Translate the sentence into an equation.
Seven times the sum of a number and 8 eguals 5.
Use the variable b for the unknown number.

Each coordinate was multiplied by 2 instead of divided by 2

the correct coordinates are

preimage                                image

A (2, 5)   → (2 * 1/2, 5 * 1/2) →   A' (1, 2.5)

B (2, 0)  → (2 * 1/2, 0 * 1/2) →    B' (1, 0)  

C (4, 0)  → (4 * 1/2, 0 * 1/2) →    C' (2, 0)

Dilation is a method of transformation that magnify or shrink the preimage depending on the scale factor

The transformation rule for dilation is as follows

(x, y) for a scale factor of r → (rx, ry)

following similar procedure for the given problem we solve with scale factor of 1/2

preimage                                 image

A (2, 5)   → (2 * 1/2, 5 * 1/2) →   A' (1, 2.5)

B (2, 0)  → (2 * 1/2, 0 * 1/2) →    B' (1, 0)  

C (4, 0)  → (4 * 1/2, 0 * 1/2) →    C' (2, 0)

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Answer:

the unit rate is 0.8x per unit y

Step-by-step explanation:

the proportional relationship is y = \(\frac{4x}{5}\)

this means that the constant of proportionality k = \(\frac{4}{5}\) = 0.8

re-writing, we have

y = 0.8x

therefore, the unit rate is 0.8x per unit y

The demand function is linear, so we can write it in the form of:

q = a - bp

Where a and b are constants and q is the quantity demanded and p is the price. We have two points, one at a price of $3.25 with a quantity of 2,500, and another at a price of $2.83 with a quantity of 3,900.

We can use these two points to solve for the values of a and b in the equation.

Plugging in the first point:

2500 = a - (3.25)b

Plugging in the second point:

3900 = a - (2.83)b

We can then solve this system of equation by substituting the first equation with the second one

3900 = a - (2.83)b

=2500 + 1400 = a - (3.25)b + (2.83)b

=a - (0.42)b

So the equation is:

q = 3900 - 0.42p

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Step-by-step explanation:

in what form do we need the equation ?

slope-intercept ?

that would be

y = ax + b

with "a" being the slope and "b" being the y-intercept (the y-value when x = 0).

in any case, since we have the slope and a point, we can start with the point-slope form :

y - yp = a(x - xp)

"a" is again the slope, and (xp, yp) is the given point.

so,

y - 5 = 1×(x - 3) = x - 3

adding 5 to both sides gives us

y = x + 2

and that is our desired equation in slope-intercept form.

Answer: a=101 b=79 c=83 d=97

Answer:

360 cm^2

Step-by-step explanation:

length x width x height

6 x 6 x 10

Answer:

360cm^3

Step-by-step explanation:

V=L*W*H

V=6*6*10

V=36*10

V=360

Answer:

f(x) = 3x² + 6x + 1

General Formulas and Concepts:

Step-by-step explanation:

Step 1: Define function

f(x) = 3(x + 1)² - 2

Step 2: Find Standard Form

Step-by-step explanation:

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

= 3 [x^2 + 2x + 1 ] -2

=3x^2 + 6x +3-2

=3x^2 + 6x + 1

f(x)=ax^2+bx+c

ax^2+bx+c = 3x^2 + 6x + 1

a = 3

b = 6

c = 1

\(\\ \sf\longmapsto V=\pi r^2h\)

\(\\ \sf\longmapsto 11.25=5\pi r^2\)

\(\\ \sf\longmapsto 2.25=\pi r^2\)

\(\\ \sf\longmapsto r^2=2.25/3.14=0.71\)

\(\\ \sf\longmapsto r=\sqrt{0.71}\)

\(\\ \sf\longmapsto r=0.84in\)

Answer:

Diameter is 3.00 inches

Step-by-step explanation:

» Volume of a cylindrical soup is given a formula below:

\({ \tt{volume = \pi {r}^{2} h}}\)

\({ \tt{11.25\pi = \pi( {r}^{2} ) \times 5}}\)

» Divide either sides by 5π

\({ \tt{ \frac{11.25\pi}{ \green{5\pi}} = \frac{\pi {r}^{2} \times 5}{ \green{5\pi}} }} \\ \\ { \tt{2.25 = {r}^{2} }} \\ { \tt{ \sqrt{ {r}^{2} } = \sqrt{2.25} }} \\ { \tt{r = 1.5 \: in}}\)

» From identical circular formulae, diameter is twice radius:

\( { \boxed{ \tt{ \: diameter = 2 \times radius \: }}} \\ { \tt{d = 2 \times 1.5}} \\ { \tt{d = 3 \: inches}}\)

Answer: D

Step-by-step explanation:

Answer:

1/4

1/6

Step-by-step explanation:

a) There is a 1/2 chance of rolling a odd number each time you roll it. Why? Because there are 3 odd numbers on a 6 sided die, 1,3,5. If we roll it twice, it would be 1/2 x 1/2 so a 1/4 chance

b) For it to be a sum of 8 the following combinations are possible, where the first number is rolled first and the second number is rolled second.

2,6

3,5

4,4

5,3

6,2  

For it to be 12, it must be

6,6

There are a total of 6 ways to achieve this, and there is a total of 36 possible combinations, therefore 6/36 = 1/6 chance of rolling a sum of 8 or 12

The total interest for the loan is $4,550. This means that over the course of 5 years, you will pay back the original loan amount of $13,000 plus $4,550 in interest for a total of $17,550.

To calculate the total interest for this loan, we need to use the simple interest formula:
Monthly EMI formula :
Interest = Principal x Rate x Time

In this case, the principal (amount borrowed) is $13,000, the rate is 7%, and the time is 5 years.

So,

Interest = $13,000 x 0.07 x 5

Interest = $4,550

It's important to keep in mind that this calculation assumes that the interest rate remains constant over the entire 5-year period.

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\((\stackrel{x_1}{-3}~,~\stackrel{y_1}{-11})\hspace{10em} \stackrel{slope}{m} ~=~ 4 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-11)}=\stackrel{m}{ 4}(x-\stackrel{x_1}{(-3)}) \implies y +11 = 4 ( x +3) \\\\\\ y+11=4x+12\implies {\Large \begin{array}{llll} y=4x+1 \end{array}}\)

The equation is:

Work/explanation:

Recall that the point slope formula is \(\rm{y-y_1=m(x-x_1)}\),

where m is the slope and (x₁, y₁) is a point on the line.

Plug in the data:

\(\rm{y-(-11)=4(x-(-3)}\)

Simplify.

\(\rm{y+11=4(x+3)}\)

Simplified to slope intercept:

\(\rm{y+11=4x+12}\)

\(\rm{y=4x+1}\) <- this is the simplified slope intercept equation

Without additional details, we cannot determine the number of two-dozen tulip arrangements the florist should expect to sell with the anticipated 4,600 more customers.

To determine the number of two-dozen tulip arrangements the florist should expect to sell if they anticipate 4,600 more customers, we need to examine the given results and make a reasonable assumption based on the available information.

Unfortunately, the given results or information regarding the number of tulip arrangements sold or the relationship between customers and sales are not provided. Without this data, it is not possible to accurately estimate the number of arrangements that will be sold with an additional 4,600 customers.

To make an accurate prediction, we would need more information such as the average number of tulip arrangements sold per customer or any patterns or trends observed in the sales data.

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Answer:

Step-by-step explanation:

Answer:

\(x=-\frac{68}{9}\)

Step-by-step explanation:

\(\frac{9}{14}=\frac{8}{x+20}\\\)

\(9(x+20)=8*14\\9x+180=112\\9x=-68\\x=-\frac{68}{9}\\\)

Answer:

D. Pythagorean

Step-by-step explanation:

Given the identity

cos²x - sin²x = 2 cos²x - 1.

To show that the identity is true, we need to show that the left hand side is equal to right hand side or vice versa.

Starting from the left hand side

cos²x - sin²x ... 1

According to Pythagoras theorem, we know that x²+y² = r² in a right angled triangle. Coverting this to polar form, we have:

x = rcostheta

y = rsintheta

Substituting into the Pythagoras firnuka we have

(rcostheta)²+(rsintheta)² = r²

r²cos²theta+r²sin²theta = r²

r²(cos²theta+sin²theta) = r²

(cos²theta+sin²theta) = 1

sin²theta = 1 - cos²theta

sin²x = 1-cos²x ... 2

Substituting equation 2 into 1 we have;

= cos²x-(1-cos²x)

= cos²x-1+cos²x

= 2cos²x-1 (RHS)

This shows that cos²x -sin²x = 2cos²x-1 with the aid of PYTHAGORAS THEOREM

Answer:

who is he and what has he done, if you don't mind me asking

The simplified form of -20/2(7 2/3) is -230/3.

To solve the expression -20/2(7 2/3), we need to follow the order of operations, which states that we should perform the operations inside parentheses first, then any multiplication or division from left to right, and finally any addition or subtraction from left to right.

First, let's convert the mixed number 7 2/3 to an improper fraction.

7 2/3 = (7 * 3 + 2) / 3 = 23/3

Now, let's substitute the value back into the expression:

-20/2 * (23/3)

Next, we simplify the multiplication:

-10 * (23/3)

To multiply a fraction by a whole number, we multiply the numerator by the whole number:

-10 * 23 / 3

Now, we perform the multiplication:

-230 / 3

Therefore, the simplified form of -20/2(7 2/3) is -230/3.

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Answer:

The proportion of individuals score at most 74 points on this test is 70%.

Step-by-step explanation:

The complete question is:

Suppose that the scores on a reading ability test are normally distributed with a mean of 70 and a standard deviation of 8. What proportion of individuals score at most 74 points on this test? Round your answer to at least four decimal places.

Solution:

Let X represent the scores on a reading ability test.

It is provided that \(X\sim N(70,8^{2})\).

Compute the probability that an individuals score is at most 74 points on this test as follows:

\(P(X\leq 74)=P(\frac{X-\mu}{\sigma}\leq \frac{74-70}{8})\)

                 \(=P(Z<0.50)\\=0.69146\\\approx 0.70\)

Thus, the proportion of individuals score at most 74 points on this test is 70%.

Answer:

1) \(\sqrt{53}(\cos286^\circ+i\sin286^\circ)\)

2) \(\displaystyle 5,-\frac{5}{2}+\frac{5\sqrt{3}}{2}i,-\frac{5}{2}-\frac{5\sqrt{3}}{2}i\)

Step-by-step explanation:

Problem 1

\(z=2-7i\\\\r=\sqrt{a^2+b^2}=\sqrt{2^2+(-7)^2}=\sqrt{4+49}=\sqrt{53}\\\\\theta=\tan^{-1}(\frac{y}{x})=\tan^{-1}(\frac{-7}{2})\approx-74^\circ=360^\circ-74^\circ=286^\circ\\\\z=r\,(\cos\theta+i\sin\theta)=\sqrt{53}(\cos286^\circ+i\sin 286^\circ)\)

Problem 2

\(\displaystyle z^\frac{1}{n}=r^\frac{1}{n}\biggr[\text{cis}\biggr(\frac{\theta+2k\pi}{n}\biggr)\biggr]\,\,\,\,\,\,\,k=0,1,2,3,\,...\,,n-1\\\\z^\frac{1}{3}=125^\frac{1}{3}\biggr[\text{cis}\biggr(\frac{0+2(2)\pi}{3}\biggr)\biggr]=5\,\text{cis}\biggr(\frac{4\pi}{3}\biggr)=5\biggr(-\frac{1}{2}-\frac{\sqrt{3}}{2}i\biggr)=-\frac{5}{2}-\frac{5\sqrt{3}}{2}i\)

\(\displaystyle z^\frac{1}{3}=125^\frac{1}{3}\biggr[\text{cis}\biggr(\frac{0+2(1)\pi}{3}\biggr)\biggr]=5\,\text{cis}\biggr(\frac{2\pi}{3}\biggr)=5\biggr(-\frac{1}{2}+\frac{\sqrt{3}}{2}i\biggr)=-\frac{5}{2}+\frac{5\sqrt{3}}{2}i\)

\(\displaystyle z^\frac{1}{3}=125^\frac{1}{3}\biggr[\text{cis}\biggr(\frac{0+2(0)\pi}{3}\biggr)\biggr]=5\,\text{cis}(0)=5(1+0i)=5\)

Note that \(\text{cis}\,\theta=\cos\theta+i\sin\theta\) and \(125=125(\cos0^\circ+i\sin0^\circ)\)

Following the pattern, the most likely next step in the series is given by the pentagon in option B.

We have to look at the number of points in each figure, hence:

Hence, the number of points increases by one for each figure, meaning that in the next step, the figure should have 5 points, representing a pentagon.

Among the options given for the answer, only one, option B, has 5 points, with the pentagon, as:

Hence, the most likely next step in the series is given by the pentagon in option B.

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Answer:

slope of perpendicular line= -⅕

slope of parallel line= 5

Step-by-step explanation:

y= 5x -4

The equation is in the slope-intercept form, thus the slope is the coefficient of x.

Slope of given equation= 5

The product of the slopes of perpendicular lines is -1.

Let the slope of the perpendicular line be m.

m(5)= -1

\(m = - \frac{1}{5} \)

Thus, the slope of the perpendicular line is -⅕.

Parallel lines have the same gradient.

Slope of parallel line= 5

What is slope-intercept form?

The inequality for which the order pair (-5, -7) is a solution will be x + y ≤ 3. Then the correct option is B.

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

Let's check all the options, then

A)  y ≤ (1/4)x - 1

At (-5, -7), we have

-7 ≤ (1/4)(-5) - 1

-7 ≤ -2.25

This is incorrect.

B)  x + y ≤ 3

At (-5, -7), we have

-5 + (-7) ≤ 3

-12 ≤ 3

This is correct.

The inequality for which the order pair (-5, -7) is a solution will be x + y ≤ 3. Then the correct option is B.

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Answer: lil t j

Step-by-step explanation:

I’m not a goat but I fit the description we walk around with then bands in my pocket

Answer:

13 1/2

Step-by-step explanation:

think of 9 as 9/1

whenever you divide fractions you must multiply by the reciprocal of the second fraction

9/1 ÷ 2/3 becomes 9/1 × 3/2

= 27/2 or 13 1/2

Answer: no one cares

Step-by-step explanation:

Answer:

175.07 apples and oranges

Step-by-step explanation:

Answer:

Set the amt of apples as x, and the amt of oranges as y.

Step-by-step explanation:

Apples: x

Oranges: y

John's expression: 0.89x+1.05y

Sam's expression: 1.02x+0.84y

Combine both expressions!

0.89x+1.05y+1.02x+0.84y

Now, combine like terms.

1.91x+1.89y

There's your answer!

Hope it helped! :)

Answer:

\( P'\cap Q' = \{1\}\)

Step-by-step explanation:

E = {1, 3, 7, 9, 11, 13, 15}

P= {3, 9, 11, 13} and Q = {3,7,9,15}

P' = {1, 7, 15} and Q = {1, 11, 13}

\( P'\cap Q' = \{1\}\)

The probability of event A given the event B is 0.35 or 7/20.

It is given that A and B are two events.

Given probabilities are as follows:

Probability of A and B is = P(A and B) = 0.14

Probability of B = P(B) = 0.4

We know that the conditional probability of event A given B is given by,

P(A | B)

= P(A and B)/P(B)

= 0.14/0.4 [Substituting the value which are given]

= 14/40

= 7/20 [Eliminating the similar values from numerator and denominator]

= 0.35

Hence the probability of event A given the event B is 0.35 or 7/20.

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