If f(x) = x^2 – 2x and g(x) = 6x + 4, for which value of x does (f + g)(x)=0?
A.-4
B.-2
C. 2
D. 4

Answer:

45

Step-by-step explanation:

Answer:

45

Step-by-step explanation:

The slope of the tangent line to the curve x = 4t₂, y = 2 24t − 14t₂ is 1 at the point (2,10).

To find the slope of the tangent line, we need to take the derivative of y with respect to x, which is dy/dx = (dy/dt) / (dx/dt).

Substituting the given values, we get dy/dx = (48t - 14) / 4, which simplifies to dy/dx = 12t - 3.

To find the point where the slope is 1, we set dy/dx = 1 and solve for t. This gives us t = (1+3)/12 = 1/3.

Substituting t = 1/3 into the equations for x and y, we get x = 4(1/3)² = 4/9 and y = 2(24/3) - 14(1/3) = 16.

Therefore, the point where the tangent line has slope 1 is (4/9, 16).

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Answer:

Step-by-step explanation:

A rational number are numbers that can be expressed as as fraction. They can be expressed as a ratio of two integers. An irrational is quite the opposite.  An irrational number cannot be expressed as a ratio of two integers.

Taking square root of two as an example;

√2 cannot be expressed as a ratio of two integers because the result will always be a decimal. If expressed as √2/1, it is still not a rational number because of the square root of 2 at the numerator. Square root of 2 is not an integer even though 1 is an integer.

Mark is wrong because √2 is irrational and it is irrational because it cannot be expressed as a ratio of two integers not due to the fact that he can write it as a fraction.

The projected population for the year 2036 for the following conditions is 232.870 million.

What is the relative growth rate?

Relative growth rate (RGR) is the rate of growth in relation to size or the rate of growth per unit of time in relation to the size of the object at that particular time. The continuous growth rate or the exponential growth rate are other names for it.

Given Data:

The relative growth is 3 % per year.

The government trying to reduce the growth rate to 2%.

The population in 2011 was 110 million.

The population growth model is given as,

\($$P(t)=P_o e^{r t}$$\)

The population in 2011 was 110 million, and the population in 2036 (after \($t=25$\) ) is given as,

\($$P(25)=110 e^{25 r}$$\)

When the rate is \($3 \%$\) per year, the population is.

\($$\begin{aligned}& P(25)=110 e^{25 \times 0.03} \\& P(2)=232.870 \text { millions }\end{aligned}$$\)

So, the projected population for the year 2036 for the following conditions is 232.870 million.

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SOLUTION

The number of diagonals and number of sides of a polygon are related with the formula

Substituting we have

Solving the quadratic equation for n, we have

So, we will go with n = 8, since the number of sides cannot be a negative number.

Now, sum of interior angles in a regular polygon is given by

So we have

So, the measure of an interior angle becomes

Hence the answer is 135 degrees

Answer:

B

Step-by-step explanation:

Answer:

Step-by-step explanation:

The roots are:

The polynomial is:

Answer:

18.

Step-by-step explanation:

3 x 6 = 18. He eats 3 slices every 5 minutes so 5 minutes x 6 is half an hour. so 18 is your answer.

If Takaya continues to eat three slices of pizza in five minutes, he could eat 18 slices in half of an hour.

The Linear equation in one variable is an algebraic equation of degree one.

it can be expressed in the form of Ax +B = 0 where x is a variable, and A and B are two integers.

Takaya can eat three slices of pizza in five minutes.

for half an hour it would be 6 times five minutes.

So, in half an hour Takaya can eat 3 × 6 = 18

Therefore, If Takaya continues to eat three slices of pizza in five minutes, he could eat 18 slices in half of an hour.

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Given:

∠HFI = 70 degrees

∠IFJ = 63 degrees

To find:

We need to find ∠GFH

Step-by-step solution:

We know that:

"Vert

Illustrative Mathematics offers resources and assistance to teachers who want to give their students a solid understanding of mathematics.

Denver, Colorado is known as "The Mile High City" because it is located at an elevation of 5280 feet above sea level. Someone tells you that Death Valley, California has an elevation of 282 feet.

Death Valley is situated beneath sea level. This is evident because its elevation is negative. The base for measuring elevation is sea level. The elevation of sea level is 0 feet. All other elevations are measured in relation to sea level. Positive elevations are found in locations above sea level, while negative elevations are found in locations below sea level. Death Valley is thus located below sea level, with an elevation of -282 feet.

We can use the following logic to determine how much higher Denver is than Death Valley:

The depth of Death Valley is 282 feet below sea level. Denver is located 5280 feet above sea level. To get from Death Valley to Denver, you'd have to climb 282 feet to reach sea level, then another 5280 feet to get to Denver, for a total of 282+5280=5562 feet. Denver, Colorado is therefore 5562 feet higher than Death Valley, California.

Your elevation would be close to zero if you were standing near the ocean. If you are at the edge of a very low tide (or a very high tide, respectively) at the Bay, your elevation could be as low as -50 feet (or as high as 50 feet) depending on how high or low the tide is and where you are standing.

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It indicates that the test is highly accurate in correctly identifying individuals with hepatitis C (high sensitivity) and accurately ruling out individuals without the disease (high specificity).

Sensitivity and specificity are two important measures of a diagnostic test's performance. Sensitivity refers to the test's ability to correctly identify individuals who have the condition, while specificity refers to its ability to correctly identify individuals who do not have the condition.

In the case of the ELISA test for hepatitis C, a sensitivity of 95% means that the test will correctly identify 95% of individuals who actually have hepatitis C as positive. This indicates a high probability of detecting the disease when it is present.

On the other hand, a specificity of 90% means that the test will correctly identify 90% of individuals who do not have hepatitis C as negative. This suggests that there is a 10% chance of a false positive result, where individuals without the disease are mistakenly identified as positive.

Overall, the high sensitivity and specificity of the ELISA test for hepatitis C make it a valuable tool in the diagnosis and screening of individuals for this infectious disease. However, it is important to consider that no test is 100% accurate, and false results can still occur. Therefore, additional confirmatory tests may be required in certain cases to ensure accurate diagnosis and appropriate medical intervention.

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The amount of interest for the year was 3,770 cents, and the regular price of the electric drill that Pamela bought before the discount was 21,927 cents

Interest = P x R x T.

Where:

P = Principal amount (the beginning balance).

R = Interest rate

T = Number of time periods

In this case, we are given that;

Principal amount (P) = $580

Interest rate (R) = 6,5 %

Time = 1 year

Hence, The amount of the interest = 6,5% of $580

                                                     = 0.065 × $580

                                                     = $37.7

1 dollar = 100 cents

Hence, $37.7 = 37.7 × 100 cents equal to 3,770 cents

P = (1 – d) x

Where,

P = Price after discount

D = discount rate

X = regular price

In this case, we are given that:

P = $32.89

D = 85% = 0,85

Hence, the regular price:

P = (1 – D) x

32.89 = (1 – 0.85) X

32.89 = 0.15X

X = 32.89/0.15

X= 219.27

1 dollar = 100 cents

Hence, $219.27 = 219.27 × 100 cents equal to 21,927 cents

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Answer:

She is wrong. She needs 140 square feet.

Explanation:

(8×10)+(4×15) = 140

Procedure for regrouping to find sum is as follows as mentioned.

Regrouping is accomplished by forming groups of tens during operations such as subtraction and addition. Regrouping is the process of rearranging numbers into groups based on place value to make operations easier.

This is known as regrouping because you are rearranging numbers into place value to complete the process.

Assume we want to add 18 and 12, which equals 30.

1. It is best to visualise your problem as a grid when regrouping with addition.

              1 2

         +   1 8

2.In this situation, the first addition would be to add 2 and 8, which equals 10. However, there is no place to write 10 on the bottom row. In this case, regrouping is required. To accomplish this, we take the 0 from the 10 and place it in the bottom row, followed by the 1 above our ten's column. Below is an updated grid:          

     1

     12

   +1 8

        0       

3.We must now add up the tens column. In this case, we have three one-digit numbers to add together. This brings us to the correct solution answer, which is 30.

1

1 2

1 8

3 0

Hence, the regrouping is the simplest way to do addition.

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the expression equivalent to f(p+r) is 5p + 5r.

The expression equivalent to f(p+r), where f(x) = 5x, is 5p + 5r. To understand this, we substitute (p+r) into the function f(x):

f(p+r) = 5(p+r)

Next, we distribute the 5 to both p and r:

f(p+r) = 5p + 5r

This equivalent expression arises from the definition of f(x) = 5x, where the function multiplies any given input x by 5. In this case, we substitute (p+r) into the function, resulting in 5 multiplied by the sum of p and r. Consequently, the expression 5p + 5r represents the value obtained by applying the function f to the sum of p and r. It is important to note that the function f(x) = 5x implies a linear relationship, where the function scales the input by a factor of 5.

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In 50 rolls of a fair pair of number cubes, we would expect to get doubles approximately 12 times.

The probability of rolling doubles on a pair of number cubes is 1/6, since there are six possible outcomes for each roll and only one of them will result in doubles. Therefore, the probability of not rolling doubles on a single roll is 5/6.

The probability of not rolling doubles on two consecutive rolls is (5/6) x (5/6) = 25/36.

Therefore, the probability of rolling doubles at least once in two consecutive rolls is 1 - 25/36 = 11/36.

Using the same logic, the probability of rolling doubles at least once in three consecutive rolls is 1 - (5/6)^3 = 91/216, and the probability of rolling doubles at least once in four consecutive rolls is 1 - (5/6)^4 = 671/1296.

We can use this pattern to find the probability of rolling doubles at least once in 50 rolls, which is approximately 1 - (5/6)^49 = 0.714, or 71.4%.

Therefore, we would expect to get doubles approximately 71.4% of the time in 50 rolls, which is approximately 35.7 times. However, since we can't roll a fraction of a time, the closest whole number is 12.

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To compute the cosine of the angle between the two planes with normals 1=⟨1,0,1⟩ and 2=⟨10,7,3⟩, we first need to find the dot product of the two normal vectors.
1⋅2 = ⟨1,0,1⟩⋅⟨10,7,3⟩ = 1(10) + 0(7) + 1(3) = 13

Next, we need to find the magnitudes of the two normal vectors.
|1| = √(1^2 + 0^2 + 1^2) = √2
|2| = √(10^2 + 7^2 + 3^2) = √174
Finally, we can use the dot product formula to find the cosine of the angle between the two normal vectors:
cosθ = (1⋅2) / (|1|⋅|2|) = 13 / (√2 ⋅ √174) ≈ 0.692
Therefore, the cosine of the angle between the two planes is approximately 0.692.
To compute the cosine of the angle between the two planes with normals 1=⟨1,0,1⟩ and 2=⟨10,7,3⟩, you need to find the dot product of the normal vectors and divide it by the product of their magnitudes.
The dot product of the normal vectors is:
(1)(10) + (0)(7) + (1)(3) = 10 + 0 + 3 = 13
The magnitudes of the normal vectors are:
||1|| = √((1)^2 + (0)^2 + (1)^2) = √(1 + 0 + 1) = √2
||2|| = √((10)^2 + (7)^2 + (3)^2) = √(100 + 49 + 9) = √158
Now, divide the dot product by the product of the magnitudes:
cosine(angle) = 13 / (√2 * √158) = 13 / (√316)
So the cosine of the angle between the two planes is 13/√316.

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Step-by-step explanation:

15/36 = 41.6%

because there are 36 total marbles. and 15 of them are either red or yellow.

Answer:

-x + 2y - 36

Step-by-step explanation:

-4(x + 9) + 3(x - y) + 5y

Distribute;

-4x - 36 + 3x - 3y + 5y

Collect like terms;

-1x + 2y - 36

The 95% confidence interval for the population proportion favoring stricter gun control laws in the district is approximately 0.4612 to 0.5188. This means that 95% are confident that the true proportion of voters in the population who favor stricter gun control laws falls within this range.

The 95% confidence interval for the population proportion favoring stricter gun control laws based on a poll of 1,100 voters in which 49% of them favored stricter laws.

To find the confidence interval, follow these steps:

1. Determine the sample proportion (p-hat): p-hat = favorable votes / total votes = 0.49.

2. Determine the sample size (n): n = 1,100 voters.

3. Calculate the standard error (SE): \(SE = \sqrt(p-hat \times (1 - p-hat) / n)\)

\(= \sqrt(0.49 \times (1 - 0.49) / 1100) \approx 0.0147.\)

4. Find the critical value (z) for a 95% confidence interval: z = 1.96 (from a standard normal distribution table).

5. Calculate the margin of error (ME): \(ME = z \times SE = 1.96 \times 0.0147 \approx 0.0288.\)

6. Find the lower and upper limits of the confidence interval:

Lower limit = p-hat - ME = \(0.49 - 0.0288 \approx 0.4612;\)

Upper limit = p-hat + ME = \(0.49 + 0.0288 \approx 0.5188.\)

In conclusion, the 95% confidence interval for the population proportion favoring stricter gun control laws in the district is approximately 0.4612 to 0.5188. This means that we are 95% confident that the true proportion of voters in the population who favor stricter gun control laws falls within this range.

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There are 3 equations required to solve a 3x3 sysytem of equation.

We can eliminate z by multiplying the third equation by 2 and adding to the first:

2x - 10y - 4z = -8

2x + 3y + 4z = 2

Adding,

4x - 7y = -6

Let's eliminate z from the second by multiplying it by 2, the third by 3, and adding.

10x - 4y + 6z = 0

3x - 15y - 6z = -12

13 x - 19 y = -12

Ok, we eliminate y by muliplying our first x,y equation by 19, the last by 7, and subtracting

4(19)x - 7(19)y = -6(19

13(7)x - 19(7)y = -12(7)

(4(19) - 13(7)) x = -6(19)+12(7)

x = ( -6(19)+12(7)) / (4(19) - 13(7)) = 2

That worked out.

7y = 4x + 6 = 4(2) + 6 = 14

y = 2

4z = 2 - 2x - 3y = 2 - 2(2) - 3(2) = 2 - 4 - 6 = -8

z = -2

x=2, y=2, z=-2

There are 3 equations required to solve a 3x3 sysytem of equation.

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Disclaimer

The question given by you is incomplete, the above anser is done as per the question

How to do 3x3 systems of equations

The area of the pyramid = 340 sq. inches

The area of a square pyramid= b^2+ 2.b.s

                                                  = 10^2 + 2*10*12

                                                  = 340 sq. inches

We can also find out the are by finding area of each sides

Area of square = 10*10 = 100 sq. inches

Area of triangle= 1/2( 12*10)

                           = 60

Area of four triangles = 4*60

                                    = 240

Total surface area = 240+100

                                = 340 sq. inches

Hence the total surface area is 340 sq. inches

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The Central Angle of the sector in radians is  0.3184 π  .

In the question ,

it is given that ,

the radius of the sector = 24 m

the area of the sector = 288 m²

we know that the Area of the sector of the circle is given by the formula

Area = πr²(θ/360)

Substituting the values , we get

288 = (3.14)*(24)²*(θ/360)

θ = (288*360)/((3.14)*(24)²)

θ = 1,03,680/1808.64

θ = 57.32°

converting the angle to radian ,

we get

θ = 57.32° ×  π/180 radian

= 0.3184 π

Therefore  , The Central Angle of the sector in radians is  0.3184 π  .

The given question is incomplete , the complete question is

A sector of a circle of radius 24 m has an area of 288 m² . find the central angle of the sector in radians .

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Answer:

1139621600

Step-by-step explanation:

The answer is 1139621600, because if it is in 2001. All you have to o is multiply by 4. I don't know if this is correct. If they gave you another year and another set of numbers I would be able to clarify it more. So...if this isn't correct. I'm so sorry.

If you think its incorrect please say so in comments below. Any questions? Say them below as well.

I hope this helped.

:)

Signed,

tyreefrankinjr

Answer: True

Step-by-step explanation:

Given: The ratio of the number of boys to the number of girls at Liam's school is 4:5.

There are 270 students at his school.

Then, Total boys = \(\dfrac{4}{4+5}\times270=\dfrac{4}{9}\times270=120\)

Total girls =\(\dfrac{5}{4+5}\times270=\dfrac{5}{9}\times270=150\)

Clearly, (Number of girls) > (Number of boys)

Difference =  (Total girls) - (Total boys)

= 150-120

= 30

So,  Statement 3: "There are exactly 30 more girls than boys". is absolutely true.

Answer:

5 weeks

Step-by-step explanation:

$18 / week

goal is $90

18x = 90

90/18 = 5

18(5) =90

It will take him 5 weeks to save enough money to buy the skateboard

Answer:

1. Yes

2. No

3. Yes

4. No

5. Yes

Step-by-step explanation:

1. Yes

2. No

3. Yes

4. No

5. Yes

In order to be sure whether given lengths form a triangle or not, we should know the following property.

If sum of any two lengths is larger than the third length then it will form a triangle otherwise not.

Answer:

4.5

Step-by-step explanation:

The triangles are similar

QT       QS

------ = ______

QR       QP

3                 5

-----------  = ---------

(4x-3)+3     25 +5

3                 5

-----------  = ---------

4x             30

Using cross products

3*30 = 5*4x

90 = 20x

90 /20 = 20x/20

4.5 =x

Option 2 is correct that is 1.79

When presented in ascending order, the value that 75% of data points fall within is known as the higher quartile, or third quartile (Q3).

The quartiles formula is as follows:

Upper Quartile (Q3) = 3/4(N+1)

Lower Quartile (Q1) = (N+1) * 1/3

Middle Quartile (Q2) = (N+1) * 2/3

Interquartile Range = Q3 -Q1,

1.74, 0.24, 1.56, 2.79, 0.89, 1.16, 0.20, and 1.84 are available.

Sort the data as follows: 0.20, 0.24, 0.89, 1.16, 1.56, 1.74, 1.84, 2.79 in ascending order of magnitude.

The data set has 8 values.

hence, n = 8; third quartile: 3/4 (n+1)th term

Q3 =3/4 of a term (9) term

Q3 =27/4 th term

Q3 = 1.74 + 1.84 / 2 (average of the sixth and seventh terms)

equals 1.76

Thus Q3 is 1.76 that is option 2

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