HELP PLS: If f(x) = 2x – 3 and g(x) = 2x2 + 5x + 1, find:
a. f(4) + g(1)

The area of a triangle with sides a = 20, b = 15, and c = 25 is 150.

The sides of the triangle are given as a = 20, b = 15, and c = 25.

We will use Hero's formula to find the area of this triangle.

It is a three-face polygon that consists of three edges and three vertices.

We use Heron's formula to find the area of a triangle with 3 sides:

Herons formula:

Area of a triangle =  \(\sqrt{s(s-a)(s-b)(s-c)}\\\)

Where a, b, and c are sides of a triangle.

And s = semi perimeter of a triangle.

s = \(\frac{a+b+c}{2}\)

If the sum of two sides of a triangle is greater than the third side of a triangle then the sides of a triangle are true.

Let the given sides be:

a = 20, b = 15 and c = 25.

(20 + 15) > 25

(20 + 25) > 15

(15 + 25) > 20 so the given sides are true.

Now,

Semi perimeter of the triangle:

s = (a+b+c) / 2

s = (20+15+25) / 2

s = 60 / 2

s = 30

Putting s = 30 in the area of the triangle.

we get,

Area of the triangle = \(\sqrt{s(s-a)(s-b)(s-c)}\\\)

Area of the triangle = \(\sqrt{30(30-20)(30-15)(30-25)}\\\\\sqrt{30\times10\times15\times5}\\\\\sqrt{22500}\\\\150\)

Thus, the area of a triangle is 150.

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Answer:

P=a+b+c

=42+17+62

=121

P=42+b+c

P=42+17+c & same as p=59+c

P=42+17+62 & same as p=121

Answer:

75%

Step-by-step explanation:

Put the number of shots she made as to the numerator and the shots there were as the denominator: 36/48

We must reduce this fraction to the lowest terms.

36/48 ÷ 12/12 = 3/4

3/4 as a percent is the same as 75/100 or 75%

Answer: 75%

Answer:

She had missed 75%

Step-by-step explanation:

36/48 shots is equal to 75/100

which equals 75%

Answer:

6x + 9 = 27

       -9     -9

6x = 18           Now divide both sides by 6

/6      /6            so the answer is 3

Step-by-step explanation:

Answer:

about 169.65

Step-by-step explanation:

The formula for the volume of a cylinder is \(\pi r^2h\).

All you have to do is plug the numbers in.

\(V=\pi (3)^2(6)\)

Then use a calculator to evaluate.

The volume of the cylinder is approximately 169.56 cubic units.

The formula for the volume of a cylinder is:

V = πr^2h

where V is the volume, r is the radius of the base, and h is the height.

Substituting the given values, we get:

V = π(3)^2(6)

V = π(9)(6)

V = 54π

Therefore, the volume of the cylinder is 54π cubic units. If you need an approximate numerical value, you can use the approximation 3.14 for π and calculate:

V ≈ 54 x 3.14

V ≈ 169.56

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The correct question is :

What is the volume of a cylinder with a base radius of 3 units and height of 6 units?

The value of the given integral is: v = [(4√(3) - 5)π/3]

To evaluate the given integral, let's calculate it step by step:

First, let's integrate with respect to z from 1 to √(4 - x² - y²):

∫[1, √(4 - x² - y²)] dz = √(4 - x² - y²) - 1

Next, let's integrate the above expression with respect to y from -√(3 - x²) to √(3 - x²):

∫[-√(3 - x²), √(3 - x²)] (√(4 - x² - y²) - 1) dy

To simplify the integration, let's convert to polar coordinates:

x = r cosθ

y = r sinθ

The bounds of integration in polar coordinates will be:

r: 0 to √(3)

θ: 0 to 2π

Now, we can rewrite the integral in terms of polar coordinates:

∫[0, 2π] ∫[0, √(3)] (√(4 - r²) - 1) r dr dθ

Evaluating the inner integral with respect to r:

∫[0, 2π] [(-1/3) (4 - r²)\(^{3/2}\) - (1/2) r²] | [0, √(3)] dθ

∫[0, 2π] [(2√(3)/3) - (1/3)(4 - 3)\(^{3/2}\) - (1/2)(√(3))²] dθ

Simplifying further:

∫[0, 2π] [(2√(3)/3) - (1/3) - (3/2)] dθ

∫[0, 2π] [(2√(3)/3) - (5/6)] dθ

Now, integrating with respect to θ:

[(2√(3)/3)θ - (5/6)θ] | [0, 2π]

[(2√(3)/3)(2π) - (5/6)(2π)] - [(2√(3)/3)(0) - (5/6)(0)]

[(4√(3)/3)π - (5/3)π] = [(4√(3) - 5)π/3]

Therefore, the value of the given integral is: v = [(4√(3) - 5)π/3]

Complete Question:

Evaluate the integral:

v = ∫∫∫ [−√3, √3] [−√(3−x²), √(3−x²)] [1, √(4−x²−y²)] dz dy dx

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Answer:

slope= -3,y - intercept y = -2

Step-by-step explanation:

- Make y the subject by taking four on the opposite side of the equal sign.

2y = -6x - 4

- Divide throughout by 2 and from there you get the gradient which is also the slope.

- To get the y - intercept,the value of x =0. Thus you get y =-2.

1. The balloon's initial temperature was ____ °C.

2. The temperature of the oil is ____ °C.

1. To find the balloon's initial temperature, we can use the combined gas law, which states that the initial pressure times the initial volume divided by the initial temperature is equal to the final pressure times the final volume divided by the final temperature. Given that the volume changes to 76.4% of its initial volume and the final temperature is -80.0 °C, we can solve for the initial temperature. First, we convert the volume change to a decimal by dividing 76.4% by 100, giving us 0.764. Plugging in the values into the combined gas law equation, we can rearrange it to solve for the initial temperature.

2. To determine the temperature of the oil, we can use the ideal gas law, which states that the pressure times the volume divided by the temperature is equal to the gas constant times the number of moles. Since the volume remains constant and we are given the initial and final pressures, we can solve for the temperature. By plugging in the values into the ideal gas law equation and solving for the temperature, we can find the temperature of the oil in °C.

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The AC is 18 feet long.

Triangles are primarily involved in the mid-point theorem. According to this rule, if the midpoints of any two triangle sides are connected, the line formed is parallel to the third side and equal to half of the third side. Contrarily, if a parallel line is drawn from one side's midpoint to any other, it will bisect the third side and be equal to half the side to which it is parallel.

As shown in the diagram,

AM = MB, CN = NB.

The midpoints of the sides AB and CB, respectively, are M and N.

So, according to the midpoint theorem,

MN ║ AC,

The alternative interior angle theorem demonstrates that

∠BMM ≅∠BAC

∠BNM ≅∠BCA

According to the AA similarity postulate,

ΔBMM ≅∠BAC

The characteristic of identical triangles

\(\frac{BM}{BA} = \frac{MN}{AC}\\ \frac{BM}{BM+MA} = \frac{MN}{AC}\\ \frac{4}{4+4} = \frac{9}{AC}\\ \frac{4}{8} =\frac{9}{AC} \\\)

4AC=72

AC=18 ft

As a result, AC is 18 feet long.

The complete question is:-

What is the length of the AC?

3 ft

4 ft

9 ft

18 ft

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The distance between the points (5, 5) and (-3, 7) is approximately 8.2 units (option a).

To find the distance between two points (x₁, y₁) and (x₂, y₂), we can use the distance formula:

Distance = √((x₂ - x₁)² + (y₂ - y₁)²)

For the given points (5, 5) and (-3, 7), the distance formula becomes:

Distance = √((-3 - 5)² + (7 - 5)²)

= √((-8)² + 2²)

= √(64 + 4)

= √68

≈ 8.2

Therefore, the distance between the points (5, 5) and (-3, 7) is approximately 8.2 units.

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The laptop will be worth $0.001286 after 15 years if its worth becomes 1/3 each year.

We can solve this problem by using the formula for geometric sequences,

an = a₁r^(n-1), here in this case, an is the worth of the laptop after n years, r is the rate at which the worth is changing that 1/3 in this case and a₁ is the value of the laptop currently. Substituting the given values, we get:

a₁₅ = 600(1/3)¹⁵⁻¹

a₁₅ = 600(1/3)¹⁴

a₁₅ = 600x0.0000021433

a₁₅ = 0.001286

Therefore, after 15 years, the laptop is worth approximately $0.001286.

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Answer:

option 4

Step-by-step explanation:

its 4 my dude .......

Answer:

location

Step-by-step explanation:

orientation doesn't change

shape doesn't change

size doesn't change

number of sides doesn't change

location does change

Given the dimensions of the triangle, QPR is as follows:

angle QPR =90^circle

Side QP = 8 sqrt3 units

Side PR = 8 units

To find, side QR =? units

Please refer to the attached figure for the representation of the given dimensions.

The base is side QP,

Perpendicular is side PR and

Hypotenuse is side QR.

In a right-angled triangle, the Pythagorean theorem holds i.e.

According to Pythagoras theorem:

text {Hypotenuse}^ {2} = text {Base}^ {2} + text {Perpendicular}^ {2}

=            QR^ {2} = QP^ {2} + PR^ {2}

Putting the values of QP and PR:

=           QR^ {2} = (8sqrt3) ^ {2} + 82} = QR^ {2} = 64 times 3+ 64 QR^ {2}

= 64 times 4 QR = 8 times 2 QR = 16 units.

So, the value of the length of the side QR is 16 units.  

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Answer:

16.   Angle 2 is 30° and angles 1 & 3 are 150°

17. Equilateral (all sides are equal)

18. A, B, D

19. A, B. (8 angles and all sides are congruent)

20. False.

Step-by-step explanation:

angle 2 is a corresponding (ish) angle to the one marked 30°, so they are the same. and then the other angle is supplementary to the 30° one, therefore they must add up to 180 degrees. 180-30= 150 so that is angle 1 and 3.

Answer:

question 1 - angle 1 and 2 the answer is 150 and angle 3 is 30

question 2 - the triangle is an equilateral

Question 3 - A,B,D

question 4 - A,B

Step-by-step explanation:

Answer:

There are 10 mm in one cm, so 100 mm is equal to 10 cm.

Let me know if this helps!

The MMPI-2 test is used for the assessment of psychopathology and personality of patients.

It includes 567 true-false questions, resulting in 10 clinical scales, among which one is the anxiety subscale.

A score of 30 or less is usually considered very low.

The questions are answered by the patient, usually in a clinical or research setting.

A one-sample t-test is conducted in the problem, whereby a sample of 18 participants in a yoga group is tested for anxiety scores.

The following are the parameters of the one-sample t-test:Groups:

18 participants

Null hypothesis: The anxiety scores of Felipe's yoga group are statistically equal to 30." value: 30

Type of test: One-tailed test

Alternative hypothesis: The anxiety scores of Felipe's yoga group are greater than 30.

Degrees of freedom: n - 1 = 17T-observed value: (35.2 - 30) / (10.4 / sqrt(18)) = 2.41T-critical value: 1.734

Reject or retain null hypothesis: Since the t-observed value (2.41) is greater than the t-critical value (1.734), Felipe should reject the null hypothesis, which implies that his yoga group's scores are greater than 30.P-value: 0.014Cohen’s d value: (35.2 - 30) / 10.4 = 0.5

If the " value were reduced to 0.01, Felipe would still reject the null hypothesis, since the p-value (0.014) is lower than the alpha level (0.01).

For the sample mean: 35.2CI for 42%: 35.2 ± 0.58CI for 79%: 35.2 ± 1.16CI for 95%: 35.2 ± 2.13

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Answer:

its F

Step-by-step explanation:

Its f since when you do the reflection on a grid you will get (1,-4)  No problem ;D

The point at which the line intersects the given plane x = 1 − t, y = 5 t, z = 2t; x − y +4z = 2

(x, y, z) =(1/2 ,5/2, 1)

The point at which the line intersects the given plane x = 1 − t, y = 5 t, z = 2t; x − y -4z = 2

(x, y, z) = (15/14,-5/14, -1/7)

The points on the line are x = 1 − t, y = 5 t, z = 2t

a) When Equation of Plane is x- y+ 4z = 2

The point of intersection of a line and a plane is the point where the meet each other and passes after.

Thus, we can rewrite the equation of plane with the values of x, y, z as x = 1 − t, y = 5 t, z = 2t, we get,

(1-t) - 5t +4(2t) = 2

⇒ 1 - 6t + 8t = 2

⇒2t = 1

⇒ t = 1/2 (= 0.5)

Putting t= 1/2 in x = 1 − t, y = 5 t, z = 2t, we get

x= 1- 1/2 = 1/2

y= 5(1/2) = 5/2  , and

z= 2(1/2) = 1

At x=1/2 , y= 5/2 and z=1 the given line intersects the plane  x- y+ 4z = 2.

b) When Equation of Plane is x- y- 4z = 2

The point of intersection of a line and a plane is the point where the meet each other and passes after.

Thus, we can rewrite the equation of plane with the values of x, y, z as x = 1 − t, y = 5 t, z = 2t, we get,

(1-t) - 5t -4(2t) = 2

⇒ 1 - 6t - 8t = 2

⇒-14t = 1

⇒ t =- 1/14

Putting t= -1/14 in x = 1 − t, y = 5 t, z = 2t, we get

x= 1-(- 1/14) = 15/14

y= 5(-1/14) = -5/14 , and

z= 2(-1/14) = -1/7

At x=15/14, y=-5/14 and z= -1/7 the given line intersects the plane (x-y-4z = 2).

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Answer:

90 degrees

Step-by-step explanation:

a triangles angles add up to 180

this means that you can add all the angles together and get 180

you can first add 30 and 60 and then subtract the sum from 180

30 + 60 = 90

180 - 90 = 90

the last angle is 90 degrees

Hey ! there

Answer:

Step-by-step explanation:

In the question we are given with two angles of the triangles that are 30° and 60° . And we are asked to find the third angle of triangle .

For solving this question we must have knowledge of angle sum property which says that the sum of all the angles which are present inside the triangle ( interior angles ) is equal to 180°.

Solution : -

As we know that ,

So ,

\( \longmapsto \qquad \: 30° + 60° + x° = 180°\)

Step 1 : Adding 30° and 60° :

\( \longmapsto \qquad \:90° + x° = 180° \)

Step 2 : Subtracting 90° from both sides :

\( \longmapsto \qquad \: \cancel{90°} - \cancel{90 ° } + x° = 180° - 90° \: \)

On further calculations , We get :

\( \longmapsto \qquad \: \blue{\underline{\boxed{\frak{x° = 90°}}}}\)

Verifying : -

Now we are verifying our answer by adding all the angles of triangle and equating them with 180° because of angle sum property. So ,

Therefore, our solution is correct .

In this case, the monthly payment for the car loan would be approximately $1,299.13.

To calculate the monthly payment for a bank loan using Excel, you can use the PMT function.

Here's how to do it:

1. Open Excel and create a new spreadsheet.

2. In cell A1, enter the loan amount: -40000 (negative because it's an outgoing payment).

3. In cell A2, enter the annual interest rate: 9%.

4. In cell A3, enter the loan duration in years: 3.

5. In cell A4, enter the formula to calculate the monthly payment: =PMT(A2/12, A3*12, A1).

6. The result in cell A4 will be the monthly payment.

So, in this case, the monthly payment for the car loan would be approximately $1,299.13.

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Answer:

65, 140, 40

Step-by-step explanation:

1. ∠ZXY is on the circle, m∠ZXY = 130/2 = 65°

Do 3) first

3) ∠SVY is inside the circle, so

m∠SVY = 1/2 * (arc SY + arc XR) = 1/2 * (40 + 40) = 40°

2) m∠XVS = 180° - m∠XVS = 180 - 40 = 140°

Answer:

5) 7

6) 14

7) 31

Step-by-step explanation:

5) 5a-4=2a+17

3a=21

a=7

6) 2(7)=14

7) 2(7)+17=31

4. C

5. 2a + 17 = 5a - 4

- 3a = - 21

a = 7

6. XY = 2(7) = 14

7. XZ = 5(7) - 4

= 31

When P = 90 lb/in^2 and V = 70 in^3, the pressure P is increasing at a rate of 14 lb/in^2/sec.

According to Boyle's law, PV = c, where P is pressure, V is volume, and c is a constant. We are given that V is decreasing at a rate of 11 in^3/sec, and we need to find the rate at which P is increasing when P = 90 lb/in^2 and V = 70 in^3.

Step 1:

Differentiate the equation PV = c with respect to time (t). This gives us:
(d(PV)/dt) = (P(dV/dt) + V(dP/dt)) = 0

Step 2:

Plug in the given values and rates. P = 90 lb/in^2, V = 70 in^3, and dV/dt = -11 in^3/sec (negative because V is decreasing):
(90)(-11) + (70)(dP/dt) = 0

Step 3:

Solve for dP/dt:
-990 + 70(dP/dt) = 0

Step 4:

Isolate dP/dt:
70(dP/dt) = 990
dP/dt = 990/70

Step 5:

Simplify to get the rate at which P is increasing:
dP/dt = 14 lb/in^2/sec

So, the pressure P is increasing at a rate of 14 lb/in^2/sec.

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Answer:

72π

Step-by-step explanation:

The volume of the composite figure can be calculated by finding the sum of the volumes of the half-sphere and the cylinder. Hence, the exact volume of the composite figure is 108π cubic centimeters.

Volume is a three-dimensional measurement of the amount of space a thing takes up. It is usually measured in cubic meters, cubic centimeters, or cubic feet. It is computed by multiplying the length, breadth, and height of the shape, or by using particular formulae for other forms such as cylinders, cones, or spheres. The volume of a thing indicates how much space it takes up.

The volume of the composite figure can be calculated by finding the sum of the volumes of the half-sphere and the cylinder.

The formula for the volume of a cylinder is

V = π\(r^2h\),

where r is the radius and h is the height.

Substituting the values given in the problem, we get:

Volume of cylinder = π\((3)^2(10)\)

                  = 90π cubic centimeters.

The formula for the volume of a half-sphere is

V = (2/3)π\(r^3\)

Substituting the value of r given in the problem, we get:

Volume of half-sphere = (2/3)π\((3)^3\)

                        = 18π cubic centimeters.

Therefore, the total volume of the composite figure is:

Volume of composite figure = Volume of cylinder + Volume of half-sphere

= 90π + 18π

= 108π cubic centimeters.

Hence, the exact volume of the composite figure is 108π cubic centimeters.

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Answer: Isosceles acute

Step-by-step explanation:

A acute triangle has all angles less than 90 degrees. An isosceles triangle have 2 equal sides

Answer:

38 students per bus

Step-by-step explanation:

225-35=190

90/5=38

The square MATH has equal side lengths MA, TH, AT and HM

Hanna's claim is correct because

The coordinate points are given as:

M(1, 2), A(-5, 3), T(-6,-3), and H(0,- 4).

Calculate the side lengths of the square using the following distance formula

d = √[(x2 - x1)^2 + (y2 - y1)^2]

So, we have:

MA = √[(1 + 5)^2 + (2 - 3)^2] = √37

AT = √[(-5 + 6)^2 + (3 + 3)^2] = √37

TH = √[(-6 + 0)^2 + (-3 + 4)^2] = √37

HM = √[(0 - 1)^2 + (-4 - 2)^2] = √37

The side lengths are equal.

Next, we calculate the slopes using:

m =(y2 - y1)/(x2 - x1)

So, we have:

MA = (2-3)/(1+5) = -1/6

AT = (3+3)/(-5+6) = 6

TH = (-3+4)/(-6+0) = -1/6

HM = (-4-2)/(0-1) = 6

See that opposite sides have the same slope

i.e MA = TH and AT = HM

And adjacent sides have their slopes to be opposite reciprocals

i.e. MA = -1/AT and TH = -1/HM

The calculated distances and slopes implies that Hanna's claim is correct

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The 200 km, 100 km, and 400 km distances traveled by the airplane at bearings of 335°, 170°, and 288°, respectively, indicates;

a) The displacement of the airplane when it lands is 485.56 kilometers

b) The bearing the airplane could have flown to complete the journey directly is 288.27°

A bearing is the measurement in degrees of an angle from the north direction

a) The path of the airplane can be represented using vectors as follows;

A bearing of 335° = N 25° W

Therefore;

\(\vec{d_1}\) = -200·sin(25°)·i + 200·cos(25°)·j

A bearing of 170° = S 10° E

Therefore;

\(\vec{d_2}\) =  100·sin(10°)·i - 100·cos(10°)·j

A bearing of 280° = N 80° W

Therefore;

\(\vec{d_3}\) = -400·sin(80°)·i + 400·cos(80°)·j

The resultant displacement of the airplane, can be found by adding the above displacement vectors as follows;

R = (100·sin(10°)-200·sin(25°) - 400·sin(80°))·i + ((200·cos(25°) - 100·cos(10°) + 400·cos(80°))·j = -461.08·i + 152.24·j

The distance of the airplane from the start is therefore;

|R| = √((-461.08)² + 152.24²) ≈ 485.56

b) The direction of the airplane obtained from the resultant vector can be presented as follows;

\(\theta = arctan\left(\dfrac{152.24}{-461.08\right)}\approx -18.27^{\circ}\)

From the other possible values of the angle, θ, we get;

θ = 180° - 18.27° ≈ 161.73°

The 161.73° is measures from the positive x-axis, and therefore is in Quadrant II

The bearing is therefore 270° + the measure of the 161.73° above the negative x-axis, which indicates;

The bearing = 270° + 180° - 161.73° = 288.27°

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The answer to the simplified expression 4⁹/4³ in index form is derived to be equal to 4⁶

To simplify a fraction written in index form, you can first express the numbers in prime factorization form by writing both the numerator and denominator as a product of prime factors. Identify common prime factors in the numerator and denominator and cancel them out. Then write the remaining factors as a product in index form.

Given the fraction 4⁹/4³, we can simplify as follows:

4⁹/4³ = (4 × 4 × 4 × 4 × 4 × 4 × 4 × 4 × 4)/(4 × 4 × 4)

we can cancel out (4 × 4 × 4) from both the numerator and denominator, living us with;

4⁹/4³ = 4 × 4 × 4 × 4 × 4 × 4

4⁹/4³ = 4⁶

Therefore, the answer to the simplified expression 4⁹/4³ in index form is derived to be equal to 4⁶

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