Z varies inversely with x and directly with y. When x=6 and y=2 z=5 what is the value of a when x=4 and y=9

The school spent approximately $26.16 per student for a zoo pass and lunch during their field trip.

The total amount spent on passes for the 34 students and 4 teachers is $654.36. The total amount spent on lunch for just the students is $303.96. It means for each student, the school spent a combined amount on passes and lunch. To find this, first, we need to identify how much was spent per student for the pass, then add this to the amount spent per student on lunch.

First, we calculate the cost of a pass for each student. Since the total cost of passes is for both students and teachers, we need to find only the cost for the students. We accomplish this by subtracting the teachers’ share. It assumes the cost of a pass for a student and a teacher is the same.

The cost per person (student or teacher) for the pass is: $654.36 / (34 students + 4 teachers) = $654.36 / 38 = $17.22 (approximately, rounding to the nearest penny).

To determine the cost per student for lunch, we just need to divide the total lunch cost by the number of students: $303.96 / 34 = $8.94 (approximately).

In the end, the total cost per student for both the pass and lunch is: $17.22 + $8.94 = $26.16

Therefore, the school spent approximately $26.16 per student for a zoo pass and lunch.

https://brainly.com/question/33678156

#SPJ12

The school spent approximately $17.22 on passes and $8.94 on lunch for each student.

Now, let's plug in the values and calculate:

Step 1:

Total spent on passes = $654.36

Step 2:

Amount spent on passes for teachers = 4 * (Amount spent on each teacher's pass)

To find the amount spent on each teacher's pass, divide the total spent on passes by the total number of passes.

Step 3:

Calculate the amount spent on passes for students.

Number of students = 34

Number of teachers = 4

Total number of passes = 34 + 4 = 38

Amount spent on each pass = Total spent on passes / Total number of passes

[tex]\[Amount\ spent\ on\ each\ pass = \frac{654.36}{38}[/tex] ≈ 17.22

Step 4:

Find the total amount spent on lunch for students.

Total spent on lunch for students = $303.96

Step 5:

Calculate the amount spent on lunch for each student.

[tex]\[Amount\ spent\ on\ lunch\ for\ each\ student[/tex] = [tex]\frac{303.96}{34}[/tex] ≈ 8.94

So, the school spent approximately $17.22 on passes and $8.94 on lunch for each student.

To find out how much money must be deposited now in an account paying 7% annual interest compounded yearly to have a balance of $1000 after 6 years, we can use the formula for compound interest. Plugging in the values given, we get an approximate deposit of $665.58.

To find out how much money must be deposited now, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where A is the future value, P is the principal (initial deposit), r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the number of years.

In this case, we have A = $1000, r = 7% (or 0.07), n = 1 (compounded yearly), and t = 6 years. Plugging in these values, we can solve for P:

A = P(1 + r/n)^(nt)

$1000 = P(1 + 0.07/1)^(1 * 6)

$1000 = P(1 + 0.07)^6

$1000 = P(1.07)^6

$1000 = P(1.5037)

P ≈ 1000 / 1.5037

P ≈ 665.58

Therefore, approximately $665.58 must be deposited now to have a balance of $1000 after 6 years.

Answer:

[tex]\$\ 25[/tex]

Step-by-step explanation:

By definition, the absolute error is defined as:

[tex]\epsilon = |x_a - x_e|[/tex]

Where:

[tex]\epsilon[/tex]: is the error

[tex]x_a[/tex]: is the approximate value

[tex]x_e[/tex]: is the exact value

In this problem the approximate value was 100 and the exact value was 75. Then we substitute these values in the formula to find the error.

[tex]\epsilon = |100 - 75|\\\epsilon = \$\ 25[/tex]

Answer:

$25

Step-by-step explanation:

|25|=25

For people doing this in 2020

Answer:

A and C do not describe a residual

Step-by-step explanation:

A residual in least squares regression is defined as the difference between the actual value and the predicted value. Symbolically, this definition is represented by alternative B.

First solve the equation for 3x

-3x+3y=12

3x=-57-6y

Now substitute the given value into the equation

-(-57-6y)+3y=12

Then solve for y

Y=-5

Then substitute the given value of y

3x=-57-6✖️(-5)

Now solve for x

X=-9

Ordered pairs

(X,Y)=(-9,-5)

Then you are left with your answer:

(-9,-5)

Hope this helps! :3

First we need to solve for X.

Solve for xx.

-3x+3y=12−3x+3y=12

Divide both sides by -3−3.

x-y=-\frac{12}{3}x−y=−

Simplify \frac{12}{3}

x-y=-4x−y=−4

Add y to both sides.

x=-4+yx=−4+y

Regroup terms.

x=y-4x=y−4

Step two:

Let's start with the normal equation.

3x+6y=-573x+6y=−57

Let x=y-4x=y−4.

3(y-4)+6y=-573(y−4)+6y=−57

Simplify.

9y-12=-579y−12=−57

Great! Now we are on step 3.

Solve for y.

9y-12=-579y−12=−57

Add 1212 to both sides.

9y=-57+129y=−57+12

Simplify -57+12−57+12 to -45−45.

9y=-459y=−45

Divide both sides by 99.

y=-\frac{45}{9}y=−

Simplify \frac{45}{9}​​  to 55.

y=-5y=−5

Step 4! Boom!!

Now let's start with what we have.

x=y-4x=y−4

Let y=-5y=−5.

x=-5-4x=−5−4

Simplify.

x=-9x=−9

Then our answers are:

x=−9

y=-5y=−5

Have an amazing day and thanks for using Brainly!

​

​​

Answer: it is 45cm^2

Step-by-step explanation:

it is because it is

ANSWER

[tex] \cos( \alpha ) + \sin( \alpha ) [/tex]

EXPLANATION

The given expression is

[tex] \frac{ \cos(2 \alpha ) }{ \cos( \alpha ) - \sin( \alpha ) } [/tex]

Recall and use the double angle identity,

[tex] \cos(2 \alpha ) = { \cos}^{2} \alpha - { \sin}^{2} \alpha [/tex]

This implies that,

[tex]\frac{ \cos(2 \alpha ) }{ \cos( \alpha ) - \sin( \alpha ) } = \frac{ \ { \cos}^{2} \alpha - { \sin}^{2} \alpha }{ \cos( \alpha ) - \sin( \alpha ) } [/tex]

Recall again that: a²-b²=(a-b)(a+b)

We use difference of two squares to obtain,

[tex]\frac{ \cos(2 \alpha ) }{ \cos( \alpha ) - \sin( \alpha ) } = \frac{ (\ { \cos}\alpha - { \sin}\alpha )(\ { \cos}\alpha + { \sin}\alpha)}{ \cos( \alpha ) - \sin( \alpha ) } [/tex]

We cancel out the common factors to get,

[tex]\frac{ \cos(2 \alpha ) }{ \cos( \alpha ) - \sin( \alpha ) } = { \cos}\alpha + { \sin}\alpha[/tex]

The expression cos(2α)cosα−sinα is equivalent to the formula 2tanα / (1+tan^2α), reached by substituting cos(2α) with 1 - 2sin^2α and recognizing the resulting function as the derivative of the tangent function.

In addressing your question on expressions equivalent to cos(2α)cosα−sinα, we will employ some trigonometric identities. The expression cos(2α)cosα−sinα is equivalent to the expression 2tanα / (1+tan^2α).

The way to reach this answer is to first know the identity cos(2α) = 1 - 2sin^2α and plug this into the equation. The result will be 2sin^2α cosα + sinα. Then, you recognize this is the derivative of the tangent function, and find that it equals 2 tanα / (1 + tan^2α).

https://brainly.com/question/3785172

#SPJ3

Answer:

The correct answer is B. 3 bags

Correct statement, question and image:

Betsy is buying topsoil for the flower bed shown below (image attached)

One bag of topsoil covers 20 square meters.

How many bags of topsoil does Betsy need to cover her flower bed?

A 2 bags

B 3 bags

C 4 bags

D 5 bags

Source:

Previous question that can be found at brainly

Step-by-step explanation:

1. Let's find the area of the triangle:

Area = (Base * Height)/2

Area = (20 * 6)/2

Area of the flower bed = 60 m²

2. Now, let's calculate the number of bags of topsoil Betsy needs to cover her flower bed:

Number of bags = Area of the flower bed/Area covered by a bag of topsoil

Number of bags = 60/20

Number of bags = 3

The correct answer is B. 3 bags

There are 3 bags of topsoil Betsy needs to cover her flower bed option (B) is correct.

The triangle can be defined as a three-sided polygon in geometry, and it consists of three vertices and three edges. The sum of all the angles inside the triangle is 180°.

The figure is missing. Please refer to the attached picture.

As we know,

The area of the triangle = (1/2)base length×hieght

= (1/2)20×6

= 60 square m

One bag of topsoil covers 20 square meters.

Number of bags = 60/20 = 3 bags

Thus, there are 3 bags of topsoil Betsy needs to cover her flower bed option (B) is correct.

Learn more about the triangle here:

brainly.com/question/25813512

#SPJ5

The logical order for the proof is as follows: [tex]\( \overline{UV} \parallel \overline{WZ} \)[/tex] (Given), [tex]\( m\angle SQV + m\angle VQT = 180^\circ \)[/tex] (Substitution Property of Equality), [tex]\( m\angle SQT = 180^\circ \)[/tex] (Definition of a Straight Angle), and [tex]\( m\angle SQV = m\angle ZRS \)[/tex] (Subtraction Property of Equality). The correct choice is: c. II, III, I

The logical order of statements and reasons in the proof is as follows: First, it's given that [tex]\( \overline{UV} \parallel \overline{WZ} \)[/tex]. Then, by the Substitution Property of Equality, we have [tex]\( m\angle SQV + m\angle VQT = 180^\circ \)[/tex]. The Definition of a Straight Angle is applied to conclude that [tex]\( m\angle SQT = 180^\circ \)[/tex].

The Angle Addition Postulate supports [tex]\( m\angle SQV + m\angle VQT = m\angle SQT \)[/tex]. The Same-Side Interior Angles Theorem establishes [tex]\( m\angle VOT + m\angle ZRS = 180^\circ \)[/tex]. Using the Substitution Property of Equality, [tex]\( m\angle SQV + m\angle VQT = m\angle VQT + m\angle ZRS \)[/tex]. Finally, the Subtraction Property of Equality yields [tex]\( m\angle SQV = m\angle ZRS \)[/tex], and, by the Definition of Congruency, [tex]\(\angle SQV = \angle ZRS\)[/tex].

The correct answer is:

c. II, III, I

For more questions on Substitution Property:

https://brainly.com/question/30239463

#SPJ6

Answer:

782

Step-by-step explanation:

You have to multiplied 23  and 34

23 X 34 = 782

Answer:

782 is the answer

Step-by-step explanation:

Multiply 23 x 34 and that gives you 782.

Its the third option :)

Answer:  the correct option is

(D) A translation 5 units to the right, followed by a 180-degree counterclockwise rotation about the origin.

Step-by-step explanation:  We are given two triangles ABC and A'B'C' on the co-ordinate grid.

We are given to select the set of transformations is performed on triangle ABC to form triangle A’B’C’.

From the graph, we note that

the co-ordinate of the vertices of triangle ABC are A(-4, -1), B(-3, -1) and C(-4, -4).

And, the co-ordinates of the vertices of triangle A'B'C' are A'(-1, 1), B'(-2, 1) and C'(-1, 4).

We know that if a point (x, y) is translated 5 units right, followed by a rotation of 180-degrees clockwise about the origin, then its new co-ordinates becomes

(x, y)   ⇒   (-x-5, -y).

So, after these two transformations, the co-ordinates of the vertices of triangle ABC will become

A(-4, -1)   ⇒   (4-5, 1) = (-1, 1),

B(-3, -1)   ⇒   (3-5, 1) = (-2, 1)

and

C(-4, -4)  ⇒  (4-5, 4) = (-1, 4).

The new co-ordinates are the co-ordinates of the vertices of triangle A'B'C'.

Thus, the required set transformations is

A translation 5 units to the right, followed by a 180-degree counterclockwise rotation about the origin.

Thus, option (D) is CORRECT.

Yes you did a little reminder for you from me is that c^2 will ALWAYS be across from the right angle(90 degree)

The side lengths of a dilation of quadrilateral LMNP can be determined by multiplying the original side lengths by the dilation scale factor. For example, a scale factor of 2 would double the side lengths, resulting in a dilated quadrilateral with doubled dimensions.

The question asks about the side lengths of a dilation of quadrilateral LMNP with original sides measuring 16, 28, 12, and 32. In mathematics, a dilation is a transformation that produces an image that is the same shape as the original, but is a different size. The scale factor of the dilation determines how much larger or smaller the dilated figure will be compared to the original.

For example, if a quadrilateral LMNP is dilated by a scale factor of 2, all side lengths would be twice as long as the original. Therefore, the dilated quadrilateral would have sides of 32 (16×2), 56 (28×2), 24 (12×2), and 64 (32×2). Conversely, if the dilation scale factor is 0.5, the sides would be half as long, resulting in lengths of 8, 14, 6, and 16 respectively.

To determine the side lengths of a dilated version of LMNP, simply multiply each of the original side lengths by the dilation scale factor. This property of similarity due to dilation applies to any polygon, maintaining the shape but altering the size proportionally in all dimensions.

since you cross multiply, 2 times 4 is 8 and 6 times the p is 6p so divide both sides by 6 and 8/6 is 1.33 so 1.33=p

Answer:

p = 4/3

Step-by-step explanation:

The problem is showing you a proportion and how to solve it.

Let's use the following proportion to explain the cross multiplication method.

[tex] \dfrac{a}{b} = \dfrac{c}{d} [/tex]

Start with the proportion above. To get rid of parentheses, multiply both sides by b and by d.

[tex] bd\dfrac{a}{b} = bd\dfrac{c}{d} [/tex]

Simplify:

[tex] ad = bc [/tex]

Now look again at the proportion we started with.

[tex] \dfrac{a}{b} = \dfrac{c}{d} [/tex]

The two products we ended up with are the same you have circled in your problem. Those products are the result of cross multiplying.

Now let's do your problem and go straight to the cross multiplication.

[tex] \dfrac{6}{2} = \dfrac{4}{p} [/tex]

6 and p are circled together, so the left side becomes 6p.

2 and 4 are circled together, so the right side becomes 2 * 4.

After cross multiplying, we have

6p = 2 * 4

6p = 8

Divide both sides by 6 to find p.

p = 8/6

Reduce the fraction

p = 4/3

What the problem shows you is that to simplify a proportion, set the cross products equal to each other, and solve the equation.

1 inch is to 3 feet

1 in. : 3 ft.

Uh... 84 is correct. Add 60 & 24 and you get 84. Hopefully that helps

Answer:

84

Step-by-step explanation:

12*7=84

12*5=60

7-5=2

84-60=24

x > -3 divide by -5 on both sides and then switch the sign bc everytime u divide by a negative number u have to switch the sign

Answer:

x < -3

Step-by-step explanation:

All you have to do is divide -5 on both sides.

-5x  < 15

------  ------

 -5     -5

x < -3

Sometimes, you might have to flip the < sign. So it will be like:

x > -3

If you want to graph the inequality, here's how it will look:

(Graph shown on bottom of answer)

Mathematics is a great, beautiful, and important thing in life! With math, you can do anything when you out your mind to it!

- Jamal Josecite

8th Grade Student

(Please give me brainliest! I need to level up!)

The Length of the rectangle is 11 ft and the width is 16 ft

Answer: Its where the variable functions matches an output, for example *(modelvariable)=(output((x))

Step-by-step explanation:

Answer:

Linear programming

Linear programming is a method to achieve the best outcome in a mathematical model whose requirements are represented by linear relationships. Linear programming is a special case of mathematical programming.

Step-by-step explanation:

[tex]2\pi r\\2\pi23\\144.51[/tex]

Answer: 46 in tall for the circle

Answer:

120 feet

Step-by-step explanation:

12 x 10 = 120

Volume is found by multiplying the length by the width by the height.

Since you are given the volume and two of the dimensions, multiply the two dimensions together, then divide the volume by that number.

11 x 5 = 55

Width = 440 / 55

Width = 8 inches.

Step-by-step explanation:

[tex]1\ ft=12\ in\to1\ in=\dfrac{1}{12}\ ft\\\\\text{Therefore, if you want to change inches to feet,}\\\text{you must divide the number of inches by 12.}\\\\\text{Examples:}\\\\36\ in=\dfrac{36}{12}\ ft=3\ ft\\\\120\ in=\dfrac{120}{12}\ ft=10\ ft[/tex]

Answer:

8

Step-by-step explanation:

To find the discriminant, we need to get the equation in standard form

9x^2+2=10x^2

Subtract  10x^2 from each side

9x^2-10x^2+2=10x^2-10x^2

-x^2 +2 =0

This is in the form ax^2+bx +c =0

where a=-1 b=0 and c=2

The discriminant is

b^2 -4ac

0^2 -4*(-1)*2

0+8

The discriminant is 8

Answer:

[tex]8\ units< x < 18\ units[/tex]

Step-by-step explanation:

we know that

The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side

so

Applying the Theorem

case 1) [tex]42+4x > 2x-6[/tex]

[tex]4x-2x > -6-42[/tex]

[tex]2x > -48[/tex]

[tex]x > -24\ units[/tex]

case 2) [tex]42+(2x-6) >4x[/tex]

[tex]42-6 >4x-2x[/tex]

[tex]36 >2x[/tex]

[tex]18 >x[/tex] -----> rewrite

[tex]x<18\ units[/tex]

case 3) [tex]4x+(2x-6) > 42[/tex]

[tex]4x+2x > 42+6[/tex]

[tex]6x > 48[/tex]

[tex]x > 8\ units[/tex]

therefore

[tex]8\ units< x < 18\ units[/tex]

Answer:

the answwee is right triangle

Step-by-step explanation:

Answer:

Right triangle,

Step-by-step explanation:

The points (-2,-1) and (-2,-4) joined make a vertical line.

Also the line between (-2,-4) and (5, -4)  is horizontal.

The 3 points make a right triangle.

Answer:

firs

Step-by-step explanation:

Answer:

[tex]\large\boxed{A.\ f(x)+g(x)=9x^2-x-3}\\\boxed{B.\ f(x)-g(x)=5x^2-9x+9}\\\boxed{g(x)-f(x)=-5x^2+9x-9}[/tex]

Step-by-step explanation:

[tex]f(x)=7x^2-5x+3,\ g(x)=2x^2+4x-6\\\\A:\\f(x)+g(x)=(7x^2-5x+3)+(2x^2+4x-6)\\f(x)+g(x)=7x^2-5x+3+2x^2+4x-6\qquad\text{combine like terms}\\f(x)+g(x)=(7x^2+2x^2)+(-5x+4x)+(3-6)\\f(x)+g(x)=9x^2-x-3[/tex]

[tex]B:\\f(x)-g(x)=(7x^2-5x+3)-(2x^2+4x-6)\\f(x)+g(x)=7x^2-5x+3-2x^2-4x+6\qquad\text{combine like terms}\\f(x)-g(x)=(7x^2-2x^2)+(-5x-4x)+(3+6)\\f(x)+g(x)=5x^2-9x+9[/tex]

[tex]C:\\g(x)-f(x)=(2x^2+4x-6)-(7x^2-5x+3)\\g(x)-f(x)=2x^2+4x-6-7x^2+5x-3\qquad\text{combine like terms}\\g(x)-f(x)=(2x^2-7x^2)+(4x+5x)+(-6-3)\\g(x)-f(x)=-5x^2+9x-9[/tex]