Solve the system for x, y, and z:

4x-2y+6z=10
x+3y+z=16
5y-z=19​

the diameter to allow an elongation of 0. 38 mm therefore required diameter is 7.65 mm

Given the data in the question;

F = 11100 N

l₀ = 310 mm = 0.31 m

E = 207 GPa = 207 × 10⁹ N/m²

Δl = 0.38 mm = 0.0005 m

So, lets assume the deformation is elastic;

d₀ = √(  [4l₀F] / [πEΔl] )

we substitute

d₀ = √(  [4 × 0.38 × 11100] / [π × (207 × 10⁹) × 0.0005]] )

d₀ = √( 10123.2 / 172787595.947 )

d₀ = √( 5.85875 × 10⁻⁵ )

d₀ = 0.007654 m

d₀ = ( 0.007654 × 1000 )mm

d₀ = 7.65 mm

Therefore, required diameter is 7.65 mm

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Gianna washes 15 cars in 5 hours as her rate of washing cars is 3 cars per hour.

What is unitary method?

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

According to the given question:

Gianna can wash 6 cars in 2 hours

Therefore, in 1 hour she can wash 6/2 cars which is 3 cars.

Gianna's rate of washing cars is 3 cars per hour

Hence by unitary method, Gianna at this rate can washes 5 x 3 cars that is 15 cars.

Gianna washes 15 cars in 5 hours as her rate of washing cars is 3 cars per hour.

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When comparing the means of two populations, it is often preferable to use a two-sample t test, rather than a one-way ANOVA f test because the non-pooled t statistic does not require the assumption that the populations have equal Variances.

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The marked-up price of the desk in the furniture store is $158.92.

The markup is the difference added to the cost of a product or service.

The markup represents the seller's profit on the cost.

The markup differs from the margin, which is the ratio of the seller's profit to the sales price.

The wholesale price of a desk = $137

Markup rate = 16%

Marked-up price = $158.92 ($137 x 1.16)

Thus, the desk is sold at the marked-up price of $158.92.

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The rate the candle burn down is 7 / 4 inches per hour.

The [tex]17\frac{1}{2}[/tex] inches candle burns down in 10 hours.  The rate the candle burn down in inches per hour can be calculated as follows:

In math, a rate is a ratio that compares two different quantities which have different units.

Hence,

rate  = length of the candle / time

length of the candle = 35  /2 inches

time  = 10 hours

rate = 35  / 2 ÷ 10

rate = 35 / 2 × 1  /10

rate = 35 / 20

rate = 7 / 4 inches per hour

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The set of ordered pairs which represents a function as required in the task content is; { (-2, 0), (-5, -5), (-1, 3), (2, 0) }.

It follows from the task content that the set of ordered pairs which represents a function is to be identified among the answer choices.

It is noteworthy to know that a function is a special kind of relation in which case each input value is assigned only one output value.

Put simply, no one input value has more than one output value assigned to it.

On this note, the answer choice which correctly represents a function among the answer choices is; { (-2, 0), (-5, -5), (-1, 3), (2, 0) }.

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By using substitution method, x = 0, and y = -3 are the solutions of the given system of equations.

What is substitution method?

In order to solve a system of equations, the substitution approach is typically utilized in mathematics. The first equation involving the variable must be solved using this method before the variable's value is substituted in the second equation.

Consider the given system of equations

-5x - 3y = 9       ..(1)

4x - 18y = 54       ..(2)

From equation (1),

-5x = 9 + 3y

[tex]x =- \frac{9+3y}{5}[/tex]              ..(3)

Plug the value of x in equation (2),

[tex]4(-\frac{9+3y}{5})- 18y = 54\\-36-12y-90y = 270\\ -36 - 102y=270\\102y = -36-270\\102y=-306\\y = -3[/tex]

Plug y = -3 in equation (3)

[tex]x = -\frac{9+3(-3)}{5} =-\frac{9-9}{5} =0[/tex]

x = 0

Hence, by substitution method x = 0 and y = -3.

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We can write the given statement as inequality as -

-(x/9) < 12

Linear inequalities are defined as expressions in which two linear expressions are compared using the inequality symbols.

Reversal property : If (a > b) then (b < a) and  if (a < b) then (b > a).

Law of Trichotomy : The "Law of Trichotomy" says that - only one of the following is true : (a < b) or (a = b) or (a > b).

The general equation of a straight line is y = mx + c

Other possible equations of lines are -

We have the following statement -

"the quotient of a number and three minus twelve is less than 12".

We can write the inequality as -

-(x/9) < 12

Therefore, we can write the given statement as inequality as -

-(x/9) < 12

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The number of miles Melissa travelled that night is approximately 667 miles.

Melissa is planning to rent out a limo for her friends and herself for prom.

Limousine rates charge a 450 flat rate plus an additional 30 cents for every mile travelled.

Melissa aid the limousines driver $200 for prom. The number of miles she travel can be calculated as follows;

using equation,

y = 450 + 0.3x

where

Therefore,

200 + 450 = 450 + 0.3x

650 = 450 + 0.3x

650 - 450 = 0.3x

200 = 0.3x

x = 200 / 0.3

x = 666.666666667

x = 667 miles

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Answer: It is A

Step-by-step explanation:

Answer:

1. 628 square units

2. 758 square units

3. 996 square units

4. 525 square units

Step-by-step explanation:

Answer: Z=80

Step-by-step explanation:

The length of the segment connecting (-4, 3) and (-5,2) is 1.4.

The length of a line segment can be measured by measuring the distance between its two endpoints.

Therefore, the length of the segment connecting (-4, 3) and (-5,2) can be found as follows:

length of the segment = √(2 - 3)² + (-5 + 4)²

length of the segment = √(-1)² + (-1)²

length of the segment = √1 + 1

length of the segment = √2

length of the segment = 1.41421356237

length of the segment = 1.4

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Answer:

the answer is y

Step-by-step explanation:

got it right on edmentum :)

Using the Pythagorean Theorem, the number of feet from the tent pole to the rope along the ground is 12 feet.

In the given question we have to determine the number of feet from the tent pole to the rope along the ground.

From the question;

A tent pole that is 5 feet tall is secured to the ground with a piece of rope that is 13 feet long from the top of the tent pole to the ground.

So the value of Hypotenuse(H) = 13 feet

Perpendicular(P) = 5 feet

Using the Pythagorean Theorem

H^2=P^2+B^2

Putting the value

(13)^2=(5)^2+(B)^2

169 = 25+B^2

Subtract 25 on both side, we get

B^2=169-25

B^2=144

Taking square root on both side, we get

B=12

Hence, the number of feet from the tent pole to the rope along the ground is 12 feet.

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The blanks are filled as below

Collinear points are those that are situated along a single straight line.

Collinear points are those that are on a line either close to or far from another point, it can be more than two points.

While coplanar points imply lying on the same plane

In the diagram,

E, F, and G are collinear points

D, B, E, F, and G are coplanar points

A, B, and C are another collinear points

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The area of scale drawing, based on the scale of drawing and specifications of sculpture is 0.315 m².

The scale drawing is -

10 cm for 8 m

As 100 cm = 1 m

So, the ratio for scale is 0.1 m for 8 m

Calculating the area -

Area = 6 × 4.2

Performing multiplication on Right Hand Side

Area = 25.2 m²

As 8 m sculpture is 0.1 m on drawing

So, 25.2 m² sculpture will be (25.2 × 0.1)/8

Performing multiplication and division on Right Hand Side

Area of scale drawing = 0.315 m²

Hence, the area of scale drawing is 0.315 m².

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They both Bihn and Inscoe can do same work in 3(1/13) hours.

How to solve work time problems?

Efficiency = (work)/(time)

Bihn can write one test =  Eight hours

Bihn's one hour work = 1/8

Inscoe can write one test = Five hours

Inscoe's one hour work = 1/5

Bihn and Inscoe 's one hour work =  1/8 + 1/5

= (5 + 8)/40

= 13/40

Both Bihn and Inscoe can do same work in 40/13

= 3(1/13) [13 * 3 + 1]

Hence, they both Bihn and Inscoe can do same work in 3(1/13) hours.

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If f (a) = b, then the point that is on the graph of f(x) is; (a, b)

The domain of a function is defined as the set of all possible input values that makes the function possible. Meanwhile, the range of a function is the set of all possible output values that makes the function possible.

Now, we are given that f(a) = b.

Usually when denoting the value of the input of a function, we can say for example that f(x) = y which means that at the input value of x, the output of the function is y and as such, (x, y) is a coordinate of the function or graph.

Thus, in our question, we can say that (a, b) is a coordinate of the graph f(a) = b

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Answer: Answer C is correct. :)

Step-by-step explanation:

Answer:

x = 22/5; m∠TKW=m∠XHK = 15.2°

Step-by-step explanation:

Angles TKW and XHK are corresponding angles (as they lie on the same side of the traversal and on the bottom left side of their respective lines) and are thus congruent and equal.

By setting the two equations equal to each other, we can find the value.

After this, we can plug in x for any one of the equations and find the measure of both angles:

[tex]8x-20=3x+2\\8x=3x+22\\5x=22\\x=\frac{22}{5} \\\\TKW=8(\frac{22}{5})-20\\ TKW=\frac{176}{5}-20\\ TKW=\frac{76}{5}=15.2\\ TKW=XHK[/tex]

Clearly,  it is a reduction with scale factor 2

The rightmost line of the black figure has  8 units and pink has 4 units similarly the first horizontal link of black has 4 while pink has 2 units. By labeling the sides of both figures and finding the ratio of the sides of the black figure to the pink figure is 2 so it is deduced that the scale factor is 2 and its reduction as black figure is an enlargement of pink.

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The pink figure is a dilation image of the black figure. The labeled point is the center of dilation. The dilation is a reduction with scale factor 2.

In mathematics, dilation means Reducing the object's size by dilation is a change. The items are enlarged or shrunk through dilation. An image that retains the original shape is created by this alteration. The size of the form does differ, though.

The rightmost line of the black figure has  8 units and pink has 4 units similarly the first horizontal link of black has 4 while pink has 2 units. By labeling the sides of both figures and finding the ratio of the sides of the black figure to the pink figure is 2 so it is deduced that the scale factor is 2 and its reduction as black figure is an enlargement of pink.

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The estimate of a 5 % tip on a bill of 83.46 by first rounding the bill amount to the nearest ten dollars is; 4 dollars.

It follows from the task content that the estimate of a 5 % tip on a bill of 83.46 by first rounding the bill amount to the nearest ten dollars is to be determined.

First, the bill amount; 83.46 must be rounded to the nearest ten dollars so that we have;

83.46 which is approximately; 80 dollars when rounded to the nearest ten.

Therefore, 5% of the required bill is; (5/100) × 80

= 4 dollars.

Therefore, the required estimate of the tip is; 4 dollars.

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By using unitary method, it can be calculated that Height of the tree is 30 feet

What is unitary method?

Unitary method is the process in which the value of single unit can be calculated from the value of multiple unit and the value of multiple unit can be calculated from the value of single unit. Sometimes Value of single unit can be less than the value of multiple unit. For example - The relation between the cost of a commodity and the quantity of the commodity

Sometimes Value of single unit can be more than the value of multiple unit. For example - The relation between the number of men and the number of days taken by those men to do a certain job.

This is a problem on unitary method

A shadow of 4.5 feet long is casted  by my friend 5 feet tall

A shadow of 1 feet is casted by an object of height [tex]\frac{5}{4.5} \ feet[/tex]

A shadow of 27 feet is casted by a tree of height [tex]\frac{5}{4.5}\times 27 \ feet[/tex]

A shadow of 27 feet is casted by a tree of height 30 feet

Height of the tree is 30 feet

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Answer:

1/2

Step-by-step explanation:

9 x 3 x 1/2 = 27 x 1/2 = 27/2 = 13 1/2

13 1/2 - 13 = 1/2

1/2 cups of ketchup are remaining.

Answer:

C. $4.00

Step-by-step explanation:

Profit, which is given by [tex]P(x)[/tex], is maximized when the price per drink is $4.00, as shown on the graph.

The measurement of angle DBC is 100°. It can be obtained by the properties of bisector of an angle and algebriac multiplication.

What is angle bisector?

An angle bisector is the ray or line segment that divides the angle into two equal parts.

Since the segment BD bisects angle ABC hence,

∠ABC = ∠ABD+∠DBC               ..... (1)

Also, since segment BD bisects angle ABC hence,

∠ABD = ∠DBC

Use this fact in equation (1)

∠ABC = ∠ABD+∠ABD

∠ABC =2 ∠ABD

Now, substitute values and use algebriac multiplication.

7x = 2(3x+25)

7x = 6x+50

7x - 6x= 50

x=50

Now, substitute the value of x in the expression of ∠ABD.

∠ABD = 3x+25

∠ABD = 3(50)+25

∠ABD = 100

Now, since ∠ABD = ∠DBC hence, ∠DBC = 100.

Hence, the measurement of angle DBC is 100°.

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Answer:

B: (5,3)

Step-by-step explanation:

We just fill in the coordinates

A: (7,9)

9=7-2

9=5

not true

B: (5,3)

3=5-2

3=3

true

C: (7,14)

14=7-2

14=5

not true

D: (5,7)

7=5-2

7=3

not true

so b is the only correct answer

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