One number is five more than another and their sum Is there less than three times the smaller find the numbers

Question: if a parabola never touches the x axis, then it doesn't have any real roots or solutions

Answer: True

A real solution only occurs if the graph touches or crosses  the x axis, as the x intercept (or root) is a visual indication of a real number solution. In this case, we have 2 complex solutions for the parabola

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Question: What number is equivalent to sqrt(-49) ?

Answer: choice A) 7i

Simplify as follows

sqrt(-49) = sqrt(-1*7^2)

sqrt(-49) = sqrt(-1)*sqrt(7^2)

sqrt(-49) = i*7

sqrt(-49) = 7i

note: be careful not to toss in -7i as one of the answers, because it's not. The square root of a number is exactly one output. For instance, if you take the square root of 25, the result is 5 (not plus or minus 5).

Answer:

The correct answer option is: [tex]S_9=\frac{9}{2} (2+26)[/tex]

Step-by-step explanation:

We know that,

the sum of the first [tex]n[/tex] terms of an Arithmetic Sequence is given by:

[tex]S_9=\frac{n(a_1+a_n)}{2}[/tex]

where [tex]n[/tex] is the number of terms,

[tex]a_1[/tex] is the first term of the sequence; and

[tex]a_n[/tex] is the first term of the sequence.

So for [tex]a_n=3n-1[/tex],

[tex]a_1=3(1)-1=2[/tex]

and

[tex]a_9=3(9)-1=26[/tex]

Putting these values in the formula to get:

[tex]S_9=\frac{9(a_1+a_9)}{2}[/tex]

[tex]S_9=\frac{9(2+26)}{2} \\\\S_9=\frac{9}{2} (2+26)[/tex]

First five terms:

[tex]a_1=3(1)-1=2[/tex]

[tex]S_1=\frac{1(2+2)}{2}[/tex]=2

[tex]a_2=3(2)-1=5[/tex]

[tex]S_2=\frac{2(2+5)}{2}[/tex]=7

[tex]a_3=3(3)-1=8[/tex]

[tex]S_2=\frac{3(2+8)}{2}[/tex]=15

[tex]a_4=3(4)-1=11[/tex]

[tex]S_4=\frac{4(2+11)}{2}[/tex]=26

[tex]a_5=3(5)-1=14[/tex]

[tex]S_5=\frac{5(2+14)}{2}[/tex]=40

Answer: the corrrect one is A s9=9/2(2+26)

[tex]7x+10=\dfrac{1}{3}(12x-3)+14x\qquad\text{use distributive property}\\\\7x+10=\dfrac{1}{3}\cdot12x-\dfrac{1}{3}\cdot3+14x\\\\7x+10=4x-1+14x\\\\7x+10=18x-1\qquad\text{substitute 10 from both sides}\\\\7x=18x-11\qquad\text{subtract 18x from both sides}\\\\-11x=-11\qquad\text{divide both sides by (-11)}\\\\\boxed{x=1}[/tex]

Answer:

I believe the correct awnser is x=1 I took the test

[tex]7x+10=13(12x-3)+14x\qquad\text{use distributive property}\\\\7x+10=(13)(12x)+(13)(-3)+14x\\\\7x+10=156x-39+14x\\\\7x+10=170x-39\qquad\text{subtract 10 from both sides}\\\\7x=170x-49\qquad\text{subtract 170x from both sides}\\\\-163x=-49\qquad\text{divide both sides by (-163)}\\\\\boxed{x=\dfrac{49}{163}}[/tex]

Answer:

[tex]A.\ a_n=n^2+1[/tex]

Step-by-step explanation:

[tex]Check:[/tex]

[tex]a_n=n^2+1\\\\a_1=1^2+1=1+1=2\qquad CORRECT\\\\a_2=2^2+1=4+1=5\qquad CORRECT\\\\a_3=3^2+1=9+1=10\qquad CORRECT\\\\a_4=4^2+1=16+1=17\qquad CORRECT\\\\a_5=5^2+1=25+1=26\qquad CORRECT[/tex]

Used PEMDAS:

P Parentheses first

E Exponents (ie Powers and Square Roots, etc.)

MD Multiplication and Division (left-to-right)

AS Addition and Subtraction (left-to-right)

First Power, next Addition

Answer: A.

Step-by-step explanation:

2, 5, 10, 17, 26

First, check the difference between each term:

2 → 5 = +3

5 → 10 = +5

10 → 17 = +7

17 → 26 = +9

Since the difference (d) is not the same, this is not an arithmetic sequence.

Now, check the second tier {3, 5, 7, 9}

3 → 5 = 2

5 → 7 = 2

7 → 9 = 2

The difference (d) of the second tier is the same, so it is an exponential sequence.

--> the only option that is an exponential sequence is option A.

Answer:

200

Step-by-step explanation:

150/3=50 so she sorts 50 items per minute, then 50*4=200

Answer:

Number of recyclable items sort in 4 minutes by Faye = 200

Step-by-step explanation:

Given that Faye can sort 150 recyclable items in 3 minutes.

   Number of recyclable items sort in 3 minutes = 150

   [tex]\texttt{ Number of recyclable items sort in 1 minute =}\frac{150}{3}=50[/tex]

Number of recyclable items sort in 4 minutes = 4 x Number of recyclable items sort in 1 minute

Number of recyclable items sort in 4 minutes = 4 x 50 = 200

Number of recyclable items sort in 4 minutes by Faye = 200

Answer:

239 ft³

Step-by-step explanation:

Multiply the squared radius by π:

2*2*3.14=12.56 ft².

Multiplying the height:

12.56*19≅239 ft³.

Answers: -4, 5

Step-by-step explanation:

[tex]e^{x^{2}}=e^{x}*e^{20}[/tex]

[tex]e^{x^{2}}=e^{x+20}[/tex]

x² = x + 20

x² - x - 20 = 0

(x + 4)(x - 5) = 0

x + 4 = 0      x - 5 = 0

 x = -4            x = 5

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Answers:

Step-by-step explanation:

domain: there are no restrictions on the x-value so x = All Real Numbers

range: since the new graph has a reflection then y < 0

y-intercept is when x = 0:

horizontal asymptote: y ≠ 0 so the H.A. is y = 0

graph:  The parent graph is: y = 2ˣ

The new graph of y = -2ˣ⁻³ has the following transformations:

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graph: see attachment

(0, 0) and (-1/3, 1)

(-1, ∞)

x = -1

The height of Cone Mountain, given the trail length and the radius, would be C. 2,520 feet

How to find the height ?

To find the height of Cone Mountain, we can use the properties of a right circular cone. The key relationship we'll use is the Pythagorean theorem :

[tex]l^2 = r^2 + h^2[/tex]

The slant height (l) is the length of the trail, which is 3,150 feet.

The radius (r) is 1,890 feet.

Pythagorean theorem:

[tex](3,150)^2 = (1,890)^2 + h^29,922,500 = 3,572,100 + h^2[/tex]

Make h the subject:

[tex]h^2 = 9,922,500 - 3,572,100\\h^2 = 6,350,400[/tex]

Take the square root of both sides to find h:

h = √(6,350,400)

h = 2,520 feet

Answer:

total earning is  $64.80

Step-by-step explanation:

Price of one work = $18.00

Payment  by owner = 1/4 of $18.00

                                 = 18/4

                                  = $4.50

Earning by tip =  20% of $18.00 =  20/100 x18 = 3.60

Total earning from one work   =   $4.50+$3.60

                                                = $ 8.10

Earning from 8 tips =  8x8.10

                                = $64.80

First question:

By definition of sine and cosine, we have

[tex]\sin30^\circ=\dfrac h{\sqrt5}\implies h=\dfrac{\sqrt5}2[/tex]

[tex]\cos30^\circ=\dfrac g{\sqrt5}\implies g=\dfrac{\sqrt{15}}2[/tex]

Second question:

By definition of tangent, we have

[tex]\tan60^\circ=\dfrac{5\sqrt2}x\implies x=\dfrac{5\sqrt2}{\sqrt3}=\dfrac{5\sqrt6}3[/tex]

Then by Pythagoras' theorem,

[tex](5\sqrt2)^2+x^2=y^2\implies y=\sqrt{(5\sqrt2)^2+\left(\dfrac{5\sqrt6}3\right)^2}=\sqrt{50+\dfrac{50}3}=\sqrt{\dfrac{200}3}=\dfrac{10\sqrt6}3[/tex]

Let the Distance traveled by the tourist by walking be : D miles

Given : Tourist walks at a rate of 4 Miles per Hour

[tex]\mathsf{\implies Tourist\;travels\;D\;Miles\;in : \frac{D}{4}\;Hours}[/tex]

Given : The Total Distance of Mountain Path = 31 Miles

Distance traveled by the tourist by hiring a Taxi is : (31 - D) Miles

Given : The Taxi travels at a constant speed of 50 miles per hour

[tex]\mathsf{\implies Tourist\;travels\;(31 - D)\;Miles\;in : (\frac{31 - D}{50})\;Hours}[/tex]

Given : The Tourist reaches the destination 2 Hours after he started

Time taken by Walking + Time Taken by travelling in Taxi = 2 Hours

[tex]\mathsf{\implies \frac{D}{4} + \frac{31 - D}{50} = 2}[/tex]

[tex]\mathsf{\implies \frac{D}{2} + \frac{31 - D}{25} = 4}[/tex]

[tex]\mathsf{\implies (\frac{25D + 2(31 - D)}{50}) = 4}[/tex]

[tex]\mathsf{\implies (\frac{25D + 62 - 2D}{50}) = 4}[/tex]

[tex]\mathsf{\implies ({23D + 62}) = 200}[/tex]

[tex]\mathsf{\implies 23D = 200 - 62}[/tex]

[tex]\mathsf{\implies 23D = 138}[/tex]

[tex]\mathsf{\implies D = 6}[/tex]

⇒ Distance traveled by the tourist by walking = 6 Miles

⇒ Distance traveled by the tourist by hiring a taxi = (31 - 6) = 25 Miles

⇒ The Distance for which tourist has to pay for cab driver is 25 Miles

The distance traveled by taxi = 25 miles

Linear motion consists of 2: constant velocity motion with constant velocity and uniformly accelerated motion with constant acceleration

• At constant velocity motion:

the speed of vo = v = constant

acceleration = a = 0

An equation of constant velocity motion

[tex]\large {\boxed {\bold {x = v \times \: t}}}[/tex]

x = distance = m

v = speed = m / s

t = time = seconds

x1, x2 = distance traveled

t1, t2 = travel time

1 = tourist, 2 = taxi

[tex]\rm x1=v1.t1=4t1\\\\x2=v2.t2=50.t2\\\\t1+t2=2~hours\\\\t1=2-t2[/tex]

Total distance = x1 + x2

[tex]\rm 31~miles=4t1+50t2\\\\31=4(2-t2)+50t2\\\\31=8-4t2+50t2\\\\23=46t2\\\\t2=0.5[/tex]

then:

[tex]\rm x2=v2.t2\\\\x2=50\times 0.5\\\\x2=\boxed{\bold{25~miles}}[/tex]

The distance of the elevator

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resultant velocity

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the average velocity

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[tex]\heartsuit[/tex]  If x = 4 is the Only Solution of the Equation x² + bx + 16 = 0

[tex]\heartsuit[/tex]  Then the Value x = 4 should satisfy the Given Equation

⇒ (4)² + b(4) + 16 = 0

⇒ 16 + 4b + 16 = 0

⇒ 4b + 32 = 0

⇒ 4b = -32

⇒ b = -8

Answer:

b^2-4ac >0  the roots are real

Step-by-step explanation:

b^2-4ac >0  the roots are real

b^2-4ac = 0 there is 1 root

b^2 -4ac <0 the root are complex

Answer: Cancellation method

Step-by-step explanation:

You divide the denominator by  the denominator number to cancel the fraction out.

The Cancellation method is used to simplify a fraction to its lowest form. It is done by finding the Greatest Common Divisor (GCD) of the numerator and the denominator and dividing both by this number.

The method used to reduce a fraction to its lowest form is the Cancellation method. This method involves finding the greatest common divisor (GCD) of the numerator and the denominator of the fraction. Once the GCD is found, divide both the numerator and the denominator by this number. This will reduce the fraction to its simplest or lowest form. For example, if we have the fraction 6/8, the GCD of 6 and 8 is 2. Dividing both 6 and 8 by 2, we retrieve the reduced fraction which is 3/4.

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Answer: [tex]\bold{[\dfrac{\pi}{4},\dfrac{5\pi}{4}]}[/tex]

Step-by-step explanation:

Step 1: Create a table

x    |   5sinx + 5cosx = y

0    |       0    +     5     =   5

[tex]\frac{\pi}{2}[/tex]   |        5    +     0    =   5

π    |        0    +    -5    =  -5

[tex]\frac{3\pi}{2}[/tex]    |       -5    +     0    =  -5

2π |        0    +      5    =   5

Notice that y = 5 at 0 and [tex]\frac{\pi}{2}[/tex] , so there will be a vertex at their midpoint.  Similarly at y = -5.

Midpoint of 0 and [tex]\frac{\pi}{2}[/tex]  is [tex]\dfrac{\pi}{4}[/tex] . Midpoint of π and [tex]\frac{3\pi}{2}[/tex] is [tex]\dfrac{5\pi}{4}[/tex]

(graph is attached to confirm interval)

The least common multiple of 7 and 3 is 21, so both the football and volleyball teams will have games on the same day again in 21 days.

The question requires us to determine when the football and volleyball teams will have games on the same day again. Since the football team plays every 7 days and the volleyball team plays every 3 days, we are looking for the least common multiple (LCM) of 7 and 3, which represents the number of days until both teams will have games on the same day again.

To find the LCM of 7 and 3, we can list the multiples of each number until we find a common multiple:

Multiples of 7: 7, 14, 21, 28, ...

Multiples of 3: 3, 6, 9, 12, 15, 18, 21, ...

The first common multiple we encounter is 21. Therefore, both teams will have games on the same day again in 21 days.

Answer:

Correct choices are A and D.

Step-by-step explanation:

According to the table for the given function [tex]h(x),[/tex] you can write the same table for the inverse function [tex]h^{-1}(x).[/tex] With this aim change [tex]x[/tex] into [tex]h^{-1}(x)[/tex] and [tex]h(x)[/tex] into x:

[tex]\begin{array}{ccccccc}x&2&5&8&11&14&17\\h^{-1}(x)&0&1&2&3&4&5\end{array}[/tex]

Then you can see that points (5,1) and (2,0) are on the graph of the inverse function.

Answer: 1/4

Step-by-step explanation:

Take any two point on the line: my starting point is -4,0 and I will be moving to 0,1.

Remember that slope = rise/run, so count up one and go to the right 4 to get to 0,1, so it would be 1/4.

Hopefully that explains it!

We can use the points (4, 0) and (0, 1) to solve.

Slope formula: y2-y1/x2-x1

= 1-0/0-4

= 1/4

Best of Luck!

Answer:

d. 40

Step-by-step explanation:

x/4 - 7=3

Add 7 to both sides

x/4 - 7+7=3+7

x/4 = 10

Multiply by 4 on each side

x/4*4 = 10*4

x = 40

Answer:The Answer of this probelm is D 40.

Step-by-step explanation:

x/4 - 7=3

First you need to add 7 to both sides

x/4 - 7+7=3+7

x/4 = 10

second you need to multiply by 4 on each side

x/4*4 = 10*4

Once you finish this should be your final answer right here x = 40

Hope this helps

[tex]\text{Let}\ k:y=m_1x+b_1\ \text{and}\ l:y=m_2x+b_2.\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\\text{We have the line in point-slope form:}\\\\y-y_1=m(x-x_1)\\\\m-slope\\\\y-2=\dfrac{7}{3}(x+5)\to m_1=\dfrac{7}{3}\\\\\text{therefore}\ m_2=-\dfrac{1}{\frac{7}{3}}=-\dfrac{3}{7}.\\\\\text{We have the slope}\ m=-\dfrac{3}{7}\ \text{and the point}\ (-4,\ 9).\ \text{Substitute:}\\\\y-9=-\dfrac{3}{7}(x-4))\\\\\boxed{y-9=-\dfrac{3}{7}(x+4)}[/tex]

Answer:

A) 1/2QP=UT

D) SU II RP

Step-by-step explanation:

A & D ARE THE ANSWERS

The correct statements are 1/2QP=UT and SU||RP.

In this question, we are given that points S, U, and T are the midpoints of the sides of triangle PQR. We need to determine which statements are correct.

Answer:

The amount owed is greater than the cars worth (apex)

Step-by-step explanation:

Answer:

8 square units

Step-by-step explanation:

Base area= Length* width

Base area= 4* 2

Base area= 8 square units

Answer:

8 square units

Step-by-step explanation:

Base area= Length* width

Base area= 4* 2

Base area= 8 square units

S(r) = 2pi*r*h + 2pi*r^2

S ' (r) = 2pi*h + 2*2*pi*r .... differentiate with respect to r

S ' (r) = 2pi*h + 4pi*r

S ' (3) = 2pi*h + 4pi*3 ... plug in r = 3

S ' (3) = 2pi*h + 12pi

S ' (3) = 2pi*2 + 12pi .... plug in h = 2

S ' (3) = 4pi + 12pi

S ' (3) = 16pi

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Answer: D) 16pi

The instantaneous rate of change of the surface area with respect to the radius, r, when r = 3, is 16π

A cylinder is a three-dimensional shape consisting of two parallel circular bases, joined by a curved surface. The center of the circular bases overlaps each other to form a right cylinder.

Given that, the surface area of a right circular cylinder of height 2 feet and radius r feet is given by S(r) = 2πrh+2πr².

We need to find, the instantaneous rate of change of the surface area with respect to the radius, r, when r = 3.

Taking the differentiation, of the formula given, S(r) = 2πrh+2πr². w.r.t radius r,

d [S(r)] / dr = 2πh + 4πr

= 2π [h + 2r]

Put h = 2, r = 3

= 16π

Hence, the instantaneous rate of change of the surface area with respect to the radius, r, when r = 3, is 16π

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Billy wants tickets huh okay.....

Alright so first off what information do we have?

We know that 4 adult tickets are 15 Euros each

2 child tickets are 10 Euros each

Ok simple calculations here

4*15 = 60

2*10 = 20

Total is 80 Euros charge

10% booking fee

so 10% of 80 is 8 (Add this onto the total bill) = 88

3% of 88 is (well 1% is 0.88 3% is 0.88 * 3 = 2.64)

Total bill now is 90.64 (Might aswell add taxes now poor billy spending a 100)

By the way your answer is 90.64