David wants to hang a mirror in his room. The mirror and frame must have an area of 8 square feet. The mirror is 2 feet wide and 3 feet long. Which quadratic equation can be used to determine the thickness of the frame, x?

Answer:

13*12 is greater than 11*14 by 2 meters^2

Step-by-step explanation:

[tex]A=wl=13*12=156m^2\\A=wl=11*14=154m^2[/tex]

Goodluck

Answer:

Jenny's room has a great area.

Step-by-step explanation:

Jenny's room

[tex]area = l \times b \\ = 13 \times 12 \\ = 156 {ft}^{2} [/tex]

Ruth's room

[tex]area = l \times b \\ = 14 \times 11 \\ = 154 {ft}^{2} [/tex]

so,

[tex]156 > 154[/tex]

So ,Jenny's room has a great area than Ruth's room.

hope this helps

brainliest appreciated

good luck! have a nice day!

Answer:

8 - 35

a. 350 unit²

b. 81.23  unit²

c. 41.57 unit²

8 - 36

Beth should buy 3 bags of fertilizer

Step-by-step explanation:

8 - 35

a. The figure consists of 9 isosceles triangles of side lengths 11 and vertex angle = 360/9 = 40°

Hence base angles = (180 - 40)/2 = 70°

Therefore, the base of the triangles = sin(40) × 11/sin(70) = 7.52

Hence area of figure = 9 × 0.5 × 7.52 × √(11² - (7.52/2)²) =349.99 ≈ 350 unit²

b. Area of a decagon

We note that the vertex angle = 36°

∴ Half the base = tan(18) × 5 = 1.62

Area = 10 × 1.62 × 5 = 81.23  unit²

c. The area of a hexagon = [tex]s^2 \times \dfrac{3\sqrt{3} }{2}[/tex]

s = 4 therefore, the area = [tex]4^2 \times \dfrac{3\sqrt{3} }{2} = 41.57 \, unit^2[/tex]

8 - 36

Area, A of a regular pentagon = [tex]A = a^2 \times \dfrac{1}{4} \sqrt{5(5 + 2\sqrt{5} )}[/tex]

a = 15 ft., therefore, A = [tex]15^2 \times \dfrac{1}{4} \sqrt{5(5 + 2\sqrt{5} )}[/tex] = 387.11 ft.²

Therefore, since a bag of fertilizer can fertilize 150 ft.², the number of bags of fertilizer that will fertilize 387.11 ft.² will be 387.11/150 = 2.58 bags

Therefore, since 2 bags of fertilizers will not be enough, Beth should buy 3 bags of fertilizer.

Answer:

F = -22

Step-by-step explanation:

F = 1.8 C + 32 for C = -30

F = 1.8 C + 32 = 1.8(-30) + 32 = -54 + 32 = -22

Answer:

The value of F is -22

Step-by-step explanation:

F=1.8 C+32

F=1.8*-30+32

F=-54+32

F=-22

Answer:

y = 120

Step-by-step explanation:

Interior angles of a triangle add up to 180°

So,

x+87+33 = 180

x + 120 = 180

Subtracting 120 to both sides

x = 180-120

x = 60°

Now

Angles on a straight line also add up to 180°

So,

x+y = 180

60 + y = 180

Subtracting 60 to both sides , we get

y = 180-60

y = 120

Answer:

4

Step-by-step explanation:

10÷2.5

Answer:

4 plants

Step-by-step explanation:

She can grow 4 plants because 10/2.5 is equal to 4. So, the answer is 4 plants.

Answer:

x^2 + {a/(a + b) + (a + b)/a}x + 1 = 0

Delta =  {a/(a + b) + (a + b)/a}^2 - 4

         =  {a/(a + b)}^2 + {(a + b)/a}^2 + 2 - 4

         =  {a/(a + b)}^2 + {(a + b)/a}^2  - 2

         =  {a/(a + b) - (a + b)/a}^2

If a is not equal to zero and a is not equal to -b => delta is always larger than 0

=>  Solution 1 =  - [ {a/(a + b) + (a + b)/a} + |{a/(a + b) - (a + b)/a}| ]/2

=>  Solution 2 = - [ {a/(a + b) + (a + b)/a} - |{a/(a + b) - (a + b)/a}| ]/2

Hope this helps!

:)

A, B, D are your answers

AP E X

Point H is the midpoint of FG, Line t intersects FG at a right angle and Line t is perpendicular to FG are true statements.

A system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space.

A. Point H is the midpoint of FG: This statement must be true because line t is the perpendicular bisector of FG, which means it passes through the midpoint of FG and intersects FG at a right angle.

Therefore, H is the midpoint of FG.

B. Line t intersects FG at a right angle: This statement must be true because line t is the perpendicular bisector of FG, which means it intersects FG at a right angle.

C. FG = FH: This statement is not necessarily true.

While H is the midpoint of FG, the length of FH depends on the position of point H along line t. It could be greater than, less than, or equal to half the length of FG.

D. Line t is perpendicular to FG

This statement must be true because line t is the perpendicular bisector of FG, which means it is perpendicular to FG.

E. Line t is parallel to FG: This statement is not true. If line t were parallel to FG, it would not intersect FG at all, let alone at a right angle as required for a perpendicular bisector.

Therefore, Point H is the midpoint of FG, Line t intersects FG at a right angle and Line t is perpendicular to FG are true statements.

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Answer:

A.) 4991/157216

B.) 2401/1336336

C.) 16399/314432

Step-by-step explanation:

Given the following :

Granny Smith = 23

Honey crisp = 14

Red delicious = 31

Probability = (number of required outcome / number of possible outcomes)

Number of possible outcomes = 23 + 14 + 31 = 68

With replacement :

A.) one of each :

P(granny Smith) × P(Honey crisp) × P(Red delicious)

P(granny Smith) = 23/68

P(Honey crisp) = 14/68 = 7/34

P(red delicious) = 31/68

(23/68 × 7/34 × 31/68) = 4991/157216

B) 4 honey crisp:

P(4 Honey crisp) = P(honey crisp) × P(honey crisp) × P(honey crisp) × P(honey crisp)

7/34 × 7/34 × 7/34 × 7/34 = 2401/1336336

C.) 2 granny Smith and 1 red delicious

P(granny Smith) × P(granny Smith) × P(red delicious)

23/68 × 23/68 × 31/68 = 16399/314432

Answer:

Subtract  12  from  7 = -5

Answer:

P (4 and F) = 1 in 21 or 4.76%

P(EVEN NUMBER AND VOWEL) = 3 in 14 or 21.43%

Step-by-step explanation:

The probability of rolling a four on a die is 1 in 6.

The probability of picking the letter F in the word GIRAFFE is 2 in 7.

Therefore:

[tex]P (4\ and\ F)=P(4)*P(F)\\ P (4\ and\ F)=\frac{1}{6}*\frac{2}{7}\\ P (4\ and\ F)=\frac{1}{21}= 4.76\%[/tex]

The probability of rolling an even number (2, 4 or 6) on a die is 3 in 6.

The probability of picking a vowel (A, E, I) in the word GIRAFFE is 3 in 7.

Therefore:

[tex]P (Even\ and\ Vowel)=P(Even)*P(Vowel)\\ P (Even\ and\ Vowel)=\frac{3}{6}*\frac{3}{7}\\ P (Even\ and\ Vowel)=\frac{3}{14}= 21.43\%[/tex]

Answer:

[tex]75^{\circ}[/tex]

Step-by-step explanation:

Given: [tex]\csc (x) = 1.0353[/tex]

To find: angle to the nearest degree

Solution:

A triangle is a polygon that has three sides, three angles ,and three vertices.

Trigonometry explains the relationship between the sides and angles of the triangle.

The angle can be expressed in two forms: degrees or radians.

[tex]\csc (x) = 1.0353\\x=74.995\approx 75^{\circ}[/tex]

Answer:

B. 6 days

Step-by-step explanation:

60 minutes-->1 hour

8064 minutes--> ?

=8064 x (1/60)

=134.4 hours

24 hours-->1 day

134.4 hours-->?

=134.4 × (1/24)

=5.6 days

≈6 days

Answer:

First number: 6

Second number: 16

Third number: 32

Step-by-step explanation:

x + y + z = 54

z = 2y

y = x + 10

Now you can substitute y = x + 10 into z = 2y

The equation becomes z = 2x + 20

Now plug it into the main equation.

x + x + 10 + 2x + 20 = 54

4x + 30 = 54

4x = 24

x = 6

y = 16

z = 32

Answer:

S(20) = [tex]\sqrt{20+2}[/tex] = 4.69 ; value of total sales after 20 months is 4.69 million dollars

S'(20) = [tex]\dfrac{1}{\sqrt{20+2} }[/tex] = 0.21 ; increase in the total sales after 20 months is 0.21 millions of dollars

S(24) = [tex]\sqrt{24+2}[/tex] = 5.10;  5.10  millions of dollars

S(25) = [tex]\sqrt{25+2}[/tex] = 5.20 ;  5.20  millions of dollars

Step-by-step explanation:

[tex]S(t) = \sqrt{t+2}[/tex]

[tex]S(t+h) = \sqrt{t+2+h}[/tex]

[tex]S(t+h) - S(t)= \sqrt{t+2+h }- \sqrt{t+2}[/tex]

[tex]\dfrac{S(t+h) - S(t)}{h}= \dfrac{\sqrt{t+2+h }- \sqrt{t+2}}{h}[/tex]

By rationalization:

[tex]\dfrac{\sqrt{t+2+h }- \sqrt{t+2}}{h} * \dfrac{ {\sqrt{t+2+h }- \sqrt{t+2}} }{ {\sqrt{t+2+h }- \sqrt{t+2}}}[/tex]

[tex]\\ \\ \dfrac{t+2+h-t-2}{h \sqrt{t+2+h }+ \sqrt{t+2} } = \dfrac {h}{\sqrt{t+2+h }+\sqrt{t+2} }[/tex]

= [tex]\dfrac {1}{\sqrt{t+2+h }+\sqrt{t+2} }[/tex]

[tex]\lim_{k \to \infty} \dfrac {1}{\sqrt{t+2+h }+\sqrt{t+2} } = \dfrac{1}{t+2}[/tex]

[tex]S' (t) = \dfrac{1}{\sqrt{t+2} }[/tex]

S(20) = [tex]\sqrt{20+2}[/tex] = 4.69 ; value of total sales after 20 months is 4.69 million dollars

S'(20) = [tex]\dfrac{1}{\sqrt{20+2} }[/tex] = 0.21 ; increase in the total sales after 20 months is 0.21 millions of dollars

S(24) = [tex]\sqrt{24+2}[/tex] = 5.10;  5.10  millions of dollars

S(25) = [tex]\sqrt{25+2}[/tex] = 5.20 ;  5.20  millions of dollars

Answer:

it is C

Step-by-step explanation:

Answer:

if the marble slab is 1 cm³ in volume the mass is 2.7 g but u did not put a volume

Answer:

wouldnt it be 10 out of 26 percent chance or 2.6

Step-by-step explanation:

there are 10 letters in county fair and 26 letters so you divide 26 by 10

The probability that Luca will win Wheel of Letters is [tex]\frac{5}{13}[/tex] given there are 26 equal sections lettered A to Z and the contestant win if the pointer lands on any letter in the phrase "COUNTY FAIR". This is obtained by using probability concept.

Given total number of outcomes are 26

Since "COUNTY FAIR" has 10 letters, number of favourable outcomes are 10.

According to definition of probability we get ,

P(winning) =[tex]\frac{10}{26}[/tex] =[tex]\frac{5}{13}[/tex]

Hence the probability that Luca will win Wheel of Letters is [tex]\frac{5}{13}[/tex] given there are 26 equal sections lettered A to Z and the contestant win if the pointer lands on any letter in the phrase "COUNTY FAIR".

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Answer:

60 ml oil, 90 g onions, 1200 g potatoes, 1350 ml milk

Step-by-step explanation:

What you need to do here is multiply all of these ingredients by 3, because the recipe serves 3 and he needs to serve 9, and 9/3 = 3. Therefore, he would have to triple the recipe.

Answer: The slope is infinite

Step-by-step explanation:

An infinite slope is simply a vertical line. When you plot it on a line graph, an infinite slope is any line which runs parallel to the y-axis. You can also describe this as any line that doesn't move along the x-axis but stays fixed at one constant x-axis coordinate, making the change along the x-axis.

Answer:

Two real solutions

Step-by-step explanation:

We have the equation [tex]u^2=80[/tex]

To get a solution, we must solve for u.

When we solve for u, we need to square root each side, but when we do this, we must add a ± to the side that opposite to the u in order to compensate. This is because you could get 80 in two different ways:

[tex](\sqrt{80} )(\sqrt{80})=80 \\\\(-\sqrt{80} )(-\sqrt{80})=80[/tex]

This would mean that when we solve for u, we would get [tex]u=[/tex] ± [tex]\sqrt{80}[/tex]

Which is the same thing as [tex]u=\sqrt{80}[/tex] and [tex]u=-\sqrt{80}[/tex]

Which are two real solutions.

Answer:

2 real solutions

Step-by-step explanation:

u^2=80 is worked out as u as a variable times 2/u 2 times and when u do that you have to find the value of u and the result should be equal to 80. plz rate as the brainliest

Answer:

65

Step-by-step explanation:

Since we know that a rectangle is 360 degrees

90+88+117 = 295

360-295=

65

Answer:

a = 7

Step-by-step explanation:

Using the rule of radicals

[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex]

Given

[tex]\sqrt{2}[/tex] ([tex]\sqrt{45}[/tex] + [tex]\sqrt{80}[/tex] ) ← distribute parenthesis by [tex]\sqrt{2}[/tex]

= [tex]\sqrt{90}[/tex] + [tex]\sqrt{160}[/tex]

= [tex]\sqrt{9(10)}[/tex] + [tex]\sqrt{16(10)}[/tex]

= [tex]\sqrt{9}[/tex] × [tex]\sqrt{10}[/tex] + ([tex]\sqrt{16}[/tex] × [tex]\sqrt{10}[/tex] )

= 3[tex]\sqrt{10}[/tex] + 4[tex]\sqrt{10}[/tex]

= 7[tex]\sqrt{10}[/tex] → in the form a[tex]\sqrt{10}[/tex]

with a = 7

Answer:

7

Step-by-step explanation:

√2 (√45 + √80) = √90+√160= 3√10+4√10= 7√10

7√10= a√10

a=7

Answer:

A

Step-by-step explanation:

The first thing to notice is the question says it is given that the person is between the ages 23 and 60, so we only care about those people. So then we want to know how likely it would be to pick someone with over 50 messages a month. So what you would do is take the amount of people who are between 23 and 60 and send over 50 text messages, and divide that by the total amount of people 23-60 (since that is the pool of people we have). Doing so we find there is 229 people aged 23-60 which then makes the answer 157/229 or A.

Answer:

Step-by-step explanation:

Answer:

therefore one pen can cost approx 15.6 p

Answer:

b

Step-by-step explanation:

Answer:

The answer is B

Step-by-step explanation:

This is because when we do the work in the boxes we can see that B is the only answer that works with it.

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Answer:

Exactly one solution

Step-by-step explanation:

4x -2y = 8

2x +y = 2

Multiply the second equation by 2

4x +2y = 4

Add the two equations together

4x -2y = 8

4x +2y = 4

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

8x = 12

x = 12/8

We know there will be one solution

Answer:Week 1:  $35.40

              Week 2: $40.90

              Week 3: $46.40

               Week 4: $51.90

Step-by-step explanation:

29.90 + 5.50(x) = y

replace x with 1, 2, 3, or 4 for each week.

Answer: x = 3

Step-by-step explanation:

From the question,

5x² – 18 = 27

Collect the like terms

5x² = 27 + 18

5x² = 45

We can th n divide both side by 5 which is the coefficient of x²

5x²/5 = 45/5

x² = 9

To get the value of x, we find the square root of 9

x² = 9

x =✓9

x = 3

The value of x is 3