angle S is 90 degrees and angle T is 45 degrees. side ST is 3 ft. how long is side SU

Answer:

Sur. area = 360 area unit , vol = 54√3 volume unit

Step-by-step explanation:

Sur. area = 6×(6×10)

Volume= (n/4)X² (cot(180/n)) , n is number of sides and X is side length

Answer:

In logic, statements and are logically equivalent if they have the same logical content. That is, if they have the same truth value in every model. The logical equivalence of and is sometimes expressed as, or. However, these symbols are also used for material equivalence. Proper interpretation depends on the context.

Step-by-step explanation:

Answer:

they have the same logical content

Step-by-step explanation:

that is if they have the same truth

Hello There!

[tex]\frac{18}{20}[/tex] as a decimal is 0.9

You can first reduce this fraction by dividing both the numerator and denominator by the Greatest Common Factor of 18 and 20 using 2.

18 ÷ 2 ≈ 9

20 ÷ 2 ≈ 10

We now have the fraction [tex]\frac{9}{10}[/tex]

Finally, we divide 9 by 10 and we get a quotient of 0.9

The equivalent value of the decimal is A = 18/20 = 0.9

Given data ,

Let the equation be represented as A

Now , the value of A is

Let the numerator of the fraction be p

where the value of p = 18

Let the denominator of the fraction be q

where q = 20

Now , the fraction is A = p/q

On simplifying the expression , we get

So , the left hand side of the equation is equated to the right hand side by the value of p/q

A = 18/20

A = 9/10

On further simplification , we get

A = 0.9

So , the decimal number is A = 0.9

Therefore , the value of A = 0.9

Hence , the expression is A = 0.9

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Answer:

Add the equations to eliminate x

Step-by-step explanation:

Let's go through each of these statements

1) Add the equations to eliminate x

   y = x + 10

+

   y = -x + 3

   _______

  2y = 13

This works!

Answer:

Add the equation to eliminate x.

Step-by-step explanation:

Add the equation to eliminate x.

Let's actually do the work!  

y = x + 10

y = −x + 3

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

2y = 13, so y = 6.5.

Subbing 6.5 for y in either of the equations above lets us calculate y.  For example, in the second equation, 6.5 = -x + 3, or 3.5 = -x, or x = -3.5.

The solution is (-3.5, 6.5).

Answer:

C

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 1, 0) and (x₂, y₂ ) = (0, - 3)

m = [tex]\frac{-3-0}{0+1}[/tex] = - 3

note the line crosses the y- axis at (0, - 3) ⇒ c = - 3

y = - 3x - 3 ← in slope- intercept form

Add 3x to both sides

3x + y = - 3 ← in standard form → C

Answer:

The volume of cone B is equal to [tex]256\pi\ ft^{3}[/tex]

Step-by-step explanation:

step 1

Find the scale factor

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional and this ratio is called the scale factor

The scale factor is equal to the ratio of its diameters

so

16/8=2

step 2

Find the volume of cone B

we know that

If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube

Let

z -----> the scale factor

Vb ----> volume of cone B

Va ----> volume of cone a

[tex]z^{3}=\frac{Vb}{Va}[/tex]

we have

[tex]z=2[/tex]

[tex]Va=32\pi\ ft^{3}[/tex]

substitute

[tex]2^{3}=\frac{Vb}{32\pi}[/tex]

[tex]Vb=(8)(32\pi)=256\pi\ ft^{3}[/tex]

The volume of cone B that is similar to cone A is calculated as: 256π ft³.

Volume of Solid A/volume of solid B = a³/b³, where a and b are the corresponding linear measures of both solids.

32π/B = 4³/8³

B(4³) = (8³)(32π)

64(B) = 16,384π

B = 16,384π/64

Volume of cone B is: 256π ft³

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Answer:

t+m=20--------> t=20-m

3t+11m=100

Substitute

3(20-m)+m=100

60m-3m+11m=100

Get rid of 60

-3m+11m=40

8m=40

Divide by 8

m=5

This tells us that there are 5 Multiple Choice questions. So the remaining 15 question on the test must be True/False questions.

If we got all 5 Multiple Choice questions correct we would score 11 points for each of the five questions and this would give us 55 points. Then if we got all 15 True/False questions correct at 3 points each, we would score 15 times 3 or 45 points. So the total number of points on the test would be 55 + 45 = 100.

Step-by-step explanation:

The answer is:

There are 15 true/false questions while there are 5 multiple choice questions.

To solve the problem, we need to write two equations using the given information.

We know that there are twenty (20) questions consisting of true/false and multiple choice questions, so, writing the first equation we have:

Let be the true/false questions "x" and the multichoice questions "y".

First equation,

[tex]x+y=20[/tex]

Also, we know that the true/false questions worth 3 points while the  multichoice questions worth 11 points making a total of 100 points for the total examen, so, writing the second equation, we have:

Second equation,

[tex]3x+11y=100[/tex]

Now, we have to isolate one of the variables in function of the other variable, so, from the first equation, we have:

[tex]x+y=20[/tex]

[tex]x=20-y[/tex]

Then, substituting "x" into the second equation, we have:

[tex]3x+11y=100[/tex]

[tex]3(20-y)+11y=100[/tex]

[tex]60-3y+11y=100[/tex]

[tex]60+8y=100[/tex]

[tex]8y=100-60=40[/tex]

[tex]y=\frac{40}{8}=5[/tex]

Then, substituting "y" into the first equation, we have:

[tex]x+y=20[/tex]

[tex]x+5=20[/tex]

[tex]x=20-5=15[/tex]

Hence, we have that there are 15 true/false questions while there are 5 multiple choice questions.

Let's prove that we are right by substituting the obtained answers into the both equations, if the equations are satisfied, the answers are ok.

Substituting into the first and the second equation, we have:

First equation,

[tex]x+y=20\\5questions+15questions=20questions\[/tex]

Second equation,

[tex]3x+11y=100points\\3*(15)+11*(5)=100points\\45points+55points=100points[/tex]

We can see that both equations are satisfied, so, the answers are ok.

Have a nice day!

Answer:

12

Step-by-step explanation:

we can see that the base's size is doubled, from that we can find that 6 will be doubled to twelve.

Answer: 12

Step-by-step explanation: The Answer is 12. This is because the numbers on the left are 2x less than on the right.

Answer:

similar triangles

Step-by-step explanation:

did it on usatestprep

Similar triangles are triangles with congruent angles and proportional sides.

In mathematics, triangles with congruent angles and proportional sides are called similar triangles.

Similar triangles have the same shape, but their sides may have different lengths. Two triangles are similar if their corresponding angles are congruent and the lengths of their corresponding sides are proportional.

For example, if angle A in triangle ABC is congruent to angle X in triangle XYZ, and the ratio of the length of AB to XY is equal to the ratio of the length of BC to YZ, then triangle ABC is similar to triangle XYZ.

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C. Expression

An inequality must contain a sign relating magnitude.

An equation must contain an equal sign.

An expression cannot have an equal sign or any symbols of inequality.

A fraction must contain a bar representing division.

Hope this helps!!

Answer: Third option

[tex]-u-v = <-2, -3>[/tex]

Step-by-step explanation:

We have the vector u and the vector v. We must perform the operation [tex]-u-v[/tex].

To perform this operation multiply the vector u by -1 and multiply the vector v by -1.

If u = (-5,6)

So

-1u = (5, -6)

If v = (7, -3)

So

-1v = (-7, 3)

Then the sum of both vectors is done by adding the components of u with the components of v.

[tex]-u-v = (5, -6) + (-7,\ 3)\\\\-u-v = (5-7\ ,\ -6 + 3)\\\\-u-v = (-2,\ -3)[/tex]

3q - 2p; all you are doing is simplifying straight across. I think you got confused by the parentheses unwrapped around 6p - 9q. Well, it is STILL the same process.

The answer is:

The correct option is:

A) Jeff, 4.5 hours; Julia 9 hours.

To solve the problem, we need to write two equations using the given information.

So, writing the first equation we have:

We know that Jeff can weed the garden twice as fas as his sister Julia, so:

[tex]JeffRate=2JuliaRate[/tex]

Also, from the statement we know that they can weed the garden in 3 hours, so, writing the second equation we have:

[tex]JeffRate+JuliaRate=\frac{1garden}{3hours}[/tex]

Then, we need to substitute the first equation into the second equation in order to isolate Julia's rate, so, solving we have:

[tex]JeffRate+JuliaRate=\frac{1garden}{3hours}[/tex]

[tex]2JuliaRate+JuliaRate=\frac{1garden}{3hours}[/tex]

[tex]2JuliaRate+JuliaRate=\frac{1garden}{3hours}[/tex]

[tex]3JuliaRate=\frac{1garden}{3hours}[/tex]

[tex]JuliaRate=\frac{1garden}{3hours*3}=\frac{1garden}{9hours}[/tex]

We have that Julia could weed the garden by herself in 9 hours.

So, calculating how long will it take to Jeff, we have:

[tex]JeffRate=2*JuliaRate\\\\JeffRate=2*\frac{1garden}{9hours}=\frac{2garden}{9hours}=\frac{1garden}{4.5hours}[/tex]

We have that Jeff could weed the same garden by himself in 4.5 hours.

Hence, the correct option is:

A) Jeff, 4.5 hours; Julia 9 hours.

Have a nice day!

Answer:

A

Step-by-step explanation:

Answer:

(−1, –1.25), (5, –2.75)

Step-by-step explanation:

If "slope-intercept form" is mentioned, then we already know that the function rule is that of a straight line with slope m and y-intercept b.

As we go from (−1, –1.25) to (5, –2.75), x increases by 6 and y decreases by 1.50.  Thus, the slope, m, is m = rise / run = -1.50 / 6, or m = -0.25 or -1/4.

Choosing one of the given points at random:  (8, -3.5), we start with the slope-intercept form y = mx + b and substitute -1/4 for m, 8 for x and -3.5 for y:    y = mx + b  becomes  -3.5 = (-1/4)(8) + b.  Then -3.5 + 2 = b, or b = -1.5.

The desired equation is y = (-1/4)x - 3/2, or y = -0.25x - 1.5

To write a function rule in slope-intercept form for the given ordered pairs, we need to calculate the slope and find the y-intercept. The slope can be calculated using the formula (Y2 - Y1) / (X2 - X1), and the y-intercept can be found by using the point-slope form and substituting one of the ordered pairs. The function rule in slope-intercept form for the given ordered pairs is y = -0.25x - 1.5.

To write a function rule in slope-intercept form, we need to find the slope (m) and the y-intercept (b). Given the ordered pairs (–12, 1.5), (−1, –1.25), (5, –2.75), (8, −3.5), we can calculate the slope using the formula m = (Y2 - Y1) / (X2 - X1). Let's choose two ordered pairs to calculate the slope:

Using (–12, 1.5) and (−1, –1.25):

m = (-1.25 - 1.5) / (-1 - (-12)) = (-2.75) / (11) = -0.25

Now, we can use the point-slope form y - y1 = m(x - x1), where (x1, y1) is one of the ordered pairs and substitute the slope and one of the points to find the y-intercept:

Using the ordered pair (–12, 1.5):

y - 1.5 = -0.25(x - (-12))

y - 1.5 = -0.25(x + 12)

y - 1.5 = -0.25x - 3

y = -0.25x - 3 + 1.5

y = -0.25x - 1.5

Therefore, the function rule in slope-intercept form (fraction form) is y = -0.25x - 1.5.

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Find the exact value of each one:

5^2 = 25

2^4 = 16

3^3 = 27

1^8 = 1

Now you can list them in order from smallest to largest:

1^8, 2^4, 5^2, 3^3

Answer:

Step-by-step explanation:

5²=25

2^4=16

3^3=27

1^8=1

1<16<25<27

so 1^8<2^4<5^2<3^3

Answer:2 > -6 or -6 < 2

Step-by-step explanation:

Answer:  2>-6 is correct

Step-by-step explanation:

We know that 2 is a grater number than -6 so what we can do is put this > but make sure that its facing the 2 and there its simple  hope I helped! :p plz rate me

Answer:

Step-by-step explanation:

8.8 laps because of the concepts of molecular osmosis used to provide a detailed explanation to kermit. Thereby omitting the theory of dark matter into the universe and thus replacing it with the new compulsive theory of 50 % growth of human anatomical secretory sections.

Answer:

D) 8.8 laps.

Step-by-step explanation:

We have been given that each player on the football team is required to run 1.5 miles in less than 15 minutes. One lap around the field is 300 yards.

We know that 1 mile equals 1760 yards.

First of all, we will convert 1.5 miles into yards by multiplying 1.5 by 1760.

[tex]\text{1.5 miles}=\text{1.5 miles}\times \frac{\text{1760 yards}}{\text{Mile}}[/tex]

[tex]\text{1.5 miles}=1.5\times \text{1760 yards}[/tex]

[tex]\text{1.5 miles}=2640\text{ yards}[/tex]

We have been given that one lap around the field is 300 yards. To find the number of laps a player must run, we will divide 2640 by 300.

[tex]\text{Number of laps a player must run}=\frac{2640\text{ yards}}{300\text{ yards}}[/tex]

[tex]\text{Number of laps a player must run}=8.8[/tex]

Therefore, a player must run 8.8 laps to meet the requirement.

Answer:

17) Ф = 57.99 ≅ 58°

18) Ф = 20.10 ≅ 21°

Step-by-step explanation:

* Lets revise the trigonometry functions

- In any right angle triangle:

# The side opposite to the right angle is called the hypotenuse

# The other two sides are called the legs of the right angle

* If the name of the triangle is ABC, where B is the right angle

∴ The hypotenuse is AC

∴ AB and BC are the legs of the right angle

- ∠A and ∠C are two acute angles

- For angle A

# sin(A) = opposite/hypotenuse

∵ The opposite to ∠A is BC

∵ The hypotenuse is AC

∴ sin(A) = BC/AC

# cos(A) = adjacent/hypotenuse

∵ The adjacent to ∠A is AB

∵ The hypotenuse is AC

∴ cos(A) = AB/AC  

# tan(A) = opposite/adjacent

∵ The opposite to ∠A is BC

∵ The adjacent to ∠A is AB

∴ tan(A) = BC/AB

* Now lets solve the problems

17) In Δ ACB

∵ m∠C = 90°

∵ BC = 16 units ⇒ opposite to angle Ф

∵ AC = 10 units ⇒ adjacent to angle Ф

∵ tanФ = opposite/adjacent

∴ tanФ = BC/AC

∴ tanФ = 16/10 = 8/5

- To find angle Ф find the inverse of tan (tan^-1)

∴ Ф = tan^-1 8/5 = 57.99 ≅ 58°

18) In Δ ACB

∵ m∠C = 90°

∵ BC = 5.6 units ⇒ opposite to angle Ф

∵ AC = 15.3 units ⇒ adjacent to angle Ф

∵ tanФ = opposite/adjacent

∴ tanФ = BC/AC

∴ tanФ = 5.6/15.3 = 56/153

- To find angle Ф find the inverse of tan (tan^-1)

∴ Ф = tan^-1 56/153 = 20.10 ≅ 21°

Answer:

17).  θ = 57.99°

18).  θ =20.10°

Step-by-step explanation:

Points to remember

Trigonometric ratios

Sin θ  = Opposite side/Hypotenuse

Cos θ = Adjacent side/Hypotenuse

Tan θ = Opposite side/Adjacent side

Question (17).

From the figure we can write,

Tan θ = Opposite side/Adjacent side

= BC/AC = 16/10 = 1.6

θ = Tan⁻¹ (1.6) = 57.99°

Question 18)

From the figure we can write,

Tan θ = Opposite side/Adjacent side

= BC/AC = 5.6/15.3 = 0.366

θ = Tan⁻¹ (0.366) = 20.10°

Answer:

All real numbers

Step-by-step explanation:

This equation is well defined for all real values of x, hence

domain : x ∈ R

Answer:

x = 2.

y =  6.

Step-by-step explanation:

Consider the triangle on the left.

Because there are 2 equal angles at the vertex on the bottom right:

3/9 = x/(8 - x)

1/3 = x / (8 - x)

3x = 8 - x

4x = 8

x = 2  (answer).

Similarly, for the second triangle:

3/y = 2/4

3/y = 1/2

y = 6

(answer).

2 pounds total!

3/6 * 4 cans = 2 pounds

Answer:

The weight of 4 cans of peaches will be 2 pounds if one can of peaches weigh 3/6 pound.

Step-by-step explanation:

We need to find the weight of 4 cans of peaches altogether.

Weight of 1 can of peaches = 3/6 pounds

Weight of 4 cans of peaches = 3/6 * 4

                                                = 12 / 6

                                                = 2 pounds.

So, The weight of 4 cans of peaches will be 2 pounds if one can of peaches weigh 3/6 pound.

Basically, the question is asking for 18% of $23.

The answer is $4.14.

The tip was $4.14, because you take 18% of $23 and then you end up with $4.14

Answer:

A = 90 - x

Step-by-step explanation:

The square on the lower right means the two line segments form a right angle.

If B = x

and C = 90

the A = 180 - x - 90    (Every triangle has 180 degrees -- no exceptions).

A = 90 - x

Answer:

[tex]\frac{1}{2}[/tex]

Step-by-step explanation:

Given a number n then the multiplicative inverse is [tex]\frac{1}{n}[/tex]

The product of a number and it's multiplicative inverse = 1

Given 2, then multiplicative inverse is [tex]\frac{1}{2}[/tex]

Answer:

Step-by-step explanation:

It's the parallelogram. The formula of an area of a parallelogram:

A = bh

b - base

h - height

We have b = 11 ft, h = 6.1 ft. Substitute:

A = (11)(6.1) = 67.1 ft²

Answer:

The values of theta where cos(theta) is 0 is equal to π/2 or 3π/2 so, the value of tan(theta) will be zero.

Step-by-step explanation:

As we know,

tan(theta) = sin(theta)/ cos(theta)

tan(theta) will be undefined whenever cos(theta) = 0

as anything divided by zero is undefined.

We need to find the values of theta where cos(theta) is 0.

cos(0) = 1

cos (π/2) = 0

cos(π) = 1

cos(3π/2) = 0

The values of theta where cos(theta) is 0 is equal to π/2 or 3π/2 so, the value of tan(theta) will be zero.

Answer:

[tex]-\frac{1}{32}[/tex]

Step-by-step explanation:

[tex]\frac{1}{2^{-2}*x^{-3}*y^{5}   }[/tex]

Substitute x = 2 and y = -4 into [tex]\frac{1}{2^{-2}*x^{-3}*y^{5}   }[/tex]

2⁻² = [tex]\frac{1}{4}[/tex]

2⁻³ = [tex]\frac{1}{8}[/tex]

-4⁵ = -1024

[tex]\frac{1}{4}[/tex]  × [tex]\frac{1}{8}[/tex] × -1024 = -32

Answer:

-480

Step-by-step explanation:

If f varies directly as g, and inversely as h, then we can write the variation equation:

[tex]f=\frac{kg}{h}[/tex], where k is the constant of variation.

If g=56 when h=-2 and f=-7, then we substitute these values into the formula to find the value of k.

[tex]-7=\frac{k(56)}{-2}[/tex]

[tex]-7\times -2=56k[/tex]

[tex]k=\frac{14}{56}=\frac{1}{4}[/tex]

The equation now becomes:

[tex]f=\frac{g}{4h}[/tex]

if f=10 and h=-12, then;

[tex]10=\frac{g}{-48}[/tex]

[tex]g=-48\times 10=-480[/tex]

The correct answer is B.

To find g when f = 10 and h = -12, use the formula for direct variation: f = kg. Substituting the given values, we can solve for g.

We are given that f varies directly as g, and f varies inversely as h. To find g when f = 10 and h = -12, we can use the formula for direct variation: f = kg, where k is the constant of variation. So, f/g = k. Substituting the given values, we have 10/g = k. To find k, we need to find g when f = -7 and h = -2. Using the same formula, we have -7/g = k. Since k is the same constant in both cases, we can equate the two equations: 10/g = -7/g. Solving for g, we get g = -70/10 = -7.

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The volume of the gigantic fridge is 2.5 times grater than the volume of the regular fridge.

The term “volume” refers to the amount of three-dimensional space taken up by an item or a closed surface. It is denoted by V and its SI unit is in cubic m.

The volume is found as the product of the area and the length;

Volume  = Area ×length

V=A×L

Volume of the regular fridge;

V=  1 m²× 2 m

V=2 m³

Volume of the large fridge;

V=  2 m²× 5/2 m

V=5 m³

The ratio of the volume of the gigantic fridge as the volume of the regular fridge is;

[tex]\rm n = \frac{5}{2} \\\\ n= 2.5[/tex]

Hence, volume of the gigantic fridge is 2.5 times grater than the volume of the regular fridge

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