4.5w=5.1w-30, how do I solve it

The required pairs of triangles in A and D are congruent triangles.

Congruent triangles are two triangles that have the same shape and size. In other words, they are identical in every way, including their angles and side lengths. When two triangles are congruent, their corresponding sides and angles are equal.

Here,

Congruent triangles are important in geometry because they have many useful properties and can be used to solve a variety of problems. For example, if two triangles are congruent, then any corresponding parts (such as their altitudes, medians, or angle bisectors) will also be congruent. This can be helpful in finding missing side lengths or angles of a triangle.

Thus, from the above definitions Pairs of triangles in A and D are congruent triangles.

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Answer:

[tex]f(x)= 3x^2[/tex] and [tex]g(x)= x+2[/tex]

Step-by-step explanation:

[tex]h(x)=(f o g) (x)[/tex]

[tex]h(x)=3(x+2)^2[/tex]

[tex](f og)(x) = f(g(x))[/tex]

g(x) is the inside function and f is the outside function

To get g(x) , we need to find the inside function in h(x)

[tex]h(x)=3(x+2)^2[/tex]

Inside function is x+2

So g(x) is x+2

when g(x)= x+2 then f(x) is [tex]3x^2[/tex]

So [tex]f(x)= 3x^2[/tex] and [tex]g(x)= x+2[/tex]

Part a) Sam got a new job with a $7.00 per hour raise. He worked for 5 hours and got paid $85.00. How much did he make before the raise?

Let

x--------> amount that Sam earned before the raise

we know that

[tex] (x+7) *5 =85 [/tex]

Solve for x

[tex] 5x+35 =85 [/tex]

[tex] 5x =85-35 [/tex]

[tex] 5x =50 [/tex]

[tex] x=10\ dollars\ per\ hour [/tex]

therefore

the answer Part a) is the option

A. $10.00 per hour

Part b) Julia knows 19 Latin words. Each day, she learns 6 new words. How many days until she knows 145?

Let

x-------> the number of days

y-------> the total words Julia Knows

we know that

[tex] y=19+6x [/tex] ------> equation [tex] 1 [/tex]

For y=[tex] 145 [/tex]

Find the value of x

Substitute in the equation [tex] 1 [/tex] the value of y

[tex] 145=19+6x [/tex]

[tex] 6x=145-19 [/tex]

[tex] 6x=126 [/tex]

[tex] x=21\ days [/tex]

therefore

the answer Part b) is the option

B. 21

Part c) Claire has a part-time job walking dogs Monday through Friday. Business has really increased. She is walking 3 more dogs per day than she did last week. If she walked a total of 35 dogs this week, how many dogs did she walk per day last week?

Let

x--------> the number of dogs that Claire walked last week per day

we know that

[tex] x=\frac{35}{5} -3\\\\ x=7-3\\\\x=4\ dogs\ per\ day [/tex]

therefore

the answer Part c) is the option

C. 4

Part d) Kayla needs to have $560.00 to buy a new laptop. She already has $200.00 in the bank. Each month she will add $45.00 to her bank account. How many more months until she has enough money to buy her laptop?

Let

x--------> the number of months

y-------> amount in the bank account in dollars

we know that

[tex] y=45x+200 [/tex]

Find the value of x for y=[tex] 560 [/tex]

[tex] 560=45x+200 [/tex]

[tex] 45x=560-200 [/tex]

[tex] 45x=360 [/tex]

[tex] x=8\ days [/tex]

therefore

the answer part d) is the option

D. 8

Part e) Mark bought a notebook for $1.45 and some pencils that cost $0.42 each. If total cost was $6.91, how many pencils did he buy?

Let

x------> the number of pencil

we know that

[tex] 6.91= 1.45+0.42x\\\\ 0.42x=6.91-1.45\\\\ 0.42x= 5.46\\\\ x= 13\ pencils [/tex]

therefore

the answer part e) is the option

B. 13

Answer: The correct option is A.

Explanation:

The given equation is,

[tex]4(x+5)-5=\frac{8x+18}{2}[/tex]

Multiply both sides by 2.

[tex]2[4(x+5)-5]=\frac{8x+18}{2}[/tex]

[tex]8(x+5)+2(-5)=8x+18[/tex]

[tex]8x+40-10=8x+18[/tex]

[tex]8x+30=8x+18[/tex]

Subtract both sides by 8x.

[tex]30=18[/tex]

This statement is false for any value of x, therefore the system of equation have no solution and option A is correct.

Answer:

Option A is correct

No solutions

Step-by-step explanation:

The distributive property says that:-

[tex]a \cdot (b+c) = a\cdot b+ a\cdot c[/tex]

Given the equation:

[tex]4(x+5)-5 = \frac{8x+18}{2}[/tex]

Using distributive property we have;

[tex]4x+20-5 = \frac{8x+18}{2}[/tex]

⇒[tex]4x+15= \frac{8x+18}{2}[/tex]

Multiply both sides by 2 we have;

[tex]8x+30 = 8x+18[/tex]

Subtract 8x from both sides we have;

[tex]30=18[/tex] False.

For any value of x, there is no solutions for the given system of equation

Therefore, No solution can be found for the linear equation

Let d denote the distance covered(in km) over the time t(in hours) with a speed of 10 km/h.

This means that the with the increasing time the distance covered will also increase.

Hence, the two variables i.e. distance and time are directly proportional to each other and also the equation which describes this relationship is given by:

                                  d=10t

Also, the relationship is Linear.

Since, the equation is linear which relates the two variable.

Answer:

1) The difference between four times the number b and 2.

2) 16 + 4*x

3) if there are 8 fewer boys than girls in the class, then g - b = 8, so the number of boys is: b = g - 8

4) 3.2*[tex]10^{-4}[/tex] is less than 1 because of the negative exponent, the expression is equivalent to 3.2/10000 = 0.00032 < 1

5) Ok, Dough is twice Anne's age. so if D is Dough's age, and A is Anne's age:

D = 2*A

and D = 34

then 34 = 2*A

if we divide both sides by 2, we get

34/2 = 2*A/2

17 = A

Anne is 17 years old.

A decimal is a number that consists of a whole and a fractional part.

Comparing the given decimal values from smallest to greatest we get,

9.675 < 9.700 < 9.750

A decimal is a number that consists of a whole and a fractional part.

It lies between integers and represents numerical value for quantities that are whole plus some part of a whole.

We have,

9.75, 9.7, 9.675

We can write from smallest to greatest values.

We can make the given decimal values in tenths, hundredths, and thousandths place values.

Let's write all the given decimal numbers till the thousandth place value as:

9.75 can be written as 9.750

9.7 can be written as 9.700

9.675 is already in the thousandth place value.

Comparing from smallest to greatest we have,

9.675 < 9.700 < 9.750

Thus,

Comparing the given decimal values from smallest to greatest we get,

9.675 < 9.700 < 9.750

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Alexandra will need approximately 8 months to save enough money for the school trip.

To calculate the number of months Alexandra needs to save money for her school trip, we'll first find out how much she saves each month after deducting her personal expenses.

Monthly earnings from paper route: $125

Monthly personal expenses: $20

Monthly savings = Earnings - Expenses

Monthly savings = $125 - $20

Monthly savings = $105

Now, let's determine how many months it will take for Alexandra to save enough money for the trip.

Total cost of the school trip: $800

Number of months needed = Total cost of trip / Monthly savings

Number of months needed = $800 / $105

Number of months needed ≈ 7.62

Therefore, Alexandra will need approximately 8 months to save enough money for the school trip.

Each month, Alexandra earns $125 from her paper route. After deducting her personal expenses of $20, she saves $105 per month. Since the school trip costs $800, we divide the total cost of the trip by her monthly savings to find out how many months she needs to save. The result is approximately 7.62, so we round up to 8 months. Therefore, Alexandra needs 8 months to save enough money for the school trip.

Complete question:

Alexandra earns $125 from her paper route each month, but she spends about $20 each month on personal expenses to pay for a school trip that costs $800 about how many months does she need to save money? Explain

Answer:  5

Step-by-step explanation:

Let x be the number of adults and y be the number of children going to the movies one Saturday.

Given : A group of 11 people are going to the movies one Saturday.

[tex]x+y=11----------------(1)[/tex]

Adults' tickets cost $11.50 each and children's tickets cost $7.25 each.

The total cost for admission to the movies is $105.25.

i.e. [tex]11.50x+7.25y=105.25-----------------(2)[/tex]

Multiply equation (1) by 11.5 , we get

[tex]11.5x+11.5y=126.5---------------------(3)[/tex]

Subtract equation (2) from (3), we get

[tex]4.25y=21.25\\\\ y=\dfrac{21.25}{4.25}=5[/tex]

Put value of y= 5 in (1), we get

[tex]x+5=11\\\\ x=11-5=6[/tex]

Hence, 5 children attends the movie.

Answer:

The answer is C

Step-by-step explanation:

The angle measures is equivalent to 23 degrees.

Vertically opposite angles are equal

To determine the angle, we have to know that vertically opposite angles are equal and angles on a straight line equal 180 degrees

Then, we can say that;

<1 = 3

< 2 = < 4

Substitute the expressions, we have;

x + 16 = 4x - 5

collect the like terms, we have;

x - 4x = -5 - 16

subtract the values, we get;

-3x = -21

divide by the coefficient, we have;

x = 7

Then, we can say;

<1 = <2 =< 3 = < 4

= 23 degrees

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Answer:

what even is this???????????????

2x-3=7

add 3 to both sides

2x = 10

divide both sides by 2

x = 10/2

x = 5

 since the equation is between 2 lines, which means absolute value x can be both positive and negative,

 so the solution set is -5 and 5

Answer:
The slope is -3/4

Explanation:
To find the slope of a line, you can use the "rise over run" method where you count how many units from one point to the next the line increases or decreases along the y-axis and place this number in the numerator of a fraction; then, count how many units to the left or right that same point is along the x-axis and place this number in the denominator. Simplify if necessary and that becomes the slope.

So, assuming each tick on the axes is 1 unit, to get from the leftmost point to the rightmost point, we go down 3 units on the y-axis ("rise" -3 units) and to the right 4 units ("run" 4 units). Therefore, the slope is -3/4

The method I like to use the most because it involves the actual math of finding a slope is plugging plotted points into the slope formula. The slope formula is  [tex]\frac{Y2 - Y1}{X2 - X1}[/tex] where two points along the line (X1, Y1) and (X2, Y2) are used.

Again, assuming, each tick is 1 unit, the plotted points on the line in the image are (-2, 2) and (2, -1). Now, we plug these ordered pairs into the formula and solve:

[tex]\frac{Y2 - Y1}{X2 - X1} = \frac{-1 - 2}{2 - (-2)} = \frac{-3}{2 + 2} = \frac{-3}{4}[/tex]

Therefore, the slope is -3/4

Final answer:

To calculate the annual increase from a monthly rate of 1.2%, use the compound interest formula to calculate the compounding effect over 12 months, resulting in an annual increase of approximately 15.47%.

Explanation:

The question asks about the annual percentage increase if prices increase at a monthly rate of 1.2%. The calculation involves compounding the monthly increase over the course of a year. To find the total percentage increase for the year, the formula for compound interest can be used, which is [tex](1 + r)^n[/tex], where r is the monthly increase rate, and n is the number of periods (months in a year).

Steps to Calculate Annual Increase:

Convert the monthly percentage increase to a decimal by dividing by 100: 1.2% / 100 = 0.012.

Add 1 to the monthly rate: 1 + 0.012 = 1.012.

Raise this sum to the power of 12, since there are 12 months in a year: [tex]1.012^{12[/tex].

Subtract 1 from the result to find the annual increase rate in decimal form.

Multiply by 100 to convert back to a percentage.

When we do the math, it turns out the prices increase by approximately 15.47% over the course of a year, when compounded monthly at a rate of 1.2%.

Prices increase by 1.447% in a year when the monthly increase is 1.2%.

To calculate the percentage increase in a year, we need to calculate the total increase over 12 months. Since prices increase at a rate of 1.2% per month, we can calculate the total increase over 12 months as follows:

1.012 x 1.012 x ... x 1.012 (12 times) = 1.01447

The total increase is 1.01447, which is equivalent to a 1.447% increase over the course of a year.

If each jar is full of 4,560 pennies, then the answer is 27,360 pennies in all.

4560*6=27360

Hope this helps.

Answer:

sandy has 4566

Step-by-step explanation:

Answer: c.

Step-by-step explanation:

The subject of this question is Mathematics, specifically involving basic algebra and arithmetic. Students are required to apply the math principles given in the example boxes throughout the chapter.

The subject of this question is Mathematics. It involves basic algebra and arithmetic to solve mathematical problems and apply the principles given in the example boxes throughout the chapter. The question likely requires students to use their math skills to solve a specific problem or answer a mathematical question.

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