Point G is on line segment FH. Given FH = 4x, GH = x, and FG = 2x + 10,
determine the numerical length of FG.

Answer:

It is ture.

4x-3=2x+13

2x-3=13

2x=16

x=8

Answer: Direct proportion because as the time goes up the distance goes up

Answer:

31° = x

Step-by-step explanation:

According to the Supplementary Angles Theorem, 123° and that acute angle right up against it, form a straight angle, so you do this:

[tex] - 123 + 180 = 57[/tex]

Now that the second angle measure is found, according to the Triangular Interior Angles Theorem, the sum of the interior angles of all triangles add up to 180°:

180° = 57° + 92° + x°

|________|

180° = 149° + x°

-149° - 149°

________________

31° = x

I am joyous to assist you anytime.

Answer:

A is true.

Step-by-step explanation:

Cos θ = adjacent / hypotenuse = x/1 = x.

Cosθ has a period pf 2π.

Answer:

The correct option is A.

Step-by-step explanation:

Draw a perpendicular form point P on x-axis.

Radius of unit circle is 1 . It means in triangle OPA

Hypotenuse = OP = 1 units

Adjacent= OA = x

Perpendicular = PA = y

In a circle angled triangle,

[tex]\cos \theta = \frac{adjacent}{hypotenuse}[/tex]

In triangle OPA,

[tex]\cos \theta = \frac{x}{1}[/tex]

[tex]\cos \theta =x[/tex]

The x-coordinate of P corresponds to cosθ.

The period of a unit circle is 2π.

Therefore, the correct option is A.

Answer:

D

Step-by-step explanation:

the value of 6 in 5426.37 is 6 which is 1/10 of 60 so the answer is 1565.44

Answer: [tex]75\%[/tex]

Step-by-step explanation:

You know that the ratio of the television's screen is [tex]5:4[/tex] . This ratio can be also written as the following fraction:

[tex]\frac{5}{4}[/tex]

The television shows an image with a ratio of [tex]20:12[/tex] which can be also written as a fraction:

[tex]\frac{20}{12}[/tex]

Set up the following proportion and solve for "x":

[tex]\frac{20}{x}=\frac{5}{4}\\\\x=\frac{4*20}{5}\\\\x=16[/tex]

Now, in order to find the percent of the screen area occupied make the following division:

[tex]\% occupied=\frac{12}{16}*100=75\%[/tex]

Answer:

x = 3

Step-by-step explanation:

[tex]7x-3(x+6)=30[/tex]

Isolate the variable by dividing each side by factors that don't contain the variable.

Answer:

Step-by-step explanation:

Answer:

|x - 4| ≤ 2

-2 ≤ x - 4 ≤ 2

2 ≤ x ≤ 6

The answers are shown below:

The arithmetic mean of a given data is the sum of all observations divided by the number of observations. For example, a cricketer's scores in five ODI matches are as follows: 12, 34, 45, 50, 24. To find his average score in a match, we calculate the arithmetic mean of data using the mean formula:

Mean = Sum of all observations/Number of observations

Mean = Sum of all observations/Number of observations

Mean = (12 + 34 + 45 + 50 + 24)/5

Mean = 165/5 = 33

The value of the middlemost observation, obtained after arranging the data in ascending or descending order, is called the median of the data.

For example, consider the data: 4, 4, 6, 3, 2. Let's arrange this data in ascending order: 2, 3, 4, 4, 6. There are 5 observations. Thus, median = middle value i.e. 4.

Given data:

0, 40, 60, 70, 75, 80, 85, 95, 95, 100

a)Mean without '0' = 40+ 60+ 70+ 75+ 80+ 85+ 95+ 95+ 100/9

                            = 700/9

                            = 77.777

Median without '0' = 80

Mean with ' 0' = 0+ 40+ 60+ 70+ 75+ 80+ 85+ 95+ 95+ 100/10 = 70

Median with '0' = 80

b)standard deviation= 18.121673811445. (without '0')

standard deviation with 0 = 28.982753492379

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Answer:

[tex]F(x)=\frac{x^2+4x+4}{x^3+5x^2}[/tex]

Step-by-step explanation:

Graph the rational function.

Answer:

[tex]\frac{3}{2}[/tex] c

Step-by-step explanation:

Given

[tex]\frac{3a+3b}{2a-2b}[/tex] ← factor numerator and denominator

= [tex]\frac{3(a+b)}{2(a-b)}[/tex]

= [tex]\frac{3}{2}[/tex] × [tex]\frac{a+b}{a-b}[/tex] = [tex]\frac{3}{2}[/tex] c

Answer:

k > 4

Step-by-step explanation:

Answer:

k< 4

Step-by-step explanation:

6(k-5)<-6

divid by : 6       (k-5)<-1

add : 5    k<-1+5

k< 4

Answer:

17

Step-by-step explanation:

if 3 pizzas serve 12 people then 17 pizzas can serve 68 people.

A ratio is a comparison between two similar quantities in simplest form.

Proportions are of two types one is the direct proportion in which if one quantity is increased by a constant k the other quantity will also be increased by the same constant k and vice versa.

In the case of inverse proportion if one quantity is increased by a constant k the quantity will decrease by the same constant k and vice versa.

Given, 3 pizzas serve 12 people.

Assuming y = kx.

12 = 3k.

k = 4.

Now,

68 = 4x.

x = 17

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Answer:

The cost of one bag of diapers is $11 and the cost of one can of formula is $13

Step-by-step explanation:

Let

x -----> the cost of one bag of diapers

y ----> the cost of one can of formula

we know that

[tex]x+2y=37[/tex] -----> equation A

[tex]2x+5y=87[/tex] ----> equation B

Solve the system by graphing

Remember that the solution of the system is the intersection point both graphs

The solution is the point (11,13)

see the attached figure

therefore

The cost of one bag of diapers is $11 and the cost of one can of formula is $13

Final answer:

The cost of one bag of diapers is $11, and the cost of one can of formula is $13, as determined by solving a system of two linear equations that describe Malik's purchases.

Explanation:

The student is presented with a system of linear equations based on the purchases made by Malik at different times. The purchases involve a bag of diapers and cans of formula, with the total amounts spent being provided. This information can be turned into a system of equations to solve for the price of one bag of diapers and the price of one can of formula.

Let D represent the cost of one bag of diapers and F represent the cost of one can of formula. From the given information, we can construct the following equations:

D + 2F = $37 (Equation 1: One bag of diapers and two cans of formula cost $37)

2D + 5F = $87 (Equation 2: Two bags of diapers and five cans of formula cost $87)

Now, let's solve this system of equations using the method of substitution or elimination. For simplicity, let's use the elimination method:

Multiply Equation 1 by 2, so it can be arranged to eliminate D:
2D + 4F = $74

Subtract Equation 1 modified from Equation 2:
(2D + 5F) - (2D + 4F) = $87 - $74,
which simplifies to F = $13.

Now plug the value of F back into Equation 1:
D + 2($13) = $37,
D + $26 = $37,
therefore D = $37 - $26,
D = $11.

Therefore, the cost of a bag of diapers is $11, and the cost of one can of formula is $13.

Answer:

1. yes

2. no

3. yes

4. no

5. yes

Step-by-step explanation:

The method i use is if the number is not a fraction than it is an integer. besides 6 for some reason.

Here is the catch if the fraction can be simplified into a whole number than it is an integer.

The explanatory variable is the car's weight, with fuel efficiency as the response variable; a likely negative association may exist, possibly linear or non-linear; a correlation like r=-0.9 or r=-0.6 is plausible; an 'unusual point' could be an outlier affecting the correlation; removing it might strengthen or weaken the correlation; converting weights to metric tons wouldn't alter the correlation.

(a) In this context, the explanatory variable is the car's weight (in pounds) and the fuel efficiency (in miles per gallon) is the response variable. This is because we are typically interested in determining the effect of a car's weight on its fuel efficiency.

(b) Based on the context, a scatterplot might show a negative association between the car's weight and its fuel efficiency. This would make sense as heavier cars often require more fuel to operate efficiently, leading to lower miles per gallon.

(c) The form of the relationship between car weight and fuel efficiency can vary. For instance, it could be linear (indicating a constant rate of change) or non-linear (indicating a rate of change that varies with weight).

(d) Without viewing the scatterplot it's not possible to definitively answer this, but based on the proposed negative relationship, a correlation of r=-0.9 or r=-0.6 would be plausible. Correlations range from -1 to 1, and a negative sign indicates an inverse relationship.

(e) An 'unusual point’ could be an outlier on the scatterplot that doesn't model the relationship between car weight and fuel efficiency like the rest of the data. This could be due to factors unique to this car, such as a highly efficient engine that gets more miles per gallon despite its weight

(f) Depending on the unique characteristics of the 'unusual point', its removal could either increase or decrease the correlation. If this point were causing the correlation to be weaker, its removal would cause the correlation to strengthen, and vice-versa.

(g) Converting the car weights to metric tons wouldn't change the correlation between weight and fuel efficiency. Correlation is unitless and depends only on the relationship between variables, not the scale they're measured on. Thus, while the specific values for weight would change, the strength, direction, and form of the relationship between weight and fuel efficiency would remain the same.

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Answer:

[tex]14a^{2}b[/tex] + [tex]28ab^{2}[/tex] - 42ab

Step-by-step explanation:

The expression 7ab(2a+4b-6) simplifies as 14a^2b + 28ab^2 - 42ab by distributing 7ab to each number within the parentheses.

This question involves distribution which is a property in Mathematics. To simplify the expression

7ab(2a+4b-6), you need to distribute or multiply 7ab with each number within the parentheses. When we do this step-by-step:

So, the expression 7ab(2a+4b-6) simplifies as 14a2b + 28ab2 - 42ab.

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Answer:

50 shapes

Step-by-step explanation:

If 20% is 10 shapes, then 30% would be 15, 40% would be 20, and so forth. when you get to 100%, the answer would be 50 shapes because the numbers of shapes is half the percentage. For example, 5% is 2.5 shapes, 10% is 5 shapes, 60% is 30 shapes.

CAN EXPLAIN FURTHER

would appreciate brainliest, but I am content with just giving you an answer :)

Answer:

rational

Step-by-step explanation:

it is rational

a rational number is that which is non-terminating (a number which cannot be terminated) and repeating . So 0.99999…. aquires both repeating and non-terminating property . Hence it is a rational number .

Answer: 30,000

Step-by-step explanation: Round 597 to nearest hundred and 52 to nearest ten.

Final answer:

To estimate 597 x 52, round 597 to 600 and 52 to 50, then multiply to get 600 x 50 = 30,000. Therefore, a reasonable estimate is 30,000.

Explanation:

The student has asked for a reasonable estimate for 597 x 52. To provide an estimate, we can round numbers to simplify the multiplication. In this case, we can round 597 to 600 and 52 to 50. Now, let's multiply these rounded numbers.

Therefore, a reasonable estimate for 597 x 52 is 30,000.

No, you cannot draw two triangles each having two 45° angles and one 90° angle that are not similar. All 45-45-90 triangles are similar by definition because they have the same shape, i.e., their angles are the same (two 45° angles and one 90° angle). These similar figures can differ in size, but not in shape.

No, it is not possible to draw two triangles each having two 45° angles and one 90° angle that are not similar. Let's break this down.

All triangles that have two 45° angles and one 90° angle are called 45-45-90 triangles. In a 45-45-90 triangle, the angles are always the same, so they are always similar by the definition of similar figures. Similar figures have the same shape, but not necessarily the same size. Their corresponding angles are congruent (the same) and their corresponding sides are in proportion.

Since all 45-45-90 triangles have the same angles - two 45° angles and one 90° angle - they are all similar to each other, regardless of their size. The size of the triangle does not matter, because the definition of similar figures is based on the shape, not the size. Hence, it is impossible to draw two 45-45-90 triangles that are not similar.

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Answer:

C. (5x^3-7)(2x^2+1)

Step-by-step explanation:

Given expression is,

10x^5+5x^3-14x^2-7

=10x^5-14x^2 + 5x^3 - 7  (By the commutative property)

=2x^2(5x^3-7)+5x^3-7     (Taking 2x^3 common from first two terms )

=(5x^3-7)(2x^2+1)      (Taking 5x^3-7 common from both terms)

\implies 10x^5+5x^3-14x^2-7=(5x^3-7)(2x^2+1)

Hence, Option C is correct

Each crate holds 6 dozen eggs.

1 dozen  = 12 eggs.

Multiply 12 by 6 to get the total number of eggs per crate:

6 x 12 = 72 eggs per crate.

The box holds 4 crates, multiply the number of each in a crate by the number of crates:

72 eggs x 4 crates = 288 total eggs.

Answer:

This answer is 8

Step-by-step explanation:

It actually is very simple. For this question you do not even need the g(x) equation to continue, so put it aside for now. F(x) means that whatever number that will take the place of x will be used in this equation. If f(x)=3x-1, then f(3)=3(3)-1

This happens because the 3 in f(3 tells you to substitute x for 3 in the equation. ) So just plug in 3 for x and solve to get the answer 8.

Answer:

This answer is 8

Step-by-step explanation:

Answer:

factoring c is the best way to solve this

Step-by-step explanation:

S = C ( 1 + R )

C = S/( 1 + R )

The equation after solving is C = S / (1 + R).

To solve for C in the equation S = C + RC, we can factor out C on the right side:

S = C + RC

S = C(1 + R)

Then, we can divide both sides by (1 + R) to isolate C:

S / (1 + R) = C

Therefore, the solution is:

C = S / (1 + R)

For example, if S = 100 and R = 0.1, then C would be:

C = 100 / (1 + 0.1)

C = 100 / 1.1

C = 90.9090909090909

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Answer: I believe the answer is 18 meters

Step-by-step explanation:

Answer:

The perimeter would be 16.

Step-by-step explanation:

3.0+3.0=6

5.0+5.0=10

10+6=16