winthrop has $4.40 worth of nickles and dimes. If winthrop has 3.5 times as many nickles as he has dimes, how many dimes does he have?

Answer:

Option D. 6√5.

Step-by-step explanation:

Please see attached photo for details.

The value of x can be obtained by using pythagoras theory as illustrated below:

In triangle ΔABC:

x² = z² + 12².... (1)

In triangle ΔABD:

15² = x² + y²...... (2)

In triangle ΔACD:

y² = z² + 3²....(3)

Substitute the value of y² in equation 3 into equation 2. We have:

15² = x² + y²

15² = x² + z² + 3²... (4)

From equation:

x² = z² + 12²

Make z² the subject

z² = x² – 12²

Substitute the value of z² into equation 4. We have:

15² = x² + z² + 3²

15² = x² + x² – 12² + 3²

15² = 2x² – 12² + 3²

225 = 2x² – 144 + 9

Collect like terms

225 + 144 – 9 = 2x²

360 = 2x²

Divide both side by 2

360/2 = x²

180 = x²

Take the square root of both side

x = √180

Expressing in surd form, we have:

x = √(36 x 5)

x = √36 x √5

x = 6√5

Answer:  Exponential function

Step-by-step explanation:

A linear function is the form[tex]f(x)=mx+c[/tex] , where m is the constant rate of change of y with respect to x and c is the y-intercept.

An exponential growth function is in the form [tex]f(x)=A(1+r)^x[/tex], where r is the rate of growth (generally in percent) and A is initial value.

If the population of a certain type of seahorse grew by 13% from year to year, then the rate of growth is 13% .

Hence it is an exponential equation.

Answer:

266.67 feet^2.

Step-by-step explanation:

The scale is 1:40.

That means that if the scale has a width of 4 inches, the room will have a width of 4 * 40 = 160 inches. 160 / 12 = 80 / 6 = 40 / 3 feet.

The length in the model is 6 inches, so the room has a length of 6 * 40 = 240 inches. 240 / 12 = 120 / 6 = 60 / 3 = 20 feet.

The area will then be (40 / 3) * 20 = 800 / 3 = 266.67 feet^2.

Hope this helps!

Answer:

288π

Step-by-step explanation:

V=4 /3πr^3 is the formula. We have the diameter, so the radius is half (6). We now have V=4 /3π(6)^3 = 4/3π216 = 288π.

Answer:

1/4

Step-by-step explanation:

The slope of a graph is always the rate of change for every value of x, in this case, days. Since she is adding 1/4 of a mile to her run each day, this means that the slope of this linear relationship is 1/4.

She increases a full mile in 4 days, just a little note.

from the above picture

2,3 = 1 quadrant

5,-6 = 4 quadrant

2,0 = on x axis

-5,2 = 2 quadrant

-2,-4 =3 quadrant

0,-2 = on y axis

Answer:

Correct answer is option D. 96.4 yd.

Step-by-step explanation:

Please refer to the attached figure for labeling of the given diagram.

ABC is a triangle with the following labeling:

A is the hole, B is the Tee and C is the point where the ball is.

Sides are labeled as:

[tex]a =255\ yd\\c = 305\ yd\\\angle B =17^\circ[/tex]

To find:

Side [tex]b = ?[/tex]

Solution:

Here, we have one angle and two sides . Third side of the triangle is to be found opposite to the given angle.

We can use cosine formula here to find the value of the unknown side.

[tex]cos B = \dfrac{a^{2}+c^{2}-b^{2}}{2ac}[/tex]

Putting all the values:

[tex]cos 17 = \dfrac{255^{2}+305^{2}-b^{2}}{2\times 255\times 305}\\\Rightarrow 0.956 = \dfrac{65025+93025-b^{2}}{155550}\\\Rightarrow 148753.2= 158050-b^{2}\\\Rightarrow b^{2}= 158050-148753.2\\\Rightarrow b^{2}= 9296.795\\\Rightarrow b= 96.42\ yd[/tex]

So, the distance between the Ball and hole is 96.42 yd

Correct answer is option D. 96.4 yd.

Answer:

D.) 96.4 yd

Step-by-step explanation:

I got it correct on founders edtell

Answer:

Step-by-step explanation:

a. Given,

v = 34 , a = 5 , t = 3

[tex]v = u + at[/tex]

plugging the values:

[tex]34 = u + 5 \times 3[/tex]

Calculate the product

[tex]34 = u + 15[/tex]

Move 'u' to L.H.S and change its sign

[tex] - u + 34 = 15[/tex]

Move constant to RHS and change its sign

[tex] - u = 15 - 34[/tex]

Calculate

[tex] - u = - 19[/tex]

The difference sign (-) will be cancelled in both sides:

[tex]u = 19[/tex]

b. Given,

v = 50 , u = 20 , a = 5

[tex]v = u + at[/tex]

plugging the values

[tex]50 = 20 + 5 \times t[/tex]

[tex]50 = 20 + 5t[/tex]

Move 5t to L.H.S and change its sign.

Similarly, Move 50 to R.H.S and change its sign

[tex] - 5t = 20 - 50[/tex]

Calculate

[tex] - 5t = - 30[/tex]

The difference sign (-) will be cancelled in both sides

[tex]5t = 30[/tex]

Divide both sides of the equation by 5

[tex] \frac{5t}{5} = \frac{30}{5} [/tex]

Calculate

[tex]t = 6[/tex]

c. Given,

v = 22 , u = 8 , t = 7

[tex]v = u + at[/tex]

plugging the values

[tex]22 = 8 + a \times 7[/tex]

[tex]22 = 8 + 7a[/tex]

Move 7a to LHS and change its sign

Similarly, Move constant to R.H.S and change its sign

[tex] - 7a = 8 - 22[/tex]

Calculate

[tex] - 7a = - 14[/tex]

The difference sign (-) will be cancelled in both sides

[tex]7a = 14[/tex]

Divide both sides of the equation by 7

[tex] \frac{7a}{7} = \frac{14}{7} [/tex]

Calculate

[tex]a = 2[/tex]

Hope this helps...

Good luck on your assignment..

Answer:

Step-by-step explanation:

Given the coordinates P(-2, -3). Q(2, - 6). R(6. - 3). S(2, 1), to determine the type of shape the quadrilateral is, we need to find the measure of the sides. To get the measure of each sides, we will take the distance between the adjacent coordinates using the formula to formula for calculating the distance between two points as shown;

D = √(x₂-x₁)²-(y₂-y₁)²

For the side PQ with the coordinate P(-2, -3). Q(2, - 6)

PQ = √(2-(-2))²-(-6-(-3))²

PQ = √(2+2)²-(-6+3)²

PQ = √4²-(-3)²

PQ = √16-9

PQ = √7

For the side QR with the coordinate Q(2, - 6) and R(6, -3)

QR = √(6-2))²-(-3-(-6))²

QR = √(4)²-(3)²

QR = √16-9

QR = √7

For the side RS with the coordinate R(6. - 3) and S(2, 1)

RS = √(2-6)²-(1-(-3))²

RS = √(-4)²-(1+3)²

RS = √16-(4)²

RS = √16-16

RS = 0

For the side PS with the coordinate P(-2, -3) and S(2, 1)

PS = √(2-(-2))²-(1-(-3))²

PS = √(4)²-(1+3)²

PS = √16-(4)²

PS = √16-16

PS = 0

For the quadrilateral to be a rectangle, then two of its sides must be equal and parallel to each other. A rectangle is a plane shape that has two of its adjacent sides equal and parallel to each other. Since two of he sides are equal i.e RS = PS and PQ = QR then the quadrilateral PQRS is a rectangle. Both rhombus and square has all of its sides equal thereby making them wrong.

Answer:

Sister is 70

Step-by-step explanation:

John is 39.

8 less than twice his age is

39*2-8 = 70

Answer:

70 years old.

Step-by-step explanation:

Since John's sister is 8 years younger than TWICE his age, we just need to multiply 39*2 which equals 78. Now we just need to subtract 8 which equals 70.

Hope this helps!! <3

Answer:

20

Step-by-step explanation:

Given that:

The study group n = 4

number of participants = 10

the sum of squares for the between-groups source of variation is  60

The objective is to determine the mean square  between groups in this study

The mean square  between groups in this study compares the means of the group with the  sum of squares for the between-groups source (i.e the grand mean)

For this analysis;

the degree of freedom = n-1

the degree of freedom = 4 - 1

the degree of freedom =  3

Thus; the mean square between groups = [tex]\dfrac{60}{3}[/tex]

the mean square between groups = 20

Answer:

It is C

Step-by-step explanation:

42.60=43.00

587.70=588.00

27.99=28.00

Answer:

t > 212

Step-by-step explanation:

Given

Boiling point = 212°F

Required

Inequality that shows temperature greater than the boiling point

From the question, temperature is represented with t.

The inequality "greater than" is represented with >

So, temperature greater than the boiling point implies that t > 212

Answer: t > 212

Step-by-step explanation:

The question says "Write an inequality that is true only for temperatures that are higher than the boiling point of water."

This means t has to be higher than 212 since it says only for temperatures that are higher than the boiling point.

But since we have to write an inequality the answer would be: t > 212.

I know I did this very late and you probably don't need it but i was bored

Answer:   [tex]t_9=\dfrac{1}{2^8}[/tex]

Step-by-step explanation:

[tex]t_n=t_1\times r^{n-1}\\\\Given: t_1=1,\quad r=\dfrac{1}{2}\\\\\\t_9=1\times\bigg(\dfrac{1}{2}\bigg)^{9-1}\\\\\\.\quad =\large\boxed{\dfrac{1}{2^8}}[/tex]

Answer:

Step-by-step explanation:

First we must know that the sum of all the exterior angle of all polygons is 360°.

Measure of each angle of a polygon = 360°/total sides of the polygon

Since a regular nonagon has 9 sides, the measure of each angle of a polygon is expressed as thus;

Measure of each angle of a polygon  = 360°/9

Measure of each angle of a polygon  = 40°

Hence the measure of an exterior angle x of a nonagon is 40°

Answer:

B in Edg

Step-by-step explanation:

Step-by-step explanation:

Hi, there!!!!

The main purpose of developing si unit is to have standard unit of measurements and to bring uniformity in whole world in terms of measurements.

I hope it helps you...

Answer:

Total number of animals in the group = 170

Step-by-step explanation:

Let the number of sheep = a

Number of dragons in the group = 75

Number of dragons opposite dragons = 37

Number of sheep opposite to the dragon = 1

Number of sheep left = a - 1

Number of sheep opposite to sheep = [tex]\frac{(a-1)}{2}[/tex]

Since. number of sheep opposite to sheep is 10 more than of dragons opposite dragons,

[tex]\frac{(a-1)}{2}[/tex] = 37 + 10

[tex]\frac{(a-1)}{2}=47[/tex]

a - 1 = 94

a = 95

Then total number of animals in the group = Total number of sheep + Total number of dragons

= 95 + 75

= 170

Therefore, total number of animals in the group are 170.

Answer:

Step-by-step explanation:

let the parabola be y=a(x+5)²+0

or y=a(x+5)²

∵ it passes through (-3,1)

1=a(-3+5)²

4a=1

a=1/4

so parabola is y=1/4(x+5)²

Answer

5.85

Step-by-step explanation:

$0.05 x 1.5 = 0,075 x 1 hour (60) = 4,5

$0.03 x 1.5 = 0,045 x half an hour (30) = 1,35

So 4.5 + 1.35 = 5.85

Answer:

Step-by-step explanation:

Cost of the conference call before 8 pm =0.15 * 0.05 = $ 0.075

Cost of the conference call after 8 pm   = 0.15 * 0.03 = $ 0. 045

Cost of the conference call from 7pm to 8pm that last  60 minutes= 0.075 * 60

= $ 4.50

Cost of the conference call 8pm to 8:30pm =0.045 * 30 = $ 1.35

Cost of the conference call 7 pm to 8:30 pm = 4.50 + 1.35 = $ 5.85

Answer:

x = 8; y = 12.

Step-by-step explanation:

x + y = 20

x = -y + 20

3x + 4y = 72

3(-y + 20) + 4y = 72

-3y + 60 + 4y = 72

y = 12

x + 12 = 20

x = 8

Check your work!

3(8) + 4(12) = 72

24 + 48 = 72

72 = 72

Hope this helps!

Answer:

X=-12 and Y= 32

Step-by-step explanation:

x+y=20 -> 1

3x+4y=72 -> 2

Form 1,

[x+y=20]×4

4x+4y=60 ->3

Form 2,

3x+4y=72

4y= 72 -3x ->4

Sub (4) into (3)

4x+72-3x= 60

x = -12

Sub X=-12 into (1)

-12+y=20

y= 32

Hope this helps.

Answer:

-∞ < x< -∞

Step-by-step explanation:

The domain is the values that x takes

The values that x can take is all real values of x

-∞ < x< -∞

Answer:

(-1, -2) last answer

Step-by-step explanation:

x = 1 is a vertical line

Answer:

(-1, -2)

Step-by-step explanation:

This is because the x-coordinate goes 2 units left to the line x = 1 and the y-coordinate remains the same.

Answer:

b) tiene la mayor frecuencia

Step-by-step explanation:

Las medidas de tendencia central se refieren a un centro alrededor del cual se encuentran todos los datos y estas medidas son: la media, la moda y la mediana. La media es el valor promedio de un grupo de datos, la moda es el dato que se repite más veces y la mediana es el valor que se encuentra en el centro cuando los datos se ubican de menor a mayor. De acuerdo a esto, la respuesta es que la moda es una medida de tendencia central que tiene la mayor frecuencia.

Los otras opciones no son correctas porque el tamaño del conjunto de datos no depende de las medidas de tendencia central, esto depende de cada situación y pueden ser muchos o pocos datos. Además la opción "al ordenar los datos de menor a mayor es el dato que se ubica en el centro" se refiere a la mediana.

Answer:

59.0

Step-by-step explanation:

Given a right angled triangle, ∆XYZ, to know which trigonometric ratio formula to apply in finding the measure of angle X, note the following:

Opposite side to angle X = 6

Hypotenuse = 7

Therefore, we would apply the following trigonometric ratio formula to solve for m<X:

[tex] sin X = \frac{6}{7} [/tex]

[tex] sin X = 0.8571 [/tex]

[tex] X = sin^{-1}(0.8571) [/tex]

[tex] X = 58.99 [/tex]

[tex] m < X = 59.0 [/tex] (rounded to nearest tenth)

Answer:

first one

Step-by-step explanation:

Step-by-step explanation:

Let the other endpoint be (x,y)

Since, (1,6) is the midpoint between (9,1) and (x,y)

Therefore,

1=(9+x)/2

=> 2=9+x

=> x= -7

and,

6=(1+y)/2

=>12= 1+y

=> y=11

So, the other endpoint is ( -7, 11)

Answer:

Step-by-step explanation:

Let the coordinates of Endpoint 2 be

(x ,y)

The midpoint of the endpoints is given by

[tex](1,6) = ( \frac{9 + x}{2} , \frac{1 + y}{2} )[/tex]

Where x and y are coordinates of Endpoint 2

Comparing with the midpoint we have

[tex]1 = \frac{9 + x}{2} \\ 2 = 9 + x \\ \\ x = 2 - 9 \\ \\ x = - 7[/tex]

[tex]6 = \frac{1 + y}{2} \\ 12 = 1 + y \\ \\ y = 12 - 1 \\ \\ y = 11[/tex]

Therefore x = - 7 and y = 11

The coordinates of Endpoint 2 are

Hope this helps you

Answer: A. Factor 2 => 4x greater

                   Factor 3 => 9x greater

                   Factor 5 => 25x greater

Step-by-step explanation: A. A cylinder is formed by 2 circles and a rectangle in the middle. That's why surface area is given by circumference of a circle, which is the length of the rectangle times height of the rectangle, i.e.:

A = 2.π.r.h

A cylinder of radius r and height h has area:

[tex]A_{1}[/tex] = 2πrh

If multiply both dimensions by a factor of 2:

[tex]A_{2}[/tex] = 2.π.2r.2h

[tex]A_{2}[/tex] = 8πrh

Comparing [tex]A_{1}[/tex] to [tex]A_{2}[/tex] :

[tex]\frac{A_{2}}{A_{1}}[/tex] = [tex]\frac{8.\pi.rh}{2.\pi.rh}[/tex] = 4

Doubling radius and height creates a surface area of a cylinder 4 times greater.

By factor 3:

[tex]A_{3} = 2.\pi.3r.3h[/tex]

[tex]A_{3} = 18.\pi.r.h[/tex]

Comparing areas:

[tex]\frac{A_{3}}{A_{1}}[/tex] = [tex]\frac{18.\pi.r.h}{2.\pi.r.h}[/tex] = 9

Multiplying by 3, gives an area 9 times bigger.

By factor 5:

[tex]A_{5} = 2.\pi.5r.5h[/tex]

[tex]A_{5} = 50.\pi.r.h[/tex]

Comparing:

[tex]\frac{A_{5}}{A_{1}}[/tex] = [tex]\frac{50.\pi.r.h}{2.\pi.r.h}[/tex] = 25

The new area is 25 times greater.

B. By analysing how many times greater and the factor that the dimensions are multiplied, you can notice the increase in area is factor². For example, when multiplied by a factor of 2, the new area is 4 times greater.

Answer:

m∠D = 94°

Step-by-step explanation:

Quadrilateral ABCD is also called a cyclic quadrilateral or a quadrilateral that is inscribed in a circle.

Opposite angles in a cyclic Quadrilateral are supplementary, i.e the sum of two opposite angles in a Quadrilateral = 180°

m∠A + m∠C = 180°

m∠A = 74°

74° + m∠C = 180°

m∠C = 180° - 74°

m∠C = 106°

In a cyclic quadrilateral, the total sum of the angles outside the circle = 360°

i.e =

m∠AB + m∠BC + mDC + mAD = 360°

m∠DAB= ( m∠C) × 2

= 106° × 2 = 212°

m∠DAB = m∠AD + m∠AB

m∠AD = 79°

212° = 79° + m∠AB

m∠AB = 212° - 79°

= 133°

m∠ABC = m∠AB + m∠BC

m∠AB = 133°

m∠BC= 55°

m∠ABC = 133° + 55°

= 188°

We are asked to find m∠D

m∠D = 1/2m∠ABC

m∠ABC = 188°

m∠D = 1/2 × 188°

m∠D = 94°

Therefore, m∠D = 94°

Answer:  $26.70 per hour

Step-by-step explanation:

Regular hours consists of 8 hrs

Overtime hours is 12 - 8 = 4 hours

Regular pay at "x" per hour = 5(8)(x) = 40x

Overtime pay at "2x" per hour = 5(4)(2x) = 40x

                                                  Total pay = 80x

Total Pay = $2136 = 80x

                     [tex]\dfrac{\$2136}{80}=x[/tex]

                   $26.70 = x

Answer:

Y= -1/5x + 1

Step-by-step explanation:

Just type it on a graphing calculator an click graph