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2 years ago

$69 shoes with a 6% tax

Mathematics

2 answers:

nlexa [21]2 years ago

7 0

6% of 69 is 4.14

So 69 + 4.14 = $73.14

Likurg_2 [28]2 years ago

4 0

Answer:

Step-by-step explanation:

69.00(1.06) = 73.14

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These two triangles are similar. What are a and b? Note: the two figures are not drawn to scale. Please help with this!

borishaifa [10]

Answer:

A.36 inches B.150 inches

Step-by-step explanation:

multaply 9×4 for A and 10×15 forB

4 0

2 years ago

Intersection point of Y=logx and y=1/2log(x+1)

GalinKa [24]

Answer:

The intersection is $(\frac{1+\sqrt{5}}{2},\log(\frac{1+\sqrt{5}}{2})$ .

The Problem:

What is the intersection point of $y=\log(x)$ and $y=\frac{1}{2}\log(x+1)$ ?

Step-by-step explanation:

To find the intersection of $y=\log(x)$ and $y=\frac{1}{2}\log(x+1)$ , we will need to find when they have a common point; when their $x$ and $y$ are the same.

Let's start with setting the $y$ 's equal to find those $x$ 's for which the $y$ 's are the same.

$\log(x)=\frac{1}{2}\log(x+1)$

By power rule:

$\log(x)=\log((x+1)^\frac{1}{2})$

Since $\log(u)=\log(v)$ implies $u=v$ :

$x=(x+1)^\frac{1}{2}$

Squaring both sides to get rid of the fraction exponent:

$x^2=x+1$

This is a quadratic equation.

Subtract $(x+1)$ on both sides:

$x^2-(x+1)=0$

$x^2-x-1=0$

Comparing this to $ax^2+bx+c=0$ we see the following:

$a=1$

$b=-1$

$c=-1$

Let's plug them into the quadratic formula:

$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$x=\frac{1 \pm \sqrt{(-1)^2-4(1)(-1)}}{2(1)}$

$x=\frac{1 \pm \sqrt{1+4}}{2}$

$x=\frac{1 \pm \sqrt{5}}{2}$

So we have the solutions to the quadratic equation are:

$x=\frac{1+\sqrt{5}}{2}$ or $x=\frac{1-\sqrt{5}}{2}$ .

The second solution definitely gives at least one of the logarithm equation problems.

Example: $\log(x)$ has problems when $x \le 0$ and so the second solution is a problem.

So the $x$ where the equations intersect is at $x=\frac{1+\sqrt{5}}{2}$ .

Let's find the $y$ -coordinate.

You may use either equation.

I choose $y=\log(x)$ .

$y=\log(\frac{1+\sqrt{5}}{2})$

The intersection is $(\frac{1+\sqrt{5}}{2},\log(\frac{1+\sqrt{5}}{2})$ .

6 0

2 years ago

Andrea bought 1 2/5 pounds of avocados at $4.20 per pound and 2 1/

guapka [62]

Answer:

$14.43¢

Step-by-step explanation:

We are given; $1\frac{2}{5}$ pounds, 1 pound = $4.20 and $2\frac{1}{4}$ pounds,1 pound = $3.80 that Andrea bought.

Now we need to find her total cost. To do that, we must first find the cost of the avocados. To do so, let us set up a graph. But before that is done, convert $1\frac{2}{5}$ to a decimal. It is 1.4. Now we can set up a graph.

Avocados

$\frac{4.2}{1}=\frac{x}{1.4}$

Switch sides

$\frac{x}{1.4}=\frac{4.2}{1}$

Apply rule: $\frac{a}{1}=a$

$\frac{x}{1.4}=4.2$

Multiply both sides by 1.4

$\frac{1.4x}{1.4}=4.2\cdot \:1.4$

Simplify

$x=5.88$

So, her cost for avocados is $5.88¢

Now we must first find the cost of the avocados. To do so, let us set up a graph. But before that is done, convert $2\frac{1}{4}$ to a decimal. It is 2.25. Now we can set up a graph.

Asparagus

$\frac{3.8}{1}=\frac{x}{2.25}$

Switch sides

$\frac{x}{2.25}=\frac{3.8}{1}$

Apply rule : $\frac{a}{1}=a$

$\frac{x}{2.25}=3.8$

Multiply both sides by 2.25

$\frac{2.25x}{2.25}=3.8\cdot \:2.25$

Simplify

$x=8.55$

So, her cost for asparagus is $8.55¢

Total cost

Now that we have found out how much both of the fruits Andrea bought costs, we need to sum it up (meaning add it) to find the total cost:

$5.88¢ + 8.55¢ =

5.88 + 8.55 = 14.43

Therefore, Andrea's total cost of the fruits is $14.43¢

8 0

2 years ago

4-21. Kelso's mom wants to put a floating blanket over the family's circular wading pool to keep the heat in and the leaves out.

astraxan [27]

Answer:

a. 78.6 square feet

b. $7.86

Step-by-step explanation:

a. This simply asks us to calculate the area of the 10 feet diameter pool

Formula for area of circle is ;

pi * r^2 = pi * d^2/4

so Area = 22/7 * 10^2/4 = 78.60 square feet

b. This will be the area of the blanket multiplied by the price per square foot of the blanket

Mathematically, we have that as;

78.60 * 0.1 = $7.86

7 0

2 years ago

The table shows the number of kilograms a newborn

olga nikolaevna [1]

Answer: y= 0.96 + 0.18x

Step-by-step explanation: I just did the assignment

7 0

2 years ago