Ask question

Ask question

All categories

3 years ago

11

A square-shaped canvas painting was enlarged by adding a 4-centimeter wide decorative frame to the length and width of the canva

s. If the area of the framed painting is 625 square centimeters, what is the side length of the bare canvas?

2 answers:

stealth61 [152]3 years ago

5 0

Answer:

17 centimeters

Step-by-step explanation:

MrMuchimi3 years ago

4 0

<u>ANSWER:</u>

The bare canvas is of 17 cm length.

<u>SOLUTION:</u>

Given, a square-shaped canvas painting was enlarged by adding a 4-centimeter wide decorative frame to the length and width of the canvas.

The area of the framed painting is 625 $cm^2$ ,

Let, the length of the bare paintings be x.

Then, after adding the frame,

length becomes x + 4 + 4 = x + 8. [we added 4 two times, because frame adds on both sides of painting.]

Now, we are given that, area of the framed painting is 625 $cm^2$

Area = 625

$Length^2$ = 625

$(x + 8)^2$ = $25^2$

x + 8 = 25

x = 25 – 8 = 17

Hence, the bare canvas is of 17 cm length.

You might be interested in

If x+y=8, y+z=7, and x+z=5, what is the value of x? What is the formula or strategy to approach this question?

joja [24]

The strategy is to work from a system with three variables and three equations down to something with two variables and two equations. In a two variable-two equation system, you can use either substitution or elimination.

First, let's organize the equations.

(1) x + y = 8

(2) y + z = 7

(3) x + z = 5

Now, we'll solve one of (1), (2), and (3) for a variable. The choice is yours, but we'll use equation (3) and solve it for x.

x + z = 5

x = 5 - z.

Now we put this into equation (1). Why (1)? It's the only one of (1) and (2) with x.

x + y = 8

5 - z + y = 8

-z + y = 3

y - z - 3 to rearrange it.

Now look at this new equation - call it (4) and the original (2).

(4) y - z = 3

(2) y + z = 7

This is a system of two equations and two variables. Either substitution or elimination works here - let's use elimination because of the -z and +z.

y - z = 3

y + z = 7

We add them together and we have that 2y = 10. Divide on both sides and y = 5. One variable down, two to go.

Now we go back to original equation (2). Substitute y = 5 to find z.

y + z = 7

5 + z = 7

z = 2.

Two down, one to go. Since we know z = 2, let's put it into (3) and find x. (Equation (1) with y = 5 works fine as well.)

x + z = 5

x + 2 = 5

x = 3

Thus x = 3, y = 5 and z = 2.

3 0

3 years ago

Here is a triangular pyramid and its net.

bazaltina [42]

Answer:

a) Area of the base of the pyramid = $15.6\ mm^{2}$

b) Area of one lateral face = $24\ mm^{2}$

c) Lateral Surface Area = $72\ mm^{2}$

d) Total Surface Area = $87.6\ mm^{2}$

Step-by-step explanation:

We are given the following dimensions of the triangular pyramid:

Side of triangular base = 6mm

Height of triangular base = 5.2mm

Base of lateral face (triangular) = 6mm

Height of lateral face (triangular) = 8mm

a) To find Area of base of pyramid:

We know that it is a triangular pyramid and the base is a equilateral triangle. $\text{Area of triangle = } \dfrac{1}{2} \times \text{Base} \times \text{Height} ..... (1)\\$

${\Rightarrow \text{Area of pyramid's base = }\dfrac{1}{2} \times 6 \times 5.2\\\Rightarrow 15.6\ mm^{2}$

b) To find area of one lateral surface:

Base = 6mm

Height = 8mm

Using equation (1) to find the area:

$\Rightarrow \dfrac{1}{2} \times 8 \times 6\\\Rightarrow 24\ mm^{2}$

c) To find the lateral surface area:

We know that there are 3 lateral surfaces with equal height and equal base.

Hence, their areas will also be same. So,

$\text{Lateral Surface Area = }3 \times \text{ Area of one lateral surface}\\\Rightarrow 3 \times 24 = 72 mm^{2}$

d) To find total surface area:

Total Surface area of the given triangular pyramid will be equal to <em>Lateral Surface Area + Area of base</em>

$\Rightarrow 72 + 15.6 \\\Rightarrow 87.6\ mm^{2}$

Hence,

a) Area of the base of the pyramid = $15.6\ mm^{2}$

b) Area of one lateral face = $24\ mm^{2}$

c) Lateral Surface Area = $72\ mm^{2}$

d) Total Surface Area = $87.6\ mm^{2}$

3 0

3 years ago

17_2_3_8=3 insert + - × or ÷ symbols to make each statement true

erastova [34]

Answer:

17-2*3-8=3

Step-by-step explanation:

We have given:

17_2_3_8=3 insert + - × or ÷ symbols to make each statement true?

<u>Solution:</u>

We will insert multiplication sign between 2 and 3 and then subtract all the terms

<u>17-2*3-8=3</u>

We will solve it according to the DMAS rule:

DMAS rule is followed when multiple arithmetic operations are there in a given problem like addition, subtraction, multiplication and division. It tells they should be performed in order of Division, Multiplication, Addition and Subtraction. Without DMAS rule all mathematical equations will come up with different answers.

Lets solve the expression and check whether the L.H.S = R.H.S

17-2*3-8=3

17-6-8=3

11-8=3

3 =3

<em>Be sure to multiply first and then subtract</em>

⇒You can also insert addition sign in place of multiplication. It will give the same answer

3 0

3 years ago

Read 2 more answers

Assume that the empirical rule is a good model for the time it takes for all passengers to board an airplane. The mean time is 4

slamgirl [31]

Answer:

The interval that describes how long it takes for passengers to board the middle 95% of the time is between 40.16 minutes and 55.84 minutes.

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 48, \sigma = 4$ .

Which interval describes how long it takes for passengers to board the middle 95% of the time?

This is between the 2.5th percentile and the 97.5th percentile.

So this interval is the value of X when Z has a a pvalue of 0.025 and the value of X when Z has a pvalue of 0.975

Lower Limit

Z has a pvalue of 0.025 when $Z = -1.96$ . So

$Z = \frac{X - \mu}{\sigma}$

$-1.96 = \frac{X - 48}{4}$

$X - 48 = -1.96*4$

$X = 40.16$

Upper Limit

Z has a pvalue of 0.975 when $Z = 1.96$ . So

$Z = \frac{X - \mu}{\sigma}$

$1.96 = \frac{X - 48}{4}$

$X - 48 = 1.96*4$

$X = 55.84$

The interval that describes how long it takes for passengers to board the middle 95% of the time is between 40.16 minutes and 55.84 minutes.

7 0

3 years ago

Help!!!Can someone help me with my math ttas fast!!

MAVERICK [17]

The answer to the question is boneless

4 0

3 years ago