The dimensions of a triangular prism are shown in the diagram. The prism is not drawn to scale.
What is the volume of the triangular prism in cubic centimeters?

Answer:

The solution would be h=-4

Step-by-step explanation:

By distributing, we are able to find this answer.

Answer:

35 ft²

Step-by-step explanation:

The shape is a triangle and its area is given by the formula below:

Area of triangle= ½ ×base ×height

Do note that the height has to be the perpendicular height, which is 5 ft in this case.

Area of triangle

= ½(14)(5)

= 35 ft²

Answer:

option 1 is correct  

☆Explanation:

¤ We that area of a Rectangle = length × breadth

¤ Here, it is said to find the area of the given figure.

Now,

Area of first Rectangle = length × breadth

= 9 cm × 4 cm

= 36 cm²

Again,

Area of the second Rectangle = length × breadth

= 14 - 4 × 5

= 10 × 5

= 50 cm²

Finally,

Area of the figure = Area of first Rectangle + Area of second Rectangle.

= 36 cm² + 50 cm²

= 86 cm²

1) K=17°

2)Jk=2.84yd

3)KL=2.71yd

Answer:g(x) = f(x) + 1.5

Step-by-step explanation: The graph of f(x) = x² was transformed to create the graph of g(x) = f(x) + 1.5. Which statement about the graphs is true?

The vertex of the graph of g is 1.5 units to the left of

the vertex of the graph of f.

B

The y-intercept of the graph of g is 1.5 units above the

y-intercept of the graph of f.

The graph of g is a reflection of the graph of f across

the y-axis.

The graph of g is a reflection of the graph of f across

the x-axis.

Answer:

100 minutes

Step-by-step explanation:

subtract 14h10 from 15h00

this will equal 50

then add the remaining 50minutes from 15h00

The question is an illustration of conditional probability, and the value of the conditional probability P(A|B) is 0.38

The question is incomplete, as the required parameters are not given.

So, I will give a general explanation.

The question is an illustration of conditional probability

The conditional probability is used to determine the probability of an event, given that another independent event has already occurred.

The conditional probability is calculated using:

P(A|B) = n(A and B)/n(B)

Assume the following parameters

n(A and B) = 9

n(B) = 24

The equation to calculate the probability expression is represented as:

P(A|B) = n(A and B)/n(B)

Substitute the assumed values

P(A|B) = 9/24

Evaluate the expression

P(A|B) = 0.38

Hence, the value of the conditional probability P(A|B) is 0.38

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Answer:

80 pages

Step-by-step explanation:

Divide 60 by 3 to get 20 because this is how many pages he can read in 1/4 hour. Then multiply that by 4 to get 80, which is how many pages he can read in a full hour.

Answer: $573.50

Step-by-step explanation:

Hi!

Your answer is 8  1-quart containers.

There are 4 quarts in a gallon.

If there is a 2-gallon bucket, and she needs to fill it using 1-quart containers, we simply multiply the number of quarts in a gallon (4) by the number of gallons total (2).

2 x 4 = 8

Answer:

D is the correct answer

Step-by-step explanation:

A is not correct because it does not meet the fourth criteria, B is not correct because it doesnt meet the second criteria, C is not correct because it does not meet the third criteria, D IS CORRECT because it meets the fourth criteria.

Answer:

15.6% gives you 24.96 which is almost the equivelenth of 160-185

Step-by-step explanation:

take the number and try to find a percent that works.

Answer:

$26

Step-by-step explanation:

4 times a week, $15 a day

It means that he have to pay $60 a week for travelling

$60-$34 = $26

By buying the pass I can save $26 a week

Answer:26 DOLLARS saved

Step-by-step explanation:

====================================================

How I got that answer:

The interval 0 < t < 30 has the midpoint of 15 since (0+30)/2 = 15

The interval 30 < t < 60 has the midpoint 45 because (30+60)/2 = 45

We add up the endpoints and then divide by 2 to get the midpoint.

Repeat this for each of the intervals mentioned.

From top to bottom, the midpoints are:

Notice we add 30 to each midpoint to get the next one. This is directly due to the fact that each interval is 30 units wide (eg: 90-60 = 30).

Multiply each midpoint by the corresponding frequency for a given row.

Then add up those products.

105+1215+900+420 = 2640

Lastly, we divide this over the sum of the frequencies 7+27+12+4 = 50 to get 2640/50 = 52.8

The average time spent on homework is estimated to be about 52.8 minutes

Note that the majority of the the students (27) are in the 30 < t < 60 interval, so the mean of 52.8 fits this interval perfectly. It's closer to the right endpoint of the interval due to the fact the other 12+4 = 16 students are above this, and they make up the second most majority compared to the 27.

The reason why 52.8 is an estimate rather than the actual mean is because we are estimating each interval by picking out the midpoint each time. The midpoint is at the direct center, so it's the best guess we can do.

Answer:

He would save $19.20.

Step-by-step explanation:

30% = 0.3

64*0.3 = 19.2

There he saves $19.20 on the coat.

Answer:

25

Step-by-step explanation:

The formula for the Pythagorean Theorem is:

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

Now,

A=7

B=24

7x7=49

24x24=576

Add,

576+49=625

Last,

Take the square root of 625

The square root of 625 is 25

c=25

To Check if the hypotenuse is correct:

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

[tex]7^2+24^2=25^2[/tex]

7x7=49

24x24=576

25x25=625

49+576=625

625=625,

Therefore the hypotenuse is 25.

Answer:

The answer is

→ No property

Step-by-step explanation:

Given equation: [tex]2x + 9 = 4x + 15[/tex]

What were supposed to do: Which properly justifies step 4.

Solve:

[tex]2x + 9 = 4x + 15[/tex]

Step 1: We must subtract 4x on both sides.

[tex]2x+9-4x=4x+15-4x[/tex]

[tex]= -2x+9=15[/tex]

Step 2: We must subtract 9 on both sides.

[tex]-2x+9-9=15-9[/tex]

[tex]= -2x=6[/tex]

Step 3: We must divide both sides by -2.

[tex]\frac{-2}{2} = \frac{6}{-2}[/tex]

[tex]= x = -3[/tex]

Result:

[tex]x=-3[/tex]

There is no Step 4.

Answer:

Inf solutions.

Step-by-step explanation:

1/2 (b+14) = b+14/2

Simplify

b+14 = b+14

B=b

Since the answers are equal on both sides there are infinite solutions,

Answer:

4. 3 cans of paint will cover 60% of Dalia's room

5. Dalia's entire room requires 5 cans of paint

Step-by-step explanation:

If Dalia has painted 1/10 of her room with 1/2 can of paint, then she will paint 2/10 of her room with 1 can of paint (since there are 2 halves in a whole).

2/10 = 1/5  ⇒  1 can of paint covers 1/5 of the room.

Therefore, to paint the entire room, she will need 5 cans of paint.

60% of 5 cans of paint = 0.6 × 5 = 3

Therefore, 3 cans of paint will cover 60% of the room.

Answer:

I'm assuming where you wrote x2, you meant 2x.

Anyway, if csc (x) = 2, since csc(x) = 1/sin(x), we know that 1/sin x = 2, so sin (x) = 1/2. Since sin2x + cos2x = 1, cos2x = 1 - sin2x, so cos x = √1 - sin2x. In this case, cos x = √ 1 - (1/2)2 = √(3/4) = (√3)/2. Finally, since sin x = opp / hyp , cos = adj/ hyp: sin x / cos x = (opp/hyp)/(adj/hyp) = opp/adj = tan x. So this means that tan x = sin x / cos x = 1/2 / √ 3 / 2 = 1/√3 = √3 / 3

At this point, all that is necessary is to use the double angle formulas for sin, cos, and tan.

sin (2x) = 2 sin x cos x = 2 (1/2) (√3/2) = √3 / 2

cos (2x) = cos2x - sin2x = (√3/2)2 - (1/2)2 = 3/4 - 1/4 = 1/2

tan (2x) = 2 tan x / (1 - tan2x) = 2 (√3 / 3) / ( 1 - (√3/3)2) = 2/√3 / (1 - 1/3) = 2/√3 / (2/3) = 3/√3 = √3

To sum up, sin (2x) = √4 / 2, cos (2x) = 1/2, and tan(2x) = ✓3.

Step-by-step explanation:

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[tex]\sin\left(\frac{x}{2}\right) = \pm\frac{\sqrt{4 + \sqrt{15}}}{\sqrt{8}}\\\cos\left(\frac{x}{2}\right) = \pm\frac{\sqrt{4 - \sqrt{15}}}{\sqrt{8}}\\\tan\left(\frac{x}{2}\right) = \pm\frac{\sqrt{4 + \sqrt{15}}}{\sqrt{4 - \sqrt{15}}}\\[/tex]

To find sin(x/2), cos(x/2), and tan(x/2), we need to use the half-angle identities for trigonometric functions.

Given: csc(x) = 4 for 90° < x < 180°

Step 1: Find sin(x). Since csc(x) is the reciprocal of sin(x), we have:

csc(x) = 1/sin(x) = 4

Now, find sin(x):

sin(x) = 1/csc(x) = 1/4

Step 2: Find cos(x). To do this, use the Pythagorean identity:

[tex]sin^2(x) + cos^2(x) = 1\\cos^2(x) = 1 - sin^2(x) \\= 1 - (1/4)^2 \\= 1 - 1/16 \\= 15/16[/tex]

Now, find cos(x):

[tex]\cos(x) = \pm \sqrt{\frac{15}{16}}[/tex]

Since x is in the second quadrant (90° < x < 180°), cos(x) is negative. So,

[tex]\cos(x) = - \sqrt{\frac{15}{16}}[/tex]

[tex]= -\sqrt{15} / 4[/tex]

Step 3: Find tan(x). To do this, use the identity:

[tex]\tan(x) = \frac{\sin(x)}{\cos(x)}\\\tan(x) = \frac{\frac{1}{4}}{-\frac{\sqrt{15}}{4}}\\\tan(x) = -\frac{1}{\sqrt{15}}[/tex]

Now, let's find sin(x/2), cos(x/2), and tan(x/2) using the half-angle identities:

Half-angle identities:

[tex]\sin \left ( \frac{x}{2} \right ) = \pm \sqrt{\frac{1 - \cos x}{2}}\\\cos \left ( \frac{x}{2} \right ) = \pm \sqrt{\frac{1 + \cos x}{2}}\\\tan \left ( \frac{x}{2} \right ) = \frac{\sin \left ( \frac{x}{2} \right )}{\cos \left ( \frac{x}{2} \right )}[/tex]

Step 4: Find sin(x/2):

[tex]\sin \left( \frac{x}{2} \right) = \pm \sqrt{\frac{1 - \cos x}{2}}\\\sin \left( \frac{x}{2} \right) = \pm \sqrt{\frac{1 + \frac{\sqrt{15}}{4}}{2}}\\\sin \left( \frac{x}{2} \right) = \pm \sqrt{\frac{4 + \sqrt{15}}{8}}\\\sin \left( \frac{x}{2} \right) = \pm \frac{\sqrt{4 + \sqrt{15}}}{\sqrt{8}}\\\sin \left( \frac{x}{2} \right) = \pm \frac{\sqrt{4 + \sqrt{15}}}{2}[/tex]

Step 5: Find cos(x/2):

[tex]\cos\left(\frac{x}{2}\right) = \pm\sqrt{\frac{1 + \cos(x)}{2}}\\\cos\left(\frac{x}{2}\right) = \pm\sqrt{\frac{1 + \left(-\frac{\sqrt{15}}{4}\right)}{2}}\\\cos\left(\frac{x}{2}\right) = \pm\sqrt{\frac{1 - \frac{\sqrt{15}}{4}}{2}}\\\cos\left(\frac{x}{2}\right) = \pm\sqrt{\frac{4 - \sqrt{15}}{8}}\\\cos\left(\frac{x}{2}\right) = \pm\frac{\sqrt{4 - \sqrt{15}}}{\sqrt{8}}\cos\left(\frac{x}{2}\right) = \pm\left(\frac{\sqrt{4 - \sqrt{15}}}{\sqrt{8}}\right)[/tex]

Step 6: Find tan(x/2):

[tex]\tan \left ( \frac{x}{2} \right ) = \frac{\sin \left ( \frac{x}{2} \right )}{\cos \left ( \frac{x}{2} \right )} = \pm \frac{\sqrt{4 + \sqrt{15}}}{\sqrt{4 - \sqrt{15}}}[/tex]

So, the values are:

[tex]\sin\left(\frac{x}{2}\right) = \pm\frac{\sqrt{4 + \sqrt{15}}}{\sqrt{8}}\\\cos\left(\frac{x}{2}\right) = \pm\frac{\sqrt{4 - \sqrt{15}}}{\sqrt{8}}\\\tan\left(\frac{x}{2}\right) = \pm\frac{\sqrt{4 + \sqrt{15}}}{\sqrt{4 - \sqrt{15}}}\\[/tex]

Note: The ± symbol indicates that there are two possible solutions due to the quadrant restrictions.

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Complete Question is:

If csc ( x ) = 4, for 90 ∘ < x < 180, then sin ( x /2 ) = ? cos ( x /2 ) = ? tan ( x /2 ) = ?

Answer:

7

Step-by-step explanation:

apply the Pythagorean theorem

[tex]10 {}^{2} = ( \sqrt{51} ) {}^{2} + x {}^{2} \\ 100 = 51 + x {}^{2} \\ 100 - 51 = x {}^{2} \\ 49 = x {}^{2} \\ x = 7[/tex]

Answer:

50

Step-by-step explanation:

I just did it with my friend.

The lines are

i)  y=-x+6

ii) y=2x-3

The solution of the system of equations is found by equalizing the 2 equations:

-x+6=2x-3

-2x-x=-6-3

-3x=-9

x=-9/(-3)=3

substitute x=3 in either i) or ii):

i)  y=-3+6=3

ii) y=2(3)-3=6-3=3

(the result is the same, so checking one is enough)

This means that the point (3, 3) is a point which is in both lines, so a solution to the system.

In graphs, this means that the lines intersect at (3, 3) ONLY

Answer: The graph where the lines intersect at (3, 3)

Answer:

4

Step-by-step explanation:

Answer:

-7.33

Step-by-step explanation:

Answer:

-7.333

Step-by-step explanation:

To solve this you have to use B O D M A S theorem and we have to solve the given expression according to the theorem.

That is,

B ⇒ Brackets

O ⇒ Of

D ⇒ Division

M ⇒ Multiplication

A ⇒ Addition

S ⇒ Subtraction

Let us solve it now.

[tex]\frac{6}{3} (13-18)+2^{4}[/tex] ÷ [tex]6[/tex]

2 ( -5) + 16÷ 6

-10 + 2.667

-7.333

Answer:

70% to about 85% of your maximum heart rate

Step-by-step explanation: