2x^2 – 9x = 35
Solve the quadratic equation using the quadratic formula.

Answer:

x = 2

Step-by-step explanation:

The axis of symmetry of a parabola is a vertical line that divides the parabola into two congruent halves.

The x -coordinate of the vertex is the equation of the axis of symmetry of the parabola.

You already know the vertex, so the axis of symmetry is the line, x = 2.

This is because the equation to graph a vertical line is x = a, where a is the x-value you want the line to intersect.

The axis of symmetry for a parabola with the vertex at (2, -4) is the vertical line x = 2.

If the vertex of a parabola is at the point (2, -4), then the axis of symmetry is a vertical line that passes through the x-coordinate of the vertex. Thus, the equation of the axis of symmetry would be x = 2. This is because, for a parabola, the axis of symmetry always passes through the vertex and is perpendicular to the directrix.

Answer:

a + b + d - 1 = c

Step-by-step explanation:

a + b + d - 1 = c

10 + 6 + 3 - 1 = 18

Answer:

C

Step-by-step explanation:

Answer:

x^2 + y^2 = 25 (third one)

Step-by-step explanation:

formula is x^2 + y^2 = r^2 (r = the radius)

the radius is 5 so r^2 is 25.

The equation of the circle is x² + y² = 5²,  is x²+ y² = 25.

To determine the equation of the circle with its center at (-0, 0) and passing through the point (-3, -4),  use the standard equation of a circle:

(x - h)² + (y - k)² = r²

Where (h, k) represents the center coordinates of the circle and r represents the radius.

In this case, the center of the circle is (-0, 0), so the equation becomes:

(x - 0)² + (y - 0)² = r²

Simplifying:

x² + y² = r²

to find the radius (r). Since the circle passes through the point (-3, -4), we can use the distance formula to find the radius:

r = √((x2 - x1)²+ (y2 - y1)²)

r = √((-3 - 0)² + (-4 - 0)²)

r = √(9 + 16)

r = √25

r = 5

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Final Answer:

$75

Explanation:

To calculate your gross base pay, you only need to consider your hourly wage and the number of hours worked. Tips, FICA taxes, federal tax withholding, and state tax withholding are not included since they are either extra income (tips) or deductions (taxes) that do not affect gross base pay.
Your hourly wage is $7.50.
You worked for 10 hours.
To calculate the gross base pay, you multiply the hourly wage by the number of hours worked:
Gross Base Pay = Hourly Wage * Hours Worked
Gross Base Pay = $7.50 * 10
Gross Base Pay = $75.00

Your gross base pay for 10 hours of work is $75.00. This is before any tips and deductions are taken into account.

The gross base pay for 10 hours of work at $7.50 per hour is calculated by multiplying the hourly wage by the number of hours worked.

Gross base pay = Hourly wage × Number of hours worked

Gross base pay = $7.50 × 10 hours

Gross base pay = $75.00

Therefore, the gross base pay is $75.00.

To determine the gross base pay, one only needs to consider the hourly wage and the number of hours worked. The gross base pay does not take into account any deductions or tips; it is simply the total amount of money earned from the hourly wage before any deductions are made. In this case, the hourly wage is $7.50, and the individual worked for 10 hours. By multiplying these two values together, we obtain the gross base pay of $75.00. This is the amount of money the individual earned from their wages alone, prior to any taxes or other deductions being subtracted.

Step-by-step explanation:

cot(x/2) = 1

Take inverse of both sides.

tan(x/2) = 1

Solve for x/2.

x/2 = π/4 + kπ

Solve for x.

x = π/2 + 2kπ

Possible values for x are π/2, 5π/2, 9π/2, etc.

Answer:

it's 3pi

Step-by-step explanation:

Answer:

American presidents are taller than the average American man

Step-by-step explanation:

We have to:

H0: m = 69.5

Ha: m> 69.5

Since the population standard deviation is unknown and the hypothesis test of the population mean, the t-test should be used. Here the sample size is large, so we can assume that the sample distribution of the sample mean It is normal.

sd = 2.77, x = 70.78 and n = 43

Then the test statistics will be:

t = (x - m) / (s / n ^ (1/2))

replacing

t = (70.78 - 69.5) / (2.77 / 43 ^ (1/2))

t = 3.03

Here the test is correct and the degree of freedom of the test is df = n-1 = 43-1 = 42.

Critical approach:

So

alpha = 0.05, the critical value of the test is 1,682.

Rejection region:

If t> 1,682, reject the null hypothesis.

Since the value of the test statistics is greater than the critical value, we reject the null hypothesis.

P-value approach:

The p-value using the Excel function "= TDIST (3,030,42,1)" is:

p value = 0.0021

Since the p-value is less than α = 0.05, we reject the null hypothesis.

Which means that American presidents are taller than the average American man.

Answer:

American presidents are taller than the average American man

Step-by-step explanation:

Given Data :  

Test statistics will be:

t = (x - m) / (s / n ^ (1/2))

t = (70.78 - 69.5) / (2.77 / 43 ^ (1/2))  

t = 3.03

df = n-1 = 43-1 = 42.

Thus the American presidents are taller than the average American man

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The answer is 5500 meters.

i.e. 5500 meters is shorter than 6 km.

Measurement is the quantification of attributes of an object or event, which can be used to compare with other objects or events. In other words, measurement is a process of determining how large or small a physical quantity is as compared to a basic reference quantity of the same kind.

Here, we have,

6 kilometers=6000m.

because, 1 kilometer=1000 meters

6000>5500

Hence,  5500 meters is shorter than 6 km.

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Answer:

18.84 km

Step-by-step explanation:

The formula for the circumference is 2πr. 6.28*3=18.84

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Have a nice day.

Final answer:

The circumference of the circle is approximately 18.84 kilometers.

Explanation:

The circumference of a circle is calculated using the formula C = 2πr, where r is the radius of the circle.

In this case, the radius of the circle is given as 3 kilometers.

So, the circumference of the circle is C = 2π(3) = 6π kilometers.

To find a numerical approximation for π, we can use the value 3.14.

Therefore, the circumference of the circle is approximately C = 6(3.14) = 18.84 kilometers. This calculation demonstrates a practical method to assess the distance around a circle based on its radius, providing a tangible measurement for the circle's outer boundary in a real-world context.

Answer:

14

Step-by-step explanation:

4 times 7 (28) divided by 2 (14)

The area of a triangle is base times height times 1/2

the answer is C                                                      

dont know if its to late to answer but here

Answer: 30

Step-by-step explanation:

I’m big smart

Answer:

30

Step-by-step explanation:

24^2 + 18^2 = c^2

(576 + 324 = c)

900 = c^2

[tex]\sqrt{900}[/tex] = 30

c = 30

Answer:

Equal Areas

Step-by-step explanation:

Area of a Rectangle =Base X Height

Area of a Parallelogram =Base X Height

If the rectangle and a parallelogram have the same base and the same height, then their areas are equal.

Take for an example,

A rectangle with a base of 5 cm and a height of 6cm

For a parallelogram with same base and height

Final answer:

A rectangle and a parallelogram with the same base and height have equal areas as both can be calculated using the formula Base x Height = Area, disregarding the shape's orientation.

Explanation:

A rectangle and a parallelogram with the same base and height will have the same area. This is because the area of both shapes can be calculated by multiplying their base by their height. For the rectangle, this is straightforward as the height is perpendicular to the base. In the case of a parallelogram, the height is also considered perpendicular to the base, but it might be oriented at an angle relative to the base's length. Despite these differences in shape orientation, the calculation Base x Height = Area still applies, resulting in equal areas if the base and height measurements are the same.

Answer:

25%

Step-by-step explanation:

There are 2 parrots out of 8 animals. Probability is 2/8 or 1/4 or 25%

Answer:

2(x^2+9)

Step-by-step explanation:

2x^2 +18

Factor out a 2

2(x^2+9)

Answer:

y<.73x+2

Step-by-step explanation:

To create an inequality that describes a scenario, you need to identify the relationship between two metric measurements. You can represent this inequality using appropriate symbols and sketch a graph to visualize the scenario.

To create an inequality that describes the scenario, you need to identify the relationship between two metric measurements.

For example, let's say we have two cars and we want to describe the age of one car relative to the other.

If Car A is at most 5 years old, we can represent this inequality as age of Car A ≤ 5.

To sketch the graph, you would plot the age of Car A on the x-axis and shade the area that represents Car A being at most 5 years old.

Answer:

12.87

Step-by-step explanation:

If the angle of depression is 25, then the angle of elevation is also 25.

You need to use tangent for this problem. (opposite and adjacent sides)

Use tan(25)= 6/x

Divide 6 by tan(25) = 12.87

Answer:

z= 18.075222

Step-by-step explanation:

Z=35.0780212-17.0027992

so z= 18.075222

Answer:

18.075222

Step-by-step explanation:

17.0027992+z=35.0780212

leave z so that it's by itself by subtracting.

z=35.0780212-17.0027992

then solve

z=18.075222

The surface area of a square pyramid is the sum of the area of the base and the area of the four side squares. The surface area of the square base pyramid is 525 in².

The surface area of a square pyramid is the sum of the area of the base and the area of the four side squares. It is given by the formula,

Surface Area of the Square pyramid = a² + 2al

where a is the length of the side of the base, and l is the length of the slant height of the pyramid.

The length of the base of the square pyramid is 15 inches, while the length of the slant height of the pyramid is 10 inches. Therefore, the surface area of the pyramid is,

[tex]\text{Surface Area of the Square pyramid} = a^2 + 2al[/tex]

                                                         [tex]\rm = (15)^2 + (2 \times 15 \times 10)\\\\= 225 + 300\\\\= 525\ in^2[/tex]

Hence, the surface area of the square base pyramid is 525 in².

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Answer:

1, 3

Step-by-step explanation:

2x^2 - 8x + 6 = 0 -->

x^2 - 4x + 3 = 0

(x-1)(x-3) = 0

x = 1, 3

OR

2x^2 - 8x + 6 = 0 -->

x^2 - 4x + 3 = 0 -->

(-(-4) +-sqrt((-4*-4) -4(1 * 3)))/2 -->

(4 +-sqrt(4))/2 -->

(4 +/-2)/2 -->

6/2 or 2/2 -->

3, 1

Final answer:

The solutions to the quadratic equation 2x^2 - 8x + 6 = 0, found using the quadratic formula, are x = 1 and x = 3.

Explanation:

To find the solutions to the quadratic equation 2x^2 - 8x + 6 = 0 using the quadratic formula, we first identify the coefficients: a = 2, b = -8, and c = 6. Then, we substitute these values into the quadratic formula 'x = (-b ± √(b^2 - 4ac)) / (2a)'. The solutions can be found by carrying out the arithmetic operations.

Plugging the values into the formula gives us:

x = (8 ± √((-8)^2 - 4*2*6)) / (4)

x = (8 ± √(64 - 48)) / (4)

x = (8 ± √(16)) / (4)

x = (8 ± 4) / 4

Therefore, we have two solutions:

x = (8 + 4) / 4 = 12 / 4 = 3

x = (8 - 4) / 4 = 4 / 4 = 1

So, the solutions to the equation 2x^2 - 8x + 6 = 0 are x = 1 and x = 3.

Answer:

1/26 or 1 out of 26

Step-by-step explanation:

only 2 red tens

52 cards in a deck

2/52=1/26

Answer:

260

Step-by-step explanation:

divide 3,648 by 14

this equals 260.57

Because he is putting the same amount of candy in each bag, you would round down. He is not going to put a fraction of candy in a bag so he would be able to make 260 bags with some candy left over.

Therefore, Mr. Fox was able to make 260 treat bags with 14 pieces of candy in each.

To solve the problem, we need to determine how many treat bags of 14 pieces each can be made from 3,648 candies. This is a simple division problem where the total number of candies is divided by the number of candies per treat bag.

Here is the step-by-step solution:

1. Start with the total number of candies Mr. Fox has, which is 3,648.

2. Determine the number of candies per treat bag, which is given as 14.

3. Divide the total number of candies by the number of candies per treat bag to find out how many treat bags can be made.

4. Perform the division: [tex]\( \frac{3,648}{14} = 260 \)[/tex].

Mr. Fox was able to make 260 treat bags.

Answer:

The natural, hexagon geometry of a snowflake

Step-by-step explanation:

Answer:

.

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

Let's start by converting this to standard form.

[tex]x^2+10x+y^2-4y=20\\(x^2+10x+25)-25+(y^2-4y+4)-4=20\\(x+5)^2+(y-2)^2=49[/tex]

The center of the circle is at (-5,2), and the radius is [tex]\sqrt{49}=7[/tex] units. Hope this helps!

The radius of the circle is r = 7 units

A circle is a closed figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle

The circumference of circle = 2πr

The area of the circle = πr²

where r is the radius of the circle

The standard form of a circle is

( x - h )² + ( y - k )² = r²,

where r is the radius of the circle and (h,k) is the center of the circle.

The equation of circle is ( x - h )² + ( y - k )² = r²

For a unit circle , the radius r = 1

x² + y² = r² be equation (1)

Now , for a unit circle , the terminal side of angle θ is ( cos θ , sin θ )

Given data ,

Let the radius of the circle be r

Now , the equation of circle is

x² + y² + 10x - 4y - 20 = 0

And , standard form of a circle is

( x - h )² + ( y - k )² = r²

We need to complete the square for both the x and y terms in the given equation:

x² + y² + 10x - 4y - 20 = 0

( x² + 10x + 25 ) + ( y² - 4y + 4 ) - 49 = 0

On Adding and subtracting constants to complete the square

( x + 5 )² + ( y - 2 )² = 49

Now we can see that the equation is in standard form.

The center of the circle is at (-5, 2), and the radius is the square root of 49, which is 7

Hence , the radius is 7 units

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Answer:

Step-by-step explanation:

let the numbers be x and y

x-y>x

or -y>0

or y<0

and x+y>21

or if we want to solve further then

y<0

and x+y>21

or y>21-x

or 21-x<y <0

so 21-x<0

or 21<x

or x>21

Final answer:

The system of inequalities for the given situation is x - y > x and x + y > 21, where x represents the first number and y represents the second number.

Explanation:

System of Inequalities:

x - y > x

x + y > 21

Here, x represents the first number and y represents the second number.

Answer:

the answer is -3

Step-by-step explanation:

To find the z-score corresponding to a blood pressure reading, you would use the formula:
[ z =fraction{(X -mu)}{sigma}]

where:
- \( X \) is the value for which you're calculating the z-score,
- \( \mu \) is the mean of the population, and
- \( \sigma \) is the standard deviation of the population.
Given the values from the question:
- \( X = 77 \) (the blood pressure score for which we're finding the z-score),
- \( \mu = 122 \) (the mean systolic blood pressure reading),
- \( \sigma = 15 \) (the standard deviation of the systolic blood pressure readings).
Now we can plug these values into the formula:
[ z = \fraction{(77 - 122)}{15} \]
[ z = \fraction{-45}{15} \]

[ z = -3 \]
So, the z-score corresponding to the blood pressure reading of 77 is -3. This means that a reading of 77 is 3 standard deviations below the mean systolic blood pressure reading for customers at the gym franchise.

Answer:

$221

Step-by-step explanation:

First we need to find what is 35% of 340. To do this, we multiply 340 by 0.35. This gives us 119. Because this is the amount they are taking off, we need to subtract it from the initial price. 340-119=221. Therefore the price after being marked down is $221 :)

Answer:

Step-by-step explanation:

Answer:

B,C,E

Step-by-step explanation:

Answer:

C) 50%

Step-by-step explanation:

The probability the student earns a B on the second exam, given that a student earns a B on the first exam is 0.5 or 50%.

Probability of an event is the ratio of number of favorable outcome to the total number of outcome of that event.

The below table shows the number of students in a class that received letter grades on 2 recent exams.

The first exam is shown across the top and is summarized as A1, B1, and C1, and the second exam is in the first column, A2, B2, and C2.  In the given table, the student get B in first exam is,

[tex]X=(7+10+3)\\X=20[/tex]

The student get B in second exam is which got B in first exam are 10.

[tex]Y=10[/tex]

The total number of students are,

[tex]2+2+1+7+10+3+1+3+1=30[/tex]

The probability the student earns a B on the second exam, given that a student earns a B on the first exam, is,

[tex]P(Y|X)=\dfrac{P(Y\cap X)}{P(X)}\\P(Y|X)=\dfrac{\dfrac{10}{30}}{\dfrac{20}{30}}\\P(Y|X)=0.5[/tex]

Thus, the probability the student earns a B on the second exam, given that a student earns a B on the first exam, is 0.5 or 50%.

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Answer:

A. 4.1 yards

Step-by-step explanation:

Multiply $10.25 by 2 because there is 2 fabrics. You would get 20.5 and divide 20.5 from 85.00 and the answer is 4.1.

He buys 5.6 yards of wool, the correct option is B.

In algebra, an equation can be defined as a mathematical statement consisting of an equal symbol between two algebraic expressions that have the same value.

A tailor pays $10.25 per yard for wool and pays $5.75 per yard for cotton.

He bought 4.8 yards of cotton and spent a total of $85.00 on the two types of fabric.

Let x be the yards of wool did he buy.

The yards of wool did he buy is given by;

[tex]\rm 10.25x + 5.75 \times 4.8 = 85\\\\10.25 x=85-27.6\\\\10.25 x=57.4\\\\x=\dfrac{57.4}{10.25}\\\\x=5.6[/tex]

Hence, he buys 5.6 yards of wool, the correct option is B.

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