Mrs. Rodriquez has 24 students in her class. Ten of the students are boys. Jeff claims that the ratio of boys to girls in this class must be 5:12. What is Jeff’s error and how can he correct it?

Answer:

u^2 +7u -8=0  where u = 3x+2

Step-by-step explanation:

(3x+2)^2 + 7(3x+2) - 8=0

Let 3x+2 = u

u^2 +7u -8=0

Answer:

{2, 4}.

Step-by-step explanation:

A = {1, 2, 3, 4, 5} and B = {2, 4}.

A ∩ B?

This means intersection or what is in common

A ∩ B =  {2, 4}.

Step-by-step explanation:

Overtime rate= r+50%= 1.5r

Regular hours= 800/r

Overtime hours= 240/1.5r

Total hours worked

Answer:

First year's interest is already given.

There are 5 more payments of interest

= 5 * 0.07 * 950 = 332.5

so amount in the account after 6 years = 950 + 332.5 = 1282.5

Answer:

The answer is 1282.50

Step-by-step explanation:

Answer:

80 = x

Step-by-step explanation:

The base angles are the same if the side lengths are the same

The unmarked angle is 50 degrees

The sum of the angles is a triangle is 180 degrees

180= 50+50+x

180 = 100 +x

180 -100 = 100+x-100

80 = x

Answer:

80°

Step-by-step explanation:

In an isosceles triangle, if the two sides are the same length, then the two angles formed on the base line are equal.

The other angle on the base line is also equal to 50°.

Angles in a triangle add up to 180°.

x° + 50° + 50° = 180°

x° + 100° = 180°

x° = 180° - 100°

x° = 80°

Answer:

1

Step-by-step explanation:

The slope is given by

m = (y2-y1)/(x2-x1)

   = (1 - -1)/(0- -2)

   = (1+1)/(0+2)

   2/2

   =1

Answer:

1

Step-by-step explanation:

by using rise over run

Step-by-step explanation:

29-12 is a 17 difference

52-29 is a 23 difference (adding 6 to the number 17)

81-52 is a 29 difference (adding 6 to the number 23)

116-81 is a 35 difference (adding 6 to the number 29)

Answer:

29-12 is a 17 difference

52-29 is a 23 difference (adding 6 to the number 17)

81-52 is a 29 difference (adding 6 to the number 23)

116-81 is a 35 difference (adding 6 to the number 29)

Step-by-step explanation:

Answer:

Option C

Step-by-step explanation:

Consider the function f ( x ) = 3x^2 + 4;

[tex]f ( x ) = 3x^2 + 4,\\\\4 = vertex ( y - intercept ),\\\\\\[/tex]

Now if this graph were to be translated 7 units down, considering the function was f ( x ) = 3x^2, the new graph would be f ( x ) = 3x^2 - 7. The same concept is applied to the graph f ( x ) = 3x^2 + 4;

[tex]4 - 7 = - 3,\\f ( x ) = 3x^2 - 3\\\\Solution - Option C[/tex]

* Note that a translation doesn't effect the rate with which the graph changes, it only effect's it's position on the coordinate plane

Hope that helps!

Answer:

its y = |x| + 2

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

just change the x into -6

-(-6)-2 = 6 - 2 = 4

Answer:

f(x)=-x-2

f(-6)=-(-6)-2

f(-6)=4

Step-by-step explanation:

Answer:

11 is the answer

Step-by-step explanation: i hope so cuz my calculations gives this answer

Make two shapes out of it.

The bottom is a rectangle 14 x 5 = 70 square cm

The top is a triangle 1/2 x 12 x 5 = 30 square cm

Total area = 70 + 30 = 100 square cm

Answer:

100 cm²

Step-by-step explanation:

The composite shape can be cut into two shapes. One triangle and one rectangle. The sum of their areas is the area of the whole composite shape.

The area of the triangle:

b × h × 1/2

(14 - 2) × 5 × 1/2

60 × 1/2

= 30 cm²

The area of the rectangle:

l × w

14 × 5

= 70 cm²

Add the areas of the two shapes.

30 cm² + 70 cm²

= 100 cm²

The area of the composite shape is 100 cm².

Answer:

The circumference formula is 2πr and we know r = 1 so the answer is 2π.

Answer: 6.28 feet

Step-by-step explanation:

The formula for circumference is C= πd Diameter is radius times two. So use a value of π which is usually 3.14 or 3.1416 for practical purposes. Multiply by the diameter. 3.14×2=6.28.

Answer:

4 units

Step-by-step explanation:

Since the y value is the same, we only have to look at the x value

-1 - -5

-1 +5

4

The distance is 4 units

Answer:

4 units

Step-by-step explanation:

if you graph these 2 points, they'll be on the same line of the graph separated by 4 units

Answer:

A right triangle is shown. The length of the hypotenuse is 16, the base is 13.9, and the other side is 8. The top angle is 60 degrees and the bottom right angle is 30 degrees.

Step-by-step explanation:

The measures of the angles of in a triangle should correspond to the length size of the side opposite each angle in a triangle.

In simple terms, this means that the larger the measure of an angle, the longer the length of the side opposite that angle. Therefore, the smallest measure of an the 3 angles in the triangle should correspond with the shortest length.

Therefore, the triangle with the correct side length would be "A right triangle is shown. The length of the hypotenuse is 16, the base is 13.9, and the other side is 8. The top angle is 60 degrees and the bottom right angle is 30 degrees." Check the attachment below to see how each side length corresponds with each angle opposite them.

Answer:

D

Step-by-step explanation:

your welcome

Answer:

x= 42

Step-by-step explanation:

(2x +1)°= 85° (vert. opp. ∠s)

2x +1= 85

2x= 85 -1 (bring constant to 1 side)

2x= 84 (simplify)

x= 84 ÷2

x= 42

Answer:

Rectangle.

Step-by-step explanation:

The 2 dimensional section would be a rectangle.

Answer:

rectangle

Step-by-step explanation:

Answer:

2 hours

Step-by-step explanation:

Time= 5 hrs

Ashley's speed= 40 mph

Beth's speed= 60 mph

Beth's time in travel= x

Since they drove the same distance, we have this equation:

Answer:

A. q = 39

Step-by-step explanation:

Since the lines are parallel, their sides will be proportional,

So,

Taking their proportion

=> [tex]\frac{60}{40} = \frac{q}{26}[/tex]

Cross Multiplying

q × 40 = 26 × 60

q = [tex]\frac{1560}{40}[/tex]

q = 39

Answer:

  a) h(t) = -16t^2 +41t +37

  b) see attached (3.270 seconds)

  c) (41+√4049)/32 seconds

  d) 1.28125 seconds; 63.265625 feet

  e) [1.5, 2]: -15; [2, 2.5]: -31; [2.5, 3]: -47

Step-by-step explanation:

a) The formula and initial values are given. Putting those values into the formula, we get ...

  h(t) = -16t^2 +41t +37

__

b) The graph is attached. It shows the t-intercept to be about 3.270 seconds.

__

c) Using the quadratic formula, we can find the landing time as ...

  [tex]t=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}=\dfrac{-41\pm\sqrt{41^2-4(-16)(37)}}{2(-16)}\\\\=\dfrac{41\pm\sqrt{4049}}{32}\qquad\text{only $t>0$ is useful}[/tex]

The exact landing time is (41+√4049)/32 seconds.

__

d) The highest point is at t=-b/(2a) = -41/(2(-16)) = 41/32 seconds.

The value of the function at that point is ...

  h(41/32) = (-16(41/32) +41)(41/32) +37 = 41^2/64 +37 = 4049/64

The maximum height is 4049/64 = 63.265625 feet.

__

e) For a quadratic function, that average rate of change on an interval is the derivative at the midpoint of the interval. Here, the derivative is ...

  h'(t) = -32t +41 . . . in feet per second

Then the average rates of change are ...

  arc[1.5, 2] = h'(1.75) = -32·1.75 +41 = -15 ft/s

  arc[2, 2.5] = h'(2.25) = -32(2.25) +41 = -31 ft/s

  arc[2.5, 3] = h'(2.75) = -32(2.75) +41 = -47 ft/s

These are the average velocity of the water balloon over the given interval(s) in ft/s. Negative indicates downward.

Answer:

(a) h(t) = -16t² + 41t + 37

(b) About 3.3 s

[tex]\large \boxed{\text{(c) }\dfrac{41+ \sqrt{4049}}{32}\text{ s}}[/tex]

(d) -15 ft/s; -31 ft/s; -47 ft/s

Step-by-step explanation:

(a) The function

h(t) = -16t² + v₀t + s₀

 v₀ = 41 ft·s⁻¹

 s₀ = 37 ft

The function is

h(t) = -16t² + 41t + 37

(b) The graph

See Fig. 1.

It looks like the water balloon lands after about 3.3 s.

(c) Time of landing

h = -16t² + 41t + 37

a = -16; b = 41; c = 37

We can use the quadratic formula to solve the equation:

[tex]h = \dfrac{-b\pm\sqrt{b^2 - 4ac}}{2a} = \dfrac{-b\pm\sqrt{D}}{2a}[/tex]

(i) Evaluate the discriminant D

D = b² - 4ac = 41² - 4(-16) × 37 = 1681 + 2368  = 4049

(ii) Solve for t

[tex]\begin{array}{rcl}h& = & \dfrac{-b\pm\sqrt{D}}{2a}\\\\ & = & \dfrac{-41\pm\sqrt{4049}}{2(-16)}\\\\ & = & \dfrac{41\pm\sqrt{4049}}{32}\\\\t = \dfrac{41- \sqrt{4049}}{32}&\qquad& t = \dfrac{41+ \sqrt{4049}}{32}\\\\\end{array}\\[/tex]

[tex]\text{The water balloon will land after $\large \boxed{\mathbf{\dfrac{41+ \sqrt{4049}}{32}}\textbf{ s}} $}[/tex]

(d) Time and maximum height

(i) Time

The axis of symmetry (time of maximum height) is at t = -b/(2a)

[tex]t = \dfrac{-41}{2(-16)} = \dfrac{41}{32} = \textbf{1.281 s}[/tex]

(ii) Maximum height

The vertex is at y = h(1.281) = h(t) = -16(1.281)² + 41(1.281) + 37  = 63.27 ft

(e) Average rate of change

(i) Arc{1.5,2}

h(1.5) = 62.5

  h(2) = 55

m = (h₂ - h₁)/(t₂ - t₁) = (55 - 62.5)/(2 - 1.5) = -7.5/0.5 = -15 ft/s

The water balloon has started to fall after it has reached peak height, so it is not going very fast

(ii) Arc{2,2.5}

h(2.5) =39.5

m = (39.5 - 55)/(2 - 1.5) = -15.5/0.5 = -31 ft/s

The balloon is in mid-fall, so gravity has caused it to speed up.

(iii) Arc{2.5,3}

h(3) = 16

m = (16 - 39.5)/(2 - 1.5) = -23.5/0.5 = -47 ft/s

The balloon is about to hit the ground, so it is falling at almost its maximum velocity.

Fig. 2 shows the height of the balloon at the above times.

Answer:

a = -3

Step-by-step explanation:

5^a = 1/125

The fraction 1/125 can be written as a power with base 5.

5^a = 5^(-3)

Cancel the same bases on both sides.

a = -3

Answer:

a = -3.

Step-by-step explanation:

5^a = 1/125

1/125 = 1 / 5^3

= 5^-3

5^a = 5^-3

so a = -3.

Answer:Land area: 302.6 mi²

Population: 8.399 million

Step-by-step explanation:

New York City can be described as very big and it has actually been ranked as the 24th biggest city in the United States in terms of land area it ...

Answer:

Land area: 783.8 km²

Population: 8.399 million

Step-by-step explanation:

Answer:

y=84

first : 84+13=97

second : 84+15=99

third : 84+23=107

fourth: 84+29=113

fifth : 84+40 =124

97+99+107+113+124 = 540

Step-by-step explanation:

sum of interior angles of a pentagon=540 degreas

y+13+y+15+y+23+y+29+y+40=540

5y=540-(13+15+23+29+40)

y=84

first : 84+13=97

second : 84+15=99

third : 84+23=107

fourth: 84+29=113

fifth : 84+40 =124

97+99+107+113+124 = 540

Answer:

C

Step-by-step explanation:

Got 100% on edge.

Answer:

I found that the answer is (5,1)

Step-by-step explanation:

4 times x(5) is 20

3 times y(1) is 3

20 + 3 = 23

bottom equation:

x(5) -- 5y(1) = 0

Answer:

the coordinates of y are (1,-4)

Step-by-step explanation:

by using midpoint formula

z(x,y)=([tex]\frac{x1+x2}{2}[/tex],[tex]\frac{y1+y2}{2}[/tex])

putting the values of coordinates

(3,-1)=[tex]\frac{5+a}{2}[/tex],[tex]\frac{2+b}{2}[/tex]

separating the coordinates

3=[tex]\frac{5+a}{2}[/tex]                and           -1=[tex]\frac{2+b}{2}[/tex]

3×2=5+a                and      -1×2=2+b

6=5+a                  and        -2=2+b

6-5=a                    and          -2-2=b

1=a                            and            -4=b

so the actual coordinates of y are (1,-4)

i hope it will help you

Answer:

D

Step-by-step explanation:

5.50. 5.50+0.25= 5.75, 5.75+0.25= 6.00, 6.00+0.25= 6.25, 6.25+0.25= 6.50

Option D is the answer:

5.50, 5.75, 6.00, 6.25, 6.50...

Answer:

V = 11/21

Step-by-step explanation:

Formula: V = 4/3πr³

Simply plug in r to find volume

V = 4/3π(1/2)³

V = 0.52381

And we have our answer!

Answer:

-2 ≤x≤5

Step-by-step explanation:

The domain is the inputs

The lowest value of x is -2 and every value of x is valid up to 5

-2 ≤x≤5