For a general quadratic equation with rational coefficients
[tex]ax^2+bx+c=0,\,\,\,\,a,b,c \in Q[/tex]
the two solutions are:
[tex]x_{1,2} = \frac{-b\pm\sqrt{b^2-4ac}}{2a}=\frac{-b\pm\sqrt{D}}{2a}[/tex]
where D is the determinant.
Clearly, a solution will a rational number as long as [tex]\sqrt{D}[/tex] is rational. However, it can be shown that a square root of an integer is only rational if its value is an integer. In other words, [tex]\sqrt{D}[/tex] is rational if and only if the determinant is a perfect square, [tex]D=n^2, \,\,\,n\in N[/tex], otherwise the square root is irrational. Therefore the coefficients of quadratic equations that are to have rational solutions must satisfy the following condition:
[tex]b^2-4ac=n^2\,\,\,n\in N[/tex]
I took a test that has 25 questions. I scored 80 %. How many questions did I get wrong and how many did I get right?
Answer:
20 good answers, 5 bad.
Step-by-step explanation:
100% - 25 questions
80% - x (correct answers)
x = [tex]\frac{80*25}{100} = 20[/tex]
25 - x = 25 - 20 = 5 bad answers
Veterinarian jasmin cato has 5/9 of a quart of medication, she wishes to prescribe this medication for 6 cats in her pet hospital. If she divides the medication evenly, how much will each cat receive?
heeeeeeeeellpp
what is the measure of xwz
Answer:
180
Step-by-step explanation:
The measure of Angles XWZ is 120 degrees.
To find the measure of XWZ, we need to consider the relationships between different angles in the diagram.
First, we know that angle XYZ is 50 degrees.
Since XY and YZ are tangent to circle O, angle XYZ is equal to angle OXZ. Therefore, angle OXZ is also 50 degrees.
Next, we know that the circumference of circle O is 120 degrees.
A full revolution around a circle is 360 degrees, so the ratio of the circumference of circle O to a full revolution is 120/360 = 1/3.
Since angle OXZ is one-third of a full revolution, it will be equal to one-third of 360 degrees, which is 120 degrees. So, the measure of angle XWZ is 120 degrees.
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The probable question may be:
In the diagram below XY and YZ are tangent to circle O . What is the measure of XWZ? As Angle XYZ is 50 degree and circumference of circle O is 120 degree.
A. 150 degree
B. 180 degree
C. 240 degree
D. 210 degree
Mr. Parker wants to rent a cargo van for a day. It will cost the daily fee of $50 plus $0.35 per mile driven. Part A Let m = the number of miles Mr. Parker drives for the day. Write an expression that shows the amount he will pay for the van
Answer:
The expression for the amount Mr. Parker will pay for the van be
x = 50 + 0.35m
Step-by-step explanation:
Let us assume that the amount Mr. Parker will pay for the van be x.
As given
Mr. Parker wants to rent a cargo van for a day.
It will cost the daily fee of $50 plus $0.35 per mile driven.
Let m = the number of miles .
Than the expression for the amount Mr. Parker will pay for the van.
x = 50 + 0.35m
Therefore the expression for the amount Mr. Parker will pay for the van be
x = 50 + 0.35m
Answer:
50+0.35m or 50+ .35m
your welcome, angel!
20 POINTS!!!! MATH HELP PLEASE I WILL BE MARKING BRAINLY PLEASE SHOW ALL OF YOUR WORK
Answer:
Letter A:
There is a 42.857143% chance of picking a black marble out of the bag. This is because there are 7 marbles total and 42.857143% of them(3/7) are black, so that is the probability.
Letter B:
There is a 14.285714% chance of picking this. The chance of picking a black black marble first is 3/7, which you multiply by the chance of picking a marble out on your second try without putting the first black marble back in ,which is 1/3. That gives you 1/7, or the percent above.
Letter C:
The probability of picking a black marble, replacing it, then picking another black marble is 18.367347%, or 9/49. You take the probability of picking out a black marble first, 3/7, and multiply it by the chance of picking another black marble after replacing the first one, which is also 3/7.
Letter D:
The probability is different for B and C because in B the chance for the second one is less because for the second pick there are less marbles and a third of them are black. In C the chance of picking a black marble in the second is the same as in the first because you are putting the original back in.
ASAP Please how to solve 27 points!
Answer:
88 ft^2
Step-by-step explanation:
To find the surface area of a rectangular figure
SA = 2(lw+lh+hw)
where l=length, w= width, h = height
let l=6, h=2, w=4
SA = 2(lw+lh+hw)
= 2 (6*4+ 6*2+ 2*4)
=2 (24+12+8)
=2 (44)
= 88
SA = 88 ft^2
[ Answer ]
88 Ft^2
[ Explanation ]
- Formula for area of a rectangular prism -
A = 2(w * l + h * l + h * w)
In other words:
Area = width times length + height times length + height times width * 2
- Width times length -
4 * 6 = 24
- Height times length -
2 * 6 = 12
- Height Times Width -
2 * 4 = 8
- Add -
24 + 12 + 8 = 44
- Multiple By 2 -
44 * 2 = 88
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A hand of five cards is dealt from a normal pack of 52 cards, find the probability that there is no aces
simplify
√49^8
A. a√24.5
B. 7a^8
C. 7√5a^8
D.7a^4
Answer: (D) 7a⁴
Step-by-step explanation:
[tex]\sqrt{49a^8}[/tex]
[tex]=\sqrt{49} \ \cdot \sqrt{a^8}[/tex]
[tex]=\sqrt{7\cdot 7} \ \cdot \sqrt{a\cdot a\cdot a\cdot a\cdot a\cdot a\cdot a\cdot a}[/tex]
Two on the inside of the radical (square root) symbol makes One on the outside. Simplify by looking for pairs.
[tex]=\sqrt{\underline{7\cdot 7}} \ \cdot \sqrt{\underline{a\cdot a}\cdot \underline{a\cdot a}\cdot \underline{a\cdot a}\cdot \underline{a\cdot a}}[/tex]
= 7 · a · a · a · a
= 7a⁴
There are 3 white marbles and 7 blue marbles in a bag. Jamie will randomly pick two marbles out of the bag without replacing the first marble chosen. What is the probability of Jamie's picking 2 white marbles?
A) 1/15
B) 1/18
C) 1/20
D) 1/7
Answer:
1/7 is the probability hope this helps
Answer:
A) 1/15
Step-by-step explanation:
The probability of picking a white marble is 3/10. Then 2 of the remaining 9 marbles are white, so the probability of picking one is 2/9.
The joint probability is (3/10)·(2/9) = 6/90 = 1/15
Calculate s75 for the arithmetic sequence defined by
The formula of a sum of an arithmetic sequence:
[tex]S_n=\dfrac{a_1+a_n}{2}\cdot n[/tex]
We have n = 75 and [tex]a_n=67-2n[/tex].
Calculate the first and seventy-fifth term:
[tex]a_1=67-2(1)=67-2=65\\\\a_{75}=67-2(75)=67-150=-83[/tex]
Substitute:
[tex]S_{75}=\dfrac{65+(-83)}{2}\cdot75=\dfrac{-18}{2}\cdot75=-9\cdot75=-675[/tex]
Answer: -675The value of [tex]\rm S_{75}[/tex] is -675 and this can be determined by using the formula of the sum of n terms in the arithmetic sequence and the given data.
Given :
[tex]\rm a_n= 67-2n[/tex] --- (1)
The following steps can be used in order to determine the value of [tex]\rm S_{75}[/tex]:
Step 1 - Substitute the value of (n = 1) in the expression (1).
[tex]\rm a_1= 67-2(1)= 65[/tex]
Step 2 - Substitute the value of (n = 75) in the expression (1).
[tex]\rm a_{75}= 67-2(75)= -83[/tex]
Step 3 - Now, the formula of sum in an arithmetic sequence is given below:
[tex]\rm S_n=\dfrac{a_1+a_n}{2}\times n[/tex]
where n is the total number of terms, [tex]\rm a_1[/tex] is the first term, and [tex]\rm a_n[/tex] is the last term.
Step 4 - Substitute the values of the known terms in the above expression.
[tex]\rm S_{75}=\dfrac{65-83}{2}\times 75[/tex]
Step 5 - Simply the above expression.
[tex]\rm S_{75} = -675[/tex]
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Danny was was 184.56 pounds last week. He is on a special weight gain program with a trainer. What was his average daily gain?
184.56:7≈26.37 pounds
Chapman’s brickyard sells bricks and blocks. A brick costs $0.38 and a block costs $1.56. The brickyard filled a $24.80 order, which contained 28 items
a. Write a system of equations that can be used to find the number of bricks and blocks in the order.
b. How many blocks were in the order?
Answer:
(a) A system of equations:
[tex]0.38x+1.56y = 24.80[/tex]
[tex]x+y = 28[/tex]
(b) Number of blocks were in the order is, 12
Step-by-step explanation:
(a)
Let x represents the number of bricks and y represents the number of blocks.
As per the given statement:
A bricks costs $ 0.38 and a block costs $1.56.
Total bricks costs = 0.38x and total block costs = 1.56y
The brickyard filled $24.80 order.
⇒ [tex]0.38x+1.56y = 24.80[/tex] ......[1]
Since, it contained 28 items.
⇒[tex]x+y = 28[/tex] ....[2]
Multiply equation [2] both sides by 0.38 we have;
[tex]0.38(x+y) = 0.38 \times 28[/tex]
Using distributive property: [tex]a\cdot (b+c) = a\cdot b + a\cdot c[/tex]
0.38x +0.38 y = 10.64 ......[3]
Subtract equation [3] from [1] to get x eliminated ;
[tex]0.38x+1.56y -0.38x -0.38y= 24.80 - 10.64[/tex]
Combine like terms;
1.18y =14.16
Divide both sides by 1.18 we have;
[tex]\frac{1.18y}{1.18} = \frac{14.16}{1.18}[/tex]
Simplify:
[tex]y = 12[/tex]
Substitutes this y value in equation [2] to solve for x;
x + 12= 28
Subtract 12 from both sides we get;
x +12-12 =28-12
Simplify:
x = 16
Therefore, a system of equations that can be used to find the number of bricks and the number of blocks in the order:
[tex]0.38x+1.56y = 24.80[/tex]
[tex]x+y = 28[/tex]
(b)
The number of blocks are in order(y), is 12.
Which matrix represents this system of equations?
-2y + 7z = 10
9x + 5y = 1
2x + z = -5
The augmented matrix is ...
[tex]\left[\begin{array}{ccc|c}0&-2&7&10\\9&5&0&1\\2&0&1&-5\end{array}\right][/tex]
Step-by-step explanation:Missing variables essentially have a coefficient of zero. Coefficients are listed in the same order in each row, and the matrix is "augmented" by the column of constants on the right side of each equation.
Answer:
0, -2, 7, 10
9, 5, 0, 1
2, 0, 1, -5
Step-by-step explanation:
A recipe calls for 3/4 cups of butter. Wanda wants to make half of the recipe. How many cups of butter does she need
Answer:
3/8 cups of butte
Step-by-step explanation:
She wants half of the recipe so that means 1/2 of the butter.
So it is 3/4 * 1/2 = 3/8 cups of butter.
Reggie bought a pair of hiking boots that were discounted by 30% off the original price. If the original price was $66.00, what was the discounted price of the hiking boots?
Answer:
He paid the discounted price of $44.22.
Step-by-step explanation:
66 x .33 = 21.78 off the original price
66 - 21.78 = 44.22 is what he paid
You may use a calculator to complete this test. if 1 egg and 1/3 cup of oil are needed for each bag of brownie mix, how many bags of brownie mix do you need if you want to use up all 3 eggs and 1 cup of oil?
Answer:
It would be three
Step-by-step explanation:
Select the intervals that must be tested. X < 5 x < 3 3 < x < 5 x > 3 x > 5
Answer:
5 and 33
Step-by-step explanation:
Answer:
x < 3
3 < x < 5
x > 5
Step-by-step explanation:
I got this right, so that's how I know this is the correct answer.
The original price of the water skis was $200. They are on sale for $150. What is the percent of discount?
Answer:
25%
Step-by-step explanation:
percent discount = [tex]\frac{discount}{original}[/tex] × 100%
discount = $200 - $150 = $50
percent discount = [tex]\frac{50}{200}[/tex] × 100% = 25%
Final answer:
To find the percent of discount, calculate the difference between the original and sale prices ($50), divide this by the original price, and multiply by 100 to get a 25% discount.
Explanation:
To calculate the percent of discount given on the water skis, you need to determine the difference between the original price and the sale price, and then find what percentage that difference is of the original price.
First, subtract the sale price from the original price to find the amount of discount:
Discount Amount = Original Price - Sale Price
Discount Amount = $200 - $150 = $50
Next, divide the discount amount by the original price and multiply by 100 to get the discount percentage:
Discount Percentage = (Discount Amount / Original Price) × 100
Discount Percentage = ($50 / $200) × 100 = 25%
Therefore, the percent of discount on the water skis is 25%.
What is the y-intercept of the line graphed?
Please enter your answer as an ordered pair in the form (x,y)
The height y (in feet) of a ball thrown by a child is
y = − 1/14x^2 + 6 x + 3
where x is the horizontal distance in feet from the point at which the ball is thrown.
How high is the ball when it leaves the child's hand? (Hint: Find y when x = 0)Your answer is y=
(b) What is the maximum height of the ball?(c) How far from the child does the ball strike the ground?
Answer:
3 ft129 ft84.5 ftStep-by-step explanation:
The given equation,
[tex]y=-\dfrac{1}{14}x^2+6x+3[/tex]
where,
x is the horizontal distance in feet and
y is the height of the ball in feet.
How high is the ball when it leaves the child's hand.
At the beginning when the ball leaves the hand of the child, the horizontal distance was 0, so putting x=0 we can get the height of the ball.
[tex]y_0=-\dfrac{1}{14}(0)^2+6(0)+3=3\ ft[/tex]
What is the maximum height of the ball.
As the quadratic function has negative leading coefficient, so it will open downwards and at the vertex we will get the maximum value of the function.
The coordinates of vertex are,
[tex]\left(-\dfrac{b}{2a},f\left(-\dfrac{b}{2a}\right)\right)[/tex]
Putting the values,
[tex]=\left(-\dfrac{6}{2\times -\frac{1}{14}},f\left(-\dfrac{6}{2\times -\frac{1}{14}}\right)\right)[/tex]
[tex]=\left(42,f\left(42\right)\right)[/tex]
Now,
[tex]y_{max}=f(42)=-\dfrac{1}{14}(42)^2+6(42)+3= 129\ ft[/tex]
How far from the child does the ball strike the ground.
At the end i.e when the ball touches the ground, the height of the ball is 0. So putting the value of y=0, in the equation,
[tex]\Rightarrow 0=-\dfrac{1}{14}x^2+6x+3[/tex]
[tex]\Rightarrow -\dfrac{1}{14}x^2+6x+3=0[/tex]
[tex]\Rightarrow -x^2+6x(14)+3(14)=0[/tex]
[tex]\Rightarrow -x^2+84x+42=0[/tex]
Solving the quadratic equation, we get
[tex]\Rightarrow x=-0.497,84.5[/tex]
As distance can not be negative, so only considering positive value,
[tex]x=84.5\ ft[/tex]
The ball is 3 feet high when it leaves the child's hand. The maximum height of the ball is 251 feet. The ball strikes the ground approximately 0.4 feet away from the child.
Explanation:To find how high the ball is when it leaves the child's hand, we need to calculate the height when x = 0. Plugging in x = 0 into the equation, we get y = -1/14(0)^2 + 6(0) + 3 = 3 feet. Therefore, the ball is 3 feet high when it leaves the child's hand.
To find the maximum height of the ball, we need to determine the vertex of the quadratic equation. The formula for the x-coordinate of the vertex of a quadratic equation in the form y = ax^2 + bx + c is given by x = -b/2a. In this case, the x-coordinate is x = -6/(-1/14) = 84 feet. Plugging x = 84 into the equation, we find y = -1/14(84)^2 + 6(84) + 3 = 251 feet. Therefore, the maximum height of the ball is 251 feet.
To find how far from the child the ball strikes the ground, we need to find the x-intercepts of the equation, which represent the points where y = 0. Setting y to 0 and solving for x, we get: -1/14x^2 + 6x + 3 = 0. Using the quadratic formula, we find two values for x: x = 14(6 ± √187) / (-2), which simplifies to approximately x = -0.4 and x = 85.4. The ball strikes the ground approximately 0.4 feet away from the child.
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The length of a rectangle is twice the with. If the perimeter of the rectangle is 60 units, find the area of the garden
w - width
2w - length
60 - perimeter
w + w + 2w + 2w = 6w - perimeter
The equation:
6w = 60 divide both sides by 6
w = 10 → 2w = 2 · 10 = 20
The area: A = width × length
A = (10)(20) = 200
Answer: The area of the garden is equal 200 square units.Function g is transformed to obtain function h as shown. h(x) =g(x+2)-5 Which statement describes how the graph of h is different from the graph of g?
Answer:
Translation 2 units to the left and 5 units down.
Step-by-step explanation:
Consider the parent function [tex]y=g(x)[/tex] and its graph.
1. The translation 2 units to the left forms from the graph of the parent function the graph of the function [tex]y=g(x+2).[/tex]
2. Then the translation 5 units down forms from the graph of the function [tex]y=g(x+2)[/tex] the graph of the function [tex]h(x)=g(x+2)-5.[/tex]
Answer:
the answer is d for plato users
Step-by-step explanation:
Jenny is a 7/9 gallon of water to water roses she uses 1/4 less water to water heaters how much water did Jenny use to water her herbs
Help me please Algebra two!
Answer:
Zeros: -3 odd mult.; 0 odd mult.; 2 odd mult.
Positive leading coefficient
Odd degree likely 3
Step-by-step explanation:
A polynomial graph has several features we look for to determine the equations.
The zeros of the function are the x-intercepts. If the x-intercepts touch but do not cross then the intercepts have an even multiplicity like 2, 4, 6, etc. If the x-intercepts cross over then they have an odd multiplicity. Degree is the exponent or multiplicity of each zero. Therefore if we know the multiplicity of each zero we can add them together to find or make an educated guess for the degree of the entire polynomial. The shape of the graph tells us what type of polynomial. Odd degrees have a backwards S shape. Even degrees have a W shape. The shape can even tell us the if the equation has a positive or negative leading coefficient. Upside down W or an M shape is negative. While a sideways S shape is negative.What are the first three terms of the sequence defined by the following equation?
an = 41 + (n- 1)5
please help <333
Answer:
B: 41, 45,51
Step-by-step explanation:
an=41 +(n-1)5
an: nth term41: first term in the sequence(n-1): position of term in the sequence, minus 15: common differenceTo find 1st term plug in 1 for n,
an=41+(1-1)5 ->41
For 2nd term
an=41+(2-1)5 ->46
3rd Term
an=41+(3-1)5 -> 51
Hope this helps.
Answer:
B.
Step-by-step explanation:
Cyclists were 2/3 finished with their ride when they reached the 18 kilometer mark how long was the ride
Answer:
Yes that is the correct answer, good job
Which rational expression is equal to a positive whole number when evaluated? A.)2^1/2
B.)8^1/3
C.)12^1/4
D.)15^1/5
Answer:
The Correct Answer is 8^1/3
Step-by-step explanation:
I had this question on OW and this was the correct answer.
Hope I helped:)
Have a great day!!!
Scaling Up Fabric Amounts This fabric list makes one Crazy Quilt. But you and a group of your friends are doing a service project and want to make 300 quilts. How much of each type of fabric will you need?
Answer:
So, the final amount of fabric needed is given by:
Red Silk = [tex]1556_{4}^{1}[/tex]
Blue Denim = [tex]1462_{2}^{1}[/tex]
Yellow Satin = [tex]1837_{2}^{1}[/tex]
Cotton Blend = [tex]1125[/tex]
Purple Felt = [tex]1293_{4}^{3}[/tex]
Step-by-step explanation:
We are provided with the amount of fabric needed to make ONE quilt.
i.e. Red Silk = [tex]\frac{83}{16}[/tex]
Blue Denim = [tex]\frac{39}{8}[/tex]
Yellow Satin = [tex]\frac{49}{8}[/tex]
Cotton Blend = [tex]\frac{15}{4}[/tex]
Purple Felt = [tex]\frac{69}{16}[/tex]
It is required to find the amount of fabric needed to make 300 quilts i.e. we need to multiply the given amount of fabric with 300.
So, the final amount of fabric needed is given by:
Red Silk = [tex]1556_{4}^{1}[/tex]
Blue Denim = [tex]1462_{2}^{1}[/tex]
Yellow Satin = [tex]1837_{2}^{1}[/tex]
Cotton Blend = [tex]1125[/tex]
Purple Felt = [tex]1293_{4}^{3}[/tex]
A square foot wall of space needs 1/8 quart of paint. Terrence has 7 quarts of paint, but uses 2 quarts to paint a pipe. How many square feet of wall can he paint with the rest of the paint
Answer:
40 square feet.
Step-by-step explanation:
We have been given that a square foot wall of space needs 1/8 quart of paint. Terrence has 7 quarts of paint, but uses 2 quarts to paint a pipe.
The amount of paint that left will be 5 quarts (7-2=5).
To find the area of wall that can be painted with the rest of paint, we will divide amount of left paint by the amount used to paint one square foot of wall.
[tex]\text{The number of square feet that can be painted with rest of paint}=5\div \frac{1}{8}[/tex]
Dividing a number by a fraction is same as multiplying the number by the reciprocal of fraction.
[tex]\text{The number of square feet that can be painted with rest of paint}=5\times \frac{8}{1}[/tex]
[tex]\text{The number of square feet that can be painted with rest of paint}=5\times 8=40[/tex]
Therefore, 40 square feet of wall can be painted with the rest of the paint.
Terrence can paint 40 square feet of wall with the rest of the paint.
Explanation:To find out how many square feet of wall Terrence can paint with the rest of the paint, we need to subtract the amount of paint he used to paint the pipe from the total amount of paint he has. Terrence has 7 quarts of paint and used 2 quarts to paint the pipe, so he has 7 - 2 = 5 quarts of paint left. Since 1/8 quart of paint is needed for 1 square foot of wall, we can find out how many square feet of wall Terrence can paint by dividing the amount of paint he has left by the amount of paint needed for 1 square foot:
Number of square feet of wall Terrence can paint = (5 quarts) / (1/8 quart per square foot) = (5 quarts) × (8/1) square feet per quart = 40 square feet.
96 penicals come in a box if 4teachers share 3boxes equally how many penicals does each teacher receive
Answer:
Step-by-step explanation:
Answer:
Each teacher gets 8 pencils
Step-by-step explanation:
What you do is take 96 and divide it by 3. After you do this you’ll get 36. If you divide 36 by 4 you’ll get 8.