Question 1 of 10
Estimate the difference of the decimals below by rounding to the nearest
whole number. Enter your answer in the space provided.
46.327
-4.801

5(2x+1)+4=6(3x+2)-7

10x+5+4=18x+12-7

10x-18x=12-7-5-4

-8x=-4 (-1)

8x=4

x=4/8 (/4)

x=1/2

Answer:

x = 1/2

Step-by-step explanation:

5(2x + 1) + 4 = 6 (3x + 2) - 7

~Simplify both sides

10x + 9 = 18x + 5

~Subtract 9 from both sides

10x = 18x - 4

~Subtract 18x to both sides

-8x = -4

~Divide -8 to both sides

x = 1/2

Best of Luck!

9514 1404 393

Answer:

  smaller : larger = 3 : 4

Step-by-step explanation:

The scale factor is the ratio of corresponding dimensions. If we use the width dimensions, we have ...

  smaller/larger = 9/12 = 3/4

The scale factor is 3/4.

9514 1404 393

Answer:

  A. y = -2x +13

  B. y = 8x -7

Step-by-step explanation:

A. We can read the y-intercept of the secant line from the graph. It is 13.

The slope can also be read from the graph, but we choose to use the slope formula:

  m = (y2 -y1)/(x2 -x1)

  m = (19 -9)/(-3 -2) = 10/-5 = -2

Then the slope-intercept formula for the line is ...

  y = mx + b . . . . . . line of slope m and y-intercept b

  y = -2x +13

__

B. The vertex of the given parabola is (0, 1). We notice that when x=1 (1 unit right of the vertex), y = 3 (2 units up from the vertex). This tells us the vertical scale factor of the parabola is 2. That means the vertex form equation is ...

  y = a(x -h)^2 +k . . . . . . . . vertex (h, k), scale factor 'a'

  y = 2(x-0)^2 +1 . . . . . . . use known values for (h, k)

  y = 2x^2 +1

The derivative of this is ...

  y' = 4x

So, at x=2, the given point A, the slope of the tangent line is ...

  m = y' = 4(2) = 8

We have a point and the slope, so we can write the point-slope form of the equation for the tangent line:

  y -9 = 8(x -2)

Rearranging to slope-intercept form, this is ...

  y = 8x -7

__

Additional comment

You can also read the slope of the tangent line from the graph. The line also goes through the point (1, 1), so has a rise of 8 for a run of 1. The y-intercept can be found from ...

  b = y -mx = 9 -8(2) = -7

This lets you write the equation of the tangent line directly from the graph.

That is, the parameters of both lines can be read from the graph, so there is very little "development" required.

Answer:

Step-by-step explanation:

vxcvxcvxcvxcvxcvcxvxcbcvbcvnxcgjfgjfgjghjghjghjghj

The revenue function is y₁ = –4x² + 400x, the cost function is y₁ = x² – 100x + 8000, and the break-even number of units is 20 or 80.

It is a polynomial that is equal to zero. Polynomial of variable power 2, 1, and 0 terms are there. Any equation having one term in which the power of the variable is a maximum of 2 then it is called a quadratic equation.

Jua Kali Products Ltd has been in operation for the last 10 years.

Its annual revenue and cost functions take the form of quadratic functions.

The following data was obtained from the records of the company.

Year          Unit Sold            Revenue             Cost

2017              5                        1900                 7525

2018             10                       3600                7100

2019             15                        5100                6725

We know that the quadratic equation is given as

[tex]\rm y = ax^2 + bx + c[/tex]

Let y₁ be the revenue function, y₂ be the cost function and x be the unis sold.

Then the revenue function will be

1900 = 25a + 5b + c  ...i

3600 = 100a + 10b + c  ...ii

5100 = 225a + 15b + c  ...iii

From equations (i), (ii), and (iii), we have

a = –4, b = 400, and c = 0

Then the revenue function will be

y₁ = –4x² + 400x

Similarly, the cost function will be

7525 = 25a + 5b + c  ...1

7100 = 100a + 10b + c  ...2

6725 = 225a + 15b + c  ...3

From equations 1, 2, and 3, we have

a = 1, b = –100, and c = 8000

Then the cost function will be

y₁ = x² – 100x + 8000

For the break-even units, the cost function and the revenue function will be equal. Then we have

[tex]\begin{aligned} x^2 -100x + 8000 &= -4x^2 + 400x\\\\5x^2 -500x + 8000 &= 0\\\\x^2 - 100x + 1600 &= 0\\\\x^2 - 80 x - 20x + 1600 &= 0\\\\x(x-80) - 20 (x-80) &= 0\\\\(x-80)(x-20) &= 0\\\\x &= 20, 80 \end{aligned}[/tex]

More about the quadratic equation link is given below.

https://brainly.com/question/2263981

Answer:

200 is equal to 20 tens I guess lol

Answer:

20 tens

Step-by-step explanation:

200÷10=20 groups of ten

Answer:

The width is 36 feet

Step-by-step explanation:

If the width of the fence is x then its length is x+3.

The perimeter is 150 feet, so we have the equation:

2(x + x + 3) = 150

4x + 6 = 150

x = 144/4 = 36 feet

Answer: See explanation

Step-by-step explanation:

From the information given in the question, we are informed that a newsletter publisher believes that less than 61% of their readers own a laptop.

The null hypothesis will be: H0: p ≥ 0.61

The alternative hypothesis will be: Ha: p < 0.61.

Answer:

12.65

Step-by-step explanation:

Pythagoras :

c² = a² + b²

c is the Hypotenuse (the side opposite of the 90 degree angle).

a and b are the side legs.

so, here we have

14² = 6² + b²

196 = 36 + b²

160 = b²

b = sqrt(160) = sqrt(16×10) = 4×sqrt(10) = 12.65

Answer:

-2 from both sides

Step-by-step explanation:

32=5x+2

-2        -2

________

30=5x

__=__

5      5

6=x

The first step to solve for X is to use subtraction property of equality to subtract 2 from both sides.

We are given the algebraic equation;

32 = 5X + 2

The first step to solve for X is to use subtraction property of equality to subtract 2 from both sides to get;

32 - 2 = 5X + 2 - 2

30 = 5X

Divide both sides by 5 using division property of equality to get;

X = 6

Read more about Algebraic Equations at; https://brainly.com/question/16863577

#SPJ6

Answer:

henc X = 30°

Step-by-step explanation:

here is the proof

when X=30° then

sin2x = sin2×30

=sin 60°

= √3/2

or else,

putting value of X = 30° then

sin2x= 2sinxcosx

= 2×sin30°×cos30°

=2×1/2×√3/2

= 2√3/4

= √3/2

hence proved sin2x= √3/2.

Answer:

d

Step-by-step explanation:

h

Answer:

x = 1

Step-by-step explanation:

-2x + 8x + 3 - 7 = 2

Combine like terms

-2x + 8x = 6x

3 - 7 = -4

We now have

6x - 4 = 2

Add 4 to both sides

6x - 4 + 4 = 2 + 4

6x = 6

Divide both sides by 6

6x/6 = 6/6

x = 1

Answer:

x = -1/4

Step-by-step explanation:

[tex]81^{x}[/tex] = 1/3

[tex]3^{4}^{x}[/tex] = [tex]3^{-1}[/tex]

4x = -1

x = -1/4

Answer:

x = - [tex]\frac{1}{4}[/tex]

Step-by-step explanation:

Using the rules of exponents

[tex](a^m)^{n}[/tex] = [tex]a^{mn}[/tex] , [tex]a^{-m}[/tex] = [tex]\frac{1}{a^{m} }[/tex]

Given

[tex]81^{x}[/tex] = [tex]\frac{1}{3}[/tex] [ note that 81 = [tex]3^{4}[/tex] ] , then

[tex](3^4)^{x}[/tex] = [tex]3^{-1}[/tex] , that is

[tex]3^{4x}[/tex] = [tex]3^{-1}[/tex]

Since the bases on both sides are equal, both 3, then equate exponents

4x = - 1 ( divide both sides by 4 )

x = - [tex]\frac{1}{4}[/tex]

Answer:

1.8

Step-by-step explanation:

First, find 40% of 15:

15(0.4)

= 6

Next, find 30% of this:

6(0.3)

= 1.8

So, the answer is 1.8

The number of sides of a regular polygon with an interior angle [tex]\[{178^ \circ }\][/tex] is 180.

A polygon is regular when all angles are equal and all sides are equal.

A regular polygon has if each interior angle.

Interior angle of given polygon =178

An exterior angle of polygon =180 −178 =2

The sum of exterior angles of any polygon is 360

Number of sides of a regular polygon

[tex]=\frac{360}{2}[/tex]

[tex]=180[/tex]

Therefore, The number of sides of a regular polygon is 180.

To learn more about the side of regular polygon visit:

https://brainly.com/question/1592456

​

Answer:

1/5

Step-by-step explanation:

the two points are(7,5) and (2,4)

let,(x1,y1)=(7,5) and (x2,y2)=(2,4)

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

=4-5/2-7

=-1/-5

=1/5(minus ,minus are cut)

Answer:

300, 16.67%

Step-by-step explanation:

Let x be the cost price. x-(1/6)x=250. 5x/6=250. x=300. Losss percentage is 16.67%

9514 1404 393

Answer:

  |x| = 1/2

Step-by-step explanation:

Perhaps the simplest equation is ...

  |x| = 1/2

__

You could get more elaborate:

  |2x| = 1

  3 -|6x| = 0

Subtracting 10 from the original equation will shift the graph down 10 units

The answer is D.

Answer:

Step-by-step explanation:

Note that the equation should be

f(t) = t^2 + 6t - 20

A. Completing the square

coefficient of the t term: 6

divide it in half: 3

square it: 3²

add 3² to complete the square and subtract 3² to keep the equation balanced:

f(t) = (t² + 6t + 3²) - 3² - 20

f(t) = (t+3)² - 29. This is the equation in vertex form.

:::::

B. Vertex (-3, -29)

The leading coefficient of the equation is +1. Since the leading coefficient is positive, the parabola opens upwards. Therefore, the vertex is a minimum.

:::::

The axis of symmetry is the vertical line passing through the vertex: x = -3

Answer:

232.045

Step-by-step explanation:

217 + 253 + 214 + 247 + 217 + 253 + 232 + 246 + 223 + 227 + 229 + 247 + 206 + 241 + 239 + 223 + 222 + 216 + 252 + 209 + 236 + 256 = 5105

5105 / 22 = 232.045454545

Answer:

C. 98

Step-by-step explanation:

The proposed regression equation is weight = b + width * m

R2 = 0.423

A.) What is the regression equation for this example?

The estimate for the y-intercepts is b= 2.3013 and the estimate for the slope is m= 0.7963

In general, we can symbolize the estimated regression equation as ^Y= b + m*Xi. For this example you have to replace it with the calculated values of the regression coefficients to obtain the estimated regression equation:

^Y= 2.3013 + 0.7963Xi

B.) What is the explanatory, or predictor, variable in this study?

The explanatory or predictor variable is the variable that is suspected to have an effect over the response variable. In this example the predictor variable is:

X: Width of a horseshoe crab (cm)

C.) If the researcher wanted to test whether there is a statistically significant relationship between these two variables, what would the test statistic be? Calculate it from the table above.

To test if the regression is significant, the parameter of study will be the slope of the regression equation, symbolically: β. If the slope is equal to zero "β=0" then there is no linear regression between the response and explanatory variable. If the slope is different from zero "β≠0" then the regression is significant and the explanatory variable affects the response variable.

The hypotheses are:

H₀: β=0

H₁: β≠0

α: 0.05

The value of the statistic under the null hypothesis is t= 8.48

D.) What can we say about the p-value?

This test is two-tailed and so is the p-value, remember that the p-value is the probabulity of obtaining a value as extreme as the value of the statistic under the null hypothesis. The distribution for this test is a t with n-2= 100-2= 98 degrees of freedom. You can calculate the p-value as:

P(t₉₈≤-8.48) + P(t₉₈≥8.48)= P(t₉₈ ≤ -8.48) + (1 - P(t₉₈ < 8.48) ≅ 0.00001

E.) Ultimately, the reason that we find test statistics is so that we can compare them to a null distribution. For regression, that is a t-distribution based on the degrees of freedom. With 98 degrees of freedom (100-2), we can safely say that the critical t (or the confidence multiplier) is what?

As mentioned before, this test is two tailed, meaning that the rejection region is divided in two:

Critical values ± = ± = ± 1.984

This means that you'll reject the null hypothesis when the statistic is t ≤ -1.984 or if the statistic is t ≥ 1.984-

F.) Find the confidence interval for the slope.

Using a 95% confidence level, the interval for the slope is:

[m ± Sm]

[0.7963 ± 1.984 * 0.0939]

[0.61; 0.98]

G.) Is there a statistically significant relationship? Answer with the test statistic and the confidence interval.

Yes, there is a significant relationship between the width and weight of the horseshoe crabs.

Using the critical value approach:

The calculated statistic is 8.48 and the critical value is ± 1.984, since the statistic is greater than the positive critical value, the decision is to reject the null hypothesis.

If you pay attention to the confidence interval, which was made at a confidence level complementary to the significance level of the hypothesis test, this interval [0.61; 0.98] doesn't include the "zero". Since the interval doesn't include the value of the parameter stated in the null hypothesis, you can conclude that this hypothesis is not true and therefore reject it.

Answer:

Ok I'm assuming that know what??

Step-by-step explanation:

Answer:

± 3

Step-by-step explanation:

let n be the number then the number squared is n² , so

6n² = 54 ( divide both sides by 6 )

n² = 9 ( take the square root of both sides )

n = ± [tex]\sqrt{9}[/tex] = ± 3

That is the number is 3 or - 3

Answer:

Step-by-step explanation:

You have not provided the answers to choose from.

The expression can be simplified to δ⁴/a, but I cannot tell if that is one of the choices.

Answer:

-3

Step-by-step explanation:

Slope is y2 - y1 / x1 - x2.

So, let's take two random points; I have chosen (0, 3) and (2, -3).

Excellent. Let's calculate the slope.

Slope = (-3 - 3) / (2 - 0) = -6 / 2 = -3.

Hope this helps!