For her vacation Mrs. Andrews bought $300 worth of traveler's checks in $10 and $20 denominations. If she has 22 travelers checks in all, how many of each denomination does she have?

Let x represent the number of $10 traveler's checks she has. Which expression represents the value of the $20 traveler's checks she has?

20 x
20(22 - x)
20(22)

Answer: The answer is x = 12

Step-by-step explanation:

Answer:

x = 12

Step-by-step explanation:

1. Get all x varibles to one side.

-7x - 11 = 25 - 10x

+ 10x            +10x

2. Get all constants to one side.  

3x - 11 = 25

+ 11         +11

3. Divide on both sides to get x alone.

3x = 36

÷3    ÷3

x = 12

Answer: m = 4

Step-by-step explanation: To solve for m in this equation, we want to get m by itself on the left side of the equation.

Since m is being multiplied by 3.6, to get m by itself, we need to divide by 3.6 on the left side of the equation. Since we divided by 3.6 on the left side, we must also divide by 3.6 on the right side.

On the left side, notice that 3.6's cancel out so we're simply left with m. On the right side, we have 14.4 divided by 3.6 which is 4. So we now have m = 4.

Finally, remember to check your answer by substituting a 4 back into the original equation.

So we have 3.6 (4) = 14.4 which is a true statement.

This means that our answer, m = 4, is correct.

Remember to show all your work when solving equations.

Answer:

B. y = 6x – 1

Step-by-step explanation:

where:

m is the slope of the line

b is the y-intercept of the line

The slope m of the line through any two points (x1, y1) and (x2, y2) is given by:

Slope Formula

The y-intercept b of the line is the value of y at the point where the line crosses the y axis. Since for point (x1, y1) we have y1 = mx1 + b, the y-intercept b can be calculated by: b = y1 - mx1

Answer:

The answer is A

Step-by-step explanation:

y - 5 = 6(x+1)

y - 5 = 6x + 6

y = 6x + 6 + 5

y = 6x + 11

Divide the total by 1 +  interest rate.

12,720 / 1.06 = 12,000

They invested $12,000

Answer:

The answer would be 5.03x10^-3   ^-^

Step-by-step explanation:

Answer:

-3.

Step-by-step explanation:

Counting the digits after the point until we get to the 5:

The count is 3.

The power is -3:

5.03 * 10^-3.

The adult weight in pounds is 185.39 lb

Solution:

Given that adult weighs 84.09 kilogram

To find : Adult’s weight in kilograms to pounds

We have the change the weight of the adult from kilogram to pound

The conversion between kilogram and pound is as follows:-

1 kilogram = 2.204623 lb

To find the adult weight in pound, we need to multiply the adult weight in kilogram by 2.204623

Converting 84.09 kg to pound:

[tex]\begin{array}{l}{84.09 \mathrm{kg}=84.09 \times 1 \mathrm{kg}} \\\\ {84.09 .09 \times 2.204623=185.39 \mathrm{lb}}\end{array}[/tex]

Therefore the weight of the person in pound = 185.39 lb

Answer:

y=x^2+4x+7

Step-by-step explanation:

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

y=x^2+2x+2x+4-3

y=x^2+4x+7

Answer:

C. y = x² + 4x + 1

Step-by-step explanation:

y = (x + 2)² - 3

y = x² + 4x + 4 - 3

y = x² + 4x + 1

Answer:

1/0.04 = 25

Step-by-step explanation:

Answer:

Step-by-step explanation:

well 1/4% wouldnt be 25% because they are 25% = 0.25 = 1/4

the percentage sign changes everything

since it is 1/4% rather than 1/4 by itself

1/4% = 0.25%

if you want to know the percent as a decimal you move the "." to the left twice

(or divide by 100)

so that means that the decimal of 0.25% would be 0.0025

To have $18,000 in 2 years with a 20% annual interest rate compounded continuously, you need to invest approximately $12,065.76.

To determine the amount of money you need to invest to have $18,000 in 2 years with a 20% annual interest rate compounded continuously, we can use the formula:

A = P * e^(rt)

Where:

Substituting the values into the formula:

18,000 = P * e^(0.20*2)

Simplifying:

18,000 = P * e^(0.40)

P = 18,000 / e^(0.40)

Using a calculator to evaluate the exponential term:

P ≈ 12,065.76

Therefore, you need to invest approximately $12,065.76 to have $18,000 in 2 years.

Answer:

(8, -4)

Step-by-step explanation:

Answer:

n= Total number of packages on trucks= 6096

n = T x P (Model Equation)

Step-by-step explanation:

No. Of delivery trucks = T = 127

Package on each truck = P = 48

Total number of packages on trucks =n= ?

Each truck contains 48 packages and total trucks were 127, to find total number of packages on trucks , we just need to multiply the number of trucks with the number of package on each truck.

Total number of packages on trucks =n= (No. Of delivery trucks) x (Package on each truck)

n = T x P (Model Equation)

n= 127 x 48

n= 6096 (Total number of packages on trucks)

Answer:

8 correct, 6 wrong : 14 problems tried!

Step-by-step explanation:

If she gets 8 points by every question correctly answered and she got 13 points in total, she must have answered at least two questions (if she answers only 1 she gets at maximum 8 points, not reaching 13 never).

So lets try to find the solution.

If she answered 2 and mistaken 1 she would get:

2*8 - 1*5 = 16 - 5 = 11 -> So this is not correct.

If she answered 3 correct she would get 24 points, with 2 mistaken  answers she would have:

8*3 - 5*2 = 24 -10 = 14

We need to see something important in this patterns:

As the wrong questions always subtract a multiple of 5, and we need a result of 13, we CAN'T have an even number of wrong questions, because this would imply a subtract of numbers like 10, 20, 30, etc; and as the correct answers only give us even numbers (8, 16, 32, 64, etc), the result of subtracting 2 even numbers would never be 13. And as we will be subtracting a number with a 5 in the units, the points for correct answers MUST have an 8 in the units, as 8-5=13.

So, lets go to the first posible number that ends in 8 and is multiple of 8 and greater than 16. This is 48. 48 = 6*8, this is, lets think about 6 correct answers that sum 48 points.

We now need to subtract a number to 48 that gives us 13. Which is?

48 - x = 13 <----> x = 35

So, we need a number of incorrect answers that sum 35. As every wrong answer sums 5 points, we need 7 wring answers (7*5 = 35):

8*6 - 5*7 = 48 - 35 = 13 points!!

There were 14 problems tried to solve

Answer:

f(2k)=0

Step-by-step explanation:

Let's suppose f(x) is such that (x-2k) is one of its factors. We can write it as

f(x)=(x-2k).g(x)

Where g(x) is any other function of x, and g(x) in non-divisible by (x-2k). If we replace x=2k into f, we get

f(2k)=(0).g(2k)=0

f(2k)=0

Answer:

A

Step-by-step explanation:

took the test

Answer:

The correct answer is D. 16 + 4 - 1 = 20 - 1

Step-by-step explanation:

Option A is not a true equation because 16 + 4 - 1 = 19 and not 20.

Option B is not a true equation because we're using the relational sign "less than" that is used by inequations or inequalities.

Option C is not a true equation because 16 + 4 - 1  = 19 and is not equal to 19 - 1 = 18.

Finally, option D is a true equation because 16 + 4 - 1  = 19 and is equal to 20 - 1 = 19.

The correct answer is D. 16 + 4 - 1 = 20 - 1

Answer:

294 square feet

Step-by-step explanation:

If the volume is one  side  at the 3rd power, then  If we know the volume, we calculate   the cubic root of 343  that is 7

So 1 side =7

The cube has 6 faces

1 face of the cube is 7*7=49

Six faces =

49*6= 294

Answer:

y = [tex]\frac{25}{6}[/tex]

Step-by-step explanation:

Given that y varies directly with x then the equation relating them is

y = kx ← k is the constant of variation

To find k use the condition y = 5 when x = 6

k = [tex]\frac{y}{x}[/tex] = [tex]\frac{5}{6}[/tex], thus

y = [tex]\frac{5}{6}[/tex] x ← equation of variation

When x = 5, then

y = [tex]\frac{5}{6}[/tex] × 5 = [tex]\frac{25}{6}[/tex]

Answer:

see the explanation

Step-by-step explanation:

we know that

The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side

In this problem

If the perimeter of triangle is equal to 36 cm

The longest side can't be equal to 18 cm

The student is incorrect

Because if the longest side is equal to 18 cm, and the perimeter is equal to 36 cm, then the sum of the other two sides is equal to 18 cm

and

Applying the triangle inequality theorem

Let

c  -----> the longest side

a and b the other two sides

we have that

if c=18 cm

a+b > c

a+b > 18 cm

therefore

If the longest side is 18 cm, the sum of the other two sides must be greater than 18 cm and the perimeter will be greater than 36 cm

Answer:

3x+15=90.

3x=75

x=25

Step-by-step explanation:

Answer:

x = 25

Step-by-step explanation:

Triangle = 180 degrees

The square indicates that the angle = 90 degrees

So we know the other two angles have to equal the remaining 90 together.

x + (2x + 15) = 90

3x + 15 = 90

3x = 75

x = 25

Answer:

112 dimes and a nickel.

because, one, 110 dimes equals 11.00 (so add the2 extra dimes.)

two, the .05 is a nickel not a .5 dime.

So that's your answer. 112 dimes and 1 nickel.

Answer:

10 pounds of tilapias and 36 pounds of salmon,

15 pounds of tilapias and 33 pounds of salmon,

20 pounds of tilapias and 30 pounds of salmon,

25 pounds of tilapias and 27 pounds of salmon,

30 pounds of tilapias and 24 pounds of salmon.

Step-by-step explanation:

Let's call the amount of pounds of tilapia X and the amount of pounds of salmon Y.

If each pound of tilapia costs $3 and each pound of salmon costs $5, we can write the following equation:

210 = 3X + 5Y

To find five different combinations to solve this equation, we can choose values for X and then calculate values of Y.

So, for X = 10, we have that:

210 = 30 + 5Y -> Y = 36

For X = 15, we have that:

210 = 45 + 5Y -> Y = 33

For X = 20, we have that:

210 = 60 + 5Y -> Y = 30

For X = 25, we have that:

210 = 75 + 5Y -> Y = 27

For X = 30, we have that:

210 = 90 + 5Y -> Y = 24

So the combinations are (10,36), (15,33), (20,30), (25,27) and (30,24)

Answer:Your answer is..

Step-by-step explanation:(10,36), (15,33), (20,30), (25,27) and (30,24)

Answer:

The value of x is 25.

Step-by-step explanation:

Given:

side AB = [tex]3x-5[/tex]

side BC = [tex]2x+20[/tex]

side AC = [tex]4x-30[/tex]

In Δ ABC is an equilateral triangle.

In equilateral triangle all three angles are same and also the sides are same.

Hence side AB = side BC

Substituting the values for side AB and side BC we get,

[tex]3x-5=2x+20\\3x-2x=20+5\\x=25[/tex]

Hence the value of x = 25.

Answer:

The value of x for the given figure is 95 And 1.67

Step-by-step explanation:

From Given figure :

Sin angle = [tex]\dfrac{\textrm perpendicular}{\textrm Hypotenuse}[/tex]

or ,  Sin C =  [tex]\dfrac{\textrm 3x - 5}{\textrm 4 x - 30}[/tex]

Cos angle =  [tex]\dfrac{\textrm Base}{\textrm Hypotenuse}[/tex]

or ,  Cos C =  [tex]\dfrac{\textrm 2x + 20}{\textrm 4 x - 30}[/tex]

Or, Cos c = [tex]\sqrt{1 - sin^{2}C }[/tex]

Or, [tex]\dfrac{\textrm 2x + 20}{\textrm 4 x - 30}[/tex] = [tex]\sqrt{1-(\frac{3x - 5}{4 x + 20} })^{2}[/tex]

or, [tex](\frac{2x+20}{4x-30}) ^{2}[/tex] = 1 - [tex](\frac{3x-5}{4x-30} )^{2}[/tex]

[tex]\frac{4x^{2}+400+80x}{16x^{2}+900-240x}[/tex]= 1- ( [tex]\frac{9x^{2}+25-30x}{16x^{2}+900-240x}[/tex] )

Or, 4x²+400+80x = [tex]16x^{2}+900-240x[/tex] - 9x² -25 +30x

or, 4x²+400+80x = 7 x² + 875 -210x

or, 3 x² + 475 -290 x = 0

Or, Solving the equation

3 x² - 285 x - 5 x + 475 = 0

or, 3 x ( x - 95 ) - 5 ( x - 95 ) = 0

or, ( x - 95 ) ( 3 x - 5 ) = 0

∴ x = 95  and x = 1.67

Hence The value of x for the given figure is 95 And 1.67  Answer

Answer:

v172

Step-by-step explanation:

This might be wrong. Because 172=289 you can substituite 289 for 172.

Answer:

For more than 500 minutes

Step-by-step explanation:

Let x be the number of minutes.

First company charges:

$0.029 per minute, then $0.029x for x minutes

and a $2 monthly fee.

In total, $(0.029x+2)

Second company charges:

$0.033 per minute, then $0.033x for x minutes

with no monthly fee.

If the charges for the first company are cheaper, then

[tex]0.029x+2<0.033x[/tex]

Multiply this inequality by 1,000:

[tex]29x+2,000<33x\\ \\33x-29x>2,000\\ \\4x>2,000\\ \\x>500[/tex]

Answer:

$3.80

Step-by-step explanation:

could be wrong though

Answer:

Step-by-step explanation:

19 divided by 5 = 3.8

3.8 to nearest hundreth is 3.80 or you could

Answer:

The last two, 250+25t and 25(10+t)

Step-by-step explanation:

Answer: 250+25t and 25(10+t)

Step-by-step explanation: trust me i just got it right on ixl.

Given information

ZW is parallel to XY

ZW is congruent to XY

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

What we want to prove: ZY parallel to WX

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

Proof:

Statement 1: ZW is parallel to XY

Reason 1: Given

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

Statement 2: ZW = XY

Reason 2: Given

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

Statement 3: Angle 3 = angle 4

Reason 3: Alternate interior angle theorem

note: it might help to erase or cover up the horizontal lines of the parallelogram temporarily to help see that angles 3 and 4 are alternate interior angles.

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

Statement 4: ZX = ZX

Reason 4: Reflexive property of congruence

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

Statement 5: Triangle WZX = Triangle YXZ

Reason 5: SAS congruence postulate

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

Statement 6: Angle 1 = Angle 2

Reason 6: CPCTC

note: CPCTC stands for "corresponding parts of congruent triangles are congruent"

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

Statement 7: ZY is parallel to WX

Reason 7: Converse of alternate interior angle theorem

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

This concludes the proof.

ZY is parallel to WX.

To prove that line segment ZY is parallel to WX, given that ZW is parallel to YZ and ZW is congruent to MY, you can use the following properties and definitions:

If ZW is parallel to YZ, and ZW is congruent to MY, it means that angle ZWM is congruent to angle YZM (corresponding angles) and angle ZMW is congruent to angle MYZ (corresponding angles).

If two lines are cut by a transversal such that corresponding angles are congruent, then the lines are parallel.

So, using the above properties, you can conclude that ZY is parallel to WX. This is because the corresponding angles ZWM and YZM are congruent, and ZMW and MYZ are congruent, which is sufficient to establish that the lines ZY and WX are parallel.

for such more question on line segment

https://brainly.com/question/280216

#SPJ2

Answer:

The explanation is below.

Step-by-step explanation:

Given

C is the midpoint of [tex]\overline{AD}[/tex] and also C is the midpoint of [tex]\overline{EB}[/tex]

[tex]\overline{AC} = \overline{DC}\\ and\\\overline{BC} = \overline{EC}[/tex]

To Prove:

[tex]\angle A \cong \angle D[/tex]

Proof:

[tex]In\ \triangle ACB\ and\ \triangle DCE\\\overline{AC} \cong \overline{DC}\ \textrm{ C is the midpoint of AD}\\\angle ACD \cong \angle DCE\ \textrm{vertically opposite angles}\\\overline{BC} \cong \overline{EC}\ \textrm{ C is the midpoint of BE}\\\therefore \triangle ACB \cong \triangle DCE\ \textrm{ By Side-Angle-Side test}\\\therefore \angle BAC \cong \angle EDC\ \textrm{corresponding parts(angles) of congruent triangles}\\\therefore \angle A \cong \angle D\ \textrm{ Proved}[/tex]