If m+p+k=70, p=2m, and k=2p, then m =

The loan's future amount is $9940

The formula to calculate Simple interest is :

I=PRT

where,

I(interest money created)

P(initial amount of money)

R(interest rate as a decimal)

T(time in years)

I=7000(.07)(6)

I=$2,940

So, the loan's future amount = $7000 + $2940 = $9940

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Answer:

C

Step-by-step explanation:

The slope m of the functions give the measure of the rate of change.

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

g(x) = [tex]\frac{5}{2}[/tex] x - 3 ← is in slope- intercept form

with slope m = [tex]\frac{5}{2}[/tex] = 2.5

Calculate the slope of f(x) using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (0, - 3.5) and (x₂, y₂ ) = (1, - 1) ← 2 points from the table

m = [tex]\frac{-1+3.5}{1-0}[/tex] = 2.5

Hence

The slopes of g(x) and f(x) are both m = 2.5, thus

The functions increase at the same rate → C

Part A

1. 14k+k<30

Add the left hand side to get;

15k<30

Divide both sides by 15.

[tex]\frac{15k}{15}\:<\:\frac{30}{15}[/tex]

k<2

2. We have 9d-3d+7>31

Group similar terms to obtain:

9d-3d>31-7

Combine similar terms:

6d>24

Divide both sides by 6

[tex]\frac{6d}{6}\:>\:\frac{24}{6}[/tex]

This implies that:

d>4

3. We have 13x-2x>77

This implies:

11x>77[tex]\frac{11x}{11} \:>\:\frac{77}{11}[/tex]

x>7

4. We have 5y<7y+18

This implies

5y-7y<18

-2y<18

Divide both sides by -2 and reverse the sign.

[tex]\frac{-2y}{-2} \:>\:\frac{18}{-2}[/tex]

[tex]y\:>\:-9[/tex]

5. The given expression is;

3f-12>-10+9f

Group similar terms:

-12+10>9f-3f

-2>6f

Divide both sides by 6.

[tex]\frac{-2}{6}\:>\:\frac{6f}{6}[/tex]

[tex]-\frac{1}{3}\:>\:f[/tex]

[tex]f\:<\:-\frac{1}{3}[/tex]

6. We have 4t-8<2t-2

Group similar terms;

4t-2t<-2+8

2t<6

t<3

7.  We have

15h+16>6h-20

Group like terms;

15h-6h>-20-16

9h>-36

Divide both sides by 9

h>-4

8. The given inequality is

4r-2r>6-r

This implies

4r-2r+r>6

3r>6

r>2

Part B

x-27=193

x=193+27

x=220

2. The given equation is

f(12)=48

or

12f=48

f=48/12

f=4

3. We have the equation 4s+2=74

4s=74-2

4s=72

s=18

4. The given equation is

9(r+1)-18=2r+12

Expand to get:

9r+9-18=2r+12

Group like terms:

9r-2r=12+18-9

7r=21

r=3

Answer:

6 weeks.

Step-by-step explanation:

Let x be the number of weeks to be found.

Then  4.5x + 18 / 4x = 15/8

Cross multiply:

36x + 144 = 60x

24x = 144

x =  6  (answer).

In approximately 1.67 weeks (or rounded to 2 weeks), Theo and James will have savings in the ratio 15:8.

We can set up an equation to represent the savings of Theo and James over time. Let x be the number of weeks they have saved. Theo will have saved £4.50x and James will have saved £4x. We can set up the equation:

£4.50x / £4x = 15 / 8

Cross-multiplying the equation gives us:

8 * £4.50x = 15 * £4x

Simplifying the equation gives us:

36x = 60x

Dividing both sides by 36x gives us:

1 = 5 / 3x

Cross-multiplying again gives us:

3x = 5

Dividing both sides by 3 gives us:

x = 5 / 3

Therefore, in approximately 1.67 weeks (or rounded to 2 weeks), Theo and James will have savings in the ratio 15:8.

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The minimum y-value is -7.

I'm only a few Brainliests away from ranking up, so one would be much appreciated.

Answer:  A) -7

Step-by-step explanation:

The Asymptote is 1 so the range of the graph is from +1 to -1.

However, there is also a shift down of 6 units, so the range of the transformed graph is from (+1-6 = -5) to (-1-6 = -7).

Therefore, the maximum is -5 and the minimum is -7.

You have to begin by using the triangle sum therom. That means Angle DEC would be 64°, Angle D would be 76°, and angle C would be 40°

Answer:

200.96 ft²

Step-by-step explanation:

The question is on surface area of a closed cylinder

Formulae= SA=2 ×pi× r² + 2×pi×r×h

Where pi=3.14

SA= 2×3.14×2² + 2×3.14×2×14

SA=25.12+175.84

SA=200.96 ft²

Answer:

Ratio would be 9 : 10

Step-by-step explanation:

Liliana surveyed 20 students that how many hours they spend on their computers each week.

The results are as follows

8, 15, 0, 11, 12, 13, 16, 13, 0, 4, 17, 14, 30, 13, 5, 12, 1, 13, 12, 21

In the above results 2 students did not use computers out of 20 students.

Therefore, The total number of students who used their computers = 20 - 2 = 18

So the ratio would be 18 : 20 or 9 : 10

Answer:

C. 18/20 or 9/10

Answer:

<CDH = 110°

Step-by-step explanation:

Given <1 = 70°

Because BF ║ CD so <1 = <3 = 70° (corresponding angles are equal)

<CDH = 180° - <3

<CDH = 180° - 70°

<CDH = 110°

Answer:

125

Step-by-step explanation:

We are given that <1=70. Using that, we know that <5 also equals 70 because of the definition of vertical angles, we then can find <2 also by subtracting 70 from 180 and dividing it by 2 to get 55. <4=<2 and <6=<5, so using substitution we can get m<CDH=125

f(x)=20+300x

Also, Rex should find a different pool because that fee is ridiculous.

The function rule in the given situation is a linear function and can be represented as C=20+300x. In this rule, 'C' is the total cost in dollars, '20' is the initial membership fee, '300' is the cost of each pool visit and 'x' is the number of pool visits.

The function rule in this situation is called a linear function. A function rule describes how to convert an input (in this case, the number of times Rex visits the pool) into an output (the total cost).

The function rule for this specific situation could be represented as C=20+300x, where 'C' is the total cost, '20' is the initial membership fee, '300' is the cost each time Rex goes to the couple, and 'x' is the number of times Rex goes to the pool.

So, each time Rex goes to the pool, you would multiply that number by 300 (the cost per visit), and then add 20 (the initial fee) to get the total cost.

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Answer:

65 ft by 39 ft

Step-by-step explanation:

Let x ft be the length of each part and y ft be the width of each part. The total perimeter of all 5 parts is

[tex]6x+10y=780[/tex]

The length of the large rectangle is 5y ft and the width of the large rectangle is x, so the total area is

[tex]A=x\cdot 5y[/tex]

From the first equation,

[tex]y=78-0.6x[/tex]

Substitute it into the area expression:

[tex]A(x)=x\cdot 5(78-0.6x)=390x-3x^2[/tex]

Find the derivative:

[tex]A'(x)=390-3\cdot 2x=390-6x[/tex]

Equate it to 0:

[tex]390-6x=0\\ \\6x=390\\ \\x=65[/tex]

Then

[tex]y=78-0.6\cdot 65=78-39=39[/tex]

Answer:

D. 254.34 cubic inches

​Step-by-step explanation:

The volume of a cylinder is given by

V = pi r^2h

Where r = 3 in and h = 9 in

V = (3.14) * (3)^2 *9

V = 254.34 in ^3

Answer:

volume of a cylinder= \pi*r^2*h

81*pi

=254.34 in^3

Answer:

The perimeter of the equilateral triangle, P = 24 units

Step-by-step explanation:

All sides of an equilateral triangle are equal. The height of the equilateral triangle is given by :

[tex]h=\dfrac{\sqrt{3} }{2}\times a[/tex]

a is the side of triangle

If the height of an equilateral triangle is, [tex]h=4\sqrt{3}[/tex]

Equation (1) becomes,

[tex]a=\dfrac{2h}{\sqrt{3} }[/tex]

Put h in above formula. So,

[tex]a=\dfrac{2\times 4\sqrt{3}}{\sqrt{3} }[/tex]

a = 8

So, the side of triangle is 8. The sum of all sides is called perimeter of any figure. So,

[tex]P=8\times 3[/tex]

P = 24 units

So, the perimeter of the equilateral triangle is 24 units. Hence, this is the required solution.

Final answer:

To find the perimeter of the equilateral triangle with a height of 4√3, we determine the side length using the relationship between the height and side length of the triangle, and then multiply by three to get a perimeter of 24 units.

Explanation:

The height of an equilateral triangle is given as 4√3. To find the perimeter, we need to determine the length of a side of the triangle. In an equilateral triangle, the height (h) creates a right-angled triangle where the height is opposite to a 60° angle, and the half of a side of the triangle (half-base) is adjacent to it. The relationship is given by the equation h = (a√3)/2, where a is the side length of the equilateral triangle. By substituting the height with 4√3, we get:

4√3 = (a√3)/2 → a = 8

Since all sides of an equilateral triangle are equal, the perimeter is three times the side length, which means the perimeter P = 3 × 8 = 24 units.

pretty sure it’s the crickets because the others one does not make sense, crickets are known for jumping up and down a lot so i’m pretty sure it’s the cricket

Answer:

Step-by-step explanation: the answer is 1 because line a and b are paralel so 1 , 5 are the same as well as (2,7)

Answer:

angle 1

Step-by-step explanation:

this is because they are alternating angles.

Answer:

Rhode Island has 1,000,000 people within an area of 1000 sq miles.....

1,000,000/1000 = 1000 people per sq mile

Step-by-step explanation:

If Alaska had the same number of people per square mile as Rhode Island, its population would be calculated as 663,000 mi^2 times 1,000 people = 663,000,000 people.

Answer:

1. 30

2. 150

3. obtuse

4. acute

5. Adjacent

Step-by-step explanation:

The correct expression for the angles are;

1) m SUT equals  30 Degrees.

2) m TUW equals  150 degrees

3) TUW is obtuse angle

4) SUT is acute angle

5) TUW and SUT are Adjacent angles

Similar to corners, right angles have a 90° measure. Acute angles are less than ninety degrees. More than 90° but less than 180° are obtuse angles. Additionally, a straight angle is 180°, which is the point at which two lines merge into one by going in the same direction.

Any angle is composed of two rays that converge at a point known as the vertex. When two angles share a ray, it indicates that they are adjacent to one another.

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Answer:

Zero is neither positive nor negative integer and is known as origin.

Answer:

The hose is ~70.71 ft long.

Step-by-step explanation:

We need to use Pythagorean theorem to figure this out. ( A^2 + B^2 = C^2)

So we first need to square 50 two times, since that's the length and height of the garden. This equals 5000.

Then we just need to find the root of 5000! This rounds out to about 70.71 ft.

Hope I could help! :)

The length of the hose which is ​stretched from one corner of the garden to another corner across the diagonal of it is 70.72 ft

The diagonal of the square is the distance from opposite vertices of it. There are two diagonals in a square which are equal in measure.

To find the diagonal of the square, the following formula is used.

d=a√2

Here, (a) is the length of the side of the square.

The side of a square garden is 50 ft long. One hose is stretch from one corner of the garden to another corner across the diagonal of it. Thus, the length of the diagonal is,

d=a√2

d=(50)√2

d=70.72 ft

Thus, the length of the hose which is ​stretched from one corner of the garden to another corner across the diagonal of it is 70.72 ft

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Hello There!

6n=13.50

This means that 6 notebooks and some amount represented as n is 13.50

When subtracting logs you actually divide.

logx^2 = log 160 - log 2

logx^2 = log (160/2)

logx^2 = log 80

Now remove the log from each side:

x^2 = 80

x = √80

x = 4√5 and -4√5

Answer:b

Step-by-step explanation:

You're answer is b. All you have to do is a measurement

Answer:

B) 1/2 (154° - 46°)

Step-by-step explanation:

Here ∠XYZ is an angle subtended by two chords from a point outside of the circle.

It is a one of the circle.

If the angle subtended by two chords from the outside point of the circle, the measure of the angle is 1/2 times difference of the major arc and minor arc.

Here Major arc = 154° and minor arc = 46°

Applying the rule, we get

m∠XYZ = [tex]\frac{1}{2} (Major arc - Minor arc)[/tex]

m∠XYZ = 1/2 (154° - 46°)

Answer:

see explanation

Step-by-step explanation:

Given

ab - ac = d + e ← factor out a from both terms on the left side

a(b - c) = d + e ← divide both sides by (b - c)

a = [tex]\frac{d+e}{b-c}[/tex]

Answer:

Step-by-step explanation:

Answer:

x^8/y^20

Step-by-step explanation:

multiply the exponents by 4.

Answer:

Median: 23

Mode: $20

Mean: The average of numbers added up and then divided, equalling in 23

Because integrated math requires skills in trigonometry, I would highly recommend pre calc first

Answer:

I would say you first evaluate your strengths by checking on both the syllabuses. Find what really interests you, your passion. Is it pre-calculus or is it integrated math.

Ability and passion go hand in hand when it comes to the performance.

Answer:

376

Step-by-step explanation:

2(8x10)=2(80)=160

2(10x6)==2(60)=120

2(6x8)=2(48)=96

160+120+96=376

Answer:

a^3 + b^3

Step-by-step explanation:

(a + b )(a^2 - ab + b^2)

Distribute

a*a^2 -a*ab+a*b^2    + b*a^2 -b*ab +b*b^2

Simplify

a^3 -a^2b +ab^2 +a^2b -ab^2+b^3

Combining like terms

a^3 +b^3

Answer:

a^3 + b^3

Step-by-step explanation:

hope this helps you! have a good day/night :D

Answer:

1) 46.6

Step-by-step explanation:

Given Data:

s1 of Triangle ABC= 4cm

s2 of Triangle ABC=6cm

s3 of Triangle ABC=8cm

As per the side-side-side SSS of a given triangle

the corresponding angles are found by the following law of cosine formula

cos A = (b2 + c2 − a2) / 2bc

Putting the values we get

cos A= (4^2+8^2-6^2)/2(4)(8)

cos A= (16+64-36)/64

A=cos^-0.6875

A=46.57!

Answer:

x= 8/3 and x= -8/3

Step-by-step explanation:

Remember the difference of two squares method

a²- b²= (a+b) (a-b)

Given;

9x²-64=0

We notice 9 and 64 are in square form thus can be written as

(3x-8) (3x+8)....................................applying the difference in squares method to simplify

Solving for x

(3x-8) (3x+8) =0

3x-8=0

3x=8

x= 8/3

or

3x+8=0

x= -8/3

Answer:

8/3 and -8/3

Step-by-step explanation: