Select all of the following that are quadratic equations. 5 x - 1 = 3 x + 8 5 x - 3 = 0 x2 - 2 x = 4 x + 1 2 x2+ 12 x = 0 x3 - 6 x2 + 8 = 0 9 x2 + 6 x - 3 = 0

Answer:

1.32%

2.24%

3. 12%

4.35%

5. 6%

6. 30%

7. 65%

8. 200%

9. 125%

10. 300%

Help full?

Answer:

60 miles

Step-by-step explanation:

Let us assume the distance between his home and place of appointment be x and t would be time taken at 40 mph

As we know that

Distance = speed × time

So,

x = 40t ............(1)

As he left the house 15 minutes late and also drove his car at 50 mph and arrive 3 minutes early

So,

15 minutes = 15 ÷ 60 = 0.25 hour

3 minutes = 3 ÷ 60 = 0.05 hour

Now the actual time taken is

= t - 0.25 - 0.05

=  t - 0.30

x = 50(t - 0.30)

x = 50t - 15.............(2)

Now

40t = 50t - 15

10t = 26

t = 3 ÷ 2 hour

Now

x = 40 × 3 ÷ 2

= 60 miles

The 2 : 5 scaled version of the deck Sam plans to build and the dimensions of the original deck indicates;

Part A; Base length of the new deck = 7.2 feet

Height of the new deck = 2.8 feet

Part B; The area of the original deck is 63 square feet

The area of the new deck is 10.08 square feet

Part C; The ratio of the areas is the square of the scale factor

A scale factor is a number or factor that is used to enlarge or reduce the dimensions a shape or size of a figure.

The base length of the triangular deck = 18 feet

The height of the triangular deck = 7 feet

The scale factor for the scaled version Sam intends to build = 2 : 5

Part A; The dimensions of the new deck are;

Base length of the new deck using the the 2 : 5 ratio is; (2/5) × 18 = 7.2 feet

The height of the new deck = (2/5) × 7 = 2.8 feet

Part B; The area of the original deck = (1/2) × 18 × 7 = 63 square feet

Area of the new dec = (1/2) × 7.2 × 2.8 = 10.08 square feet

Part C; The ratio of the areas is; 10.08/63

Ratio of the area = 10.08/63 = 4/25 = 4 : 25

The scale factor is; 2 : 5

Learn more on scale factors here: https://brainly.com/question/28822248

#SPJ1

The inverse function of f(x) can be written as:

f⁻¹(x) = (x + 6)/7

Two functions f(x) and f⁻¹(x) are inverses if for every value of x the compositions are equal to the identity, this means that:

f( f⁻¹(x) ) = x

f⁻¹( f(x)) = x

Here we know that:

f(x) = 7x - 6

Evaluating this in the inverse we will get:

f(f⁻¹(x) )  = 7*f⁻¹(x)  - 6

And that must be equal to x, by definition, then we can solve:

x = 7*f⁻¹(x)  - 6

x + 6 = 7*f⁻¹(x)

(x + 6)/7 = f⁻¹(x)

That is the inverse function.

Learn more about inverse functions at:

https://brainly.com/question/14391067

#SPJ1

Answer:

Step-by-step explanation:

9 tins of cat food feed her 2 cats for 18 days

Step-by-step explanation:

Sally has 2 cats

food eaten by 1 cat each day =

food eaten by 2 cat each day=  tins

sally buys 9 tins of cat food

then

tins  required in = 1 day

1 tin required in

i.e  1 tin required in  2 days

9 tin  required  for = 9×2 = 18 days

hence ,  9 tins of cat food feed her 2 cats for 18 days

#Learn more :

Sue has 2 cats. Each cat eats 1/4 tin of food each day. Sue buys 8 tine of cat food. Has sue got enough cat food to feed her 2 cats for 14 days?

Answer:

A)

Step-by-step explanation:

rise/run

down 5, left 3

The shape of the ABCD is a rhombus. The diagonals are not equal to each other.

What is the 2-dimensional shape?

A 2d shape is a two-dimensional shape with horizontal and vertical axes (x-axis and y-axis). 2D shapes are flat shapes with only length and width. These shapes have no thickness or height.

Given the vertices of ABCD are  A(-3,0), B (1,5), C(-3,10) and D(-7,5).

The formula distance between points (x₁, y₁) and (x₂, y₂) is √[(x₂ - x₁)² + (y₂ - y₁)²].

The distance between A and B is √[(1 - (-3))²+(5 - 0)²] = √(4²+5²) = 6.4

The distance between B and C is √[(-3 - 1)²+(10 - 5)²] = √(4²+5²) = 6.4

The distance between C and D is √[(-7 - (-3))²+(5 - 10)²] = √(4²+5²) = 6.4

The distance between A and D is √[(-7 - (-3))²+(5 - 0)²] = √(4²+5²) = 6.4

The distance between A and C is √[(-3 - (-3))²+(10 - 0)²] = √(10²) = 10

The distance between B and D is √[(-7 - 1)²+(5 - 5)²] = √(8²) = 8

The slope of a line passes through the points (x₁, y₁) and (x₂, y₂) is (y₂ - y₁)/(x₂ - x₁).

The slope of AB is (5-0)/(1-(-3))=5/4

The slope of BC is (10-5)/(-3-1)=-5/4

The slope of CD is (5-10)/(-7-(-3))=5/4

The slope of AD is (5-0)/(-7-(-3))=-5/4

The number of vertices of the quadrilateral is 4.

Thus it is either a square or rectangle or rhombus or parallelogram.

Since the length of all sides is equal thus it is either a square or rhombus.

Since the diagonals are not equal it is a rhombus.

To learn more about quadrilateral, click on the below link:

https://brainly.com/question/29077336

#SPJ1

Answer:

9.4ft²

Step-by-step explanation:

The formula for the area of a rectangle is base*height, or b*h.

Since we know the final area of the room and one of the side lengths, we can plug those into the formula I just stated so that we get

15*h=141

All that's left to do is solve for h, which is the other side that we are solving for. To do this, we will divide 15 on both sides:

15h/15=141/15

The 15s on the left side cancel out, and we simply divide 141 by 15 to get our final answer of 9.4ft².

The equation to show the perimeter of the rectangle is P = 2(2w + 5)

From the question, we have the following parameters that can be used in our computation:

Length = 5 more than the width

Also, we have

Perimeter = 58

This means that

P = 2(w + 5 + w)

P = 2(2w + 5)

In (a), we have

P = 2(2w + 5)

This gives

2(2w + 5) = 58

So, we have

2w + 5 = 29

2w = 24

w = 12

Next, we have

l = 12 + 5

l = 17

Lastly, we have

Area = 17 * 12

Area = 204

Read more about area at

https://brainly.com/question/24487155

#SPJ1

Answer:

KL = 7, so B is the correct answer.

Answer:

you can give 10 cents in 4 different ways

A, percentages

You would see percentages on a circle graph, because it's how many parts of the whole that they take up.

Happy to help, have a great day! :)

Answer:

13.5

Step-by-step explanation:

ngl i asked siri

Answer:  we move (5, 1/3) to (5-3, 1/3*3) = (2, 1)

Step-by-step explanation:

Answer:

Step-by-step explanation:

Red Graph: y = x^2 -4x - 5

Blue Graph: x = 2  Axis of symmetry

Points

x intercepts (-1,0),(5,0)

y intercepts: (0,-5)

vertex: (2,-9)

Note: it is just a matter of putting the function on the graph and than read what you are asked for. Between this part of the answer, and the graphs, you should be able to see what you are asked for.

Answer:

0,70 s

Step-by-step explanation:

We have to solve the associated equation:

-16t^2 + 48t + 64 = 90

1) divide each member by 2

-8t^2 + 24t + 32 = 45

2) add at both member -45

-8t^2 + 24t + 32 -45 = 45-45

-8t^2 + 24t - 13 = 0

3). multiply the two members by -1

8t^2 - 24t + 13 = 0

4) find Δ/4 with the reduce formula

Δ/4 = 144 -104 = 40

5) find the approximate  solutions with the reduce formula

t1 = (12 + 6,42)/8 = 2,29 s

t2 = (12 - 6,42)/8  = 0,70 s

we have to take the smallest value because the biggest describe when the rocket will reach 90 feet when it is descending

The ethical issues about testing with animals is it resulting in suffering and they have the right to live without human interference.

This is defined as a procedure which is carried in order to support or refute a hypothesis.

The blood pressure returning to normal when the drugs were used on the animals is a good assumption as most parts of the animal and human body work similarly.

Read more about Experiment here https://brainly.com/question/17274244

#SPJ1

Answer:

  с  60,800,000

Step-by-step explanation:

Any scientific or graphing calculator can evaluate this expression for you.

__

When adding numbers in scientific notation, they need to have the same multiplier exponent. Here, it is convenient to use 10^6:

  8.0×10^5 = 0.8×10^6

  6.0×10^7 = 60×10^6

Then the sum is ...

  (0.8 +60)×10^6 = 60.8×10^6 = 60,800,000

The statistical analysis is created using the chi-squared test. The significance level used is 5% because of the probability to reject the null hypothesis. The given data indicate that there are significant preferences among the four flavors of ice cream.

When the sample sizes are big, the statistical hypothesis test known as the chi-squared test is utilized in the study of contingency tables. This test is primarily used to determine whether two categorical factors have independent effects on the test statistic. We shall use a significance level of α=0.05 in this case.

First, determine the null and alternative hypotheses.

Null hypothesis H₀: There is no preference in choosing ice cream flavors.

Alternate hypothesis H₁: There is a preference in choosing ice cream flavors.

The probability of choosing a particular flavor of ice cream is 1/4. Then, the Ei= (1/4)×80= 20.

Now construct the chi-square table. And find the chi-square value,

\(\begin{aligned}\chi^2&=\sum\frac{(O_i-E_i)^2}{E_i}\\&=3.2+0.2+3.2+0.2\\&=6.8\end{aligned}\)

Find the degree of freedom (df).

df = n-1 = 4-1 = 3.

From the chi-square table, using the chi-square value and df, we get the p-value,

P(χ²＞6.8)= 0.0786

Here, the p-value is greater than 0.05. As a result, the alternative hypothesis is accepted and the null hypothesis is rejected. From this, we can tell that there is a significant preference in choosing the flavors.

To know more about the chi-square test:

https://brainly.com/question/14082240

#SPJ4

Answer:

the answer is b

Step-by-step explanation

Answer:

Step-by-step explanation:

To show that the expression \(\ln(\sqrt{2} + 1) - \ln\left(\frac{1}{\sqrt{2}}\right)\) is equal to \(-\ln\left(1 - \frac{1}{\sqrt{2}}\right)\), we can simplify both sides of the equation using the properties of logarithms. Here are the steps:

Step 1: Simplify the expression on the left side:

\(\ln(\sqrt{2} + 1) - \ln\left(\frac{1}{\sqrt{2}}\right)\)

Step 2: Apply the logarithmic property \(\ln(a) - \ln(b) = \ln\left(\frac{a}{b}\right)\) to combine the logarithms:

\(\ln\left(\frac{\sqrt{2} + 1}{\frac{1}{\sqrt{2}}}\right)\)

Step 3: Simplify the expression within the logarithm:

\(\ln\left(\frac{(\sqrt{2} + 1)}{\left(\frac{1}{\sqrt{2}}\right)}\right)\)

Step 4: Simplify the denominator by multiplying by the reciprocal:

\(\ln\left(\frac{(\sqrt{2} + 1)}{\left(\frac{1}{\sqrt{2}}\right)} \cdot \sqrt{2}\right)\)

\(\ln\left(\frac{(\sqrt{2} + 1) \cdot \sqrt{2}}{\left(\frac{1}{\sqrt{2}}\right) \cdot \sqrt{2}}\right)\)

\(\ln\left(\frac{(\sqrt{2} + 1) \cdot \sqrt{2}}{1}\right)\)

Step 5: Simplify the numerator:

\(\ln\left(\frac{(\sqrt{2} + 1) \cdot \sqrt{2}}{1}\right)\)

\(\ln\left(\sqrt{2}(\sqrt{2} + 1)\right)\)

\(\ln\left(2 + \sqrt{2}\right)\)

Now, let's simplify the right side of the equation:

Step 1: Simplify the expression on the right side:

\(-\ln\left(1 - \frac{1}{\sqrt{2}}\right)\)

Step 2: Simplify the expression within the logarithm:

\(-\ln\left(\frac{\sqrt{2} - 1}{\sqrt{2}}\right)\)

Step 3: Apply the logarithmic property \(\ln\left(\frac{a}{b}\right) = -\ln\left(\frac{b}{a}\right)\) to switch the numerator and denominator:

\(-\ln\left(\frac{\sqrt{2}}{\sqrt{2} - 1}\right)\)

Step 4: Simplify the expression:

\(-\ln\left(\frac{\sqrt{2}}{\sqrt{2} - 1}\right)\)

\(-\ln\left(\frac{\sqrt{2}(\sqrt{2} + 1)}{1}\right)\)

\(-\ln\left(2 + \sqrt{2}\right)\)

As we can see, the expression \(\ln(\sqrt{2} + 1) - \ln\left(\frac{1}{\sqrt{2}}\right)\) simplifies to \(\ln(2 + \sqrt{2})\), which is equal to \(-\ln\left(1 - \frac{1}{\sqrt{2}}\right)\).

The subspace of P3 consisting of all vectors of the form at^3 + bt^2 + ct + d, where b + c = 0, has dimension 3. This is because the subspace is spanned by the basis {t^3, t^2, 1}.

The subspace of p3 consisting of all vectors of the form at^3 + bt^2 + ct + d where b + c = 0, can be written as:

{at^3 + bt^2 + (-b)t + d} = {at^3 + (b-c)t^2 + d}

Thus, we see that this subspace can be generated by the set {t^3, t^2, 1}.

Since this set contains 3 linearly independent vectors, it is a basis for the subspace. Therefore, the dimension of the subspace is 3.

To know more about subspace:

https://brainly.com/question/30318872

#SPJ4

Answer:

Explanation:

Let the height of the small cylinder be h

Let the radius of the small cylinder be r

The surface area of the small cylinder is:

Simplify the expression by setting SA = 20π

Let the height of the large cylinder be H

Let the radius of the large cylinder be R

The surface area of the large cylinder will be:

Divide equation (2) by equation (1)

Answer:

\(\displaystyle x=\left\{0, \frac{2\pi}{3}, \frac{4\pi}{3}\right\}\)

Step-by-step explanation:

We want to solve the equation:

\(-2\cos^2(x)=-\cos(x)-1\)

Over the interval [0, 2π).

First, notice that this is in quadratic form. So, to make things simpler, we can let u = cos(x). Substitute:

\(-2u^2=-u-1\)

Rearrange:

\(2u^2-u-1=0\)

Factor:

\((2u+1)(u-1)=0\)

Zero Product Property:

\(2u+1=0\text{ or } u-1=0\)

Solve for each case:

\(\displaystyle u=-\frac{1}{2}\text{ or } u=1\)

Back-substitute:

\(\displaystyle \cos(x)=-\frac{1}{2}\text{ or } \cos(x)=1\)

Using the unit circle:

\(\displaystyle x=\left\{0, \frac{2\pi}{3}, \frac{4\pi}{3}\right\}\)

The solution to the equation 3 / 5x-2 = 2 / 3x-1 is x = 1.

Given the equation in the question;

3 / 5x-2 = 2 / 3x-1

To solve for x, cross multiply the equation

3 / 5x-2 = 2 / 3x-1

3( 3x - 1 ) = 2( 5x - 2 )

Apply distributive property

3( 3x - 1 ) = 2( 5x - 2 )

3×3x + 3×-1 = 2×5x + 2×-2

9x - 3 = 10x - 4

Subtract 10x from both sides

9x - 10x - 3 = 10x - 10x - 4

9x - 10x - 3 = - 4

Add 3 to both sides

9x - 10x - 3 + 3 = - 4 + 3

9x - 10x  = - 4 + 3

-x = -1

Divide both sides by -1

-x/-1 = -1/-1

x = 1

Therefore, the value of x is 1.

Learn to solve more equations here: https://brainly.com/question/9236233

#SPJ1

Explanation:

The area of this playing field is its width times its length. The length of the field is:

And its width is 50ft, so the area is:

And we know that the area is 2100 ft², so we can replace that into the expression above and solve for x:

x = 7

Answer:

The answer is option B. 7

Answer:

Diagnostic

Step-by-step explanation:

The teacher made a diagnostic decision relative to Roberts skill level. Before she made this decision, she first started with the process of evaluation to know his strength and also establish his weakness. With the knowledge she has gotten she now plans to him with meaningful learning and an efficient curriculum that would help him in mastering multiplication first before division.