PLEASE HELP 100 PTS!

What are the solutions to the system of equations?

y=x2−4x+3
y=−x+3

Enter your answers in the boxes.

The value of x is 94 degree.

we know that

The inscribed angle measures half that of the arc comprising

So, <K = 1/2 (80+92)

<K = 1/2 x 172

<K = 86 degree

Now, inscribed quadrilateral, the opposite angles are supplementary

So, <K + x= 180

86 + x = 180

x = 180- 86

x= 94 degree

Thus, the value of x is 94 degree.

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Answer:

  (a)  Multiply (200.96)(22).

Step-by-step explanation:

You want the volume of the cylinder with base area 200.96 mm² and height 22 mm.

The volume is found using the formula ...

  V = Bh

where B is the base area, and h is the height.

For base area 200.96 mm² and height 22 mm, the volume is ...

  V = (200.96)(22) mm³

You find the volume by multiplying 200.96 and 22.

<95141404393>

Option 2 is the correct graph for the function f(x) = [tex]4[(1/2)^{x}][/tex] .

Given ,

f(x) = [tex]4[(1/2)^{x}][/tex]

Mathematically the graph will of exponential in nature.

So,

Let us assume few values to understand the nature of graph.

Firstly,

Let x= 1

f(x) = [tex]4[(1/2)^{1}][/tex]

f(x) = 2

Let x = 2

f(x) = [tex]4[(1/2)^{2}][/tex]

f(x) = 1

Let x = 3

f(x) = [tex]4[(1/2)^{3}][/tex]

f(x) = 0.5

Thus from these values of f(x) corresponding to the values of x second graph will be correct .

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The inequality to solve for p is 6p > 600 and the solution is p > 100

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

Selling price = $6 per apple

So, we have

Total = 6p

Also, we have

Spendings = $600

To make profit, we have

6p > 600

Divide by 6

p > 100

Hence, the inequality to solve for p is 6p > 600 and the solution is p > 100

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Answer(s):

Inequality Form:

-3.75 < x < -2.25

Interval Notation:  

x ∈ ( -3.75, -2.25)

Step-by-step explanation:

Equation:  |0.2x +0.6| <0.15

{0.2x + 0.6 > -0.15

{0.2x + 0.6 < 0.15

{(0.2x + 0.6) + (-0.6) > -0.15 + (-0.6)

{(0.2x + 0.6) + (-0.6) < 0.15 + (-0.6)

{0.2x + 0.6 - 0.6 > -0.15 - 0.6

{0.2x + 0.6 - 0.6 < 0.15 - 0.6

{0.2x > - 0.75

{0.2x < -0.45

{0.2x / 0.2 > - 0.75/0.2

{0.2x / 0.2 < - 0.45/0.2

{x > - 0.75/0.2

{x < - 0.45/0.2

{x > -3.75

{x < -2.25

-3.75 < x < -2.25

Answer: x ∈ ( -3.75, -2.25)

Hope this helps!

The points on the scatter plot show the different predictions. The straight line drawn is called the line of regression.

Errors in prediction for each point can be determined by drawing a vertical line from the point to the line of regression. As seen in the image, all of the prediction points are found on the line except for points (14,25) and (16,25). Therefore, these points contain errors in prediction.

The graph that represent this data using the points is added as an attachment

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

The x and y values

Where

x = stars

y = price

To determine the graph that represent the data, we enter the x and y values in a graphing tool to create the graph

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The slope of the line passing through the points (-6, 1) and (8, -7) is -4/7.

Slope is simply expressed as change in y over the change in x.

Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given the data in the question;

Point A: ( -6,1 )

x₁ = -6

y₁ = 1

Point B: ( 8,-7 )

x₂ = 8

y₂ = -7

Now, plug the given x and y values into the slope formula above and simplify:

[tex]Slope\ m = \frac{y_2 - y_1}{x_2 - x_1} \\\\Slope\ m = \frac{-7 - 1}{8 - (-6)} \\\\Slope\ m = \frac{-7 - 1}{8 + 6} \\\\Slope\ m = \frac{-8}{14} \\\\Slope\ m = -\frac{4}{7}[/tex]

Therefore, the slope of the line is -4/7.

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The function that describes the table of values is y = 1/2x + 2

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

x= (-8) (-4) (4) (8)

y= (-2) (0) (4) (6)

From the table, we can see that

As x increases by 4

The y values increase by 2

So, we have

m = Slope = 2/4 = 1/2

The equation is calculated as

y = mx + c

So, we have

y = 1/2x + c

Using the other points, we have

1/2 * -4 + c = 0

So, we have

c = 2

This gives

y = 1/2x + 2

Hence, the function that describes the table of values is y = 1/2x + 2

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The time period with the given principal, rate of interest and amount is 10 years.

Given that,

Principal = $1000, time period = 1 year and rate of interest =$40.

We know that, Simple interest = (Principal×Rate×Time)/100

48 = (1000×r×1)/100

4800=1000r

r=4800/1000

r=4.8%

Principal=$200, time period= 3 years and amount = $248

Simple interest = 248-200

= $48

48=(200×r×3)/100

4800=600r

r=4800/600

r=8%

Principal=$5000, rate of interest=2% and amount=$6000

Simple interest =6000-5000=$1000

Here, 1000=(5000×2×t)/100

1000=(100t)

t=10 years

Therefore, the time period with the given principal, rate of interest and amount is 10 years.

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The surface area of the triangular prism is 137ft².

To get the surface area of a triangular prism, we will calculate the area of each face and then sum them up.

Base area = (4 ft * 5 ft) / 2

Base area = 20ft/2

Base area = 10 ft²

Since triangular prism has two triangular bases, the total area of the triangular bases is:

= 2 * Base area

= 2 * 10 ft²

= 20 ft².

Perimeter of the triangular base:

= 4 ft + 5 ft + 4 ft

= 13 ft

Face area = Perimeter * Height

Face area = 13 ft * 3 ft

Face area = 39 ft²

The total area of the rectangular faces is:

= 3 * Face area

= 3 * 39 ft²

= 117 ft².

The Surface area of the triangular prism will be:

= Total area of triangular bases + Total area of rectangular faces

= 20 ft² + 117 ft²

= 137 ft².

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Simplification of the expression gives:

-3x² - 7x + 16

Simplification is a way of determining an answer for a complex calculation that may involve numbers on division, multiplication, square roots, cube roots, plus and minus, etc.

We have the expression:

(-8x+10) - (3x²-x+6)

We can simplify as follow:

(-8x+10) - (3x²-x+6) = -8x+10 -3x²+x+6    (remove parenthesis)

                               = -3x² - 8x + x + 10 + 6  (collect like terms)

                               = -3x² - 7x + 16  (add/subtract like terms)  

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Answer: 48

Step-by-step explanation:

This isn't college

J=2S

J+S=72

3S=72

S=24

24*2=48

Juan has 48

The first three pairs are of vertically opposite angles.

Given figure,

Vertical angles are the angles that are opposite to each other.

Hence the pairs of vertical angles will be opposite to each other as well as will be equal to each other.

So,

Vertical opposite angles are :

Option A

Option B

Option C

Thus 3 pairs will be considered for vertical angles .

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The measure of central angle DBC is 68 degree.

Hence, option C is correct.

In the given figure,

Measure of intercepted arc = 68 degree,

We have to find the measure of central angle DBC

We know that,

When two circle radii intersect in the center of a circle, they produce a vertex. These circle arms may begin at two distinct positions along the arc of such a circle. The two radii cross to produce a central angle, which serves to divide a circle into separate sectors.

A central angle is generated in the center of a circle when two radii within the circle overlap. As previously stated, a central angle in geometry is one whose vertex forms at the canter of the circle and whose arms cross the circle at two separate positions.

By connecting these two locations, an arc on the circle is formed. As a result, a central angle is the angle formed by an arc in the center of a circle.

Thus by property of central angles,

central angle = measure of intercepted arc

Hence,

⇒ m ∠DBC = 68 degree.

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Based on the information provided, the triangle ABC is an Isosceles triangle.

If triangle ABC is equal to triangle DEF and AB is equal to EF, it means that the corresponding sides and angles of the two triangles are congruent.

Based on the information given, we can conclude that triangle ABC is an isosceles triangle. An isosceles triangle is a triangle that has two sides of equal length. In this case, sides AB and EF are equal in length, making triangle ABC isosceles.

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He went to station Y, and the cost for 20 liters is 32 pounds.

Here we know taht Daniel went to a petrol store, and bought 15 L of petrol for 24 pounds.

So we need to use the graphs of the linear relations to see which store he went to.

We can see that in store X, for 15L the cost is 28 pounds, and for store Y the cost is 24 pounds.

So the correct option is Y.

Now, for 20 litres in that station, (using the same graph) we can see that the cost will be C=  32 pounds.

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Answer:

The fourth vertex needed to create the rectangle is (-7,-25).

Step-by-step explanation:

As per the property of a rectangle, the lengths of the opposite sides of a rectangle are the same.

Let,

point A=(-4,-25)

point B=(-4,-12)

point C=(-7,-12)

Thus, point D or the fourth vertex is (-7,-25).

Refer to the image for a better understanding.

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The polar coordinates (r, θ) for the given rectangular coordinates are

(10, π/3)

To convert rectangular coordinates (5, 5√3) to polar coordinates (r, θ), we can use the following formulas:

r = √(x² + y²)

θ = arc tan (y/x)

Given the rectangular coordinates (5, 5√3), we have:

x = 5

y = 5√3

let's calculate the values

r = √(5² + (5√3)²

= √(25 + 75)

= √100

= 10

θ = arctan(5√3/5)

= arctan (√3)

= π/3 (since θ is in the interval [0,2π))

Therefore, the polar coordinates (r, θ) for the given rectangular coordinates are (10, π/3).

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The distance to second base is approximately 127.28 feet. Round to the nearest hundredth

Since the angle is 45 degrees, the other side of the right triangle are equal, hence we have two sides of 90 ft to be used to find the hypotenuse

Using Pythagoras theorem given by the  the formula

hypotenuse² = opposite² + adjacent²

plugging the values as in the problem

let x be the required distance

x² = 90² + 90²

x² = 16200

x = √16200

x = 90√2

x = 127.28 ft (to the nearest hundredth)

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The  best measure of center for the data shown is the median, and its value is 17.

The median is the best measure of center for the given data set. To find the median, we arrange the numbers in ascending order:

10, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24

Since the data set has an odd number of values, the median is the middle value, which in this case is 17.

Therefore, the best measure of center for the data shown is the median, and its value is 17.

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Ricardo's annual interest rate is equal to 6%.

In Mathematics and Financial accounting, compound interest can be calculated by using the following mathematical equation (formula):

[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]

Where:

By substituting the given parameters into the formula for compound interest, we have the following;

[tex]2721.03 = 1500(1 + \frac{r}{4})^{4 \times 10}\\\\1.81402=(1 + \frac{r}{4})^{40}[/tex]

By taking 40th root of both sides of the equation, we have:

1.01500002226 = 1 + r/4

r/4 = 1.01500002226 - 1

r = 0.01500002226 × 4

Interest rate, r = 0.06 ×  100

Interest rate, r = 6%.

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Answer:

The polynomial 2x^3 + x^2 - 2x - 1 can be factored as (x + 1)(2x^2 - x - 1).

Step-by-step explanation:

To find the factors of the polynomial 2x^3 + x^2 - 2x - 1, we can use synthetic division or long division to divide the polynomial by the factor x + 1.

Using synthetic division:

-1 | 2 1 -2 -1

| -2 1 1

___________________

2 -1 -1 0

The result of the division is 2x^2 - x - 1.

So, the polynomial 2x^3 + x^2 - 2x - 1 can be factored as (x + 1)(2x^2 - x - 1).

Answer:

Step-by-step explanation:

Solution

verified

Verified by Toppr

given, 2x

3

+x

2

−2x−1

=x

2

(2x+1)−1(2x+1)

=(x

2

−1)(2x+1)

=(x+1)(x−1)(2x+1)

Answer:

A

Step-by-step explanation:

the inscribed angle JKL is half the measure of its intercepted arc

the sum of the arcs in a circle in a circle = 360°

since LK is a diameter the arc KL is equal to the measure of its central angle , that is

arc LK = 180° , then

LJ + JK + KL = 360°

LJ + 74° + 180° = 360°

LJ + 254° = 360° ( subtract 254° from both sides )

LJ = 106°

Then

∠ JKL = [tex]\frac{1}{2}[/tex] × 106° = 53°

Answer:

Hi

Please mark brainliest ❣️

Step-by-step explanation:

-3 1/4 ÷ 2 1/3

Change to improper fraction

-13/4 ÷ 7/3

-13/4 × 3/7

-39/28 or -1 11/28

Answer:

It takes 135 of the 1/3 unit cubes to fill the prism.

Step-by-Step Explanation:

The volume of the prism is 5 cubic units. This means the prism can be filled with five 1×1×1 unit cubes

How many cubes with 1/3 unit side lengths can fit in a cube with 1-unit side lengths?

There are 27 cubes with 1/3 unit side lengths in 1 cubic unit.

Since the rectangular prism is made up of 5 cubic units, we would have 5×27 total cubes with 1/3 unit side lengths.

It takes 135 of the 1/3 unit cubes to fill the prism.

The correct matches are:

-10u³ ⇒ -15u³ + 5u³

  5u³ ⇒ 10u³ + (-5u³)

 15u³ ⇒ 10u³ + 5u³

 -5u³ ⇒ 5u³ + (-10u³)

For the expressions:

Expression 1:

-15u³ + 5u³

To add these expression taking u³,

⇒ (-15 + 5)u³

⇒ -10u³

Expression 2:

⇒ 10u³ + (-5u³)

To add these expression taking u³

⇒ (10 - 5)u³

⇒ 5u³

Expression 3:

⇒ 10u³ + 5u³

To add these expression taking u³

⇒ 15u³

Expression 4:

⇒ 5u³ + (-10u³)

To add these expression taking u³

⇒ (5 - 10)u³

⇒ -5u³

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The complete question is attached below:

Angle 4 is equal to the sum of the measures of the two nonadjacent interior angles because of the corresponding angles theorem for parallel lines and a transversal.

Angle 4 can be considered as the sum of two nonadjacent interior angles because of the properties of parallel lines and a transversal line. When a transversal line intersects two parallel lines, it creates several pairs of corresponding angles, alternate interior angles, alternate exterior angles, and consecutive interior angles.

In this case, we have two parallel lines and a transversal line that intersects them.

Angle 4 is formed by the intersection of the transversal line with one of the parallel lines.

The two nonadjacent interior angles that we are interested in can be identified as the adjacent angles on the other parallel line, corresponding to the same transversal line.

According to the corresponding angles theorem, when two parallel lines are cut by a transversal line, the corresponding angles formed are congruent.

Therefore, the two nonadjacent interior angles that correspond to angle 4 are congruent.

Since congruent angles have the same measure, we can conclude that the measure of angle 4 is equal to the sum of the measures of the two nonadjacent interior angles.

This property holds true for any pair of parallel lines intersected by a transversal line.

It is a fundamental concept in geometry that helps us understand the relationships between angles formed by parallel lines and transversals, and it is useful in solving various geometric problems and proofs.

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Using the distributive property, the boxes would be filled as follows;

(4 × 3 ) + (4 × 7 )

Mathematicians use the distributive property to explain how multiplication distributes across addition or subtraction. It offers a rule for expanding terms and condensing expressions.

With the help of the distributive property, we can factor polynomials, simplify expressions, and solve equations more quickly in algebra and arithmetic.

We know that;

4 × (3 + 7) =(4 × 3 ) + (4 × 7 )

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