Determine whether the following function is increasing or decreasing.g(x) = 4 – 4x

The equation for a transformed cosine wave with the following properties is  y = 3cos2x + 4

An equation for a transformed cosine wave with the following properties can be written in the form:

y = A× cos(B(x - C)) + D

Where:

A = amplitude (positive value)

C = phase shift (horizontal shift of the wave)

D = vertical shift (shift of the wave up or down)

Here we have

Amplitude = 3

Period = π

Horizontal shift = None

Vertical shift  = 4 units  up  

As we know Period P = 2π/B

From the data => 2π/B = π

=> B = 2  

Hence,

Equation for a transformed cosine wave, y = 3 × cos(2(x - 0)) + 4

=> y = 3 × cos(2(x )) + 4

=> y = 3cos2x + 4  

Therefore,

The equation for a transformed cosine wave with the following properties is  y = 3cos2x + 4

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The percentage of pennies is given by the equation A = 40 %

A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, %

The difference between an exact value and an approximation to it is the approximation error in a data value. Either an absolute error or a relative error might be used to describe this error.

Percentage change is the difference between the measured value and the true value , as a percentage of the true value

Percentage change =( (| Measured Value - True Value |) / True Value ) x 100

Given data ,

Let the percentage of pennies be represented as P

Now , the equation will be

The total number of coins = 600 coins

The number of pennies = 240 pennies

So , the percentage of pennies = ( number of pennies / total number of coins ) x 100

On simplifying the equation , we get

The percentage of pennies A = ( 240/600 ) x 100

The percentage of pennies A = 0.4 x 100

The percentage of pennies A = 40 %

Hence , the percentage is 40 %

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Answer:

okay ans is A(w)=w2+5w-1/8piw2

Answer:

V = 3312 ft^3

Step-by-step explanation:

This figure is formed from a rectangular prism and a square-based pyramid

Given:

h (prism) = 11 ft

a (prism's base) = a (pyramid's base) = 12 × 18 = 216 ft^2

h (pyramid) = 24 - 11 = 13 ft

First, we can find the volume of the prism:

\(v(prism) = a(base) \times h\)

\(v(prism) =216\times 11 = 2376 \: {ft}^{3} \)

Now, let's find the volume of the pyramid:

\(v(pyramid) = \frac{1}{3} \times a(base) \times h\)

\(v(pyramid) = \frac{1}{3} \times 216 \times 13 = 936 \: {ft}^{3} \)

In order to find the total volume of the given figure, we have to add these 2 volumes together:

\(v(total) = 2376 + 936 = 3312 \: {ft}^{3} \)

Answer:

v=3

Step-by-step explanation:

15v-9v=18

6v = 18

6      6

 v = 3

Answer:

Step-by-step explanation:

thats the answer...

just:  Expand the polynomial using the FOIL method.

Answer:

(x-1)(x-1)=(x-1)² because it's the same thing multiplied by itself

Using FOIL method:

(x-1)(x-1)=

x²-x-x+1=

x²-2x+1

Answer:

Opposite of -88 feet

Step-by-step explanation:

the opposite of -88 is positive 88, which means its coming off of the ground. negative would go into the ground.  

Answer:

y = 1.5x(or d) + 8

Step-by-step explanation:

1.5 is the slope and 8 is the y intercept(the constant term)

Answer:

26) 70

27) 12.86 sec

28) 350 feet

Step-by-step explanation:

26) Given points A(0, 0) and B(16, 1120)

slope m = \(\frac{y_2-y_1}{x_2-x_1}\)

\(=\frac{1120-0}{16-0}\\ \\=\frac{1120}{16}\\ \\=70\)

slope = 70

27) eq of a line is :

y = mx + c

y = 70x + c

Since the line passes through A(0,0) substituting the points in the equation,

0 = 70(0) + c

⇒ c = 0

eq of line: y = 70x

given distance is 900 ft

y = distance and x = time

⇒ y = 900

sun in eq,

900 = 70x

⇒ x = 900/70

⇒ x = 12.86

28) time is 5 sec

⇒ x = 5

sub in eq

y = 70(5)

⇒ y = 350

The length of the line segment AB is 5 units.

Unfortunately, you haven't provided any information about PQ such as its location or any other data to help solve the question.

Therefore, it's impossible to determine the length of PQ using the given options. However, here is an explanation of how to find the length of a line segment using the distance formula, which may help you in solving similar questions in the future.

The distance formula is used to find the distance between two points in a coordinate plane, such as the length of a line segment. The formula is:

d = √((x₂ - x₁)² + (y₂ - y₁)²)

where d is the distance, (x₁, y₁) and (x₂, y₂) are the coordinates of the two points.

To use the distance formula, you first need to find the coordinates of the two points that make up the line segment. Then, substitute these coordinates into the formula and simplify to find the distance.

For example, let's say you have two points: A(1, 2) and B(4, 6), and you want to find the length of the line segment AB. Using the distance formula:

d = √((4 - 1)² + (6 - 2)²)
d = √(3² + 4²)
d = √(9 + 16)
d = √25
d = 5

Remember, the distance formula can be applied to any two points in a coordinate plane to find the distance between them.

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Answer:

y-1= -1/3(x+3)

Step-by-step explanation:

y-y1=m(x-x1)

y-1=m(x+3)

the slope is rise over run

the slope is -1/3

Answer:

y - 1 = 3/2 (x + 3)

Step-by-step explanation:

To find the equation of a line parallel to the given line and passing through the point (-3, 1), we can use the point-slope form of a linear equation. The point-slope form is given by:

y - y₁ = m(x - x₁)

Where (x₁, y₁) is the given point and m is the slope of the line.

First, let's calculate the slope of the given line using the two points (-2, -4) and (2, 2):

slope = (y₂ - y₁) / (x₂ - x₁)

= (2 - (-4)) / (2 - (-2))

= 6 / 4

= 3/2

Since the line we want to find is parallel to the given line, it will have the same slope. Therefore, the slope (m) of the new line is also 3/2.

Now we can substitute the values into the point-slope form using the point (-3, 1):

y - 1 = (3/2)(x - (-3))

y - 1 = (3/2)(x + 3)

The equation in point-slope form of the line parallel to the given line and passing through the point (-3, 1) is:

y - 1 = 3/2 (x + 3)

Answer:

7 pales per horse

Step-by-step explanation:

35 ÷ 5 = 7

Answer: 7 pails each.

Step-by-step explanation:

35 pails / 5 horses = 7 pails each

35/5=7

Answer:

As in explanation.

Step-by-step explanation:

A) SSE means "Error Sum of Squares". The source of it is the sum of squared deviations within groups.

B) SSTR means "Treatment Sum of Squares". It's source is the weighted sum of squared deviations of group means from grand mean. It's the sum of squares between groups.

C) SST means "Total Sum of Squares''. It's source is total sum of squared deviations from the grand mean. It is a sum of SSE and SSTR.

A) SSE means "Error Sum of Squares". The source of it is the sum of squared deviations that lies within groups.

B) SSTR means "Treatment Sum of Squares". It's source that represents the weighted sum of squared deviations of group means from the grand mean. It's the sum of squares between groups.

C) SST means "Total Sum of Squares''. It's source that represents total sum of squared deviations from the grand mean. It is a sum of SSE and SSTR.

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Answer:

Step-by-step explanation:

\(\frac{d}{dx} [cos(3x^2) \sqrt[3]{5x^3 -1} +sin(4x^3)]^4\\\\=4[cos(3x^2) \sqrt[3]{5x^3 -1} +sin(4x^3)]^3\; \frac{d}{dx} [cos(3x^2) \sqrt[3]{5x^3 -1} +sin(4x^3)] --- eq(1)\)

Lets look at the derivative part:

\(\frac{d}{dx} [cos(3x^2) \sqrt[3]{5x^3 -1} +sin(4x^3)] \\\\= \frac{d}{dx}[cos(3x^2) \sqrt[3]{5x^3 -1} ] + \frac{d}{dx}[sin(4x^3)]\\\\=cos(3x^2) \frac{d}{dx}[ \sqrt[3]{5x^3 -1} ] + \sqrt[3]{5x^3 -1}\frac{d}{dx}[ cos(3x^2) ] + cos(4x^3) \frac{d}{dx}[4x^3]\\\\=cos(3x^2) \frac{1}{3} (5x^3 -1)^{\frac{1}{3} -1} \frac{d}{dx}[5x^3 -1] + \sqrt[3]{5x^3 -1} (-sin(3x^2))\frac{d}{dx}[ 3x^2] + cos(4x^3)[(4)(3)x^2]\)

\(=\frac{cos(3x^2) 5(3)x^2}{3(5x^3 - 1)^{\frac{2}{3} }} -\sqrt[3]{5x^3 -1}\; sin(3x^2) (3)(2)x + 12x^2 cos(4x^3)\\\\=\frac{5x^2cos(3x^2) }{(5x^3 - 1)^{\frac{2}{3} }} -6x\sqrt[3]{5x^3 -1}\; sin(3x^2) + 12x^2 cos(4x^3)\)

Substituting in eq(1), we have:

\(\frac{d}{dx} [cos(3x^2) \sqrt[3]{5x^3 -1} +sin(4x^3)]^4\\\\=4[cos(3x^2) \sqrt[3]{5x^3 -1} +sin(4x^3)]^3\; [\frac{5x^2cos(3x^2) }{(5x^3 - 1)^{\frac{2}{3} }} -6x\sqrt[3]{5x^3 -1}\; sin(3x^2) + 12x^2 cos(4x^3)]\)

Answer:

We accept the null hypothesis, that is, the the mean amount of garbage per bin is not different from 50.

Step-by-step explanation:

A sanitation supervisor is interested in testing to see if the mean amount of garbage per bin is different from 50.

This means that the null hypothesis is:

\(H_{0}: \mu = 50\)

And the alternate hypothesis is:

\(H_{a}: \mu \neq 50\)

The test statistic is:

\(z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}\)

In which X is the sample mean, \(\mu\) is the value tested at the null hypothesis, \(\sigma\) is the standard deviation and n is the size of the sample.

50 tested at the null hypothesis:

This means that \(\mu = 50\)

In a random sample of 36 bins, the sample mean amount was 50.67 pounds and the sample standard deviation was 3.9 pounds.

This means that \(n = 36, X = 50.67, \sigma = 3.9\)

Value of the test statistic:

\(z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}\)

\(z = \frac{50.67 - 50}{\frac{3.9}{\sqrt{36}}}\)

\(z = 1.03\)

p-value:

Since we are testing if the mean is differente from a value and the z-score is positive, the pvalue is 2 multipled by 1 subtracted by the pvalue of z = 1.03.

z = 1.03 has a pvalue of 0.8485

1 - 0.8485 = 0.1515

2*0.1515 = 0.3030

0.3030 > 0.01, which means that we accept the null hypothesis, that is, the the mean amount of garbage per bin is not different from 50.

Answer:

0 because if all the mice ran away then they would be gone

The area of the kite is A = 48 units²

Given data ,

Let the area of the kite be represented as A

Now , the value of A is

Let the first diagonal of the kite be d₁ = 12 units

Let the second diagonal of the kite be d₂ = 8 units

Now , Area of kite = ( 1/2 ) d₁ x d₂

On simplifying , we get

A = ( 1/2 ) ( 12 ) ( 8 )

A = 48 units²

Therefore , the value of A is A = 48 units²

Hence , the area of the kite is A = 48 units²

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Answer:

150 seconds

Step-by-step explanation:

use the velocity equation of

\(V=\frac{delta(D)}{Delta(T)\\}\)

Where V is in feet per second, Delta D represents the change in displacement and delta t represents the change in time

all you need to do is rearrange the equation to find Delta(T)

as such...

\(Delta(t)*V=Delta(D)\\Delta (t)=\frac{Delta(D)}{V}\\Then\ insert\ your\ corresponding\ values\\\Delta(t)=\frac{270 ft}{1.8 feet/sec} \\Delta (t)= 150sec\)

Option C is the correct answer, which is if there is no difference in the proportions then all the defective parts are made on the two assembly lines, then the probability of observing a difference is equal to 0.006 is 0.018.

The hypothesis is mostly stated in writing while during the proposal state. This may help to keep the research effort focused on the primary objective and to create a stronger basis for interpreting the study’s results.

As compared to a hypothesis that emerges as a result of inspecting the data.

The test is divided into two ways

Alternate hypothesis and Null Hypothesis

The alternate hypothesis is being the proportion of defective parts made on the old assembly line is greater than on the new assembly line.

The Null Hypothesis states that if the proportion of defective parts made up of the old assembly line is equal to that of the new assembly line then the value of the p is 0.018 is equal to 0.06.

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Full question:

A factory manager selected a random sample of parts produced on an old assembly line and a random sample of parts produced on a new assembly line. The difference between the sample proportion of defective parts made on the old assembly line and the sample proportion of defective parts made on the new assembly line (old minus new) was 0.006. Under the assumption that all conditions for inference were met, a hypothesis test was conducted with the alternative hypothesis being the proportion of defective parts made on the old assembly line is greater than that of the new assembly line. The p-value of the test was 0.018.

Which of the following is the correct interpretation of the p-value?

A. If there is a difference of 0.018 in the proportions of all defective parts made on the two assembly lines, the probability of observing that difference is 0.006.

B. If there is a difference of 0.006 in the proportions of all defective parts made on the two assembly lines, the probability of observing that difference is 0.018.

C. If there is no difference in the proportions of all defective parts made on the two assembly lines, the probability of observing a difference equal to 0.006 is 0.018.

D. If there is no difference in the proportions of all defective parts made on the two assembly lines, the probability of observing a difference of at least 0.006 is 0.018.

E. If there is no difference in the proportions of all defective parts made on the two assembly lines, the probability of observing a difference of at most 0.006 is 0.018.

The method of counting seeds by touching each can be more effective in enhancing strong number sense in children as it allows them to experience each number physically and helps them in developing a strong sense of numbers.

In order to enhance strong number sense in children, there are various methods that can be used.

In the given scenario, Mme Potatana asked the children to count as a whole class from 1 to 20 while Ntate Mafodi asked the children in his class to count seeds from the school's ground in a pile by touching each as they count.

Both methods have their own benefits, but the method of counting seeds by touching each can be more effective in enhancing strong number sense in children.

The method of counting seeds by touching each can be more effective in enhancing strong number sense in children because it allows them to experience each number physically.

This helps them in developing a strong sense of numbers. By touching each seed as they count, children can feel and see each number, which helps them in understanding numbers better. Additionally, it helps in developing the concept of one-to-one correspondence and counting by rote.

Here are some appropriate examples for enhancing strong number sense using the method of counting seeds by touching each:

1. Use counters: Provide children with counters such as small objects, blocks, or toys. Ask them to count the number of counters by touching each as they count.

2. Counting on fingers: Encourage children to count on their fingers. This helps them in developing a strong sense of numbers and helps them in understanding the concept of one-to-one correspondence.

3. Counting objects in a pile: Ask children to count objects in a pile by touching each as they count. This helps in developing the concept of counting by rote and helps in enhancing strong number sense.

Overall, the method of counting seeds by touching each can be more effective in enhancing strong number sense in children as it allows them to experience each number physically and helps them in developing a strong sense of numbers.

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Being a girl and playing a sport are C. No, they are not independent events, because P(girl) 0.49 and P(girl plays a sport) ~ 0.62.

Let's consider the probabilities:

P(girl) = (number of girls) / (total number of students) = 135 / 275 ≈ 0.49

P(girl plays a sport) = (number of girls playing a sport) / (total number of students) = 76 / 275 ≈ 0.276

If being a girl and playing a sport were independent events, the joint probability would be the product of the individual probabilities:

P(girl) × P(girl plays a sport) ≈ 0.49 × 0.276 ≈ 0.13524

However, the actual joint probability is different from the expected value:

P(girl, plays a sport) ≈ 76 / 275 ≈ 0.276

Since the joint probability does not match the product of the individual probabilities, we can conclude that being a girl and playing a sport are not independent events based on the given data.

Therefore, option C. No, they are not independent, because P(girl) 0.49 and P(girl plays a sport) ~ 0.62. is the correct answer.

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Answer:

Step-by-step explanation:

Given the sequence \(a_n = \frac{9+14n^{2} }{n+15n^{2} }\)

To find the limit of the sequence, we will first divide the numerator and the denominator through by the highest power of n which is n² as shown;

\(\lim_{n \to \infty} \frac{9/n^{2} +14n^{2}/n^{2} }{n/n^{2} +15n^{2}/n^{2} }\\ \lim_{n \to \infty} \frac{9/n^{2} +14 }{1/n +15n^{2}/n^{2 }}\\\)

As \(n\) tends to \(\infty\), \(\frac{a}{n}\) tends to zero where n is any constant, The limit of tyhe sequence as n tends to infinity becomes;

\(= \frac{9/\infty+14 }{1/\infty+15 }\\= \frac{0+14}{0+15} \\= 14/15\\\)

Therefore \(\lim_{n \to \infty} \frac{9+14n^{2} }{n+15n^{2} } = 14/15\)

Since the limit of the sequence gave a finite number , the sequence converges.

Note that the only case when the sequence diverges id when the limit of the sequence is infinite

The arrow is at a height of 48 ft after approx. 3 - √6 s and after 3 + √6 s.

To find the time it takes for the arrow to reach a height of 48 ft, we can use the formula for the height of the arrow:

s = v0t - 16t^2

Here, s represents the height of the arrow, v0 is the initial velocity, and t is the time.

Given that the initial velocity, v0, is 96 ft/s and the height, s, is 48 ft, we can set up the equation:

48 = 96t - 16t^2

Now, let's solve this equation to find the time it takes for the arrow to reach a height of 48 ft.

Rearranging the equation:

16t^2 - 96t + 48 = 0

Dividing the equation by 16 to simplify:

t^2 - 6*t + 3 = 0

We now have a quadratic equation in the form of at^2 + bt + c = 0, where a = 1, b = -6, and c = 3.

Using the quadratic formula:

t = (-b ± √(b^2 - 4ac)) / (2a)

Plugging in the values:

t = (6 ± √((-6)^2 - 413)) / (2*1)

t = (6 ± √(36 - 12)) / 2

t = (6 ± √24) / 2

Simplifying the square root:

t = (6 ± 2√6) / 2

t = 3 ± √6

Therefore, the arrow reaches a height of 48 ft after approximately 3 + √6 seconds and 3 - √6 seconds.

In summary, the arrow takes approximately 3 + √6 seconds and 3 - √6 seconds to reach a height of 48 ft, assuming an initial velocity of 96 ft/s.

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Note the complete question is

The height of an arrow shot upward can be given by the formula s = v0*t - 16*t², where v0 is the initial velocity and t is time.How long does it take for the arrow to reach a height of 48 ft if it has an initial velocity of 96 ft/s?  

Solve (t-3)^2=6

The arrow is at a height of 48 ft after approx. ___ s and after ___ s.

The arc length parameter along the curve from the point where t = 0 by evaluating the integrals s is equal to \(\sqrt{54}\) and the length of the indicated portion of the curve is \(\sqrt{54}+1\)

To find the arc length parameter along the curve,  to evaluate the integral of the magnitude of the velocity vector with respect to t.

The velocity vector is the derivative of the position vector r(t) with respect to t:

\(v(t) = dr/dt\)

Plugging value of r into v

\(v(t) = 5i + 2j - 7k\)

Now, to find the magnitude of the velocity vector:

\(|v(t)| = \sqrt{5^2 + 2^2 + (-7)^2}\)

On adding gives:

\(|v(t)| = \sqrt{54}\)

The arc length parameter s is given by the integral of |v(t)| with respect to t with the limits from t = 0 to t = 1

\(s = \int_{t=0}^1 |v(t)| dt\)

Plugging the values of v(t) in the above equation:

\(s = \int_0^1\sqrt{54}\,dt\)

Take out the constant from the integral sign results:

\(s = \sqrt{54} \int_0^1\,dt\)

On integrating gives:

\(s = \sqrt{54}\times t |_{0}^1\)

on multiplying gives:

\(s = \sqrt{54} t |_{0}^s\)

Evaluated limits from t = 0 to t = 1:

\(s = \sqrt{54} (1-0).\)

On multiplying inside the brackets gives:

\(s = \sqrt{54} \times 1 - \sqrt{54} \times 0\)

Simplifying further:

\(s = \sqrt{54} \times 1\)

On multiplying with 1 gives:

\(s = \sqrt{54}\)

Now, given that the curve is traversed from t = -1 to t = s,

so the length of the indicated portion of the curve is simply:

\(s - (-1)\):

Length \(= s - (-1) \\= s + 1 \\= \sqrt{54} +1\)

Therefore,  arc length parameter along the curve from the point where t = 0 by evaluating the integrals s is equal to \(\sqrt{54}\) and the length of the indicated portion of the curve is \(\sqrt{54}+1\).

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Answer: negative one third

Answer:

-1/3

Explanation:

There's a formula that I'll use to find the slope - it's called the slope formula.

\(\sf{m=\dfrac{y_2-y_1}{x_2-x_1}}\)

Plug in the data:

\(\sf{m=\dfrac{8-4}{-4-8}}\\\\\sf{m=\dfrac{4}{-12}\)

Simplify:

\(\sf{m=-\dfrac{4}{12}}\)

\(\sf{m=-\dfrac{1}{3}}\)

Hence, the slope is negative one-third.

Answer:

50 days are needed to make $2500.

Step-by-step explanation:

Number of tons per day:

One ton equals 2000 pounds, as the problem states as a hint.

The company collects 200 pounds per day.

1 ton - 2000 pounds

x tons - 200 pounds

2000x = 200

x = 200/2000

x = 0.1

0.1 tons per day.

A recycling company makes $500 per ton of aluminum scrap collected.

0.1*500 = $50 per day.

How many days are needed to make $2500?

1 day - $50

x days - $2500

50x = 2500

x = 250/5

x = 50

50 days are needed to make $2500.

Answer:

  $142.32, profit on sale of the policy

Step-by-step explanation:

You want to know the expected value of a $280,000 life insurance policy sold for $270, if the probability the insured will live for the year is 0.999544.

The insurance company expects to have to pay the $280,000 death benefit for 0.000456 of the policies issued. That means their expected payout on any one policy is ...

  0.000456 × $280,000 = $127.68

The company gets a premium of $270 for the policy, so the expected value of the policy to the company is ...

  $270 -127.68 = $142.32

The expected value of the policy to the company is $142.32.

This represents its profit from sale of the policy.

__

Additional comment

Of course, the company has expenses related to the policy, perhaps including a commission to the agent selling it, and expenses related to handling claims. That is to say that not all of the difference between the premium and the average death benefit is actually profit. It is what might be called "contribution margin."

<95141404393>

a) The confidence level of 99% means that we are 99% sure that the interval contains the true population proportion.

b) The 99% confidence interval for the population proportion is given as follows: (0.3145, 0.4055). It means that we are 99% sure that the true population proportion is between 0.3145 and 0.4055.

c) The 95% confidence interval would be narrower, as it would have a lower critical value, thus the margin of error would also be lower.

A confidence interval of proportions has the bounds given by the rule presented as follows:

\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In which the variables used to calculated these bounds are listed as follows:

The confidence level is of 99%, hence the critical value z is the value of Z that has a p-value of \(\frac{1+0.99}{2} = 0.995\), so the critical value is z = 2.575.

The parameters for this problem are given as follows:

\(\pi = 0.36, n = 739\)

The lower bound of the interval is given as follows:

0.36 - 2.575 x sqrt(0.36 x 0.64/739) = 0.3145.

The upper bound of the interval is given as follows:

0.36 + 2.575 x sqrt(0.36 x 0.64/739) = 0.4055.

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he two numbers that multiply to -35 and add to get -18 are -5 and 3.

To see why, you can use the factoring method. First, find two numbers that multiply to give you -35. The factors of -35 are -1, 1, -5, and 5. So, the two numbers that multiply to -35 are either -5 and 7 or 5 and -7.

Next, find which pair of numbers adds up to -18. It's clear that 5 and -7 add up to -2, so they don't work. However, if we choose -5 and 3, we get:

-5 + 3 = -2

So, -5 and 3 are the two numbers that multiply to -35 and add to -18.