Helene invested a total of $1,000 in two simple-interest bank accounts. One account paid 6% annual
interest; the other paid 7% annual interest. The total amount of interest she earned after one year was
$66. Enter and solve a system of equations to find the amount invested in each account. Enter the interest
rates in order as given in the problem. (Hint: Change the interest rates into decimals first.)
x+y = 1,000
0.06
x+ 0.07
y = 66
Helene invested $
at 6% and $
at 7%.​

Answer:

The percent of down payment of the cost $2500 is 16% .

Step-by-step explanation:

Given:

Down payment = $400.

Cost = $2500.

Now, to find the percent of down payment of the cost.

According to question:

$400 / $2500 × 100.

⇒[tex]\frac{400}{2500} \times 100[/tex]

⇒[tex]0.16\times 100[/tex]

⇒[tex]16[/tex].

Therefore, the percent of down payment of the cost $2500 is 16%.

16% is the answer to your question.

Answer:

6. [tex]\displaystyle y - 1 = 2(x + 5)[/tex]

5. [tex]\displaystyle y + 4 = -3(x - 2)[/tex]

4. [tex]\displaystyle y - 5 = -2(x + 1)[/tex]

3. [tex]\displaystyle y - 2 = 3(x - 4)[/tex]

2. [tex]\displaystyle y - 4 = -3(x + 2)[/tex]

1. [tex]\displaystyle y - 5 = 2(x - 1)[/tex]

Step-by-step explanation:

In the Point-Slope Formula [y - y₁ = m(x - x₁)], all the negative symbols give the OPPOSITE terms of what they really are, so be EXTREMELY CAREFUL inserting the coordinates into the formula with their CORRECT SIGNS.

I am joyous to assist you anytime.

Answer:

The value of x = 13.5.

Step-by-step explanation:

In this question x is missing.

So, the question would be:

tan 34° = x/20.

Now, to find the value of [tex]x[/tex]:

[tex]tan 34 = \frac{x}{20}[/tex]

[tex]\frac{x}{20} = tan 34[/tex]

Multiplying both sides by 20 we get:

[tex]x=tan 34\times 20[/tex]

On simplifying both sides we get:

[tex]x=13.49[/tex]

So, to get the value of [tex]x=13.49[/tex] to nearest tenth is 13.5. As we see in hundredth place it is 9 and 4 in tenth place, so after rounding to tenth place 4 will change to 5 so the value is 13.5.

Therefore, the value of x = 13.5.

Answer:13.5

Step-by-step explanation:

Answer:

-15

Step-by-step explanation:

x-1/2(x+5)=-10

x-1/2x-5/2=-10

2/2x-1/2x-5/2=-10

1/2x-5/2=-10

1/2x=-10+5/2

1/2x=-20/2+5/2

1/2x=-15/2

x=(-15/2)/(1/2)

x=(-15/2)(2/1)

x=-15/1

x=-15

Answer:

Distance = |b - c|

Step-by-step explanation:

Suppose a, b, and c are all negative numbers.

We have to describe the way to find the distance between points (a,b) and (a.c).

Since the x-coordinates of the two points are the same and are a, therefore, the distance between the y-coordinates of the two points will give the distance between the two points.

Mathematically the distance d will be given by d = |b - c|, where |x| is the absolute value function of x. (Answer)

Answer:

2 should be your answer

Step-by-step explanation:

There is 2 horizontal and 2 vertical in total there are 2 lines of symmetry.

Answer:

20%

Step-by-step explanation:

% of error is given by the following formula:

% Error = [tex]\frac{|\textrm {Approx Value  - Exact Value}|}{\textrm {Exact Value}} \times 100[/tex]

Now, Jessie estimated the weight of his cat to be 12 pounds i.e. Approximate value is 12 pounds.

Again, The actual weight of the cat is 15 pounds i.e. the exact value is 15 pounds.

Therefore, the % error = [tex]\frac{|12 - 15|}{15} \times 100 = \frac{3}{15} \times 100 = 20[/tex]% (Answer)

Answer:

20%

Step-by-step explanation:

Jessie thinks to greatly of his cat

and I took the test

Jason hit 11 homeruns.

Step-by-step explanation:

Homeruns hit by Nathan = 19

Let,

Homeruns hit by Nathan = x

Homerun hit by Jason = y

According to given statement;

x = 2y - 3   Eqn 1

We know that Nathan hit 19 homeruns, therefore, putting x=19 in Eqn 1

[tex]19=2y-3\\19+3=2y\\22=2y\\2y=22[/tex]

Dividing both sides by 2;

[tex]\frac{2y}{2}=\frac{22}{2}\\y=11[/tex]

Jason hit 11 homeruns.

Keywords: linear equations, addition

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The lines are:  B) Perpendicular

Step-by-step explanation:

we have to convert both lines in slope-intercept form to find slopes

So,

[tex]3x - 6y = -13\\-6y = -3x-13\\\frac{-6y}{-6} = \frac{-3x-13}{-6}\\\frac{-6y}{-6} = \frac{-3x}{-6}+\frac{-13}{-6}\\y = \frac{1}{2} +\frac{13}{6}[/tex]

Let m1 be the slope of first line

[tex]m_1 = \frac{1}{2}[/tex]

For the second line:

[tex]18x + 9y = 5\\9y = -18x+5\\\frac{9y}{9} = \frac{-18x+5}{9}\\\frac{9y}{9} = \frac{-18}{9}x+\frac{5}{9}\\y = -2x+\frac{5}{9}[/tex]

Let m2 be the slope of line 2

So,

If the lines are parallel, their slopes are equal

If the lines are perpendicular, product of their slopes is -1

We can see that

[tex]\frac{1}{2} * -2 = -1[/tex]

Hence,

The lines are:  B) Perpendicular

Keywords: Slopes, Parallel lines

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The lines given by the equations 3x - 6y = -13 and 18x + 9y = 5 are neither parallel nor perpendicular because their slopes, 1/2 and -2 respectively, are neither equal nor negative reciprocals of each other.

To decide whether the pair of lines given by the equations 3x - 6y = -13 and 18x + 9y = 5 is parallel, perpendicular, or neither, we need to find the slope of each line. First, we convert the equations into the slope-intercept form, which is y = mx + b where m is the slope.

For the first equation, 3x - 6y = -13, we solve for y:

The slope of this line is 1/2.

For the second equation, 18x + 9y = 5, we also solve for y:

The slope of this line is -2.

Since the slopes of the two lines are neither equal (which would make them parallel) nor negative reciprocals of each other (which would make them perpendicular), the lines are neither parallel nor perpendicular.

Rewriting the expression 15x+9 as 9+ 15x is an example of the commutative property of addition

The commutative property of addition states that when two numbers are being added, their order can be changed without affecting the sum.

To “commute” means to move around or travel.  

According to the commutative property of addition, changing the order of the numbers we are adding, does not change the sum

When two numbers are added, the sum is the same regardless of the order of the addends. For example 4 + 2 = 2 + 4

For addition, the rule is a + b = b + a

Here in the problem 15x + 9 is equivalent to 9 + 15x

Hence, rewriting the expression 15x+9 as 9+ 15x is an example of the commutative property of addition

The process of rewriting 15x + 9 as 9 + 15x uses the Commutative property of addition. This asserts that changing the order of addition doesn't affect the sum.

Rewriting the expression 15x+9 as 9+15x is an example of the Commutative property of addition. The Commutative property states that the order in which you add or multiply numbers does not affect the sum or product. So in your case, 15x + 9 =  9 + 15x because of the Commutative property of addition. This is true for addition of ordinary numbers as well, for instance 2 + 3 will yield the same result as 3 + 2.

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The value of b is 14

The value of c is 65

Step-by-step explanation:

The quadratic equation ax² - bx + c = 0, where a = 1 has two roots

∵ The quadratic function is g(x) = ax² + bx + c

∵ a = 1

∴ g(x) = x² + bx + c

∵ g(x) has two complex roots (-7 + 4i) and (-7 - 4i)

∴ g(x) = 0

∴ x² + bx + c = 0

∵ The general form of the quadratic equation is x² - bx + c = 0,

   with sum of roots b and product of roots c

- Compare them

∴ x² - (-b) + c = 0

∵ -b = the sum of the two roots

∴ -b = (-7 + 4i) + (-7 - 4i)

- Add like terms

∴ -b = (-7 + -7) + (4i + -4i)

∴ -b = -14 + 0

∴ -b = -14

- Multiply both sides by -1

∴ b = 14

The value of b is 14

∵ c is the product of the two roots

∴ c = (-7 + 4i)(-7 - 4i)

- Remember (a + b)(a - b) = a² - b²

∵ (-7 + 4i)(-7 - 4i) = (-7)² - (4i)²

∵ (-7)² = 49

∵ (4i)² = 16i²

∵ i² = -1

∴ (4i)² = -16

∴ (-7)² - (4i)² = 49 - (-16) = 49 + 16 = 65

∴ (-7 + 4i)(-7 - 4i) = 65

∴ c = 65

The value of c is 65

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Answer:

E=5

Step-by-step explanation:

Given,

[tex]32= 2^E[/tex]

We know [tex]32[/tex] can be written as [tex]2^5[/tex]

Substituting [tex]2^5[/tex] in place of [tex]32[/tex]

We get,

[tex]2^5 = 2^E[/tex]

Since the base is equal, now comparing the exponent.

Therefore [tex]E=5[/tex] is the missing exponent.

Answer:

E = 5 and [tex]32 = 2^5[/tex]

Step-by-step explanation:

Given:

[tex]32 = 2^E[/tex]

Now we know that E is denoted as an exponent term,

Exponent term indicates the value which can be to the power of a number.

Now 32 can be written as,

[tex]32 = 2\times 2\times2\times 2\times2[/tex]

Hence from above we can say that 2 can be multiplied 5 times to get the value as 32.

hence we can say that,

[tex]32 = 2^5[/tex]

Hence E=5

Bella can cut 24 pieces of ribbon from this long strip

Solution:

Given that Bella has 85 feet of ribbons in total

She needs identical strips of ribbon measuring 3.5 feet each

To find: Number of peices of ribbon can she cut from long strip

Number of peices of ribbon can she cut from long strip can be calculated by dividing the total feet of ribbon she has by length of identical strips she needs

Mathematically written as:

[tex]\text { Number of Strip that can be cut }=\frac{\text { Total length of ribbon }}{\text { Length of each piece }}[/tex]

[tex]\begin{array}{l}{\text { Number of Strip that can be cut }=\frac{85}{3.5}} \\\\ {\text { Number of Strip that can be cut }=24.28 \approx 24}\end{array}[/tex]

Hence , the number of strip can be 24 each of size 3.5 feet

Answer:

X=-15

Step-by-step explanation:

Multiply both sides by 11

5x-2=-77

add 2 to both sides

5x=-75

Divide both sides by 5

x=-15

The value of x equal to -15 will make the given equation a true statement.

It is a mathematical statement that shows that two mathematical expressions are equal.

The given equation is

(5x-2) / 11 = -7

Multiply both sides by 11

i.e. 5x-2 = -77

Then add 2 to both sides

i.e. 5x = -75

Divide both sides by 5

i.e x = -15

Hence, the value of x that will make the equation 5x-2/11 = -7 a true statement is -15.

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Answer:

x=-6

Step-by-step explanation:

Use Substitution

so 5-2x=-4x-7

I'ma move that -4x to the other side by making it a positive

5+2x=-7

than I'ma move that 5 to the other side by making it a negative

2x=-12

to isolate the x you dived by both sides by the 2

x=-6

I doubled checked and it's -6

Answer:

Pull out like terms: 12 + 2x = 2 • (x + 6)

Solve: x+6 = 0

Then you get; X=-6

I hope this is right and hopefully it helped you

The equation of the line that passes through the point (3 , 5) and is

perpendicular to the line x = 4 is y = 5 ⇒ answer 1

Step-by-step explanation:

Let us revise some notes about the horizontal and vertical lines

∵ The equation of the given line is x = 4

- From the 4th note above the given line is a vertical line

∴ The given line is a vertical line

- The perpendicular line to a vertical line is a horizontal line

∴ The perpendicular line to the given line is horizontal

∵ The perpendicular line passes through the point (3 , 5)

∵ The equation of the horizontal line is y = b, where b the

   y-coordinate of any point lies on the line

∵ The point (3 , 5) lies on the line

- The y-coordinate of the point is 5

∴ b = 5

∴ The equation of the perpendicular line is y = 5

The equation of the line that passes through the point (3 , 5) and is

perpendicular to the line x = 4 is y = 5

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Answer:

b

Step-by-step explanation:

The equation:

3

x

2

−

5

x

−

12

=

0

is in the form:

a

x

2

+

b

x

+

c

=

0

with  

a

=

3

,  

b

=

−

5

,  

c

=

−

12

The roots are given by the quadratic formula:

x

=

−

b

±

√

b

2

−

4

a

c

2

a

x

=

5

±

√

(

−

5

)

2

−

4

(

3

)

(

−

12

)

2

(

3

)

x

=

5

±

√

25

+

144

6

x

=

5

±

√

169

6

x

=

5

±

13

6

That is:

x

=

5

+

13

6

=

18

6

=

3

or  

x

=

5

−

13

6

=

−

8

6

=

−

4

3

Answer:

8 tomatoes are required to balance 1 cabbage

Step-by-step explanation:

Given :

Two lemons and seven tomatoes are required  to balance one cabbage:

2 Lemons + 7 tomatoes = 1 cabbage                 (equation 1)

two lemons balance one tomato

2 lemons = 1 tomato

put in equation 1:

1 tomato + 7 tomatoes = 1 cabbage

8 tomatoes = 1 cabbage

8 tomatoes required to balance one cabbage

Answer:

a) Mr. Sanchez's class sold 28 fruit pies and Mr. Kelly's class sold 32 bottles of fruit juice.

b) Mr. Kelly's class

c) Mr. Kelly's classs earned  $1.40 more than Mr. Sanchez's class.

Step-by-step explanation:

Let x be the number of fruit pies sold and y be the number of bottles of fruit juice sold.

Together, the classes sold 60 items, so

x + y = 60

Mr. Sanchez’s class sold fruit pies for $1.55 each, so x fruit pies cost $1.55x.

Mr. Kelly’s class sold bottles of fruit juice for $1.40 each, so y bottles of fruit juice cost $1.40y.

Together, the classes  earned $88.20 for their school, so

1.55x + 1.40y = 88.20.

a) You get the system of two equations:

[tex]\left\{\begin{array}{l}x+y=60\\ \\1.55x+1.40y=88.20\end{array}\right.[/tex]

From the first equation:

[tex]x=60-y[/tex]

Substitute it into the second equation:

[tex]1.55(60-y)+1.4y=88.2\\ \\155(60-y)+140y=8,820\\ \\9,300-155y+140y=8,820\\ \\-15y=8,820-9,300\\ \\-15y=-480\\ \\15y=480\\ \\y=32\\ \\x=60-32=28[/tex]

Mr. Sanchez's class sold 28 fruit pies and Mr. Kelly's class sold 32 bottles of fruit juice.

b) Mr. Sanchez's calss earned:

[tex]\$1.55\cdot 28=\$43.40[/tex]

Mr. Kellyz's calss earned:

[tex]\$1.40\cdot 32=\$44.80[/tex]

Since [tex]\$44.80>\$43.40,[/tex] Mr. Kelly's class earned more.

c) Mr. Kelly's classs earned  [tex]\$44.80-\$43.40=\$1.40[/tex] more than Mr. Sanchez's class.

Answer:

Reasoning and Proof Unit Test

Step-by-step explanation:

1. 67

2. counterexample

3. If you join the gym, then it is free for the first three months.

Hypothesis: you join the gym

Conclusion: it is free for the first three months

4. Yes; two lines intersect at right angles if (and only if) they are perpendicular

5. An angle is obtuse if and only if its measure is greater than 180

6. Symmetric Property

7. 12

8. RT-ST

9. x=8, y=9

10. 7

11. Symmetric Property

12. invalid

13. A. is Substitution Property of Equality, B. is Supplementary Angles, C. is Subtraction Property of Equality

14. (A) 180, (B) 180, (C) transitive property, (D) 3, (E) 3

15. The value of x is 3.

a) Addition of line segments

b) Substitution rule

c) Simplification by addition of like terms

d) Collecting lie terms

e) Dividing both sides by 8

AB = 2x

BC = 6x + 8

AC = 32

AB + BC = AC (Addition rule)

Addition of the component segments of a line

2x + 6x + 8 = 32 (Substitution rule)

Substituting for AB, BC, and AC in the equation AB + BC = AC

8x + 8 = 32 (Simplification)

Simplifying 2x + 6x + 8 = 32 by adding like terms

8x = 24 (Collecting like terms)

8x = 32 - 8

8x = 24

x = 3 (Divide both sides by 8)

8x / 8 = 24/8

x = 3

16. If it is square it is a Quadrilateral.

17. 7y = 8x - 14

7(6) = 8x - 14

Collect like terms.

42 = 8x - 14.

8x = 42 + 14

8x = 56

x = 56/8

x = 7

These are all the correct answers as of 2022

Answer:

$14.4

Step-by-step explanation:

I don't really understand the question, but this is what I think it is

Eric needs to have $60 in savings if he wants to spend only 40% of it on a $24 video game.

To determine how much Eric must have in savings to spend only 40% on a $24 video game, we set up a simple equation where 40% of his total savings (S) equals the price of the game ($24). The equation is 0.40 × S = $24. Solving this equation for S (total savings), we divide both sides by 0.40:

× S = $24
÷ 0.40 ÷ 0.40

S = $24 ÷ 0.40
S = $60

Therefore, Eric must have a total of $60 in savings to spend only 40% on the video game.

Answer:

5460

Step-by-step explanation:

Answer:

Ashley should have added 4.5 to both sides.

Step-by-step explanation:

Given expression:

[tex]-4.5+m=17[/tex]

Ashley's solution:

Subtracted 4.5 to both sides and got,

[tex]m=12.5[/tex]

Correct solution:

Adding 4.5 to both sides.

[tex]-4.5+m=17[/tex]

 [tex]+4.5[/tex]          [tex]+4.5[/tex]

∴ [tex]m=21.5[/tex]

Error made by Ashley was subtracting 4.5 both sides. Instead he should have added 4.5 both sides.

Answer: 30.5

Step-by-step explanation:

30.5 times 4 equals 122

Answer:27

Step-by-step explanation: