Answer:
(x - 10)(x + 10)
Step-by-step explanation:
x² - 100 ← is a difference of squares and factors in general as
a² - b² = (a - b)(a + b)
Hence
x² - 100
= x² - 10² = (x - 10)(x + 10)
A farmer wants to put a fence around a garden in the shape of a square. The fence posts are placed every 2 meters. One side of the garden is 10m long. How many posts does the farmer need?
Answer:
The farmer would need 80 posts.
Step-by-step explanation:
If one side of the garden is 10m long, and the garden is a square, we can assume that all 4 sides will be 10m. That makes it 40m in total. Times 40×2 and you get 80.
What is the point-slope form of a line that has a slope of 1/2 and passes through point (–7, 2)?
Answer:
D
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
here m = [tex]\frac{1}{2}[/tex] and (a, b) = (- 7, 2), hence
y - 2 = [tex]\frac{1}{2}[/tex] (x - (- 7)) → D
y - 2 = [tex]\frac{1}{2}[/tex](x + 7)
The point-slope form of the equation will be [tex]y-2 = \dfrac{1}{2}(x-(-7))[/tex]. The correct option is D.
In mathematics, slope refers to the measure of the steepness or inclination of a line or a curve. It quantifies the rate at which one variable changes with respect to another variable. The slope is commonly denoted by the letter "m."
Given that the slope of the line is 1/2. The point through which the line is passing is (-7,2).
The general form of the equation of the line passing through the point (-7,2) and the slope is 1/2 can be written as,
[tex]y-y_1 = m(x-x_1)[/tex]
The equation of the line in point-slope form can be written as,
[tex]y - y_1 = m(x-x_1)\\y-2=\dfrac{1}{2}(x-(-7))[/tex]
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Please help me this is urgent 15 points and brainiest
If m∠EQD=(5x+2)°, what is the value of x?
=====================================================
Explanation:
The angle EQD is an inscribed angle that cuts off the arc from E to D (the shortest path). Note how central angle ECD also cuts off this same arc. By the inscribed angle theorem, we know that
inscribed angle = (1/2)*(central angle)
angle EQD = (1/2)*(angle ECD)
We can multiply both sides by 2 and flip the equation to get
angle ECD = 2*(angle EQD)
Now replace "angle EQD" with 5x+2
angle ECD = 2*(5x+2)
2*(5x+2) = angle ECD
Next, replace "angle ECD" with 104 as this is the measure of this central angle.
2*(5x+2) = angle ECD
2*(5x+2) = 104
From here, we solve for x
2*(5x+2) = 104
2*5x + 2*2 = 104
10x + 4 = 104
10x+4-4 = 104-4 ..... subtracting 4 from both sides
10x = 100
10x/10 = 100/10 ...... dividing both sides by 10
x = 10
What is the solution to the inequality X squared <49
[tex]x^2<49\\x<7 \wedge x>-7\\x\in(-7,7)[/tex]
If a person eats 1/3 of their meal, what percent have they eaten
Workers have packed 1,400 glasses in 7 boxes. If they pack 3 more boxes, how many glasses will they have packed in all?
1box = 1400/7 = 200
200×3=600
1400+600=2000
Answer:
2000
Step-by-step explanation:
Given :Workers have packed 1,400 glasses in 7 boxes.
To Find :If they pack 3 more boxes, how many glasses will they have packed in all?
Solution:
Workers packed no. of glasses in 7 boxes = 1400
Workers packed no. of glasses in 1 box = [tex]\frac{1400}{7}[/tex]
Workers packed no. of glasses in 3 boxes = [tex]\frac{1400}{7} \times 3[/tex]
= [tex]600[/tex]
So, initially they packed 1400 glasses
If they pack 3 more boxes so, the pack 600 glasses more
So, The total no. of glasses have packed by workers = 1400+600 = 2000
Hence they have packed 2000 glasses in all.
Three sisters went shopping for Mother’s Day. Each sister bought a gift for their mom. Maggie spent 3 times as much as Karen. Karen spent half as much as Jasmine. All together, they spent $60. Then, solve your equation to determine how much each sister spent on their gift.
Answer:
Let j = amount Jasmine spent, k = amount Karen spent, and m = amount Maggie spent.
m = 3k, k = (1/2)j
j + k + m = $60
2k + k + 3k = $60
6k = $60
k = $10, m = $30, j = $20
Jasmine spent $20, Karen spent $10, and Maggie spent $30.
Use the graph of f(x) to evaluate the following:
Answer:
[tex]\large\boxed{\dfrac{1}{2}}[/tex]
Step-by-step explanation:
[tex]\text{The average rate of change of function}\ f(x)\\\text{over the interval}\ a\leq x\leq b\ \text{is given by this expression:}\\\dfrac{f(b)-f(a)}{b-a}.\\\\\text{Read from graph the values of function for}\ x=3\ \text{and}\ x=5.\\(look\ at\ the\ picture)\\\\f(3)=1,\ f(5)=2\\\\\text{Substitute:}\\\\\dfrac{f(5)-f(3)}{5-3}=\dfrac{2-1}{2}=\dfrac{1}{2}[/tex]
Which unit of measure would be appropriate for the volume of a cylinder that is 8 meters tall and has a radius of 4 meters
Answer: cubic meters : m³
Step-by-step explanation:
Cylinder volume is the product of area of the base by height.
Area of the base is the product of π·radius² = square meters : m²
Volume = square meters·meters = m²·m = cubic meters : m³
[tex]\textit{\textbf{Spymore}}[/tex]
Which table shows the correct methods used to justify the solution steps?
Answer:
x = 8
Step-by-step explanation:
Step 1 : Simplify the equation
3(x-5) + 7x = 65
3x - 15 + 7x = 65
Step 2 : Make x the subject
3x + 7x = 65 + 15
10x = 80
x = 80/10
x = 8
!!
Answer:
The answer is B
Step-by-step explanation:
The reasoning behind this is because in the second step, if you were to add all of the numbers you would get the solution of -5x or something like that.
Hope this helps!
what transformation was not done to the linear parent function, f(x)=x, to get the function g(x)=-3(x-4)-7
A. Reflection over the x-axis
B. Shift down 7 units
C. Shift right 4 units
D. Horizontal stretch by a factor of 3
Answer: D. Horizontal stretch by a factor of 3.
Step-by-step explanation:
Below are some transformations for a function [tex]f(x)[/tex]:
If [tex]f(x)-k[/tex], then it is shifted "k" units down.
If [tex]f(x-k)[/tex], then it is shifted rigth"k" units.
If [tex]-f(x)[/tex], then it is reflected across the x-axis.
If [tex]cf(x)[/tex] and [tex]c>1[/tex], then it is stretched vertically by a factor of "c".
If [tex]f(cx)[/tex] and [tex]0<c<1[/tex], then it is stretched horizontally by a factor of [tex]\frac{1}{c}[/tex].
Based on this, the transformations done to the function [tex]f(x)=x[/tex] to get the function [tex]g(x)=-3(x-4)-7[/tex] are:
- It is shifted 7 units down.
- It is shifted rigth 4 units.
- It is reflected over the x-axis.
- It is vertically stretched by a factor of 3.
Therefore, the transformations that was not done to the function [tex]f(x)=x[/tex] to get the function [tex]g(x)=-3(x-4)-7[/tex] is:
Horizontal stretch by a factor of 3.
Complete the solution of the equation. Find the value of y when x equals -7.
-4x-9y=-26
Answer:
y = 6Step-by-step explanation:
Put x = -7 to the equation -4x - 9y = -26, and solve it for y:
-4(-7) - 9y = -26
28 - 9y = -26 subtract 28 from both sides
-9y = -54 divide both sides by (-9)
y = 6
Sketch the graph of y = (x - 3)2 - 25, then select the graph that corresponds
to your sketch.
Answer:
Option C. Graph C
Step-by-step explanation:
we have
[tex]y=(x-3)^{2}-25[/tex]
This is the equation of a vertical parabola open upward (vertex is a minimum)
The vertex is the point (3,-25)
therefore
The graph is C
The graph in the attached figure
Answer:c
Step-by-step explanation:
Please it us urgent
i think its a
hope that helps
Answer:
A.
Step-by-step explanation:
Vertex form for a absolute value function is f(x)=a|x-h|+k
The vertex is (h,k)
If a is positive it is open up
If a is negative it is open down
So looking at the a part we can rule out 2 choices B and D
Finding the vertex is enough because A and C different in that slightly
The vertex is (-2,3)
So the absolute value function should look like this f(x)=a|x+2|+3
So the answer is A.
Two companies allow you to pay monthly for your food truck permits. Company A charges a one time fee of $150 and $45 per month. Company B charges a one time fee of $125 and $50 per month.
The simultaneous Equations for both total costs are;
Company A: y = 45x + 150
Company B: y = 50x + 125
Thus, both companies charge the same amount of money for food truck permits for 5 months
How to find the equation of the total charges?
We are told that;
Company A charges a one time fee of $150 and $45 per month.
Company B charges a one time fee of $125 and $50 per month.
Thus, using the concept of the equatiom of a line In slope intercept form, we have:
Company A: y = 45x + 150
Company B: y = 50x + 125
let's use the number 5 for x as an example
45(5) + 150 = 375
50(5) + 125 = 375
So both companies charge the same amount of money for food truck permits for 5 months.
Complete question is;
Two companies allow you to pay monthly for your food truck permits. Company A charges a one time fee of $150 and $45 per month. Company B charges a one time fee of $125 and $50 per month. Write an equation or a system of equations and explain what each solution tells you about the situation
evaluate x -2 y 0 / x 3 y -2 when x = 2 and y = 5
Answer:
5/8
Step-by-step explanation:
first plug in for x & y, then solve. you should get 5/8
2 -2 +5 +0 / 2 +3 +5 -2
5/8
Answer:
125/32
Step-by-step explanation:
Which table represents a linear function?
Answer: The 3rd from the left.
Step-by-step explanation:
Help please i only have a little bit of time
Answer:
d
Step-by-step explanation:
i jut did it in google calculator (trust me)
Hello There!
First, our formula for finding the volume of a cylinder is Pi*radius^2*height
Now, let'd get into solving for the volume. First, we need to find the radius so in this problem, we are given the diameter so to find the radius, we just divid the diameter by 2. Once we divide, our radius comes out to 6.5.
Next, in our formula it says we have to square our radius so we would multiply 6.5 by 6.5 to get a product of 42.25.
Lastly, we need to multiply 42.25 by our height which is our last step in our formula. Once we multiply 42.25 by the height of the cylinder which is 11, we get a product of 464.75.
464.75 rounded to the nearest tenth is 464.8
Your answer is the first one
Select the correct answer from the drop-down menu.
Divide the binomial by the monomial to find the quotient.
48r4y – 725672
-12.12y
Answer:
[tex]-(4x^2)+6(x^4)y[/tex]
Step-by-step explanation:
Here apply the law of indices where ;
[tex]A^x*A^y=A^{x+y}[/tex]
Given;
You should first simplify the numerator using the denominator as a factorThen cancel the like termFollowed by further factorization[tex]\frac{48x^4y-72x^6y^2}{-12x^2y} \\\\\\\frac{-12x^2y(4x^2-6x^4y^2)}{-12x^2y} \\\\\\=-4x^2+6x^4y\\\\\\=-(4x^2)+6(x^4)y[/tex]
The coordinates G(7,3), H(9, 0), (5, -1) form what type of polygon?
an obtuse triangle
an acute triangle
O an equilateral triangle
a right triangle
Answer:
Is an acute triangle
Step-by-step explanation:
we know that
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
we have
G(7,3), H(9, 0), I(5, -1)
step 1
Find the distance GH
substitute in the formula
[tex]d=\sqrt{(0-3)^{2}+(9-7)^{2}}[/tex]
[tex]d=\sqrt{(-3)^{2}+(2)^{2}}[/tex]
[tex]GH=\sqrt{13}\ units[/tex]
step 2
Find the distance IH
substitute in the formula
[tex]d=\sqrt{(0+1)^{2}+(9-5)^{2}}[/tex]
[tex]d=\sqrt{(1)^{2}+(4)^{2}}[/tex]
[tex]IH=\sqrt{17}\ units[/tex]
step 3
Find the distance GI
substitute in the formula
[tex]d=\sqrt{(-1-3)^{2}+(5-7)^{2}}[/tex]
[tex]d=\sqrt{(-4)^{2}+(-2)^{2}}[/tex]
[tex]GI=\sqrt{20}\ units[/tex]
step 4
Verify what type of triangle is the polygon
we know that
If applying the Pythagoras Theorem
[tex]c^{2}=a^{2}+b^{2}[/tex] ----> is a right triangle
[tex]c^{2}> a^{2}+b^{2}[/tex] ----> is an obtuse triangle
[tex]c^{2}< a^{2}+b^{2}[/tex] ----> is an acute triangle
where
c is the greater side
we have
[tex]c=\sqrt{20}\ units[/tex]
[tex]a=\sqrt{17}\ units[/tex]
[tex]b=\sqrt{13}\ units[/tex]
substitute
[tex]c^{2}= (\sqrt{20})^{2}=20[/tex]
[tex]a^{2}+b^{2}=(\sqrt{17})^{2}+(\sqrt{13})^{2}=30[/tex]
therefore
[tex]c^{2}< a^{2}+b^{2}[/tex]
Is an acute triangle
Answer:
ACUTE !!!!!!!!
Step-by-step explanation:
How to solve for y and simplify
Answer:
y = [tex]\frac{2}{5}[/tex]
Step-by-step explanation:
Given
- 3y = - [tex]\frac{6}{5}[/tex]
Multiply both sides by 5 to eliminate the fraction
- 15y = - 6 ( divide both sides by - 15 )
y = [tex]\frac{-6}{-15}[/tex] = [tex]\frac{6}{15}[/tex] = [tex]\frac{2}{5}[/tex]
A family is planning a wedding celebration in a gazebo. They want to know the area so that they can determine how many people can comfortably fit inside. They take some measurements and find that each side is 8 ft long and the apothem is 9.7 ft. What is the area of the enclosed gazebo?
Answer:
The area of the enclosed gazebo is [tex]310.4\ ft^{2}[/tex]
Step-by-step explanation:
I assume that is a regular octagon (eight equal aides)
we know that
The area of a regular polygon is equal to
[tex]A=\frac{1}{2}(P)(a)[/tex]
where
P is the perimeter of the polygon
a is the apothem
Find the perimeter P (the octagon has 8 sides)
[tex]P=8(8)=64\ ft[/tex]
[tex]a=9.7\ ft[/tex]
substitute
[tex]A=\frac{1}{2}(64)(9.7)[/tex]
[tex]A=310.4\ ft^{2}[/tex]
Analyze the diagram below and complete the instructions that follow.
550
450
Answer:
130 degrees
Step-by-step explanation:
let the angle be x
2x+45+55=360(Sum of angles in quad)
2x=260
x=130
The measure of <Q is 130 degree.
What is Angle Sum Property?There are four angles in a quadrilateral. Its inner angles add up to 360 degrees.
The angle sum property of a Quadrilateral states that the sum of all four inner angles is 360 degrees.
We have
<T = 55
<R= 45
let us consider the two angles are Equal.
Using angle sum Property
<T + <R + Q + <S = 360
45+ 55 + x + x = 360
100 + 2x = 360
2x = 260
x = 130
Thus, the measure of <Q is 130 degree.
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Which expression is equivalent to
28p^9 q^-5/12p^-6 q^7
Answer:
7p^15 / q^12
Step-by-step explanation:
7p^9+6 q^-5-7 / 3 #28 is divided by 12
7p^15 / q^12 #Answer
Answer:
7p^15/3q^12 is equivalent to 28p^9 q^-5/12p^-6 q^7
Step-by-step explanation:
Given Parameter:
28p^9 q^-5/12p^-6 q^7
Required; To simplify.
To simplify the above expression, we'll apply 2nd law of indices.
But first, let's rewrite the expression.
28p^9 q^-5/12p^-6 q^7 becomes
(28 * p^9 * q^-5) / (12 * p^-6 * q^7)
Then we collect similar indices. This is done as follows
(28/12) * (p^9/p^-6) * (q^-5/q^7)
From second law of indices (law of division);
If the two terms have the same base () and are to be divided their indices are subtracted.
For instance x^a/x^b = x^(a - b).
Applying this law; we have
(28/12) * (p^9/p^-6) * (q^-5/q^7) becomes
(28/12) * (p^(9 - (-6))) * (q^(-5-7))
(28/12) * (p^(9+6)) * (q^-12)
(28/12) * p^15 * q^-12
Simplify 28/12
(4*7)/(4*3) *p^15 * q^-12
(7/3) * p^15 * q^-12
(7/3) * p^15 * 1/q^12
7p^15/3q^12
Hence, 7p^15/3q^12 is equivalent to 28p^9 q^-5/12p^-6 q^7
The bearing of Q from P is 150° and the bearing of P from R is 15°.if Q and R are 244metres and 324metres respectively from P.(i) represent this information on a diagram (ii) calculate the distance between Q and R correct to two decimal place(iii) find the bearing of R from Q,correct to thr nearest degree.
PLEASE HELP ME OUT
You are trying to pick 2 elective classes for next year. You would like to take one music class and one physical education class. There are 9 different music classes and 10 different physical education classes offered at your school.
How many different combinations of these elective classes can you select?
Answer:
90
Step-by-step explanation:
There are 9 options for the first choice and 10 options for the second. Multiply them together to get the full number of combinations, which is 90.
5. (03.02)
If g(x) = x2 + 3, find g(4). (2 points)
16
19
8
11
Answer:
19
Step-by-step explanation:
g(x)=x^2+3
g(x)=(4^2)+3
g(x)=16+3=19
if g of x = x squared + 3, then 4 squared = 16, plus 3 = 19
Answer:
option(B) g(4) =19.
Step-by-step explanation:
Given:If g(x) = [tex]x^{2}[/tex] + 3.
To find: g(4).
Solution: We have given that
g(x) = [tex]x^{2}[/tex] + 3.
for x=4.
g(4) = [tex]4^{2}[/tex] + 3.
g(4) = 16+3
g(4) =19.
Therefore, option(B) g(4) =19.
Please help!!!!! Thanks
Answer:
Look to the attached file
Step-by-step explanation:
Which of the following is a factor of 2x^4 + 20x^3 + 50x^2?
A. 2x^3
B. x^4
C. x+4
D. x+5
Answer:
D. x + 5
Step-by-step explanation:
2x^4 + 20x^3 + 50x^2
= 2x^2 (x^2 + 10x + 25)
= 2x^2 (x + 5)^2
= 2x^2 (x + 5) (x + 5)
Answer
D. x + 5
For this case we have the following expression:
[tex]2x ^ 4 + 20x ^ 3 + 50x ^ 2[/tex]
It is observed that we can extract common factor [tex]2x ^ 2[/tex], since it is common in the three terms:
[tex]2x ^ 2 (x ^ 2 + 10x + 25) =[/tex]
If we factor the expression into parentheses, we must look for two numbers that add 10 and multiply 25. These are: 5 and 5.
Rewriting the expression we have:
[tex]2x ^ 2 ((x + 5) (x + 5))[/tex]
Thus, one of the factors of the original expression is[tex]x + 5[/tex].
Answer:
Option D
Rationalize the denominator and simplify. 6 /5-3
Final answer:
To rationalize the denominator and simplify the expression 6 / (5-3), multiply the numerator and denominator by 1/2. Then, simplify the expression to get 3/1 = 3.
Explanation:
To rationalize the denominator and simplify the expression 6 / (5-3), we can start by multiplying the numerator and denominator by a skillfully chosen factor. In this case, we can choose 1/2 as the factor.
The numerator becomes 6 * 1/2 = 3, and the denominator becomes (5-3) * 1/2 = 2/2 = 1.
Therefore, the simplified expression is 3/1 = 3.