3.7.2 checkup geometry practice problems

The equation representing the story 2 is equivalent to -

3(x + 6) = 24.

Given is are the mathematical word problems as stories.

According to the story 2 -

Diego has 24 ounces of juice. He pours equal amounts for each of his 3 friends, and then adds 6 more ounces for each.

Let the amount of juice poured for each friend at the start be {x}. Then, we can write it as {3x}. For six ounce more per friend, the expression will be (6 x 3). Total juice will be equal to -

3x + (6 x 3) = 24

3x + 3(6) = 24

3(x + 6) = 24

Therefore, the equation representing the story 2 is equivalent to -

3(x + 6) = 24.

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6 to the 15th power

Step-by-step explanation: for exponents with the same base number just add the exponents (example): 3 to the 3rd power looks like this 3 x 3 x 3  but if we add 3 to the firth power, 3 x 3 x 3 x 3 x 3 then the entire thing becomes 3 to the eighth power, 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3

By using the 68-95-99.7 Rule, the percent of scores in the data set that are expected to be below a score of 120 is 84.13%.

In Mathematics, the Empirical Rule is sometimes referred to as the 68-95-99.7 rule and it can be defined as a statistical rule which states that:

At the middle 68% of the normal distribution, we have the following standard score:

μ - σ = 108 - 12 = 96.

μ - σ = 108 + 12 = 120.

Where:

At the middle 95% of the normal distribution, we have:

μ - σ = 108 - 2(12) = 84.

μ - σ = 108 + 2(12) = 132.

At the middle 99.7% of the normal distribution, we have:

μ - σ = 108 - 3(12) = 72.

μ - σ = 108 + 3(12) = 144.

Now, we can determine the percent (P) of scores in the data set that are expected to be below a score (x) of 120;

P(x < 120) = P((x - μ)/σ < (120 - 108)/12)

P(x < 120) = P((x - μ)/σ < 12/12)

P(x < 120) = P(z < 1)

P(x < 120) = 0.8413

P(x < 120) = 84.13%

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The equation of perpendicular is x+y=3

The equation perpendicular to ax+by+c=0 is bx-ay+c=0.

Here we are given x-y+3=0

a=1,b=-1c=3

the equation is -1x-y+3=0

x+y=3

The equation of perpendicular is x+y=3.

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This measurement written in scientific notation is 4.75 x 10-5 centimeters.

Solution:

Step 1: The given wavelength of blue light is 0.0000475 centimeters.

Step 2: To convert this number into scientific notation, we need to move the decimal point 4 places to the left.

Step 3: This results in 4.75 x 10-5 centimeters.

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Answer:

29+8x

Step-by-step explanation:

Answer:8x+29

Step-by-step explanation:

Distribute the 8 onto the 3+x

We arrive with: 5+24+8x

Add like terms: 29 + 8x

Answer:

the constant of proportionality is 16

Step-by-step explanation:

To find the constant you have to find what 1 equals so when dividing 48 by 3 you get 16.

The volume of gravel in truck bed given its width, height and length is 24 cubic meters

The truck bed has the shape of a cuboid

Volume of a cuboid = Length × width × height

Width of the dump truck= 3 meters

Length of the dump truck= 4 meters

Height of the dump truck= 2 meters

Volume of a cuboid = Length × width × height

= 4 × 3 × 2

= 24 cubic meters

Hence, the gravel in the dump truck has the volume 24 cubic meters

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The way the y-values alter when the x-values rise by a certain amount is different for linear and exponential relationships: The y-values in a linear connection differ equally. The ratios of the y-values are equal in an exponential relationship.

The way the   y-values change when the xx-values rise by a certain amount is different for linear and exponential relationships:

The y-values have equal differences in a connection that is linear.

The y-values have identical ratios in an exponential relationship.

Vertical growth

Think at how this table illustrates the relationship:

x    12   15  18  21

y   -2     5   12  19

Here, the xx-values grow by a constant difference of 3  units,

x           +3                    +3                     +3

       12          15                    18                      21

and the yy-values increase by a constant difference of 7.

y           +7               +7              +7

      -2             5                12              19

Because each y-value is 7 77 more than the one before it, this connection can be characterized as linear.

Exponential growth is a second example.

Think at how this table illustrates the relationship:

x        0     1     2         3

y        1       3   9     27

x              +1              +1             +1

         0               1               2               3

and a 3 constant factor is applied to the y-values.

y                *3              *3           *3

          1              3               9                27

Since each y-value is 3 times more than the one before it, this connection is exponential.

The Complete Question.

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Answer: which tea bag is 60?

Step-by-step explanation:

Answer: ratio of black tea bags = 36, green bags = 24

Step-by-step explanation: first you add the ratio 6 and 4, which will give you ten, then you divide them consecutively by 10 and multiply by 60. this will give you 6/10 [tex]*[/tex] 60 = 36 and 4/10 [tex]*[/tex] 60 = 24.

I hpoe i have satisfied you with my answer

The coordinates of the other two vertices of the square are

Plotting the points shows that the coordinates given are diagonals of the square

The property of the square used now is that the diagonal are equal

Investigating the sets of vertices B (2, 5) and D (0, -3) &  (5, 0) and (-3, 2) will show that they will given equal length of diagonals

B (2, 5) and D (0, -3)

d = √{(x₂ - x₁)² + (y₂ - y₁)²}

d =√{(2 - 0)² + (5 + 3)²}

d =√{4 + 64}

d = √68

(5, 0) and (-3, 2)

d =√{(5 + 3)² + (2 - 0)²}

d =√{64 + 4}

d = √68

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Answer:

4

Step-by-step explanation:

2+2=4

Answer:

Step-by-step explanation:

If x means times and 2 x 1 is equal to 2 because 2 x 1 is just saying I'd there was 2 ones so 2 x 2 is 4 because there is 2 two so it would be 2 +2 is

The overall net force operating on an item in the lateral direction is referred to as a lateral force.

An element of a wooden container or crate that is positioned at an angle to other elements to increase strength.

The square of the hypotenuse's length (c) equals the squares of the lengths of a right triangle's opposite sides (a) and (b), according to the formula a2 + b2 = c2 (b). Therefore, using two arms of 54 units each, we can compute the diagonal's length as follows: (542 + 542) = c2, or the diagonal's squared length.

The total net force operating on an item in the lateral direction is referred to as a lateral force. The horizontal direction and lateral direction are frequently used interchangeably.

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Answer:

$171 each week

Step-by-step explanation:

5643/33 = 171

Answer:

Step-by-step explanation:3/10

a) find that x = 140/2 = 70.

b) side length [tex]x[/tex] the maximum area that the playground can have is x = 70

c)  The maximum area that the playground can have is 980 square meters

a. The playground is a rectangle, and the perimeter of a rectangle is given by 2(l + w) = 2x. The given information is that the perimeter is 280 meters, so we can set up the equation 2x = 280. Solving for x, we find that x = 140/2 = 70.

Now that we know the perimeter, we can find the area of the playground by using the formula A = lw. Since the perimeter is fixed at 280 meters, we can express the area of the playground as a function of x:

A(x) = lw = (x/2)(280 - x) = 140x - x^2

b. To find the side length x that gives the maximum area, we need to take the derivative of the area function and set it to zero.

A'(x) = 140 - 2x = 0

x = 70

c. Plugging x = 70 back into the area function, we get:

A(x) = 140x - x^2 = 140 * 70 - 70^2 = 140 * 70 - 4900 = 980.

The maximum area that the playground can have is 980 square meters.

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Using sampled data from a population (sample space) that has a definite size and follows a particular probability distribution, a Confidence Interval is a region is constructed.

A confidence interval shows the likelihood that a parameter will be between two values that are close to its mean. The level of certainty or uncertainty in a sampling process is measured by confidence intervals.

A Confidence Interval is a zone created using sampled data from a population (sample space) that has a fixed size and follows a specific probability distribution. The interval is built to include a selected population statistic with a certain probability.

A confidence interval in statistics is an educated prediction regarding a population trait. An original estimate plus or minus an error margin makes up a confidence interval (the amount by which you expect your results to vary, if a different sample were taken).

Therefore, the correct answer is option C. neither.

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(7, -1) and are two points that are located on the graph of f-1(x) (6,1)

Make use of the slope formula to determine the slope.

To find the y-intercept (b), use one of the points and the slope.

The slope-intercept form of a line is y = mx + b, and you may obtain the equation for the line by plugging in the values for m and b once you have those values.

Given is the values table:

x f(x) (x)

-1 7

1 6

3 5

4 1

6 -1

To get the inverse function of f-1, swap the points (x)

x f^-1(x) (x)

7 -1

6 1

5 3

1 4

-1

The aforementioned table's points are (7, -1), and (6,1)

Therefore, the points (7, -1) and are on the graph of f-1(x) (6,1).

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Answer: ±i-4

Step-by-step explanation:

To solve this equation by completing the square, we first have to adjust the equation.

Let's rewrite it in this form:

x^2+8x+16+1=0

Then we can complete the square.

(x+4)^2+1=0

(x+4)^2 = -1

x+4 = ±i

x = ±i-4

Two expressions joined by an equals sign form an equation.

a )B(-2, -5) and C(1, 1)

The point - slope form of the equation ,

y- y₁= m (x-x₁) --- (1)

(x₁, y₁) = (-2, -5)

The slope = m

[tex]m =\frac{y_{2}- y_{1}}{x _{2}- x _{1}} \\\\m = \frac{1+ 5}{1 +2} \\\\m = \frac{6}{3} = 2[/tex]

Substituting (x₁, y₁) = (-2, -5)  and m = 2 in (1),

y- y₁=m (x-x₁)

y +5 = 2 (x + 2)

y +5 = 2x + 4a

y = 2x +4 - 5

y = 2x - 1

b ) B(-2, -5) and C(1, 1)

The slope- intercept form of the equation ,

y = mx +b ---- (1)

The slope = m

[tex]m =\frac{y_{2}- y_{1}}{x _{2}- x _{1}} \\\\m = \frac{1+ 5}{1 +2} \\\\m = \frac{6}{3} = 2[/tex]

(x₁, y₁) = (-2, -5)

Substituting (x₁, y₁) = (-2, -5)  and m = 2 in (1),

-5 = 2(-2) + b

-5 = -4 + b

-5 +4 = b

b = - 1

The y- intercept , b is -1

Substituting b = -1  and m = 2 in (1)

y = 2x - 1

c )  B(-2, -5) and C(1, 1)

The general form of the equation,

Ax + By +C = 0 -- (1)

Here,

A = [tex]y_{1} -y_{2}[/tex]  

B = [tex]x _{2}- x _{1}[/tex]

C = [tex]x_{1}y_{2}- x_{2}y_{1}[/tex]

(-5 -1 )x + (1 +2)y + (-2 +5) = 0

-6x + 3y + 3 = 0

3y = 6x - 3

y = 2x- 1

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Two expressions joined by an equals sign form an equation.

a )B(-2, -5) and C(1, 1)

The point - slope form of the equation ,

y- y₁= m (x-x₁) --- (1)

(x₁, y₁) = (-2, -5)

The slope = m

m=y[tex]_{2}[/tex]-y[tex]_{1}[/tex]/x[tex]_{2}[/tex]-x[tex]_{1}[/tex]

m= 1+5/1+2

m=6/3 =2

Substituting (x₁, y₁) = (-2, -5)  and m = 2 in (1),

y- y₁=m (x-x₁)

y +5 = 2 (x + 2)

y +5 = 2x + 4a

y = 2x +4 - 5

y = 2x - 1

b ) B(-2, -5) and C(1, 1)

The slope- intercept form of the equation ,

y = mx +b ---- (1)

The slope = m

m=y[tex]_{2}[/tex]-y[tex]_{1}[/tex]/x[tex]_{2}[/tex]-x[tex]_{1}[/tex]

m= 1+5/1+2

m=6/3 =2

(x₁, y₁) = (-2, -5)

Substituting (x₁, y₁) = (-2, -5)  and m = 2 in (1),

-5 = 2(-2) + b

-5 = -4 + b

-5 +4 = b

b = - 1

The y- intercept , b is -1

Substituting b = -1  and m = 2 in (1)

y = 2x - 1

c )  B(-2, -5) and C(1, 1)

The general form of the equation,

Ax + By +C = 0 -- (1)

Here,

A =y[tex]_{1}[/tex]-y[tex]_{2}[/tex]  

B = x[tex]_{2}[/tex] -x[tex]_{1}[/tex]

C = x[tex]_{1}[/tex]y[tex]_{2}[/tex] - x[tex]_{2}[/tex]y[tex]_{1}[/tex]

(-5 -1 )x + (1 +2)y + (-2 +5) = 0

-6x + 3y + 3 = 0

3y = 6x - 3

y = 2x- 1

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If in preparation for a party, Tori is putting desserts onto platters and the chocolate cake is cut into 24 pieces and the cheesecake is cut into 42 pieces. the greatest number of platters she can prepare is 6.

Given data:

Chocolate cake = 24 pieces

Cheesecake = 42 pieces

So,

The greatest common divisor (GCF) of 24 and 42 is 6

So,

24 pieces / 6 = 4

42 pieces /6 =7

Based on this he can take 4 chocolate cakes and 7 cheesecake while the greatest  number of platters she can prepare is 6.

Therefore 6 is the  greatest number of platters she can prepare.

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Explanation:

Let's isolate x.

2x+1 > 11

2x > 11-1

2x > 10

x > 10/2

x > 5

The inequality sign doesn't flip. It only flips if we multiplied or divided both sides by a negative number.

The solution set consists of values larger than 5. If x was an integer, then the roster set of solutions would be {6, 7, 8, 9, 10, 11, ...}

A non-solution is anything not in that set. If x is an integer, then a non-solution lives in the set {..., -3, -2, -1, 0, 1, 2, 3, 4, 5}.

Pick one of those values to write the final answer. I'll go with the value 2.

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

Check:

2x+1 > 11

2*2 + 1 > 11 ... replace x with 2

4 + 1 > 11

5 > 11

We arrive at a false statement to show that x = 2 is a non-solution.

In the triangle ΔMRW the measure of ∠W = 80°.

What is a triangle?

A triangle is a three-sided polygon with three vertices. The triangle's internal angle, which is 180 degrees, is constructed. It implies that the internal angles of a triangle add up to 180 degrees. It is the polygon with the fewest sides.

In the given ΔMRW the measure of ∠R = 50°.

In the image it can be seen that ∠W and ∠M are not equal to or greater than 90°.

In the image it can also be seen that ∠M and ∠R are equal as WR = WM and ΔMRW is a isosceles triangle.

Hence, the angles ∠W and ∠M are acute angles.

Let the measure of ∠W be x.

It can be seen in the diagram that ∠M = 50°.

Also, when the triangle is measured using a protractor the measure of ∠M is found to be 50°.

Then it is known that sum of angles of a triangle results in 180°.

∠W + ∠M + ∠R = 180°

So, substitute the values of the angles in the equation -

x + 50° + 50° = 180°

x + 100° = 180°

x = 180° - 100°

x = 80°

Therefore, the value for ∠W = 80°.

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Therefore, in the rhombus figure whose vertices are Ox=6, x is equal to 12.Equation is (2x + 39)0 and (6x-9)° and the values of Ox are 7.5, 12, 18, and 18.75.

Having four edges and four corners, a quadrilateral is a four-sided polygon in geometry. The phrase is a contraction of the Latin terms quadri and latus (meaning "side"). Having four sides, four vertices, and four corners, a rectangle is a two-dimensional form. Essentially, there are two types of concave and convex. Convex quadrilaterals can also be divided into a number of subclasses, such as trapezoids, parallelograms, rectangles, squares, and rhombuses. A rectangle is a form that exists in two dimensions and has four straight sides. The various shapes of quadrilaterals include parallelograms, trapezoids, rectangles, kites, squares, and rhombuses.

given

2x+39 = 6x-9

2x = 6x - 48

-4x = -48

x = -48 / -4

x = 12

Therefore, in the rhombus figure whose vertices are Ox=6, x is equal to 12.Equation is (2x + 39)0 and (6x-9)° and the values of Ox are 7.5, 12, 18, and 18.75.

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When we add an outlier, the range may increase , but it will never decrease .

We know that the outlier has to do with a value that lies outside the range of the values that we have. It is a value that is not consistent with the rest of the measurement. The outlier may be too large or too small to fit into the rest of the data.

In the case that we have here, we can see that the outlier is a value that is very much higher than the rest of the measurement and this outlier is going to make the range of the measure to increase.

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The product of 7 and the cube of a number, N is 7N³

Word problems are sentences describing a 'real-life' situation where a problem needs to be solved by way of a mathematical calculation.

In order to determine the product of 7 and the cube of a number. We need to represent the number with a letter.

Let N represent the number.

Thus, we can then write that the product of 7 and the cube of a number, N is:

7 × N³ = 7N³

Note: product means multiplication

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The unit rate for the graph given is 5/4 cm s⁻¹.

Given is a graph as shown in the image.

Unit rate is defined as the rate at which {y} changes per unit change in {x}. Mathematically -

{r} = Δy/Δx

{r} = (y₂ - y₁)/(x₂ - x₁)

We can write the unit rate as -

r = (10 - 0)/(8 - 0)

r = 10/8

r = 5/4

Therefore, the unit rate for the graph given is 5/4 cm s⁻¹.

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The maximum possible number of parasites for the class containing the value 47 is equal to 50.

In a frequency distribution table, a class width can be defined as the difference between the upper (maximum) and lower (minimum) boundaries of any class in a data set. This ultimately implies that, all classes must all have the same width in a frequency distribution table or histogram.

Mathematically, the class width of a data set can be calculated by using this formula:

Class width = max - min

Where:

Based on the histogram above, the class width with a value of 47 is given by;

Class width = 45 to 50

Therefore, the maximum (upper) possible number is 50.

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