Put all equations into y= and see which have matching graphs.

Richard’s checking account balance was $57.34 at the beginning of the week. During the week, he recorded the transactions below.

Tomtit [17]

Answer:

US$ 132.45

Step-by-step explanation:

See attachment for the missing table.

Given:

Richard’s checking account balance at the beginning of the week = $57.34

Richard’s account balance at the end of the week from the given table:

Deposits of the week = US$ 163.75

Expenses of the week = Groceries + Credit card bill + Gas

Expenses of the week = 25.37 + 50 + 13.27

Expenses of the week = US$ 88.64

Richard’s account balance at the end of the week = Richard’s checking account balance at the beginning of the week + Deposits of the week - Expenses of the week

Replacing with the real values:

Richard’s account balance at the end of the week = 57.34 + 163.75 - 88.64

=US$ 132.4

7 0

3 years ago

Read 2 more answers

In a right triangle ABC, CD is an altitude, such that AD=BC. Find AC, if AB=3 cm, and CD= 2 cm.

konstantin123 [22]

Consider right triangle ΔABC with legs AC and BC and hypotenuse AB. Draw the altitude CD.

1. Theorem: The length of each leg of a right triangle is the geometric mean of the length of the hypotenuse and the length of the segment of the hypotenuse adjacent to that leg.

According to this theorem,

$BC^2=BD\cdot AB.$

Let BC=x cm, then AD=BC=x cm and BD=AB-AD=3-x cm. Then

$x^2=(3-x)\cdot 3,\\ \\x^2=9-3x,\\ \\x^2+3x-9=0,\\ \\D=3^2-4\cdot (-9)=9+36=45,\\ \\\sqrt{D}=\sqrt{45}=3\sqrt{5},\\ \\x_1=\dfrac{-3-3\sqrt{5} }{2}0.$

Take positive value x. You get

$AD=BC=\dfrac{-3+3\sqrt{5} }{2}\ cm.$

2. According to the previous theorem,

$AC^2=AD\cdot AB.$

Then

$AC^2=\dfrac{-3+3\sqrt{5} }{2}\cdot 3=\dfrac{-9+9\sqrt{5} }{2},\\ \\AC=\sqrt{\dfrac{-9+9\sqrt{5} }{2}}\ cm.$

Answer: $AC=\sqrt{\dfrac{-9+9\sqrt{5} }{2}}\ cm.$

This solution doesn't need CD=2 cm. Note that if AB=3cm and CD=2cm, then

$CD^2=AD\cdot DB,\\ \\2^2=AD\cdot (3-AD),\\ \\AD^2-3AD+4=0,\\ \\D$

This means that you cannot find solutions of this equation. Then CD≠2 cm.

8 0

3 years ago

Read 2 more answers

5. Adam drives his car with an average velocity of 85 km/h eastward. How long will it take him to drive

NISA [10]

Answer:

x = 6.59 hrs = about 6 hours, 35 minutes

Step-by-step explanation:

Adam drives at 85 km / h. Let's set up equivalent fractions to see how long if he drives 560 km.

$\frac{85 km}{1 hr} = \frac{560 km}{x hr}$

Cross-multiply:

85x = 560

Solve for x:

560/85 = x

x = 6.59 hrs = about 6 hours, 35 minutes

7 0

2 years ago

Solve the following systems: 3x+4y=0 2x+3y=1

yanalaym [24]

Answer:

Answer is x= -4 and y= 3

Step-by-step explanation:

$given \: equations \: are \\ 3x + 4y = 0 \: \: and \: 2x + 3y = 1 \\ multiply \: by \: 2 \: in \: first \: equation \\ 6x + 8y = 0 \\ multiply \: by \: 3 \: in \: second \: equation \\ 6x + 9y = 3 \\ subtracting \: the \: above \: mentioned \: equation \: \\ we \: get \: - y = - 3 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: y = 3 \\ substitute \: y = 3 \: in \: first \: equation \\ 3x + 4(3) = 0 \\ 3x = - 12 \\ x = - 4$

HAVE A NICE DAY!

THANKS FOR GIVING ME THE OPPORTUNITY TO ANSWER YOUR QUESTION. 

7 0

2 years ago

the moon is 240,000 miles away from the earth. what is this distance written as a whole number multiplied by the power of ten

Nadusha1986 [10]

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4 0

3 years ago