Answer:
y = sqrt(29)/2 - 1/2 or y = -1/2 - sqrt(29)/2
Step-by-step explanation:
Solve for y:
y^2 + y - 7 = 0
Add 7 to both sides:
y^2 + y = 7
Add 1/4 to both sides:
y^2 + y + 1/4 = 29/4
Write the left hand side as a square:
(y + 1/2)^2 = 29/4
Take the square root of both sides:
y + 1/2 = sqrt(29)/2 or y + 1/2 = -sqrt(29)/2
Subtract 1/2 from both sides:
y = sqrt(29)/2 - 1/2 or y + 1/2 = -sqrt(29)/2
Subtract 1/2 from both sides:
Answer: y = sqrt(29)/2 - 1/2 or y = -1/2 - sqrt(29)/2
Answer:
y=sqrt(29)/2-1/2, -sqrt(29)/2-1/2
Step-by-step explanation:
y^2+y-7=0
completing the square,
(b/2)^2=(1/2)^2=1/4
(y+1/2)^2=7+1/4
(y+1/2)^2=28/4+1/4
(y+1/2)^2=29/4
y+1/2=sqrt(29/4)
y=sqrt(29/4)-1/2
y=sqrt(29)/2-1/2
y=-sqrt(29)/2-1/2
the diameter of the sweep of the main rotor of the eh101 helicopter is 18.6 meters. A toy model of it has a sweep of 31 centimeters. What is the scale of the model?
Answer:
The actual length of 60 cm is modeled as 1 cm length.
Step-by-step explanation:
The diameter of the sweep of the main rotor of the helicopter is 18.6 meters i.e. 1860 cm.
Now, the toy model of the helicopter has a sweep of 31 cm.
Therefore, the scale in which the model is made is 1860 : 31 i.e. 60 : 1 ratio.
So, the actual length of 60 cm is modeled as 1 cm length. (Answer)
Answer:
The scale of the model to the actual is 1:60
Step-by-step explanation:
The scale of the model may be computes as the ratio of the diameter of the original sweep to the diameter of the model. Given that the diameter of the sweep of the main rotor of the eh101 helicopter is 18.6 meters and that of the model is 31 cm, the scale of the model
= 31cm to 18.6m
since 100cm = 1m,
18.6m = 18.6 * 100cm
= 1860 m
31cm to 18.6m = 31cm to 1860cm
= 1 to 60
Let's say you opened your laptop and positioned the
screen so it's exactly at 90° - a right angle - from your
keyboard. Now, let's say you could take the screen and
push it all the way down beyond 90°, until the back of the
screen is flat against your desk. It looks as if the angle
disappeared but hasn't. What is the angle called, and
what is the measurement?
A. Straight angle at 180°
B. Linear angle at 90°
C. Collinear angle at 120°
D. Horizontal angle at 180°
it will surely look like an angle on a straight line. which adds up.to 180,so the answer is horizontal angle at 180degrees
Final answer:
The correct answer is A. Straight angle at 180°, describing the angle formed when a laptop screen is moved from a 90° position to lying flat against the desk.
Explanation:
The question asks about the angle formed when a laptop screen is opened from a right angle (90°) to lying flat against the desk, covering a full range from vertical to horizontal. This describes a straight angle, which measures 180°. Initially, the laptop screen at a 90° angle to the keyboard represents a right angle. Pushing the screen down to lie flat transitions this to a straight angle, where the angle between the keyboard and the back of the screen spans a flat, straight line. Therefore, the correct answer is A. Straight angle at 180°.
Triangle ABC is rotated to create the image A'B'C'.
On a coordinate plane, 2 triangles are shown. The first triangle has points A (negative 1, negative 1), B (1, negative 1), and C (0, negative 4). The second triangle has points A prime (1, 1), B prime (negative 1, 1), and C prime (0, 4).
Which rule describes the transformation?
(x, y) → (x, –y)
(x, y) → (y, x)
(x, y) → (–x, –y)
(x, y) → (–y, –x)
Answer:
The transformation used here is,
(x, y) → (-x , -y)
Step-by-step explanation:
Triangle ABC is rotated to create the image of triangle A'B'C'
Co-ordinates of A, B, C are,
A = (-1 , -1) ; B = (1 , -1) ; C = (0, -4)
Co-ordinates of A' ,B' , C' are,
A'= (1 , 1) ; B' = (-1 , 1) ; C' = (0, 4)
Hence, the transformation used here is,
(x, y) → (-x , -y)
Answer:
(x, y) → (–x, –y)
Step-by-step explanation:
Coordinates of triangle ABC:
A (-1, -1)
B (1, -1)
C (0, -4)
If we apply the transformation (x, y) → (–x, –y) we will get:
A (-1, -1) → (1, 1) which correspond to point A'
B (1, -1) → (-1, 1) which correspond to point B'
C (0, -4) → (0, 4) which correspond to point C'
Solve
394.029 + 5.38
Answer:
399.409
Step-by-step explanation:
Add both numbers to get your answer.
Answer:
The answer is
399. 409
The following graph is of an exponential function of the form y=a*bx.
What values of a and b would make this equation work?
a=
b=
Answer:
a= 15
b=1/3
Step-by-step explanation:
key rule: see the graph carefully to get the following identified points.from the given graph, it can be seen that, the curve passes through (0,15)by substituting this point in y=a*(b)^x,15=a*(b)^0
15=a
it can also be seen that the curve passes through (1,5)by substituting this point in y=a*(b)^x,5=a*b
5=15*b ( since, we have found that a=15 from the before steps)
dividing both the sides by 15,5/15=b=1/3
hence,a= 15
b=1/3.
what is the square root of 10
Answer:
3.1622776 OR √ 10
Step-by-step explanation:
The result can be shown in multiple forms.
Exact Form:
√ 10
Decimal Form:
3.16227766
3.1622776
Step-by-step explanation:
[tex]\sqrt{10}-\text{it's an irrational number}\\\\\text{You can only have an approximation}\ \sqrt{10}\approx3.1623[/tex]
Table The table shows the number of carnival tickets purchased and the corresponding number of entries in the raffle drawing. If x is the number of tickets purchased and y is the number of entries in the raffle drawing, then the equation represents the table. How many entries would be in the raffle drawing if 20 tickets were purchased?
Answer:
Step-by-step explanation:
Following are the response to the given table:
Consider the linear function is [tex]\bold{y= 12x+b}[/tex], where by x is the number of purchased tickets and y is the amount of raffle participation.[tex]\begin{cases}R+b=3 & R=1 \\ 2R+b=4 &b=2 \end{cases}[/tex]Therefore, whenever [tex]\bold{x=20}[/tex], the equation [tex]\bold{ y=x+2 }[/tex] reflects the tables (numerical substitution method). when [tex]\bold{ x=20 \ \ \ y= 20+2=22}[/tex]As just a result, [tex]\bold{ 22}[/tex] tickets were purchased again for roffle drawing.Therefore, the final answer is "[tex]\bold{y=x+2 \ and \ 22}[/tex]".
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Solve the system of linear equations by elimination.
3x - 2y = 4
6x- 2y = -2
Answer:
the value of x is (-2) and y is (-5)
Give formula to calculate Selling price when profit is given in percentage.
Jeffrey is a kickboxing instructor who will be teaching classes at a local gym. To get certified
as an instructor, he spent a total of $200. Jeffrey will be earning a base salary of $50 per
month from the gym, plus an additional $3 for every class he teaches. If Jeffrey teaches a
certain number of classes during his first month as an instructor, he will earn back the
amount he spent on certification. How many classes will that take?
If Jeffrey takes 50 classes in his first month as an instructor, he will earn back the amount he spent on certification.
Step-by-step explanation:
Amount spent on certification = $200
Base salary = $50
Payment per class = $3
Let, x be the number of classes.
J(x) = 50+3x
He needs to earn $200 dollars in first month, therefore,
50+3x=200
[tex]3x=200-50\\3x=150[/tex]
Dividing both sides by 3
[tex]\frac{3x}{3}=\frac{150}{3}\\x=50[/tex]
If Jeffrey takes 50 classes in his first month as an instructor, he will earn back the amount he spent on certification.
Keywords: function, linear equation
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Can anyone Help me please
Option A: 21 pairs is the right answer
Step-by-step explanation:
Given
total strength of cycling team = 7
Captains to be selected = 2
As the order of selection doesn't matter, the combinations will be used to get the number of ways the pair can be chosen
Combination is solved as:
[tex]C(n,r) = \frac{n!}{r!(n-r)!}[/tex]
Here
n=7
r = 2
[tex]C(7,2) = \frac{7!}{2!(7-2)!}\\C(7,2) = \frac{7!}{2!*5!}\\=21\ pairs[/tex]
Hence,
Option A: 21 pairs is the right answer
Keywords: Combination
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Sheila has $47 to buy graphing pads for her math class. Each pad costs $8,
How many pads can she buy? Do not include units in your answer.
Answer:
5 tablets can be bought
Step-by-step explanation:
47/8= 5
The graph shows how many apples Erin can pick if she maintains a constant rate. What is the linear equation for this relationship? How many apples can she pick per hour?
An equation that represents the relationship between the x and y-values is y = 75x.
Erin can pick 75 apples per hour.
What is a proportional relationship?In Mathematics and Geometry, a proportional relationship is a type of relationship that produces equivalent ratios and it can be modeled or represented by the following mathematical equation:
y = kx
Where:
y represents the y-variable.x represents the x-variable.k is the constant of proportionality.Next, we would determine the constant of proportionality (k) by using various data points as follows:
Constant of proportionality, k = y/x
Constant of proportionality, k = 75/1 = 150/2
Constant of proportionality, k = 75.
Therefore, the required linear equation that models the graph can be written as follows;
y = kx
y = 75x
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Does anyone mind helping me with this? It seems simple enough.
The question is: Radical x-3 = radical x + 3 (the +3 is outside of the radical). We are solving for X in this question.
Answer:
x = 4
Step-by-step explanation:
It is given that [tex]\sqrt{(x - 3)} = \sqrt{x} + 3[/tex], and we have to solve the given equation for x.
Now, we have [tex]\sqrt{(x - 3)} = \sqrt{x} + 3[/tex]
Squaring both sides we get
[tex][\sqrt{(x - 3)}] ^{2} = [\sqrt{x} + 3]^{2}[/tex]
⇒ x - 3 = x + 6√x + 9 {Since we know the formula of (a + b)² = a² + 2ab + b²}
⇒ 6√x = - 12
⇒ √x = -2
Again squaring both sides we get
⇒x = 4 (Answer)
Give your answer in its simplest form.
Use [tex]\frac{a^n}{a^m}=a^{n-m}[/tex].
[tex]
\dfrac{2m^2t^6}{m^4t^2}=2m^{2-4}t^{6-2}=\boxed{2m^{-2}t^4}
[/tex]
Hope this helps.
Answer:
2m⁻²t⁴
Step-by-step explanation:
Rule:
If aᵇ / aˣ, then aᵇ ⁻ ˣ
[tex]\frac{2m^2t^6}{m^4t^2} = 2 m^{2-4} t^{6-2} = 2m^{-2} t^{4}[/tex]
my teacher keeps explaining what a "vertical line test" is and how it helps solve a linear equation plz explain and dumb it down for me hahahaha thx.(Im new here btw)
The vertical line test is a visual way to determine if a curve is a graph of a function or not. A function can only have one output, y, for each unique input, x. If the vertical line you drew intersects the graph more than once for any value of x then the graph is not the graph of a function.
Evaluate x + y when x = -94 and y = 24
A: -118
B: -70
C: 70
D: 118
The simplification of the equation when x = -94 and y = 24 will be B: -70
What is a simplification of an expression?Usually, simplification involves proceeding with the pending operations in the expression. Simplification usually involves making the expression simple and easy to use later.
We have been given an equation as x + y
We have to find the solution when x = -94 and y = 24
Therefore, substitute the values;
x + y = (-94 +24)
Now Evaluate;
(-94 +24) = -70
Hence, the correct answer is B.
Therefore, The simplification of the equation when x = -94 and y = 24 will be B: -70
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ASAP! A biologist is to set up an aquarium in his laboratory. He intends to buy 11 piranhas and 5 sharks. He has a budget of £200. If p represents one piranhas and s one shark, write down an equation for the price of one piranhas in terms of the price of sharks.
Answer:
p = (200 -5s)/11
Step-by-step explanation:
I think you meant p is the price of piranhas, and a is the price of one shark.
You have:
11p + 5s = 200
11p = 200 - 5s
p = (200-5s)/11
Does that help? ;)
Factor the polynomial x^4-16. How many real zeros does the function g(x)=x^4-16 have?
Answer:
(x-2)(x+2)(x^2 + 4)
Step-by-step explanation:
This can be done by difference of squares:
(x^2 - 4) (x^2 + 4)
And now (x^2 - 4) can be further factored:
(x-2)(x+2)(x^2 + 4) is your answer
Clearly, There are only 2 zeroes that we can get from this, 2 and -2
Hope this helps!
If you think I helped please mark brainliest! Would really appreciate!
Answer:
[tex]\large\boxed{x^4-16=(x^2+4)(x+2)(x-2)}[/tex]
[tex]\large\boxed{g(x)=x^4-16\ \text{has two real zeros}\ x=-2\ \text{and}\ x=2}[/tex]
Step-by-step explanation:
[tex]x^4-16=x^4-2^4=x^{(2)(2)}-2^{(2)(2)}\\\\\text{use}\ (a^n)^m=a^{(n)(m)}\\\\=(x^2)^2-(2^2)^2\\\\\text{use}\ a^2-b^2=(a+b)(a-b)\\\\=(x^2+2^2)(x^2-2^2)=(x^2+4)(x+2)(x-2)[/tex]
The zeros of g(x):
[tex]g(x)=x^2-16=(x^2+4)(x+2)(x-2)\\\\g(x)=0\iff(x^2+4)(x+2)(x-2)=0\iff x^2+4=0\ \vee\ x+2=0\ \vee\ x-2=0\\\\x^2+4=0\qquad\text{subtract 4 from both sides}\\x^2=-4\qquad\bold{FALSE}\\\\x+2=0\qquad\text{subtract 2 from both sides}\\\boxed{x=-2}\\\\x-2=0\qquad\text{add 2 to both sides}\\\boxed{x=2}[/tex]
Greenfield village is spread across 240 acres of land. Only 37% of the land is used for the exhibits, while the rest of the land consists of forest, rivers and pastures. How many acres are used for exhibits?
Answer:
The land which are used for exhibits are 89 acres (approximately).
Step-by-step explanation:
Given:
Village is spread across 240 acres of land. 37% of land is used for the exhibits.
Now, we have to find acres of land which are used for exhibits.
So, here it is given that land used for exhibits is 37%, and we have to calculate the quantity from the percentage given:
According to question:
37% of 240 acres of land.
[tex]\frac{37}{100}\times 240[/tex]
[tex]0.37\times 240[/tex]
[tex]88.80[/tex]
So, the land used for exhibits are 88.80 acres.
Therefore, the land which are used for exhibits are 89 acres (approximately).
How many total blocks will she travel if she goes to Amanda‘s house and then to Karen’s and finally back home
Answer:
19 blocks
Step-by-step explanation:
To amanda's house, it is 5 blocks (we count 1 to 6 = 5 units)
From amanda's to Karen's, is 6 units (we count from -1 to 5 = 6 units)
Now, to find Karen to own place, we have to use the Pythaogrean Theorem. It is applicable for right triangle (which is shown, Amanda's place is the right angle).
The two distance we found are the two legs of the triangle and the other side (what we need to find) is the hypotenuse (which is the side opposite of right angle). The theorem says:
Leg^2 + Another Leg^2 = Hypotenuse^2
We know the 2 legs' length, so we can solve for hypotenuse (Karen to Own place Distance). Shown below:
[tex]5^2 + 6 ^ 2 \\=25+36\\=61[/tex]
So, we have:
Hypotenuse^2 = 61
Hypotenuse = Sqrt(61) = 7.81
Rounded to nearest block, that is 8 blocks
So, total distance traveled is:
5 + 6 + 8 = 19 blocks
Can someone please help me?
GEORGINA WAS GIVEN THAT THE LENGTH OF THE RECTANGLE WAS 2.5 INCHES LONGER THEN ITS WIDTH AND THE PERIMETER OF THE RECTANGLE WAS 75.4 INCHES.
FIND THE LENGTH AND WIDTH OF THE RECTANGLE Alegebraically. SHOW ALL WORK
Answer:
Length of the rectangle is [tex]18.85\ inches[/tex],and the width of the rectangle is [tex]16.35\ inches[/tex]
Step-by-step explanation:
Let the width of the rectangle be [tex]x[/tex] inches
Then
The length of the rectangle will be [tex]x+2.5[/tex] inches
So perimeter [tex]=2(length + width)[/tex]
Plugging the values:
⇒ [tex]2(x+x+2.5)=75.4[/tex]
⇒ [tex]2(2x+2.5)=75.4[/tex]
⇒ [tex]4x+10=75.4[/tex]
Subtracting [tex]10[/tex] from both sides.
⇒ [tex]4x=65.4[/tex]
⇒ [tex]x=\frac{65.4}{4}=16.35\ inches[/tex]
So the width of the rectangle is [tex]16.35\ inches[/tex]
And the length of the rectangle is [tex]18.85\ inches[/tex]
24 x + 6 Y is greater than or equal to 200
Answer:
I'm pretty sure this is undefined. It's either it does or does not equal to 200..
Step-by-step explanation:
n/a
Mohit pays rupees 9000 as an amount on the sum of rupees 7000 that he had borrowed for 2 years.
Find the rate of interest.
pls answer fast
I will mark u as the brainliest
Answer:
The required rate of interest = 14.285%
Step-by-step explanation:
Here, The principal amount = 7,000
The final paid amount = 9,000
Time = 2 years
Let us assume the rate of interest = R
Now, Simple Interest = Amount - Principal
= 9,000 - 7,000 = 2,000
So, the SI on the given principal for 2 years = 2,000
[tex]\textrm{SIMPLE INTEREST } = \frac{P \times R \times T}{100}\\\implies 2000 = \frac{7,000 \times R \times 2}{100}\\\implies R = \frac{2,000 \times 100}{7,000 \times 2} = 14.285[/tex]
or, R = 14.285%
Hence, the required rate of interest = 14.285%
Which of the following is the saluting to the inequality 9+2x>5x? A. 2 B.3 c.4 d.8
Answer:
x < 3
Step-by-step explanation:
We are given an equation of inequality of single variable x.
So, we have to solve the inequality and get the solution in terms of another inequality.
The given equation is 9 + 2x > 5x
⇒ 9 > 5x - 2x
⇒ 9 > 3x
⇒ 3x < 9 {Since if a > b then we can write b < a as they means the same.}
⇒ x < 3 (Answer)
{Dividing both sides of an inequality with a positive number need no change in inequality sign}
find the HCF of following !! a) 15,63,99 B) 66,33,78
Answer:
(a) 3, (b) 3
Step-by-step explanation:
HCF is highest common factor. Each number is split into multiples while the common factors are then multiplied together.
(a) HCF of 15, 63, 99
15 = 3 X 5 ----------------------------- (i)
63 = 3 X 3 X 7 ---------------------------(ii)
99 = 3 X 3 X 11 ---------------------------(iii)
From the three equations, 3 is the only common factor; 3 appears in equations (i), (ii) and (iii)
hence the HCF of 15, 63 and 99 is 3
(b) HCF of 66, 33, 78
66 = 2 X 3 X 11 ----------------------------- (iv)
33 = 3 X 11 ---------------------------(v)
78 = 2 X 3 X 13 ---------------------------(vi)
From the three equations, 3 is still the only common factor; 3 appears in equations (iv), (v) and (vi)
hence the HCF of 166, 33, 78 is 3
Part I: Describe the center and radius of the circle.
The center is at ___.
The radius is __ units.
Part II: Use the equation below to identify the value of each variable for the circle.
Standard Form Equation of a Circle(x - h)2 + (y - v)2 = r2
(h, v) = center
r = radius length
h =__ v =__r =__
Part III: Use Parts I and II to write the standard form equation of the circle.
Answer:
Center (2,4) , radius=3, h=2 v=4 & r=3
Step-by-step explanation:
Ok so in order to find the center of the circle, use the graph (like you can see that the x is 2,if you count down from 5 to the left. the y is 4,because it's below 5 in the y pole).So the center is (2,4)
Now, in order to find the length of the radius, you need to do the following:
Take the center point (2,4) and the point where the circle ends (2,1) . Because radius is a straight, you can substract the y values of the two points : 4-1=3
As you can see in the equation, the h symbolizes the x of the center point and the v symbolizes the y.The r is the radius that we already found(3)
So it's shouldn't be a problem now to find the equation of the circle,simply replace the values with their numbers:
(x-2)^2 + (y-4)^2 = 9
The center is at (2, 4). The radius is 3 units. The value of h, v, and r are 2, 4, and 3 respectively. The standard equation of the circle is (x - 2)² + (y - 4)² = 9.
How do find the required values?The required value can be found by counting the coordinates from the given graph.
The value of the center and the radius of the circle can be found below:A diagram is provided. We should observe the diagram, we can see that the center of the circle is at (2,4) on the graph.
We can also find that the radius of the circle is 3 units by counting the lines.
The center of the circle is denoted by (h, v) = (2, 4). The radius r is 3 units.
We have found the center and the radius. We can use this to make the standard equation of the circle.
The standard equation of a circle is given by:
(x - h)2 + (y - v)2 = r2
Now substitute the values h, v and, r:
(x - 2)² + (y - 4)² = 9
Therefore, we have found that the center is at (2, 4)and the radius is 3 units. The value of h, v, and r are 2, 4, and 3 respectively. The standard equation of the circle is (x - 2)² + (y - 4)² = 9.
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how do i find the slope
Answer:
slope = - 7
Step-by-step explanation:
The equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b) a point on the line
y - 4 = - 7(x - 6) ← is in point- slope form
with slope m = - 7
There are 24% of boys in a school. If the number of girls are 456, find the total number of students in the school.
Answer:
600 students
Step-by-step explanation:
100% - 24% = 76%
76% = 456
100%= x
76x = 456x100
x = 45600÷76
x= 600 students (total)
Answer: 600
Step-by-step explanation:
Since there are 24% of boys in a school , this means that the number of girls will be :
100% - 24 %
= 76%
That means there are 76% of girls in the school.
Let the total number of students in the school be x, this means that
24% of x = number of boys
76% of x = number of girls
Since the total number of girls is given to be 456 , then
76% of x = 456
0.76x = 456
x = 456/0.76
x = 600
That means there are 600 students all together in the school
Choosing a number from 1 to 10 what is the probability of choosing a number less than 3?
About 2% chance.
There are ten numbers and you want to choose a number less than three. There are only two numbers less than three; 1 & 2. Because there are only 2 numbers less than three and 10 to choose from, it becomes a 2% chance.
Answer: 20%
Step-by-step explanation: