Ask question

Ask question

All categories

3 years ago

5

If $-2 < x \le 3,$ then find all possible values of $5x + 1.$ Give your answer in interval notation. We suggest you study Sec

tion 9.1 if you find this problem difficult.

1 answer:

Sergeu [11.5K]3 years ago

4 0

Answer:

Step-by-step explanation:

-2<x≤3

multiply by 5

-10<5x≤15

add 1

-9<5x+1≤16

(5x+1)∈(-9,16]

You might be interested in

What is the arithmetic sequence

Alexxx [7]

Answer:

The second choice.

Step-by-step explanation:

It is the second one.

The common difference = -4.

None of the others have a common difference between the terms in the second row.

6 0

3 years ago

Below is a drawing of a wall that is to be covered with either wallpaper or paint. The wall is 8 ft. high and

Snowcat [4.5K]

84 sq. ft of the wall has to be covered with paint or wallpaper.

Step-by-step explanation:

Step 1: Find the area of wallpaper to be covered by calculating the area of the wall and subtracting the areas of the window, mirror and fireplace from it. All are rectangular in shape with are given by A = length × width

Area of the wall = 8 × 16 = 128 ft²

Area of the window = 18/12 × 14 = 1.5 × 14 = 21 ft² (since 1 ft = 12 in)

Area of the fireplace = 5 × 3 = 15 ft²

Area of the mirror = 4 × 2 = 8 ft²

Step 2: Calculate the area to be painted or covered with wallpaper

Area of the wall to be covered with paint or wallpaper = 128 - (21 + 15 + 8)

= 128 - 44

= 84 ft²

5 0

4 years ago

Read 2 more answers

a card is drawn at random from a pack of 52 playing cards. find the probability tht the card drawn is neither an ace nor a king

Mazyrski [523]

Answer:

$\frac{11}{13}$

Step-by-step explanation:

There are 4 aces and 4 kings.

$\frac{8}{52} =\frac{2}{13}$

Now just subtract that from 1.

$\frac{11}{13}$

5 0

3 years ago

The equation of circle having a diameter with endpoints (-3, 1) and (5, 7) is

nydimaria [60]

The equation of a circle:
$(x-h)^2+(y-k)^2=r^2$
(h,k) - the coordinates of the center
r - the radius

The center is the midpoint of the diameter.
$(-3,1) \\
x_1=-3 \\ y_1=1 \\ \\
(5,7) \\
x_2=5 \\ y_2=7 \\ \\
\hbox{the midpoint: } (\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}) \\
\frac{x_1+x_2}{2}=\frac{-3+5}{2}=\frac{2}{2}=1 \\
\frac{y_1_y_2}{2}=\frac{1+7}{2}=\frac{8}{2}=4 \\
\Downarrow \\
(1,4) \\ h=1 \\ k=4$

The radius is half the diameter, or the distance from one of the endpoints to the center.
$r=\sqrt{(x_1-h)^2+(y_1-k)^2}=\sqrt{(-3-1)^2+(1-4)^2}=\\
=\sqrt{(-4)^2+(-3)^2}=\sqrt{16+9}=\sqrt{25}=5 \\ \Downarrow \\
r^2=5^2=25$

The equation of the circle:
$\boxed{(x-1)^2+(y-4)^2=25}$

8 0

3 years ago

Read 2 more answers

Q.The rectangular front windshield of the bus has the length of 1.5√3 m and the width of 1.5 m . The wipers are attached to the

galina1969 [7]

Answer:

Area covered by wiper=area of arc(A0D)+area of traingleAOB+area of arc(BOC)

We know AO and OB are wipers,whose lengths are 1.5

In ∆ABC

AB^2+BC^2=AC^2

(1.5√3)^2+(1.5)^2=(AC)^2

2.25×3+2.25=(AC)^2

2.25×4=AC^2

AC=3

Also AO=1.5

similarly using Pythagoras theorem in ∆OBC

we get

OC=1.5

this shows that point O is the bisector of diagonal AC

so,AO=OC

also from property of rectangle we know that, diagonal bisects each other equally

so,O will also be the bisector of diagonal BD

hence OB=OD=1.5

AC=BD (property of triangle)

AC/2=BD/2

OB=OC,hence OB=OC=OD=OA=1.5=AD=BC

Hence OAD will be an equilateral triangle

so

angle OAD=60

similarly angleOBC=60

area of sector=angle of that sector ×area of circle/360

area of arc(AOD)+arc(BOC)=60/360 ×3.14 ×1.5×1.5 +60/360 ×3.14×1.5×1.5

=2×(60/360)×1.5×1.5

area of triangleAOB=area of rectangle/4 (diagonal divides the rectangle in 4 equal parts)

area of triangle=1.5×1.5√3/4

=>1.5×2.6/4=3.90/4

=0.975 or 0.98(approx)

Area covered by wiper=.98+2×60/360 ×3.14×1.5×1.5

=.98+0.75×3.14=2.35+0.97

=2.35+.98

Percentage of area of windshield covered by wiper=3.3×100/3.9=84.61

hence percentage of area of windshield covered by wiper is 85percent(approx)

plz mark brainlest

5 0

3 years ago