'Θ' = 1.9 radians.

To find the arc length 's', we simply multiply the radius by the angle:

s = 2 cm * 1.9 radians = 3.8 cm.

Therefore, the length of the arc intercepted by a central angle of 1.9 radians in a circle with a radius of 2 cm is 3.8 cm.

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Answer:

2.6 pounds of apples; 1.2 pounds of bananas

Step-by-step explanation:

A = pounds of apples and B = pounds of bananas

The total weight is 3.8 pounds, so:

A + B = 3.8

Apples are $1.90 per pound and bananas are $0.75 per pound, and the total cost is $5.84, so:

1.90A + 0.75B = 5.84

We can solve the system of equations using either elimination or substitution.

Using substitution:

1.90A + 0.75(3.8 - A) = 5.84

1.90A + 2.85 - 0.75A = 5.84

1.15A = 2.99

A = 2.6

B = 3.8 - A

B = 1.2

Answer:

(a + b) = 8x +4

(a - b) = -2x +16

(a * b) = [tex]15x^{2}+32x-60[/tex]

Step-by-step explanation:

We have been given the functions;

a(x) = 3x + 10 and b(x) = 5x − 6

Part A:

(a + b) = a(x) + b(x) # we simply add the two given functions

(a + b) = 3x + 10 + 5x − 6

(a + b) = 8x + 4

Part B:

(a - b) = a(x) - b(x) # we simply subtract the two given functions

(a - b) = (3x + 10 ) - (5x − 6)

(a - b) = 3x + 10 -5x +6

(a - b) = -2x + 16

Part C:

(a * b) = a(x)*b(x)

# we simply find the product of the two given functions

(a * b) = (3x + 10)*(5x − 6)

(a * b) = [tex]15x^{2}-18x+50x-60=15x^{2}+32x-60[/tex]

Part A

The functions a(x) = 3x + 10 and b(x) = 5x − 6 to complete the function operations listed below.

(a+b)(x)=a(x)+b(x)

(a+b)(x)=(3x+10)+(5x-6)

(a+b)(x)=3x+5x+10-6

(a+b)(x)=8x+4

Part B.

(a-b)(x)=a(x)-b(x)

(a-b)(x)=(3x+10)-(5x-6)

Expand the parenthesis to get:

(a-b)(x)=3x+10-5x+6

(a-b)(x)=3x-5x+10+6

(a-b)(x)=-2x+16

Part C

(a*b)(x)=a(x)*b(x)

(a*b)(x)=(3x+10)*(5x-6)

We expand to get:

[tex]a \times b = 15 {x}^{2} - 18x + 50x - 60[/tex]

[tex]a \times b = 15 {x}^{2} + 32x - 60[/tex]

Answer :FDG AND IGJ

Step-by-step explanation: Since EGF is 90 degrees then and EGD equals 38 degrees you need to subtract 38 from 90 and you are left with 52 degrees for angle FGD. The alternate interior angle to FGD is IGJ which would make the angles congruent.

The measure of angle IGJ is 38 degrees.

Let's derive the measure of angle IGJ step by step:

Given: Angle EGD = 38 degrees

To find: Angle IGJ

In triangle IGJ, we know that the sum of the interior angles is 180 degrees. Therefore, we can write:

Angle I + Angle G + Angle J = 180 degrees

Now, let's focus on angle G. Angle G is opposite to angle EGD in triangle EGD. According to the angle opposite to the side in a triangle theorem (or the angle opposite to the side is equal in a triangle theorem), we can say:

Angle G = Angle EGD

Given that Angle EGD = 38 degrees, we have:

Angle G = 38 degrees

Now, let's substitute this value into the equation for triangle IGJ:

Angle I + 38 degrees + Angle J = 180 degrees

Now, let's isolate angle I and angle J by subtracting 38 degrees from both sides:

Angle I + Angle J = 180 degrees - 38 degrees

Angle I + Angle J = 142 degrees

Now, we have an equation relating angle I and angle J. However, we need more information to determine the measure of either angle. But, we know that the sum of the angles in triangle IGJ is 180 degrees. Therefore, we can conclude that:

Angle I + Angle G + Angle J = 180 degrees

Angle I + 38 degrees + Angle J = 180 degrees

Angle I + Angle J = 180 degrees - 38 degrees

Angle I + Angle J = 142 degrees

Since the sum of angles I and J is 142 degrees, and we know that angle G is 38 degrees, the remaining angle (IGJ) must be equal to angle G:

Angle IGJ = Angle G = 38 degrees

Therefore, the measure of angle IGJ is 38 degrees.

Complete question

If angle EGD=38 degrees, what is angle IGJ?