a student showed the steps below while solving the equation 14=log5(2x-3) by graphing. which step did the student make the 1sr error

Answer:

D

Step-by-step explanation:

we let that,

(3,2)=(x,y)

given the equation that,

x-4y=10

so,we substitute the values of (x,y)=(3,2)it become

3-4(2)=-5

and test another coordinates(-3,3)

-3-4(3)=-15

botha answers doesn't give 10 as the answer so the answer is D(neither)

Answer:

TRUE

Step-by-step explanation:

We are given 2 triangles, ∆ABC and ∆DEF.

For the two trinagles to be considered similar, both must have their set of corresponding angles congruent to each other. That is, their corresponding angles are equal.

From the information given, the following are the set of corresponding angles:

<B = <E = 31°

<B = <D = 90°

<C = <F = 59° [180 - (90+31)]

The corresponding angles of both triangles are congruent. Therefore, it is guaranteed that ∆ABC is similar to ∆DEF (∆ABC ~ DEF).

The algebraic description maps the point (x, y) 8 units to the left and 12 units up is (x, y) -> (x - 8, y +12)

Translation is the way of changing the position of an object on an xy plane.

If the coordinate points (x, y) is translated  8 units to the left and 12 units up, the resulting coordinate will be:

(x, y) -> (x - 8, y +12)

Hence the algebraic description maps the point (x, y) 8 units to the left and 12 units up is (x, y) -> (x - 8, y +12)

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Answer:

4.24m³

Step-by-step explanation:

The inside diameter of 1.2 m of the pipe

Radius of the inside pipe = Diameter/2 = 1.2/2 = 0.6m

The outside diameter of 1.8 m

Radius of the outer of the pipe = 1.8/2 = 0.9m

Height of the pipe = 3.0m

A Pipe looks like the shape of the cylinder. Hence,

Volume of concrete in the pipe = Volume of the outer section of the Pipe - Volume of the inner section of the pipe

Volume of the outer section of the Pipe = πr²h

h = 3.0m

r = 0.9

= π × 0.9² × 3.0

= 7.63m³

Volume of the inner section of the Pipe = πr²h

h = 3.0m

r = 0.6

= π × 0.6² × 3.0

= 3.39m³

Volume of concrete in the pipe = Volume of the outer section of the Pipe - Volume of the inner section of the pipe

= 7.63m³ - 3.39m³

= 4.24m³

Therefore, volume of concrete in the pipe is 4.24m³

Plug in a = 2 m/s^2 and d = 10 m, and solve for t (in s):

[tex]a=\dfrac{2d}{t^2}\iff2\dfrac{\rm m}{\mathrm s^2}=\dfrac{2\cdot10\,\mathrm m}{t^2}[/tex]

[tex]\implies t^2=\dfrac{20\,\rm m}{2\frac{\rm m}{\mathrm s^2}}=10\,\mathrm s^2[/tex]

[tex]\implies t=\sqrt{10}\,\mathrm s[/tex]

So the answer is C.

Answer:

The length of BC is √105 cm or 10.2 cm.

Step-by-step explanation:

You have to apply Pythagoras Theorem, c² = a² + b² where c represents hypotenuse, a and b are the sides :

[tex] {c}^{2} = { a}^{2} + {b}^{2} [/tex]

[tex]let \:a =BC \:, \: b = 8 \: , \: c = 13[/tex]

[tex] {13}^{2} = {BC}^{2} + {8}^{2} [/tex]

[tex]169 = {BC}^{2} + 64[/tex]

[tex] {BC}^{2} = 169 - 64[/tex]

[tex] {BC}^{2} = 105[/tex]

[tex]BC = \sqrt{105} [/tex]

[tex]BC = 10.2 \: cm \: (3s.f)[/tex]

Answer:

[tex] \boxed{\sf Length \ of \ BC = \sqrt{105} \ cm} [/tex]

Given:

AB = 13 cm

AC = 8 cm

To Find:

Length of BC

Step-by-step explanation:

Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides”.

[tex] \therefore \\ \sf {AC}^{2} + {BC}^{2} = {AB}^{2} \\ \sf \implies {8}^{2} + {BC}^{2} = {13}^{2} \\ \\ \sf {8}^{2} = 64 : \\ \sf \implies 64 + {BC}^{2} = {13}^{2} \\ \\ \sf {13}^{2} = 169 : \\ \sf \implies 64 + {BC}^{2} = 169 \\ \\ \sf Substract \: 64 \: from \: both \: sides : \\ \sf \implies (64 - 64) + {BC}^{2} = 169 - 64 \\ \\ \sf 64 - 64 = 0 : \\ \sf \implies {BC}^{2} = 169 - 64 \\ \\ \sf 169 - 64 = 105 : \\ \sf \implies {BC}^{2} = 105 \\ \\ \sf \implies BC = \sqrt{ 105 } \ cm [/tex]

So,

Length of BC = [tex] \sqrt{105} [/tex] cm

Answer:

3 grams will be left after 6 half-lives

Step-by-step explanation:

Half-live:

Time it takes for the substance to be reduced by hall.

After n half lives:

The amount remaing is:

[tex]A(n) = A(0)(0.5)^{n}[/tex]

In which A(0) is the initial amount and n is the number of half-lives.

Starting with 210 grams of a radioactive isotope, how much will be left after 6 half-lives?

This is A(6) when A(0) = 210. So

[tex]A(n) = A(0)(0.5)^{n}[/tex]

[tex]A(6) = 210(0.5)^{6} = 3.3[/tex]

Rounding to the nearest gram

3 grams will be left after 6 half-lives

answer: 1020000

step-by-step explanation:

(7.8*10^5+(2.4*10^5)                                         given expression

(7.8*10^5)+(2.4*10^5)                                        group with parenthesis

(7.8+2.4)*10^5                                                   combine like terms

10.2*10^5                                                           preform addition

10.2*100000                                                     evaluate the exponent

1020000                                                           multiply out

Answer:

The cheap one is 8 while the costly one is 17.5

Step-by-step explanation:

Let the cheaper candle be x

And the costly candle b y

X+y = 25.5.... equation one

2.20x +7.3y = 25.5(5.7)

2.2x + 7.3y = 145.35....equation two

Solving simultaneously

X+y = 25.5

2.2x + 7.3y = 145.35

2.2X+2.2y = 56.1

2.2x + 7.3y = 145.35

5.1y= 89.25

Y= 17.5

X+y = 25.5

X+ 17.5 = 25.5

X= 25.5-17.5

X= 8

The cheap one is 8 while the costly one is 17.5

Answer:

Angle L is a base angle and measures 72°.

Step-by-step explanation:

Triangle JKL is isosceles.

The measure of angle J is 72°

The measure of angle K is 36°

Angles in a trinagle add up to 180° so angle L is;

180° - (36° + 72°) = 72°

An isosceles triangle means that two of its sides are equal and two base angles are equal. So base  angles are angles J and L and measures 72° each.

Answer:

I think it's B

Step-by-step explanation:

I hope this helps.

Answer:

The sum is 66  

Step-by-step explanation:

There are a couple formulas to remember.

aₙ = a₁ + d(n-1)

Sₙ = [tex]\frac{n}{2}[/tex] · (a₁ + aₙ)

In your case "d" equals 4 and a₁ equals 1, that's how we know what the sequence will progress.

Let's plug in the values for the first equation:

aₙ = 1 + 4 (n-1)

Next we can simplify:

aₙ = 1 + 4n-4

aₙ = 4n - 3

Now we can plug in the value for "n" which is 6 for this particular problem:

a₆ = 4 · 6 - 3

a₆ = 21

We can now use the second equation to find the sum:

S₆ = [tex]\frac{6}{2}[/tex] · (1 + 21)

S₆ = 66    

Hope this helps =)

Answer:

B

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

[tex] \frac{42}{100} \times 350 = 147[/tex]

Answer:

undefined! one cannot divide by 0

Step-by-step explanation:

Answer:

undefined!

Step-by-step explanation:

Answer:

[2.5 ,4]

Step-by-step explanation:

The graph in this interval has a vertex while opening up wich means it's a minimum

Answer:

5

Step-by-step explanation:

25/5

=5✖️5=25

=5/1

Answer:

25÷5 = 5 and 25/5 = 125

Step-by-step explanation:

hope this helps!

Answer: C

Step-by-step explanation:

G(F(x)) means F(x) is being plugged into every x in G(x). Since we are given the G(x) and F(x) functions, we can directly plug 2x-5 into x²+1.

G(F(x))=G(2x-5)

G(F(x))=(2x-5)²+1                            [use FOIL method to expand (2x-5)²]

G(F(x))=(4x²-10x-10x+25)+1           [combine like terms]

G(F(x))=4x²-20x+26

Now that we have found G(F(x))=4x²-20x+26, we know that the answer is C.

The above question is not complete because it was not written and arranged properly

Complete Question

1) A cone has a diameter of 8 units and a height of 8 units. Its radius is 4 units, and its volume is ______ cubic units.

2) A cylinder with the same height and radius as the cone will have a volume ______ of cubic units.

3) If a sphere has the same radius as the cylinder, its volume is ______the volume of the cylinder.

Answer:

1) Volume of the cone = 134.04cubic units

2)Volume of the cylinder = 402.12cubic units

3) Volume of the sphere= 268.08 cubic units. Hence, if a sphere has the same radius as the cylinder, its volume is 2/3 times the volume of the cylinder.

Step-by-step explanation:

1) A cone has a diameter of 8 units and a height of 8 units. Its radius is 4 units, and its volume is ______ cubic units.

Volume of a cone = 1/3πr²h

h = 8 units

r = 4 units

Volume = 1/3 × π × 4² × 8

134.04cubic units

2) A cylinder with the same height and radius as the cone will have a volume ______ of cubic units.

Volume of a cylinder = πr²h

Height and radius is the same as that of the cones hence,

h = 8 units

r = 4 units

= π × 4² × 8

= 402.12cubic units.

3) If a sphere has the same radius as the cylinder, its volume is ______the volume of the cylinder.

Volume of a Sphere = 4/3πr³

r = radius of the cylinder = 4 units

Volume of a Sphere = 4/3 × π × 4³

= 268.08 cubic units.

From the above question, we are asked to compare the volume of the sphere with the volume of the cylinder

Volume of the sphere : Volume of the cylinder

268.08 cubic units : 402.12 cubic units

268.08/402.12 = 2/3

Therefore, the volume of the sphere is 2/3 times the volume of the cylinder

Answer:

40091.

Step-by-step explanation:

Multiply 40.091 by 10 three times to get the answer.

40.091 * 10 = 400.91

400.91 * 10 = 4009.1

4009.1 * 10 = 40091.

The expression 40.091 x 10³ can be represented as 40091.

The term xⁿ, read as x to the power n, shows an exponent n, which implies x is multiplied by itself n times.

In the question, we are asked to arrange the cards showing '.', '0', '0', '1', '4', and '9', to show the solution to the expression 40.091 x 10³.

Now, 10³ is 10 to the power 3, where 3 is the exponent, so 10 is multiplied by itself 3 times = 10*10*10 = 1000.

Now, the expression 40.091 x 10³ = 40.091 * 1000 = 40091.

∴ The expression 40.091 x 10³ can be represented as 40091.

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Answer:

Step-by-step explanation:

Using the formula for calculating the distance between two points to calculate the length of WX.

D = √(y₂-y₁)²+(x₂-x₁)²

Given the endpoints W(2,-7) and X(5,-4), x₁ = 2, y₁ = -7, x₂ = 5 and y₂ = -4

Substituting this values into the formula to get the length of WX will give;

WX = √(-4-(-7))²+(5-2)²

WX = √(-4+7)²+3²

WX = √3²+3²

WX = √18

WX = √2*9

WX = 3√2 units

Hence the length of WX is 3√2 units.

Answer:

3[tex]\sqrt{2}[/tex]

Hope this helps!

Step-by-step explanation:

Answer:

236

Step-by-step explanation:

The interquartile range is the right edge of the box minus the left edge of the box

The right edge of the box is 301

The left edge of the box is 65

301 -65 =236

The interquartile range is 236

Answer:

65

Step-by-step explanation:

To find interquartile range, you substract upper quartile( 130 in this problem) and the lower quartile(65 in this problem)

Finally, you get the answer 65.

Hope this helps!

Answer:

0.99865

Step-by-step explanation:

The question above is modelled by gaussian distribution. Gaussian distribution is also known as Normal distribution.

To solve the above question, we would be using the z score formula

The formula for calculating a z-score

z = (x-μ)/σ,

where x is the raw score

μ is the population mean

σ is the population standard deviation.

In the above question,

x is 115 liters

μ is 100

σ is the population standard deviation is unknown. But we were given variance in the question.

Standard deviation = √Variance

Variance = 9

Hence, Standard deviation = √9 = 3

We go ahead to calculate our z score

z = (x-μ)/σ

z = (115 - 100) / 3

z = 15/ 3

z score = 5

Using the z score table of normal distribution to find the Probability of having a z score of 5

P(x = 115) = P(z = 5) =

0.99865

Therefore the probability that this year it will produce 115 liters of wine = 0.99865

Answer:

79 degrees

Step-by-step explanation:

There's a bunch of theorems you have to memorize.

This is an inscribed angle.

The measure of angle RST is 1/2 of the intercepted arc.

<RST = 1/2(158) = 79

Answer:

1. can

2. less

3. 5

Step-by-step explanation:

To find out if Waclaw could make it to the gas station using 10 miles, we need to add the number of miles he has to go in order to reach his destination.

[tex]4\frac{7}{8}+4\frac{3}{4} = 9\frac{5}{8}\\[/tex]

9 5/8 is less than 10, so he can make it to the gas station.

We can also find out the answer without even adding the numbers together, because both values are less than five, and when that happens, the sum cannot be 10 or more, so Waclaw can make it to the gas station.

Answer:

1). 18

Step-by-step explanation:

1). The numbers above are real numbers but on a care ful look the number below it is a squrea of the number above but it's position ois swapped.

What am I saying., Let's take for example the number 4.

4² = 16 but what's written is 61

Let's take 5

5² = 25 but what's written is 52

Let's take 6

6² = 36bl but what's written is 63.

So as for 9

9²= 81 but what will be in the box = 18

2).this number two is something special

Answer:

Empirical Rule

Step-by-step explanation:

The Empirical Rule is also known as the Sigma rule or the 68-95-99.7% rule. The rule state that for a given data set, 68% of all data values will fall within the first standard deviation from the mean. The rule also states that 95% of all data values would fall within two standard deviations, while almost all the data which amounts to about 99.7% will fall within three standard deviations.

The empirical rule is used in forecasting based on the given datasets because it is a certainty that after obtaining the standard deviation, data values can be assigned to the categories they fall into, under the Empirical rule.

Answer:

B. Y = -3X

C. Y = 4 - 3X

Step-by-step explanation:

Y = -3X + 2

This is in the form y= mx +b where m is the slope

The slope is -3

Parallel lines have the same slope

A. Y = 1/3 X - 2   the slope is 1/3

B. Y = -3X   The slope is -3  

C. Y = 4 - 3X Y = -3x+4  the slope is -3

Answer:

239 who are you

Step-by-step explanation:

Answer:

Step-by-step explanation:

To decipher how many eggs you have left, we must read the statement well.

I have 5 eggs if I break 2 eggs it is to cook them and when they are cooked they will be eaten, so we simply do the following:

5 -2= 3

Now you only have 3 eggs left.

Step-by-step explanation:

Given:

5 eggs

Required:

Number of eggs after breaking, cooking and eating 2.

Solution:

I won't count the eggs as 6.

Broken=cooked=eaten=2

5-2=3

Hope it helps ;) ❤❤❤