find the x and y intercepts of 2x-9y = 4

Answer:Option B. x = -1, 19

Step-by-step explanation:

The given equation is x² - 18x = 19

We can get the value of x by factorizing the expression or by quadratic formula.

We will try to factorize the equation first. If we find no factors then we will apply quadratic formula to get the value of x.

x² - 18x - 19 = 0

x² - 19x + x - 19 = 0

x(x - 19) + 1(x - 19) = 0

(x - 19)(x + 1) = 0

x = 19, -1 will be the solutions.

So there is no need to apply quadratic formula.

Option B. x = -1, 19 is the answer.

Step-by-step explanation:

Answer:

24c+9

Step-by-step explanation:

I assume these equations are the sides so we just add all of them together

(10c+4)+(6c+4)+(8c+1)

We combine like terms

(10c+6c+8c)+(4+4+1)

24c+9

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The measures of angle 4 (m<4) and angle 7 (m<7) are 42° and 96°, respectively.

To find the measures of angles 4 and 7, we need to apply some geometric principles. Since the top and bottom pieces of the crib are parallel to each other, we can use the property of alternate interior angles.

Angle 4 (m<4) is formed by a transversal (the line connecting the top and bottom pieces of the crib) intersecting two parallel lines. Given that angle m<2 is 42°, we know that angle 4 is congruent to angle 2. Therefore, m<4 = m<2 = 42°.

Angle 7 (m<7) is formed by a transversal intersecting two parallel lines as well. However, in this case, angle 7 is an exterior angle, which is equal to the sum of the two remote interior angles. The remote interior angles are angles 2 and 4. We know that m<2 = 42° (as given) and m<4 = m<2 = 42° (as explained above). Therefore, the sum of angles 2 and 4 is 42° + 42° = 84°. Since angle 7 is an exterior angle, it is equal to 180° minus the sum of the remote interior angles. Thus, m<7 = 180° - 84° = 96°.

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Divisor is an integer, not equal to zero.

A divisor is a number that divides another number either outright or with a remainder. The divisor is represented in the division formula as follows:

Dividend ÷ divisor = quotient.

A divisor is any number that divides another number.

A factor is a divisor but all divisors are not factors.

Given expression,

33 + 63 - 222 - 4

= 96 - -226

= - 130

The dividend is an integer, divisor can be any integer except 0.

Hence, divisor can be any integer except 0.

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The addition of the 7 / 4 + 1 / 2 + 5 / 3 + 1 / 3 + 1 / 4 + 1 / 2 is 5.

A fraction represents a portion of a total. This entire may refer to a place or a group of places. The Latin word "fraction," which means "to break," is the source of the English term "fraction."

The distribution of food and supplies as well as the lack of a metal currency were among the mathematical issues that the Egyptians utilized fractions to solve because they were the first civilization to understand fractions.

Given:

7 / 4 + 1 / 2 + 5 / 3 + 1 / 3 + 1 / 4 + 1 / 2

Rearrange the number as shown below,

7 / 4 + 1 / 4 + 1 / 2 + 1 / 2 + 5 / 3 + 1 / 3

Add the like terms as shown below,

(7 + 1) / 4 + (1 + 1) / 2 + (5 + 1) / 3

8 / 4 + 2 / 2 + 6 / 3

Divide the terms as shown below,

2 + 1 + 2

5

Thus, the addition is 5.

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Answer:

The slope is -1  (option C in your list)

Step-by-step explanation:

We use the formula for the slope:

slope = (4 - (-1))/ (-3 - 2) = 5 / -5 = -1

The simplification of the fraction 1/3(5x-8) + 2/3 of x is (7x-8)/3

Simplified fractions are the fractions in their lowest, reduced and simplest form. The numerator and denominator of the fraction are reduced to an extent.

For example to simplify 25/100 , we find a common factor that can go through the two terms. 25 is a common factor . therefore 25/100 = 1/4

To simplify 1/3(5x-8) + 2/3 of x

By opening the parentheses

5x/3- 8/3+2x/3

therefore we have (5x-8+2x)/3

= (7x-8)/3

This means that the simplification of 1/3(5x-8) + 2/3 of x is (7x-8)/3

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Spotify charges $0.98 for individual song and $10 for entire album

According to the question,

Spotify charges "x" dollars for individual songs and "y" for entire album

Also, Person A pays $14.9 to download 5 individual songs and 1 album

Which can be written as

=> 5x + y = 14.9 --------------(1)

Person B pays $22.95 to download 3 individual songs and 2 albums

=> 3x + 2y = 22.95 ---------(2)

Solving these two linear equations by elimination method

Multiplying equation (1) by 2

=> 10x + 2y = 29.8

Now, subtracting these equation

10x + 2y - 3x - 2y = 29.8 - 22.95

=> 7x = 6.85

=> x = 0.98

Replacing value of x in equation (1),

=> 5(0.98) + y = 14.9

=> 4.9 + y = 14.9

=> y = 10

Hence , Spotify charges $0.98 for individual song and $10 for entire album

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The percentage of people have an IQ score less then 77 to the nearest tenth is 0.9

The ratio of sum of observations to the total number of observation is known as mean. It is one of the central tendency in the statistics. It gives an idea about the central value present in the data. The most sensitive measure of central tendency is mean. It is very easy to calculate. Mean playa a crucial role in daily life. The two types of means are Arithmetic mean and Geometric mean.

Standard deviation is a measure in the statistics. The amount of variation of a set of values is known as standard deviation. Standard deviation is denoted by σ.

P(x<77)

By using normal distribution,

Z= x-μ/σ

Z= (77-100)/15

Z=23/15=1.533

p(Z<1.533)= 0.9370

Therefore, the percentage of people have an IQ score less then 77 to the nearest tenth is 0.9

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Answer: -80

Step-by-step explanation:

4. Compute the derivative.

\(y = 2x^2 - x - 1 \implies \dfrac{dy}{dx} = 4x - 1\)

Find when the gradient is 7.

\(4x - 1 = 7 \implies 4x = 8 \implies x = 2\)

Evaluate \(y\) at this point.

\(y = 2\cdot2^2-2-1 = 5\)

The point we want is then (2, 5).

5. The curve crosses the \(x\)-axis when \(y=0\). We have

\(y = \dfrac{x - 4}x = 1 - \dfrac4x = 0 \implies \dfrac4x = 1 \implies x = 4\)

Compute the derivative.

\(y = 1 - \dfrac4x \implies \dfrac{dy}{dx} = -\dfrac4{x^2}\)

At the point we want, the gradient is

\(\dfrac{dy}{dx}\bigg|_{x=4} = -\dfrac4{4^2} = \boxed{-\dfrac14}\)

6. The curve crosses the \(y\)-axis when \(x=0\). Compute the derivative.

\(\dfrac{dy}{dx} = 3x^2 - 4x + 5\)

When \(x=0\), the gradient is

\(\dfrac{dy}{dx}\bigg|_{x=0} = 3\cdot0^2 - 4\cdot0 + 5 = \boxed{5}\)

7. Set \(y=5\) and solve for \(x\). The curve and line meet when

\(5 = 2x^2 + 7x - 4 \implies 2x^2 + 7x - 9 = (x - 1)(2x+9) = 0 \implies x=1 \text{ or } x = -\dfrac92\)

Compute the derivative (for the curve) and evaluate it at these \(x\) values.

\(\dfrac{dy}{dx} = 4x + 7\)

\(\dfrac{dy}{dx}\bigg|_{x=1} = 4\cdot1+7 = \boxed{11}\)

\(\dfrac{dy}{dx}\bigg|_{x=-9/2} = 4\cdot\left(-\dfrac92\right)+7=\boxed{-11}\)

8. Compute the derivative.

\(y = ax^2 + bx \implies \dfrac{dy}{dx} = 2ax + b\)

The gradient is 8 when \(x=2\), so

\(2a\cdot2 + b = 8 \implies 4a + b = 8\)

and the gradient is -10 when \(x=-1\), so

\(2a\cdot(-1) + b = -10 \implies -2a + b = -10\)

Solve for \(a\) and \(b\). Eliminating \(b\), we have

\((4a + b) - (-2a + b) = 8 - (-10) \implies 6a = 18 \implies \boxed{a=3}\)

so that

\(4\cdot3+b = 8 \implies 12 + b = 8 \implies \boxed{b = -4}\).

The maximum and minimum points of the function are (a) (3π/2, -1) (-π/2, -1), (π/2, 3)

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

y = –2 cos (x + π/2) + 1.

Calculating the maximum

Here, we have

y = –2 cos (x + π/2) + 1.

Next, we plot the graph of the function

From the graph of the function, we have the maximum points to be (π/2, 3)

Calculating the minimum

Here, we have

y = –2 cos (x + π/2) + 1.

Next, we plot the graph of the function

From the graph of the function, we have the minimum points to be

(3π/2, -1) (-π/2, -1)

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Answer:.

Step-by-step explanation im not sure

Answer:

Step-by-step explanation:

47.)  sin20 = 6/b

b = 6(sin20) = 17.5

c = √6²+17.5² = 18.5

48.)  tan61 = y/18

y = 18(tan61) = 32.5

z = √18²+32.5² = 37.1

49.)  r = √25²+23² = 34

50).  d = √30²+7² = 30.8

51.)  sin71 = j/19

j = 19(sin71) = 18

k = √19²-18² = 6.2

52.)  y = √4²-1² = √7 = 2.6

53.)  sin49 = f/26

f = 26(sin49) = 19.6

h = √26²-19.6² = 17

54.)  t = √7²+4² = 8.1

Answer: Sam was 2.5 Km far from his house

Step-by-step explanation:

Sam's parents gave him a map to reach his house.

As per Map Sam was =1.5cm from his home.

To find actual distance from house

If we consider actual distance  of sam house =X

We have,

If each 3 cm on scale drawing equals 5 km

We know on map 3cm  = 5Km

If 1.5 cm = X Km

We need to cross multiple

 3X =1.5 × 5

 3X = 7.5

X= 7.5÷3

X= 2.5 Km

Sam was 2.5 Km far from his house.

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Answer:

Step-by-step explanation:

take 32 degree as reference angle

using sine rule

sin 32=opposite/hypotenuse

0.52=x/13

0.52*13=x

6.76=x

Answer:

380 seconds

Step-by-step explanation:

Convert 6 minutes to seconds by multiplying 6 times 60, because there are 60 seconds per minute.
6 x 60 = 360

Now add the 20 seconds.
360 + 20 = 380

6 minutes and 20 seconds are equal to 380 seconds.

Answer:

perimwter = 2(4x-6 + 2x+4) = 2 (6x-2) = 12x-4

The solutions are x = -1 and y = 3 of the given system of equations 2x+y=1, −3x+4y=15 which is determined by Cramer's rule.

We put the tiles in the right order and entered the final result for each x and y.

The main principle is to split determinants as shown by the vertical bars (these are not absolute value bars).

The determinant of the matrix \(\begin{bmatrix}2 & 1 \\-3 & 4 \\\end{bmatrix}\), which are the coefficients of the left-hand side of each original equation supplied to you, is in each denominator.

This matrix's numerators are somewhat different. The x determinant requires you to replace the first column with 1 and 15 to produce \(\begin{bmatrix}1 & 1 \\15 & 4 \\\end{bmatrix}\), which aids in determining the x solution. The y solution is similar, except we replace the y column rather than the x column. This explains the \(\begin{bmatrix}2 & 1 \\-3 & 15 \\\end{bmatrix}\).

You just evaluate each determinant using the formula once you have the right determinants in place and then simplify the outcomes.

Thus, the solutions are x = -1 and y = 3 of the given system of equations 2x+y=1, −3x+4y=15 which is determined by Cramer's rule.

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The required information required to show that the triangles are congruent are;

5) A) ∠ZXY ≅ ∠TXY

6) A) \(\overline{JH}\) ≅ \(\overline{NH}\)

7) D) ∠X ≅ ∠Y

8) C) ∠B ≅ ∠S

9) A) \(\overline{FE}\) ≅ \(\overline{DL}\)

10) D) \(\overline{KI}\) ≅ \(\overline{RT}\)

Congruent triangles are triangles in which their corresponding sides and angles are equivalent.

5) The indicated rule is ASA; Angle-Side-Angle

∠XYT ≅ ∠XYZ (Indicated markings)

\(\overline{XY}\) ≅ \(\overline{XY}\) (Reflexive property)

Required information for ASA is; ∠ZXY ≅ ∠TXY

The correct option is therefore;

A) ∠ZXY and ∠TXY

6) The congruence rule is LL; (Leg-Leg)

The vertex angles at the point the triangles meet are congruent angles, which are 90 degrees angle.

The required information are therefore; \(\overline{JH}\) ≅ \(\overline{NH}\)

The correct option is therefore;

A)\(\overline{JH}\) ≅ \(\overline{NH}\)

7) The congruence rule is AAS; Angle-Angle-Side

∠XYZ ≅ ∠EYZ

\(\overline{YZ}\) ≅ \(\overline{YZ}\) (Reflexive property)

The required information is therefore; ∠X ≅ ∠Y

The correct option is; D) ∠X ≅ ∠Y

8) The congruence rule is ASA; Angle-Side-Angle

\(\overline{CB}\) ≅ \(\overline{TS}\)

The required information is; ∠B ≅ ∠S

The correct option is therefore; C) ∠B ≅ ∠S

9) The congruence rule is LL; Leg-Leg

\(\overline{FD}\) ≅ \(\overline{DF}\) (Reflexive property)

The required information is therefore; \(\overline{FE}\) ≅ \(\overline{DL}\)

The correct option is therefore; A) \(\overline{FE}\) ≅ \(\overline{DL}\)

10) The congruence rule is LL; Leg-Leg

The congruent legs are; \(\overline{IJ}\) and \(\overline{TS}\)

The required information are therefore; \(\overline{KI}\) ≅ \(\overline{RT}\)

The correct option is therefore;

D)  \(\overline{KI}\) ≅ \(\overline{RT}\)

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Answer:

y=7

Step-by-step explanation:

-3(-3)-y=2

9-y=2

9-2=y

y=7

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Answer:

15-20i

Step-by-step explanation:

Hello,

When l =-1

6+l = 6-1 = 5

and 5(3-4i)=15-20i

Thanks

A mean is an arithmetic average of a set of observations. The mean height of the five students is 148.

A mean is an arithmetic average of a set of observations. it is given by the formula,

Mean = (Sum of observations)/Number of observations

Given that the mean height of three boys is 150 centimeters. Therefore, the sum of height of the three boys is,

Mean Height of boys = Sum of height of boys / Number of boys

150 = Sum of height of boys/ 3

Sum of height of boys = 150 x 3 = 450

Also, given that the mean height of two girls is 145 centimeters. Therefore, the sum of height of the two girls is,

Mean Height of girl = Sum of height of girls/ Number of girls

145 = Sum of height of girls/ 2

Sum of height of girls = 145 x 2 = 290

Further, the mean height of five students is,

Mean height of five students = Sum of height of students / Number of students

Mean height of five students = (450 + 290)/ 5

Mean height of five students = 740 / 5

                                                = 148

Hence, the mean height of the five students is 148.

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Answer:

Step-by-step explanation:

Answer:

23 + 31

Step-by-step explanation:

Answer:  Choice B)  \(\sqrt{2}\)

Work Shown:

\(\sec^2(\theta) = \tan^2(\theta) + 1\\\\\sec^2(\theta) = (\tan(\theta))^2 + 1\\\\\sec^2(\theta) = (-1)^2 + 1\\\\\sec^2(\theta) = 2\\\\\sec(\theta) = \sqrt{2}\\\\\)

Note: secant is positive in quadrant Q4, when theta is between 3pi/2 radians and 2pi radians (270 degrees and 360 degrees). So that's why we don't consider the minus form of the plus minus.

Answer:

82° because

98° + 70° = 168°

360° - 168° = 192°

192° is for two angles, so it can't be 192°, 220°

it's not VERY obtuse angle. So it remains only 82°

Answer:

B and C are correct

Step-by-step explanation:

Answer: 9/5

Step-by-step explanation:

Answer:

Step-by-step explanation:

To simplify the expression 3 x (3/4) whole to a unit fraction, we can start by multiplying the whole number 3 by the denominator of the fraction, which is 4:

3 x (3/4) = (3 x 4)/4 x (3/4) = 12/4 x 3/4

We can simplify the fraction 12/4 by dividing both the numerator and denominator by 4:

12/4 = 3

Substituting this back into the expression, we have:

3 x (3/4) = 3/1 x (3/4) = 9/4

Therefore, 3 x (3/4) whole is equal to the unit fraction 9/4.