Sophie has 60 pencils.
The ratio of sharpened pencils to blunt pencils is 4:1
How many sharpened pencils does Sophie have?

The given measure of the angle in standard form, -17•π/6, gives;

A. The terminal side of the angle, -17•π/6 is located in the third quadrant

B. The reference angle is 150°

C. The values of the six trigonometric functions are;

Trigonometric ratios relates an angle to the ratio of the sides of a right triangle containing the angle.

A. The given measure of the angle is -17•π/6

2•π radians = 360°

π radians = 180°

-17•π/6 = -(2+(5/6))•π

Therefore, the terminal side makes one complete revolution clockwise starting from the x–axis, it then makes a further -(5/6)•π, clockwise, which is -(5/6)×180° = -150°

The terminal side therefore moving clockwise, passes the fourth quadrant and stops at the third quadrant at -150°, which is equivalent to 210° clockwise rotation from the x–axis

B. The reference angle is the acute angle between the terminal side and the x–axis

Therefore;

C. The six trigonometric functions are;

cosine, sine, tangent, cotangent, secant, and cosecant

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Answer: I hope this helpful

Step-by-step explanation:

The given measure of the angle in standard form, -17•π/6, gives;A. The terminal side of the angle, -17•π/6 is located in the third quadrantB. The reference angle is 150°C. The values of the six trigonometric functions are;cos(-17•π/6) = -(√3)/2sec(-17•π/6) = -2•(√3)/3sin(-17•π/6) = -0.5cosec(-17•π/6) = -2tan(-17•π/6) = (√3)/3cot(-17•π/6) = √3What are trigonometric ratios?Trigonometric ratios relates an angle to the ratio of the sides of a right triangle containing the angle.A. The given measure of the angle is -17•π/62•π radians = 360°π radians = 180°-17•π/6 = -(2+(5/6))•πTherefore, the terminal side makes one complete revolution clockwise starting from the x–axis, it then makes a further -(5/6)•π, clockwise, which is -(5/6)×180° = -150°The terminal side therefore moving clockwise, passes the fourth quadrant and stops at the third quadrant at -150°, which is equivalent to 210° clockwise rotation from the x–axisThe terminal side is in the third quadrant B. The reference angle is the acute angle between the terminal side and the x–axisTherefore;The reference angle is 150°C. The six trigonometric functions are;cosine, sine, tangent, cotangent, secant, and cosecantcos(-17•π/6) = -(√3)/2sec(-17•π/6) = -2/(√3) = -2•(√3)/3sin(-17•π/6) = -0.5cosec(-17•π/6) = -2tan(-17•π/6) = (√3)/3cot(-17•π/6) = 3/(√3) = 3•√3/3 = √3Learn more about trigonometric ratios here:brainly.com/question/11967894#SPJ1Explore all similar answersTHANKS 25.0(3 votes)Need a bit more clarification? Get a high-quality answer with step-by-step explanations from a professional in just minutes instead!GET A VERIFIED ANSWERAdvertisementStill have questions?FIND MORE ANSWERSReady to dive into rabbit hole and unlock a badge.ASK YOUR QUESTIONHelp others with Mathematics questions+1 NEW QUESTION6 minutes agoFirst questionA regular hexagon and a regular pentagon have the same perimeter. All measurements are given in centimetres. The hexagon has a side length given by 7m +3. The pentagon has a side length given by 8m + 6. Work out the value of m.ADD ANSWER+5017 minutes ago(y)/(a)-b=(y)/(b)-a if a is not equal to bADD ANSWER+523 minutes agoFirst questionProducts A and B are made according to the bill of materials diagram shown below. Scheduled quantities of the end products are, for A, 95 units in week 4, 150 units in week 6, and 130 units in week 8, and for B, 80 units in week 3, 70 units in week 6. Lead-times: A = 2 weeks, B = 1 week.ADD ANSWER+524 minutes agoFind the compound interest earned by the deposit. Round to the nearest cent. 1) $3000 at 5% compounded semiannually for 6 years 2) $700 at 8% compounded quarterly for 5 yearsADD ANSWER+725 minutes agoFind the simple interest and the final value of the deposit that earns the given rate for the indicated length of time. Round your answers to the nearest cent. $6282 earning 9% for 9 monthsADD ANSWER+5LOAD MOREPreviousNext

Answer:

Step-by-step explanation:

We have been given that human body temperatures have a mean of 98.20° F and a standard deviation of 0.62°. Sally's temperature can be described by z = -1.5.

To find Sally's temperature we will use z-score formula.

, where  = Mean, = Standard deviation.

Let us substitute our given values in z-score formula.

Multiply 0.62 to both sides of equation.

Add 98.20 to both sides of equation.

Therefore, Sally's temperature will be 97.27 degrees Fahrenheit.

Answer:

About $4.88.

Step-by-step explanation:

Answer:

x = -16

Step-by-step explanation:

Answer:

Jami has $13.5

Mami has $18.5

Step-by-step explanation:

Let j = Jami's money

     m - Mami's money

j + m = 32

j = m -  5 (Since Jami basically has 5 less than Mami)

Substitute the j in the top equation

m - 5 + m = 32

2m - 5 = 32

Add 5 to both sides

2m - 5 = 32

2m = 37

Divide both sides by 2

2m/2 = 37/2

m = 37/2 = 18.5

Now plug the new m into the bottom equation

j = 18.5 - 5

j = 13.5

Inequalities are used to represent unequal expressions

The solution to the system of inequalities is (-1,1)

The system of inequalities is given as:

y > x + 2 and

y < 2x + 3

To do this, we start by plotting the graphs of the two inequalities

y > x + 2 and  y < 2x + 3

See attachment for the graph

From the attached graph, both lines meet at (-1,1)

Hence, the solution to the system of inequalities is (-1,1)

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Answer:

350

Step-by-step explanation:

if this is wrong or correct please let me know and sorry if its wrong which i am pretty sure it's correct :)

Answer:

A’ is (3,-3)

B’ is (-1,-4)

C’ is (-1,2)

D’ is (3,1)

Step-by-step explanation: i forgot how i did this but i did it last week in math or somthing sorry if its wrong it was right for me

Answer:

Between 8 and 9

Step-by-step explanation:

We know that the equation for the volume of a cone is V = 1/3(pi)r^2h

So,

V = 1/3(pi)r^2h

150pi = 1/3(pi) r^2 h --> the pi's cancel out and then we are left with...

3(150) / h = r^2

Plug in values and simplify --> r = sqrt.(450/6) and you end up getting 8.66025403784.

Hope that helps!

Answer: x=4

Step-by-step explanation:

Answer:

C) x = -2

Step-by-step explanation:

Original equation:

[tex]12+\sqrt{1-4x}=15\\[/tex]

subtract 12 from both sides:

[tex]\implies \sqrt{1-4x}=3[/tex]

square both sides:

[tex]\implies 1-4x=9[/tex]

subtract 1 from both sides:

[tex]\implies -4x=8[/tex]

divide both sides by -4:

[tex]\implies x=-2[/tex]

[tex]\\ \tt\rightarrowtail 12+\sqrt{1-4x}=15[/tex]

[tex]\\ \tt\rightarrowtail \sqrt{1-4x}=3[/tex]

[tex]\\ \tt\rightarrowtail 1-4x=3^2[/tex]

[tex]\\ \tt\rightarrowtail 1-4x=9[/tex]

[tex]\\ \tt\rightarrowtail -4x=8[/tex]

[tex]\\ \tt\rightarrowtail x=-2[/tex]

Answer:

-12 meters because it is BELOW the surface of the ocean

Answer:

[tex]-\dfrac{14}{15}-\dfrac{1}{3}v[/tex]

Step-by-step explanation:

Given expression:

[tex]-\dfrac{6}{5}-\dfrac{2}{3}v+\dfrac{4}{15}+\dfrac{1}{3}v[/tex]

Collect like terms:

[tex]\implies \dfrac{4}{15}-\dfrac{6}{5}+\dfrac{1}{3}v-\dfrac{2}{3}v[/tex]

Make the denominators for the like terms the same:

[tex]\implies \dfrac{4}{15}-\dfrac{6 \times 3}{5 \times 3}+\dfrac{1}{3}v-\dfrac{2}{3}v[/tex]

[tex]\implies \dfrac{4}{15}-\dfrac{18}{15}+\dfrac{1}{3}v-\dfrac{2}{3}v[/tex]

Combine like terms:

[tex]\implies \dfrac{4-18}{15}+\dfrac{1-2}{3}v[/tex]

[tex]\implies -\dfrac{14}{15}-\dfrac{1}{3}v[/tex]

Answer:

-14/15 - 1/3w

Step-by-step explanation:

khan

Answer:

[tex]\displaystyle 3x - 2y = 13\:or\:y = 1\frac{1}{2}x - 6\frac{1}{2} \\ [0, -6\frac{1}{2}] \\ 1\frac{1}{2} = m[/tex]

Step-by-step explanation:

First, figure the rate of change [slope] out:

[tex]\displaystyle \frac{-y_1 + y_2}{-x_1 + x_2} = m \\ \\ \frac{-1 + 16}{-5 + 15} = \frac{15}{10} = 1\frac{1}{2} \\ \boxed{1\frac{1}{2} = m}[/tex]

Now locate the initial value [y-intercept] by plugging an ordered pair into the slope-intercept formula. It does not matter which ordered pair you use:

_______________________________________________

[tex]\displaystyle y = mx + b[/tex]

16 = 1½[15] + b >> [tex]\displaystyle 16 = 22\frac{1}{2} + b; -6\frac{1}{2} = b[/tex]

OR

1 = 1½[5] + b >> [tex]\displaystyle 1 = 7\frac{1}{2} + b; -6\frac{1}{2} = b[/tex]

[tex]\displaystyle [0, -6\frac{1}{2}][/tex]

_______________________________________________

You now have your initial value. All that is left is to write the equation of this line, which can be written two ways:

> Slope-Intercept Form

[tex]\displaystyle y = 1\frac{1}{2}x - 6\frac{1}{2}[/tex]

> Standard Form [tex]\displaystyle [Ax + By = C][/tex]

y = 1½x - 6½

- 1½x - 1½x

___________

–1½x + y = –6½ [We CANNOT leave the equation this way, so multiply by –2 to eradicate the fraction\denominatour (if you wrote the equation as mixed numbers\if you wrote the equation as improper fractions).]

–2[–1½x + y = –6½]

[tex]\displaystyle 3x - 2y = 13[/tex]

With that, you have defined all the information.

[tex]\displaystyle -3x + 2y = -13[/tex]

*About this equation, INSTEAD of multiplying by –2, you multiply by its oppocite, 2. Now, you can leave it like this, but UNIVERSALLY, the A-term is positive, so you must multiply the negative out as well.

I am joyous to assist you at any time.

Answer:

14.8

Step-by-step explanation:

42.79-27.99=14.8

When subtracted $27.99 from $42.79, we get $14.8.

Subtraction is one of the most basic arithmetic operation in mathematics. Subtraction implies taking away one value from the another. Subtract x from y implies y - x. The number after from comes first. On subtraction, the sign (positive/negative) of the greater number of the two numbers given, is the sign (positive/negative) of the answer. Subtraction is also called as difference.

Given in the question,

Take $27.99 from $42.79

This implies,

= 42.79 - 27.99

= 14.8

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Answer:

1.57

Step-by-step explanation:

Answer:

$1,110

Step-by-step explanation:

You have to use the interest formula to calculate how much each brother will have after a year.

A = P(1+r)^t

A = future/ending value

P = principle

R = interest rate

T = time (given in years)

Charles = 30,000(1+.025)^1 = 30,750

Brian = 30,000(1+.062)^1 =31,860

31,860-30,750=1,110

Brian will have $1,110 more than Charles after 1 year

Answer:

2/6 or 1/3

Step-by-step explanation:

Nothing it is just basic mathematics

Fraction form

[tex]\\ \tt\rightarrowtail \dfrac{2}{6}[/tex]

[tex]\\ \tt\rightarrowtail \dfrac{1}{3}[/tex]

Answer:

15

Step-by-step explanation:

In the function f(x), x is the variable. So, whatever is in the parentheses, replacing x, should replace x throughout the entire function. So, to find f(4) simply plug in 4 for x.

f(4) = 4^2 - 4 + 3

f(4) = 4^2 - 1

f(4) = 16 - 1

f(4) = 15

Answer:

f(4) = 15

Step-by-step explanation:

Substitute 4 for x and solve for f(4).

[tex]f(x)=x^2-x+3\\f(4)=(4)^2-4+3\\f(4)=16-4+3\\f(4)=15[/tex]

Answer:

Divide each term in

4

x

=

28

by

4

.

4

x

4

=

28

4

Cancel the common factor of

4

.

Tap for more steps...

x

=

28

4

Divide

28

by

4

.

x

=

7

Step-by-step explanation:

hope it helps you

Consider a trapezoid GJKF with:

GH=JH (hypothesis)

FL=KL (hypothesis)

so HL is the median of trapezoid GJKF

so: HL=1/2(2.5+1.2)=1.85

Answer:

0.25 and 25%

Step-by-step explanation:

25% is the same as 1/4

0.25 is the same as 1/4

Answer:

1/4 = 0.25

1/4 = 25%

1/4 or 1 divided by 4 equals 0.25 (decimal) and 25% (percentage).

Answer:

-5 and 2

-5 and 2-3 and 0

-5 and 2-3 and 0-2 and - 1

(When you add them you'll get - 3)

Hope this helps!

Answer: I believe is is C, rotations and translations

Step-by-step explanation:

This is because a congruent figure is one that has the same side lengths and angle measures.

Stretches and dilations are non-rigid transformations which change the length of the sides of a shape. While rotations, transformations, and reflections are rigid transformations which preserve angle measure and side length.

So, while a shape can be similar using stretches and dilations, they cannot be congruent.

Answer:

C

Step-by-step explanation:

Because if you can read the whole thing u can find what you need to find

[tex]\tt =\dfrac{135}{15}=9\:ft/s[/tex]

Answer: D) 12 units

Explanation:

There are 12 spaces between T and S.

You can count the spaces out, or subtract and use absolute value.

You could use the distance formula, but it's a bit overkill in this situation. The distance formula is only ever needed whenever we don't have horizontal or vertical line segments.

Edit: The solution has been corrected to the correct value.