For a series of concrete structures, a civil engineer records the number of cracks that develop in each one and the number of fastening bolts used in that structure. The scatterplot shows her results. Based on her line of best fit, which of the following statements is true?

Answer:

b) 8.5 feet

Step-by-step explanation:

Answer:

Answer is 9.6

Step-by-step explanation:

From the illustration above. See attachment for interpretation of this illustration.

To find the part label a in the attachment which is the length of the foot of the guide wire from the ground to the palm tree, we apply the sine rule, which says

a/sineA = b/sineB

In this case

a = ? , A = 58° , b = 6ft, B = 32°

So

a/sine58 = 6/sine32

a/0.848 = 6/0.5299

a = 6*0.848/0.5299

a = 5.088/0.5299

a = 9.601 ~ 9.6

Answer:

2.  Circumcenter is (-2, 1)

4.  Orthocenter is (5, 0)

6. II ∠DOS and ∠CAT are vertical and III ∠DOS and ∠CAT are adjacent

8.  m∠PBC = 30°

10.  KV, VM, KM

12.  DC is greater

14.  x = 12

Step-by-step explanation:

2.  Equation of the perpendicular bisector of AB is x = -2 and the equation of the perpendicular bisector of BC is y = 1.

Circumcenter is the point of intersection of the perpendicular bisectors of the sides of the triangle.

Hence, circumcentre is (-2, 1).

4.  Orthocenter is the point of intersection of the altitudes. Here, AB and BC are two altitudes and B is their point of intersection.

Hence, the orthocenter is (5, 0).

6.  Adjacent angles are angles separated by a line and vertical angles are angles vertically opposite to each other.

Hence, statements II and III contradict to each other.

8.  If P is equidistant from all the three sides, then P is the center of the in-circle and hence it is the incenter of the triangle.

If P is the incentre, then PB is the internal bisector.

Therefore, ∠PBC = [tex]\frac{1}{2}[/tex] ∠ABC = 30°

10.  From the triangle sum property, ∠ M = 180 - (110 + 40) = 30.

Since, the side opposite to the smallest is the shortest, the correct order is:

KV, VM, KM

12.  Clearly, ∠ ABD is acute. Therefore, ∠ DBC > ∠ ABD.

Since, side opposite to larger angle is greater, DC is greater.

14.  Let the sides of the top triangle be p and q. So, two sides of whole triangle are 2p and 2q.

Now, if we compare the top small triangle and the whole triangle, they are similar by SAS similarity since,

the top angle is common and [tex]\frac{p}{2p}=\frac{q}{2q}=\frac{1}{2}[/tex].

Since, corresponding parts of similar triangles are proportionate,

[tex]\frac{3x}{5x+12} =\frac{1}{2}[/tex]

6x = 5x + 12

6x - 5x = 12

x = 12

Answer:

2.  Circumcenter is (-2, 1)

4.  Orthocenter is (5, 0)

6. II ∠DOS and ∠CAT are vertical and III ∠DOS and ∠CAT are adjacent

8.  m∠PBC = 30°

10.  KV, VM, KM

12.  DC is greater

14.  x = 12

Step-by-step explanation:

Answer:

angle(TSW) is 18

Step-by-step explanation:

we are given angles

angle(RST)=2x+8

angle(TSW)=3x+14

angle(RSW)=7x-2

Firstly, we will draw diagram

so, we get

angle(TSW)=angle(RST)+angle(RSW)

so, we can plug values

[tex]3x+14=2x+8+7x-2[/tex]

now, we can solve for x

[tex]9x-3x=14-6[/tex]

[tex]6x=8[/tex]

now, we can solve for x

[tex]x=\frac{4}{3}[/tex]

now, we can find angle (TSW)

angle(TSW) is

[tex]=3\times \frac{4}{3} +14[/tex]

[tex]=4 +14[/tex]

[tex]=18[/tex]

So, angle(TSW) is 18

To solve for x, we set up an equation based on the sum of angles forming a straight line. Solving the equation, we find x=12. Substituting x into the equation for angle tsw, we find that angle tsw measures 50 degrees.

To find the value of x for the angles rst, tsw, and rsw, you need to understand that they are all connected by their location on a straight line or a point. If angles rst and tsw are adjacent angles that form a straight line, their measures would add up to 180° because a straight line measures 180°. The same is true for the angle rsw if it is the full angle at that point or the sum of angles rst and tsw.

The equations are given as:

Since angle rsw is the full angle, you can write the equation:

7x - 2 = (2x + 8) + (3x + 14)

Now, solve for x:

7x - 2 = 2x + 8 + 3x + 14

7x - 2 = 5x + 22

7x - 5x = 22 + 2

2x = 24

x = 24 / 2

x = 12

Now that we have the value of x, we can find angle tsw by substituting x into its equation:

angle tsw = 3x + 14

angle tsw = 3(12) + 14

angle tsw = 36 + 14

angle tsw = 50°

Answer:

see explanation

Step-by-step explanation:

to find the intercepts, that is where the line crosses the x and y axes

• let x = 0, in the equation for the y-intercept

• let y = 0, in the equation for x-intercept

x = 0

⇒ - 5 = 4y ( divide both sides by 4 )

y = - [tex]\frac{5}{4}[/tex] ← y- intercept

y = 0

7x - 5 = - 6x ( add 6x to both sides )

13x - 5 = 0 ( add 5 to both sides )

13x = 5 ( divide both sides by 13 )

x = [tex]\frac{5}{13}[/tex] ← x- intercept

Answer:

770

Step-by-step explanation:

3.5 x 220 = 770

770/3.5 = 220

770/220 = 3.5

To find what 3.5 multiplied by 220 is, you simply multiply the two numbers together to get 770. This can be related to weight calculations in personal training contexts.

This question demands basic understanding of mathematical operations (addition, subtraction, multiplication, division) in general and about multiplication in particular.

The question What's 3.5 x 220? is asking for the product of the two numbers, 3.5 and 220, which is a mathematics calculation. To find the answer, you multiply 3.5 by 220, which equals 770.

Another way is to find 350% of 220 which means 350/100 * 220 = 770

This calculation is relevant for the student's personal training classes, potentially relating to the amount of weight lifted or the calculation of potential energy.

Therefore, as per the above explaination, the correct answer is 770.

Answer:

3 miles per hour

Step-by-step explanation:

We need to subtract the two numbers to find the difference in speeds

4/5 - 3/4

We need to get a common denominator of 20

4/5 *4/4 - 3/4 *5/5

16/20 - 15/20

1/20  

The car going 4/5 miles per minute is going 1/20 miles per minute faster than the car going 3/4 miles per minute.

The question asks for miles per hour, not miles per minute.  We know  that there are 60 minutes per hour.

1/20 miles per minute * 60 minutes / hour

60/20 miles/hour

3 miles/ hour

The car going 4/5 miles per minute is going 3 miles per hour faster than the car going 3/4 miles per minute.

Answer:

The area of the box is equal to 9^3 = 729 in^3

729<1000  

Step-by-step explanation:

No since the volume of the box is less than the total volume of the cubes

Question

Find 1/8 of 12. Express your answer in simplest form.

1 1/2

2/3

1/96

12/8

Answer:

Step-by-step explanation:

12 : 8 = 1.5 (1 1/2)

To find 1/8 of 12, multiply 12 by 1/8 and simplify the fraction to its simplest form, which is 3/2.

To find 1/8 of 12, we can multiply 12 by 1/8. Multiplying fractions is done by multiplying the numerators together and multiplying the denominators together. In this case, 12 multiplied by 1 equals 12, and 8 multiplied by 1 equals 8, so the answer is 12/8.

However, 12/8 is not in simplest form because the numerator and denominator have a common factor of 4. To simplify the fraction, we divide both the numerator and denominator by 4. 12 divided by 4 is 3, and 8 divided by 4 is 2. So, the simplest form of 12/8 is 3/2.

https://brainly.com/question/660389

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To find the height of the ramp at its highest point, we can use trigonometry and the sine function.

To find the height of the ramp at its highest point, we need to determine the vertical component of the ramp. We can use trigonometry to do this. Assuming the ramp forms a right triangle with the ground, we can use the sine function to calculate the height:

height = ramp length * sin(angle)

Given that the ramp length is 24.5 feet and the angle is not provided, we cannot calculate the exact height without that information. Please provide the angle, and I'll be happy to help you find the height.

a)

well, she put 4000, and she earned in interest 960, so her accumulated amount is just their sum, 4960.

b)

now, it doesn't say, so we're assuming is simple interest, as opposed to compound interest.

[tex]\bf ~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\dotfill&960\\ P=\textit{original amount deposited}\dotfill & \$4000\\ r=rate\to r\%\to \frac{r}{100}\dotfill\\ t=years\dotfill &3 \end{cases} \\\\\\ 960=(4000)(r)(3)\implies \cfrac{960}{(4000)(3)}=r\implies 0.08=r \\\\\\ \stackrel{\textit{converting to percentage}}{r=0.08\cdot 100}\implies r=\stackrel{\%}{8}[/tex]

c)

let's make the rate 1% greater then, and check

[tex]\bf ~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\dotfill\\ P=\textit{original amount deposited}\dotfill & \$4000\\ r=rate\to \stackrel{8+1}{9\%}\to \frac{9}{100}\dotfill&0.09\\ t=years\dotfill &3 \end{cases} \\\\\\ I=(4000)(0.09)(3)\implies I=1080 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{at 9\%}}{1080}-\stackrel{\textit{at 8\%}}{960}\implies \stackrel{\textit{that much more}}{120}[/tex]

Step-by-step explanation:

Let's get an important definition out of the way first. A parallelogram is a quadrilateral with two pairs of parallel sides. We can translate this idea to coordinate geometry by saying that each pair of opposite sides must have the same slope.

Slope, as you might remember, is a measure of change. Specifically, it's the change in a line's y value (Δy) divided by the corresponding change in its x value (Δx). This means that if we can prove that:

We'll have proved our figure is a quadrilateral. Let's prove those cases, then. For KA and IT:

[tex]slope_{KA}\stackrel{?}{=}slope_{IT}[/tex]

To find the slope of any line segment, we can find the difference between the corresponding coordinates of its endpoints and divide the difference in y-coordinates by the difference in x-coordinates. Since the endpoints of KA are K(0, 0) and A(a, 0), the slope of these points is

[tex]slope_{KA}=\frac{0-0}{a-0} =\frac{0}{a} =0[/tex]

We can do this same for IT using its endpoints I(a + b, c) and T(b, c):

[tex]slope_{IT}=\frac{c-c}{b-(a+b)} =\frac{0}{-a}=0[/tex]

Since 0 = 0, we can say that [tex]slope_{KA}=slope_{IT}[/tex], and we've proven our first condition. Now we just need to prove that [tex]slope_{KT}=slope_{AI}[/tex]:

[tex]slope_{KT}\stackrel{?}{=}slope_{AI}[/tex]

Using K(0, 0) and T(b, c), [tex]slope_{KT}=\frac{c-0}{b-0}=\frac{c}{b}[/tex], and using A(a, 0) and I(a + b, c), [tex]slope_{AI}=\frac{c-0}{(a+b)-a}=\frac{c}{b}[/tex], proving that [tex]slope_{KT}=slope_{AI}[/tex].

Since we've proven that [tex]slope_{KA}=slope_{IT}[/tex] and [tex]slope_{KT}=slope_{AI}[/tex], we've proven that the quadrilateral KAIT is, by definition, a parallelogram.

Answer:

12) -60/1 =60

14) 110

16)45

18) 7

32) -18

Step-by-step explanation:

Answer:

PT, VP

Step-by-step explanation:

if p is the center and T V and W are on the circle

the radius goes from the center of the circle to the edge of the circle

then PW PT and PW are radii of the circle

Answer:

The right option is A) 0.72%

Step-by-step explanation:

We have given,

Number of shares = $100

Park stock per share = $52.89

Total parks stock = 100×52.89 = $5289

Since company paid annual dividends of $0.38 per share.

Total annual dividend company paid = 100×0.38 =$38

Total annual yield in % = [tex]\frac{38}{5289} *100[/tex] = 0.718 % ≈0.72%

Hence the right option is A) 0.72%

A.72% I took the test at k12

Put the value of x = 4 to the expression 3x + 2.

(3)(4) + 2

first multiplication and next addition

= 12 + 2 = 14

Answer:

Distributive Property

Step-by-step explanation:

They distributed the -3 to x and 4. In this case, to distribute the -3, you multiply it to each term.

-3 × x = -3x.

-3 × 4 = -12.

-3x - 12

Answer:

Do you have the rest of the answers for the test??? I'm taking it right now

Step-by-step explanation:

Let the smaller number = X

Then the larger number is 3x+4 ( four more than 3 times the smaller number)

The sum of both numbers = 80

so you have X + 3X+4 = 80

Simplify the left side:

4x+4 = 80

Subtract 4 from each side:

4x = 76

Divide both sides by 4:

X = 76/4

X = 19

The smallest number is 19

The largest number is 80 - 19 = 61 ( check: 3*19 = 57+4 = 61)

The two numbers are 19 and 61

Answer:

Step-by-step explanation:

Here is a diagram of a seven sided regular polygon. You use this diagram to find out how many degrees total are in the interior of a the heptagon. There are 5 such triangles which means that since each triangle has 180o the total amount of the interior angles must be 5 * 180 = 900

Since there are 7 interior angles, the answer to how large each one of them is is found by

900/7 = 129.57 which is slightly off because it is a rounded error.

In general, the size of the angles  in a  regular polygon

180(n - 2 ) / n

Where n is the number of degrees in each interior angle. For example for an 8 sided figure you would get

180(8 - 2) / 8 = 180 * 6/8 = 133 degrees.

Answer:

the answer would be 28.

Step-by-step explanation:

you're multiplying the top and bottom by 7. 3 *7=21 for the bottom

4*7 = 28 for the top

Hope this helps

-Kayla

Answer:

The answer is A. 28

Step-by-step explanation:

When you divide 21 into 3 you get 7.

So you have to multiply 7 to get 21. Whatever you do to the bottom or top you have to do to the opposite so you have to  multiply 7 by 4 and you get 28.

Hope this helps

Answer:

The slope is  -14/11

Step-by-step explanation:

To find the slope, use the formula

m = (y2-y1)/ (x2-x1)

   = (8--6)/ (-1-10)

   = (8+6)/(-1-10)

   = 14/-11

  = -14/11

Answer:

x = 2.5 inches. Or

x = 5/2

Step-by-step explanation:

Length: 7 + 2x

Width: 5 + 2x

Note that you have to add x at each end of the picture and onto each part of the width.

The entire area is 120 square inches.

Formula

L*W = Area

(2x + 7)(2x + 5) = 120

Solution

4x^2 + 10x + 14x + 35 = 120                Subtract 120 from both sides. Add xs

4x^2 + 24x + 35 - 120 = 0

4x^2 + 24x - 85 = 0                             Factor

(2x + 17)(2x - 5)

2x + 17 has no meaning. It will give -  8.5 which is not possible.

2x - 5 =0

2x = 5                                                  Divide by 2

x = 5/2

x = 2.5

Note: I don't know which one the computer is looking for.

Answer:

7/11 = 0.6363... and so on.

Step-by-step explanation:

How I did it: 7/11  =      11   so over the 7 you put a 0 and . over the 0s you put 636363 under the 7 you put a 6 and under the 0 next from the 7 you put a 6 also under the 6. then you put a line under the 66. under the 6 from the right you put a 4 next to the four you put a 0 then you make 33 under the 40 and make a line. on the 3 of the right side you put a 7 under and take a 0 again you put 66 under the 70 and make a line, underthe line you put 40 again but you put the 4 under the 6 on the right side and then put 33 under 40 make a line and put 7 on the right side of the 33 and the 0: 70. thats it I hope you understood! and it helped.

Goodluck!

^.^

Answer:

Correct choice is D

Step-by-step explanation:

The graph of the function shows that the function is not continuous at point x=3.

When moving to the point x=3 from the left side, you can see that y approaches to -1. When moving to the point x=3 from the right side, then y approaches to -3 and at x=3, y=7. This gives you that the limit doesn't exist.

Answer:

[tex]1-4x[/tex]

Step-by-step explanation:

A product of two numbers is the result we get from multiplying them together. The product of 4 and x would then be [tex]4\times x[/tex], which we can rewrite as [tex]4x[/tex]. We're then told by the statement "one minus the product..." that we'll be taking this [tex]4x[/tex] away from 1, giving us the answer [tex]1-4x[/tex].

Answer:

The numerical expression would be 1-4x

Step-by-step explanation:

[One] - [minus] [the product of]  

4 and  x is the product of 4 and 4.x

The answer is 12

i hope this helps

Answer:

the answer is 12 units squared

Step-by-step explanation:

count the boxes and add the halves together.

Hope this helps :)