Evaluate 5x 2+ 2(4x – 7) – 8x for x = 3.

Hi Student!

Looking at the question provided we are asked to find two integers.  It further specifies that those two integers should be the boundaries around the number that is produced from the square root of 11.  

Now that we know what the question is asking for, we can move onto answering the question.  We know that \(1^2\) is equal to \(1\), \(2^2\) is equal to \(4\), \(3^2\) is equal to \(9\), and \(4^2\) is equal to \(16\).  The number that was provided to us inside of the square root was 11.  That means that it would be between the number 9 and 16 which is given using \(3^2\) and \(4^2\).  

Therefore, the square root of 11 would be between the numbers 3 and 4.  The final answer is option E, 3 and 4

Answer:

d = 17

Step-by-step explanation:

The given arithmetic sequence is :

31, 48, 65, 82, ...

We need to find the common difference for this sequence.

First term, a₁ = 31

Second term, a₂ = 48

Common difference = a₂-a₁

= 48-31

= 17

So, the common difference for this arithmetic sequence is equal to 17.

\(\cfrac{3}{5}\div\cfrac{3}{7}\implies \cfrac{~~\begin{matrix} 3 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{5}\cdot \cfrac{7}{~~\begin{matrix} 3 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\implies \cfrac{7}{5}\implies 1\frac{2}{5}\)

The percentage of boys in the combined group is 60% and the percentage of girls in the combined group is 40%.

Given the number of boys and girls in two groups of students travelling together, we have to determine the percentage of boys and girls in the combined group. Let's solve this problem step by step. Solution:Step 1: Let the number of boys in the combined group be B and the number of girls in the combined group be G.B = 40 + 50 = 90 (Adding the number of boys from both groups)G = 25 + 35 = 60 (Adding the number of girls from both groups)Step 2: Find the total number of students in the combined group.Total students in the combined group = B + G = 90 + 60 = 150 studentsStep 3: Calculate the percentage of boys and girls in the combined group.Percentage of boys = (Number of boys in the combined group/Total number of students in the combined group) × 100= (90/150) × 100 = 60%Percentage of girls = (Number of girls in the combined group/Total number of students in the combined group) × 100= (60/150) × 100 = 40%

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The set of transformations that could be applied to ABCD, to create A″B″C″D″ is a reflection over the y-axis, followed by a rotation of 180°

"It is a geometric transformation where all the points of an object are reflected on the line of reflection."

For the given question,

The Rectangle ABCD is formed by ordered pairs A at (-4, 2), B at (-4, 1), C at (-1, 1), D at (-1, 2)

The Rectangle A″B″C″D″ is formed by ordered pairs A" at (-4, -2), B" at   (-4, -1), C" at (-1, -1) and D" at (-1, -2)

We can observe that the coordinates of ABCD are of the form (-x, y)  where x, and y, are positive numbers

The form of the ordered pair of the vertices of the A″B″C″D″ will be (-x, -y)

The coordinates of the point (-x, y) after a reflection over the y-axis would be of the form (x, y)

And after rotation of 180°, the coordinates would be (-x -y).

Hence, the set of transformations that could be applied to ABCD, to create A″B″C″D″ is a reflection over the y-axis, followed by a rotation of 180°.

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Answer:

d my friend

Step-by-step explanation:

Answer:

exact form 3/2 decimal  form 1.5 mixed number form 1 1/2

Step-by-step explanation:

Answer:

\( \huge{ \bold{ \boxed{ \tt{x = - \frac{3}{2} }}}}\)

☯\( \underline{ \underline{ \sf{Question}}} : \)

☯ \( \underline{ \underline{ \sf{To \: find}}} : \)

\( \text{Given \: Equation : \: 3(x - 2) + 4 = x - 5}\)

You must distribute first ! In this equation , you have the distributive property on left hand side of the equation. You must first get rid of the parentheses.

⇢ \( \text{3 × \: x - 3× 2 + 4 = x - 5} \)

⇢ \( \text{3x - 6 + 4 = x - 5}\)

On the left hand side , you have two numbers : - 6 and 4. Remember that ' The negative and positive numbers are subtracted but posses the sign of the bigger number. '

⇢\( \sf{3x - 2 = x - 5}\)

Move x to left hand side and change it's sign.

Similarly , move 2 to right hand side and change it's sign.

⇢\( \sf{3x - x = - 5 + 2}\)

On the left hand side , you have like terms. Combine the like terms : 3x - x = 2x

⇢\( \sf{2x = - 5 + 2}\)

On the right hand side , - 5 + 2 = -3

⇢\( \sf{2x = - 3}\)

Divide both sides by 2

⇢\( \sf{ \frac{2x}{2} = - \frac{3}{2} }\)

⇢\( \boxed{\sf{x = - \frac{3}{2} }}\)

-----------------------------------------------------------------

✏ CHECK :

\( \text{3(x - 2) + 4 = x - 5}\)

Substitute \( \sf{ - \frac{3}{2}} \) for x into the original equation. And simplify !

⇾ \( \sf{3( - \frac{3}{2} - 2) + 4 = - \frac{3}{2} - 5}\)

⇾\( \sf{3( \frac{ - 3 - 2 \times 2}{2} ) + 4 = \frac{ - 3 - 5 \times 2}{2}} \)

⇾\( \sf{3( \frac{ - 3 - 4}{2} ) + 4 = \frac{ - 3 - 10}{2}} \)

⇾\( \sf{3( \frac{ - 7}{2} ) + 4 = \frac{ - 13}{2}} \)

⇾\( \sf{ \frac{ - 21}{2} + 4 = \frac{ - 13}{2}} \)

⇾\( \sf{ \frac{ - 21 + 4 \times 2}{2} = \frac{ - 13}{2}} \)

⇾\( \sf{ \frac{ - 21 + 8}{2} = \frac{ - 13}{2}} \)

⇾\( \sf{ \frac{ - 13}{2} = \frac{ - 13}{2}} \)

Since both sides are equal , x = \( \boxed{ - \sf{ \frac{ 3}{2} }}\) is the correct answer.

And we're done !!

Hope I helped!

Have a wonderful day ! ツ

~TheAnimeGirl ♡

Answer:

3(1)-4=-1 2(1)+5=7

Answer:

5z+1

Step-by-step explanation:

it was simple

On solving the provided question, we cans ay that lateral surface area of cuboid = 2h(l+b) = 2*2(5+4) = 36 cm sq.

A cuboid is a solid or three-dimensional form in geometry. A cuboid is a convex polyhedron having 8 vertices, 12 sides, and 6 rectangular faces. Another name for a cuboid is a cuboid. A cube is a cuboid with six square faces. Boxes include things like books and bricks. The following are the key variations between cubic and cubic: In contrast to a cube, which has rectangular faces, a cube has six equally sized square faces. Even though the cube and cuboid structures have a similar appearance, they differ in some ways in terms of side length, diagonal, and area.

lateral surface area of cuboid = 2h(l+b)

h = 2cm

l = 5cm

b = 4cm

lateral surface area of cuboid = 2h(l+b) = 2*2(5+4) = 36 cm sq.

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Using the z-distribution, it is found that the p-value is of 0.0192.

At the null hypothesis, it is tested if commercial trucks owners do not violate laws requiring front license plates at a higher rate than owners of passenger cars, that is, the subtraction is of at most 0, hence:

\(H_0: p_2 - p_1 \leq 0\)

At the alternative hypothesis, it is tested if commercial truck owners violate the laws more, that is, the subtraction is positive, hence:

\(H_1: p_2 - p_1 > 0\)

For each sample, the size, the proportion and the standard error are given by:

\(n_1 = 2165, p_1 = \frac{235}{2165} = 0.1085, s_1 = \sqrt{\frac{0.1085(0.8915)}{2165}} = 0.0067\)

\(n_2 = 330, p_1 = \frac{50}{330} = 0.1515, s_1 = \sqrt{\frac{0.1515(0.8485)}{330}} = 0.0197\)

For the distribution of differences, the mean and the standard error are given by:

\(\overline{p} = p_2 - p_1 = 0.1515 - 0.1085 = 0.043\)

\(s = \sqrt{s_1^2 + s_2^2} = \sqrt{0.0067^2 + 0.0197^2} = 0.0208\)

The test statistic is given by:

\(z = \frac{\overline{p} - p}{s}\)

In which \(p = 0\) is the value tested at the null hypothesis.

Hence:

\(z = \frac{\overline{p} - p}{s}\)

\(z = \frac{0.043 - 0}{0.0208}\)

\(z = 2.07\)

The p-value is found using a z-distribution calculator, for a right-tailed test, as we are testing if the proportion is more than a value, with z = 2.07.

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The true statements are:

(B) Both figures are congurent.

(C) The two figures have the same orientation but different positions.

(E) Corresponding angles and sides have the same measures.

In geometry, how an item is positioned in the space it occupies—such as a line, plane, or rigid body—is described in terms of its orientation, angular position, attitude, bearing, and direction.

It refers more particularly to the fictitious rotation required to shift an object from a reference placement to its present location.

To get to the current positioning, a rotation might not be sufficient.

It could be required to include a fictitious translation known as the object's location (or position, or linear position).

Together, the position and orientation completely explain where the object is situated in space.

Therefore, the true statements are:

(B) Both figures are congurent.

(C) The two figures have the same orientation but different positions.

(E) Corresponding angles and sides have the same measures.

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Answer:

C. The amount of snowfall was constant for two hours

Step-by-step explanation:

The percentage change in GDP is 2.04%

Percentage Change is the difference coming after subtracting the old value from the new value and then divide by the old value and the final answer will be multiplied by 100 to show it as a percentage. Generally, to convert a fraction into a percent, we multiply it by 100.

The formula of percentage change is given as

Percentage change =[ (New increase - old value) / old value] * 100

Percentage change = [(14.72 - 14.42) / 14.72] * 100

Percentage change = 2.04%

In this case, there is a percentage decrease of 2.04%

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Answer:

0.482 is the probability of the fair die of getting at most 1 five.

Step-by-step explanation:

Getting at most 1 five means there can be 1 five or 0 five.

Condition 1:

Condition 2:

We sum up the favorable outcomes ( 0 five and 1 five) and divide it by the total outcomes to find the probability.

P = ( Number of favorable outcomes) / (Total number of outcomes)

p = (3125 +625)/6^5 => 3750 / 7776 => 0.482

p = 0.482

Therefore the probability is 0.482.

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Answer:

2 2/9

Step-by-step explanation:

Answer:

4x>13

Step-by-step explanation:

4 × X=4x

>=more than symbol

The inverse of the equation is determined as \(y = \log_{6}(-3x)\).

option D is the correct answer.

The inverse of the equation is calculated by applying the following method;

The given equation;

y = - 6ˣ/3

The inverse of the equation is calculated as;

multiply through by 3

\(-3x = 6^y\)

Take the logarithm of both sides of the equation with base -6:

\(\log_{6}(-3x) = y\)

Finally, replace y with x to obtain the inverse equation as follows;

\(y = \log_{6}(-3x)\)

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To sketch the graph of the function y = 4(4)^x, we can start by plotting a few points to get an idea of the shape of the graph.

Let's choose some x-values and calculate the corresponding y-values:

For x = -2, y = 4(4)^(-2) = 4(1/16) = 1/4

For x = -1, y = 4(4)^(-1) = 4(1/4) = 1

For x = 0, y = 4(4)^0 = 4(1) = 4

For x = 1, y = 4(4)^1 = 4(4) = 16

For x = 2, y = 4(4)^2 = 4(16) = 64

Now we can plot these points on a coordinate plane and connect them to form the graph of the function.

The graph of y = 4(4)^x will start at the point (0, 4) and increase rapidly as x increases. It is an exponential growth function where the base is 4.

The domain of the function is all real numbers since there are no restrictions on the values of x.

The range of the function is the set of positive real numbers greater than zero. As x increases, y grows without bound, approaching positive infinity but never reaching zero or becoming negative.

Answer: 2.

Step-by-step explanation: Both lines intersect each other 2 times.

Answer:

2 solutions

Step-by-step explanation:

The solution to a system of equations is the point where two lines intersect.

Given the information above, we can see the lines intersect at two different points, making the answer 2 solutions.

Have a lovely rest of your day/night, and good luck with your assignments! ♡

Answer:

Yes, they are proportional because if you increase or decrease either amount they will both change. They will always have the same size. For example if I want to double the flour, I will have to double the milk as well because they have the same ratio.

Answer:

The amount of flour and the amount of milk are in direct proportion because when the amount of flour increases, the amount of milk increases. If I want to make a product (e.g. cake) that was 16 times bigger, I'd make the flour 16 times bigger and the milk 16 times bigger.

Step-by-step explanation:

Answer:

I hope it can help

Step-by-step explanation:

Yan po sana maka tulong

we are asked to find an expression to determine the diameter of a tree as a function of time. Since we are told that the initial diameter is 15 cm and that the diameter increases 0.5 cm/year. This means that to the 15 cm of the initial diameter we need to add the amount that the diameter increased per year by the number of years, that is, is "x" is the number of years, that we need to add 0.5x. The equation is then:

Where D is the diameter.

The mean number of movies that the students saw is 13.5 (rounded to the nearest tenth).

To find the mean number of movies the students saw, you need to calculate the average of the given data. Here are the reported numbers of movies seen by the 6 students: 14, 11, 15, 19, 12, 10.

To calculate the mean, you sum up all the reported numbers and divide by the total number of students. In this case, the total number of students is 6.

So, let's calculate the mean:

(14 + 11 + 15 + 19 + 12 + 10) / 6 = 81 / 6 = 13.5

Therefore, the mean number of movies that the students saw is 13.5 (rounded to the nearest tenth).

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The point charges placed 0.500 m apart are 10.4 nC and 43.9 nC. Then, the electric field halfway between these charges will be -4824 N/C.

The physical field that surrounds particles with an electrical charge is called an electric field. All other charged particles in the field are affected by it, either being attracted to it or being repelled by it.

The electric field because of a point charge q is written as \(E=\frac{kq}{r^2}\)

Positive point charges cause the electric field to point away from the point, whereas negative point charges cause the electric field to point in the direction of the point. Then, the electric field of the midpoint p in the diagram is written as,

\(\begin{aligned}E_p&=\mathrm{\frac{k(10.4\;nC)}{(0.25\;m)^2}-\frac{k(43.9\;nC)}{(0.25\;m)^2}}\\&=\mathrm{\frac{k(10.4-43.9)\times10^{-9}\;C}{(0.25\;m)^2}}\\&=-\mathrm{\frac{9\times 10^9\;Nm^2/C^2\times 33.5\times10^{-9}\;C}{(0.25\;m)^2}}\\&=-\mathrm{4824\;N/C}\end{aligned}\)

The required answer is -4824 N/C.

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The number she'd have is:

Explanation:

First, let's see which number is in the tens place and which number is in the ones place (the units place).

In the number 548, the place value of 5 is hundreds, the place value of 4 is tens, and the place value of 8 is ones (or units).

So if Sera adds two to the units, she'll have 10. But, since we can't write the number as 5410 (that would be a totally different number), we just write 0 in the units place, and shift 1 to the tens place, which gives us :

550

That's not all, since we also add 1 to the tens:

560

Answer:

227.75 cm

Step-by-step explanation:

a coin (Circle) with diameter 2.9cm

(radius) r = diameter ÷ 2

r = 2.9cm ÷ 2

r = 1.45cm

1 complete revolutions (perimeter or circumference of a circle ) = 2πr

= 2 × π × r

where r = radius, π is a constant = 22/7

= 2 × 22/7 × 1.45

= 9.11cm

thus in one complete revolution the coin travels a distance of 9.11cm.

therefore in 25 complete revolutions the coin will travel a distance of = 25 × 9.11 cm = 227.75 cm.

The distance covered in complete 25 revolutions of a coin with diameter of 2.9 when it's rolled is = 227.75 cm

Answer:

3:8

Step-by-step explanation:

You can divide both numbers by 4, that gets you to your simplest ratio. :)

The ratio of the triangles to the total shape will be equal to 3: 8.

An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value.

For instance, if there is 1 boy and 3 girls, you may express the ratio as 1: 3 (there are 3 girls for every boy), meaning that there are 1 in 4 boys and 3 in 4 girls.

Given that there are 20 circles and 12 triangles. The ratio will be calculated as,

Ratio = triangles / total shape

Ratio = 12 / ( 20+ 12 )

Ratio = 12 / 32

Ratio = 3 / 8

Therefore, the ratio of the triangles to the total shape will be equal to 3: 8.

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