find the value of the variable and the measure of each labeled angle

value=
measure=

Answer:

Step-by-step explanation:

ax²+6x+c=0

disc=6²-4×a×c=36-4ac≥0,(∵ it has two real solutions.)

36-4ac≥0

36≥4ac

4ac≤36

ac≤9

Answer:

62 sq cm

Step-by-step explanation:

if you find the area of the entire shape (12x6) you can then subtract out the cut-out portion (5x2)

72 - 10 = 62

The partial fraction decomposition of the function is given as follows:

A/x + B/x² + C/(5x² + 9) + D/(5x² + 9)².

The function in this problem is defined as follows:

(x^4 + x² + 1)/(x²(5x² + 9)²)

Then the partial fraction decomposition is built considering the terms of denominator, as follows:

When a term is elevated to a power, the terms with the lower powers also have to be considered. For example, for the denominator x², x is also considered, hence the denominators are given as follows:

Then, considering the coefficients A, B, C and D, the partial fraction decomposition of the function is given as follows:

A/x + B/x² + C/(5x² + 9) + D/(5x² + 9)².

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Answer:

b & c

Step-by-step explanation:

Answer:

x = 4

Step-by-step explanation:

if a line is parallel to a side of a triangle and it intersects the other two sides then id divides those sides proportionally.

DE is such a line , then

\(\frac{BD}{AD}\) = \(\frac{BE}{EC}\)  ( substitute values )

\(\frac{x+2}{x}\) = \(\frac{3}{2}\) ( cross- multiply )

3x = 2(x + 2)

3x = 2x + 4 ( subtract 2x from both sides )

x = 4

Answer:

7.He borrowed $1853.33

8.She received $28990.936

Step-by-step explanation:

7.Let x be the amount borrowed by Tyson

Rate of interest = 7.5%

Time = 2.5 years

Simple Interest = 347.50

Formula : \(Si = \frac{P \times T \times R}{100}\)

Where SI = simple interest

P = Principal

T = Time

R = Rate of interest

Substitute the values in the formula :

\(347.50=\frac{x \times 2.5 \times 7.5}{100}\\\frac{347.50 \times 100}{2.5 \times 7.5}=x\\1853.33=x\)

Hence he borrowed $1853.33

8) Principal = 20000

Rate of interest = 9.5%

No. of compounds per year = 2

Time = 4 years

Formula : \(A=P(1+\frac{r}{n})z^{nt}\)

Where A= amount

r = Rate of interest

n = no. of compounds

t = time

Substitute the values in the formula :

So, \(A=20000(1+\frac{9.5}{200})^{2(4)}\)

A=28990.936

Hence she received $28990.936

Answer:

3.  72 questions

4.  180 students

5.  120 students

6.  9 puzzles

Step-by-step explanation:

\(\begin{aligned}\implies \rm 80\% \;of \; 90 \; questions & =80\% \times 90\\&= \dfrac{80}{100} \times 90\\& = \dfrac{7200}{100}\\& = 72\end{aligned}\)

Therefore, a student must answer 72 questions correctly to pass the test.

\(\begin{aligned}\implies \rm 40\%\; of\; 450\; students & = 40\% \times 450\\& = \dfrac{40}{100} \times 450\\& = \dfrac{18000}{100}\\& = 180\end{aligned}\)

Therefore, at least 180 students must plan to attend in order for the school to have the festival.

\(\begin{aligned}\implies \rm 40\% \; of \; 300 \; students & = 40\% \times 300\\& = \dfrac{40}{100} \times 300\\& = \dfrac{12000}{100}\\& = 120\end{aligned}\)

Therefore, 120 students chose recycling.

If 55% of 20 puzzles are completed, then 45% of 20 puzzles are left to complete, since 100% - 55% = 45%.

\(\begin{aligned}\implies \rm 55\% \; of \; 20 \; puzzles & = 45\% \times 20\\& = \dfrac{45}{100} \times 20\\& = \dfrac{900}{100}\\& = 9\end{aligned}\)

Therefore, Magdalena has 9 puzzles left to complete.

Answer:

Angle E equals 45 degrees and angle J equals 35 degrees.

If all angles of two triangles match up with one another, then you have yourself a pair of two similar triangles.

Hope it helps, have a fantastic day.

Step-by-step explanation:

We all know from geometry that all the angles of a triangle add up to 180 degrees.

We can form the following equation:

\(100 + 35 + E = 180\)

\(E\) here represents the measure of angle E.

Add together like terms:

\(135 +E = 180\)

Then subtract 135 from both sides:

\(E = 45\)

We can, likewise, form another equation for angle J :

\(100 + 45 + J = 180\)

Add together like terms:

\(145 +J = 180\)

Then subtract 145 from both sides:

\(J = 35\)

Angle E equals 45 degrees and angle J equals 35 degrees.

If all angles of two triangles match up with one another, then you have yourself a pair of two similar triangles.

Constructing an angle bisector using only a straightedge and compass involves drawing the Angle, creating two arcs that intersect the angle, and using those arcs to create a line segment that bisects the angle.

To construct an angle bisector using a straightedge and compass, there are several steps that you need to follow. The correct order of steps for constructing an angle bisector of ABC using only a straightedge and compass are listed below:

Step 1: Draw the angle ABC with a straightedge.

Step 2: Place the point of the compass on point B and swing an arc that intersects both lines that make up the angle. Label the two points where the arc intersects the angle as points D and E.

Step 3: Without changing the compass width, place the point of the compass on point D and swing an arc that intersects the ray that extends from point B. Label the point of intersection as point F.

Step 4: Without changing the compass width, place the point of the compass on point E and swing an arc that intersects the ray that extends from point B. Label the point of intersection as point G.

Step 5: Draw the line segment FG with a straightedge. This line segment is the angle bisector of angle ABC.

In summary, constructing an angle bisector using only a straightedge and compass involves drawing the angle, creating two arcs that intersect the angle, and using those arcs to create a line segment that bisects the angle. Following these steps will allow you to construct the angle bisector of ABC accurately.

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F is conservative if we can find a scalar funciton f such that grad(f) = F.

This would entail

\(\dfrac{\partial f}{\partial x}=10yz\)

\(\dfrac{\partial f}{\partial y}=10xz\)

\(\dfrac{\partial f}{\partial z}=10xy\)

Integrate both sides of the first equation with respect to x :

\(f(x,y,z)=10xyz+g(y,z)\)

Differentiate both sides with respect to y :

\(\dfrac{\partial f}{\partial y}=10xz=10xz+\dfrac{\partial g}{\partial y}\)

\(\implies\dfrac{\partial g}{\partial y}=0\implies g(y,z)=h(z)\)

Differentiate both sides with respect to z :

\(\dfrac{\partial f}{\partial z}=10xy=10xy+\dfrac{\mathrm dh}{\mathrm dz}\)

\(\implies\dfrac{\mathrm dh}{\mathrm dz}=0\implies h(z)=C\)

So we have

\(f(x,y,z)=10xyz+C\)

that satisfies

\(\nabla f(x,y,z)=\mathbf F(x,y,z)\)

and so F is indeed conservative.

Answer:

b

Step-by-step explanation:

it is

The required area of the back of the doghouse is 912 square inches.

You are a woodworker who is designing a custom doghouse.
The customer has chosen a different siding for the back of the house
The base of the triangle measures 3 feet, 2 inches, and the height is 4 feet.

The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should not be greater than 180°

Here,
Height of doghouse = 4 feet = 4 * 12 = 48 inches
Base of doghouse = 4 feet 2 inches = 36 * 12 + 2 = 38 inches
Area of the triangle = 1 / 2 * base * height

Area of the triangle = 1 / 2 * 48 * 38
Area of the triangle = 912 square inches

Thus, the required area of the back of the doghouse is 912 square inches.

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Answer: C

Step-by-step explanation:

1. divide 3 by 2 to find out how many pounds of blueberries she picked each day. 3/2 is 1.5

2. multiply 1.5 by 16 to convert to ounces. 1.5x16 is 24.

3. she picked 24 ounces of blueberries each day.

The ability of the twins to divide the oddly shaped plot into two Identical plots along the grid lines depends on the presence of a line of symmetry.

To determine whether the set of twins can divide the oddly shaped plot of land into two identical plots along the grid lines, we need to consider the characteristics of the plot and the conditions required for the division.

For the division to be possible, the plot needs to have a line of symmetry that can be used to create two identical halves. A line of symmetry divides an object into two equal and mirrored parts.

If the plot of land has a line of symmetry, the twins can divide it by drawing a line along the symmetry axis. This line should cut the plot into two equal halves, ensuring that both plots are identical.

However, if the plot does not have a line of symmetry, it may not be possible to divide it into two identical plots along the grid lines. In this case, the twins would need to consider alternative methods of division or compromise on the goal of having two identical plots.

To determine if the plot has a line of symmetry, the twins can examine its shape and characteristics. They can look for any symmetrical patterns, such as equal sides or mirrored shapes, that indicate the presence of a line of symmetry.

If the plot does not have an obvious line of symmetry, the twins might need to explore other options, such as dividing the plot into two equal areas based on other criteria, such as the length or width of each half.

the ability of the twins to divide the oddly shaped plot into two identical plots along the grid lines depends on the presence of a line of symmetry. If such a line exists, they can divide the plot by drawing a line along the symmetry axis. However, if the plot lacks symmetry, they may need to consider alternative methods of division or adjust their expectations.

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Note the full question may be :

To determine whether the twins can divide the oddly shaped plot of land into two identical plots along the grid lines, we need more specific information about the shape and dimensions of the plot. the shape of the plot (rectangular, triangular, irregular), the lengths of its sides, any existing grid lines or divisions within the plot.

Answer:

The answer is D. Cone

Step-by-step explanation:

Answer:

y=2x-5

Step-by-step explanation:

Answer:

y = -3x + 7

Step-by-step explanation:

Parallel lines have equal slopes, so we already know that the slope of the other line is -3.

Now we can plug in (2,1) into point-slope:

                             \(\begin{gathered}\bf{y-1=-3(x-2)}\\\bf{y-1=-3x+6}\\\bf{y=-3x+6+1}\\\bf{y=-3x+7}\end{gathered}\)

Therefore, the equation is y = -3x + 7

Info related to the question

Answer:

1734

base is 68

height 51

Step-by-step explanation:

Using the rules of indices to evaluate the expressions given, that with a value of 1 is (3² * 3⁵)/3¹⁰

1.)

\(7^{-6} \times 7^{5} = 7^{-6+5} = 7^{-1} = \frac{1}{7}\)

2.)

10³/10² = 10¹ = 10

3.)

(5⁶)²/5⁸ = 5¹²/5⁸ = 5⁴ = 625

4.)

(3² * 3⁵)/3¹⁰ = 3¹⁰/3¹⁰ = 3⁰ = 1

Therefore, the expression which has a value of 1 is the option D

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Answer:

I know i am 5 days late but the answer is C: 1000 miles!

Step-by-step explanation:

if the distance traveled in miles was 500 in just 1 hour, this would mean you have to add another 500 to equal to 2 hours.

500+500=1000

The value of dy/dx is ( v du/dx - u dv/dx)/v²

From the question, we have

y = (1+x)u/(1+x)v

y = u/v

dy/dx = d/dx(u/v)

d/dx(u/v) = ( v du/dx - u dv/dx)/v²

Derivatives:

A function's varied rate of change with respect to an independent variable is referred to as a derivative. When there is a variable quantity and the rate of change is irregular, the derivative is most frequently utilized. The derivative is used to assess how sensitive a dependent variable is to an independent variable (independent variable). In mathematics, a quantity's instantaneous rate of change with respect to another is referred to as its derivative. Investigating the fluctuating nature of an amount is beneficial. In calculus, a function's derivative measures how sensitively its output value changes in response to changes in its input value.

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The roots of the given quadratic equation are 5 and -4

Quadratics are the polynomial equation which has the highest degree of 2. Also, called quadratic equations.

Given is an equation 3x²-13x-10 = 0, we need to solve by using completing the square method,

The given equation is =

3x²-13x-10 = 0

3(x²-13x/3-10/3) = 0

3(x²-2x·13x/6-10/3) = 0

Adding and subtracting (13/6)²

3(x²-2x·13x/6+(13/6)²-(13/6)²-10/3) = 0

3[(x-13/6)²-169/36-10/3] = 0

3[(x-13/6)²-289/36] = 0

(x-13/6)²-289/36 = 0

(x-13/6)² = 289/36

Taking roots,

x-13/6 = ±17/6

x = 17/6+13/6

x = 5

Or,

x = -17/6+13/6

x = -4

Hence, the roots of the given quadratic equation are 5 and -4

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F(5) would be the y value of where the line is when it is at x 5

The line crosses at -6.5

F(5) = -6.5

The evaluation of the given Boolean expressions are:

a) A && !B =  false              b) B∥C = true

c) B==C = false                   d) A&&!C = true

e) (B∥C)&&(!A) =  false        f) (A!=B)∥(B!=C)  = true

Information available in the problem:

A = true

B = true

C = true

a) Since A and B are both true, !B (which means "not B") is false. Therefore, A && !B evaluates to false, because the logical AND operator returns true only if both of its operands are true.

Hence,

A && !B = true && false = false

b) Since B is true, the result of B∥C will be true, regardless of the value of C. This is because the logical OR operator returns true if at least one of its operands is true.

Hence,

B∥C = true ∥ false = true

c) Since B is true and C is false, B and C have different values, and therefore B==C will evaluate to false. This is because the equality operator returns true only if its operands have the same value.

Hence,

B==C = true == false = false

d) Since A is true and !C (which means "not C") is true, A&&!C evaluates to true. This is because the logical AND operator returns true only if both of its operands are true.

Hence,

A&&!C = true && !false = true && true = true

e) Since B is true, the result of B∥C will be true, regardless of the value of C. This is because the logical OR operator returns true if at least one of its operands is true. Therefore, B∥C evaluates to true.

Since A is true and !A (which means "not A") is false, !A evaluates to false.

Therefore, (B∥C)&&(!A) evaluates to false, because the logical AND operator returns true only if both of its operands are true.

Hence,

(B∥C)&&(!A) = true && false = false

f) Since A is true and B is true, A!=B (which means "A is not equal to B") is false, because A and B have the same value.

Since B is true and C is false, B!=C (which means "B is not equal to C") is true, because B and C have different values.

Therefore, (A!=B)∥(B!=C) evaluates to true, because the logical OR operator returns true if at least one of its operands is true.

Hence,

(A!=B)∥(B!=C) = false ∥ true = true

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The percent change in Pilar's shell collection from the beginning of the day to the end is,  22.5%

Percentage is a way to express a number as a fraction of 100. It is often used to represent ratios and proportions in a more convenient and understandable form, especially in financial and statistical contexts. For example, 50% means 50 per 100, or half of a given quantity. It is denoted using the symbol "%".

Given that,

Pilar has 40 shells in her collection.

She collects 6 more shells in the morning and 3 more shells in the afternoon.

The percent change in Pilar's shell collection from the beginning of the day to the end = ?

At the beginning of the day, Pilar has 40 shells.

In the morning, she collects 6 more shells, bringing her total to

= 40 + 6

= 46 shells.

Then, in the afternoon, she collects 3 more shells, bringing her total to

=46 + 3

= 49 shells.

To find the percent change in Pilar's shell collection from the beginning of the day to the end, we can use the formula:

percent change = (final value - initial value) / initial value * 100%

Plugging in the values we have:

percent change = (49 - 40) / 40 x 100%

percent change = 9 / 40 x 100%

percent change = 22.5%

Therefore, there is a 22.5% increase in Pilar's shell collection from the beginning of the day to the end.

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The side length of the cube is 5.6 feet (rounded to the nearest tenth).

We can calculate the side length of a cube with a volume of 141 cubic feet using the formula for cube volume , which is \(V = s^3\), where V is the volume and s is the side length.

We can calculate s by taking the cube root of both sides of the equation:

\(s = (V)^{(1/3)\)

Substituting V = 141, we get:

\(s = (141)^{(1/3)\)

By using a calculator to evaluate this expression, we may determine:

s ≈ 5.6

As a result, the cube's side length is roughly 5.6 feet (rounded to the closest tenth). This indicates that if we increase the side length by three, it will become longer. (\(s^3\)), we will get the volume of the cube, which is 141 cubic feet.

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Answer:

-20 is the answer :) hoped I helped

Step-by-step explanation:

you can find the answer by vertical opposite angle

if the value of x is computed and it's equal to 78 you will find the answer

78=(12x+18)^

78=(12×5+18)

78=(60+18)

78=78 the problem is solved

may u get branliest please please

Answer:

B'''(6, -15), C'''(-3, -12)

Step-by-step explanation:

For point B,

\(B(1,\,2) \to B'(1,\,-2) \to B''(2,\,-5) \to B'''(6,\,-15)\)

For point C,

\(C(-2,\,1) \to C'(-2,\,-1) \to C''(-1,\,-4) \to C'''(-3,\,-12)\)

Reflecting a point across the x-axis:  leave the x-coordinate the same; replace the y-coordinate with its opposite.

<1, -3>  These are translations: add 1 to x, subtract 3 from y.

Dilate k=3:  multiply both x and y by 3.

The confidence interval, expressed as a trilinear inequality, is 71.6%

What does a confidence interval mean?

The range of values we see in our sample and expect to find the value that most accurately represents the population are referred to as a confidence interval.

The lower bound is 71.6% - 8.2% = 63.4% and the upper bound is 71.6% + 8.2% = 79.8%.

Thus the confidence interval, expressed as a trilinear inequality, is 63.4% < p < 79.8%, where p= 71.6%.

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