The diagram shows a solid cuboid with base 10 cm by 6 cm.
The height of the cuboid is x centimetres.
x
10
6
(a) Find an expression, in terms of x, for the total surface area of the cuboid.
(b) The total surface area of the cuboid is 376 cm².
Form an equation in x and solve it to find the height of the cuboid.
Answer (a)
(b)
cm² [1]
cm [2]

In the triangle , the value of x is 57.

What is triangle?

A triangle is a form of polygon with three sides; the intersection of the two longest sides is known as the triangle's vertex. There is an angle created between two sides. One of the crucial elements of geometry is this.

Certain fundamental ideas, including the Pythagorean theorem and trigonometry, rely on the characteristics of triangles. The angles and sides of a triangle determine its kind.

Here in the given triangle , SD=99 , SF=44 , RF = 76 and FE = 76+3x

RE = FE - RF

=> RE = 76+3x-76 = 3x

Now using triangle proportionality theorem then,

=> [tex]\frac{SF}{SD}=\frac{RF}{RE}[/tex]

=> [tex]\frac{44}{99}=\frac{76}{3x}[/tex]

=> 3x = [tex]\frac{76\times99}{44}[/tex] = 171

=> x = 171/3 = 57

Hence the value of x is 57.

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Answer:

(-11, -14)

Step-by-step explanation:

Point (-8, -9)

Translation left 3 units

(-8, -9) → (-11, -9)

Down 5 units

(-11, -9) → (-11, -14)

So, the final point will be at (-11, -14)

ANSWER 1: The supplementary angle measures 58 degrees.

A=S+64=58+64=122

ANSWER 2: The angle measures 122 degrees.

double checking

A+S=180

122+58=180

180=180

Therefore , the solution of the given problem of fraction comes out to be  a = 2/9.

Any arrangement of parts or pieces that are the same dimension can represent the whole. Quantity is referred to in standard English as "a portion" in a given measure. 8, 3/4. Fractions are included in wholes. In mathematics, integers are represented by the ratio which is the divisor to the ratio. These are all examples of basic fractions that are divided by whole integers. The residue is a difficult fraction even though the fraction itself includes a fraction.

Here,

We can begin by separating out the variable component (a + 6) on one side of the equation and simplifying to find a:

=> 9/10 = 8/(a + 6)

Adding (a + 6) to both edges results in:

=> 9/10 * (a + 6) = 8

As the left edge is widened:

=> 9a/10 + 54/10 = 8

54/10 from both groups subtracted:

=> 9a/10 = 2/10

By 9/10ths dividing both sides:

=> a = (2/10)/(9/10)

=> a = 2/9

The answer is therefore a = 2/9.

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Answer: 60.84mm

Step-by-step explanation:

The area of Triangle is:

A = 1/2 * base * height

7.8mm * 3mm = 23.4mm

23.4mm * 1/2
= 11.7mm

Now, find the area of the rectangle:

A = Base * Height

9.3mm * 7.8mm = 72.54mm

Now subtract the area of the triangle from the area of the rectangle

72.54mm - 11.7mm = 60.84mm

Answer:

0.5 feet or 6 inches

Step-by-step explanation:

To find the height of the ball on the 10th bounce, we need to use the given equations. Let h be the height of the ball in feet after n bounces (including the initial drop), and k be a constant that depends on the coefficient of restitution. We also have a starting height of 10 feet and a height of 2 feet after 5 bounces, so:

10 = k * 5h

4 = k * 10h

We can solve these two equations for k, then use them to solve for h:

k = (10 - 4) / (5 * 4) = 0.5

Substituting this value into the original height equation, we get:

h = k^2 * 2 = 0.25 * 2 = 0.5

So, the height of the ball on the 10th bounce is 0.5 feet, or 6 inches.

Answer: 0.09766 feet (0.10 rounded to the nearest tenth)

Step-by-step explanation:

The value of a in the revenue function of the local company is -780, which is obtained by using the given information about the revenue at a selling price of $25.

We are given that the revenue function of the local company is:

R(x) = (a - 20)x + 80,000

We also know that when the selling price is $25, the revenue is $60,000. We can use this information to solve for the value of a:

R(25) = (a - 20)(25) + 80,000 = 60,000

Simplifying this equation, we get:

25a - 500 + 80,000 = 60,000

25a + 79,500 = 60,000

25a = 60,000 - 79,500

25a = -19,500

a = -780

Therefore, the value of a is -780.

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The statements B, D and E can be used to justify that the function is linear.

A function is the central idea of calculus in mathematics. Certain types of functions are the relations. A function in mathematics is a rule that generates a different output for each input x. A mapping or transformation in mathematics serves as the representation of a function. Several people use letters like f, g, and h to denote these operations.

Here in the question,

Given equation is y = 2x - 5

Now we know that the general form of a equation is y = mx + c

So, y = 2x - 5 is a linear equation as it is in the slope equation form.

Now, from the equation,

Slope, m = 2.

Graph of the function is a straight line.

Therefore, we can say that the equation is a linear equation as it has a slope, m=2. The graph is a straight line, and the equation is in the form of y = mx+c.

Hence, the statements B, D and E can be used to justify that the function is linear.

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The complete question is:

Consider the function defined by

y x = − 2 5.

Which statements can be used to justify that the function is linear?

Select all that apply.

A The coefficient of x is greater than 1.

B The function has a constant slope of 2.

C The function has a negative y –intercept.

D The graph of the function is a straight line.

E The equation is written in the form y mx b = +.

PLS HELP ASAP!

Answer:

42944[tex]cm^{2}[/tex]

Step-by-step explanation:

(240*180)-(16*16)

43200-256

42944

The probability of waiting longer than one hour for a taxi is approximately 0.5488

Let X be the time between arrivals of taxis at the intersection. Then, X follows an exponential distribution with a mean of 10 minutes, i.e., E(X) = 10.

We want to find the probability of waiting longer than one hour (i.e., 60 minutes) for a taxi. Let Y be the waiting time for a taxi. Then, Y = kX, where k is a constant.

We can find k as follows

E(Y) = E(kX) = kE(X) = 10k

Since the mean waiting time is one hour (i.e., 60 minutes), we have

E(Y) = 60 minutes = 1 hour

Therefore, we get

10k = 1

k = 1/10

Now we can find the probability of waiting longer than one hour for a taxi as follows

P(Y > 60) = P(kX > 60) = P(X > 6) [since k = 1/10]

where the last step follows from the fact that X follows an exponential distribution with mean 10, so P(X > x) = e^(-x/10) for any x > 0.

Therefore, we get

P(Y > 60) = P(X > 6) = e^(-6/10) = e^(-0.6) ≈ 0.5488

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The given question is incomplete, the complete question is:

The time between arrivals of taxis at a busy intersection is exponentially distributed with a mean of 10 minutes. (a) What is the probability that you wait longer than one hour for a taxi?

Answer:

x -intercept  ---> (-6,0)

y-intercept ---> (0, 9)

Step-by-step explanation:

3x = -18

3x/3 = -18/3

x = (-6,0)

-2y = -18

-2y/-2 = -18/-2

y = (0, 9)

Answer: (i) The length of the wire is 2147.76 cm.

(ii) The volume of the wire is 43.16 cm^3.

Step-by-step explanation:

Given : Diameter of copper wire = 8mm = 0.08cm

length of the cylinder = 24 cm

diameter of the cylinder = 49 cm

(i) To calculate the length of the wire.

As we know, surface area of the cylinder = πrl = 3.14*28.5*24 = 2147.76cm.

Hence, the surface area of the cylinder will be the length of the wire, as the wire is evenly wrapped n the surface of the cylinder.

Therefore, the length of the wire is 2147.76 cm.

(ii) To calculate the volume of the wire.

As we know, the formula for the volume of the cylinder = πr^2h

now the volume of the wire is = 3.14*0.08*0.08*2147.76 = 43.16 cm^3.

Therefore, the volume of the wire is 43.16 cm^3.

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Answer:

10.8 miles

Step-by-step explanation:

Use Pythagorean Theorem

[tex]a^{2} +b^{2} = c^{2}[/tex]

[tex]9^{2} +6^{2} = c^{2}[/tex]

[tex]c^{2} = 117[/tex]

[tex]c=\sqrt{117}[/tex]

Rounded to 10.8

The distance from point A to point B is 568.07ft.

What is the distance?

Distance is a measurement of how far apart two things or points are, either numerically or occasionally qualitatively. The distance can refer to a physical length in physics or to an estimate based on other factors in common usage.

Here, we have

Given: A boat is heading toward a lighthouse, whose beacon light is 130 feet above the water. From point. A, the boat’s crew measures the angle of elevation to the beacon, 6°, before they draw closer. They measure the angle of elevation a second time from point  B at some later time to be 11°.

Assuming a flat earth

initial measurement

tan6 = 130 / d₁

d₁ = 130/tan6 = 1236.86... ft

d₂ = 130/tan11 = 668.79...ft

distance from A to B

1236.86 - 668.79 = 568.07ft

Hence, the distance from point A to point B is 568.07ft.

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Answer:

568

Step-by-step explanation:

i got this as a question and that was the correct answer

The minimum length the ramp will need to be so that it is safe for hand-powered wheelchairs is approximately 19.7 feet.

To calculate the minimum length of the ramp, we can use trigonometry. We know that the height of the ramp is 1.5 feet and that the angle of elevation should be no greater than 4.8°. Let's call the length of the ramp L.

The tangent of 4.8° is given by:

[tex]$$\tan(4.8\degree) \approx 0.084$$[/tex]

We can use this to set up an equation:

[tex]$$\frac{1.5}{L} \leq 0.084$$[/tex]

Solving for L, we get:

[tex]$$L \geq \frac{1.5}{0.084} \approx 17.9$$[/tex]

So the minimum length the ramp will need to be is approximately 17.9 feet. However, we should round up to ensure that the angle of elevation is no greater than 4.8°. Therefore, the minimum length the ramp will need to be so that it is safe for hand-powered wheelchairs is approximately 19.7 feet.

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Answer:

x = 43 degrees

Step-by-step explanation:

47+90 degrees = 137

that little box means that is a 90-degree angle.

(because straight angles are measured 180 degrees) :

180 - 137 = 43

that missing part between 90 degrees (the box) and 47 degrees equals 43.

because 43 is positioned from x where it is, x is also equivalent to 43 degrees.

and just for bonus that's a 90 degree angle to the right of "x" and that's a 47 degree angle to the left of "x" because these angles are all OPPOSITE.

therefore they are congruent.

To calculate how many sheets of graph paper each of the 26 students in Mr. Ramirez's math class will get if they all get the same number, we need to divide the total number of sheets by the number of students:

Number of sheets per student = Total number of sheets / Number of students

Number of sheets per student = 250 / 26

Number of sheets per student ≈ 9.615

So each student will get approximately 9 sheets of graph paper.

To calculate how many sheets will be left over, we can use the modulo operator (%), which returns the remainder of a division:

Sheets left over = Total number of sheets % Number of students

Sheets left over = 250 % 26

Sheets left over = 12

So there will be 12 sheets of graph paper left over after each of the 26 students has received approximately 9 sheets.

The price of the tablet computer after discount and marked up is $663.3.

What is discount?

Discount is the state of having a bond's price lower than its face value. The difference between the purchase price and the item's par value is the discount.

Discounts are different types of price reductions or deductions from a product's cost. It is frequently employed in consumer transactions when consumers receive discounts on a range of goods. The % discount rate is provided.

Here the original price of tablet computer = $670

During a sale , store offered 10% discount then

=> Price of tablet computer = 670× ( 100%-10%) = 670 × 90%

Now after the sale the price of the tablet computer marked up 10%. Then,

=> Price of tablet computer = 670 × 90% × (100%+10%)

=> Price of tablet computer = 670 × 90% × 110%

=> Price of tablet computer = 670 × [tex]\frac{90}{100} \times \frac{110}{100}[/tex]

=> Price of tablet computer = 670 × 0.9 × 1.1 = $663.3

Hence the price of the tablet computer after discount and marked up is $663.3.

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After answering the provided question, we can state that So the equation difference in the measures of the two angles is 63 degrees.

In mathematics, an equation is a proclamation stating the justice or two phrases. An equation is made up of two sides that are separated by an algebraic equation (=). Equations can be used to solve problems and find solutions to mathematical questions. They can involve different mathematical operations such as addition, subtraction, multiplication, division, exponents, and roots.

Since ∠A is a right angle, its measure is 90 degrees.

Therefore, we have:

m∠B - m∠A = [(9x-24) - (11x+13)]°

m∠B - m∠A = (9x - 24 - 11x - 13)°

m∠B - m∠A = (-2x - 37)°

|m∠B - m∠A| = |-2x - 37|°

And since ∠A is a right angle, its measure is 90 degrees, so we have:

|m∠B - m∠A| = |-2x - 37|° = |90 - (11x + 13)|°

11x + 13 = 90

11x = 77

x = 7

m∠A = 90°

m∠B = (9x - 24)° = (9(7) - 24)° = 27°

|m∠B - m∠A| = |27 - 90|° = 63°

So the difference in the measures of the two angles is 63 degrees.

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Answer:

School A: 240 students

School B: 380 students

Step-by-step explanation:

We get these answers by dividing the number of students in each school by 2.

I hope this helps!

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The required time the cyclist would take to ride 156 miles with a rate of 24 mph is 6.5 hours.

Speed is defined as when an object is in motion, the distance covered by that object per unit of time is called speed.

Here,

To find the time it takes a cyclist to cover a certain distance at a constant rate, you can use the formula:

time = distance/speed.

Plugging in the given values, you get:

[tex]\text{time} = 156 \ \text{miles} \div 24 \ \text{mph} = 6.5 \ \text{hours}[/tex].

So it would take the cyclist 6.5 hours to ride 156 miles at a constant rate of 24 mph.

The measure of ∠BAC is 140° which is the interior angle of the circle.

It is given that the lines BD and CD are tangent to the circle.

It is required to find the measure of ∠BAC if ∠BDC = 40°

What is a circle?

It is described as a group of points, each of which is equally spaced from a fixed point (called the centre of a circle).

We have BD and CD are tangent to circle ∠BDC = 40°

Here we can see in the figure that ∠BAC is the interior angle.

∠ACD = 90° and ∠ABD=90° (because AC is the perpendicular to DC)

So the measure of the ∠BAC is:

= 360 - ∠ACD - ∠ABD - ∠BDC

= 360 - 90 - 90 - 40

= 140°

Thus, the measure of ∠BAC is 140° which is the interior angle of the circle.

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Answer:

see below

Step-by-step explanation:

All you need to do is plot the coordinates on the plot.

ex (1,2); (2,2); (3,3) etc.

See attached screenshot

Lily took a certain number, multiplied it by 3, and then subtracted 8 from the product, which resulted in 7. The initial number was 5.

The equation that describes this situation is: 3k - 8 = 7.

To solve for k, we can isolate the variable by adding 8 to both the sides of the equation:

3k - 8 + 8 = 7 + 8

3k = 15

Finally, we can solve for k by dividing both sides of the equation by 3:

k = 5

Therefore, Lily started with the number 5, tripled it to get 15, and then subtracted 8 to get an answer of 7.

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[tex](\stackrel{x_1}{-3}~,~\stackrel{y_1}{2})\hspace{10em} \stackrel{slope}{m} ~=~ 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-\stackrel{y_1}{2}=\stackrel{m}{ 4}(x-\stackrel{x_1}{(-3)}) \implies y -2= 4 (x +3)[/tex]

[tex]y-2=4x+12\implies y=4x+\underset{ \stackrel{\uparrow }{b} }{14}\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]

[tex](\stackrel{x_1}{-9}~,~\stackrel{y_1}{-5})\qquad (\stackrel{x_2}{w}~,~\stackrel{y_2}{3}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{3}-\stackrel{y1}{(-5)}}}{\underset{\textit{\large run}} {\underset{x_2}{w}-\underset{x_1}{(-9)}}} ~~ = ~~\stackrel{\stackrel{\textit{\small slope}}{\downarrow }}{ -8 }\implies \cfrac{3+5}{w+9}=-8\implies \cfrac{8}{w+9}=-8 \\\\\\ \cfrac{8}{-8}=w+9\implies -1=w+9\implies -10=w[/tex]

Answer:

  715 mL

Step-by-step explanation:

You want the total volume in two containers that have the volume ratio 4:7 and a difference in volumes of 195 mL.

Considering the question in terms of "ratio units," we see the difference of ratio units is 7-4 = 3, and the total of ratio units is 7+4 = 11. Then the total volume will be 11/3 times the difference in volume:

  total volume = (11/3)(195 mL)

  total volume = 715 mL

__

Additional comment

Though it is not necessary, as a check you can work out the volumes of the containers. The smaller will be 4/3 times the difference: 260 mL, and the larger will be 7/3 times the difference: 455 mL. The total is ...

  455 +260 = 715 . . . mL

and the difference is ...

  455 -260 = 195 . . . mL

If you prefer to work with equations for the volume, you can let x and y represent the volumes of the smaller and larger containers. Now you have ...

  x/y = 4/7

  y -x = 195

Substituting for y gives ...

  x/(195 +x) = 4/7

  7x = 4(195) +4x

  3x = 4(195)   ⇒   x = (4/3)·195 . . . . as above

Then the total volume is ...

  x+y = 195 +2x = 195(1 +2·4/3) = 11/3·195 . . . as above

Step-by-step explanation:

Given that:

Part of the graph of the function f(x) = (x – 1)(x + 7) is shown below. Which statements about the function are true? Select three options. The vertex of the function is at (–4,–15). The vertex of the function is at (–3,–16). The graph is increasing on the interval x > –3. The graph is positive only on the intervals where x < –7 and where x > 1. The graph is negative on the interval x < –4.

Solution:

1) The vertex of the function is at (–4,–15).

Ans.This is false.

2) The vertex of the function is at (–3,–16).

Ans. This is true. from the graph it is clearly shown A is vertex of graph.Which is (-3,-16)

3)The graph is increasing on the interval x > –3.

Ans. This region is located in graph with red colour,here it is easily shown that in this region graph continuously increasing.

This is true.

4)The graph is positive only on the intervals where x < –7 and where x > 1.

Ans: Yes,it is true.

Because when x<-7 graph is decreasing but have positive values and when x>1,graph is increasing and have positive values.

5)The graph is negative on the interval x < –4.

Ans:Yes,yellow part is shown the region of x<-4

here value of graph continuously decreasing.

Hope this helps!

Answer for 9/10 + 5/8 = 61/40

A statement that shows the two mathematical expressions which are equal to each other is known as an equation. It may have one or more variables, and the objective is frequently to determine the values of the variables that hold the equation true.

According to the question; add two fractions, we need to find a common denominator.

The common denominator for 10 and 8 is 40.

therefore, to convert both fractions to have a denominator of 40:

9/10 = (9/10) × (4/4) = 36/40

5/8 = (5/8) × (5/5) = 25/40

Here the fractions have the same denominator (40), we can add them:

36/40 + 25/40 = 61/40

Therefore, 9/10 + 5/8 = 61/40.

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Suppose a certain medical test has a false positive rate of 6 out of 3,500, then during the period in which 27 false positives were obtained, the number of people tested was 15,750.

Step 1: Determine the probability of a false positive. The probability of a false positive is given as 6 out of 3500, so it can be expressed as a fraction: 6/3500

Step 2: Determine the number of false positives in the given period. The problem states that 27 false positives returned during the period, therefore: False positive rate x number of people tested = number of false positives 6/3500 x number of people tested = 27

Step 3: Solve for the number of people tested. 6/3500 x number of people tested = 27 Number of people tested = 27 / (6/3500) Number of people tested = 15,750 Therefore, during the period in which 27 false positives were obtained, the number of people analyzed was 15,750.

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