solve each inequality and graph its solution

Answer:

41 1/4 turns

Step-by-step explanation:

create a proportion:

turns / inches = turns / inches

't' = turns

16.5 / 1 = t / 2.5

cross-multiply to get:

t = 41.25 or 41 1/4

use desmos graphing calculator

Answer:

No solution

Step-by-step explanation:

There is no solution to the system of equations y=3x+2 and 6x-2y=8, meaning that they are parallel to each other on a graph, with no points ever intersecting on each other's lines.

262.5 gallons of milk does the class drink in 10 weeks.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

The kindergarten class at Stokes Elementary drinks about 210 pints of milk per week.

as, we know that

1 pint= 0.125 Galloon

So, 210 pints milk = 210 x 0.125 = 26.25 Galloon

Then, In 10 weeks amount of milk drink

= 26.25 x 10

= 262.5 Gallon

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Answer:

View the link for the answer

Answer:

Step-by-step explanation:

The upper right angle is supplement to 130° and a corresponding angle to (3x + 5)

130 + (3x + 5) = 180

3x + 5 = 50

3x = 45

x = 15

Answer:

Range is {3,-1, 15}

Step-by-step explanation:

Answer:

{3, -1, 15} is the range.

Step-by-step explanation:

Answer:

=============================================================

Explanation:

The letter O looks very similar to the number zero, so I'm going to use other letters to avoid confusion. For the smaller circle on the left, it'll have center P. The circle on the right will have center Q. See the diagram below.

Based on that, we can say that PQ = 20 cm.

Let x = length of PK

PK + KQ = PQ

KQ = PQ - PK

KQ = 20 - x

We'll keep this in mind for later. I'll refer to this as "Fact 1" when it does come up later.

------------------------

We're given this equation

3AK=2BK

Let's get the numbers to one side and the letters to the other side like so:

3AK=2BK

3AK/BK = 2

AK/BK = 2/3

We'll use this later as well.  I'll refer to this as "Fact 2" when it does come up later.

------------------------

Next, draw a segment from P to A to form triangle PAK (also shown in the diagram below). Do the same for points Q and B to form triangle QBK.

The segments PA and PK are radii of the smaller circle, so PA = PK which leads to triangle PAK being isosceles. Triangle QBK is also isosceles for similar reasoning.

The angles AKP and QKB are vertical angles, so they are congruent.

The facts mentioned so far boil down to the two triangles being similar triangles (use the angle angle method to prove).

------------------------

Now that we know the triangles are similar, we can use a proportion to solve for x.

PK/KQ = AK/KB

PK/KQ = 2/3  .... use fact 2

x/(20-x) = 2/3 .... use fact 1

3x = 2(20-x) .... cross multiply

3x = 40 - 2x

3x+2x = 40

5x = 40

x = 40/5

x = 8

So,

The radius of the smaller circle on the left is 8 cm.

The radius of the larger circle on the right is 12 cm.

Answer:

2/9

Step-by-step explanation:

28 marbles in all

"Half of the marbles are red."

28/2 = 14 red

"Half of the non-red marbles are white..."

14/2 = 7 white

"...and the rest are blue."

25 -14 -7 = 7 blue

"Todd chose a white marble at random... " -from the bag that has...

14 red 7 white 7 blue

"... and kept it."- so now the marbles left in the jar are...

14 red 6 white 7 blue

P (white) = Number of white marbles/ Total number of marbles = 6/27 = 2/9

Answer:

[tex]-54[/tex]

Step-by-step explanation:

If the number being halved is x, we can write the expression

[tex]7-0.5x=34[/tex]

Now, bring like terms and solve!

[tex]-0.5x=27[/tex]

Multiple both sides by -2 and you get

[tex]x=-54[/tex]

Wanna check the answer? Well...

[tex]7-(-54*0.5)=7+27=34[/tex]

Answer:

63.1°

Step-by-step explanation:

Complementary angles sum 90°

90 - 26.9 = 63.1°

Solving steps:-

5x+3y=−4

y−2x=6

-->To solve a pair of equations using substitution, first solve one of the equations for one of the variables. Then substitute the result for that variable in the other equation.

5x+3y=−4,−2x+y=6

-->Choose one of the equations and solve it for x by isolating x on the left hand side of the equal sign.

5x+3y=−4

-->Subtract 3y from both sides of the equation.

5x=−3y−4

--> Divide both sides by 5.

x = 1/5(-3y - 4)

--> Multiply 1/5 −3y−4.

x = -3/5y - 4/5

--> Substitute -3y - 4/ 5 for x n the other equation, −2x+y=6.

-2 (-3/5y - 4/5) + y = 6

--> Multiply −2 times -3y - 4/ 5

6/5y + 8/5 + y = 6

--> Add 6y/5 to y

11/5y + 8/5 = 6

--> Subtract 8/5 from both sides of the equation.

11/5y = 22/5

--> Divide both sides of the equation by 11/5, which is the same as multiplying both sides by the reciprocal of the fraction.

y = 2

--> Substitute 2 for y in x= -3/5y - 4/5. Because the resulting equation contains only one variable, you can solve for x directly.

x = -3/5 x 2 - 4/5

--> Multiply -3/5 times 2.

x = -6 - 4/ 5

--> Add -4/5 to -6/5 by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

x = -2

--> The equation is now solved.

Answer : x = -2, y = 2

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you know that y=mx +c then in the place of m is 3 then answe is also three.

Substitute x = √7 sin(t) and dx = √7 cos(t) dt. Then

∫ √(7 - x²) dx = ∫ √(7 - (√7 sin(t))²) • √7 cos(t) dt

… = √7 ∫ √(7 - 7 sin²(t)) cos(t) dt

… = 7 ∫ √(1 - sin²(t)) cos(t) dt

… = 7 ∫ √(cos²(t)) cos(t) dt

We require that -π/2 ≤ t ≤ π/2 in order for the substitution we made to be reversible. Over this domain, cos(t) ≥ 0, so

√(cos²(t)) = |cos(t)| = cos(t)

and the integral reduces to

… = 7 ∫ cos²(t) dt

Recall the half-angle identity for cosine:

cos²(t) = (1 + cos(2t))/2

Then the integral is

… = 7/2 ∫ (1 + cos(2t)) dt

… = 7/2 (t + 1/2 sin(2t)) + C

… = 7t/2 + 7/4 sin(2t) + C

Get the antiderivative back in terms of x. Recall the double angle identity for sine:

sin(2t) = 2 sin(t) cos(t)

We have t = arcsin(x/√7), which gives

sin(t) = sin(arcsin(x/√7)) = x/√7

cos(t) = cos(arcsin(x/√7)) = √(7 - x²)/√7

Then

∫ √(7 - x²) dx = 7/2 arcsin(x/√7) + 7/4 • 2 sin(arcsin(x/√7)) cos(arcsin(x/√7)) + C

… = 7/2 arcsin(x/√7) + x/2 √(7 - x²) + C

The angles are 29° and 61°.

Let the smaller angle be x

Let the larger angle be x+32.

The sum of the complimentary angles will be 90°.

Therefore, x + x + 32° = 90°

2x + 32° = 90°

2x = 90° - 32°

2x = 58°

x = 58/2

x = 29°

The larger angle = x + 32 = 29 + 32 = 61°

Answer:

y= -4/2x+ -4

Step-by-step explanation:

looked at the graph

[tex]x^2 +18x +90 = 0\\\\\text{Apply quadratic formula,}~~ x = \dfrac{-b \pm \sqrt{b^2 -4ac}}{2a} \\\\\text{In this case, a = 1 , b = 18 and c = 90.}\\\\\implies x = \dfrac{-18 \pm \sqrt{18^2 - 4 \cdot 1 \cdot 90}}{2(1)}\\\\\implies x = \dfrac{-18 \pm \sqrt{-36}}2\\\\\implies x = \dfrac{-18 \pm 6i}2\\\\\implies x= -\dfrac{18}2 \pm \dfrac{6i}2\\\\\implies x= -9 \pm 3i[/tex]

Answer:

1/24

Step-by-step explanation:

multiply 1/9 and 3/8. The product of the two factors is 3/ 72. Seeing the two factors on the other hand, we can cancel out 3. Hence the final answer to this problem in lowest terms becomes 1/24.

The perpendicular bisector theorem gives the statements that ensures

that [tex]\overleftrightarrow{FG}[/tex] and [tex]\overleftrightarrow{AB}[/tex] are perpendicular.

The two statements if true that guarantee  [tex]\overleftrightarrow{FG}[/tex] is perpendicular to line [tex]\overleftrightarrow{AB}[/tex] are;

Reasons:

The given diagram is the construction of the line [tex]\mathbf{\overleftrightarrow{FG}}[/tex] perpendicular to line [tex]\mathbf{\overleftrightarrow{AB}}[/tex].

Required:

The two statements that guarantee that  [tex]\overleftrightarrow{FG}[/tex] is perpendicular to line [tex]\overleftrightarrow{AB}[/tex].

Solution:

From the point C arcs E and D are drawn to cross line [tex]\overleftrightarrow{AB}[/tex], therefore;

[tex]\overline{CE} = \mathbf{\overline{CD}}[/tex] arcs drawn from the same radius.

[tex]\overleftrightarrow{FG}[/tex] is perpendicular to line [tex]\overleftrightarrow{AB}[/tex], given.

Therefore;

[tex]\overline{DF} = \overline{EF}[/tex]  by perpendicular bisector theorem.

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The first five terms of the geometric sequence is 6, 18, 54, 162 and 486

Geometric progression is given by:

[tex]nth\ term=ar^{n-1}[/tex]

where a is the first term, r is the common ratio

Given that first term is 6, and common ratio is 3, Hence a = 6, r = 3

[tex]First\ term=6\\\\Second \ term=6(3)^{2-1}=18\\\\Third \ term=6(3)^{3-1}=54\\\\Fourth \ term=6(3)^{4-1}=162\\\\Fifth \ term=6(3)^{5-1}=486[/tex]

The first five terms of the geometric sequence is 6, 18, 54, 162 and 486

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Answer:

it's 11

Step-by-step explanation:

Answer:

Multiplied by -4

Step-by-step explanation:

-5 (-4) = 20

20 (-4) = -80

-80 (-4) = 320

Answer:

20

Step-by-step explanation:

you know the ratio is 4:3 so you do 4+3=7 then you do 140÷7=20 so I bar represents 20

Answer:

$88

Step-by-step explanation:

442.70 rounded to the nearest 10 dollars is 440.

20%= .2.

440 times .2 =

88

Answer:

y= -1x+4

Step-by-step explanation:

-1/1 is simplified to -1

Answer:

A: 16.8

Step-by-step explanation:

4.2 and 16.8 both have decimal place values. If you line up the decimals when you add them, then you get 21.

The next number of the sequence 1, 15, 155, ...... will be 1555.

A sequence is a list of elements that have been ordered in a sequential manner, such that members come either before or after.

A sequence in arithmetic is an enumerated collection of items in which duplicates are permitted and order is important. It has members, just like a set. The distance of the order is defined as the number of items.

The sequence is given below.

1, 15, 155, ......

The next number of the sequence will be given by adding the digit 5 in the one's place. Then the sequence is given as,

1, 15, 155, 1,555, 15,555, 155,555,......

Then the number will be 1555.

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