For questions 3 – 4, use the following functions:
f(x) = 2x+3
g(x)= x+ + -7
3. Find (f + g)(x).
+

Answer:

1.49 is the answer.

Step-by-step explanation:

3 ÷ 2.009

=> 1.49328023892

≈ 1.49

Hoped this helped.

Answer:

22

Step-by-step explanation

nickels are 5 cents so 5 times 4 is 20 and pennies are 1 cent so 2 times 1 is 2

20+2 = 22 cents

Answer:

22 cents

Step-by-step explanation:

1 nickel = 5 scents  

1 penny = 1 scent

4 times 5 = 20

2 times 1 = 2

20 + 2 = 22

Hope that helps!

The solution to the system of equations is x = -3 and y = -4.

To solve the system of equations:

Equation 1: 2x - y = -10

Equation 2: 3x + 2y = -1

We can use the method of substitution or elimination to find the values of x and y.

Let's use the method of elimination:

Multiply Equation 1 by 2 to make the coefficients of y in both equations equal:

2(2x - y) = 2(-10)

4x - 2y = -20

Now, we can eliminate y by adding Equation 2 and the modified Equation 1:

(3x + 2y) + (4x - 2y) = -1 + (-20)

7x = -21

x = -3

Substitute the value of x into Equation 1 to solve for y:

2(-3) - y = -10

-6 - y = -10

y = -10 + 6

y = -4

Therefore, the solution to the system of equations is x = -3 and y = -4.

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Answer:

a

Step-by-step explanation:

πr2h=π·42·3≈150.79645

and then we round

Answer:

(12 ÷ 4) × (18 ÷ 6)

Step-by-step explanation:

(12 ÷ 4) × (18 ÷ 6)

If we solve this or simply this, we would get 9 as our result.

Let's solve and see. Mind you, we've used each of the given numbers just once in the expression.

Thus:

(12 ÷ 4) × (18 ÷ 6)

Solve the parentheses first

3 × 3 = 9.

Therefore,

(12 ÷ 4) × (18 ÷ 6) = 9

Answer: The required three consecutive odd integers are 7, 9 , 11.

Step-by-step explanation:

Let x , x+2 , x+4 be the three consecutive odd integers.

As per given ,  

10(x) = 59+x+4

⇒10x= 59+x+4

⇒ 9x= 63

⇒ x= 7   [ divide both sides by 7]

Hence, the required three consecutive odd integers are 7, 9 , 11.

Answer:

C

Step-by-step explanation:

Each slope down in the graph represents a drink. so the first drink ended at 30 sec and the second one started at 60 sec so he waited 30 sec inbetween.

Based on the image attached, the solution for GE  is approximately 22.72.

To  be able to solve the equation √129 + √129 = GE, one need to simplify the  expression and then isolate GE.

Step 1: One can add the square roots:

Note that the equation:

√129 + √129 = GE.

Step 2:  Do put together the square root terms:

2√129 = GE.

Step 3:  Then Divide by 2:

√129 = GE/2.

Step 4: The Square both sides:

129 = (GE²)/4.

Step 5: So, Multiply by 4:

516 = GE².

Lastly, Take the square root:

√516 = √(GE²)

√516 = GE

GE = 22.72. approx.

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See text below



Step 26

Solve the equation for GE:

√129+√129 = GE

GE=2/129

Show steps

Answer:

Step-by-step explanation:

Starting with the first equation:

4(0.8f - 0.5) = -0.4

Simplifying:

3.2f - 2 = -0.4

Adding 2 to both sides:

3.2f = 1.6

Dividing by 3.2:

f = 0.5

Therefore, f equals 0.5.

Moving on to the second equation:

2/3(t + 9) = -4

Multiplying both sides by 3/2:

t + 9 = -6

Subtracting 9 from both sides:

t = -15

Therefore, t equals -15.

Answer:

Step-by-step explanation:

To show that the expression \(\ln(\sqrt{2} + 1) - \ln\left(\frac{1}{\sqrt{2}}\right)\) is equal to \(-\ln\left(1 - \frac{1}{\sqrt{2}}\right)\), we can simplify both sides of the equation using the properties of logarithms. Here are the steps:

Step 1: Simplify the expression on the left side:

\(\ln(\sqrt{2} + 1) - \ln\left(\frac{1}{\sqrt{2}}\right)\)

Step 2: Apply the logarithmic property \(\ln(a) - \ln(b) = \ln\left(\frac{a}{b}\right)\) to combine the logarithms:

\(\ln\left(\frac{\sqrt{2} + 1}{\frac{1}{\sqrt{2}}}\right)\)

Step 3: Simplify the expression within the logarithm:

\(\ln\left(\frac{(\sqrt{2} + 1)}{\left(\frac{1}{\sqrt{2}}\right)}\right)\)

Step 4: Simplify the denominator by multiplying by the reciprocal:

\(\ln\left(\frac{(\sqrt{2} + 1)}{\left(\frac{1}{\sqrt{2}}\right)} \cdot \sqrt{2}\right)\)

\(\ln\left(\frac{(\sqrt{2} + 1) \cdot \sqrt{2}}{\left(\frac{1}{\sqrt{2}}\right) \cdot \sqrt{2}}\right)\)

\(\ln\left(\frac{(\sqrt{2} + 1) \cdot \sqrt{2}}{1}\right)\)

Step 5: Simplify the numerator:

\(\ln\left(\frac{(\sqrt{2} + 1) \cdot \sqrt{2}}{1}\right)\)

\(\ln\left(\sqrt{2}(\sqrt{2} + 1)\right)\)

\(\ln\left(2 + \sqrt{2}\right)\)

Now, let's simplify the right side of the equation:

Step 1: Simplify the expression on the right side:

\(-\ln\left(1 - \frac{1}{\sqrt{2}}\right)\)

Step 2: Simplify the expression within the logarithm:

\(-\ln\left(\frac{\sqrt{2} - 1}{\sqrt{2}}\right)\)

Step 3: Apply the logarithmic property \(\ln\left(\frac{a}{b}\right) = -\ln\left(\frac{b}{a}\right)\) to switch the numerator and denominator:

\(-\ln\left(\frac{\sqrt{2}}{\sqrt{2} - 1}\right)\)

Step 4: Simplify the expression:

\(-\ln\left(\frac{\sqrt{2}}{\sqrt{2} - 1}\right)\)

\(-\ln\left(\frac{\sqrt{2}(\sqrt{2} + 1)}{1}\right)\)

\(-\ln\left(2 + \sqrt{2}\right)\)

As we can see, the expression \(\ln(\sqrt{2} + 1) - \ln\left(\frac{1}{\sqrt{2}}\right)\) simplifies to \(\ln(2 + \sqrt{2})\), which is equal to \(-\ln\left(1 - \frac{1}{\sqrt{2}}\right)\).

Answer:

352sq.cm.

Step-by-step explanation:

There are a total of 5 cubes.

To find the surface area of the corner cubes, we have have to multiply 4^2 * 5 because one of the surface is attached to the other cube's surface. 16*5 is one cube's surface area, so times 2 gives us 160.

To find the surface area of the cubes in the middle, we have to multiply 4^2 * 4 because two of their sides are attached to other cube's side. So 16*3 = 64 and we have 3 of them so it's 192.

Now adding all the surface area, 192 + 160, we get a total of 352 for the surface area of that figure.

Answer:

2 to the 1/6 th power

Step-by-step explanation:

square root = 1/2

Cube root = 1/3

so 1/3 x 1/2= 1/6

can i please have brainlest

Answer:

2 to the 1/6 th power

Step-by-step explanation:

square root = 1/2

Cube root = 1/3

so 1/3 x 1/2= 1/6

can i please have brainlest

Answer:

Step-by-step explanation:

a.

Sally has $28.00 in her bank account and starts saving $18.25 every week.

Let x represent the number of weeks from when he have $28.00 in her account.

and y represent the amount in her account at week x;

We can write the function of the case as;

where m is the amount she saves every week, and b the initial amount in her account.

So, the function will be;

b.

Her friend Suzy has $161.00 in her bank account and is withdrawing $15 every week.​

Using the same rule as in a above;

The function will be;

c.

The graph of the two functions is shown below;

d.

The point where the two lines intersect is shown in the graph above.

The point is at;

Which is at week 4 and balance $101.

e.

The point at which they intersect is the point where they both have the same values.

It is the week when both Sally and Suzy have the same amount in there account.

So, at the fourth week (week 4) Sally and Suzy both have $101 in their account

Answer:

560

Step-by-step explanation:

16 times 5 times 4=320

6 times 16 divide 2 then multiple 5

The rate of the slower car is 77km/hr

Velocity is the rate of change of displacement with time. It is measured in meter per second and it is a vector quantity.

velocity = displacement/time

displacement = velocity × time

represent the faster car by v1 and the slower car by v2

v1 = v2+16

V2 = v1-16

Total displacement = 680km

680 =( v1+V2)t

680 = (v1+V2)4

v1+v2 = 680/4

v2+16+v2 = 170

2v2 = 170-16

2v2 = 154

v2 = 154/2

v2 = 77km/hr

therefore the rate of the slower car is 77km/hr

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Answer: 22%

Step-by-step explanation: 454- 353= 101

101/454= 22%

a. The answer is: The fewest number of multibase blocks required to represent 20 longs in base seven is 2 flats.

b. The answer is: The fewest number of multibase blocks required to represent 10 longs in base three is 3 flats and 1 unit.

a. To represent 20 longs in base seven, we need to find the fewest number of multibase blocks required.

In base seven, we have the following conversions:

1 long = 1 unit

1 flat = 10 units

1 block = 10 flats

To represent 20 longs, we can use 2 flats (each flat representing 10 units) and 0 units since there are no remaining units.

So, the fewest number of multibase blocks required would be 2 flats.

Therefore, the answer is: The fewest number of multibase blocks required to represent 20 longs in base seven is 2 flats.

b. To represent 10 longs in base three, we need to find the fewest number of multibase blocks required.

In base three, we have the following conversions:

1 long = 1 unit

1 flat = 3 units

1 block = 3 flats

To represent 10 longs, we can use 3 flats (each flat representing 3 units) and 1 unit since there is one remaining unit.

So, the fewest number of multibase blocks required would be 3 flats and 1 unit.

Therefore, the answer is: The fewest number of multibase blocks required to represent 10 longs in base three is 3 flats and 1 unit.

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The equation to represent this relationship is y = 1500(0.6)^x

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

Initial, a = 1500

Rate = 40%

Since the value of the refrigerator decreases by 40% each year, the value of the refrigerator after x years can be expressed as:

y = 1500(1 - 40%)^x

Evaluate the difference

y = 1500(0.6)^x

Hence, the expression is y = 1500(0.6)^x

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Answer:

x =34

Step-by-step explanation:

180 - 100 = 80

80 = ( x + 12 ) + x

80 = 2x + 12

68 = 2x

x = 34

Answer:

we can conclude that it appears plausible that the tension distribution is normal since the sample of 30 readings is taken.

Step-by-step explanation:

We are given that the accompanying normal probability plot was constructed from a sample of 30 readings on tension for mesh screens behind the surface of video display tubes used in computer monitors.

According to Central Limit Theorem we can have a normal distribution if we take a large sample.

So the question is how much sample size do we need?

The rule of thumb is to take a sample size of at least 30 to ensure a normal distribution.

Therefore, we can conclude that it appears plausible that the tension distribution is normal since the sample of 30 readings is taken.

Answer:

Below

Step-by-step explanation:

There are 16 oz/ lb

$29.44 / ( 2 lb * 16 oz/lb) = $ . 92 /oz

Answer:

6 + 7/10x + 2/y

Step-by-step explanation:

Hope this helps :)

To find :

Solving the equation :

\( \longmapsto \sf { \dfrac{4(3x-5)}{1+5} = 13} \)

\( \longmapsto \sf { \dfrac{12x-20}{6} = 13} \)

\( \longmapsto \) 12x - 20 = 6 × 13

\( \longmapsto \) 12x - 20 = 78

\( \longmapsto \) 12x = 78 + 20

\( \longmapsto \) 12x = 98

\( \longmapsto \) x =\( \sf { \dfrac{98}{12} } \)

\( \longmapsto \bf\red { x = \dfrac{49}{6} } \)

Value of x is 49/6.

Answer:

Step-by-step explanation:

\({\underline{\underline{\bf{\red{\:\:\:Given\: Equation\:\:\:}}}}}\)

\(\mapsto\:\:\sf{\dfrac{4(3x-5)}{1+5}=13}\)

\({\underline{\underline{\bf{\blue{\:\:\:Solution\:\:\:}}}}}\\\\\)

\(\\\)

\(\qquad:\longrightarrow\:\:\:\:\sf\red{\dfrac{4(3x-5)}{1+5}=13}\)

\(\\\)

\(\qquad:\longrightarrow\:\:\:\:\sf\orange{\dfrac{4(3x-5)}{6}=13}\)

\(\\\)

\(\qquad:\longrightarrow\:\:\:\:\sf\green{\dfrac{2(3x-5)}{3}=13}\)

\(\\\)

\(\qquad:\longrightarrow\:\:\:\:\sf\blue{\dfrac{6x-3}{10}=13}\)

\(\\\)

\(\qquad:\longrightarrow\:\:\:\:\sf\purple{6x-10=39}\)

\(\\\)

\(\qquad:\longrightarrow\:\:\:\:\sf\red{6x = 39+10}\)

\(\\\)

\(\qquad:\longrightarrow\:\:\:\:\sf\blue{6x = 49}\)

\(\\\)

\(\qquad:\longrightarrow\:\:\:\:{\underline{\boxed{\sf{\purple{x = \dfrac{49}{6}}}}}}\)

\(\\\)

The simplified expression of x(3x + 5)-5(2x - 1) is 3x² - 5x + 5

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

x(3x + 5)-5(2x - 1)

Open the brackets

So, we have

3x² + 5x - 10x + 5

Evaluate the like terms

So, we have

3x² - 5x + 5

Hence, the simplified expression is 3x² - 5x + 5

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By considering these rules and properties of integers, the correct result of 6 was obtained.

When writing the response, I considered the following information:

The product or quotient of two integers with different signs is negative. This rule was used to determine that 2(-12) equals -24, not 24.

To subtract an integer, add its opposite. This rule was applied when subtracting -30 from -24, resulting in -24 - (-30) = -24 + 30.

To add integers with opposite signs, subtract the absolute values. The sum has the same sign as the integer with the greater absolute value.

This rule was used to calculate -24 + 30 = 6, where the absolute value of 30 is greater than the absolute value of -24.

By considering these rules and properties of integers, the correct result of 6 was obtained.

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To find the height of the cylinder when the volume is given as 1500 in³ and the radius is 7 inches, we can use the formula for the volume of a cylinder:

Volume = π * r² * h

Substituting the given values, we have:

\(1500 = 3.14 * 7^2 * h1500 = 3.14 * 49 * h1500 = 153.86 * h\)

To solve for h, we divide both sides of the equation by 153.86:

h = 1500 / 153.86

h ≈ 9.75

Rounding the answer to the nearest hundredth, the height of the cylinder is approximately 9.75 inches.

Therefore, the height of the cylinder is 9.75 inches.

Note: It is important to use the accurate value of π, which is approximately 3.14159, for precise calculations. However, in this case, since you specified to use 3.14 for π, I have used that approximation to calculate the height.

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We must draw a triangle ΔABC with the side AC = 4 cm.

1) First, we draw a line with a length of 4 cm, and we call the extremes of the line A and C

2) Now, we draw a second line from point A to that we call B:

3) Finally, we joint the vertex B and C:

Answer:

17.32 meters

Step-by-step explanation:

Let’s call the height of the tower H. The distance from the point to the base of the tower is 10 m. The angle of elevation from the point to the top of the tower is 60 degrees.

Using trigonometry, we can calculate that:

tan (60) = H / 10

H = 10 * tan (60)

H = 10 * √3

H = 17.32 m

Therefore, the height of the tower is 17.32 meters.

Let me know if I helped :)

Answer: $107,836.69 or about $107,837 (to the nearest dollar)

Step-by-step explanation:

Formula to the  accumulated amount received after investing principal amount (P) at rate of interest (r) compounded monthly for t months :

\(A=P(1+\dfrac{r}{12})^{t}\)

As per given , A = $130,000

r= 7.5% = 0.075

t= 30 months

Now,

\(130000=P(1+\dfrac{0.075}{12})^{30}\\\\\Rightarrow 130000=P(1+0.00625)^{30}\\\\\Rightarrow 130000=P(1.00625)^{30}\\\\\Rightarrow 130000=P \times1.20552661036\\\\\Rightarrow\ P=\dfrac{130000}{1.2055266}=107,836.69\)

Hence he need to invest $107,836.69 .