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4 years ago

12

Mr. Ortiz pays a state tax of 10.4% on certain purchases. Which expression is the same as the total cost of p, a purchase of $14

.00, plus a 10.4% tax?
Drag and drop the expressions into the box that mean the same as the cost of p, a purchase of $14.00, plus a 10.4% tax.

1 answer:

Nata [24]4 years ago

4 0

Answer:

idk

Step-by-step explanation:

IDK

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What is 4x + 4(9x − 2) − 3 equal to specifically?

Naily [24]

Answer:

40x-11

Step-by-step explanation:

8 0

3 years ago

The base of a triangle exceeds the height by 7 centimeters. If the area is 400 square centimeters, find the length of the base a

zvonat [6]

Answer:

Base = 32 cm

Height = 25 cm

Step-by-step explanation:

Area of a triangle can be calculated as:

$Area = \frac{1}{2}\times Base \times Height$

We are given that the base of triangle exceeds the height by 7 cm. This can be expressed in an equation form as:

Base = Height + 7

Lets use B to represent base and H to represent height

B = H + 7

The equation of area can be stated as:

$Area=\frac{1}{2}bh\\\\ Area=\frac{1}{2}(h+7)(h)\\\\ 400=\frac{1}{2}h(h+7)\\\\ 800=h^{2}+7h\\\\ h^{2}+7h-800=0$

This is a quadratic equation which can be solved using a quadratic equation as shown below:

$h=\frac{-7+-\sqrt{49-4(1)(-800)} }{2(1)} \\\\ h=\frac{-7+-57}{2}\\\\h=-32,25$

Since the height cannot be negative, we'll consider the positive value only i.e height is equal to 25 cm.

Therefore, the length of base will be 25 + 7 = 32 cm.

8 0

3 years ago

If logb2=x and logb3=y, evaluate the following in terms of x and y:

Alja [10]

$log_b{162} = x + 4y\\\\log_b324 = 2x+4y\\\\log_b\frac{8}{9} = 3x-2y\\\\\frac{log_b27}{log_b16} = 3y-4x$

<em><u>Solution:</u></em>

Given that,

$log_b2 = x\\\\log_b3 = y --------(i)$

<em><u>Use the following log rules</u></em>

Rule 1: $log_b(ac) = log_ba + log_bc$

Rule 2: $log_b\frac{a}{c} = log_ba - log_bc$

Rule 3: $log_ba^c = clog_ba$

$a) log_b{162}$

Break 162 down to primes:

$162 = 2^1 \times 3^4$

$log_b{162} =log_b 2^1. 3^4\\\\By\ rule\ 1\\\\ log_b{162} = log_b 2^1 +log_b 3^4\\\\By\ rule\ 3\\\\1log_b2 + 4log_b3\\\\1x+4y\\\\x+4y$

Thus we get,

$log_b162 = x + 4y$

Next

$b) log_b 324$

Break 324 down to primes:

$324 = 2^2 \times 3^4$

$log_b324 = log_b 2^2.3^4\\\\By\ rule\ 1\\\\log_b324 = log_b2^2 + log_b3^4\\\\By\ rule\ 3\\\\log_b324 = 2log_b2 + 4log_b3\\\\From\ (i)\\\\log_b324 = 2x + 4y$

Next

$c) log_b\frac{8}{9}$

By rule 2

$log_b\frac{8}{9} = log_b8 - log_b9\\\\log_b\frac{8}{9} = log_b 2^3 - log_b3^2\\\\By\ rule\ 3\\\\log_b\frac{8}{9} = 3 log_b2 - 2log_b3\\\\From\ (i)\\\\log_b\frac{8}{9} = 3x - 2y$

Next

$d) \frac{log_b27}{log_b16}$

By rule 2

$\frac{log_b27}{log_b16} = log_b27 - log_b16\\\\ \frac{log_b27}{log_b16} = log_b3^3 - log_b2^4\\\\By\ rule\ 2\\\\ \frac{log_b27}{log_b16} = 3log_b3 - 4log_b2 \\\\From\ (i)\\\\\frac{log_b27}{log_b16} = 3y - 4x$

Thus the given are evaluated in terms of x and y

3 0

3 years ago

Multiple choice someone please answer pleaseeee

Marysya12 [62]

Answer:

x= 54.09

Step-by-step explanation:

cos = adjacent/ hypotenuse

cos75 = 14/x

x = 14/cos75

x = 54.09814627

6 0

3 years ago

Find g(x), where g(x) is the translation 7 units up of f(x)=x2.

AfilCa [17]

Answer:

$g(x)=x^2+7$

$g(x)$ in the form $a(x-h)^2+k$ would be:

$g(x)=(x-0)^2+7$

Step-by-step explanation:

Given:

Parent function:

$f(x)=x^2$

Translation occurs 7 units up to get $g(x)$

Translation Rules:

$f(x)\rightarrow f(x)+c$

If $c>0$ the function shifts $c$ units to the up.

If $c$ the function shifts $c$ units to the down.

So, from the above rules $g(x)$ can be represented as:

$g(x)=f(x)+7$ [7 units up]

$g(x)=x^2+7$

Writing $g(x)$ in the form $a(x-h)^2+k$ where $a, h, and\ k$ are integers.

$g(x)=1(x-0)^2+7$

$g(x)=(x-0)^2+7$

3 0

4 years ago

Read 2 more answers