Abdul deposited $460 into a savings account that has a simple interest rate of 3.5%. Isaac deposited $550 into a savings account that has a simple interest rate of 2.8%. Who earned more interest in one year?

Answer:

x = −2

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

3(4x+6)=x−4

(3)(4x)+(3)(6)=x+−4(Distribute)

12x+18=x+−4

12x+18=x−4

Step 2: Subtract x from both sides.

12x+18−x=x−4−x

11x+18=−4

Step 3: Subtract 18 from both sides.

11x+18−18=−4−18

11x=−22

Step 4: Divide both sides by 11.

[tex]\frac{11x}{11}[/tex] = [tex]\frac{-22}{11}[/tex]

x = −2

Answer:

8640

Step-by-step explanation:

I = Prt

I = (48000)(0.03)(6)

I = 8640

Step-by-step explanation:

Given

sin(α+β) cos(α-β) +cos(α+β) sin(α -β)

We can see it is in the formula of

sin(A + B) = sinA cosB + cosA sinB

So now

Sin ( α + β + α - β)

= sin 2α

Or we can write sin2α as

= 2 sin α * cos α

Hope it will help :)❤

Answer:

x=2, y=4. (2, 4).

Step-by-step explanation:

2x+3y=16

3x+4y=22

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

3(2x+3y)=3(16)

-2(3x+4y)=-2(22)

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

6x+9y=48

-6x-8y=-44

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

y=4

2x+3(4)=16

2x+12=16

2x=16-12

2x=4

x=4/2

x=2

Answer:

6+8-2=12, 15-12=3 answer=3

Answer: 30

Step-by-step explanation:

Answer:

x = 9/2 or 4.5

Step-by-step explanation:

In order to solve this problem, you first need to identify whether or not the two triangles formed in the image are similar; you can tell that they are similar by the AAA property because they share a vertex, and the other two angles are congruent because of the Corresponding Angles Theorem. Now that you know the triangles are similar, you need to identify the corresponding sides:

x + 6 corresponds to x

21 corresponds to 9 (21 because 30 - 9 = 21)

You can find the scale factor by dividing 21 by 9:

21 ÷ 9 = 7/3

Now that you know the scale factor, you can write and solve an equation:

7/3x = x + 6 (given)

4/3x = 6 (subtract x from both sides)

x = 9/2 (multiply both sides by 3/4)

Answer: 6.6

Step-by-step explanation:

Answer: sqrt(61)

Step-by-step explanation:

For parts a) and c1), refer to the attached picture.

For part b), the distance formula is:

d = sqrt[(x2 - x1)^2 + (y2 - y1)^2]

Using x1 = -1, y1 = -4, x2 = -6, y2 = 2:

d = sqrt[(-6 + 1)^2 + (2 + 4)^2] = sqrt[25 + 36] = sqrt(61)

Part c2) Another way to find the length of AB without using the distance formula is by drawing the line and measuring it according to the scale.

Part d) This will only work as long as the graph paper is accurately made, and the scale computation is done correctly. However, this will only give approximations, and will not give an exact answer when radicals are involved.

Answer:

Step-by-step explanation:

[tex]{ \sf{ factorise \: \: { \underline{ \green { \tt{ {x}^{2} (x + 2) - x(x + 2) - 12(x + 2)}}}}}}[/tex]

[tex]{ \sf{ \blue{ \:taking \: (x + 2) \: common}}} \\ \\{ \dashrightarrow { \sf{ \green{(x + 2)( {x}^{2} - x - 12)}}}}[/tex]

[tex]{ \dashrightarrow{ \sf{ \green{(x + 2)( {x}^{2} - (4x - 3x) - 12)}}}} \\ \\ { \dashrightarrow{ \sf{ \green{(x + 2)( {x}^{2} - 4x + 3x - 12)}}}}[/tex]

[tex]{ \dashrightarrow{ \green{ \sf{(x + 2)(x(x - 4) + 3(x - 4))}}}} \\ \\ { \dashrightarrow{ \underline{ \boxed{ \green{ \sf{(x + 2)(x + 3)(x - 4)}}}}}}[/tex]

[tex]3x^2-5x=2[/tex]

Answer:

10

Step-by-step explanation:

sqrt (8^2+6^2) = 10

hope it helps

Answer:

96 cm

Step-by-step explanation:

Multiply 6x4x4=96

Answer:

40°

Step-by-step explanation:

If your are reffering to a triangle the answer would be 40 since the three angles of a triangle must always add up to 180° so you would add b+d (110+30) resulting in 140 which you would then subtract from 180 getting you 40°

Answer: C

Step-by-step explanation:

Answer:

[tex](5y + 1)^{2} - (2(y - 1))^{2} [/tex]

Step-by-step explanation:

1) Rewrite it in the form a² - b², where a = 5y + 1 and b = 2(y - 1 ).

[tex](5y + 1) ^{2} - (2(y - 1)) ^{2} [/tex]

2) Use multiplication Distributive Property: (xy)^a = x^a y^a.

[tex](5y + 1)^{2} - {2}^{2} (y - 1 {)}^{2} [/tex]

3) Simplify 2² to 4.

[tex](5y + 1 {)}^{2} - 4(y - 1 {)}^{2} [/tex]

4) Rewrite it in the form a² - b², where a = 5y + 1 and b = 2(y-1).

[tex](5y + 1 {)}^{2} - (2(y - 1))^{2} [/tex]

Therefor, the answer is ( 5y + 1 )² - (2( y - 1 ))².

Answer:

0=7

Step-by-step explanation:

Distribute

4−5=2(2+1)

4−5=4+2

Add 5 to both sides of the equation

4 − 5 = 4 + 2

4 − 5 + 5 = 4 + 2 + 5

Simplify Add the numbers

Add the numbers

4 = 4 + 7

Result

0=7

Answer:

Took FLVS test and got it right

A. y=x, x-axis, y=x, y-axis.

Step-by-step explanation:

Took FLVS test and got it right

A. y=x, x-axis, y=x, y-axis.

Answer:

± 7

Step-by-step explanation:

Given

[tex]\sqrt{56-7}[/tex]

= [tex]\sqrt{49}[/tex]

= + 7 or - 7 , that is ± 7

Answer:

±7

Step-by-step explanation:

56 - 57

______

gives you 49

which then turns into ±7

⇒⇒⇒Hope this helps!

Answer:

The tangent ratio is the value received when the length of the side opposite of angle theta is divided by the length of the side adjacent to angle theta. It is very commonly abbreviated as tan.

Answer:

the answer is 24

Step-by-step explanation:

i got it correct on my test

Answer:

Step-by-step explanation:

[tex]\huge\large \fbox \green{Answer :}[/tex]

B. 5sqrt(2)

[tex]\huge\Large \fbox \green{Explanation:}[/tex]

We have

We need to find third side of triangle

( x)² = (√34 )² + (4)² ....( by Pythagoras Theorem)

x ² = 34 + 16

x ² = 50

x = √50

x = 5 √2

Hence, the third side is 5√2

Answer:

The area of LQM is [tex]48cm^2[/tex]

Step-by-step explanation:

Given

Area of PNQ = 8

Area of LPQ = 16

See attachment for triangles

The area of PNQ is calculated as:

[tex]Area = \frac{1}{2} * PQ * PN[/tex]

Substitute 8 for Area

[tex]8 = \frac{1}{2} * PQ * PN[/tex]

[tex]PQ * PN = 16[/tex]

The area of LPQ is calculated as:

[tex]Area = \frac{1}{2} * PQ * LP[/tex]

Substitute 16 for Area

[tex]16= \frac{1}{2} * PQ * LP[/tex]

From the attachment:

[tex]PN + LP =LN[/tex]

Make LP the subject

[tex]LP = LN -PN[/tex]

So:

[tex]16= \frac{1}{2} * PQ * (LN -PN)[/tex]

We have:

[tex]16= \frac{1}{2} * PQ * (LN -PN)[/tex] and [tex]PQ * PN = 16[/tex]

Equate both expressions:

[tex]\frac{1}{2} * PQ *(LN - PN) = PQ * PN[/tex]

Divide both sides by PQ

[tex]\frac{1}{2} (LN - PN) = PN[/tex]

Multiply both sides by 2

[tex]LN - PN = 2PN[/tex]

[tex]LN= 3PN[/tex]

Since PNQ is similar to LNM, the following equivalent ratios exist:

[tex]\frac{LM}{PQ} = \frac{LN}{PN}[/tex]

Substitute [tex]LN= 3PN[/tex]

[tex]\frac{LM}{PQ} = \frac{3PN}{PN}[/tex]

[tex]\frac{LM}{PQ} = 3[/tex]

[tex]LM = 3PQ[/tex]

Area of LQM is:

[tex]Area = \frac{1}{2} * LM * LP[/tex]

This gives:

[tex]Area = \frac{1}{2} * 3PQ * LP[/tex]

[tex]Area = 3 *\frac{1}{2} *PQ * LP[/tex]

Recall that:

[tex]16= \frac{1}{2} * PQ * LP[/tex]

So:

[tex]Area = 3 *16[/tex]

[tex]Area = 48cm^2[/tex]

Answer:

1) b - correct statement: The interquartile range of the number of volunteers is 16

2) c - correct statement: About 50% of the students have between a 75 and a 90

Step-by-step explanation:

1B --> 66 - 50

2C --> About 50% of the students have between a 75 and a 90