given -1/2 x>6.choose the solution set

Answer:

[tex]\large\boxed{y=3(x-2)^2-8}[/tex]

Step-by-step explanation:

The vertex form of an equation of a parabola y = ax² + bx + c:

[tex]f(x)=a(x-h)^2+k[/tex]

(h, k) - vertex

[tex]h=\dfrac{-b}{2a},\ k=f(h)[/tex]

We have the equation:

[tex]y=3x^2-12x+4\\\\a=3,\ b=-12,\ c=4[/tex]

Substitute:

[tex]h=\dfrac{-(-12)}{2(3)}=\dfrac{12}{6}=2\\\\k=f(2)=3(2^2)-12(2)+4=3(4)-24+4=12-24+4=-8[/tex]

Finally:

[tex]y=3(x-2)^2+(-8)=3(x-2)^2-8[/tex]

Answer:   [tex]\bold{\dfrac{-2\pm \sqrt{22}}{3}}[/tex]

Step-by-step explanation:

[tex]3x^2+4x-6=0\quad \rightarrow \quad a=3,\ b=4,\ c=-6\\\\\\\text{Quadratic formula is: }x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}\\\\\\x=\dfrac{-(4)\pm \sqrt{(4)^2-4(3)(-6)}}{2(3)}\\\\\\.\ =\dfrac{-4\pm \sqrt{16+72}}{2(3)}\\\\\\\\.\ =\dfrac{-4\pm \sqrt{88}}{2(3)}\\\\\\\\.\ =\dfrac{-4\pm 2\sqrt{22}}{2(3)}\\\\\\\\.\ =\dfrac{-2\pm \sqrt{22}}{3}[/tex]

Answer:

[tex]\large\boxed{y+3=\dfrac{3}{2}(x+4)}[/tex]

Step-by-step explanation:

The point-slope form of an equation of a line:

[tex]y-y_1=m(x-x_1)[/tex]

We have

[tex]m=\dfrac{3}{2},\ (-4,\ -3)[/tex]

Substitute:

[tex]y-(-3)=\dfrac{3}{2}(x-(-4))\\\\y+3=\dfrac{3}{2}(x+4)[/tex]

Answer:

[tex]-2x+3y=21[/tex]

Step-by-step explanation:

The equation was given to us in slope-intercept form.

Thus;

[tex]y=\frac{2}{3}x+7[/tex]

We multiply each term by 3 to obtain;

[tex]3y=2x+21[/tex]

We add [tex]-2x[/tex] to both sides to obtain;

[tex]-2x+3y=21[/tex]

This equation is in the form;

[tex]ax+by=c[/tex] (standard form).

The correct choice is D.

Answer:

-2x+3y = 21

Step-by-step explanation:

We have given a equation in slope-intercept form .

y = 2/3x+7

We have to rewrite above equation in standard form.

The standard form of equation is :

Ax+By = C

Multiplying by 3 to both sides of above equation, we have

3y = 3(2/3x+7)

3y = 2x+21

Adding -2x to both sides of above equation, we have

-2x+3y = -2x+2x+21

-2x+3y = 21 which is standard form of given equation.

Answer:

A) 40 in.^3

Step-by-step explanation:

volume = (1/3)(LWh)

volume = (1/3)(5 in.)(3 in.)(8 in.)

volume = 40 in.^3

Answer:

40.^3

Step-by-step explanation:

took the test

Answer:

116 cm²

Step-by-step explanation:

The area of a circle = πr² ← r is the radius

shaded area = external area - internal area

                      = π × 6.5² - π × 2.3²

                      = π( 42.25 - 5.29)

                      = π × 36.96 ≈ 116 cm²

Answer:

Step-by-step explanation:

Area of a circle = πr²

Shaded area = External area - Internal area

                      = π × 6.5² - π × 2.3²

                      = π × (42.25 - 5.29)

                      = π × 36.96 = 116.113 cm²

When repetition is allowed, there can be 64 different 3-letter words made from the letters 'FGHI'. When repetition is not allowed, there can be 24 different 3-letter words made from those letters.

In this question, we are asked to find the number of 3-letter words that can be made from the letters 'FGHI' with and without repetition. When repetition is allowed, each letter can be chosen independently for each position, so we have 4 choices for each position. Therefore, the total number of words is 4*4*4 = 64. When repetition is not allowed, each letter can only be used once, so we have 4 choices for the first position, then 3 choices for the second position, and finally 2 choices for the third position. Therefore, the total number of words is 4*3*2 = 24.

https://brainly.com/question/29594564

#SPJ12

Answer:   B. 34°

Step-by-step explanation:

∠RQS + ∠SQT = ∠RQT

[tex]\bigg(\dfrac{1}{2}x+4\bigg)+\bigg(\dfrac{3}{4}x-6\bigg)=2x-47\\\\\\.\qquad\qquad\qquad\dfrac{5}{4}x-2=2x-47\\\\\\.\qquad\qquad\qquad\quad -2=\dfrac{3}{4}x-47\\\\\\.\qquad\qquad\qquad\qquad 45=\dfrac{3}{4}x\\\\\\.\qquad\qquad\qquad\qquad 180=3x\\\\\\.\qquad\qquad\qquad\qquad 60=x[/tex]

[tex]\angle RQS=\dfrac{1}{2}x+4\\\\.\qquad=\dfrac{1}{2}(60)+4\\\\.\qquad=30+4\\\\.\qquad=34[/tex]

Answer:the answer is -7

Step-by-step explanation:

156=2b+5(-8-6b)

2b+5(-8-6b)

expand 2b+5(-8-6b) ---> -28b-40

-28b-40=156

add 40 to both sides

-28b-40+40=156+40

simplify

-28b=196

divide both sides by -28

(-28b/-28b) = (196/-28b)

simplify

b=-7

Answer:

[tex]\large\boxed{Q1.\ x>1}\\\boxed{Q2.\ x>1}\\\boxed{Q3.\ x\leq-3}[/tex]

Step-by-step explanation:

[tex]Q1.\\7x+3>10\qquad\text{subtract 3 from both sides}\\\\7x+3-3>10-3\\\\7x>7\qquad\text{divide both sides by 7}\\\\\dfrac{7x}{7}>\dfrac{7}{7}\\\\\boxed{x>1}\\\\Q2.\\-3+5x<7x-5\qquad\text{add 3 to both sides}\\\\-3+3+5x<7x-5+3\\\\5x<7x-2\qquad\text{subtract 7x from both sides}\\\\5x-7x<7x-7x-2\\\\-2x<-2\qquad\text{change the signs}\\\\2x>2\qquad\text{divide both sides by 2}\\\\\dfrac{2x}{2}>\dfrac{2}{2}\\\\\boxed{x>1}[/tex]

[tex]Q3.\\-2x+5\geq3x+20\qquad\text{subtract 5 from both sides}\\\\-2x+5-5\geq3x+20-5\\\\-2x\geq3x+15\qquad\text{subtract 3x from both sides}\\\\-2x-3x\geq3x-3x+15\\\\-5x\geq15\qquad\text{change the signs}\\\\5x\leq-15\qquad\text{divide both sides by 5}\\\\\boxed{x\leq-3}[/tex]

x>1

x>1

X>-3

Step-by-step explanation:

a. Angles ABC and CBD are supplementary, so you know that [tex]m\angle ABC=180^\circ-24^\circ=156^\circ[/tex]

The interior angles of any triangle sum to 180 degrees in measure, so that [tex]m\angle ACB=180^\circ-156^\circ-16^\circ=8^\circ[/tex].

By the law of sines, we then have

[tex]\dfrac{\sin8^\circ}{7600\,\mathrm{ft}}=\dfrac{\sin16^\circ}{BC}\implies BC=\dfrac{(7600\,\mathrm{ft})\sin16^\circ}{\sin156^\circ}\approx15052\,\mathrm{ft}[/tex]

b. In triangle BCD, we have

[tex]\sin24^\circ=\dfrac{CD}{BC}[/tex]

and so

[tex]CD=\sin24^\circ\dfrac{(7600\,\mathrm{ft})\sin16^\circ}{\sin8^\circ}\approx6122\,\mathrm{ft}[/tex]

Answer:

Step-by-step explanation:

include the striking deviation because it may explain an unusual occurrence is correct. Striking deviations or outliers can be useful in describing data set.

Answer:7/8

Step-by-step explanation:

7 divided by 8 = 7/8

if you split that with 8 people, you multiply 7/8 and 8, and you'll get 7, which is the number of soup cans you started with.

Answer:

60 / 120 is terminating, the rest are repeating.

Answer:

56/72 is repeating, 21/22 is repeating, 11/121 is repeating, and 60/120 is terminating

Step-by-step explanation:

Answer:

Pi is not a terminating decimal

Step-by-step explanation:

1234567890

Answer:

Yes!

Step-by-step explanation:

3.14 ends and it does not repeat. Otherwise it would be a repeating decimal.

Answer:

b=16

Step-by-step explanation:

12*100=1200

1200/75

------------------

16

Check

16*0.75=12

Answer:

Part a) The exterior surface area is equal to [tex]160\ ft^{2}[/tex]

Part b) The volume is equal to [tex]240\ ft^{3}[/tex]

Part c) The volume water left in the trough will be [tex]84\ ft^{3}[/tex]

Step-by-step explanation:

Part a) we know that

The exterior surface area is equal to the area of both trapezoids plus the area of both rectangles

so

Find the area of two rectangles

[tex]A=2[12*5]=120\ ft^{2}[/tex]

Find the area of two trapezoids

[tex]A=2[\frac{1}{2}(8+2)h][/tex]

Applying Pythagoras theorem calculate the height h

[tex]h^{2}=5^{2}-3^{2}[/tex]

[tex]h^{2}=16[/tex]

[tex]h=4\ ft[/tex]

substitute the value of h to find the area

[tex]A=2[\frac{1}{2}(8+2)(4)]=40\ ft^{2}[/tex]

The exterior surface area is equal to

[tex]120\ ft^{2}+40\ ft^{2}=160\ ft^{2}[/tex]

Part b) Find the volume

We know that

The volume is equal to

[tex]V=BL[/tex]

where

B is the area of the trapezoidal face

L is the length of the trough

we have

[tex]B=20\ ft^{2}[/tex]

[tex]L=12\ ft[/tex]

substitute

[tex]V=20(12)=240\ ft^{3}[/tex]

Part c)

step 1

Calculate the area of the trapezoid for h=2 ft (the half)

the length of the midsegment of the trapezoid is (8+2)/2=5 ft

[tex]A=\frac{1}{2}(5+2)(2)=7\ ft^{2}[/tex]

step 2

Find the volume

The volume is equal to

[tex]V=BL[/tex]

where

B is the area of the trapezoidal face

L is the length of the trough

we have

[tex]B=7\ ft^{2}[/tex]

[tex]L=12\ ft[/tex]

substitute

[tex]V=7(12)=84\ ft^{3}[/tex]

Answer:

3/8

Step-by-step explanation:

another way of writing 1/2 is 4/8, so now it should be easy.  if you have 7/8 and sell 4/8 that leaves 3/8

Answer: 3/8

Step-by-step explanation:

Answer:

Step-by-step explanation:

AThe shortest column of the line plot

BThe shortest bar of the bar graph

CThe column farthest to the left on the line plot

DThe average bar height of the bar graph

Answer:

The shortest column of the line plot

Answer:

p = 48.2

Step-by-step explanation:

p = 2L + 2w

p = 2(8.3) + 2(15.8)

p = 16.6 + 31.6

p = 48.2

Answer:

P = 48.2 ft

Step-by-step explanation:

P =2l+2w

Given: l  = 8.3 ft and w = 15.8 ft

Plug in

P =2(8.3) + 2(15.8)

P = 16.6 + 31.6

P = 48.2 ft

Answer:

Step-by-step explanation:

Plug x for y and y for x.

y = 2x^2 + 2

x = 2y^2 + 2

Then isolate the y variable.

x - 2 = 2y^2

sqrt(x - 2) = 2y

(sqrt(x - 2))/2 = y

Answer:

[tex]\large\boxed{1,052\ cm^3=1.052\ liters}[/tex]

Step-by-step explanation:

[tex]1Liter=1dm^3\\\\1dm=10cm\to1dm^3=(10cm)^3=1,000cm^3\\\\1052\ cm^3=\dfrac{1,052}{1,000}dm^3=1.052\ dm^3=1.052\ Liters[/tex]

Answer:

8

Step-by-step explanation:

6 / .75(3/4)

• They're 180°

• Short, thin, or thick

• Could be curved, zig-zag, straight, bent etc.

• Perpendicular

A line is characterized by its length exceeding its width and the path it takes. Its qualities can express emotions and control the viewer's attention, with variations such as curved or angular, smooth or staccato, and different thicknesses. Lines play a crucial role in defining shapes and in expressive forms of writing such as calligraphy.

The characteristics of a line in design are defined by its length being greater than its width and by the paths it takes. A line is essentially a point in motion and is characterized by how it is used in art to determine motion, direction, and energy. When speaking of the qualities of a line, we refer to its character which can animate a surface. Lines can be curved or angular, and can progress smoothly or with a staccato rhythm, and they can be thick or thin, pale or bold.<\/p>

Lines have an emotional and expressive content that is understood both rationally and emotionally; they can control the viewer's attention and direction. Different types of lines like outline or contour line define shapes. Moreover, lines are integral to objects and writing symbols, where they denote meaning and can be expressive in themselves, illustrating their significance in calligraphy and other forms of art.<\/p>

Gestures are also related to lines, where a line produced by the artist's movement can be interpreted in various ways, like conveying calm with evenly drawn horizontal lines or rigidity with straight lines, which can be impactful depending on the context.<\/p>

Answer:

Hilda needs 64 ft² of tile

8601 in² will be uncovered post mounting

Step-by-step explanation:

Ar=10•6=60 ft²

At=[4•2]/2=8/2=4 ft²

total area=Ar+At=60+4=64ft²

......

Atv=31•57=1767 in²

Aw=(12•8)•(9•12)=10368 in²

Au=Aw-Atv=10368-1767=8601 in²

Hilda will need 64 square feet of tile to cover the space. Francine will have 8601 square inches of the wall not covered by the TV once it is mounted.

To determine how many square feet of tile Hilda will need, let's calculate the area of both the rectangular and triangular parts separately and then sum them up. The area of the rectangle can be found by multiplying the length and the width, so we have:
10 feet * 6 feet = 60 square feet.
Next, we calculate the triangular area using the formula for the area of a triangle (A = base * height / 2), giving us:
4 feet * 2 feet / 2 = 4 square feet.
Adding both areas gives us a total of:
60 square feet + 4 square feet = 64 square feet needed for tiling.

For Francine's TV and the uncovered wall area, we first convert the wall measurements to inches (1 foot = 12 inches):
8 feet = 96 inches wide
9 feet = 108 inches tall
Then we calculate the area of the wall and subtract the TV's area:
Wall area: 96 inches * 108 inches = 10368 square inches
TV area: 31 inches * 57 inches = 1767 square inches
Uncovered wall area:
10368 square inches - 1767 square inches = 8601 square inches.

Answer:

what is her error?

Step-by-step explanation:

Answer:

Do you have a picture?

Answer:

15 teams, 4 girls and 3 boys on each team.

Step-by-step explanation:

What's the greatest common multiple of 60 and 45?  It's 15.

This is the greatest number of teams that can be formed.

60/15 = 4; thus, there will be 4 girls on each team.

45/15 = 3; thus, 3 boys on each team

The greatest number of co-ed basketball teams that can be formed with an equal number of girls and boys is 3, with each team consisting of 4 girls and 3 boys.

To determine the greatest number of co-ed basketball teams that can enter the tournament with an equal number of girls and boys, you need to find the greatest common divisor (GCD) of the number of girls and boys. In this case, we have 60 girls and 45 boys. The GCD of 60 and 45 is 15, which means the largest number of teams that can be formed where each team has the same number of girls and boys is 15 (since 60 \/ 15 = 4 girls per team and 45 \/ 15 = 3 boys per team).

Answer 1: The greatest number of teams that can enter are 3 teams.

Answer 2: There would be 4 girls and 3 boys on each team.

Hey there!

Let's start by adding 5 to both sides. This eliminates the -5.  

1 = r/20

Now to solve for r we can multiply both sides by 20.

20 = r

Check

-4 = 20/20 - 5

-4 = 1 - 5

-4 = -4

Your answer is r = 20.

Hope this helps!

Answer:

Step-by-step explanation:

-4 = [tex]\frac{r}{20}[/tex] - 5

⇒ -4 + 5 = [tex]\frac{r}{20}[/tex]

⇒ 1 = [tex]\frac{r}{20}[/tex]

⇒ 1 × 20 = r

⇒ 20 = r

Answer:

40 m

Step-by-step explanation:

A= b(h)

A= 8(5)

A= 40 m

Answer:

It is a parallelogram and the area is 40.

Step-by-step explanation:

The area of a parallelogram is a=bh.

The base is 8 and the height is 5. All you do is times 8 and 5 to get 40.