What is the standard form of the following equation?
y=−2/5x+4 Use integers for A, B, and C. Enter your answer in the box.
Which statement best explains whether △PQR is congruent to △XYZ?
△PQR is congruent to △XYZ because △PQR can be mapped to △XYZ by a rotation of 180° about the origin.
△PQR is congruent to △XYZ because △PQR can be mapped to △XYZ by a translation 5 units down followed by a reflection across the y-axis.
△PQR is not congruent to △XYZ because there is no sequence of rigid motions that maps △PQR to △XYZ.
△PQR is congruent to △XYZ because △PQR can be mapped to △XYZ by a reflection across the y-axis followed by a reflection across the x-axis.
what are the zeros of the quadratic function f(x)=8x2-16x-15
Answer: The zeroes of the given polynomial f(x) are
[tex]x=1-\sqrt{\dfrac{23}{8}},~~~x=1+\sqrt{\dfrac{23}{8}}.[/tex]
Step-by-step explanation: We are given to find the zeroes of the quadratic function below:
[tex]f(x)=8x^2-16x-15.[/tex]
To find the zeroes, we must find the roots of the following equation
[tex]f(x)=0\\\\\Rightarrow 8x^2-16x-15=0~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex].
We know that the roots of the quadratic equation of the form [tex]ax^2+bx+c=0,~a\neq 0[/tex] is given by
[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}.[/tex]
In the given quadratic equation , a = 8, b = -16 and c = - 15.
Therefore, the roots of the equation are
[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\\\\Rightarrow x=\dfrac{-(-16)\pm\sqrt{(-16)^2-4\times 8\times (-15)}}{2\times 8}\\\\\\\Rightarrow x=\dfrac{16\pm\sqrt{256+480}}{16}\\\\\\\Rightarrow x=\dfrac{16\pm\sqrt{786}}{16}\\\\\\\Rightarrow x=\dfrac{16\pm4\sqrt{46}}{16}\\\\\\\Rightarrow x=\dfrac{4\pm\sqrt{46}}{4}\\\\\\\Rightarrow x=1\pm\sqrt{\dfrac{46}{16}}\\\\\\\Rightarrow x=1\pm\sqrt{\dfrac{23}{8}}\\\\\\\Rightarrow x=1-\sqrt{\dfrac{23}{8}},~~~x=1+\sqrt{\dfrac{23}{8}}.[/tex]
Thus, the zeroes of the given polynomial f(x) are
[tex]x=1-\sqrt{\dfrac{23}{8}},~~~x=1+\sqrt{\dfrac{23}{8}}.[/tex]
Option (C) is correct.
The zeroes of the given polynomial f(x) = 8x^2-16x-15 are x = 1 + [tex]\sqrt{23}[/tex] / 8 and x = 1 -[tex]\sqrt{23}[/tex] / 8 Thus, Option C is correct.
What is a quadratic equation?A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.
We are given to find the zeroes of the quadratic function f(x) = 8x^2 - 16x-15
f(x) = [tex]8x^2-16x-15[/tex] = 0
We know that the roots of the quadratic equation ax² + bx + c = 0 is
x = -b ± [tex]\sqrt{b^2 - 4ac}[/tex] / 2a
In the given quadratic equation , a = 8, b = -16 and c = - 15.
So,
x = -b ± [tex]\sqrt{b^2 - 4ac}[/tex] / 2a
x = -(-16) ± [tex]\sqrt{(-16)^2 - 4(8)(-15)}[/tex] / 2(8)
x = 16 ± [tex]\sqrt{256+ 480}[/tex] / 16
x = 16 ± [tex]\sqrt{786}[/tex] / 16
x = 4 ± [tex]\sqrt{46}[/tex] / 4
x = 1 ± [tex]\sqrt{23}[/tex] / 8
Thus, the zeroes of the given polynomial f(x) are
x = 1 + [tex]\sqrt{23}[/tex] / 8 and x = 1 -[tex]\sqrt{23}[/tex] / 8. Option C is correct.
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I feel really stupid but how do you solve: v+9/3+8
A personal trainer buys a weight bench for $500 and some weights (w) for $24 each. the trainer has a budget of $860.00. how many weights can the personal trainer purchase
Final answer:
To find out how many weights the personal trainer can purchase, subtract the cost of the weight bench from the budget and divide the remaining amount by the cost of each weight. The personal trainer can purchase 15 weights within the given budget.
Explanation:
To find out how many weights the personal trainer can purchase, we need to subtract the cost of the weight bench from the budget and divide the remaining amount by the cost of each weight.
Step 1: Subtract the cost of the weight bench ($500) from the budget ($860): $860 - $500 = $360.
Step 2: Divide the remaining amount ($360) by the cost of each weight ($24): $360 ÷ $24 = 15.
The personal trainer can purchase 15 weights within the given budget.
This budgeting approach demonstrates a systematic way for the personal trainer to allocate funds effectively, ensuring that both essential equipment and a sufficient quantity of weights can be acquired. By following these steps, the trainer maximizes the utility of the available budget, making informed decisions to support an efficient and well-equipped training environment.
Write the fraction 20/32 in simplest form.
The fraction given 20/32 can be written as 5/8 in its simplest form.
How to simplify fractions?The principle of simplifying fraction is to make both the numerator and the denominator smaller numbers but as proportional as the original fraction. This is convenient for mathematical operations and even for understanding proportions.
Now, to simplify fractions we need to divide the nominator and the denominator, the process is shown below:
20/32 divide both numbers by 420/ 4 = 532/ 4 = 8This means the new fraction is 5/8.
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One leg of a right triangle is 6 in. longer than the other leg. the hypotenuse of the triangle is 25 in. what is the length of each leg to the nearest inch?
The problem can be solved using the Pythagorean theorem. The lengths of the legs of the triangle are calculated as 15 inches for the shorter leg and 21 inches for the longer leg.
Explanation:In solving this mathematical problem, we can employ the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides- This theorem is normally written as a² + b² = c². We can let one leg of the right triangle be 'a', the other leg be 'a+6' (since one leg is 6 inches longer than the other), and the hypotenuse is 25 inches. From the equation, we substitute a and b with the values and get:
a² + (a + 6)² = 25²
This equation is solved to get the lengths of the legs. Solving results in 'a' being 15 inches (the shorter leg) and 'a+6' equals to 21 inches (the longer leg).
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what are the solutions to the system 10 + y = 5x + x2 5x + y = 1
Answer:
(1, -4) and (-11, 56)
What is the answer for 35=-7z
Sarah has a collection of nickels, dimes, and quarters worth $13.80. she has 10 more dimes than nickels and twice as many quarters as dimes. how many coins of each kind does she have?
Need help doing this problem!!
MATH HELP 20 POINTS!!!
A) Variable = x ( miles Tim walked )
B) Tim walked X miles, Molly walked 4+x miles ( 4 more than Tim)
Equation: x + x+4 = 10
C) x +x+4 = 10
2x+4 = 10
2x =6
x = 3
D)
Tim walked 3 miles, Molly walked 7 miles
How to do this ?? How
The volume of air inside a rubber ball with radius r can be found using the function v(r)=4/3 πr3 . What does v[5/7] represent?
a. the radius of the rubber ball when the volome equals 5/7 cubic feet
b. the volome of the rubber ball when the radius equals 5/7 feet
c. that the volume of the rubber ball is 5 cubic feet when the radius is 7 feet
d. that the volume of the rubber ball is 7 cubic feet when the radius is 5 feet
we know that
The volume of a sphere (rubber ball) is equal to
[tex]V=\frac{4}{3} \pi r^{3}[/tex]
where
r is the radius of the sphere (rubber ball)
The volume in function notation is equal to
[tex]V(r)=\frac{4}{3} \pi r^{3}[/tex]
in this problem we have
[tex]V(\frac{5}{7})[/tex]
that means
The radius of the rubber ball is [tex]\frac{5}{7}\ ft[/tex]
and
The volume of the rubber ball is [tex]V(\frac{5}{7})\ ft^{3}[/tex]
therefore
the answer is the option B
the volume of the rubber ball when the radius equals [tex]5/7[/tex] feet
Evaluate the determinant for the following matrix [144] [522] [155]
Factor this expression completely.
mn - 4m - 5n + 20
Simplifying expressions with negative exponents calculator
To simplify expressions with negative exponents, rewrite the negative exponent as the reciprocal of the base raised to the positive exponent.
Explanation:When simplifying expressions with negative exponents, you can use the rule that states a negative exponent can be rewritten as the reciprocal of the base raised to the positive exponent. For example, x^-3 can be rewritten as 1/x^3. You can use this rule with negative exponents in the numerator or denominator, as well as with negative exponents inside parentheses. Here’s an example:
8x^-2 / (2y^-3) = 8 / (2y^3x^2)
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Heather works as a waitress at her family`s restaurant. she works 2 hours every morning during the breakfast shift and returns to work work each evening for the dinner shift. In the last 4 days ,she worked 28 hours. If Heather works the same number of hours every evening, how many hours did she work during each dinner shift?
I will give you 25 points for my other qusetion
PLEASE HELP ASAP!!! Explain how you found the answer!!
kims sisters age = x
kim = 2x
A) 2x +x = 36
B) 2x+ x = 36
3x =36
x = 36/3
x = 12
kim's sister is 12
kim is 24
The 440 yard dash in track has been replaced by the 400 meter dash. which is the longer distance and by how many meters? hint: 1 yard = 3 feet
Final answer:
The 400 meter dash is the longer distance by 2.336 meters.
Explanation:
In order to determine which is the longer distance, we need to convert both the 440 yards and the 400 meters into the same unit of measurement. Since 1 yard is equal to 0.9144 meters, we can convert the 440 yards into meters by multiplying it by 0.9144:
440 yards * 0.9144 meters/yard = 402.336 meters
Therefore, the 400 meter dash is the longer distance by 2.336 meters.
how do you find the derivative of 4
by rule the derivative of a constant is 0
so the answer for this is 0
The clean up hitter on a baseball tean batted 1/3 of the runs the team scored. The hitter batted in 3 runs. Select the equation that represents the number of n of runs the team scored. Then solve the equation:
a.1/3n=3B.n/3=1/3C.3n=1/3D.3n=9
Soda is sold in aluminum cans that measure 6 inches in height and 2 inches in diameter. how many cubic inches of soda are contained in a full can?
A cylinder is a three-dimensional figure that has a radius and a height.
The volume of a cylinder is given as:
Volume = π r²h
The amount of soda in a full can is 18.84 cubic inches.
What is a cylinder?A cylinder is a three-dimensional figure that has a radius and a height.
The volume of a cylinder is given as:
Volume = π r²h
Example:
The volume of a cup with a height of 5 cm and a radius of 2 cm is
Volume = 3.14 x 2 x 2 x 5 = 62.8 cubic cm
We have,
Aluminum cans:
Height = 6 inches
Diameter = 2 inches
Radius = diameter/2 = 2 / 2 = 1 inches
The aluminum can is in the shape of a cylinder.
The volume of the aluminum can:
= πr²h
= 22/7 x 1 x 1 x 6
= 18.84 cubic inches
The amount of soda in a full can is 18.84 cubic inches.
Thus,
The amount of soda in a full can is 18.84 cubic inches.
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what is the recursive formula for this geometric sequence? -3,-21
Solve quadratic equations using completing the square then write in vertex form
what is the slope of the line given by the equation y=2.3x
License plates in a particular state display 22 letters followed by 33 numbers. how many different license plates can be manufactured for this state?
The total number of different license plates that can be manufactured in this state is 676,000. This is calculated by multiplying the 676 combinations of letters by the 1,000 combinations of numbers.
To find out how many different license plates can be manufactured in this state,
2 letters followed by 3 numbers. Each letter can be any of the 26 letters in the alphabet, and each number can be any digit from 0 to 9.Therefore, the total number of combinations for the letters is:
26 (choices for the first letter) * 26 (choices for the second letter) = 676The total number of combinations for the numbers is:
10 (choices for the first number) * 10 (choices for the second number) * 10 (choices for the third number) = 1000By multiplying these together, we get the total number of license plates:
676 * 1000 = 676,000Therefore, there can be 676,000 different license plates manufactured in this state.
If TOWN A has a yearly population of 3,225 and is growing by 100 people each year and TOWN B has a yearly population of 3,300 and is growing by 75 people per year, after how many years will the two populations be equal?
Find the coordinates of the other endpoint of the segment with the given endpoint (6,2) and midpoint (2,0)