There are 238 juniors at a high school The ratio of boys to girls in the junior class is 3:4. How many juniors are girls?

Answer:

[tex]f(0)=g(0)[/tex] and [tex]f(2) = g(2)[/tex]

Step-by-step explanation:

According to the question, the curved red line represents [tex]g(x)[/tex] and the straight blue line represents [tex]f(x)[/tex].

The important thing here is that the equality of functions [tex]f(x)=g(x)[/tex] is represented as a common function between their curves. So, we just need to find such a common point for both.

[tex]f(x)[/tex] has points (0, 4) and (2, 0).

[tex]g(x)[/tex] has points (0,4) and (2,0).

Notice that both functions have the same y-value for x=0 and x=2, that means

[tex]f(0)=g(0)[/tex] and [tex]f(2) = g(2)[/tex].

Therefore, the right answer is the first choice.

The correct answer is option A which is f(2) = g(2) and f(0) = g(0)

A function in mathematics set up a relationship between the dependent variable and independent variable. on changing the value of the independent variable the value of the dependent variable also changes.

According to the question, the curved red line represents g(x) while the straight blue line represents f(x).

The important thing here is that the equality of functions f(x) = g(x)  is represented as a common function between their curves. So, we just need to find a common point for both.

f(x) has points (0, 4) and (2, 0).

g(x) has points (0,4) and (2,0).

Notice that both functions have the same y-value for x=0 and x=2, which means

f(2) = g(2) and f(0) = g(0)

Therefore correct answer is option A which is f(2) = g(2) and f(0) = g(0)

To know more about function follow

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Answer:

9

Step-by-step explanation:

x − 3y

Let x =3 and y = -2

3 -3(-2)

3 + 6

9

Answer:

a) [tex]\boxed{4m^2+20m+25}[/tex]

b) [tex]\boxed{m^2-m+\frac{1}{4} }[/tex]

Step-by-step explanation:

a) [tex](2m+5)^2[/tex]

Using formula [tex](a+b)^2 = a^2+2ab+b^2[/tex]

=> [tex](2m)^2 + 2(2m)(5)+(5)^2[/tex]

=> [tex]4m^2+20m+25[/tex]

b) [tex](m-\frac{1}{2} )^2[/tex]

Using Formula [tex](a-b)^2 = a^2-2ab+b^2[/tex]

=> [tex](m)^2 - 2(m)(\frac{1}{2} ) + (\frac{1}{2} )^2[/tex]

=> [tex]m^2-m+\frac{1}{4}[/tex]

Answer:

a) [tex]\boxed{4m^2 + 20m + 25}[/tex]

b) [tex]\boxed{m^2 - m + \frac{1}{4} }[/tex]

Step-by-step explanation:

[tex](2m + 5)^2[/tex]

[tex](2m + 5) (2m + 5)[/tex]

Use FOIL method.

[tex]2m(2m + 5)+5(2m + 5)[/tex]

[tex]4m^2 + 10m + 10m + 25[/tex]

[tex]4m^2 + 20m + 25[/tex]

[tex](m - \frac{1}{2} )^2[/tex]

[tex](m- \frac{1}{2})(m- \frac{1}{2})[/tex]

Use FOIL method.

[tex]m(m- \frac{1}{2})- \frac{1}{2}(m- \frac{1}{2})[/tex]

[tex]m^2- \frac{1}{2} m- \frac{1}{2}m+ \frac{1}{4}[/tex]

[tex]m^2-m+ \frac{1}{4}[/tex]

Answer:

The amount spent on shower water by Trevor's family in the past month is $86.4

Step-by-step explanation:

The given information are;

The number of people in Trevor's family house are 6

The volume of water each person showered with during the month = 72 litres

The water costs = $0.20 per litre

The total volume of water used for shower by the 6 people = 72 × 6 = 432 litres

The amount spent on shower water by Trevor's family in the past month = The total volume of water used for shower × The cost per litre of water

The amount spent on shower water by Trevor's family in the past month = 432 × 0.2 = $86.4.

Answer:

$86.4

Step-by-step explanation:

Answer:

[tex]3x^2+2x+1[/tex]

Step-by-step explanation:

Sum means to add and second power means that the exponent is "2". So, the expression is:

=> [tex]3x^2+2x+1[/tex]

It cannot be simplified further.

Answer:

x = -5.

Step-by-step explanation:

The solutions of the equation is when the two functions intersect. That is at (-5, 5.5), so where x = -5.

Hope this helps!

Answer:

x = -5

Step-by-step explanation:

f(x) = g(x) has more than one solution, because they intersect at two points.

The question asks for one solution of f(x) = g(x).

One point where they intersect is at (-5, 5.5), as shown in the graph.

(x , y)

x = -5, y = 5.5

Answer:

6.09

Step-by-step explanation:

in ADB

[tex]a ^{2} + b^{2} = c ^{2} [/tex]

to get hypotenuse=8.96

this is height of ABC so use tan

[tex] tan(55.8)= 8.96 \x[/tex]

x=6.09

Answer:

D

Step-by-step explanation:

To find x, we first to to find the line between A&B.

Use the pythagoram theorem to do this A^2+B^2=C^2

4.9^2+7.5^2=C^2

80.26=C^2

square root each side

Side AtoB=8.958

We now know the side length of the opposite and adjacent for the angle C. So according to SohCahToa we need to use Tangent.

So Tan(55.8)=(8.958/x)

We you solve for x, the answer is 6.088

Answer:

The percentage by which the booster club fell short is 33% as shown on the chart

Step-by-step explanation:

To represent the given data pictorially, a pie chart is suitable

The circumference of the pie chart will represent the amount to be raised by the booster club and a sector of the circle which is two-thirds of the circumference represents the amount raised

Given that the amount raised = 2/3×Goal = $15,000, we have;

We represent the amount raised as a sector of the circle as follows;

Sector angle = 2/3×360° = 240°

Total sector of goal amount = Entire circle = 360°

Amount club fell short = 360° - 240° = 120°

The goal amount = 3/2 × $15,000

Percentage by which the club fell short = 120/360×100 = 1/3×100 = 33.33%

[tex]-6w-16>44[/tex]

Add both sides by 16

[tex]-6w>60[/tex]

Divide both sides by -6 (Note: Since we're dividing by a negative number, the inequality symbol needs to be reversed)

[tex]w<-\dfrac{60}{6}[/tex]

[tex]w<10[/tex]

This is the solution to the inequality. Let me know if you need any clarifications, thanks!

Answer:

Hamish's earning = $20

Harry's earning = $26

Step-by-step explanation:

Given the following :

Let Harry's earning per hour = x

Let Hamish earning per hour = y

Harry earns a dollar more than more than 5/4 the amount hamish earns per hour;

Therefore,

x = 5/4y + 1

x - 5/4y = 1 - - - - (1)

the amount Harry earns per hour is $2 less than 7/5 the amount Hamish earns per hour

x = 7/5y - 2 - - - - (2)

Substituting (2) into (1)

7/5y - 2 - 5/4y = 1

7/5y - 5/4y = 1 + 2

7/5y - 5/4y = 3

Taking the L. C. M

(28y - 25y) / 20 = 3

28y - 25y = 60

3y = 60

y = 20

Substitute y = 20 into (1)

x - 5/4(20) = 1

x - 100/4 = 1

x - 25 = 1

x = 1 + 25

x = 26

y = Hamish's earning = $20

x = Harry's earning = $26

Answer:

A) a=25

B) b=14

Step-by-step explanation:

A) a/5+3=8

First you need to subtract 3 from both sides.

(a/5+3)-3=(8)-3

Then simplify

a/5=5

Multiply both sides by 5

(a/5)*5=(5)*5

Then simplify

a= 25

B )3b/7-1=5

First you need to add 1 to both sides

(3b/7-1)+1=(5)+1

Simplify

3b/7=6

Multiply both sides by 7

(3b/7)*7=(6)*7

Simplify

3b=42

Divide both sides by 3

(3b)/3=(42/3)/3

Simplify

b= 14

(Brainliest???) :P

Answer:

15%

Step-by-step explanation:

Question:

The price of a jacket was slashed from Rs.960 to Rs.816.Then the rate of discount offered is​

Solution

Original price= Rs.960

Discount price= Rs.816

Difference in price=Original price - discount price

=Rs. 960 - Rs. 816

=Rs. 144

Percentage discount= Difference in price / Original price × 100

=Rs. 144 / Rs. 960 × 100

=0.15 × 100

=15%

The percentage discount =15% NOT 10% as you have written

Answer: -2

Step-by-step explanation:

When x = 1, y = -2.

Hope it helps <3

Answer:

Step-by-step explanation:

28800 = 2 * 2 * 2 * 2 * 2 * 3 * 3 * 10 * 10

You need one 2

You need one 3

You need one 10

28800 * 2 * 3 * 10 = 2 * 2 * 2 * 2 * 2 * 2 * 3 * 3 * 3 * 10 * 10 * 10

(2*6 * 3* 3^3 * 10^3) ^(1/3)

2*2 * 3 * 10 is the cube root

120

Answer:

The area of △ABC is equal to the area of △DEF

Step-by-step explanation:

On a coordinate plane, triangles A B C and D E F are shown. Triangle A B C has points (4, 2), (7, 2), (4, 6). Triangle D E F has points (negative 2, negative 1), (4, negative 3), and (4, negative 1).

How do the areas of triangle ABC and DEF compare? The area of △ABC is 1 square unit less than the area of △DEF. The area of △ABC is equal to the area of △DEF. The area of △ABC is 1 square unit greater than the area of △DEF. The area of △ABC is 2 square units greater than the area of △DEF.

Answer: The length of the sides of the triangle ABC are given below:

[tex]AB=\sqrt{(7-4)^2+(2-2)^2} =3\ unit\\\\BC=\sqrt{(4-7)^2+(6-2)^2} =5\ unit\\\\AC=\sqrt{(4-4)^2+(6-2)^2} =4\ unit[/tex]

The area of triangle ABC is given as:

Area = 1/2 × base × height = 1/2 × 3 × 4 = 6 unit²

The length of the sides of the triangle DEF are given below:

[tex]DE=\sqrt{(4-(-2))^2+(-3-(-1))^2} =\sqrt{40} \ unit\\\\EF=\sqrt{(4-2)^2+(-1-(-3))^2} =2 \ unit\\\\DF=\sqrt{(4-(-2))^2+(-1-(-1))^2} =6 \ unit[/tex]

The area of triangle DEF is given as:

Area = 1/2 × base × height = 1/2 × 2 × 6 = 6 unit²

The area of triangle ABC is equal to 6 unit² and the area of triangle DEF is equal to 6 unit² , therefore The area of △ABC is equal to the area of △DEF

Answer:

b

Step-by-step explanation:

edge exam

Answer:

Below

Step-by-step explanation:

Coterminal angles are angles with same terminal angles

Mathematically speaking these angles should have the same coordinates in a trigonomitrical circle

●●●●●●●●●●●●●●●●●●●●●●●●

Angles like 0° and 360° are coterminal since to we made a spin from 0° to 360°

For two angles A and B to be coterminal they should verify this relation :

A = B + k*360° with k an integer

So A-B = k*360°

●●●●●●●●●●●●●●●●●●●●●●●●

7) :

35° and 395°

395° -35° = 360°

360° is a multiple of 360° so these angles are coterminal

8) :

140° and 860°

860° - 140° = 720°

720° is a multiple of 360°

720 = 360° × 2

9) :

350° and -710°

350 -(-710) = 350+ 710 = 1060°

1060° isn't a multiple of 360°

So these angles aren't coterminal

10) :

130° and -230°

130 -(-230) = 130+230 = 360°

So these angles are coterminal

11) :

30° and -690°

30 -(-690) = 30+ 690 = 720°

720 is a multiple of 360 so these angles are coterminal

12) :

210° and 10°

210-10 = 200

200 isn't a multiple of 360 so these angles aren't coterminal

Answer:

[tex]p=- \frac{15}{2}[/tex]

[tex]p=2[/tex]

Step-by-step explanation:

[tex]2p^2+11p=30[/tex]

Subtract 30 on both sides.

[tex]2p^2+11p-30=30-30[/tex]

[tex]2p^2+11p-30=0[/tex]

Factor left side of the equation.

[tex](2p + 15)(p-2)=0[/tex]

Set factors equal to 0.

[tex]2p+15=0[/tex]

[tex]2p=-15[/tex]

[tex]p=\frac{-15}{2}[/tex]

[tex]p-2=0[/tex]

[tex]p=2[/tex]

Answer: The least possible value of k is -6.

Step-by-step explanation:

Let 'k' be the negative even integer that is greater than -7.86 .

On number line, -7.86 lies between -7 and -8 such that

-7 > -7.86 > -8

So, -7 is the least integer that is greater than -7.86.

Since, -6 > -7 . That means -6 is the least negative even integer that is greater than -7.86 .

Hence, the least possible value of k is -6.

Answer:

0.9168

Step-by-step explanation:

From the data given:

Mean = 110

standard deviation = 5

Let consider a random sample n =49 which have a mean between 109 and 112.

The test statistics can be computed as:

[tex]Z_1 = \dfrac{x- \bar x}{\dfrac{\sigma}{\sqrt{n}}}[/tex]

[tex]Z_1 = \dfrac{109- 110}{\dfrac{5}{\sqrt{49}}}[/tex]

[tex]Z_1= \dfrac{-1}{\dfrac{5}{7}}[/tex]

[tex]Z_1[/tex]  = -1.4

[tex]Z_2= \dfrac{x- \bar x}{\dfrac{\sigma}{\sqrt{n}}}[/tex]

[tex]Z_2 = \dfrac{112- 110}{\dfrac{5}{\sqrt{49}}}[/tex]

[tex]Z_2 = \dfrac{2}{\dfrac{5}{7}}[/tex]

[tex]Z_2 =2.8[/tex]

Thus; P(109  <  [tex]\overline x[/tex]  <  112) = P( - 1.4 < Z < 2.8)

= P(Z < 2.8) - P( Z < -1.4)

= 0.9974 - 0.0806

= 0.9168

Answer:

C.  6√5

Step-by-step explanation:

√20 +√80= √4*5 + √16*5 = 2√5 + 4√5 = 6√5

Answer:

(6x + 1)^2.

Step-by-step explanation:

1 + 12x + 36x^2

= 36x^2 + 12x + 1

= (6x + 1)(6x + 1)

= (6x + 1)^2.

Hope this helps!

Answer:

[tex](6x+1)^2[/tex]

Step-by-step explanation:

Answer:

second option

Step-by-step explanation:

Answer:

the surface area is 124

the volume is 72

Step-by-step explanation:

Hi there! :)

Answer:

SA = 124 cm².

V = 72 cm³

Step-by-step explanation:

Volume of a rectangular prism: V = l × w × h

Given:

l = 4 cm

w = 9 cm

h = 2 cm

V = 4 × 9 × 2

V = 36 × 2

V = 72 cm³

Surface area: SA = 2(wl + hl + hw)

SA = 2((4 · 9) + (2 · 4) + (9 · 2))

SA = 2(36 + 8 + 18)

SA = 2(62)

SA = 124 cm².

Hope this helped you!

(-x^2+2x+3) + (-x^2-2x-1) = -2x^2 + 2

============================================

Explanation:

We have two large red tiles labeled with -x^2 on them. They add to -2x^2 which is found in every answer choice listed. This means that we must have a plus sign between the two parenthesis groups. If we had a subtraction sign, then -x^2 minus -x^2 would turn into 0x^2 or just 0, and the x^2 terms would go away entirely.

Because we must have a plus sign between the parenthesis, this means the answer is between C and D.

Now focus on the x terms. The slash marks mean that all of the x terms pair up and add to 0. They go away as there aren't any x terms that haven't been slashed. That explains why there are no x terms on the right hand side of any of the answer choices.

The question is: which of C or D has the x terms add to 0x? The answer would be choice D since 2x + (-2x) = 2x-2x = 0x. Choice C has 2x+2x = 4x which is what we don't want.

Lastly, choice D is further proven correct by noticing that the constants 3 and -1 add to 3+(-1) = 3-1 = 2. We have two small blue squares that add to 2 after the cancellations have happened.

Answer:

Option C: 38 is p more than 25

Step-by-step explanation:

the equation 25 + p = 38

can be read as 38 is 25 plus p units, or similarly ;

38 is p units more than 25.

Therefore from the three sentences you are showing, only the last one (option C) is the correct one.

Answer:

$14,580

Step-by-step explanation:

To start off, 10% of 20,000-one easy way to do this is to multiply 20,000 by 0.1, which is 10% in decimal form

-In doing that, you get 2,000

-Now the question says that the value is depreciated which means it goes down in value, so subtract 2,000 from 20,000 to 18,000

-the value of the car after one year is now $18,000

Now, let's move to the second year.  This time find 10% of 18,000

-multiply 18,000 by 0.1 to get 1,800

-since the value is depreciating, or becoming less, we will subtract 1,800 from 18,000 to get 16,200

-the value of the car after two years is now $16,200

Finally, let's look at the value of the car after three years.  Only this time, we will now find 10% of 16,200

-multiply 16,200 by 0.1 to get 1,620

-since value is being depreciated, or lessened, we will once again be subtracting.  Subtract 1,620 from 16,200 to get 14,580

Therefore, the value of the car after three years is now $14,580.

Answer:

SAA or AAS

Step-by-step explanation:

∠BAC = ∠BCA   Given

∠BDA = 90° and ∠BDC = 90°   Given

∠BDA = ∠BDC All 90° angles are congruent

BD = DB Reflexive property

ΔADB = ΔCDB   SAA

Answer:

V = 15 pi m^3

Step-by-step explanation:

The volume of a cone is

V = 1/3 pi r^2 h

The radius is 3 and the height is 5

V = 1/3 pi ( 3)^2 *5

V = 15 pi m^3

Answer:

15 pi m3

Step-by-step explanation: