You can always compute the distance between two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] using the pythagorean theorem:
[tex]d = \sqrt{(x_1-x_2)^2+(y_1-y_2)^2}[/tex]
In your case, we have
[tex]d = \sqrt{(0-a)^2+(a-0)^2} = \sqrt{2a^2}=a\sqrt{2}[/tex]
Answer:
[tex]\sqrt{2}a[/tex]
Step-by-step explanation:
We are asked to find the distance between point (0,a) and point (a,0) on a coordinate grid.
We will use distance formula to solve our given problem.
The distance between two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is given by formula:
[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex], where D represents distance between two points.
Let point [tex](0,a)=(x_1,y_1)[/tex] and point [tex](a,0)=(x_2,y_2)[/tex].
Substitute the values in distance formula:
[tex]D=\sqrt{(0-a)^2+(a-0)^2}[/tex]
[tex]D=\sqrt{(-a)^2+(a)^2}[/tex]
[tex]D=\sqrt{a^2+a^2}[/tex]
[tex]D=\sqrt{2a^2}[/tex]
Factor out perfect square:
[tex]D=\sqrt{2}a[/tex]
Therefore, the distance between two points would be [tex]\sqrt{2}a[/tex].
what is the area of this parallelogram
h=2in b=10in
Final answer:
The area of the parallelogram is calculated as the product of its base and height, resulting in 20 square inches.
Explanation:
The area of a parallelogram is calculated using the formula: Base x Height. In this case, the base (b) is 10 inches and the height (h) is 2 inches. Therefore, the area of the parallelogram can be found by multiplying the base by the height:
Area = Base x Height
Area = 10 in x 2 in
Area = 20 square inches
This calculation gives us the total area of the parallelogram in square inches.
The area of a parallelogram given its base and height dimensions as 10 in and 2 in is 20 square inches.
The area of a parallelogram can be calculated using the formula:
Area = Base x Height
Given that the base, b, is 10 inches and the height, h, is 2 inches, the area would be:
Area = 10 inches x 2 inches = 20 square inches
Complete the equation of a line through (-3,3) with a slope of 1/3
y=1/3x+
[tex]\bf (\stackrel{x_1}{-3}~,~\stackrel{y_1}{3})~\hspace{10em} slope = m\implies \cfrac{1}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-3=\cfrac{1}{3}[x-(-3)] \implies y-3=\cfrac{1}{3}(x+3) \\\\\\ y-3=\cfrac{1}{3}x+1\implies y=\cfrac{1}{3}x+4[/tex]
The One Snip-it Is Questions The Other Is Answers Thank You
Answer:
< FAD and <DAH make 90 degrees so they are complementary
<EAC and CAH make a straight line so they are supplementary
Step-by-step explanation:
Complementary angles add to 90 degrees
< FAD and <DAH make 90 degrees so they are complementary
Supplementary angles add to 180 degrees ( a straight line)
<EAC and CAH make a straight line so they are supplementary
10 POINTS AND BRAINLIEST! I NEED HELP ASAP!
Complete the function table, then write a rule for the function.
Answer:
[tex] - 3 | - 9 \\ - 2 | - 4 \\ - 1 | - 1 \\ \: \: 0 \: | \: 0 \\ \: \: \: 1 | - 1[/tex]
Step-by-step explanation:
[tex] - ( - 3) ^{2} = - 9 \\ - ( - 2) {}^{2} = - 4 \\ - ( - 1) {}^{2} = 1 \\ - (0) {}^{2} = 0 \\ - (1) {}^{2} = - 1[/tex]
then our rule is
[tex]f(x) = - (x) ^{2} [/tex]
[tex]where \: x \: is \: the \: input \: \\ and \: f(x) \: is \: the \: output .[/tex]
This is my idea. I hope it can help you.
hundred plus the product of a number and -2 equals 50. What is the number
Answer:
The number is 25
Step-by-step explanation:
We let the number be x. The product of x and -2 is;
x(-2) = -2x
a hundred plus the above product is;
100 + (-2x) = 100 - 2x
The above result is said to be equal to 50;
100 - 2x = 50
2x = 100 - 50
2x = 50
x = 25
the number we are looking for is 25.
The student is asking for help with a basic algebra problem. To solve this problem, we need to set up an equation based on the description provided: 'hundred plus the product of a number and -2 equals 50.' This translates to the algebraic equation 100 + (-2) n = 50. Our goal is to find the value of 'n'.
We first simplify the equation by subtracting 100 from both sides, which gives us -2n = 50 - 100. This simplifies to -2n = -50. Next, we divide both sides of the equation by -2 to isolate 'n'. The simplification gives us n = -50 / -2, which results in n = 25. Therefore, the number we are looking for is 25.
What is the zero of the following function
Answer:
A. [tex]x=-6[/tex]
Step-by-step explanation:
The zero of a function refers to the x-intercept of the graph of the function.
It is also the solution or the root of the function.
From the graph, the curve intersects the x-axis at x=-6.
Therefore the zero of the given function is:
[tex]x=-6[/tex]
The correct answer is A.
Please help will give brainliest
Answer:
[tex]b = 537[/tex]
Step-by-step explanation:
For this triangle we have to
[tex]a=640\\A=70\°\\B=52\°[/tex]
Now we use the sine theorem to find the length of b:
[tex]\frac{sin(A)}{a}=\frac{sin(B)}{b}=\frac{sin(C)}{c}[/tex]
Then:
[tex]\frac{sin(A)}{a}=\frac{sin(B)}{b}\\\\b=\frac{sin(B)}{\frac{sin(A)}{a}}\\\\b=a*\frac{sin(B)}{sin(A)}\\\\b=(640)\frac{sin(52)}{sin(70)}\\\\b=537[/tex]
Simplify -14x^3/x^3- 5x^4 where x=?
Step-by-step explanation:
[tex]\dfrac{-14x^3}{x^3-5x^4}\qquad\text{where}\ x^3-5x^4\neq0\\\\x^3-5x^4\neq0\qquad\text{distributive}\\\\x^3(1-5x)\neq0\iff x^3\neq0\ \wedge\ 1-5x\neq0\\\\x\neq0\ \wedge\ x\neq\dfrac{1}{5}\\\\\dfrac{-14x^3}{x^3(1-5x)}\qquad\text{cancel}\ x^3\\\\=\dfrac{-14}{1-5x}\qquad\text{where}\ x\neq\dfrac{1}{5}[/tex]
Two angle are supplementary angle A has a measure of 3x+12 and angle B has a measure of 4x+28, what is the measure of each angle?
Answer:
A measures 72 and B measures 108
Step-by-step explanation:
If the angles are supplementary, that means that they add up to equal 180. 3x + 12 + 4x + 28 = 180. Doing some algebra there gives you that 7x = 140 and x = 20. Sub in 20 to angle A to get 3(20) + 12 = 72, and sub in 20 to angle B to get 4(20) + 28 = 108. And of course, 108 + 72 = 180.
What is the value of x?
Enter your answer in the box.
x =
It’s 25 because (24x24)+(7x7) squared is 25
Find the local and global extrema for the graph of ƒ(x) = x(25 – x).
To find the local and global extrema of the function f(x) = x(25 - x), we first find the derivative and set it equal to zero. Next, we evaluate the function at the critical point and the endpoints of the interval [0, 20]. The local maximum is 156.25 and the global maximum is also 156.25.
Explanation:To find the local and global extrema of the function f(x) = x(25 - x), we can start by finding the critical points. Critical points occur where the derivative of the function is equal to zero or undefined. Let's find the derivative of f(x) first:
f'(x) = 25 - 2x
Setting f'(x) equal to zero, we get:
25 - 2x = 0
Solving for x:
x = 12.5
The critical point is x = 12.5. Now, let's evaluate f(x) at the endpoints of the interval [0, 20] and the critical point:
f(0) = 0
f(20) = 0
f(12.5) = 12.5(25 - 12.5) = 156.25
Therefore, the local maximum is f(12.5) = 156.25 and the global maximum value on the given interval is also f(12.5) = 156.25.
Help me find Train A's speed speed in miles per hour pleaseeeee
Answer: it should be 25.
Step-by-step explanation: this is because the slope of the line is 25. you can see that because, when finding the slope, you see that it goes up 50 and over 2. 50/2 (rise/run) is 25.
Answer:
25
Step-by-step explanation:
On the graph, you can see the train has traveled from 0 to 150 miles (the Y-axis), and it did that in 6 hours (X-axis).
That means that it traveled 150 miles in 6 hours.
A speed is a distance divided by a time (like miles/hour). So, to get the speed, we need to divide the distance traveled by the time it took to do it:
S = 150 miles / 6 hours = 25 miles per hour
What is the slope intercept equation of the line (0,4) and (2.-2)
Answer:
y= -3x + 4
Step-by-step explanation:
Answer:
[tex]slope=-3\\b=4\\[/tex]
Equation of the line
[tex]y=-3x+4[/tex]
Step-by-step explanation:
To find the slope we need two points, [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] In this case we have the points [tex](0,4)[/tex] and [tex](2, -2)[/tex]
[tex]slope=\frac{y_2-y_1}{x_2-x_1}[/tex] (1)
We replace the points in the equation (1)
[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\frac{-2-4}{2-0} =\frac{-6}{2} =-3[/tex]
We know the equation of the line:
[tex]y=mx+b[/tex] (2)
To find b we replace the slope, x and y with one of the points in the equation (2)
[tex]4=-3*0+b\\4=0+b\\b=4[/tex]
We substitute m and b in the general equation of the line
[tex]y=-3x+4[/tex]
What is the solution to the equation below?
x/4=x+1/3
A) x=-4
B) x=-1
C) 1/7
D) 4/7
Answer:
[tex]\large\boxed{A)\ x=-4}[/tex]
Step-by-step explanation:
[tex]\dfrac{x}{4}=\dfrac{x+1}{3}\qquad\text{cross multiply}\\\\3x=4(x+1)\qquad\text{use the distributive property}\\\\3x=4x+4\qquad\text{subtract}\ 4x\ \text{from both sides}\\\\-x=4\qquad\text{change the signs}\\\\x=-4[/tex]
F(x)=a^x,which of the following expressions is equal to [f(1)]^2
[tex]
f(x)=a^x \\
f(1)^2\Longrightarrow f(1)=(a^x)^2 \\
f(1)=\boxed{a^{2x}}
[/tex]
Use differentiation method to find the slope of the tangent hence the
equation of the tangent as shown below.
Circle with radius = 5
and centre at (-3,1)
Tagent of the
circle at x = -6
Answer:
The equation of the tangent at x=-6 is [tex]y=-\frac{3}{4}x-\frac{15}{2}[/tex]
Step-by-step explanation:
The equation of a circle with center (h,k) with radius r units is given by:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
The given circle has center (-3,1) and radius 5 units.
We substitute the center and the radius into the equation to get;
[tex](x--3)^2+(y-1)^2=5^2[/tex]
[tex](x+3)^2+(y-1)^2=25[/tex]
To find the slope, we differentiate implicitly to get:
[tex]2(x+3)+2(y-1)\fra{dy}{dx}=0[/tex]
[tex]2(y-1)\frac{dy}{dx}=-2(x+3)[/tex]
[tex]\frac{dy}{dx}=-\frac{x+3}{y-1}[/tex]
When x=-6;we have [tex](-6+3)^2+(y-1)^2=25[/tex]
[tex]\implies 9+(y-1)^2=25[/tex]
[tex]\implies (y-1)^2=25-9[/tex]
[tex]\implies (y-1)^2=16[/tex]
[tex]\implies y-1=\pm \sqrt{16}[/tex]
[tex]\implies y-1=\pm4[/tex]
[tex]\implies y=1\pm4[/tex]
[tex]y=-3[/tex] or [tex]y=5[/tex]
From the graph the reuired point is (-6,-3).
We substitute this point to find the slope;
[tex]\frac{dy}{dx}=-\frac{-6+3}{-3-1}[/tex]
[tex]\frac{dy}{dx}=-\frac{3}{4}[/tex]
The equation is given by [tex]y-y_1=m(x-x_1)[/tex].
We plug in the slope and the point to get:
[tex]y--3=-\frac{3}{4}(x--6)[/tex]
[tex]y=-\frac{3}{4}(x+6)-3[/tex]
[tex]y=-\frac{3}{4}x-\frac{9}{2}-3[/tex]
[tex]y=-\frac{3}{4}x-\frac{15}{2}[/tex]
(80pts) The ratio of the number of A's in the class to B's in the class was 2:5. How many people got A's if there were 40 people who got B's?
Make a proportion using the ratio (A:B) given and number of As and Bs really gotten in the class ([tex]\frac{A's}{B's}[/tex])
[tex]\frac{2}{5} = \frac{A}{40}[/tex]
Cross multiply
2 * 40 = 5 * A
80 = 5A
Isolate A by dividing 5 to both sides
80/5 = 5A/5
16 = A
If 40 people in the class got B's then 16 people got A's
Hope this helped!
~Just a girl in love with Shawn Mendes
16 people got A's if there were 40 people who got B's
The ratio of the number of A's in the class to B's in the class is given as:
Ratio = 2 : 5
This can be rewritten as:
A : B = 2 : 5
When there are 40 B's, we have:
A : 40 = 2 : 5
Multiply the second ratio by 8
A : 40 = 16 : 40
By comparison, we have:
A = 16
Hence, 16 people got A's if there were 40 people who got B's
Read more about ratios at:
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what would the adverage be of 12 and 13 if thats possible to find one?
Answer:
12.5
Step-by-step explanation:
Average = (numbers added together)/ number of numbers
=(12+13)/ (2)
=25/2
=12.5
Answer:
12.5
Step-by-step explanation:
To find the average of two numbers: (n₁ + n₂)/2, where n₁ and n₂ are the numbers to find the average of.
Plug in: (12 + 13)/2
Add: 25/2
Divide: 12.5
What is the experimental probability as a decimal
Answer:
P(not red) = 0.6
Step-by-step explanation:
red = 20, blue = 10, green = 9, yellow = 11
total number of times, spinning a four colored spinner = 50
P(not red) = [tex]\frac{10 + 9 +11}{50}[/tex]
= [tex]\frac{30}{50}[/tex]
= 0.6
Expand each expression
Answer:
5log(a) +2log(b)
Step-by-step explanation:
you were close, but you dont multiply the exponents together since a and b are two different variables
Answer:
[tex]5\log(a)+2\log(b)[/tex]
Step-by-step explanation:
The logarithm of a product is the sum of the logarithms:
[tex]\log(a^5b^2) = \log(a^5)+\log(b^2)[/tex]
By the same rule, we have [tex]\log(a^n)=n\log(a)[/tex]:
[tex]\log(a^5)+\log(b^2) = 5\log(a)+2\log(b)[/tex]
Help me answer this question please
Answer:
Step-by-step explanation:
√(x)
Shifted 3 units down:
√(x) - 3
Shifted 2 units to the right:
√(x-2) - 3
It's the last one.
ANSWER
[tex]y = \sqrt{x - 2} - 3[/tex]
EXPLANATION
The given equation is
[tex]y = \sqrt{x} [/tex]
This is the parent square root function.
If we apply the transformation;
[tex]y = \sqrt{x - k} - c[/tex]
Then the parent function will shift c units down and k units to the right.
When we the given function 3 units down and 2 units right the equation becomes:
[tex]y = \sqrt{x - 2} - 3[/tex]
Let f(x) = -2x -2. The graph of g(x) = f(x) + k is shown below. Identify the value of k.
k should be 1, Check by calculating the x values for f(x) and confronting them with g(x)
The graph of g(x) is a vertical shift of the graph of f(x) by 1 unit up. Thus, the value of k is 1.
The graph of g(x) = f(x) + k is a vertical shift of the graph of f(x) by k units. We can see from the graph that the graph of g(x) is shifted up by 1 unit relative to the graph of f(x).
Therefore, the value of k is 1.
To confirm this, we can plug in a point on the graph of g(x) into the equation for g(x) and solve for k.
For example, we can see that the point (-1, 2) is on the graph of g(x). Plugging this point into the equation for g(x), we get:
2 = -2(-1) - 2 + k
2 = 0 - 2 + k
k = 2 + 2
k = 4
However, we know that this cannot be the correct answer, because the graph of g(x) is shifted up by 1 unit relative to the graph of f(x). Therefore, the only possible value of k is 1.
For similar question on vertical shift.
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y
=
–3x + 6
y
=
9
What is the solution to the system of equations?
(–21, 9)
(9, –21)
(–1, 9)
(9, –1)
Answer:
(-1, 9)Step-by-step explanation:
[tex]\left\{\begin{array}{ccc}y=-3x+6\\y=9\end{array}\right\\\\\text{Put the value of y to the first equation:}\\\\9=-3x+6\qquad\text{subtract 6 from both sides}\\3=-3x\qquad\text{divide both sides by (-3)}\\-1=x\to x=-1[/tex]
Answer:
(-1,9) is correct in edg2020
Step-by-step explanation:
Simplify the algebraic expression: 4(3x + y) – 2(x – 5y)
A. 12x + 4y
B. 10x – 4y
C. 10x + 14y
D. 12x – 6y
Answer:
C
Step-by-step explanation:
First use distribution
4(3x+y)= 12x+4y
and
-2(x-5y)= -2x+10y
combine the 2 answers
10x+14y
The algebraic expression 4(3x + y) – 2(x – 5y) simplifies to 10x + 14y after distributing the multipliers and combining like terms.
Explanation:To simplify the algebraic expression 4(3x + y) – 2(x – 5y), we'll follow these steps:
Distribute the 4 into the parentheses: 4 * 3x = 12x and 4 * y = 4y.Distribute the -2 into the parentheses: -2 * x = -2x and -2 * -5y = 10y.Combine like terms by adding the x terms and the y terms separately, which gives: 12x + 4y - 2x + 10y.Simplify the expression by further combining like terms: (12x - 2x) = 10x and (4y + 10y) = 14y.The final simplified expression is 10x + 14y, which corresponds to option C.
What happens to the mean of the data set {2, 4, 7, 6, 3, 6, 7} if the number 25 is added?
Answer:
It goes up by 2.5
Step-by-step explanation:
Mean equation: (n₁ + n₂ + n₃ + ...)/n
Current mean: (2 + 4 + 7 + 6 + 3 + 6 + 7)/7 = 35/7 = 5
New mean: (2 + 4 + 7 + 6 + 3 + 6 + 7 + 25)/8 = 60/8 = 7.5
Difference: 7.5 - 5 = 2.5
Answer:
the answer is 60
Step-by-step explanation:
2+4= 6
6+7= 13
13+6= 19
19+3=22
22+6= 28
28+7= 35
35+25= 60
Ezra is saving money to buy a snowboard that costs $225. He already has $45 and can earn the rest by walking ten dogs. If d represents how much he earns for walking each dog, which of the following equations can be solved to find how much Ezra is paid for walking each dog?
A. 225 = 45d – 10
B. 225 – 45 = 10d
C. 25 + 45 = 10d
D. 45 = 225 – d
Answer:
B. 225 - 45 = 10d
Step-by-step explanation:
The remainder Ezra needs to save can be earned by walking ten dogs.
Let remainder = r
Let dogs = d
This means:
r = 10d
Make 'r' numerical values.
r = Total cost of snowboard - Current savings
r = $225 - $45
Therefore:
225 - 45 = 10d
The equations that can be solved to find how much Ezra is paid for walking each dog is B. 225 - 45 = 10d.
What is the subject in an equation?The subject in an equation is the/a variable(s) we're solving the equation for.
Usually, we want it to stay separated and clean without mixing with other constants or variables so that its value is clearly visible.
Ezra is saving money to buy a snowboard that costs $225.
He already has $45 and can earn the rest by walking ten dogs.
If d represents how much he earns for walking each dog,
Let r be the remainder that needs to save can be earned by walking ten dogs.
So,
r = 10d
Make 'r' numerical values.
r = Total cost of snowboard - Current savings
r = $225 - $45
Therefore,
225 - 45 = 10d
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What is the measerment of the missing angle?
Answer:
80°
Step-by-step explanation:
Since they are vertical angles, they are congruent to each other.
∠r ≅ 80°
Answer : 80
Opposite angles have same size
HELP ASAP MARKING BRAINLEST
what is the radius of the circle with the following equation?
x^2 + (y-3)^2=121
Answer:
The circle's center points are (0,3) and the radius is 11
Step-by-step explanation:
Sharon pays $98.75 for twenty-five 14-ounce boxes of Yummy flakes cereal. How much does on box of cereal cost
Answer:
$3.95
Step-by-step explanation:
The cost of one Yummy flake cereal box which Sharon bought is $3.95.
What is a unitary method?A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.
Given, Sharon pays $98.75 for twenty-five 14-ounce boxes of Yummy flakes cereal.
This means Sharon bought 25 boxes of cereal for $98.75.
Now to obtain the cost of one cereal box we have to divide the total amount by the total no.of boxes.
Therefore the cost of one cereal box is,
= (98.75/25).
= $3.95.
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A square pyramid has a volume of 20 cubic feet and a base length of 5 feet. What is it's height?
Answer:
The height of the pyramid is [tex]2.4\ ft[/tex]
Step-by-step explanation:
we know that
The volume of a square pyramid is equal to
[tex]V=\frac{1}{3}b^{2}h[/tex]
we have
[tex]V=20\ ft^{3}[/tex]
[tex]b=5\ ft[/tex]
substitute and solve for h
[tex]20=\frac{1}{3}(5)^{2}h[/tex]
[tex]60=(25)h[/tex]
[tex]h=60/(25)=2.4\ ft[/tex]