Proportions in Triangles (9)

Answer : The total volume of figure is, [tex]162in^3[/tex]

Step-by-step explanation :

First we have to calculate the volume of cuboid A.

[tex]V_A=l\times b\times h[/tex]

where,

[tex]V_A[/tex] = volume of cuboid A

l = length of cuboid = 9 in

b = breadth of cuboid = 5 in

h = height of cuboid = 2 in

[tex]V_A=9in\times 5in\times 2in[/tex]

[tex]V_A=90in^3[/tex]

Now we have to calculate the volume of cuboid B.

[tex]V_B=l\times b\times h[/tex]

where,

[tex]V_B[/tex] = volume of cuboid B

l = length of cuboid = 9 in

b = breadth of cuboid = 1 in

h = height of cuboid = 2 in

[tex]V_B=9in\times 1in\times 2in[/tex]

[tex]V_B=18in^3[/tex]

Now we have to calculate the volume of cuboid C.

[tex]V_C=l\times b\times h[/tex]

where,

[tex]V_C[/tex] = volume of cuboid C

l = length of cuboid = 9 in

b = breadth of cuboid = 1 in

h = height of cuboid = (8-2=6) in

[tex]V_C=9in\times 1in\times 6in[/tex]

[tex]V_C=54in^3[/tex]

Now we have to calculate the total volume of figure.

Total volume of figure = [tex]V_A+V_B+V_C[/tex]

Total volume of figure = [tex]90in^3+18in^3+54in^3[/tex]

Total volume of figure = [tex]162in^3[/tex]

Thus, the total volume of figure is, [tex]162in^3[/tex]

Answer:

Step-by-step explanation:

Given that an equation in variable x as follows:

[tex]e^x =2x+3[/tex]

Let us start with x=0

We have left side = 1 and right side = 3.

Error = 2

ii) x=1: left side = e =2.718 and right side = 6.

Error = 3.282

iii) x =2: Left side = 7.388 and right side = 7

Error = 0.388

iv) x=3

Left side = 20.079

Right side = 9

Error = 11.079

Since error is the least when x=0, we can say 0 is the best approximation.

Answer:

70 sentences

Step-by-step explanation:

7 x 5 x 2= 70

Hence, the answer is:

                [tex]\dfrac{1}{4}[/tex]

It is given that:

A correct answer is awarded 4 points, but an incorrect answer costs the student 1 point.

This means that the point +4 is added if the answer is correct.

and -1 will be added if the answer is incorrect.

Also, the probability of getting a correct answer is: 1/4

( since out of 4 choices only one option is correct)

and the probability of getting a incorrect answer is: 3/4

( since out of 4 choices 3 are incorrect)

Hence, the expected point the student should expect to get per question is:

[tex]E(X)=\dfrac{1}{4}\times (+4)+\dfrac{3}{4}\times (-1)\\\\i.e.\\\\E(X)=1-\dfrac{3}{4}\\\\i.e.\\\\E(X)=\dfrac{1\times 4-3}{4}\\\\i.e.\\\\E(X)=\dfrac{4-3}{4}\\\\i.e.\\\\E(X)=\dfrac{1}{4}[/tex]

A student who guesses on a multiple-choice question with four options should expect to earn an average of 0.25 points per question due to the probabilities of correct and incorrect answers and their respective points.

When guessing on a multiple-choice question with four possible answers, the probability of a correct guess is 1/4, while the probability of an incorrect guess is 3/4. The expected points per question is calculated by multiplying the probability of each outcome by the points awarded or deducted for that outcome and summing these products. With 4 points for a correct answer and a loss of 1 point for an incorrect answer, the calculation is as follows:

(1/4) × 4 points + (3/4) × (-1 point) = 1 point - 3/4 points = 1/4 points

Therefore, the student should expect to earn 0.25 points per question on average if they were to guess on each question.

Answer:

(2, 1).

Step-by-step explanation:

Dilated by factor 3:

C = (6, 3) ----> C' would be (6 * 1/3, 3 *1.3) = (2, 1).

Answer:

  4.2 or 15.8 metres

Step-by-step explanation:

We assume your model for the height of the water stream is supposed to be ...

  h(x) = -0.15x^2 +3x

This will have a value of 10 when ...

  -0.15x^2 +3x = 10

  .15x^2 -3x +10 = 0 . . . . . subtract the left side to get standard form

For a quadratic equation of the form ...

  ax² +bx +c = 0

The solutions are given by the "quadratic formula:"

[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

The above equation matches the template with a=0.15, b=-3, c=10. Putting these values into the formula gives ...

[tex]x=\dfrac{-(-3)\pm\sqrt{(-3)^2-4\cdot 0.15\cdot 10}}{2\cdot 0.15}=\dfrac{3\pm\sqrt{3}}{0.3}\\\\x=10\pm\dfrac{10}{3}\sqrt{3}[/tex]

  x ≈ 4.2 or 15.8

The firefighter can stand at 4.2 metres or 15.8 metres from the fire to get the water to arrive at the building 10 metres up.

Answer:

3.58

Step-by-step explanation:

Given :

y = 2x + 4 -------- eq1

y = 2x - 4 -------- eq2

sanity check : both equations have same slope, so we can conclude that they are both parallel to one another.

Step 1: consider equation 1, pick any random x-value and find they corresponding y-value. we pick x = -2

This gives us y = 2(-2) + 4 = 0

Hence we get a point (x,y) = (-2,0)

Step 2: express equation 2 in general form (i.e Ax + By + C = 0)

y = 2x-4 -------rearrange---> 2x - y -4 = 0

Comparing with the general form, we get A = 2, B = -1, C = -4

Recall that the distance between 2 parallel lines is given by the attached formula (see attached picture).

substituting the values for A, B, C and (x, y) from the previous step:

d = | (2)(-2) + (-1)(0) + (-4) |  / √(2² + (-1)²)

d = | -4 + 0 - 4 |  / √(4 + 1)

d = | -8 |  / √5

d = 8  / √5

d = 3.5777

d = 3.58 (rounded 2 dec. pl)

Answer:

y-7 = 1/2(x-1) point slope form

y = 1/2x+13/2  slope intercept form

Step-by-step explanation:

y=-2x+9

This equation is in the form y= mx +b so the slope is -2

We want a line perpendicular

Take the negative reciprocal

m perpendicular is - (-1/2)

m perpendicular = 1/2

We have a slope of 1/2 and a point.  We can use point slope form

y-y1 = m(x-x1)

y-7 = 1/2(x-1)  point slope form

y-7 = 1/2x-1/2

Adding 7 to each side

y-7+7 =1/2x -1/2+7

y = 1/2x-1/2 +14/2

y = 1/2x +13/2  slope intercept form

Answer:

Step-by-step explanation:

For a. we start by dividing both sides by 200:

[tex](1.05)^x=1.885[/tex]

In order to solve for x, we have to get it out from its position of an exponent.  Do that by taking the natural log of both sides:

[tex]ln(1.05)^x=ln(1.885)[/tex]

Applying the power rule for logs lets us now bring down the x in front of the ln:

x * ln(1.05) = ln(1.885)

Now we can divide both sides by ln(1.05) to solve for x:

[tex]x=\frac{ln(1.885)}{ln(1.05)}[/tex]

Do this on your calculator to find that

x = 12.99294297

For b. we will first apply the rule for "undoing" the addition of logs by multipllying:

[tex]ln(x*x^2)=5[/tex]

Simplifying gives you

[tex]ln(x^3)=5[/tex]

Applying the power rule allows us to bring down the 3 in front of the ln:

3 * ln(x) = 5

Now we can divide both sides by 3 to get

[tex]ln(x)=\frac{5}{3}[/tex]

Take the inverse ln by raising each side to e:

[tex]e^{ln(x)}=e^{\frac{5}{3}}[/tex]

The "e" and the ln on the left undo each other, leaving you with just x; and raising e to the power or 5/3 gives you that

x = 5.29449005

For c. begin by dividing both sides by 20 to get:

[tex]\frac{1}{2}=e^{.1x}[/tex]

"Undo" that e by taking the ln of both sides:

[tex]ln(.5)=ln(e^{.1x})[/tex]

When the ln and the e undo each other on the right you're left with just .1x; on the left we have, from our calculators:

-.6931471806 = .1x

x = -6.931471806

Question d. is a bit more complicated than the others.  Begin by turning the base of 4 into a base of 2 so they are "like" in a sense:

[tex](2^2)^x-6(2)^x=-8[/tex]

Now we will bring over the -8 by adding:

[tex](2^2)^x-6(2)^x+8=0[/tex]

We can turn this into a quadratic of sorts and factor it, but we have to use a u substitution.  Let's let [tex]u=2^x[/tex]

When we do that, we can rewrite the polynomial as

[tex]u^2-6u+8=0[/tex]

This factors very nicely into u = 4 and u = 2

But don't forget the substitution that we made earlier to make this easy to factor.  Now we have to put it back in:

[tex]2^x=4,2^x=2[/tex]

For the first solution, we will change the base of 4 into a 2 again like we did in the beginning:

[tex]2^2=2^x[/tex]

Now that the bases are the same, we can say that

x = 2

For the second solution, we will raise the 2 on the right to a power of 1 to get:

[tex]2^x=2^1[/tex]

Now that the bases are the same, we can say that

x = 1

Answer:

  √35

Step-by-step explanation:

The right triangles are all similar, so the ratios of long leg to hypotenuse are the same for all:

  z/7 = 5/z

  z² = 35 . . . . multiply by 7z

  z = √35

Answer:

Step-by-step explanation:

The right triangles are all similar, so the ratios of long leg to hypotenuse are the same for all:

 z/7 = 5/z

 z² = 35 . . . . multiply by 7z

 z = √35

Answer:

51,111%

Step-by-step explanation:

We know that 45% have a dog but no cat.  While 23% have both a dog and a cat.

Then Pr(X has cat|X has dog) = Pr(X has dog and cat)/Pr(X has dog)

= Pr(X has dog and cat)/Pr(X has dog) = 0.23/0.45 = 0.51 ≈ 51,111%

The probability that a student’s family owns a cat if the family owns a dog is 51,111%

Answer:

51.1% is the correct answer.

Step-by-step explanation:

Answer:

The first choice is the one you want

Step-by-step explanation:

First thing you need to know about this greatest integer graph is that it is aptly called a step graph.  It literally looks like stair steps on your calculator: short horizontal lines that are not connected vertically.  Really cool graph.

Second thing you need to know is about transformations of functions.  ANY side-to-side movement in ANY function will be in a set of parenthesis (or absolute value symbols, or under a radical sign, or inside the greatest integer brackets, etc.) and ANY up or down movement will be either added or subtracted.  Added means you move the function up from its starting position, subtracting means you move the function down from its starting position.  Since we have no numbers inside the greatest integer brackets, there is no side-to-side movement.  Since there is a "-2" after the brackets, we are moving the whole function down.

If you do not know how to graph these without a calculator and you have no idea what this graph looks like, I recommend going to your calculator to see it.  First, call up your "y = " window.  Next, hit 2nd-->0 (catalog), then hit the x^2 button (this will take you to the letter I in the catalog).  Scroll down til you see "int( " and hit that button.  It will take you back to the "y = " window.  Enter an x after that set of parenthesis and then close it, then hit " - 2 " and then "graph".  Your steps should begin to appear.  Notice that the horizontal line between x = 0 and x = 1 is at y = -2.  The parent graph has this line between x = 0 and x = 1 on y = 0.  The -2 in ours moved the graph down from y = 0 to y = -2

Summing up, the first choice is the one you want as your answer.

Answer:

A:

The steps are at y=-2

Step-by-step explanation:

edge 2021

Answer:

The equation that represents the new path is y=(1/3)x+4

Step-by-step explanation:

step 1

Find the slope of the give line

we have

y=-3x-6

so

the slope m is equal to

m=-3

step 2

Find the slope of the perpendicular line to the given line

Remember that

If two lines are perpendicular, then their slopes are opposite reciprocal of each other

so

we have

m=-3 -----> slope of the given line

therefore

The slope of the perpendicular line is equal to

m=1/3

step 3

With m=1/3 and the point (-3,3) find the equation of the line

y-y1=m(x-x1)

substitute

y-3=(1/3)(x+3)

y=(1/3)x+1+3

y=(1/3)x+4 -----> equation that represent the new path

Answer:

84=2l+2w

w=21

Step-by-step explanation:

84=2(l+w)

42=l+w

l=42-w

Area=l×w

A=(42-w)×w

Differentiate A=42w-w×w

with respective to "w".

dA/dw= 42-2w

For a minimum or maximum area

dA/dw=0

then, 42-2w=0

w=21

proving "A" is maximum when "w=21"

dA/dw>0 when w<21

dA/dw<0 when w>21

Therefore Area is maximum when "w=21"

The most extensive rectangular garden this man can build with his 84 feet of fencing would be a square with length and width of 21 feet each, yielding a total area of 441 square feet.

A rectangular garden's perimeter can be expressed as P = 2l + 2w, where l is the length and w is the park's width. Given 84 feet of fencing (the total perimeter), this equation becomes 84 = 2l + 2w. Simplified, this gives l + w = 42. Expressing w in terms of l gives w = 42 - l.

Next, breathing, we substitute w into the area formula A = l * w, get A = l * (42 - l). This area expression of one variable forms a quadratic equation, A = -l² + 42l. This suggests that the site is maximized from the quadratic formula when l = -b/2a = 42/2 = 21. So, the length and width of the most significant garden area are both 21 feet, representing a square.

https://brainly.com/question/34713449

#SPJ3

Answer:

B) There is a gap in Plot A, but not in Plot B.

Step-by-step explanation:

Plot A shows the number of hours ten girls watched television over a one-week period. Plot B shows the number of hours ten boys watched television over the same period of time. There is a gap in Plot A, but not in Plot B compares the shape of the dot plots.

The correct answer is B) There is a gap in Plot A, but not in Plot B

Explanation:

A dot plot is a type of graphic used in statistics to show information collected about a group of subjects or elements. In this, each dot or circle represents a subject related to a specific scale for example, in the case presented, the scale is the number of hours subjects watched television.

According to this, the statement that is true about the dot plots presented is that there is a gap in plot A because most subjects reported watching television for 3 to 7 hours; however, one of the subjects watched television 10 hours. This implies, a gap or space in the graphic because there is an interval in the scale with no subjects as most are grouped in a cluster except by one. This does not occur in plot B because all subjects form one cluster or group.

For this case we have to graph, we can see in the figure that the graph of the Neperian logarithm grows faster than the graph of the logarithm.

The graph of ln (x) is the second attached

Answer:

Option A

The log (x) graph will grow slower than the ln (x) graph.

See attached image

Answer:

The correct option is B

Step-by-step explanation:

We will consider the following things and figures.

The bank statement of July 31 for Walgreens showed a balance of $6,008.10

There was a deposit in transit made on July 1 for $1,100.10 along with the outstanding checks of $4,580.54.

=$6,008.10-$4,580.54+$1,100.10

=$1,427.56+$1,100.10

=$2,527.66

Thus the correct option is B....

Answer:

Is always a quadrilateral.

Is a parelleogram.

Answer:

  "is always"

Step-by-step explanation:

A rhombus is a 4-sided polygon that has all sides equal lengths. It is a quadrilateral and a parallelogram. A square is a special case of a rhombus.

Answer:

  7π cm² ≈ 22.0 cm²

Step-by-step explanation:

The shaded area is the difference between the area of Circle B and the areas of Circle C and Circle O. That is, those white areas are subtracted from the area of Circle B to get the shaded area.

The formula for the area of a circle is

  A = πr²

Using this, we find ...

  Circle B area = π(3 cm)² = 9π cm²

  Circle C area = Circle O area = π(1 cm)² = π cm²

Then the shaded area is ...

  Shaded Area = Circle B area - Circle C area - Circle O area

  = (9π cm²) - (π cm²) - (π cm²)

  = 7π cm² ≈ 22 cm²

Answer:

$61.18

Step-by-step explanation:

The price last week was an unknown. We will call it x. x is an entire amount, so it is 100% of x.

This week, the price is 15% lower. Since 100% - 15% = 85%, the price this week is 85% of what it was last week. Last week it was x, so this week, the price is 85% of x.

85% of x = $52

0.85x = $52

Divide both sides by 0.85:

0.85x/0.85 = $52/0.85

x = $61.1764...

Answer: $61.18

Final answer:

To determine the original price of the shoes before a 15% discount, divide the discounted price, $52, by 0.85. The original price of the shoes was approximately $61.18.

Explanation:

The question asks to find the original price of the shoes before they were discounted by 15%. To find the original price, you can use the formula for calculating the original price after a discount has been applied. If the current price represents 85% (100% - 15%) of the original price, you can set up the equation as follows: $52 = 85% of the original price.

To find the original price, divide the current price by 85% (or 0.85 in decimal form): Original Price = $52 ÷ 0.85. This calculation gives an original price of approximately $61.18, rounding to the nearest cent.

Answer:

Length of arc AB= 2πr (angle) /360

= 2π×6× 30°/360

= π.

ANSWER

The length of arc AB is π units.

EXPLANATION

The length of an arc of a circle is calculated using the formula:

[tex]l = \frac{ \theta}{360} \times 2\pi \: r[/tex]

Where [tex] \theta = 30 \degree[/tex]

is the angle of sector and r=6 units is the radius of the circle.

We substitute these values into the formula to find the length of arc AB.

[tex]l = \frac{30}{360} \times 2 \times \pi \: \times 6[/tex]

[tex]l = \pi[/tex]

The length of the arc is π units.

So put 1 as the coefficient.

The distance is,

[tex]d(A,B)=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Where [tex]A(x_1,y_1),B(x_2,y_2)\longrightarrow A(-3,-2),B(-1,-2)[/tex]

[tex]d(A,B)=\sqrt{(-1-(-3))^2+(-2-(-2))^2}=\sqrt{4}=2[/tex]

The distance between points A, B is 2 units.

Hope this helps.

r3t40

The formula for distance between two points is:

[tex]\sqrt{(x_{2} -x_{1})^{2} + (y_{2} -y_{1})^{2}}[/tex]

In this case:

[tex]x_{2} =-1\\x_{1} =-3\\y_{2} =-2\\y_{1} =-2[/tex]

^^^Plug these numbers into the formula for distance like so...

[tex]\sqrt{(-1 - (-3))^{2} + (-2 - (-2))^{2}}[/tex]

To solve this you must use the rules of PEMDAS (Parentheses, Exponent, Multiplication, Division, Addition, Subtraction)

First we have parentheses. Remember that when solving you must go from left to right

[tex]\sqrt{(-1 - (-3))^{2} + (-2 - (-2))^{2}}[/tex]

-1 - (-3) = 2

[tex]\sqrt{(2)^{2} + (-2 - (-2))^{2}}[/tex]

-2 - (-2) = 0

[tex]\sqrt{(2)^{2} + (0)^{2}}[/tex]

Next solve the exponent. Again, you must do this from left to right

[tex]\sqrt{(2)^{2} + (0)^{2}}[/tex]

2² = 4

[tex]\sqrt{4 + (0)^{2}}[/tex]

0² = 0

[tex]\sqrt{(4+0)}[/tex]

Now for the addition

[tex]\sqrt{(4 + 0)}[/tex]

4 + 0 = 4

√4 <<<This can be further simplified to...

2

***Remember that the above answers are in terms of units

Hope this helped!

~Just a girl in love with Shawn Mendes

Explanation:

The point of a reflecting telescope is to reflect the light toward the eyepiece. That's what each reflecting surface does. By arranging the locations of the foci in the manner described, the light path is made to go from one focus to another, and finally to the focus at the eyepiece location.

Each conic surface is a reflecting surface that reflects the light closer to the eyepiece.

Answer:

Inside a telescope, the parabolic mirror reflects parallel light rays entering the telescope to its focus, which is also the focus of the hyperbolic mirror. The hyperbolic mirror then reflects those light rays to its other focus, where the image is observed.

Step-by-step explanation:

Answer:

0.64 kilometres

Step-by-step explanation:

Step 1: Find the perimeter in metres

Perimeter of square = 4 x (Length)

Perimeter = 4 (160)

Perimeter = 640 metres

Step 2: Convert from metre to kilometre

1 km = 1000 m

x km = 640 m

Cross multiply

1000x = 640

x = 0.64 kilometres

Therefore, the perimeter of the square base is 0.64 kilometres.

!!

Answer:

A 1/2

Step-by-step explanation:

x - 2y = 3

-2y = -x + 3

y = 1/2 x - 3/2

please mark brainliest :)

Answer:

A.  1/2

Step-by-step explanation:

Solve the equation for y.

x - 2y = 3

Subtract x from both sides.

-2y = -x + 3

Divide both sides by -2.

[tex] y = \dfrac{1}{2}x - \dfrac{3}{2} [/tex]

The slope-intercept equation of a line is y = mx + b, where m is the slope.

In the case, m = 1/2.

Answer: slope = 1/2

Answer:

  v = 40 . . . ft/sec

Step-by-step explanation:

Put the value 25 where h is in the formula and do the arithmetic.

  V = √(64·25) = (√64)(√25) = 8·5

  V = 40 . . . . feet per second

Answer:

There's one important property which states that when a number is multiplied by its reciprocal, equals 1.

The commutative property of multiplication states that two or more numbers can be multiplied in any order, therefore, the expression:  (7)×(13/29)×(1/7) can be changed to  (7)×(1/7)×(13/29) and the result won't be altered.

Now, given that 7 and 1/7 are reciprocals, the result is 1. Therefore, the result of the multiplication equals (13/29)

Answer:

communitive property

Step-by-step explanation:

Answer: 45 degree angle

Answer:  She have to sell 32.5 kg to cover her weekly expenses.

Step-by-step explanation:

Since we have given that

Selling price  of cumin  per kg = $7.20

Quantity of cumin she sells = 90 kg

Net profit she get = $414

Total amount she get after selling 90 kg is given by

[tex]90\times 7.20=\$648[/tex]

So, Weekly expenses would be

[tex]\$648-\$414\\\\=\$234[/tex]

Quantity of cumin she need to sell to cover her weekly expenses is given by

[tex]\dfrac{234}{7.20}\\\\=32.5\ kg[/tex]

Hence, She have to sell 32.5 kg to cover her weekly expenses.

Answer:

Answer is in the attachment.

Step-by-step explanation:

To graph x>2 consider first x=2. x=2 is a vertical line and if you want to graph x>2 you need to shade to the right of the vertical line.

To graph x+y<2, I will solve for y first.

x+y<2

Subtract x on both sides:

  y<-x+2

Consider the equation y=-x+2.  This is an equation with y-intercept 2 and slope -1 or -1/1.  So the line you have in that picture looks good for y=-x+2. Now going back to consider y<-x+2 means we want to shade below the line because we had y<.

Now where you see both shadings will be intersection of the shadings and will actually by your answer to system of inequalities you have.  In my picture it is where you have both blue and pink.

I have a graph in the picture that shows the solution.

Also both of your lines will be solid because your question in the picture shows they both have equal signs along with those inequality signs.

Just in case my one graph was confusing, I put a second attachment with just the solution to the system.