Answer:
Set the area equal to x2, solve for x, and then multiply the value of x by 4.
Step-by-step explanation:
The area of the picture is given by
A = s^2 where s is the side length
Let the side length be x
A = x^2
Take the square root of each side
sqrt(A) = sqrt(x^2)
x = sqrt(A)
We want to find the perimeter since we are framing the border
P = 4s since the picture is a square
P = 4 * x
Answer:
B.
Step-by-step explanation:
Let's let x represent the side length of the square.
Since the picture is a square, all the lengths are the same. Moreover, the area of the square is x times x or x squared. Thus:
[tex]A=x^2[/tex]
The amount of framing Sachiko needs is represented by the perimeter of the square. The perimeter of a square is determined by the formula:
[tex]P=4x[/tex]
Now, if Sachiko knows the area and she wants to find the perimeter, she can do the following:
First, the area is equal to x^2. So, she should first just find the length itself. So her first step should be to set the area equal to x^2 and then solve for x.
Then, when she has found her length, she just need to multiply it by 4 to get the perimeter or the amount of framing she needs.
Thus, the answer is choice B.
Solve the radical equation the square root of 8x+9=x+2, how would you start it?
Answer: I will start it by squaring both sides of the equation.
The solution is x = 5 or x=-1
Step-by-step explanation:
[tex]\sqrt{8x+9} =x+2[/tex] Square the left and right sides. The square root of 8x+9 squared is 8x+9 and the x+2 squared is x^2 + 4x +4. We will now have the new equation,
8x + 9 = [tex]x^{2}[/tex] + 4x + 4 now set them equal zero first sutract x^2 from both sides
-x^2 -x^2
-x^2 + 8x + 9 = 4x +4 subtract 4x from both sides
-4x -4x
-x^2 +4x + 9 = 4 Finally subtract 4 from both sides
-4 -4
-x^2 + 4x +5 = 0 Remember the largest degree has a negative coefficient so divide them all by -1.
x^2 - 4x -5 = 0 Now find two numbers that their product is -5 and their sum is -4. the numbers 1 and -5 works out.
Now rewrite the whole equation as,
x^2+ 1x -5x -5=0 Factor by grouping on the left side
x(x+1) -5(x+1)= 0 Factor out x+1
(x+1)(x-5) = 0 Now apply the zero product
x+1 = 0 or x-5 = 0
-1 -1 +5 +5
x = -1 or x = 5
Of the 30 girls who tried out for the basketball team at Prescott Junior High, 12 were selected. Of the 40 boys who tried out, 16 were selected. Are the ratios of the number of students on the team to the number of students trying out the same for both boys and girls? How do you know?
Answer: Yes. They are thesame
Step-by-step explanation:
Of the 30 girls who tried out for the basketball team at Prescott Junior High, 12 were selected. In this scenario the ratio will be:
= 12/30
= 2/5
= 2:5
Of the 40 boys who tried out, 16 were selected. In this scenario, the ratio will be:
= 16/40
= 2/5
= 2:5
The ratio for both are thesame as we got 2:5 for both.
The equation x + 2 = [tex]\sqrt{3x + 10}[/tex] is of the form x + a = [tex]\sqrt{bx + c}[/tex], where a, b, and c are all positive integers and b > 1. Using this equation as a model, create your own equation that has extraneous solutions. (Hint: Substitute 7 for x, and choose a value for a. Then square both sides so you can choose a, b, and c that will make the equation true.) (I know this is a handful but I'm really in need of help right now, thanks to everyone in advance!)
Answer:
Extraneous solution for Equation x + 1 = √7x + 15 : x = - 2
Step-by-step explanation:
We are given the equation x + a = √bx + c. As the hint says, let's substitute 7 for x first, receiving the following equation.
7 + a = √7b + c
Now let's say a = 1 and c = 8. Through substitution we solve for b,
7 + 1 = √7b + 8
8 = √7b + 8
8² = (√7b + 8)²
64 = 7b + 8
7b = 64 - 8 = 56
b = 56 / 7 = 8
Therefore, the equation x + 1 = √8x + 8 ( substitute the value of b ) will have a solution of x = 7. Let's simplify this equation and see if we receive any extraneous solutions.
x + 1 = √8x + 8
(x + 1)² - (√8x + 8)² = 0
(x + 1)² - 8x + 8 = 0
(x + 1)² - 8(x + 1) = 0
(x + 1)(x + 1 - 8) = 0
(x + 1)(x - 7) = 0
x = - 1 and x = 7
We already know that x = 7, but x = - 1 is not an extraneous solution. Therefore let's simplify the equation x + 1 = √7x + 15 and see if we receive any extraneous solutions.
(x + 1)² - (√7x + 15)² = 0
(x + 1)² - 7x + 15 = 0
x² - 5x - 14 = 0
(x - 7)(x + 2) = 0
x = 7 and x = - 2
In this case x = - 2 is an extraneous solution. We can check by substituting it back into the equation x + 1 = √7x + 15.
- 2 + 1 = √7(- 2) + 15
- 1 = √- 14 + 15
- 1 = √1
- 1 ≠ 1 - hence proved that x = - 2 is our extraneous solution
The equation with extraneous solution is [tex]x +5 = \sqrt{6x + 4[/tex]
The equation is given as:
[tex]x + 2 = \sqrt{3x + 10[/tex]
The form of the equation is given as:
[tex]x +a = \sqrt{bx + c[/tex]
Now, we assume that x = 7.
So, the equation becomes
[tex]7 +a = \sqrt{7b + c[/tex]
Assume that the value of a is 5
[tex]7 +5 = \sqrt{7b + c[/tex]
Add 7 and 5
[tex]12 = \sqrt{7b + c[/tex]
Square both sides of the equation
[tex]144= 7b + c[/tex]
Assume that the value of b is 6.
So, the equation becomes
[tex]144= 7(6) + c[/tex]
[tex]144= 42 + c[/tex]
Assume that c is 4
[tex]144= 42 + 4[/tex]
[tex]144= 46[/tex]
The above equation is false because 144 does not equal 46.
The values of a, b and c that makes the equation false are:
[tex]a=5[/tex]
[tex]b = 6[/tex]
[tex]c = 4[/tex]
So, we have:
[tex]x +a = \sqrt{bx + c[/tex]
[tex]x +5 = \sqrt{6x + 4[/tex]
Hence, the equation with extraneous solution is [tex]x +5 = \sqrt{6x + 4[/tex]
Read more about extraneous solutions at:
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4. Fatore as expressões. a) 4x4y2 –6x3y3 +8x2y4 = b) 18ab3c² +27a3b4c3 -9a2b5c4 -45a2b3c2 = c) a2+3ab-2ac-6bc= d) x3–3x2y2 +6y3 – 2xy = e) x2 +z+x3y+xyz=zx2 -z2 = f) a4b6-9c2 = g) 9a4-b4 = h) 25x6 + 10x3y+y2 = i) 49x4 +14x2 +1= j) 20a2b2 – 2a4 – 50b4 =
Answer:
don't ask many questions at 1time
What is the slope of the line that passes through the points (5,–10) and
(-3,-10)? Write your answer in simplest form.
Answer:
Slope = 0Step-by-step explanation:
The slope of a line between two points can be found by using the formula
[tex]m = \frac{y2 - y1}{x2 - x1} [/tex]
where
(x1 , y1) and (x2 , y2) are the points
From the question the points are
(5,–10) and (-3,-10)
Their slope is
[tex]m = \frac{ - 10 + 10}{ - 3 - 5} = \frac{0}{ - 8} = 0[/tex]
We have the final answer as
Slope = 0
Hope this helps you
Answer:
0
Step-by-step explanation:
Simplify by dividing negative three over eight divided by five over nine..
Answer:
-15/24 or -0.625
Step-by-step explanation:
-3/8 ÷ 5/9
First, we can use the multiplication fraction conversion trick to switch the last fraction's numerator and denominator
It would look like this: -3/8 x 9/5
Use the cross out method to simplify the fractions as lowest as possible
-1/8 x 3/5 = -15/24
How do you do this problem? See attached image
Round each decimal to the indicated place value 3.41469 ten thousandths
Answer:
3.4147
Step-by-step explanation:
Answer:
the number rounded to the nearest ten thousandth is : 3.4147
Step-by-step explanation:
3.41469 Round to ten thousandths
put the number in value chart:
ones . tenth hundredth thousandth ten thousandth h.thousandth
3 . 4 1 4 6 9
now look at the number after the ten thousandth it is 9 which is more than five , five and more add one to the value below
add (1) to 6
the number rounded to the nearest ten thousandth is : 3.4147
Please answer this! I need help ASAP
Answer:
<MON = 57°
Step-by-step explanation:
they are complementary angles so they add up to 90°
3x - 15 + 5x - 23 = 90
8x - 38 = 90
8x = 128
x = 16
5(16) - 23 = 57
Using the image as a reference, what is the csc of angle 90 - x?
Answer:
Option (F)
Step-by-step explanation:
From the figure attached,
ΔABC is a right triangle.
m∠A + m∠B + m∠C = 180°
m∠A + 90° + x° = 180°
m∠A = 180 - (90 + x)
= (90 - x)°
By applying cosec rule in this triangle,
csc(A) = [tex]\frac{\text{Hypotenuse}}{\text{Opposite side}}[/tex]
csc(90 - x) = [tex]\frac{\text{AC}}{\text{BC}}[/tex]
= [tex]\frac{5}{3}[/tex]
= 1.67
Therefore, Option (F) will be the correct option.
anna is biking at x miles per hour. sara bikes at 10 mi/h. which expression represents the average of anna’s and sara’s speeds?
Step-by-step explanation:
It is given that,
Speed of Anna is x miles/hour
Speed of Sara is 10 mi/h
We need to find an expression that represents the average of Anna's and Sara's speeds. Average of two objects is given by :
[tex]v=\dfrac{v_1+v_2}{2}[/tex]
ATQ,
[tex]v=\dfrac{x+10}{2}[/tex]
The above expression represents the average speed of Anna and Sara.
Find major of 1 in the diagram.
Answer:
85° (C).
Step-by-step explanation:
35° should go over to the other side of the line:
180 - 35 = 145°
Find angle 1:
145 + 130 + angle 1 = 360°
360° = 275° + angle 1
angle 1 = 360 - 275
angle 1 = 85°
85° which is C is the answer.
Answer:
Your correct answer is option C. 85 degrees.
Step-by-step explanation:
35 degrees goes over to the other side of the line:
180 - 35 = 145°
All you need to do is find angle 1.
145 + 130 + angle 1 = 360 degrees
360 degrees = 275 degrees + angle 1
angle 1 = 360 - 275
angle 1 = 85 degrees.
Therefore, option C. is the correct answer.
could someone please help me with this question
Answer:
Proportional: second and third, non-proportional: first and fourth
Step-by-step explanation:
Proportional relationships are linear functions that pass through the origin. Using this definition, we can conclude that the proportional relationships are the second and third options whereas the non-proportional relationships are the first and fourth options.
Answer:
proportional relationship: the second one and the third one the first and the fourth one
Non-proportional relationship: the first and the fourth one
Step-by-step explanation:
Like the first person said, a proportional relationship is when a linear line passes thru the origin, which is known as (0,0), so the second and the third are the only ones that do that, plus they have a y-intercept of a 0 and the others don't.
A hypothesis is:_______
a. a testable prediction about the relationship between variables.
b. a simple explanation for a psychological finding.
c. an observed relationship between independent and dependent variables.
d. an unprovable assumption about psychological processes.
Answer:
a. A testable prediction about the relationship between variables
Step-by-step explanation:
A hypothesis is the FIRST step in conducting research or experimenting. In other terms, a scientific guess based on limited knowledge. Contrary to our hypothesis, conclusion comes last in researching and states the summary of the information gathered.
The reason why it isn't letter D is because a hypothesis's provability can only be determined once you have your conclusion, which is after you have conducted a research or experiment.
The letters B and C are too unrelated to what an hypothesis is.
- 8th grade student :)) (also buried under her own mountain of assignments and activities)
why is it important that the real numbers have the property of being complete
Answer:Real numbers must be complete in order to fill the number line.
Step-by-step explanation: No steps I got this answer from my algebra notes.
Completeness as a property of real numbers ensures that the limit of a sequence exists within the set due to the absence of gaps or missing points
Completeness of real numbers means that there are no gaps in between a sequence of real numbers or on a real number line.
The importance of completeness of real numbers is of particular importance in other to ensure that mathematical calculations and analysis hold for all sequence of real numbers in a set.
With the presence of gaps or holes in real numbers, then the limit of a sequence of real numbers may not exist within a specified set.
Learn more : https://brainly.com/question/16492781?
Two two-digit numbers have the same digits. The sum of the digits of each number is 10. The difference between the numbers is 18. What are the numbers?
Answer:
46 and 64
Step-by-step explanation:
4 + 6 = 10
6 + 4 = 10
64 - 46 = 18
The length of a rectangle is 6 inches more than the width. The perimeter of the rectangle can
be no more than 48 inches. What is the maximum length?
Answer:
15 inches
Step-by-step explanation:
Hello!
To find the perimeter of a rectangle we have to add all the sides
l + l + w + w = p
We know the length is 6 inches more than the width
l = w + 6
We can put w + 6 for l
w + 6 + w + 6 + w + w = p
We can simplify this
4w + 12 = p
The perimeter is no more than 48
4w + 12 = 48
Subtract 12 from both sides
4w = 36
Divide both sides by 4
w = 9
Now we can put 9 in for w in the equation to find the length
l = 9 + 6
l = 15
The answer is 15 inches
Hope this helps!
Click to review the online content. Then answer the question(s) below, using complete sentences. Scroll down to view additional questions Online Content: Site 1 What are some considerations you need to make before choosing a career?
Answer:
some considerations before choosing which career or path you will take career wise for the future is what you enjoy doing. what is also very important is understanding how many classes of college or university is required if you are up to the challenge and how many years it'll take before starting that career.
PLEASE HELP! Create a table of points from the equation f(x)=3x^2-8x+2. (I'll add a picture of the tables)
===============================================
Explanation:
If we replace x with 0, then we get...
f(x) = 3x^2-8x+2
f(0) = 3(0)^2 - 8(0) + 2
f(0) = 3(0) - 8(0) + 2
f(0) = 0 - 0 + 2
f(0) = 2
Showing that the input x = 0 leads to the output y = f(x) = 2
The answer is between choice A and choice D because of this. Something like choice B is eliminated because this table shows x = 0 leading to y = -3 which is not correct.
-----------
Let's plug in x = 1
f(x) = 3x^2-8x+2
f(1) = 3(1)^2 - 8(1) + 2
f(1) = 3(1) - 8(1) + 2
f(1) = 3 - 8 + 2
f(1) = -5 + 2
f(1) = -3
So x = 1 leads to y = -3. We can rule out choice D and confirm it is choice A.
We don't need to try other x values since we have the answer, but I recommend practicing with other x values to help confirm that the first table is the answer.
find the area of a trapezoid whose height is 2 meters and whose bases are 6 meters and 10 meters
Answer:
16 m^2
Step-by-step explanation:
The area of a trapezoid is given by
A = 1/2 (b1+b2) *h
= 1/2 ( 6+10) * 2
= 16 m^2
4b+9b simplified version
Answer:
13b
Step-by-step explanation:
Add 4b and 9b together because they are like terms,
so 4b + 9b = 13b
Answer:
13b
Step-by-step explanation:
4b+9b
Combine like terms
13b
Find the positive numbers such that the sum of and its reciprocal is as small as possible.Does this problem require optimization over an open interval or a closed interval
Answer:
Yes and closed interval
Step-by-step explanation:
The computation is shown below:
For the sum and the reciprocal as small as the possible equation is as follows
[tex]\(\frac{d}{dx}\left(x+\frac{1}{x}\right)=0.\)[/tex]
Now take out the derivates,
So,
[tex]\(1-\frac{1}{x^2}=0,\)[/tex]
or we can say that
[tex]\(x^2-1=0\rightarrow x=\pm1.\)[/tex]
As the only positive number is to be determined i.e
x = 1
So this problem needed the optimization over a closed interval and the same is to be considered.
Pythagorean Theorema a=24 b=26 c=?
Answer: 2√313
Step-by-step explanation:
Pythagorean theorem: a²+b²=c²
c²=a²+b²
c²=24²+26²
c²=576+676
c²=1252
c=√1252
c=2√313
Hope this helps!! :)
Please let me know if you have any question or need any further explanation
If x + 3(2x-5) = 6 then x =
O
-3
3
O 15
O Option 4
O-14
Answer:
[tex] \boxed{ \boxed{ \bold{ \sf{3}}}}[/tex]Step-by-step explanation:
[tex] \sf{x + 3(2x - 5) = 6}[/tex]
Distribute 3 through the parentheses
⇒[tex] \sf{x + 6x - 15 = 6}[/tex]
Collect like terms
⇒[tex] \sf{7x - 15 = 6}[/tex]
Move constant to right hand side and change it's sign
⇒[tex] \sf{7x = 6 + 15}[/tex]
Add the numbers
⇒[tex] \sf{7x = 21}[/tex]
Divide both sides of the equation by 7
⇒[tex] \sf{ \frac{7x}{7} = \frac{21}{7} }[/tex]
Calculate
⇒[tex] \sf{x = 3}[/tex]
Hope I helped!
Best regards!
The value of x is 3 for the equation x + 3(2x-5) = 6.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The given equation is x + 3(2x-5) = 6
x plus three times of two times of x minus five equal to six.
We need to find the value of x.
x + 3(2x-5) = 6
Apply distributive property.
x+6x-15=6
7x-15=6
Add 15 on both sides
7x=6+15
7x=21
Divide both sides by 7
x=3
Hence, the value of x is 3 for the equation x + 3(2x-5) = 6.
To learn more on Equation:
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is x^2+y^2=5 a function? why or why not?
Answer:
No.
Step-by-step explanation:
A function must past the Vertical Line Test. We know that our equation x² + y² = 5 is a circle, and so some x-values have the same y-values, etc. Since not every x-value has its own y-value, our equation is not a function.
We can see this using a graph:
Since the vertical line test passes 2 points with the same x-value, it is not a function.
The difference of twice a number and 3 is -21 translated
Answer:
2x-3=-21.
2x=-21+3.
2x=-18.
x=-18/2.
x= -9.
Answer:
[tex]\Huge \boxed{2x-3=-21}[/tex]
Step-by-step explanation:
Let the number be x.
The difference of two values is the result from subtracting them.
[tex]2x-3=-21[/tex]
Add 3 to both sides.
[tex]2x=-18[/tex]
Divide both sides by 2.
[tex]x=-9[/tex]
The number is -9.
*PLEASE ANSWER, DIFFICULT QUESTION* What is the volume of this beach ball if its width is 24 inches? (Use 3.14)
Answer:
7234.56 in³
Step-by-step explanation:
4/3πr³
4/3 (3.14)(12)³
7234.56 in³
Answer:
7,234.56 cm^2
Step-by-step explanation:
We want to find the volume of the beach ball. The beach ball is in the shape of a sphere. The formula for the volume of a sphere is :
[tex]V=\frac{4}{3} \pi r^3[/tex]
We know the width, or diameter of the sphere is 24 cm. We need to find the radius. The radius is half the diameter.
r= d/2
r= 24 cm/2
r= 12 cm
The radius is 12 cm, and we can substitute it into the formula.
[tex]V=\frac{4}{3} \pi (12 cm) ^3[/tex]
First, evaluate the exponent.
(12 cm)³= 12 cm * 12cm * 12 cm= 144 cm² * 12 cm = 1728 cm³
[tex]V=\frac{4}{3} \pi * 1728 cm^3[/tex]
Substitute 3.14 in for pi.
[tex]V=\frac{4}{3} * 3.14 * 1728 cm^3[/tex]
Multiply all three numbers together.
[tex]V= 4.18666666 * 1728 cm^3[/tex]
[tex]V= 7234.55999 cm^3[/tex]
Round to the nearest hundredth. The 9 in the thousandth place tells us to round the 5 to a 6 in the hundredth place.
[tex]V= 7234.56 cm^3[/tex]
The volume of the beach ball is 7,234.56 cubic centimeters and choice 3 is correct.
2(M+7)+5m-6
Umm I need help
Answer:
7m+8
Step-by-step explanation:
distributive prop then pemdas
Given T(x,y)=(x+5,y+4) and the point P(2,3), what is T(P)?
==============================================
Explanation:
T(P) is the notation applying the translation rule T(x,y) = (x+5, y+4) to the point P(2,3)
The x+5 means we add 5 to the x coordinate of P. We have x = 2 become x+5 = 2+5 = 7. The point P shifts 5 units to the right to go from (2,3) to (7,3)
Then the point shifts 4 units up to arrive at (7, 7). We shift 4 units up due to the y+4 in the translation rule.
Or put another way, y = 3 is the y coordinate of P. So y+4 = 3+4 = 7 is the new y coordinate.
Each side of a sandbox is 7 feet long. It will cost $1.00 per square foot to replace the sand in the sandbox. What would be the total cost to replace the sand?
Answer: $7.00
Step-by-step explanation:
each foot is $1, so times 7 is 7 dollars.
Answer:
49
Step-by-step explanation:
7 x 1 is 7.
7 x 7 is 49.
49 is answer.