If x1 and x2 are solutions to 3x^2+15x+9=0 quadratic equation, then

x1+x2=

The triangles ∆DEF and ∆DGF are isosceles triangles, and the values of the following lengths are: EF = 44, FG = 36, and DF = 62.

EH is a perpendicular bisector of FD implies triangle ∆DGF is an isosceles triangle so:

FE is equal to ED and FG is equal to GD

7x + 9 = 9x - 1

9x + 7x = 9 + 1 {collect like terms}

2x = 10

x = 10/5 {divide through by 5}

x = 2

7y + 8 = 10y - 4

10y - 7y = 8 + 4 {collect like terms}

3y = 12

y = 12/3 {divide through by 3}

y = 4

EF = 7(5) + 9 = 44

FG = 7(4) + 8 = 36

DF = 2(FH)

FH = 3(5) + 4(4) = 31

DF = 2(31) = 62.

Therefore, the isosceles triangles ∆DEF and ∆DGF have the values of the following lengths as: EF = 44, FG = 36, and DF = 62.

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Answer: -4c + 16

Step-by-step explanation:

So to expand all you do is simply multiply the number outside the bracket (-4) but the numbers inside the bracket one by one as such:
-4 * c = -4c
-4 * -4 = 16

Therefore your answer is -4c + 16 as it can not be simplified further because there as no more like terms to be collected. Hope this helped! ^^

Step-by-step explanation:

-4c+16=

divide both sides by -4

-4c\-4=16\-4

c=16\-4

c=-4

The type of transaction described in the problem is called an installment purchase.

What is the simple interest?

Simple interest is a type of interest that is calculated on the principal amount of a loan or investment for a specific period of time.

The type of transaction described in the problem is called an installment purchase. In this type of transaction, a buyer pays a deposit at the time of purchase and then makes periodic payments, typically over a fixed period of time, until the full purchase price is paid off. In this case, the buyer pays a deposit of R999 and then pays off the remaining balance over a period of 3 years using simple interest.

To calculate the total amount that the buyer will pay over the 3-year period, we need to calculate the amount of interest that will be charged on the remaining balance. Since simple interest is being used, we can use the formula I = Prt, where I is the interest, P is the principal (the remaining balance), r is the interest rate, and t is the time period.

Assuming an annual interest rate of, for example, 5%, the interest charged on the remaining balance of R4000 (the original price minus the deposit) over 3 years would be:

I = Prt

I = 4000 * 0.05 * 3

I = R600

So the total amount that the buyer will pay over the 3-year period is:

R999 (deposit) + R4000 (remaining balance) + R600 (interest) = R5599

the total cost of the binoculars over the 3-year period will be R5599.

Hence, The type of transaction described in the problem is called an installment purchase.

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Answer:

the answer is m =-2

beause my teacher told me

Answer:

The complete system of inequalities to model this scenario is s ≥ 0, l ≥ 0, 8s + 12l ≤ 160, and s - l < 30.

Step-by-step explanation:

Answer:  8s + 12l ≤ 160.

Step-by-step explanation: I would explain.. but I figured maybe I'd spare you the struggle and give you the answer. If you NEED steps, DM me.

The best-fit line to represent the black data points is the blue line.

The plot of absorbance vs. concentration shows 8 data points with 3 lines drawn to represent the data. In order to determine the best-fit line, we need to evaluate the lines based on how well they represent the data points.

(a) The red line is the middle line and goes through 1 data point, with 3 data points above it and 4 data points below it. This line has a slope that is between the slopes of the other two lines. However, it doesn't go through many of the data points and the slope is not consistent with the majority of the data points.

(b) The green line is the top line and touches 3 of the data points, with the rest of the data points below it. This line has a steeper slope compared to the red line, but it doesn't touch many of the data points and has a significant deviation from the majority of the data points.

(c) The blue line is the bottom line and has 2 data points below it and 6 data points above it. This line has a slope that is more consistent with the majority of the data points, and it has the least deviation from the data points compared to the other two lines.

In mathematical terms, the blue line has the least sum of squared residuals, meaning it has the smallest difference between the observed values and the predicted values.

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In order to achieve a bigger splash in their next trial, all the students must need to do is use a ball with a larger circumference.

Displacement and volume are defined as a dimensional object dropped into a liquid that will always displace its own volume from the liquid.

For a basketball, the circumference is a function of its volume. In other words, the larger the circumference, the larger the volume.

This defines that a basketball with a larger volume will displace more water from the pool than one with a lower volume.

Finally, to make a bigger splash, a basketball with a larger circumference would be needed.

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The expression can be used to find the number of CDs that are not country music is 52-c. The correct option is D.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Kayla has 52 CDs in her music collection. Let c represent the number of country music CDs in Kayla's collection.

The expression can be used to find the number of CDs that are not country music is written as below:-

E =  52-c

The correct option is D for the required expression.

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Answer:

4/3

Step-by-step explanation:

to find slope just choose any two points on the line and subtract them. I prefer choosing points that lie on the grid for instance in #11

I will choose Point 1: (4,3) and Point 2: (1,-1) because the intersect the grid and I can do 'clean' subtractions.

Slope = rise/run

= change in y/change in x

= y2-y1/x2-x1

= ( -1 - 3 ) / ( 1 - 4 )

= - 4 / -3

= 4/3

The solution is, 5orange = 1.25 cup

                          24orange= 6 cup

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

here, we have,

Abby squeezed the juice from 4 oranges and made 1 cup of orange juice. Each orange provides the same amount of juice.

now,

from 5 orange we get = 5/4

                                     =1.25 cup

and, 6 cup from = 4*6

                          =24 orange

Hence, The solution is, 5orange = 1.25 cup

                                      24orange= 6 cup

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Answer:

Alex deleted 45 selfies.

This is Single-Blinded Randomized Controlled trial type of study because the recipient is unaware that they are receiving a treatment, only the researchers are aware of who is receiving which treatment. So the option d is correct.

One of the most rigorous research designs is experimental research, which is frequently referred to as the "gold standard" in research designs.

This design involves the researcher manipulating one or more independent variables (as treatments), randomly assigning individuals to various treatment levels (random assignment), and observing the effects of the treatments on outcomes (dependent variables).

Experimental research has a distinct advantage in that it may link cause and effect through treatment manipulation while controlling for the erroneous effect of unrelated variables, which is known as internal validity (causality).

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The complete question is:

A team of researchers randomly separates their study's participants into two groups, giving one group a placebo and the other a new treatment to be tested. As the treatment is somewhat experimental, participants do not know whether they receive the placebo but researchers do know whether a specific participant receives the placebo. What type of study is this?

a. Standard Deviation Study

b. Type 1 Study

c. Case-Control Study

d. Non-Blinded Randomized Controlled Trial

e. Single-Blinded Randomized Controlled trial

The probability he can hit at least 9 of 10 shots anyway is 0.0463 or 4.63%

Divide the total number of outcomes by the entire number of different ways an event could happen to arrive at the probability. There are differences between probability and odds. Odds are determined by dividing the probability of a situation happening by the probability that it won't happen. Probability is a metric used to determine how likely an event is to occur. The likelihood that the coin will land with the heads side up is measured using the probability concept when we toss it in the air. Here is an example of how probability is used in everyday life that you probably already know about. Prior to a major outing, we always consult the weather prediction.

Given[tex]=60[/tex]%[tex]=0.60[/tex]

n[tex]=10[/tex]

Definition binomial probability:

[tex]P(X=k)=(n^{k} )*(P^{k} )*(1-P)^{n-k}[/tex]

Evaluate for [tex]k=9[/tex] and [tex]k=10[/tex]

P[tex](X=9)=0.0403[/tex]

P[tex](X=10)=0.0060[/tex]

Add the corresponding probabilities:

P[tex](x\geq 9)=P(X=9)+P(X=10)=0.0403+0.0060=0.0463=4.63[/tex]%

Command Ti83/84 command: binompdf(10,0.60,9)+binompdf(10,0.60,10)

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The number of RPM flown on this flight from Los Angeles to Sydney is 2,150,960 Miles.

Revenue Passenger Miles (RPM) is a measure of how much passenger traffic an airline is serving, and is calculated by multiplying the number of revenue passengers (passengers paying a fare) by the distance travelled in miles. For this flight, the number of RPM is calculated as follows:

RPM = (Number of Revenue Passengers) x (Distance Travelled in Miles)

RPM = (285 Passengers) x (7,536 Miles)

RPM = 2,150,960 Miles

Therefore, the number of RPM flown on this flight from Los Angeles to Sydney is 2,150,960 Miles.

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Answer:

Multiply 1/4*3= 3/4. So a motorcycle can go 3/4 of a mile on 3 gallons of gas

Step-by-step explanation: Hope this helps!!, Mark me Brainliest, :)))

The persuasion technique that is being used in this case is the black-or-white technique.

This is a persuasion strategy or technique that implies showing the audience there are only two possibilities and the two possibilities are very different (black-or-white). This aims to show the audience they should choose a specific possibility because it is better than the other alternative.

This is the technique being implemented here because the speaker purposes two possibilities buying Mopster mop or having a dirty floor to encourage the audience to purchase this product.

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The probability that at least two bulbs must be selected to obtain one that is rated 75W is 2/3.

Number of 40W bulbs = 7

Number of 60W bulbs = 5

Number of 75W bulbs = 6

We are to find the probability that at least two bulbs must be selected to obtain one that is rated 75 w

Let's say the x is the event in which at least 2 bulbs must be selected to obtain one that is rated 75W and y is the event in which just one bulb was selected which is rated 75 W

So, P(x) = 1 - P(y)

P(x) = 1 - 6/(7 + 5 + 6)

P(x) = 1 - 6/18

P(x) = 1 - 1/3

P(x) = 2/3

Hence, the probability that at least two bulbs must be selected to obtain one that is rated 75W is 2/3.

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Answer: The hypotenuse are both 13 cm

Step-by-step explanation:

The length of the hypotenuse of a right triangle can be found using the Pythagorean theorem, which states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

So, in this case:

c^2 = a^2 + b^2

c^2 = 5^2 + 12^2

c^2 = 25 + 144

c^2 = 169

c = √169

c = 13

So the length of the hypotenuse is 13 cm.

Next, we can use the Pythagorean theorem to find the length of the segments into which the bisector of the right angle divides the hypotenuse. Let's call the length of the segments x. Then, the segments form two right triangles with legs of length x and (13-x)/2.

Using the Pythagorean theorem on each triangle, we have:

x^2 + ((13-x)/2)^2 = 13^2

x^2 + (13-x)^2/4 = 169

x^2 + (13^2 - 2x(13) + x^2)/4 = 169

x^2 + (13^2 - 2x(13))/4 = 169

x^2 + (169 - 26x)/4 = 169

x^2 + 169 - 26x = 676

x^2 - 26x + 507 = 0

Now, we can use the quadratic formula to find x:

x = (-b ± √(b^2 - 4ac)) / 2a

a = 1, b = -26, c = 507

x = (26 ± √(26^2 - 4 * 1 * 507)) / 2 * 1

x = (26 ± √(676)) / 2

x = (26 ± 26) / 2

x = 26 / 2

x = 13

So, the lengths of the segments into which the bisector of the right angle divides the hypotenuse are both 13 cm, to the nearest tenth.

The simplified form of the expression (42x + 62y) + (38x - 4y) is 80x + 58y.

Given the expression in the question

(42x + 62y) + (38x - 4y)

To simplify, collect and add like terms.

(42x + 62y) + (38x - 4y)

42x + 62y + 38x - 4y

Collect like term

42x + 38x - 4y + 62y

Add 42x and 38x

80x - 4y + 62y

Add -4y and 62y

80x + 58y

Therefore, the simplified form is 80x + 58y.

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Answer:

x = 8

Step-by-step explanation:

since the triangles are similar then the ratios of corresponding sides are in proportion , that is

[tex]\frac{RT}{WU}[/tex] = [tex]\frac{RS}{WV}[/tex] ( substitute values )

[tex]\frac{6x+15}{28}[/tex] = [tex]\frac{108}{48}[/tex] ( cross- multiply )

48(6x + 15) = 28 × 108 = 3024 ( divide both sides by 48 )

6x + 15 = 63 ( subtract 15 from both sides )

6x = 48 ( divide both sides by 6 )

x = 8

The

speed

indicated in kilometers per hour is 85 km/h, as shown on the circular scale of the automobile

speedometer

.

The automobile

speedometer

is an instrument that measures the speed of a vehicle. It has a circular

scale

that reads both miles per hour (mph) and kilometers per hour (km/h). To determine the

speed

in kilometers per hour, the user must first locate the needle on the scale. The needle should be pointing to a specific number that corresponds to both mph and km/h. For example, if the needle is pointing to 85, then the speed indicated in kilometers per hour is 85 km/h. It is important to note that if the needle is located between two

numbers

, the user should determine the approximate speed by interpolating the two numbers. To find the speed in miles per hour, the user can simply look at the number that corresponds to the needle on the scale. In this case, the speed indicated in miles per hour is 53 mph.

The complete question: An automobile speedometer with circular scales reading both miles per hour and kilometers por hour is shown. What speed is indicated in miles per hour? 100 120 140 80 160 *60 180 200 40 20 220 Own 240 Express your answer in miles per hour v.2 mph

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The solution to the quadratic equation is ±6

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

2x^2 - 20 = 52

2x^2 = 32x^2

16x = ±4

The error in the above steps is appending x^2 to 32 after collecting the like terms.

Also, the like terms are not properly added

The correct solution is as follows

2x^2 - 20 = 52

Collect the like terms

2x^2 = 72

Divide by 2

x^2 = 36

Take the square root of both sides

x = ±6

Hence, the solution is ±6

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Answer:

SOH-CAH-TOA, the rest are just reciprocals of these

Step-by-step explanation:

sinY= o/h = 6/√61
cosY= a/h = 5/√61
tanY =o/a = 6/5
cosecY = h/o = √61/6
secY = h/a = √61/5
tanY = a/o = 5/6

Answer:

Step-by-step explanation:

Sin = 6/[tex]\sqrt{61][/tex]

Cos=5/[tex]\sqrt{61[/tex]

tan=6/5

cosec=    [tex]\sqrt{61\\[/tex]/6

sec=[tex]\sqrt{61\\[/tex]/5

cot= 5/6

The equation of the blue graph is option B. G(x) = (x - 4)² + 1.

Transformation of geometrical figures or points is the manipulation of a given figure to some other way.

The given function is f(x) = x².

From the figure, we can see that the graph of f(x) is shifted left to 4 units.

Then the function becomes (x - 4)².

Then the function is shifted up to 1 unit.

The resulting function is G(x) = (x - 4)² + 1.

Hence the correct equation of the graph is G(x) = (x - 4)² + 1.

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Answer:

The third angle is 60

Step-by-step explanation:

The interior angle of a triangle is equal to the 180 minus the exterior angle.

[tex]180-80= 100[/tex]

So one of the interior angles is equal to 100

All of the interior angles of a triangle add up to 180

[tex]180=100+20+x[/tex]

[tex]x=60[/tex]

It would be appropriate to construct a t-interval to estimate the population mean.

To determine whether it is appropriate to construct a t interval to estimate the population means, we need to consider if the sample size is large enough and if the population standard deviation is known.

If the sample size is less than 30 and the population standard deviation is not known, then it would be appropriate to use a t-interval.In this case, the sample size is 32, which is large enough to assume that the sample mean is an accurate representation of the population mean.

However, the population standard deviation is not known, so it would be appropriate to use a t interval. The t interval can be calculated using the sample mean, sample standard deviation, and degrees of freedom, which is the sample size minus 1.

The t interval will provide a range of values that we can be confident the population mean falls within, given the sample mean and variability.

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How much time do students spend on the internet? We collect data from the 32 members of our AP Statistics class and calculate the mean amount of time that each student spent on the Internet yesterday. Discuss whether it would be appropriate to construct a t interval to estimate the population mean.

Answer:

[tex]\angle HLG=18 \textdegree[/tex]

Step-by-step explanation:

The sum of the angles in the top quadrant must add up to 90º.

We are given

[tex]25m+22[/tex]  and  [tex]9m[/tex]

The sum of those must equal 90.

Therefore we can write

[tex](25m+22)+(9m)=90[/tex]

Rearrange and remove the parenthesis.

[tex]9m+25m+22=90[/tex]

Add [tex]9m[/tex] and [tex]25m[/tex].

[tex]34m+22=90[/tex]

Subtract 22 form both sides of the equation.

[tex]34m=68[/tex]

Divide both sides of the equation by 34.

[tex]m=2[/tex]

Now we can evaluate [tex]\angle HLG[/tex].

[tex]\angle HLG=9m\\m=2\\\angle HLG=9*2\\\angle HLG=18 \textdegree[/tex]

The distance between the top of the ladder and the ground is decreasing at a rate of 10 meters per minute.

Let's call the distance between the bottom of the ladder and the wall as "x".

At a certain instant, x = 3636 meters

The rate of change of x with respect to time is 10 meters per minute, so dx/dt = 10 m/min.

At that same instant, the height of the ladder above the ground can be expressed as

h = (3939 - x)

since the ladder is 3939 meters long

The rate of change of h with respect to time can be found using the chain rule of differentiation.

dh/dt = dh/dx * dx/dt = -10 m/min

So, at the instant when the bottom of the ladder is 3636 meters from the wall, the rate of change of the distance between the top of the ladder and the ground is -10 meters per minute. This means that the distance between the top of the ladder and the ground is decreasing at a rate of 10 meters per minute.

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Answer:

Below

Step-by-step explanation:

L x W = area

60 * W = 1800

W = 1800/60 = 30 ft