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3 years ago

5

To place a picture in his class newsletter, Joaquin must reduce the picture by a scale factor of 0.3. Find the dimensions of the

reduced picture if the original is 15 centimeters wide and 10 centimeters high.

1 answer:

Law Incorporation [45]3 years ago

4 0

This is the concept of scale factors. Given that Joaquin has reduce the dimensions of a picture by scale factor of 0.3 and the original dimension was 10 cm length by 10 cm width, the new dimension will be:
New length=(old length)×(scale factor)
New width=(old width)×(scale factor)
Plugging the values in the above formulas we get:

New length=15x0.3=4.5 cm

New width=10×0.3=3 cm

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What is the solution set of the quadratic inequality 6x2+1<0

Free_Kalibri [48]

Answer:

Solution set of the quadratic equation is, Empty set

Step-by-step explanation:

Given the quadratic equation: $6x^2+1>0$

Subtraction property of equality states that you subtract the same number to both sides of an equation.

Subtract both sides by 1 we get;

$6x^2+1-1>0-1$

Simplify:

$6x^2>-1$

Division property of equality states that you divide the same number to both sides of an equation.

Divide both sides by 6 we get;

$\frac{6x^2}{6} >\frac{-1}{6}$

Simplify:

$x^2>\frac{-1}{6}$

For any x in real number there does not exist any number x which satisfy

$x^2>\frac{-1}{6}$ , therefore, there is no solution for this set of the quadratic inequality or in other word we can say that set of the solution is Empty set.

3 0

4 years ago

Read 2 more answers

PLEASE HELP ILL MARK BRAINLIEST !!!

Alexus [3.1K]

Answer:

a) the common difference is 20

b) $x_8=115 , x_{12}=195$

c) the common difference is -13

d) $a_{12}=52, a_{15}=13$

Step-by-step explanation:

a) what is the common difference of the sequence xn

Looking at the table, we get x_3=16, x_4=36 and x_5= 56

Deterring the common difference by subtracting x_4 from x_3 we get

36-16 =20

So, the common difference is 20

b) what is x_8? what is x_12

The formula used is: $x_n=x_1+(n-1)d$

We know common difference d= 20, we need to find $x_1$

Using $x_3=16$ we can find $x_1$

$x_n=x_1+(n-1)d\\x_3=x_1+(3-1)d\\15=x_1+2(20)\\15=x_1+40\\x_1=15-40\\x_1=-25$

So, We have $x_1 = -25$

Now finding $x_8$

$x_n=x_1+(n-1)d\\x_8=x_1+(8-1)d\\x_8=-25+7(20)\\x_8=-25+140\\x_8=115$

So, $\mathbf{x_8=115}$

Now finding $x_{12}$

$x_n=x_1+(n-1)d\\x_{12}=x_1+(12-1)d\\x_{12}=-25+11(20)\\x_{12}=-25+220\\x_{12}=195$

So, $\mathbf{x_{12}=195}$

c) what is the common difference of the sequence $a_m$

Looking at the table, we get a_7=104, a_8=91 and a_9= 78

Deterring the common difference by subtracting a_7 from a_8 we get

91-104 =-13

So, the common difference is -13

d) what is a_12? what is a_15?

The formula used is: $a_n=a_1+(n-1)d$

We know common difference d= -13, we need to find $a_1$

Using $a_7=104$ we can find $x_1$

$a_n=a_1+(n-1)d\\a_7=a_1+(7-1)d\\104=a_1+7(-13)\\104=a_1-91\\a_1=104+91\\a_1=195$

So, We have $a_1 = 195$

Now finding $a_{12}$ , put n=12

$a_n=a_1+(n-1)d\\a_{12}=a_1+(12-1)d\\a_{12}=195+11(-13)\\a_{12}=195-143\\a_{12}=52$

So, $\mathbf{a_{12}=52}$

Now finding $a_{15}$ , put n=15

$a_n=a_1+(n-1)d\\a_{15}=a_1+(15-1)d\\a_{15}=195+14(-13)\\a_{15}=195-182\\a_{15}=13$

So, $\mathbf{a_{15}=13}$

5 0

3 years ago

A spaceship is traveling at a steady rate. The table shows the distance the spaceship travels in a given period of time. Find th

nika2105 [10]

The distance of the spaceship in discuss as in the task content given can be evaluated as; 800miles.

<h3>What is the distance the spaceship travels in 4 minutes?</h3>

The distance travelled by the spaceship in discuss can be evaluated by means of the slope of the linear relationship as follows;

Hence it follows from ratios that by observation, the linear relationship has a slope of 200mi/min.

Consequently, we can evaluate the distance travelled after 4 minutes as;

Distance = 200 × 4 = 800mi.

Ultimately, the distance travelled per minute by the spaceship is; 800mi.

Remarks:

600 miles

520 miles

800 miles

1,080 miles

Read more on ratios;

brainly.com/question/13513438

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4 0

2 years ago

1<br> Enter the correct answer in the box.<br> Simplify the expression (62,4.

adelina 88 [10]

Answer:

248

Step-by-step explanation:

(62)4

= 62 x 4

= 248

4 0

3 years ago

A square has an area of 576 square inches. How long is each side in feet?

Maru [420]

The area of this square is said to be 576 square inches.
The formula for the area of a square is the length of one side squared.
Let's use l to represent the side length.
This means l^2 = 576.
To find l, find the square root of both sides.
<span>√576 = 24
</span>
The length of each side of the square is 24 inches.
But the question is asking for it in feet.
12 inches = 1 foot so 24 inches = 2 feet
This means each side of the square is 2 feet long.

Answer:
2 feet

5 0

3 years ago