The first term of an arithmetic sequence is 1 and the sum of the first four terms is 100. Find the first four terms ​

Answer:

There are no "following values" in the problem.

Step-by-step explanation:

ƒ(x) = -2x + 3

For any value of X, enter that number in the equation and calculate f(x) [y].

For example, if x is 2:  

ƒ(x) = -2x + 3

ƒ(2) = -2(2) + 3

y =  -2(2) + 3

y = -4+3

y = -1

The ordered pair for when x=2 would be (2,-1)

Answer:

∠1 and ∠2, ∠7 and ∠8

Answer:

∠1 and ∠7, ∠2 and ∠8

Step-by-step explanation:

just took the quiz

Answer:

i think 150 degrees

Step-by-step explanation:

the 30° angle and ∠1 are a linear pair, and are supplementary. therefore they add up to 180°
∠1 + 30° = 180°

The cost of the path around the swimming pool with length 15m and width 12m is $1,190

Pathway with 2m wide:

Area of the path = length × width

= 17m × 14m

= 238 square meters

Total cost of the path = 238 square meters × $5

= $1,190

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The proportion that is equivalent to the original equation is [tex]\frac{x+1}{2x} =\frac{x^2-7x+10}{4x}[/tex]

Given the following expression

[tex]\frac{1}{2} + \frac{1}{2x} =\frac{x^2-7x+10}{4x}[/tex]

In order to find the equivalent proportion, we will find the LCM of the right side expression to have:

[tex]\frac{1}{2} + \frac{1}{2x} =\frac{x^2-7x+10}{4x}\\\frac{x+1}{2x} =\frac{x^2-7x+10}{4x}[/tex]

Hence the proportion that is equivalent to the original equation is [tex]\frac{x+1}{2x} =\frac{x^2-7x+10}{4x}[/tex]

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Answer: For the next part

✔ x = 1 and x = 8

✔ x = 0

Unit conversion is a way of converting some common units into another without changing their real value. The correct option is D.

Unit conversion is a way of converting some common units into another without changing their real value. for, example, 1 centimeter is equal to 10 mm, though the real measurement is still the same the units and numerical values have been changed.

The complete question is mentioned in the below image.

Given that 2 inches are 5 centimeters. Therefore, the ratio of an inch to centimeters are,

2 inches = 5 centimeters

1 inch = 5/2 centimetes

Now, if using the ratio, the measurements are converted then,

A.) 7 inches = 7 × (5/2)centimeters = 17.5 centimetes

B.) 5 inches = 5 × (5/2)centimeters = 12.5 centimetes

C.) 8 inches = 8 × (5/2)centimeters = 20 centimetes

D.) 3 inches = 3 × (5/2)centimeters = 7.5 centimetes

As it can be observed that the correct statement is D If 2 inches is 5 centimeters, then 3 inches is 7.5 centimeters. Hence, the correct option is D.

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Figure A is a diagram which represents the statement "If it is a tree, then it has leaves."

In figure A, we can observe that the subset representing "trees" lie inside another subset which represents "has leaves." Thus, we can logically deduce that the statement "All trees have leaves" and "if it is a tree, it has leaves" is represented by figure A.

On the other hand, we can observe that the subset representing "has leaves" lie inside another subset which represents "trees," which contradicts the given statement "If it is a tree, then it has leaves."

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Answer:

Y + 15 = 30

Y = 30 - 15

Y = 15

15 is not equal to 20

False

Answer:

Step-by-step explanation:

The measure of <YAC from the figure is. 68 degrees

The given figure is made up of line and angles.

Since the line AC is tangential to the circle, hence <BAC = 90 degrees and;

<BAY + <YAC = 90degrees

Determine the measure of <BAY

<BAY = 1/2(arcBY)

<BAY = 1/2(44)

<BAY = 22degrees

From the expression above;

<YAC = 90 - 22

<YAC = 68 degrees

Hence the measure of <YAC from the figure is. 68 degrees

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The area  of Vivian’s garage door is 62.5 square feet

The Vivian garage is made up of a trapezoid and a rectangle. The area of the door is expressed as;

Area = Area of rectangle + area of trapezoid

Area = (5 * 8) + 0.5(7 + 8)*3
Area= 40 +22.5
Area = 62.5 square feet

Hence the area  of Vivian’s garage door is 62.5 square feet

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Answer:

3(4n) + 2 + 6n

12n + 2 + 6n

12n + 6n + 2

18n + 2 is not equal to 13n + 2

hence both the expression are not equivalent

By analytical methods and algebraic handling and on the basis that x is increased by 25 %, we conclude that the variable x² is increased by 18.75 %.

In this case we have a linear variable x, whose increase is described by the following expression:

y = x · (1 + r/100)     (1)

Where r is the increase rate.

If we square (1), then we find that:

y² = x² · (1 + r/100)² = (1 + r'/100)     (2)

Where r' is the equivalent increase rate.

(1 + r/50 + r²/10000) = (1 + r'/100)

r'/100 = r/50 + r²/10000

r' = r/2 + r²/100

If we know that r = 25, then the equivalent increase rate is:

r' = 25/2 + 25²/100

r' = 18.75

By analytical methods and algebraic handling and on the basis that x is increased by 25 %, we conclude that the variable x² is increased by 18.75 %.

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By applying a composition of f(x) = - (1/2) · x² + 5 · x with respect to g(x) = x² + 2 and evaluating the resulting expression at x = - 2, the value of f(g (-2)) is 12. (Correct choice: C)

Let be f and g functions, there is a composition of f with respect to g when the input of the former is substituted by the output of the latter. It is to notice that composition is a binary operation between functions.

If we know that f(x) = - (1/2) · x² + 5 · x, g(x) = x² + 2 and x = -2, then the composed function evaluated is:

f(g (x)) = - (1/2) · (x² + 2)² + 5 · (x² + 2)

f(g (- 2)) = - (1/2) · 6² + 5 · 6

f(g (- 2)) = 12

By applying a composition of f(x) = - (1/2) · x² + 5 · x with respect to g(x) = x² + 2 and evaluating the resulting expression at x = - 2, the value of f(g (-2)) is 12. (Correct choice: C)

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Answer: 98

Given following:

[tex]\Longrightarrow \sf x = \dfrac{\sqrt{3} +\sqrt{2} }{\sqrt{3} - \sqrt{2} }[/tex]

[tex]\Longrightarrow \sf y = \dfrac{\sqrt{3} -\sqrt{2} }{\sqrt{3} + \sqrt{2} }[/tex]

Solve for x² + y²:

[tex]\rightarrow \sf \left(\:\dfrac{\sqrt{3}\:+\sqrt{2}\:\:}{\sqrt{3}\:-\:\sqrt{2}\:}\right)^2\:+\:\left(\dfrac{\sqrt{3}\:\:-\sqrt{2}\:\:}{\sqrt{3}\:+\:\sqrt{2}\:\:}\:\right)^2[/tex]

simplify following

[tex]\rightarrow \sf 49+20\sqrt{6}+49-20\sqrt{6}[/tex]

add/subtract similar terms

[tex]\rightarrow \sf 98[/tex]

Answer:

14.16

Step-by-step explanation:

we first calculate the total amount of money paid, which is 35.40 plus 20%, we use this calculation:

35.40×1.20 = 42.48

now, this amount is split to 3 people, so:

42.48/3 = 14.16

and that is our answer

The regression line is y = 10x + 300, and the value of calories is 90 and when x = 14 the value of y = 440 from the regression line, but the actual value is 330.

A mathematical notion called the line of the best fit connects points spread throughout a graph.

It's a kind of linear regression that uses scatter data to figure out the best way to define the dot's relationship.

From the data given, we can write the slope and y-intercept form:

y = mx + b

here, m = 10 and b = 300

y = 10x + 300

The number of fat grams in an item has that number of fat calories.

As we have the regression line:

y = 10x + 300

Put x = 1 in the regression line:

y = 10(1) + 300

y = 310 calories

For x = 14

y = 10(14) + 300 = 440

But the actual value from the graph is 330.

Thus, the regression line is y = 10x + 300, and the value of calories is 90 and when x = 14 the value of y = 440 from the regression line, but the actual value is 330.

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Answer: If Peter bought 8 toys, the cost of the toys will be 29.

From the equation, y = 3x + 5, they have given the value of x as eight. So if we put eight in the equation and solve it, we will get the value of y. I believe there are some errors in the question as it doesn't specify that y is the cost. Also cost requires some sort of unit, which is not given in the context. I can't really tell if it is dollars or rubles or pounds etc. So I just gave it as the way it is. Since no other clues are given, this is most likely it.

y = 3x + 5

y = 3(8) + 5

y = 24 + 5

y = 29

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The way that the consistency of data is evaluated if more than one data collector is used is; Inter - rater reliability

When researching data about anything, it is pertinent to note that sometimes, we have to use more than one data collector just to get a more thorough result which only one person may not be able to generate.

Now, the way that consistency of data is evaluated when more than one data collector is used is via Inter-rater reliability. This is because Inter-rater reliability is the extent to which two or more raters or observers agree.

The benefit of Inter-rater reliability is that It addresses the issue of consistency of the implementation of a rating system. Inter-rater reliability can be evaluated by using a number of different statistics.

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The true statement is Peter walks at a rate of 13 over 4 miles per hour.

Direct variation is when two variables move in the same direction. If one variable increases, the other variable increases. When the hour Peter walks increases, the distance he walks also increases.

Here are the options:

Peter walks at a rate of StartFraction 4 over 13 EndFraction miles per hour.

Peter walks at a rate of 4 miles per hour.

Peter walks at a rate of StartFraction 13 over 4 EndFraction miles per hour.

Peter walks at a rate of 13 miles per hour.

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The range in the average rate of change in temperature of the substance is from a low temperature of 1 F to a high of -11 F.

The conversion formula for a temperature that is expressed on the Celsius (°C) scale to its Fahrenheit (°F) ;

°F = (9/5 × °C) + 32.

Given function:

f(x)= -6 sin(7/3 x+ 1/6) -5

The function will be maximum at the 7/3 x +1/6= 3π/2

So, the maximum temperature will be

= -6 sin (3π/2) -5

= 6 -5

= 1 F

The function will be minimum at the 7/3 x +1/6= π/2

Therefore, the maximum temperature will be

= -6 sin (π/2) - 5

= -6 -5

= -11 F

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Answer:

D. 4

Explanation:

Linear relationship refers to relationships which give straight lines when graphed. All the segments, except segment 4, show straight-line, linear relationships.

As section 4 is curved, it show nonlinear relationship.

Answer:

440cm²

Step-by-step explanation:

*Area= (a+b)/2×h

(19+25)/2*20

= _ * 440cm². *_

Answer:

440cm²

Step-by-step explanation:

I believe its right

Answer:

  2

Step-by-step explanation:

Corresponding sides are proportional in these similar triangles.

__

  short side/long side = k/4 = 4/8

  k = 4(4/8) . . . . multiply by 4

  k = 2

_____

Additional comment

The lengths of the hypotenuses can be found the same way, or using the Pythagorean theorem. Using side ratios, we have ...

  l² = k(k+8) = 2(10) = 20 . . . . from MN/MO = ML/MN

  l = 2√5

  m² = 8(8+2) = 80 . . . . from LN/LO = LM/LN

  m = 4√5

The similarity statements are ...

  ΔLMN ~ ΔLNO ~ ΔNMO

The shape of the cross-section resulting from the cut is rhombus.

A rhombus simply means a shape that has opposite sides to be parallel and the sides are equal.

Given:

object is cut by a vertical plane containing A and B and bisecting two of the horizontal edges.

Edges of the object in the diagram are equal in length and that the object is cut by a vertical plane containing A and B.

Hence, the shape of the cross-section resulting from the cut is a rhombus.

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We have the equation of a line:

[tex]y=-\dfrac{5}{4}x-1[/tex]

The formula of a slope of a line passes through points A, B:

[tex]A(x_A,\ y_A),\ B(x_B,\ y_B)\\\\m=\dfrac{y_B-y_A}{x_B-x_A}[/tex]

Complete the table:

Put the values of x to the equation of a line and calculate the value of y:

[tex]x=0\\\\y=-\dfrac{5}{4}\cdot0-1\\\\y=-1\\\\\\x=4\\\\y=-\dfrac{5}{4}\cdot4-1\\\\y=-6[/tex]

Substitute to the formula of a slope:

[tex]m=\dfrac{-6-(-1)}{4-0}\\\\m=\dfrac{-6+1}{4}\\\\\huge\boxed{m=-\dfrac{5}{4}}[/tex]

Answer:

I don't see a correct answer.  See below.

Step-by-step explanation:

Thanks for clarifying the question.  But if 27√3 is the correct expression, I don't see an answer option that fits.  

√3 = 1.732

27*(1.732) = 46.77

But all the answer options are whole numbers.  The presence of√3 makes it difficult to find an expression that would result in a whole number.  Expressions such as:

27/√9 = 9, or

√27/√3 = 3

would be more consistent with producing a whole number result.

I hope this helps.

Answer:

p = 39       f = 44    

Step-by-step explanation:

p = $ 1.73

f = $ 1.44

equation

p + f = 83

1.73 p + 1.44 (83 - p) = $ 130.83

p = 39 (amount of times fruit pies were sold).

Therefore,

p = 39

f = 44