Find the greatest common factor of 28 and 42.
2
4
7
14

Answer:

[tex]\sqrt{28} \approx 5.3[/tex]

Step-by-step explanation:

The Pythagorean Theorem says if you have a right triangle, then relationship between the three sides is the sum of the square of each leg is the hypotenuse squared.

So [tex]a^2+b^2=c^2[/tex]

where a and b are legs and c is the hypotenuse.

Plug in your a,b, and c. In this case it is a,6, and 8.

This means we have

[tex]a^2+6^2=8^2[/tex]

Simplify where you can before we begin the solving (the moving around of things to other sides).

[tex]a^2+36=64[/tex]

Now time for the solving. We are first going to get [tex]a^2[/tex] by itself.

To do this, we just need to subtract 36 on both sides giving us:

[tex]a^2=64-36[/tex]

[tex]a^2=28[/tex]

Now to get rid of the square on a, just square root both sides:

[tex]a=\sqrt{28}[/tex].

Answer:

90 sq. ft.

Step-by-step explanation:

To find the "volume," you will need to multiply every the LxWxH.

Length = L

Width = W

Height = H

Then the answer is 90 sq. ft.

Answer:

Surface area = 126 square ft .

Step-by-step explanation:

Given : Rectangular cuboid .

To find : Find the total area of the solid figure.

Solution : We have given Rectangular cuboid .

Length = 3 ft .

Width = 5 ft .

Height = 6 ft .

Surface area = 2 ( l*w + w*h + l *h).

Plug the values

Surface area = 2 ( 3*5 + 5*6 + 3 *6).

Surface area = 2 (15 + 30 + 18).

Surface area = 2 ( 63).

Surface area = 126 square ft .

Therefore, Surface area = 126 square ft .

Answer:

B

Step-by-step explanation:

Answer:

Its B) 60°

Step-by-step explanation:

135°=75°+CAD

135°-75°=CAD

60°=CAD

Answer:

B. All squares are rectangles.

Step-by-step explanation:

B is the correct answer, because all the squares are rectangles have 4 sides.

The accurate statement is that all squares are rectangles.

The statement that is true among the options provided is All squares are rectangles. This is because squares have all the properties of a rectangle, which is a quadrilateral with four right angles, but with the additional property of having all four sides of equal length. Therefore, because a square fulfills all the criteria of a rectangle, we can conclude that all squares are indeed rectangles. On the other hand, not all rectangles are squares since rectangles do not require all sides to be equal, only that the opposite sides are equal. Similarly, not all quadrilaterals are rectangles because other quadrilaterals, like rhombuses or kites, do not have the necessary four right angles. Finally, while all rectangles are parallelograms (a quadrilateral with opposite sides that are equal and parallel), not all parallelograms have right angles and thus are not all rectangles.

To elaborate, a rectangle is defined as a parallelogram with right angles. When it comes to comparing areas, the area of a rectangle is calculated by multiplying its base by its height. And in the case of squares, since all sides are equal, it's just the side length squared. However, when you have two shapes with equal area -- for instance, a square and a rectangle -- the one with the longer perimeter would be the one with the less compact shape, which in most cases would be the rectangle unless it is also a square.

Answer:

[tex]\frac{2}{3}\text{ feet}[/tex]

Step-by-step explanation:

Let the equation that models the height of the tree after x years,

y = mx + c

Where, m is constant amount of increasing and c is any constant,

Given,

When x = 0, y = 4,

⇒ 4 = m(0) + c ⇒ c = 4,

Now, the height of plant after 4th year = m(4) + c = 4m + c

Also, the height of plant after 6th year = m(6) + c = 6m + c

According to the question,

6m + c is [tex]\frac{1}{5}[/tex] more than 4m + c,

[tex]6m+c=4m+c + \frac{1}{5}(4m+c)[/tex]

[tex]6m+c = \frac{6}{5}(4m+c)[/tex]

[tex]30m+5c=24m+6c[/tex]

[tex]6m=c[/tex]

By substituting the value of c

6m = 4

⇒ [tex]m=\frac{4}{6}=\frac{2}{3}[/tex]

Hence, 2/3 feet of height is increased each year.

Answer:

765.

Step-by-step explanation:

Sum of n terms = a1 (r^n - 1) / (r - 1) where a1 = the first term and r = the common ratio.

Here r = 6/3 = 2 and  a1 = 3.

Sum of 8 terms = 3 * ( 2^8 - 1) / 2 -1)

= 3 * 255

= 765 (answer).

By looking at the graph, we can visually determine that the value of y when point x = -2 is -4.

Answer:

-4

Step-by-step explanation:

The y value at x=-2 is -4 because when you go to -2 on the x-axis the function is below there.  You can only go straight up or straight down to determine the y-value that corresponds to x=-2 so we go down because the function is below the x-axis there.

We are going to go down until we get on the graph of the line.  Scroll over with eyeballs to see that the y there is -4 (use the y-axis).

So the ordered pair (-2,-4) is on our line and when x=-2, y=-4.

Another example:

y=0 when x=2

Another example:

y=2 when x=4

Another example:

y=-3 when x=-1

Answer: 0.8025

Step-by-step explanation:

Given : The number of defective calculators : 17

The number of calculators are not defective : 37

Total calculators : 37+17=54

The probability of the calculators are defective : [tex]\dfrac{17}{54}=\dfrac{1}{3}[/tex]

Binomial distribution formula :-

[tex]P(x)=^nC_xp^x(1-p)^{n-x}[/tex], where P(x) is the probability of success in x trials, n is total trials and p is the probability of success for one trial.

The probability that at least one of the calculators is defective is given by :-

[tex]P(x\geq1)=1-P(0)\\\=1-(^4C_0(\dfrac{1}{3})^0(1-\dfrac{1}{3})^4)\\\\=1-(\dfrac{2}{3})^4=0.80246913\approx0.8025[/tex]

Answer:

Step-by-step explanation:

They are all true

the answer is a

a square should have 4 lines or sides the same length any longer or shorter would make it a rectangle

Explanation:

A fraction of an hour costs the same as an hour.

  actual time ⇒ time charged ⇒ cost of parking

  5 min ⇒ 1 hour ⇒ $3

  1 hour ⇒ 1 hour ⇒ $3

  1 hour 50 min ⇒ 2 hours ⇒ $6

  2 hours ⇒ 2 hours ⇒ $6

  2 hours 1 min ⇒ 3 hours ⇒ $9

  3 1/2 hours ⇒ 4 hours ⇒ $12

Answer:

x=9

Step-by-step explanation:

I have answered ur question

Answer:

4.

Step-by-step explanation:

The smallest number of hot dogs packages and hot dog buns that has the same amount of is the least common multiple between 6 and 8.

6 = 3*2

8 = [tex]2^{3}[/tex]

So, the least common multiple is the product of each multiple with the biggest exponent, that is [tex]2^{3}*3=24[/tex]. Then, Xanthia has to buy 4 hot dog packages to have 24 hotdogs and 24 hotdog buns.

To solve this problem, we first find the least common multiple (LCM) of 6 and 8. 6=2*3 and 8=2^3, so their LCM is 2^3*3=24. Therefore, Xanthia can buy 24÷6=4 hot dog packages and 24÷8=3 hot dog bun packages to have an equal number of hot dogs and hot dog buns. So you have an answer of 4.

Please give me brainliest, I'm trying to get to a higher rank... You don't have to tho, I respect that someone else deserves it sometimes.

Answer:

2/3

Step-by-step explanation:

These two figures are similar since they have the same shape but not the same size

Yellow figure is larger than the orange figure therefore, the yellow figure is a larger or a dilated version of the orange figure.

Scale factor = Small side

                       Large side

Scale factor = 10/15

Scale factor = 2/3

The scale factor of this dilation is 2/3. The orange figure is dilated 2/3 times to form the yellow figure.

!!

Answer:

It's 2/3

Step-by-step explanation:

Trust me

Answer:

  y = 2/3x + 5/3

Step-by-step explanation:

The slope of the line is ...

  slope = (change in y)/(change in x) = (3-1)/(2-(-1)) = 2/3

Then the point-slope form of the desired line can be written ...

  y = m(x -h) +k . . . . . slope m through point (h, k)

  y = 2/3(x +1) +1 . . . . slope 2/3 through point (-1, 1)

  y = 2/3x + 5/3 . . . . . . simplify to slope-intercept form

The equation that describes a line through points (-1, 1) and (2, 3) in slope-intercept form is y = 2/3x + 5/3, determined by calculating the slope and y-intercept.

The question asks to find the equation in slope-intercept form that describes a line through (-1, 1) and (2, 3). In order to do this, we need to find the slope and y-intercept of the line.

The slope of the line (m) can be determined by using the formula m = [tex](y_2 - y_1) / (x_2 - x_1)[/tex]. Inserting the given points into this formula gives: m = (3 - 1) / (2 - (-1)) = 2 / 3 = 2/3.

To find the y-intercept (b), we can use the point-slope form of the equation and solve for 'b', y = mx + b, insert the slope we found and one of the given points, let's utilise (-1, 1): 1 = 2/3*(-1) + b, which simplifies to b = 5/3.

So, the equation of the straight line in slope-intercept form is y = 2/3x + 5/3.

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The pattern in the sequence 9, 3, 1, 1/3 involves each number being a third of the previous number. Following this rule, the next number after 1/3, obtained by dividing by 3, is 1/9.

To determine the next number in the sequence 9, 3, 1, 1/3, we need to identify the pattern or rule that is being followed. Observing the sequence, each subsequent number appears to be a third of the previous number. The first number is 9, and dividing by 3 gives us 3. Dividing the second number, 3, by 3 gives us 1.

Similarly, dividing the third number, 1, by 3 gives us 1/3. Following this logic, to find the next number in the sequence, we divide 1/3 by 3.

Using the arithmetic of division with fractions, we have (1/3) ÷ 3 = (1/3) ÷ (3/1) = 1/9. Therefore, the next number in the sequence is 1/9. We can assume that the rule being applied in this sequence is to divide each number by 3 to find the next number, which aligns with the mathematical pattern identification techniques commonly used.

The next number in the sequence is 1/9.

To find the next number in the sequence 9, 3, 1, 1/3, we need to identify the pattern. This sequence is a geometric sequence where each term is obtained by multiplying the previous term by a common ratio.

Step-by-step:

To find the next term, we continue this pattern:
1/3× (1/3) = 1/9

Answer: First option is correct.

Step-by-step explanation:

Since we have given that

4.05, 1.35, 0.45, 0.15, ...

Since it is a geometric sequence.

So, here, a = 4.05

r = [tex]\dfrac{a_2}{a_1}=\dfrac{1.35}{4.05}=0.33[/tex]

So, we know the formula for nth term in geometric sequence.

[tex]a_n=ar^{n-1}\\\\a_n=4.05(0.3)^{n-1}[/tex]

Hence, First option is correct.

Answer:

an=4.05^(1/3)n−1

Step-by-step explanation:

Answer: 30

Step-by-step explanation:

Let x be the number of Beetles.

Then , the number of Acuras = [tex]\dfrac{1}{2}x[/tex]

Also, The number of Camrys is 80% of the number of Acuras and Beetles together.

Thus , the number of Camrys =[tex]0.8(x+\dfrac{1}{2}x)[/tex]

Now, the total number of cars in parking lot will be :-

[tex]x+\dfrac{1}{2}x+0.8(x+\dfrac{1}{2}x)=81\\\\\Rightarrow\ \dfrac{3x}{2}+0.8(\dfrac{3x}{2})=81\\\\\Rightarrow\ \dfrac{3x+2.4x}{2}=81\\\\\Rightarrow\ 5.4x=2\times81\\\\\Rightarrow\ x=\dfrac{162}{5.4}=30[/tex]

Hence, there are 30 Beetles.

Answer:

30 of the cars

Step-by-step explanation:

I just did the question on Alcumus.

Hope this helped! :)

so the rainwater flows as R(x), and the decrease of the flow will be D(x), the new smaller pipe after the decrease will have water flowing at R(x) - D(x)

[tex]\bf \begin{cases} R(x)=-0.1x^3+1.4x^2-1.5x\\ D(x)=-0.04x^3+0.5x^2+x \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{R(x)}{(-0.1x^3+1.4x^2-1.5x)}-\stackrel{D(x)}{(-0.04x^3+0.5x^2+x)} \\\\\\ (-0.1x^3+1.4x^2-1.5x)+0.04x^3-0.5x^2-x \\\\\\ -0.1x^3+1.4x^2-1.5x+0.04x^3-0.5x^2-x \\\\\\ -0.10x^3+0.04x^3+1.4x^2-0.5x^2-1.5x-x\implies \stackrel{H(x)}{-0.6x^3+0.9x^2-1.6x}[/tex]

To find the rate of water flow through the smaller pipe, subtract the decrease function from the original rate function.

To find the rate at which rainwater flows through the smaller pipe, we need to subtract the decrease function from the original rate function. Let's call this new function H(x). So, H(x) = R(x) - D(x).

Substituting the given values, H(x) = (-0.1x^3 + 1.4x^2 - 1.5x) - (-0.04x^3 + 0.5x^2 + x). Simplifying, H(x) = -0.1x^3 + 1.4x^2 - 1.5x + 0.04x^3 - 0.5x^2 - x.

Combining like terms, H(x) = -0.06x^3 + 0.9x^2 - 2.5x.

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Answer:

A(2,2)

Step-by-step explanation:

Let the vertex A has coordinates [tex](x_A,y_A)[/tex]

Vectors AB and AB' are perpendicular, then

[tex]\overrightarrow {AB}=(2-x_A,6-y_A)\\ \\\overrightarrow {AB'}=(-2-x_A,2-y_A)\\ \\\overrightarrow {AB}\perp\overrightarrow {AB'}\Rightarrow \overrightarrow {AB}\cdot \overrightarrow {AB'}=0\Rightarrow (2-x_A)(-2-x_A)+(6-y_A)(2-y_A)=0[/tex]

Vectors AC and AC' are perpendicular, then

[tex]\overrightarrow {AC}=(4-x_A,3-y_A)\\ \\\overrightarrow {AC'}=(1-x_A,4-y_A)\\ \\\overrightarrow {AC}\perp\overrightarrow {AC'}\Rightarrow \overrightarrow {AC}\cdot \overrightarrow {AC'}=0\Rightarrow (4-x_A)(1-x_A)+(3-y_A)(4-y_A)=0[/tex]

Now, solve the system of two equations:

[tex]\left\{\begin{array}{l}(2-x_A)(-2-x_A)+(6-y_A)(2-y_A)=0\\ \\(4-x_A)(1-x_A)+(3-y_A)(4-y_A)=0\end{array}\right.\\ \\\left\{\begin{array}{l}-4-2x_A+2x_A+x_A^2+12-6y_A-2y_A+y^2_A=0\\ \\4-4x_A-x_A+x_A^2+12-3y_A-4y_A+y_A^2=0\end{array}\right.\\ \\\left\{\begin{array}{l}x_A^2+y_A^2-8y_A+8=0\\ \\x_A^2+y_A^2-5x_A-7y_A+16=0\end{array}\right.[/tex]

Subtract these two equations:

[tex]5x_A-y_A-8=0\Rightarrow y_A=5x_A-8[/tex]

Substitute it into the first equation:

[tex]x_A^2+(5x_A-8)^2-8(5x_A-8)+8=0\\ \\x_A^2+25x_A^2-80x_A+64-40x_A+64+8=0\\ \\26x_A^2-120x_A+136=0\\ \\13x_A^2-60x_A+68=0\\ \\D=(-60)^2-4\cdot 13\cdot 68=3600-3536=64\\ \\x_{A_{1,2}}=\dfrac{60\pm8}{2\cdot 13}=\dfrac{34}{13},2[/tex]

Then

[tex]y_{A_{1,2}}=5\cdot \dfrac{34}{13}-8 \text{ or } 5\cdot 2-8\\ \\=\dfrac{66}{13}\text{ or } 2[/tex]

Rotation by 90° counterclockwise about A(2,2) gives image points B' and C' (see attached diagram)

Answer:

b. 5/7

Step-by-step explanation:

The line goes through the points (0, 0) and (7, 5).  Let's use those points in the slope formula:

[tex]m=\frac{5-0}{7-0}=\frac{5}{7}[/tex]

The slope of that line is 5/7

The slope of the given line is 5/7

In the given graph, the line passes through the center (0, 0) and (7, 5)

So the slope will be   [tex]\frac{5-0}{7-0} = \frac{5}{7}[/tex]

So option B is correct

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Answer:

  A. 25°

Step-by-step explanation:

The angles on either side of the bisector are congruent, so ...

  (3x -5)° = (x +15)°

  2x = 20 . . . . . . . . . . . . divide by °; add 5-x

  x = 10 . . . . . . . . . . . . . .divide by 2

Substitute this result into the expression for the angle measure:

m∠BAC = (3·10 -5)° = 25°

Answer:

The slope is 2

Step-by-step explanation:

The slope of a line passing through two points is given by:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

which is the difference between the y-coordinates of two points divided by the difference between x-coordinates of two points

We are given:

Difference between x-coordinates = 3

Difference between y-coordinates = 6

So,

[tex]m = \frac{6}{3}\\=2[/tex]

The slope of the line that passes through these points is 2 ..

Answer:

  12.9 m

Step-by-step explanation:

Let d represent the length of the diagonal. Then d-2 is the length and d-6 is the width. The Pythagorean theorem can be used to relate these measures, which are the legs and hypotenuse of a right triangle.

  d² = (d-2)² + (d-6)²

  d² = d² -4d +4 + d² -12d +36 . . . . eliminate parentheses

  0 = d² -16d +40 . . . . . . . . . . . . . . . subtract d², collect terms

  0 = d² -16d +64 -24 . . . . . . . . . . . rearrange the constant to make a square

  0 = (d -8)² -24 . . . . . . write in vertex form

  d -8 = √24 . . . . . . . . . add 24 and take the square root

  d = 8 + √24 . . . . . . . . the negative square root is extraneous in this problem

  d ≈ 12.9 . . . meters

The length of the diagonal is about 12.9 meters.

Answer:

Option C.) Geometric, common ratio = 3

Step-by-step explanation:

we know that

In a Geometric Sequence each term is found by multiplying the previous term by a constant

The constant is called the common ratio

In this problem we have

For x=1, f(1)=3

For x=2, f(2)=9

For x=3, f(3)=27

For x=4, f(4)=81

so

f(2)/f(1)=9/3=3 -----> f(2)=3*f(1)

f(3)/f(2)=27/9=3 -----> f(3)=3*f(2)

f(4)/f(3)=81/27=3 -----> f(4)=3*f(3)

f(n+1)/f(n)=3 -----> f(n+1)=3*f(n)

therefore

This is a Geometric sequence and the common ratio is equal to 3

The sequence is a geometric sequence with a common ratio of 3.

The sequence given is a geometric sequence. A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio. In this case, the common ratio can be found by dividing a term in the sequence by its preceding term. For example, if we divide the second term (9) by the first term (3), we get 3. The same goes for the rest of the terms in the sequence. Therefore, the correct answer is Option C: Geometric, common ratio = 3.

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Answer:

86 because 180 subtract 94 is 86

Answer:

The correct answer is option D. 94 °

Step-by-step explanation:

From the figure we get,

l║ m ║ o and  n║ p

To find the measure of <16

It is given that, m<1 = 94°

m<1 + m<4 = 180  [ Same side exterior angles of parallel lines are supplementary]

m<4 = 180 - m<1 = 180 - 94 = 86°

Similarly, m<4 + m<16 = 180

m<16 = 180 - m<4 = 180 -  86 = 94°

The correct answer is option D. 94 °

[tex]\bf (\stackrel{x_1}{-4}~,~\stackrel{y_1}{3})~\hspace{10em} slope = m\implies -4 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-3=-4[x-(-4)]\implies y-3=-4(x+4)[/tex]

[tex]\bf y-3=-4x-16\implies y=-4x-13\impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]

Answer:

B. H0: μd = 0 Ha: μd < 0

Step-by-step explanation:

Let μ1 and μ2 represent the number of correct answers during the timed condition and the unlimited time condition, respectively.

Let μd be the mean of the differences in the number of correct answers (timed − un timed) of all sixth graders.

The answer is B. H0: μd = 0 Ha: μd < 0

Here we have to check that the students will get few correct answers in the timed condition as compared to the unlimited time condition.

To know this, difference was calculated so we get the correct hypotheses as : H0: μd = 0 and Ha: μd < 0 .

Answer:

Also "H0: μ1 − μ2 = 0 Ha: μ1 − μ2 < 0" is correct

Step-by-step explanation:

Answer:

x = (C-By)/A

Step-by-step explanation:

Ax + By = C

Subtract By from each side

Ax + By-By = C-By

Ax = C -By

Divide each side by A

Ax/A = (C-By)/A

x = (C-By)/A

Answer:

[tex]\large\boxed{y=\dfrac{3}{5}x-2}[/tex]

Step-by-step explanation:

The slope-intercept form of an equation of aline:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept

The formula of a slope:

[tex]m=\dfraxc{y_2-y_1}{x_2-x_1}[/tex]

From the graph we have the points:

(-5, -5)

y-intercept (0, -2) → b = -2

Calculate the slope:

[tex]m=\dfrac{-2-(-5)}{0-(-5)}=\dfrac{3}{5}[/tex]

Put the value of the slope and the y-intercept to the equation of a line:

[tex]y=\dfrac{3}{5}x-2[/tex]

Final answer:

Chung has a ratio of 6 trucks to 5 cars (6:5), and Brian has a ratio of 4 trucks to 5 cars (4:5). Chung has a higher ratio of trucks to cars compared to Brian.

Explanation:

To compare the ratios of trucks to cars for Chung and Brian, we simply write down the number of trucks and cars each has and form a ratio for each. For Chung, the ratio of trucks to cars is 6 trucks to 5 cars, which can be written as 6:5 or ⅓. For Brian, the ratio of trucks to cars is 4 trucks to 5 cars, or 4:5 or ⅔.

Now, by comparing these two ratios, we see that Chung has a higher ratio of trucks to cars (6:5) compared to Brian (4:5), which means Chung has more trucks relative to cars in his toy box than Brian does.

To compare Chung's and Brian's ratios of trucks to cars, we have to calculate each ratio and then compare them.
**Chung's Ratio:**
Chung has 6 trucks and 5 cars. The ratio of trucks to cars for Chung is the number of trucks divided by the number of cars.
Chung's trucks to cars ratio = Number of trucks / Number of cars
                            = 6 / 5                    
**Brian's Ratio:**
Brian has 4 trucks and 5 cars. The ratio of trucks to cars for Brian is the number of trucks divided by the number of cars.
Brian's trucks to cars ratio = Number of trucks / Number of cars
                            = 4 / 5
Both ratios are to be compared now.
**Comparing Ratios:**
Chung's ratio is 6/5, which is 1.2 when converted into a decimal.
Brian's ratio is 4/5, which is 0.8 when converted into a decimal.
Since 1.2 (Chung's ratio) is greater than 0.8 (Brian's ratio), we can conclude that Chung has a higher ratio of trucks to cars compared to Brian.
Therefore, the correct comparison of their ratios is: "Chung has a higher ratio of trucks to cars than Brian."