[tex]x^2=24\\\\x=\sqrt{24} \vee x=-\sqrt{24}\\\\x=2\sqrt6 \vee x=-2\sqrt6[/tex]
The solutions to the quadratic equation is x = ±2√6
Given data ,
Let the quadratic equation be represented as A
Now , the value of A is
x² = 24
Taking square roots on both sides , we get
√x² = √24
Now , the value of x is
x = ±√24
On simplifying the equation , we get
x = ±2√6
where the two solutions of x are having both positive and negative roots
So , the solutions of equation are
x = +2√6 and x = -2√6
Hence , the solution is x = ±2√6
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Danny paid a total of $13.65 for two steaks that weighed 0.65 lb and 0.75 lb.
What was the average price per pound that Danny paid for the steaks?
To find the price per pound, simply add 0.65 + 0.75 then divide.
0.65 + 0.75 = 1.40 13.65 / 1.40 = 9.75
Danny paid $9.75 per pound!
Lets go through the steps
1) Add the weights together which gives us 1.4 lb
2) Divide the cost by the weight 13.65/1.4 = $9.75 lb
At which position is the northern hemisphere experiencing spring?
The image includes the position and tilt of Earth in its orbit around the sun. Earth is tilted away from the sun in position A. In position B, the sun shines evenly on Earth from pole to pole. Earth is tilted toward the sun in position C. In position D, the sun shines evenly on Earth from pole to pole.
Public Domain
Point A
Point B
Point C
Point D
The northern hemisphere is experiencing spring at Point B.
Spring is one of the four seasons. It follows winter and is followed by summer. During the spring, in the northern regions of the Northern Hemisphere, the trees become much greener and many plants flower; gradually it gets warmer and the chance of frost decreases.
Astronomical spring starts in the Northern Hemisphere usually on March 20 and ends usually on June 21.
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Answer: point b
Step-by-step explanation:
The scale of a map says 4cm represents 5km what distance on the map (in centimeters) represents an actual distance of 4 km?
Answer:
3.2 cm on the map (in centimeters) represents an actual distance of 4 km
Step-by-step explanation:
The scale of a map says 4cm represents 5km
We are supposed to find what distance on the map (in centimeters) represents an actual distance of 4 km
5 km = 4 cm
1 km = [tex]\frac{4}{5} cm[/tex]
4 km = [tex]\frac{4}{5} \times 4 cm[/tex]
4 km = [tex]3.2 cm[/tex]
Hence 3.2 cm on the map (in centimeters) represents an actual distance of 4 km
Three hundred twenty-two thousand nine hundred and seven dollars
Not sure exactly what your asking but the numerical form of that would be $322,907.
322,907
3=the hundred thousandth place which in this case is 3
2=the ten thousandth place which in this case is 2
2=the thousandth place which in this case is 2
9=the hundredth place which in this case is 9
0=the tenth place which in this case is 0
7=the ones place which in this case is 7
Hope this helps!
Someone help me please
co= same planar = plane
coplanar means "same plane"
Answer: D
If 5 pounds of potatoes cost $3.75. How much do 12 pounds of potatoes cost?
5 pounds= 3.75
12 pounds= x
5x= 12*3.75
5x=45
12 pounds costs $9
chip earns a base salary of $500 per month as a salesman.In addition to the salary,he earns $90 per product that he sells .if his goal is to earn $5000 per month,how many products does he need to sell
To earn his desired $5000, Chip must sell 50 products per month. Firstly, his desired income minus his base salary is calculated this gives the additional income needed from products ($4500). Dividing this by the amount per product, gives the number of product sales needed (50).
Explanation:Chip earns a basic salary of $500 per month. His goal is to earn $5000. The additional income he earns comes from selling products at $90 each. If he wants to reach his goal, we need to first subtract his base salary from his goal income.
$5000 - $500 = $4500
This means that he needs to earn $4500 from selling products. We then divide this by the amount he makes per product to find the number of products he needs to sell.
$4500 / $90 = 50
So, Chip needs to sell 50 products in order to meet his income goal of $5000 per month.
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Using the discriminant, determine the number of real solutions.
2x^2+7x-15=0
- no real solutions
-one real solution
-two real solutions
Answer:
Since discriminant is positive, therefore, the given quadratic equation has two real solutions. Correct answer is the last option.
Step-by-step explanation:
We have been given a quadratic equation and we need to figure out the number of real solutions of the equation.
[tex]2x^{2}+7x-15=0[/tex]
We know that discriminant of a general quadratic equation [tex]ax^{2}+bx+c=0[/tex] is given by [tex]D=b^{2}-4ac[/tex]
For the given quadratic equation [tex]2x^{2}+7x-15=0[/tex], we have [tex]a=2,b=7,c=-15[/tex]. Upon substituting these values in the formula for discriminant, we get:
[tex]D=7^{2}-4(2)(-15)[/tex]
[tex]D=49+120[/tex]
[tex]D=169[/tex]
Since discriminant is a positive number, therefore, the given quadratic equation has two real solutions. Hence, the last option is the correct answer.
Answer:
two real solutions
Step-by-step explanation:
Please solve this problem with full sentences and explain it please.
Question 2
(02.05 MC)
Triangle PQR is transformed to triangle P'Q'R'. Triangle PQR has vertices P(8, 0), Q(6, 2), and R(−2, −4). Triangle P'Q'R' has vertices P'(4, 0), Q'(3, 1), and R'(−1, −2).
Plot triangles PQR and P'Q'R' on your own coordinate grid.
Part A: What is the scale factor of the dilation that transforms triangle PQR to triangle P'Q'R'? Explain your answer. (4 points)
Part B: Write the coordinates of triangle P"Q"R" obtained after P'Q'R' is reflected about the y-axis. (4 points)
Part C: Are the two triangles PQR and P''Q''R'' congruent? Explain your answer. (2 points)
ANSWER TO QUESTION 1.
We plot the points:
[tex]P(8,0)[/tex]
[tex]Q(6,2)[/tex]
and
[tex]R(-2,-4)[/tex]
We plot the image triangle also with the points,
[tex]P'(4,0)[/tex]
[tex]Q'(3,1)[/tex]
and
[tex]R(-1,-2)[/tex]
See graph in attachment.
ANSWER TO QUESTION 2.
The scale factor is the ratio of the image length to the object length.
[tex]Scale\: factor=\frac{|P'Q'|}{|PQ|}[/tex].
We need to use the distance formula to determine the two lengths.
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]|P'Q'|=\sqrt{(3-4)^2+(1-0)^2}[/tex]
[tex]|P'Q'|=\sqrt{(-1)^2+(1)^2}[/tex]
[tex]|P'Q'|=\sqrt{1+1}[/tex]
[tex]|P'Q'|=\sqrt{2}[/tex]
[tex]|PQ|=\sqrt{(6-8)^2+(2-0)^2}[/tex]
[tex]|PQ|=\sqrt{(-2)^2+(2)^2}[/tex]
[tex]|PQ|=\sqrt{4+4}[/tex]
[tex]|PQ|=\sqrt{8}[/tex]
[tex]|PQ|=2\sqrt{2}[/tex]
Therefore the scale factor of the dilation is
[tex]Scale\: factor=\frac{\sqrt{2}}{2\sqrt{2}}[/tex].
[tex]Scale\: factor=\frac{1}{2}[/tex].
ANSWER TO QUESTION 3
For a reflection in the y-axis we negate the x-coordinates. That means we are using the y-axis as our mirror line. The mapping is given as follows:
[tex]P'(4,0)\rightarrow P''(-4,0)[/tex]
[tex]Q'(3,1)\rightarrow Q''(-3,1)[/tex]
and
[tex]R(-1,-2)\rightarrow R''(1,-2)[/tex]
ANSWER TO QUESTION 4
We can see from the diagram that, PQR is bigger than P"Q"R".
The reason is that PQR was reduced by scale factor of half and then reflected in the y-axis to obtain P"Q"R".
Since dilation is not a rigid motion, the two triangles PQR and P''Q''R" are not equal in all respect, therefore they are not congruent.
PLEASE HELP THIS IS DUE TOMORROW I WILL GIVE YOU BRAINLIEST
A bird is flying 43 5/9 feet above the sea. A fish is swimming 23 2/3 feet below the surface of the sea, directly below the bird. What is the vertical distance between the bird and the fish?
Answer:
67.23
Step-by-step explanation:
Please refer to the attachment photo for explanation
Final answer:
The vertical distance between the bird and the fish is 67 2/9 feet.
Explanation:
To calculate the vertical distance between the bird and the fish, we need to add the distance the bird is flying above the sea to the distance the fish is swimming below the sea.
The bird is flying at a height of 43 5/9 feet above the sea, which can be converted to an improper fraction for easier calculation:
43 5/9 = (43×9 + 5)/9 = 392/9 feet
The fish is swimming at 23 2/3 feet below the surface of the sea, which also can be converted to an improper fraction:
23 2/3 = (23×3 + 2)/3 = 71/3 feet
To find the total distance, we add these two fractions:
392/9 (bird's height) + 71/3 (fish's depth)To add these fractions, we need a common denominator. The lowest common denominator for 9 and 3 is 9.
392/9 + 71/3×3/3 = 392/9 + 213/9Total distance = 392/9 + 213/9 = 605/9 feetWhen we convert the improper fraction back to a mixed number, we get:
605/9 feet = 67 2/9 feetSo, the vertical distance between the bird and the fish is 67 2/9 feet.
If y varies inversely as the square of x, and y= 1/8 when x=1, find y when x=5
y = k / x² ( y varies inversely as the square of x )
y = 1/8 when x = 1:
1/8 = k / 1²
8 k = 1
k = 1/8
For x = 5:
y = 1/8 / 5² = 1/8 : 25 = 1/8 · 1/25 = 1/200
Answer: A ) 1/200
Hope This Helps!!!
Solution is given in image attached.
what is the value of x?
A) x=2.25
B) x=11.25
C) x=13
D) x=22
A total of 676 tickets were sold for the school play. They were either adult tickets or student tickets. There were 74 fewer student tickets sold than adult tickets. How many adult tickets were sold?
There were 375 adult tickets sold.
Explanation:This question involves a concept in basic algebra. Let's denote the number of adult tickets as A and the number student tickets as S. From the problem, we know that the total number of tickets sold is 676, so A+S=676. The problem also tells us that there were 74 fewer student tickets sold than adult tickets, so we know that S=A-74.
We can substitute the value of S from the second equation into the first equation which gives us A+(A-74)=676. By solving this equation we find that A=375, so there were 375 adult tickets sold.
Let's denote the number of adult tickets sold as x. Since there were 74 fewer student tickets sold, the number of student tickets sold is x - 74. The total number of tickets sold is the sum of the adult and student tickets, which is 676.
Therefore, we can write the equation:
x + (x - 74) = 676
Simplifying the equation:
2x - 74 = 676
Adding 74 to both sides:
2x = 750
Dividing by 2:
x = 375
So, 375 adult tickets were sold.
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Help please 10 minutes
Slope Formula: (y² - y¹) / (x² - x¹)
1 + 7 = 8
-1-1 = -2
8/2 = 4
-2/2 = 1
4/1 = -4
Your answer is B.
Hope this Helps!!
The slope-intercept form:
[tex]y=mx+b\\\\m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have (1, -7) and (-1, 1).
Substitute:
[tex]m=\dfrac{1-(-7)}{-1-1}=\dfrac{8}{2}=4[/tex]
Therefore we have
[tex]y=4x+b[/tex]
Substitute the coordinates of the first point to the equation of line:
[tex]-7=-4(1)+b[/tex]
Answer:
[tex]\dfrac{1+7}{-1-1}=-4;\ -7=-4(1)+b[/tex]
Find the degree measure of 15.26 rad
Answer: " 874.33 ° " .
___________________________________
Step-by-step explanation:
15.26 rad * ( 180 degree / [tex]\pi[/tex] rad ) ;
= [ (15.26 * 180) / [tex]\pi[/tex] ] degrees ;
= [ ( 2746.8 ) / [tex]\pi[/tex] ] degrees.
= [ ( 2746.8) / 3.14) ] degrees ;
= 874.3336 degrees;
→ round to: " 874.33 degrees ."
____________________________________
Final answer:
To find the degree measure of radian 15.26, multiply 15.26 by 57.3, resulting in 874.798 degrees.
Explanation:
To convert radians to degrees, you can use the conversion factor: 1 radian = 57.3 degrees.
Given that 15.26 radians is the measure:
Multiply 15.26 by 57.3 to get the degree measure.
15.26 radians * 57.3 degrees/radian = 874.798 degrees
Write 5.9×10^−8 in decimal form.
If you mean standard form its
.000000059
Question number 3 lol I need help please
the answer is b. to calculate 5% interest you multiply whatever by 0.05, this immediately eliminates any other answer
you are decorating a clean soup can to make a pencil holder. you are going to glue yarn around the top and bottom of the can. the total amout of (y) yarn in inches (in inches) you need is given by the equation y = 4πr where r is the radius of the can. solve for r.
I will give brainliest
Answer:
r = y / (4π)
37.68 = 4 x 3.14 x r
37.68 = 12.56 r
so r = 37.68 ÷ 12.56 = 3
Step-by-step explanation:
We want to solve the given equation for r.
We will get:
r = y/(4*π)
The equation for the total amount of "y" tarn in inches is:
y = 4*π*r
Where π = 3.14159
And r is the radius of the soup can.
We want to solve the given equation for r, this means that we need to isolate r.
To do it, we just need to divide by 4*π in both sides, so we get:
y/(4*π) = 4*π*r/(4*π) = r
Then we got:
r = y/(4*π)
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What is 16x9+67x9 can someone help me?
Answer: 747
Step-by-step explanation:
16x9+67x9
First multiply 16 and 9 which is equal to 144
144+67x9
now multiply 67 and 9 which is equal to 603
144+603
Now add 144 and 603 which is equal to 747
So the answer to 16x9+67x9 is 747
use PEMDAS
16 * 9 + 67 * 9 =
144 + 603 =
747
A blueprint for a room has a scale of 1 in. to 3 ft. On the blueprint, one wall measures 9 in. in length. If L represents the length of the actual wall, what is L?
If the scale is 1 inch to 3 feet, and the wall is 9 inches, then our equation would be:
9 x 3 = L 9 x 3 = 27 So, L = 27!
1 in to 3 is times 3. So 9 times 3 is 27. L=27
Which graph represents the piece wise-defined function? y={−x+3 if x<12x−4 if x≥1
For the interval (-∞, 1), put x = 0.5, then y = - 0.5 + 3 = 2.5.
Therefore, (0.5, 2.5) is a point on y = -x + 3.
Put x = - 1, then y = -(-1) + 3 = 1 + 3 = 4.
Therefore, (-1, 4) is another point on y = -x + 3.
Joining (0.5, 2.5) and (-1, 4), we get the graph of the line y = -x + 3.
For the interval [1, ∞), put x = 1, then y = 2(1) - 4 = -2.
Therefore, (1, -2) is a point on y = 2x - 4.
Put x = 2, then y = 2(2) - 4 = 4 - 4 = 0.
Therefore, (2, 0) is another point on y = 2x - 4.
Joining (1, -2) and (2, 0), we get the graph of the line y = 2x - 4.
The graph of the piecewise-defined function is: [tex]function \(y = \begin{cases} 3 & \text{if } x < -2 \\ 0 & \text{if } x = 1 \\ -1 & \text{if } x > 1 \end{cases}\)[/tex]is attached accordingly.
What is a piecewise-defined function?A piecewise-defined function is a mathematical function that is defined by different rules or formulas over different intervals or regions of its domain.
The graph of the piecewise function is attached accordingly.
The graph of the piecewise function [tex]\(y\)[/tex] consists of two linear segments with a clear transition at [tex]\(x = 1\)[/tex]:
1. For [tex]\(x < 1\)[/tex], the equation [tex]\(y = -x + 3\)[/tex] defines a downward-sloping line that intersects the y-axis at [tex]\(y = 3\)[/tex].
2. For , the equation [tex]\(y = 2x - 4\)[/tex] defines an upward-sloping line that intersects the y-axis at [tex]\(y = -4\)[/tex].
These two segments meet at the point (1, -1), creating a kink in the graph. This piecewise function effectively combines two linear functions with different slopes, resulting in a non-continuous graph at [tex]\(x = 1\)[/tex].
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ome friends are going on a coaster ride at an amusement park. They board their car on a platform that is 10 and one half feet above the ground. The car starts by going up 80 and one half feet. Then the car goes down 50 and one fourth feet and comes to a stop. What is the change in height from where the friends started on the platform to where they are when the car stops?
The change in height from the starting platform to the stopping point of the roller coaster is 40.75 feet above the ground.
To determine the change in height from where the friends started on the platform to where they stop, we need to calculate the total distance the car traveled vertically. The car first ascends 80 and one half feet and then descends 50 and one fourth feet. The starting platform is 10 and one half feet above the ground.
First, we add the height of the platform to the initial ascent:
10.5 feet (height of platform) + 80.5 feet (initial ascent) = 91 feetNext, we subtract the descent:
91 feet (total height after ascent) - 50.25 feet (descent) = 40.75 feetThe change in height is the final position above the ground minus the starting position, yielding a total change in height of 40.75 feet.
HELP WITH QUESTION YOU WILL GET 40:POINTS
Daniela, Casey, Hope.
Solve by making each a ratio. Daniela - 0.0495, Casey - 0.050, Hope - 0.052
find the mean of each of the scores. To do so, divide the total with the amount of games.
Daniela = 101/5
D = 20.2 per game
Casey = 154/8
C = 19.25 per game
Hope = 227/12
H = 18.92 per game
You are ordering each of them from least to greatest:
Hope, Casey, Daniela is your answer, with 18.92, 19.25, 20.20 respectively.
hope this helps
Which equation represents a linear function that has a slope of and a y-intercept of –6?
The equation representing a linear function with a slope of 4 / 5 and a y-intercept of -6 is y = 4 / 5 x - 6.
The equation of a linear function can be written in the form:
y = 4 / 5 x + b
where "m" represents the slope of the line, and "b" represents the y-intercept (the value of y when x is 0).
Given that the slope is 4/5 and the y-intercept is -6, the equation would be:
y = 4 / 5 x - 6
So, the equation representing a linear function with a slope of 4.5 and a y-intercept of -6 is y = 4.5x - 6.
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Complete question is :
Which equation represents a linear function that has a slope of 4/5 and a y-intercept of –6?
The answer is 65. What do I do to get that answer?
You do what you did in your head if you know the answer is 65 and it's not on the paper.
If your friend answered it for you then sorry I can't help cause I'm horrible at word problems.
use the distributive property to write an expression equivalent to 5×(3+4)
Final answer:
To use the distributive property to write an expression equivalent to 5×(3+4), distribute the 5 to both the 3 and the 4 and simplify.
Explanation:
To use the distributive property to write an expression equivalent to 5×(3+4), we need to distribute the 5 to both the 3 and the 4. This means we need to multiply 5 by each number inside the parentheses:
5 × 3 = 15
5 × 4 = 20
So, the expression equivalent to 5×(3+4) is 15 + 20, which simplifies to 35.
I am F years old and my brother is B years older.What was the difference of our ages two year ago?
Answer:
So the difference of ages 2 years ago is [tex]B[/tex] years.
Step-by-step explanation:
The difference of age between me and my brother will not change whether we go back in time or forward in time, it will always be the same difference as of now. In this case it is B years. To further prove this we can do a calculation as below,
If I am F years old and brother is [tex]B[/tex] years older, the age of my brother is,
Age of the brother = [tex]F+B[/tex]
Age of me 2 years ago = [tex]F-2[/tex]
Age of my brother 2 years ago = [tex]F+B-2[/tex]
So the difference of ages 2 years ago can be calculated as,
Age of my brother 2 years ago - Age of me 2 years ago
=[tex]F+B-2[/tex] - [tex]F-2[/tex]
=[tex]F+B-2-(F-2)[/tex]
=[tex]F+B-2-F+2[/tex]
=[tex]B[/tex]
how many times does 100 go into 750
100 can go into 750 7.5 times :)
750 divided by 100 is 7.5 so 100 goes into 750 7.5 times
What are the x- and y-intercepts of 2x+4y=8
x-intercept: (4,0)
y-intercept: (0,2)
Question1, shop A trainers normal price £85 1/3 off and shop B trainers normal price £80 30% off in which shop are the trainer cheaper?
you must show your working
Question2, in a sale all items are reduced by 30% on the final day the sale price are reduced by 20% work out the final day price of a sofa that was priced at £290 before the sale started
Question 1:
Shop A trainers normal price= £85
[tex]\frac{1}{3}[/tex] is off so it becomes [tex]\frac{1}{3}\times85=28.33[/tex]
So price becomes: [tex]85-28.33=56.67[/tex]
Shop B trainers normal price= £80
30% is off so it becomes: [tex]\frac{30}{100}\times80=24[/tex]
So price becomes: [tex]80-24=56[/tex]
So, Shop B has cheaper trainers.
Question 2:
In a sale all items are reduced by = 30%
On the final day the sale price are reduced by = 20%
On the day before the last day of the sale, the price of the sofa was [tex]0.7\times290=203[/tex]
As given, on the last day of the sale, the price was again reduced to 80% of the price the day before, so price becomes: [tex]0.8\times203=162.40[/tex]
Hence the price was £162.40