Translate the following sentence into an equation. Five times a number less than eighteen is equal to thirteen.

Answer:

[tex]\fbox{\begin{minipage}{13em}approximately 5397.9 dollar\end{minipage}}[/tex]

Step-by-step explanation:

Given:

Lachlan invested $4300 over 5 years at 4.6% p.a., compounded every 6 months.

Solve for:

Total value of his investment.

Step 1: Define the formula to calculate the total value of Lachlan's investment

Total value = Principal x (1 + rate/2)^(Year x 2)

(the rate is divided by 2 and the year is multiplied by 2 because this is compounded semi-annual, not compounded annual)

Step 2: Perform the calculation:

With Principal = 4300$, Rate = 4.6% =4.6/100 = 0.046, Year = 5

=> Total value = 4300 x (1 + 0.046/2)^(5 x 2) ≈ 5397.9$

Hope this helps!

:)

Answer:

210 cm^2

Step-by-step explanation:

3x-1 + 4x+1 + 3x = 70

10x = 70

x = 7

Now, Area of the triangle is 1/2 * b * h

therefore,

1/2 * 3x * 3x-1

1/2 * (3*7) * (3*7 -1)

1/2 * 21 * 20

21 * 10

210

210 is the area!

Hope this helps! mark as brainliest if helped! thanks!

210 cm^2

3x-1 + 4x+1 + 3x = 70

Simplify  

10x = 70

divide by 10

x = 7

So,

1/2 * 3x * 3x-1

1/2 * (3*7) * (3*7 -1)

1/2 * 21 * 20

21 * 10

210 would be your final answer

Step-by-step explanation:

Answer:

I believe the answer will be 36 for the dog legs.

Step-by-step explanation:

first you get a calculator

then you type in 18 divided by 50

then you hit enter

then the answer will come up as 0.36

Answer:

i) The maximum height  of the ball 'x' = 1.5 seconds

ii)   The maximum height  = 42

 Step-by-step explanation:

Step(i):-

Given h(x) = - 16 x² + 48 x +6   ...(i)

Differentiating equation (i) with respective to 'x'

[tex]h ^{l} (x) = - 16 (2 x) +48 (1)[/tex]   ...(ii)

Equating Zero

- 3 2 x + 4 8 = 0

- 32 x = - 48

    x = 1.5

step(ii):-

The maximum height of the ball 'x' = 1.5

Again Differentiating equation (ii) with respective to 'x'

[tex]h ^{ll} (x) = - 16 (2 x) < 0[/tex]

The maximum height 'x' = 1.5

h(x) = - 16 x² + 48 x +6  

h(1.5) = - 16 (1.5)² +4 8 (1.5) +6

         =   42

The maximum height at x = 1.5 is  = 42

Final answer:-

i) The maximum height  of the ball 'x' = 1.5 seconds

ii)   The maximum height  = 42

Answer:

30 m

Step-by-step explanation:

We use the area of a kite which is diagonal 1 multiply it by diagonal 2 then divide by two

Answer:

15:2; there are 2 counselors to every 15 campers

Step-by-step explanation:

Answer:

[tex]\angle\,JLF = 114^o[/tex]  which agrees with option"B" of the possible answers listed

Step-by-step explanation:

Notice that in order to solve this problem  (find angle JLF) , we need to find the value of the angle defined by JLG and subtract it from [tex]180^o[/tex], since they are supplementary angles. So we focus on such, and start by drawing the radii that connects the center of the circle (point "O") to points G and H, in order to observe the central angles that are given to us as [tex]90^o[/tex] and [tex]138^o[/tex]. (see attached image)

We put our efforts into solving the right angle triangle denoted with green borders.

Notice as well, that the triangle JOH that is formed with the two radii and the segment that joins point J to point G, is an isosceles triangle, and therefore the two angles opposite to these equal radius sides, must be equal. We see that angle JOH can be calculated by : [tex]360^o-90^o-138^o=132^o[/tex]

Therefore, the two equal acute angles in the triangle JOH should add to:

[tex]180^o-132^o=48^o[/tex] resulting then in each small acute angle of measure [tex]24^o[/tex].

Now referring to the green sided right angle triangle we can find find angle JLG, using: [tex]180^o-24^o-90^o=66^o[/tex]

Finally, the requested measure of angle JLF is obtained via: [tex]180^o-66^o=114^o[/tex]

Answer:

12 inches

Step-by-step explanation:

A=0.5bh

A=0.5xh

60=0.5*10*x

60=5x

5x=60

x=12

Answer:

A = ½ * base * height

A = ½ * x * (2x-3)

17.5 = ½ * (2x² - 3x)

35 = 2x² - 3x

0 = 2x² - 3x - 35

2x² - 3x - 35 = 0 .......... (the equation)

(2x + 7)(x - 5) = 0

2x + 7 = 0

2x = - 7

x = -7/2 = -3.5

x-5 = 0

x = 5

since we have two result of x, then we can choose the positive one x = 5

so the base is 5 m and the height is

h = (2x - 3) = 2*5 - 3 = 10-3 = 7 m

Answer:

There are 40 windows on the 10th floor

Step-by-step explanation:

Since we know one cube has 4 "windows" (each hole on its side not counting top and bottom) we can calculate that for each "floor" 4 more windows are added. So in other words, if "x" equals the amount of "floors" the equation for solving this would be 4x = # of windows.

7. x=20

8. x=19

Step-by-step explanation:

7. The shape is a parallelogram and the angles that are labeled are opposite from each other, meaning that they are congruent. So, 4x-40=2x (and solve)

8. Same case as last time (parallelogram), and the angles labeled are congruent. So, 2x+19=3x (and solve)

Answer:

the second number line in the second row OR The number line D in the attached image

Step-by-step explanation:

Lets start solving the question.

(For ease of understanding each line i have labeled them please see the attachment to relate my explanation)

first read the question it i mentioned that which number line currently shows 0.8+0.3.

After reading the question it is clear that which ever line will represent it will be the addition of 08.+0.3.

here please take a note that we are dealing with a number line hence the sign also matters.

Now lets start analyzing lines one by one.To make it easy i have attached an image where i have labeled the lines as A,B,C,D,E,and F for the ease  of understanding.

so take the first line A into consideration,

its starting from 0.3 and ending at 0 means its decrementing you can also determine it with the direction. any line that originates from the origin and goes to the right shows increment and addition and the lines that originates from origin and goes to the left shows decrement.

so here we can easily all those lines which are showing a leftward directions as it is decrementing and we want a line that increments 0.8+0.3

so now th lines A,B,F and H can be skipped.

We are done with analyzing line A, line B is skipped and now lets start with C.

here the line start from 0 and ends at 0.8 so it cant be the line as 0.8+0.3 yields 0.11.

so line C can't be the correct one.

Now lets consider the next line that is D.

here it starts at 0.8 and ends at 0.11 means exactly showing an increment of 0.3 also its showing a positive directions as its heading to the right.

so this is the line that correctly shows 0.8+0.3.

Now consider line E it cant be the correct line as its showing only 0 to 0.8.

and now the line that will confuse you is line G.

it starts at 0.3 and ends at 0.11 here there is increment of 0.8 though it seems like correct but it cant be the line showing 0.8+0.3 as we have to select the line that originates at 0.8 and shows an increment of 0.3 and not the one which originates at 0.3 and ends at 0.11 showing an increment of 0.8.

Also the question itself is asking 'LINE' and not 'LINES' so you can take such minute things also into Consideration for avoiding any kind of confusion.

I hope this will help  you.

Answer:

B

Step-by-step explanation:

Answer:

Step-by-step explanation:

x ≥ 2800

12*75=900

900< x

Answer:

2/15

Step-by-step explanation:

75u = 12 - 2

75u = 10

u = 10 / 75 = 2/15

Answer:

75u=12-2

75u=10

u=10/75

Answer:

1/6

Step-by-step explanation:

Since there is only 1 letter R in 6 options it is 1/6 (im not entirely sure)

Answer:   5/6

The complement of an event is basically the complete opposite.

If you define event A to be the event of selecting an R, then the complement of event A is not selecting R.

The probability of selecting R is 1/6 because there is 1 letter R out of 6 letters total. The complement of this is 5/6. You could count out 5 letters that aren't R, out of 6 total, or you can subtract 1/6 from 1 to get

1 - (1/6) = (6/6) - (1/6) = (6-1)/6 = 5/6

Answer:

Negative

Step-by-step explanation:

D has the exact same value but

this time it the other way so your answer

should be -D = 3/2

Nathan is facing West and when he takes a quarter-turn anticlockwise, then he will be facing South.

A quarter-turn anticlockwise means turning [tex]90^{\circ}[/tex] toward the left side.

Suppose a circle where Nathan is facing West.

Now when he takes a quarter-turn anticlockwise means [tex]90^{\circ}[/tex] toward the left side, he would end up facing South.

So, the direction in which he is facing is South.

Learn more about anticlockwise here-https://brainly.com/question/16610588

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Answer:

Perimeter = 28 yards

Area = 49 square yards.

Step-by-step explanation:

Distance formula:

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

Let as consider the vertices of the floor are A(-2,-3), B(-2,4), C(5,4) and D(5,-3).

Using distance formula, we get

[tex]AB=\sqrt{(-2-(-2))^2+(4-(-3))^2}=\sqrt{(-2+2)^2+(4+3)^2}=\sqrt{0+7}^2=7[/tex]

Similarly,

[tex]BC=\sqrt{(5-(-2))^2+(4-4)^2}=7[/tex]

[tex]CD=\sqrt{(5-5)^2+(4-(-3))^2}=7[/tex]

[tex]AD=\sqrt{(5-(-2))^2+(-3-(-3))^2}=7[/tex]

It is conclude that, [tex]AB=BC=CD=AD[/tex].

From the given points it is clear that all sides lie on either vertical or horizontal lines.

Since all sides are equal, and adjacent sides are perpendicular, therefore, the base is a square with edge 7 yards.

Perimeter of square floor is

[tex]P=4a=4(7)=28\text{ yards}[/tex]

Area of square floor is

[tex]A=a^2=7^2=49\text{ sq. yards}[/tex]

Therefore, the perimeter is 28 yards and the area is 49 square yards.

Answer:

C. 4

Step-by-step explanation:

arc length = radius*θ ,

where θ is an angle in radians.

12 = 3*θ

θ = 12/3 = 4

Answer:Choose the statement that is not true based on these diagrams. answer= m∠A = m∠2

The statement that is not true based on these diagrams will be;

⇒ m ∠A = m∠2

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

In Triangle ABC,

⇒ Angle C is 108 degrees and angle B is 34 degrees.

Now,

Since, In Triangle ABC,

⇒ Angle C is 108 degrees and angle B is 34 degrees.

Hence, We get;

⇒ m ∠A + m ∠B + m ∠C = 180°

Substitute all the values, we get;

⇒ m ∠A + 34° + 108° = 180°

⇒ m ∠A + 142° = 180°

⇒ m ∠A = 180° - 142°

⇒ m ∠A = 38°

Thus, The incorrect statement is,

⇒ m ∠A = m∠2

Learn more about the triangle visit:

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Answer:

[tex]Range = [24, 375][/tex]

Step-by-step explanation:

Given

[tex]f(x) = 3x^3[/tex]

[tex]Domain = [2,5][/tex]

Required

Find the Range

The range is calculated by solving for f(2) and f(5). In other words, the range is calculated when x is 2 and x is 5

When x = 2;

f(2) is as follows;

[tex]f(2) = 3*2^3[/tex]

[tex]f(2) = 3 * 8[/tex]

[tex]f(2) = 24[/tex]

When x = 5;

f(5) is as follows;

[tex]f(5) = 3*5^3[/tex]

[tex]f(5) = 3 * 125[/tex]

[tex]f(5) = 375[/tex]

Hence, the range of the function is [24, 375]

Answer:

Option B

Step-by-step explanation:

Consider the steps below;

[tex]3x - 4y = 25,\\3x + 2y = 1\\\\3x - 4y = 25,\\+ ( - 3x - 2y = - 1 )\\\\- 6y = 24,\\y = - 4\\\\3x - 4y = 25,\\3x - 4 * ( - 4 ) = 25,\\3x + 16 = 25,\\3x = 9,\\x = 3\\\\Solution, x = 3, y = - 4[/tex]

To solve this system of equations, I applied process of elimination, which I thought was most convenient. Multiplying the bottom equation by - 1, I added both equations to cancel out the x's and solved for the value of y. Substituting this value of y into the top equation, I solved for the value of x;

Solution ⇒ Option B

Answer:

Step-by-step explanation:

[tex]y^{4}\sqrt{16x^{8}y^{12}z^{4}}=y^{4}\sqrt{4*4*x^{4*2}y^{6*2}z^{2*2}}\\\\ =y^{4}\sqrt{4^{2}*(x^{4})^{2}*(y^{6})^{2}*(z^{2})^{2}}\\\\=y^{4}*4*x^{4}*y^{6}*z^{2}\\\\=4x^{4}y^{4+6}z^{2}\\\\\\=4x^{4}y^{10}z^{2}[/tex]

Answer:

33 hours

Step-by-step explanation:

Take the distance and divide by the rate to get the time

1650/50 = the number of hours

33 hours

Answer:

33 hours

Step-by-step explanation:

mph stands for miles per hour

So, 1650/50=33, which finds how long in hours

So, if your speeds stays constant it should take 33 hours

Answer:

50 lbs.

Step-by-step explanation:

Answer:

45.65

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

The substance in the second beaker must have lost heat for it to solidify

Answer:

Step-by-step explanation:

The thermometer’s temp could have made the liquid to chemically react?

Answer:

1/5

Step-by-step explanation:

F(x)=x^2

g(x)=1/(2x+3)

g(f(-1))=?

x=-1→f(-1)=(-1)^2→f(-1)=1

g(f(-1))=g(1)=1/[2(1)+3]=1/(2+3)→g(f(-1))=1/5

Answer: -24

Step-by-step explanation:

Answer:

17/24

Step-by-step explanation:

(a+b)÷2

a= 2÷3

b= 3÷4

=(2/3 + 3/4)÷2

=(8+9/12)÷2

=17/24