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3 years ago

If you pay $ 34.02 for a jacket that includes a 5% sales tax, what is the price of the jacket before the sales tax?

Mathematics

2 answers:

Jobisdone [24]3 years ago

3 0

105% =$34.02
100% (cost without sales tax) = 34.02/1.05 =$32.40

gavmur [86]3 years ago

3 0

$32.32 because 100%-5%= 95% so 34.02x95%= 32.319 and that is rounded off to $32.32

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In the figure, PQ is parallel to RS. The length of RP is 5cm; the length of PT is 30cm; the length of QT is 60cm. What is the le

rjkz [21]

The triangles PTQ and RTS are similar; so the ratios of corresponding sides are equal.

Let us denote the unknown length SQ as x.

We could make the following similarity relation;

$\begin{gathered} \frac{30}{30+5}=\frac{60}{60+x} \\ \end{gathered}$

Cross multiply to obtain;

$\begin{gathered} 30(60+x)=60(35) \\ 1800+30x=2100 \\ \text{collect like terms} \\ 30x=2100-1800 \\ 30x=300 \\ \text{divide both sides by 30} \\ \frac{30x}{30}=\frac{300}{30} \end{gathered}$

Therefore;

$x=10\operatorname{cm}$

Therefore, the answer is option A

3 0

1 year ago

Anyone please answer !!!!! Happy holidays!

ValentinkaMS [17]

Answer:

(4, 0)

Step-by-step explanation:

$6x-3y=24\\-3y=24-6x\\y=-8+2x\\0=-8+2x\\8=2x\\$

x=4 when y=0, and in x-intercepts, we are trying to find the value of x when y=0, which is why (4, 0) is the point of interception.

5 0

2 years ago

Read 2 more answers

Find the standard equation of a sphere that has diameter with the end points given below. (3,-2,4) (7,12,4)

DiKsa [7]

Answer:

The standard equation of the sphere is $(x-5)^{2} + (y-5)^{2} + (z-4)^{2} = 53$

Step-by-step explanation:

From the question, the end point are (3,-2,4) and (7,12,4)

Since we know the end points of the diameter, we can determine the center (midpoint of the two end points) of the sphere.

The midpoint can be calculated thus

Midpoint = $(\frac{x_{1} + x_{2} }{2}, \frac{y_{1} + y_{2} }{2}, \frac{z_{1} + z_{2} }{2})$

Let the first endpoint be represented as $(x_{1}, y_{1}, z_{1})$ and the second endpoint be $(x_{2}, y_{2}, z_{2})$ .

Hence,

Midpoint = $(\frac{x_{1} + x_{2} }{2}, \frac{y_{1} + y_{2} }{2}, \frac{z_{1} + z_{2} }{2})$

Midpoint = $(\frac{3 + 7 }{2}, \frac{-2+12 }{2}, \frac{4 + 4 }{2})$

Midpoint = $(\frac{10 }{2}, \frac{10}{2}, \frac{8 }{2})\\$

Midpoint = $(5, 5, 4)$

This is the center of the sphere.

Now, we will determine the distance (diameter) of the sphere

The distance is given by

$d = \sqrt{(x_{2} - x_{1})^{2} +(y_{2} - y_{1})^{2} + (z_{2}- z_{1})^{2} }$

$d = \sqrt{(7 - 3)^{2} +(12 - -2)^{2} + (4- 4)^{2}$

$d = \sqrt{(4)^{2} +(14)^{2} + (0)^{2}$

$d = \sqrt{16 +196 + 0$

$d =\sqrt{212}$

$d = 2\sqrt{53}$

This is the diameter

To find the radius, r

From $Radius = \frac{Diameter}{2}$

$Radius = \frac{2\sqrt{53} }{2}$

∴ $Radius = \sqrt{53}$

r = $\sqrt{53}$

Now, we can write the standard equation of the sphere since we know the center and the radius

Center of the sphere is $(5, 5, 4)$

Radius of the sphere is $\sqrt{53}$

The equation of a sphere of radius r and center $(h,k,l)$ is given by

$(x-h)^{2} + (y-k)^{2} + (z-l)^{2} = r^{2}$

Hence, the equation of the sphere of radius $\sqrt{53}$ and center $(5, 5, 4)$ is

$(x-5)^{2} + (y-5)^{2} + (z-4)^{2} = \sqrt{(53} )^{2}$

$(x-5)^{2} + (y-5)^{2} + (z-4)^{2} = 53$

This is the standard equation of the sphere

6 0

3 years ago

Write an expression showing 5 less than the number .

loris [4]

Answer:

if the number is anything then I pick 10 so 5 because 10 - 5 = 5 I guess lol

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

4b + 5 = 1 + 5b what is b?

Alla [95]

Answer: b = 4

Step-by-step explanation:

Given

4b + 5 = 1 + 5b

Subtract 4b on both sides

4b + 5 - 4b = 1 + 5b - 4b

5 = 1 + b

Subtract 1 on both sides

5 - 1 = 1 + b - 1

$\boxed{b=4}$

Hope this helps!! :)

Please let me know if you have any questions

3 0

3 years ago