A triangle has a base of (3x+7) and a height of (5x-1)a second triangle is drawn with a base that is tripled and its height is doubled. Find the difference between the area of the original triangle and the area of the new triangle

Answer:

Option A. f(x) = 4x + 7

Step-by-step explanation:

To obtain the answer to the question, we simply try each of the equation using the first two value of x in the table to see which of them will satisfy the table. This is illustrated below:

For option A

1. f(x) = 4x + 7

x = - 1

f(x) = 4(-1) + 7

f(x) = - 4 + 7

f(x) = 3

2. f(x) = 4x + 7

x = 0

f(x) = 4(0) + 7

f(x) = 0 + 7

f(x) = 0

For option B

1. f(x) = 7x - 4

x = - 1

f(x) = 7(-1) - 4

f(x) = - 7 - 4

f(x) = - 11

2. f(x) = 7x - 4

x = 0

f(x) = 7(0) - 4

f(x) = 0 - 4

f(x) = - 4

For Option C

1. f(x) = -4x - 1

x = - 1

f(x) = -4(-1) - 1

f(x) = 4 - 1

f(x) = 3

2. f(x) = -4x - 1

x = 0

f(x) = -4(0) - 1

f(x) = 0 - 1

f(x) = - 1

For Option D

1. f(x) = x + 7

x = - 1

f(x) = - 1 + 7

f(x) = 6

2. f(x) = x + 7

x = 0

f(x) = 0 + 7

f(x) = 7

From the illustrations made above, only option A satisfy the table.

Answer:

Amount invested in account with 5% annual interest = $300

Amount invested in account with 7% annual interest = $400

Amount invested in account with 8% annual interest = $900

Step-by-step explanation:

Let the money invested in account with 5% annual interest = [tex]x[/tex]

As per question statement,

Money invested in account with 8% annual interest = [tex]3x[/tex]

Given that total amount invested in three accounts = $1600

So, Money invested in account with 7% annual interest = 1600- [tex]3x[/tex] -[tex]x[/tex] = 1600- [tex]4x[/tex]

For one year, the compound interest is same as that of Simple Interest.

Formula for simple interest is given as:

[tex]SI =\dfrac{PRT}{100}[/tex]

Where, P is the amount invested

R is the annual rate of interest

T is the time for which the amount is invested.

As per question statement:

[tex]\dfrac{x\times 5\times 1}{100}+\dfrac{(1600-4x)\times 7\times 1}{100}+\dfrac{3x\times 8\times 1}{100} =115\\\Rightarrow 5x\times +1600\times 7-28x+24x=11500\\\Rightarrow 29x-28x = 11500-11200\\\Rightarrow \bold{x =\$300}[/tex]

Amount invested in account with 5% annual interest = $300

Amount invested in account with 7% annual interest = $1600-$1200 = $400

Amount invested in account with 8% annual interest = $900

Answer:

C. 4.09 m

Step-by-step explanation:

Let the length of the shadow cast by a person be x m.

[tex] \tan \: 24 \degree = \frac{height \: of \: person}{length \: of \: the \: shadow} \\ \\ 0.4452286853 = \frac{1.82}{x} \\ \\ x = \frac{1.82}{0.4452286853} \\ \\ x = 4.08778693 \: m \\ x = 4.09 \: m[/tex]

The length of the shadow cast by a person 1.82m tall is 4.99m.

The angle of elevation is an angle a person's sight is making with the object if he stands in the front of an object.

We have been given that the angle of elevation to the sun is 24 degree and the person is 1.82m tall. Then the length of the shadow will be:

tan(24)=1.82/length of the shadow

0.445286853=1.82/length of the shadow

length of the shadow=4.087

=4.09 (approx)

Hence the length of the shadow cast by a person 1.82m tall is 4.09m if the angle of elevation to the sun is 24 degrees.

Learn more about angle of elevation at https://brainly.com/question/88158

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Answer:

Change In velocity= 13.72 ms^-1

Step-by-step explanation:

fish experiences an acceleration of

9.8 m/s^2 over a period of 1.4s

Change in velocity/time= acceleration

Time in seconds= 1.4 s

Acceleration in meter per second square= 9.8 m/s^2

Change in velocity/time= acceleration

Change In velocity= acceleration*time

Change In velocity= 9.8*1.4(m/s^2 *s)

Change In velocity= 13.72 ms^-1

Answer:

11^5/3

Step-by-step explanation:

when you move the 5 over to the right, it always goes above the other exponent. if that makes sense? I use this shortcut.

another way of showing is:

[tex]x\frac{a}{b} = \sqrt[b]{x^a}[/tex]

Answer:

[tex]11^{\frac{3}{5} }[/tex]

Step-by-step explanation:

Proof:

The power of a fraction is:

[tex]x^{\frac{a}{b} } =\sqrt[b]{x^{a} }[/tex]

Answer:

Step-by-step explanation:

5+4g+8=1

To solve the equation first group like terms.

Send the constants to the right side of the equation

That's

4g = 1 - 5 - 8

Simplify

4g = - 12

Divide both sides by 4

[tex]g = - \frac{12}{4} [/tex]

We have the final answer as

Hope this helps you

Answer:

A) 4 students

B) 32.5%

C) 19/40

Step-by-step explanation:

Using set notation to solve the problem with universal set n(U) = 40

Let n(A) be the number of students that pass account

n(E) be the number of students that pass economics

n(M) be the number of students that pass mathematics

n(AUEUM)' be number of students that failed in all the 3 subjects.

n(AUEUM) be number of students that pass in all the 3 subjects.

n(U) = n(AUEUM)+ n(AUEUM)'

Find the remaining solution in the attachment

Answer:

y+1 = 3(x-4)

Step-by-step explanation:

Point slope form is

y-y1 = m(x-x1) where m is the slope and (x1 , y1) is a point on the line

y - -1 = 3(x-4)

y+1 = 3(x-4)

Answer:

[tex]\Huge \boxed{{x=15\°}}[/tex]

Step-by-step explanation:

Angles on a straight line add up to 180 degrees.

We can create an equation.

x + 165 = 180

Solve for x.

Subtract 165 from both sides.

x + 165 - 165 = 180 - 165

Simplify the equation.

x = 15

Answer:

15°

Step-by-step explanation:

Angle of a line with a center is 180°

To find x:

x = 180 - 165°

x = 15°

15° is the answer.

Answer:

68,67 cm^2

Step-by-step explanation:

Let's calculate first the total area of pastry that we have.

Let A be that area.

The pastry has rectangular form so its area is:

● A = width × length

The width here is 16 and the length is 20

● A = 20 × 16

● A = 320 cm^2

■■■■■■■■■■■■■■■■■■■■■■■■■■

Let's calculate the are of the 20 pastry circles

Let A' be the area of one circle.

● A' = Pi × r^2

r is the radius wich is the diameter over 2.

● d/2 = 4/2 = 2 cm

● A' = Pi × 2^2

● A' = 4Pi cm^2

The area of 20 pastry circles is 20A'

● 20A'= 20 × 4 × Pi

● 20A'= 80Pi

■■■■■■■■■■■■■■■■■■■■■■■■■■

Let A" be the area of the remaining pastry

● A" = A-20A'

● A" = 320 - 80Pi

● A" = 68.67 cm^2

Answer:

4 - 16 ÷ 4 + 4² =

Step-by-step explanation:

= 4 - 16 ÷ 4 + 4²

= 4 - 16 ÷ 4 + 16

= 4 - ( 16 ÷ 4 ) + 16

= 4 - 4 + 16

= 16

Answer:

Write out your decimal as the numerator of a fraction:

0.50 /1

Multiply to remove the 2 decimal places:

0.50 /1 ×  100 /100=  50 /100

Find the Greatest Common Factor of 50 and 100:

GCF is 50

Divide both numerator and denominator by 50:

50 ÷ 50

100 ÷ 50 =  1 /2

therefore your answer is 1/2

Hope this helps! （づ￣3￣）づ╭❤～

Answer:

115/198

Step-by-step explanation:

The correct answer is 115/198.

Answer:

The amount each took home was 20 unit currency.

Step-by-step explanation:

The given parameters are

The number of apples with each of the seven apple women = 20, 40, 80, 100, 120, and 140

The number of apples each woman has can be written in the following formula obtained online which is a series formula

a·n + (n - 1), (a + b)·n + (n - 2), (a + 2·b)·n + (n - 3), (a + 3·b)·n + (n - 4), (a + 4·b)·n + (n - 5), (a + 5·b)·n + (n - 6), (a + 6·b)·n + (n - 7)

Which gives;

a·n + (n - 1) = 20

(a + b)·n + (n - 2)=40

(a + 2·b)·n + (n - 3) = 60

(a + 3·b)·n + (n - 4) = 80

(a + 4·b)·n + (n - 5) = 100

(a + 5·b)·n + (n - 6) = 120

(a + 6·b)·n + (n - 7) = 140

Solving the above system, we get

n = 7, a = 2, b = 3

Which gives

2×7 + 6 = 20

5×7 + 5=40

8×7 + 4 = 60

11×7 +  3 = 80

14×7 + 2 = 100

17×7 + 1 = 120

20×7 + 0 = 140

Whereby all the women sold the apples for the same sum price, based on market pricing if groups of apples are sold at 1 unit currency for 7, and extras are sold for 3 unit currency per extra 1, we have the amount taking home by each of them given as follows;

2×1 + 6×3 = 20

5×1 + 5×3=20

8×1 + 4×3 = 20

11×1 +  3×3 = 20

14×1 + 2×3 = 20

17×1 + 1×3 = 20

20×1 = 20

Therefore, the amount each took home was 20 unit currency.

Answer:

45 km per hour

Step-by-step explanation:

We want to find the tricycle's speed in kilometers per hour.

Therefore, we must divide the kilometers traveled by the number of hours.

speed= kilometers / hours

The tricycle travels 180 kilometers in 4 hours.

speed= 180 km / 4 hrs

Divide 180 km by 4 hrs.

⇒ 180/4=45

speed= 45 km / hour

The tricycle's speed is 45 kilometers per hour.

Answer:

y intercept

y = -5

Answer:

see below

Step-by-step explanation:

This solution is based off of the Triangle Inequality, which states that the sum of the two shortest sides of a triangle must be greater than the longest side of the triangle. The solution looks at the diagram on the bottom where y = DB. Looking at ΔABD, to find the range of values for y, we must consider two possible cases: y is either the shortest side or the longest side. If y is the shortest side then y + 5 > 6 which means y > 1 and if y is the longest side then 6 + 5 > y which means 11 > y. Therefore, the range of values for y is 1 < y < 11.

Next, they made y as small as possible, which would be 1.1 in this case. Looking at ΔDCB, again, to find the range of values for x, we must consider two possible cases: x is either one of the shortest sides or x is the longest side. If x is one of the shorter sides then 1.1 + x > 8 so x > 6.9 and if x is the longest side, 1.1 + 8 > x so 9.1 > x. Therefore, the range of values for x is 6.9 < x < 9.1. The smallest integer value that satisfies this inequality is x = 7.

Answer:

w = 16

Step-by-step explanation:

7/8 *w = 14

Multiply each side by 8/7

 8/7 *7/8 *w = 14*8/7

 w = 14/7*8

 w = 2*8

w = 16

Answer:

w = 16

Step-by-step explanation:

7 / 8w = 14

multiply both sides by 8:

8 * (7/8w) = 14 * 8

simplify

7w = 112

w = 112 / 7

w = 16

Answer:

15/2, 13/2.

Step-by-step explanation:

Here's a graph as well.

Answer in fraction form = (15/2, 13/2)

Answer in decimal form = (7.5, 6.5)

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

Explanation:

To get the midpoint, we average the two endpoint values. We handle the x and y coordinates separately.

The x coordinates of each point are 6 and 9. They average to (6+9)/2 = 15/2 = 7.5; so you add up the x coordinates and divide by 2.

The y coordinates are handled the same way. Add them to get 4+9 = 13 and then divide by 2 to get 13/2 = 6.5

The midpoint is (15/2, 13/2) = (7.5, 6.5)

Answer:

In descending order, you answer would be (70v - 18). Hope this helps!

Step-by-step explanation:

Answer:

the answer is C on edge

Step-by-step explanation:

So every 5 inches in height, there are 32 marbles. You want to know how many marbles there are per 18 inches in height.

[tex]\frac{32}{5} = \frac{x}{18}[/tex]

To get from 5 to 18, you multiply by 3.6.

Do the same thing to the numerator; 32 × 3.6 = 115.2.

Since 0.2 marbles is no marbles, you round down.

There are 115 marbles in the box.

♡ Hope this helps! ♡

❀ 0ranges ❀

Answer:

50°

Step-by-step explanation:

angle ABE and angle CBD are vertical angles and has same measure so <ABE = 50°

I think you multiply 3/5 times 14. You would get 8.4 pounds which would be 8 2/5.

The individuals in this data set are C) Cities

Same idea as last time, but now we're listing cities and their associated weather data.

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

The data set contains B) 4 variables, 2 of which are categorical

The four variables are

The two categorical variables are "kind of precipitation" and "severe weather alert". This is because the choices for each of these variables is a list of labels rather than numeric values. We cannot do things like find the average of the kind of precipitation as it doesn't make sense to do so. Each of these categorical variables are also nominal. This means they simply have a label or name. We cannot do things like order the data.

Answer:

Step-by-step explanation:

Perimeter of a rectangle = 2l + 2w

where

l is the length

w is the width

From the question

Perimeter = 402 yards

The statement

the length of the field is 9 yards less than quadruple the width is written as

l = 4w - 9

Substitute this is expression into the above formula and solve for the width

That's

402 = 2( 4w - 9) + 2w

402 = 8w - 18 + 2w

10w = 402 + 18

10w = 420

Divide both sides by 10

Substitute this value into l = 4w - 9

That's

l = 4(42) - 9

l = 168 - 9

Therefore

length = 159 yards

width = 42 yards

Hope this helps you

Answer:

D. The length is 5 times the width

because width is x

and the length is x x x x x

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

Explanation:

There are two methods to approach this type of problem.

-------------------------------------

Method 1

A = junior

B = girl

P(A) = probability of selecting a junior

P(B) = probability of selecting a girl

P(B) = (number of girls)/(number total)

P(B) = (4+7+3+4)/(4+4+5+7+2+3+1+4)

P(B) = 18/30

P(B) = 9/15

P(A and B) = probability of selecting a girl who is a junior

P(A and B) = (number of girl juniors)/(number total)

P(A and B) = 3/30

P(A and B) = 1/10

P(A given B) = P(A and B)/P(B)

P(A given B) = (1/10) divided by (9/15)

P(A given B) = (1/10) times (15/9)

P(A given B) = (1*15)/(10*9)

P(A given B) = 15/90

P(A given B) = 1/6

-------------------------------------

Method 2

This method doesn't involve dividing two fractions which could get messy, which is why I find this the easier route. Since we are given the person is a girl, this means we only need to focus on the "girls" column. There are 3 who are juniors out of 4+7+3+4 = 18 total. The probability of selecting a girl junior is 3/18 = 1/6

Well when you take x*5 and put that into a glizzy then you swallow it whole the answer will come out to about answer B

Answer:

Below.

Step-by-step explanation:

1.   You can construct a square knowing only 1 measurement, the length of each side.

2. Also a rectangle can be constructed only knowing 2 measurements: the length and the width.

Answer:

29 more points

Step-by-step explanation:

We basically need to find, what's the distance from -14 to 15.

We know that from -14 to 0 is 14 points, and from 0 to 15 is 15 points.

So in total we travelled [tex]15+14=29[/tex] points.

Hope this helped!