Find all solutions to the equation.
cos x = sin x (6 points)

Answer: X= 3/4

Simplified: 1/3

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Explanation:

x = original amount of caster oil (in quarts)

Since 15% remains, this means you used 85% of the original amount x.

Note how 15% + 85% = 100%

So,

85% of x = 34 quarts

0.85x = 34

x = 34/0.85

x = 40

You started with 40 quarts of oil.

15% of that remains, meaning 0.15*40 = 6 quarts of oil are left over.

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We could also solve like this

(amount used)/(amount total) = (percent)/(100)

34/x = 85/100

34*100 = x*85

3400 = 85x

85x = 3400

x = 3400/85

x = 40

So we end up with the same x value as before, and we follow the same set of steps at the end of the first section to end up with the answer of 6 quarts.

Answer:

97

Step-by-step explanation:

Arc AT = angle at the center 97°

Answer:

radical is sqrt we find 180 sqrt root

Step-by-step explanation:

first we write sqrt 180

sqrt 180 = ?

we can choose first two letters

18 are two letters

4^2 + 2 = 18

so first + third number choose

4 , 2 are number choose

4 + 2 sqrt (4+2-1)

6 sqrt 5

sqrt 180 = 6sqrt 5

Answer:

Step-by-step explanation:

Here's the game plan. In order to find a point on the x-axis that makes AC = BC, we need to find the midpoint of AB and the slope of AB. From there, we can find the equation of the line that is perpendicular to AB so we can then fit a 0 in for y and solve for x. This final coordinate will be the answer you're looking for. First and foremost, the midpoint of AB:

and

Now for the slope of AB:

and

 So if the slope of AB is 1/3, then the slope of a line perpendicular to that line is -3. What we are finding now is the equation of the line perpendicular to AB and going through (0, 3):

and filling in:

y - 3 = -3(x - 0) and

y - 3 = -3x + 0 and

y - 3 = -3x so

y = -3x + 3. Filling in a 0 for y will give us the coordinate we want for the x-intercept (the point where this line goes through the x-axis):

0 = -3x + 3 and

-3 = -3x so

x = 1

The coordinate on the x-axis such that AC = BC is (1, 0)

Answer:

Volume of sphere = 4/3 * π * r³

Since 36π = 4/3 * π * r³, r³ = 27 and r = 3.

Step-by-step explanation:

There are 3 even numbers out of 6 total numbers.

Rolling an even number would be 3/6 = 1/2

She would expect half the rolls should be even.

144/2 = 72

The answer is 72 times.

Answer:

4a 2/7.

I could solve just this

Answer:

For #3b, shade in 1 1/2 bars

For 4a, i think it is 3/7

4b is prob 43%

5 i think is abt 0.2 miles

Answer:

a. 90º

Explanation:

The chords ST and RA intesect at Y, so that SY is now perpendicular to RY and they form an angle 90 degrees at that point. However angles mSA and mRT are both at the circumference of the circle(a chord is a line from point of a circle's circumference to the other) and are both 90 degrees because angle at the circumference is half of angle at the centre in same arc.

The distance traveled depends on the amount of time Marlene rides her bike

The function f(t) = 16t represents the scenario

Answer:

options (2), (3) and (5)

Step-by-step explanation:

2.

the distance traveled depends upon the amount of time she rides her bike.

as she travels 16 miles in 1 hr. she'll ride 32 miles in 2 hrs. so all values of distance traveled by her depends upon the time she takes.

3.

yes the initial is 16 miles per hour as the output of 1hr will be 16 and that's what the initial value is 16 miles for one hour. or 16 miles per hour.

5.

f(t) = 16t represents the scenario

where f(t) will be the output of the function that is d, distance when the output is t that is time.

Answer:

x = 5

arcEF = 58degrees

arcGH = 55degrees

Step-by-step explanation:

Find the diagram attached

The sum of angle on the straight line EH is 180degrees

Hence arcEF+ arcFG + arcGH = 180

10x+8 + 67 + 11x = 180

21x + 75 = 180

21x = 180 - 75

21x = 105

x = 105/21

x = 5

Since EF = 10x+8

arcEF = 10(5) + 8

arcEF = 50+8

arcEF = 58degrees

Also, arcGH = 11x

arcGH = 11(5)

arcGH = 55degrees

Answer:

5 3/5

Step-by-step explanation:

3 1/2 * 1 3/5

Change to  improper fractions

(2*3+1)/2  * (5*1+3)/5

7/2 * 8/5

56/10

Change back to a mixed number

50/10 +6/10

5 +3/5

5 3/5

Answer: $15

Step-by-step explanation:

-$50 + $75 = $15

Answer:

θ ≈ 50°, AB ≈ 15.6

Step-by-step explanation:

Using the tangent ratio in the right triangle

tanθ = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{BC}{AC}[/tex] = [tex]\frac{11.9}{10}[/tex] = 1.19 , then

θ = [tex]tan^{-1}[/tex] (1.19 ) ≈ 50° ( to the nearest degree

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Using the cosine ratio in the right triangle

cos50° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{AC}{AB}[/tex] = [tex]\frac{10}{AB}[/tex] ( multiply both sides by AB )

AB × cos50° = 10 ( divide both sides by cos50° )

AB = [tex]\frac{10}{cos50}[/tex] ≈ 15.6 ( to 1 dec. place )

Answer: [tex]\frac{33}{65}[/tex]

Step-by-step explanation:

cosine of ∠T = [tex]\frac{adjacent}{hypotenuse}[/tex]

For ∠T,

cosine of ∠T = [tex]\frac{33}{65}[/tex]

The value of the trigonometric relation cos ∠T = 0.507

Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles

The six trigonometric functions are sin , cos , tan , cosec , sec and cot

Let the angle be θ , such that

sin θ = opposite / hypotenuse

cos θ = adjacent / hypotenuse

tan θ = opposite / adjacent

tan θ = sin θ / cos θ

cosec θ = 1/sin θ

sec θ = 1/cos θ

cot θ = 1/tan θ

Given data ,

Let the triangle be represented as ΔTUV

where the measure of ∠UVT = 90°

And , the measure of side UT = 65 units

The measure of VU = 56 units

And , the measure of TV = 33 units

From the trigonometric relations ,

cos θ = adjacent / hypotenuse

On simplifying , we get

cos ∠T = TV / UT

cos ∠T = 33 / 65

cos ∠T = 0.50769

Hence , the trigonometric relation is solved

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Answer:

Yes by AAA

Step-by-step explanation:

Angle A is the same for both triangles. Angle D is congruent to Angle A since BC and DE are parallel lines and same with angle E. So by AAA the triangles are similar

Answer:

408 cm²

Step-by-step explanation:

the total SA = (2×½×6×8) + (10+8+6)×15

= 48 + 360

= 408 cm²

The total surface area of the prism that has a triangular base of 10 cm, 8 cm, and 6cm and it is 15 cm long is 408 cm².

In order to create the triangle base, the three triangular sides slant upward. A pyramid with a triangular base is also known as a tetrahedron since it is made up of four triangles.

The shape of a pyramid's base is often used to describe it. A hexagonal pyramid has a base that is a hexagon, as does a triangular pyramid, for example. Pyramids with triangular bases are called triangular pyramids.

A triangle's area is equal to half the sum of its base and height, according to the formula for triangular bases. Whether it be a scalene triangle, an isosceles triangle, or an equilateral triangle, this formula can be used to determine their properties.

The total surface area of the prism calculations are,

b = 6 cm, h = 8 cm, l = 10 cm, and L = 15 cm

[tex]Total\ Surface\ Area = (2\times \frac{1}{2} \times b \times h) + (l+h+b) \times \\ L=(2\times \frac{1}{2} \times 6 \times 8) + (10+8+6) \times 15\\= 48 + 360\\= 408 cm^2[/tex]

Therefore, total surface area of the prism that has a triangular base of 10 cm, 8 cm, and 6cm and it is 15 cm long is 408 cm².

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Answer:

[tex]{ \bf{f(x) = {x}^{3} + {ax}^{2} - 1 }} \\ { \tt{f( - 1) : {( - 1)}^{3} + a {( - 1)}^{2} - 1 = 0}} \\ { \tt{f( - 1) : a - 2 = 0}} \\ a = 2[/tex]

The polynomial function [tex]$x^3 + ax^2 -1[/tex] will have -1 as a root at the value of

a = 2.

A polynomial function exists as a function that applies only non-negative integer powers or only positive integer exponents of a variable in an equation like the quadratic equation, cubic equation, etc.

Given: A root exists at a value of x such that the polynomial exists equivalent to zero.

Let, the polynomial equation be [tex]$x^3 + ax^2 -1[/tex]

then [tex]$\mathbf{f}(\mathbf{x})=\mathbf{x}^{3}+a \mathbf{x}^{2}-\mathbf{1}$[/tex]

Put, x = -1, then we get

[tex]$\mathbf{f}(-1)=(-1)^{3}+\mathrm{a}(-1)^{2}-1=0$[/tex]

f(-1) = a - 2 = 0

a = 2

Therefore, the value of a = 2.

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Answer:

(50,-30)

Step-by-step explanation:

Reflecting a point across the y axis is just like flipping a page on a book. The x  coordinate is flipped and the y coordinate stays the same.

Answer:

Step-by-step explanation:

As you can see in the venn diagram that is attached below, The individuals that drink milk are in green, those that drink curd are in yellow, and those that drink both are in light blue. Since the sum of those that drink milk with those that drink curd is 110 and a total of 120 students were surveryed. Then this means that 10 of the students neither drink milk nor curd. These students are represented outside of the venn diagram but within the box of surveyed students.

Answer:

54.7 mm

Step-by-step explanation:

use the formula area= 1/2 base time height

A=1/2bh

Answer:

54.7mm

Step-by-step explanation:

Area=1/2b×h

218.8=0.5×8×h

218.8=4h

h=218.8÷4

h=54.7

Answer:

The one in the middle 100% correct

Answer:

second option

Step-by-step explanation:

Ratio of square to circle = 1 : 3

In the second option:

Square = 2  & circles = 6

Ratio = 2 : 6  and after simplifying, Ratio = 1 : 3

Answer:

5. B

6. B

7. D

8. D

< means a filled in circle.

Hope this helps!

Answer:

c. -x -y = 5

Step-by-step explanation:

parallel means same x

Given:

The graph of a quadratic function.

To find:

The equation of the quadratic function in factored form.

Solution:

From the given graph it is clear that the graph of the function intersect the x-axis at point (-3,0) and (2,0).

Since -3 and 2 are the zeros of the function, therefore (x+3) and (x-2) are the factors of the required quadratic function.

Now, the function can be written as:

[tex]f(x)=a(x+3)(x-2)[/tex]             ...(i)

The graph of the function intersect the y-axis at (0,-6). Substituting [tex]x=0,f(x)=-6[/tex] in (i), we get

[tex]-6=a(0+3)(0-2)[/tex]

[tex]-6=a(3)(-2)[/tex]

[tex]-6=-6a[/tex]

[tex]\dfrac{-6}{-6}=a[/tex]

[tex]1=a[/tex]

Substituting [tex]a=1[/tex] in (i), we get

[tex]f(x)=1(x+3)(x-2)[/tex]

Therefore, the required function is [tex]f(x)=1(x+3)(x-2)[/tex].

Answer:

Step-by-step explanation:

This is an isosceles triangle because 2 of the sides are the same length (marked with single slashed through them). The Isosceles Triangle Theorem tells that if 2 sides are congruent to each other, then the angles opposite those sides are congruent to each other as well. That means that the bottom left angle measures 68. According to the Triangle Angle-Sum Theorem, all the angles of a triangle have to add up to equal 180, so:

x = 180 - 68 - 68 so

x = 44

A population that is neither growing nor declining will have a TFR (Total Fertility Rate) of 2.1.

A population that is neither growing nor declining will have a Total Fertility Rate (TFR) of 2.1. The TFR is the average number of children that a woman of reproductive age will have in her lifetime.

A TFR of 2.1 is considered to be the replacement level for a population, meaning that the population will remain stable over time as births are balanced by deaths.

A TFR less than 1.0 would indicate a population in decline, while a TFR greater than 2.1 would indicate a population in growth.

Therefore, a population that is neither growing nor declining will have a TFR (Total Fertility Rate) of 2.1.

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Answer:

are you asking how many points are needed to get 90% in

a class that has a total of 3400 points ?

id so that is : 3060

Step-by-step explanation:

Answer:

2000

Step-by-step explanation:

set up equation

.7x+x=3400

combine like terms

1.7x=3400

divide by 1.7 on both sides

x=2000

Oxygen

Step-by-step explanation:

That's what I think