Directions: Solve each of the following problems. Show your solution. (5 points each)
1. Bailey’s rectangular dog pen for his Irish setter must have an area of 400 square feet.
Also ,the length must be 10 feet longer than the width. Find the dimension of the pen.
Answer:
400=(×+20)× is the equation or
400=×^2+20×
(×+10)= square root of 500
×+10=10 radical 5
final answer -10 + or - 10 radical 5=×
hoose the statement that describes its
solution.
3(x + 8) - 9x = 6(4- x)
O There is no solution.
оо
There is only one solution.
ws
о
All real numbers are solutions.
Answer:
3rd option
Step-by-step explanation:
3(x + 8) - 9x = 6(4 - x) ← distribute parenthesis on both sides
3x + 24 - 9x = 24 - 6x , collect like terms on left side )
24 - 6x = 24 - 6x
Since both sides are the same then any value of x will make the equation true.
That is all real numbers are solutions
Answer: C g(x) is a function because f(x) is one-to-one.
Step-by-step explanation:
given r||s, what is the measure of <1 ?
Step-by-step explanation:
post the full question
hope this helps you.
6. Kori is on a road trip to Colorado, and uses the equation y = 60x+ 200 to determine the
number of miles she has driven after x hours. If she drives for a maximum of 12
hours, what is the domain of this situation?
The domain is the set of x-values for which the equation is true.
Since the maximum time is 12 hours, then the domain is less than or equal to 12.Since time can't be negative or 0, then the minimum is greater than 0. ∴ domain would be 0 < x ≥ 12HELP ME I WILL GIVE YOU BRAINLIEST AND A 5.0 REVIEW
Power: An _________________ that has a base and an exponent.
Answer:
Base
Step-by-step explanation:
A power is the product of multiplying a number by itself. Usually, a power is represented with a base number and an exponent. The base number tells what number is being multiplied. The exponent, a small number written above and to the right of the base number, tells how many times the base number is being multiplied.
identify the errors made in finding the inverse of y = x2 + 12x. An image shows a student's work. Line 1 is x = y squared + 12 x. Line 2 is y squared = x minus 12 x. Line 3 is y squared = negative 11 x. Line 4 is y = Start Root negative 11x End Root, for x greater-than-or-equal 0.
solving for the inverse of y = x² + 12x
Line 1: x = y² + 12 x.
Line 2 y² = x - 12 x.
Line 3 is y²= - 11 x.
Line 4 is y = √(- 11x) for x ≥ 0.
The error lies in Line 1. All x's have to be switched with y's and vice versa for the method to work.
As such Line 1 should be x = y² + 12y NOT (x = y² + 12 x)
Since Line one is wrong, it messes with all the other lines.
What is the value of 2.3+8−12?
1.) 10.8
2.) 10.3
3.) 9.8
4.) 9.5
Answer:
2
Step-by-step explanation:
to answer this algebraic question use BDMAS rule
first solve bracket then division, multiplication,addition then subtraction.
6+8-12
14-12
2
Answer:
9.8
Step-by-step explanation:
convert your decimal into a fraction so 2.3= 23/10
23/10 + 8 - 1/2
then calculate your sum or difference
leaving you with
49/5
meaning your answer is
9.8
Given the definitions of f(x)f(x) and g(x)g(x) below, find the value of (f\circ g)(2).(f∘g)(2). f(x)= f(x)= \,\,-5x-11 −5x−11 g(x)= g(x)= \,\,2x^2+2x-5 2x 2 +2x−5
Sarah has $31,000 in a savings account. The interest rate is 8% per year. How much simple interest will she earn in 5 years?
Answer:
$12,400
Step-by-step explanation:
Interest = Principal x Rate x Time (in years)
I = 31000 x .08 x 5
I = 12,400
A cleaning solution uses 5 cups of soap for every 2 cups of vinegar. If Emery put 4 cups of soap in a container, how
many cups of vinegar must she use?
1.6 cups of vinegar used for 4 cups of soap.
What is Unitary Method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Given:
For 5 cups of soap = 2 cups of vinegar
For 1 cups of soap = 2/5 cups of vinegar used.
Now we have to find how much vinegar required for 4 cups of soap.
So, for 4 cups of soap
=2/5 * 4
=8/5
=1.6 cups of vinegar used.
Hence, 1.6 cups of vinegar used.
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Which equation has only one unique solution?
A.
|3 − x| = 3
B.
|x − 2| − 7 = 7
C.
-4|x| + 1 = -3
D.
9 − |2x − 1| = 9
The equation with only one unique solution is 9 − |2x − 1| = 9, with the solution x = 1/2. D.
To determine which equation has only one unique solution, let's analyze each equation:
|3 − x| = 3
In this equation, the absolute value term represents a distance.
By setting up two cases, where the absolute value is positive and negative, we can find the solutions.
Case 1:
3 - x = 3
Solving for x, we have x = 0.
Case 2:
x - 3 = 3
Solving for x, we have x = 6.
Thus, this equation has two solutions.
|x − 2| − 7 = 7
Similar to equation A, the absolute value term represents a distance.
By adding 7 to both sides, we have |x - 2| = 14.
This equation implies that the distance between x and 2 is 14.
There are two possible values for x: x = 2 + 14 = 16 and x = 2 - 14 = -12.
This equation has two solutions.
-4|x| + 1 = -3
To solve this equation, we isolate the absolute value term:
-4|x| = -4
Dividing both sides by -4:
|x| = 1
The absolute value of any number is always positive or zero.
The equation |x| = 1 has two solutions: x = 1 and x = -1.
9 − |2x − 1| = 9
The absolute value term represents a distance.
Subtracting 9 from both sides, we have |2x - 1| = 0.
The only way the absolute value of a real number can be equal to zero is if the number inside the absolute value is zero.
Thus, we set 2x - 1 = 0 and solve for x:
2x - 1 = 0
2x = 1
x = 1/2
Equation D has only one unique solution: x = 1/2.
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ive answered a and b but struggling to answer c. how do you work it out?
Answer:
-2, 1.5
Step-by-step explanation:
(y1 + y2)/2 = y midpoint formula
so, (-1 + 4) = 3
3 / 2 = 1.5
y = 1.5
Step-by-step explanation:
To find the midpoint:
Use the formula;
d = (x2 + x1)/2, (y2 + y1)/2 where x2 = -2, x1 = -2, y1 = -1, y2 = 4
Substitute the values into the equation above. This gives;
d = (-2 + -2)/2, (4 + -1)/2
= (-4/2), (3/2)
=(-2, 1.5) <<<<<<< ✓ Ans
I hope this helps. Thank you
If cosec ∅ = √2, find the value of 1+sin²∅+cos²∅/1+sec²∅-tan²∅.
Given: [tex]cosec[/tex] [tex]A[/tex] [tex]=\sqrt{2}[/tex]
∴ [tex]A=\frac{\pi }{4} =45^{0}[/tex]
[tex]sin[/tex] [tex]A[/tex] [tex]=sin[/tex] [tex]45^{0}[/tex] = [tex]\frac{1}\sqrt{2}[/tex]
[tex]cot[/tex] [tex]A[/tex] [tex]=cot[/tex] [tex]45^{0}[/tex] [tex]=1,[/tex]
[tex]tan[/tex] [tex]A[/tex] [tex]=[/tex] [tex]tan[/tex] [tex]45^{0}[/tex] [tex]=1[/tex]
[tex]cos[/tex] [tex]A[/tex] [tex]=[/tex] [tex]cot[/tex] [tex]45^{0}[/tex] [tex]=\frac{1}{\sqrt{2} }[/tex]
∴ [tex]=2[/tex]
[tex]\large\underline{\sf{Solution-}}[/tex]
METHOD 1: Using Trigonometric values.
We have given that,
[tex]\sf\cosec\theta=\sqrt2[/tex]
So,
[tex]\sf\theta=45^{\circ}[/tex]
We need to find:
[tex]\sf\dfrac{1+\sin^2\theta+\cos^2\theta}{1+\sec^2\theta-\tan^2\theta}[/tex]
So,
[tex]\sf\longmapsto\dfrac{1+\sin^2(45^{\circ})+\cos^2(45^{\circ})}{1+\sec^2(45^{\circ})-\tan^2(45^{\circ})}[/tex]
[tex]\sf\longmapsto\dfrac{1+\left(\frac{1}{\sqrt2}\right)^2+\left(\frac{1}{\sqrt2}\right)^2}{1+(\sqrt2)^2-(1)^2}[/tex]
[tex]\sf\longmapsto\dfrac{1+\frac{1}{2}+\frac{1}{2}}{1+2-1}[/tex]
[tex]\sf\longmapsto\dfrac{1+1}{2}[/tex]
[tex]\sf\longmapsto\dfrac{2}{2}[/tex]
[tex]\sf\longmapsto\bf1[/tex]
METHOD 2: Using Trigonometric Identities
We need to find:
[tex]\implies\dfrac{1+\sin^2\theta+\cos^2\theta}{1+\sec^2\theta-\tan^2\theta}[/tex]
But, we know that,
[tex]\sf\red⇛ \sin^2\phi+\cos^2\phi=1[/tex]
And,
[tex]\sf\red⇛ \sec^2\phi-\tan^2\phi=1[/tex]
So,
[tex]\sf\longmapsto\dfrac{1+(\sin^2\theta+\cos^2\theta)}{1+(\sec^2\theta-\tan^2\theta)}[/tex]
[tex]\sf\longmapsto\dfrac{1+1}{1+1}[/tex]
[tex]\sf\longmapsto\dfrac{2}{2}[/tex]
[tex]\sf\longmapsto\bf1[/tex]
Therefore, by both methods the answer is 1.
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Similar questions
Prove that:
\cos( \frac{3\pi}{2} + \theta) \cos(2\pi + \theta) [ \cot( \frac{3\pi}{2} - \theta) + \cot(2\pi + \theta) ] = 1...
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geometry pls help! im
beggingggg!
Answer: D; B
Step-by-step explanation: 1 and 4 are alternate exterior angles if you use process of elimination, all the other pairs are, alternate exterior, corresponding or same side interior angles. angles 1 and 4 are in between lines a and b when lines a and b have the transversal of c. with process of elimination, c is the only logical answer, as 1 and 4 both lie on that line. which leaves you with two answers. if you draw out lines a and b with a transversal of c and the lines b and e with the transversal of c, then B is the only logical answer. goodluck :) i just finished this unit :D
In the equation x + 10 = 22, what do you need to do to solve the problem ?
Answer:
In the given equation we need to find out the value of x to make this equation true.
First write the equationx+10 = 22Now place 10 to the other side[By placing 10 to the other side the symbol will change into -]x = 22-10Now subtract 10 from 22x = 12∴ 12 + 10 = 22If y = 132 when x =11, what is the value of y when x = 17?
Answer:
204
Step-by-step explanation:
Walmart sells its video games for $42.99. Virginia sales tax is 5%.
A. What is the sales tax for the video game?
B. What would the total price be for the video game?
A) multiply the price of the game by 5%
42.99 x 0.05 = 2.1495 rounds to 2.15
Amount of tax = $2.15
B) add the amount of tax to the price of the game:
42.99 + 2.15 = 45.14
Total cost = $45.14
Help pls :) thanks!!!!!
Given :-
A bag has 20 counters .16 are green .To find :-
The probability that it is green .Solution :-
As we know that ,
P = Total no. of favourable outcomes/Total number of possible outcomesSubstitute ,
P(of getting a green ) = 16/20 P(of getting a green ) = 4/5Answer:16/20 equals 4/5
Step-by-step explanation:they are asking what is the probability that it is green so we know that 16 counters is green and total counters is 20 so it’s 16/20 and then you simplify it the answer is 4/5
What does m represent in the equation y = mx + b?
A. the y-intercept of the
graph of y = mx + b
B. the slope of the graph of
y = mx + b
C. the run in the ratio rise
/ run
D. None of these
Answer:
B. the slope of the graph of y = mx + b
Step-by-step explanation:
m is the slope.
y is the y value
x is the x value
b is the y intercept
the answer is
d. none of these
In triangles ABC and AWXY, ZA= Wand ZB= ZX.
Which of the following must to be true to prove AABC= AWXY by the AAS
theorem?
A. ZCZY
B. BC XY
O
C. AB BC
D. ABW
Answer:
c
Step-by-step explanation:
The solution is, C. AB = WX, must to be true to prove AABC= AWXY by the AAS theorem.
What is Triangle?A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.
here, we have,
We are given,
Triangles ABC and WXY having ∠A=∠W and ∠B=∠X
Now, it is give that the triangles hold AAS theorem.
Since, we already have two corresponding angles equal i.e. ∠A=∠W and ∠B=∠X.
So, by AAS Theorem, the corresponding sides between these angles must be equal.
Thus, we have, AB = WX.
Hence, option C is correct. C. AB = WX, must to be true to prove AABC= AWXY by the AAS theorem.
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Chris
goes to a shop to buy meat, vegetables and fruit.
(a) The costs of the meat, vegetables and fruit are in the ratio
meat : vegetables : fruit = 2:2:3.
The cost of the meat is $2.40.
Calculate the total cost of the meat, vegetables and fruit.
Answer:
meat = $2.40
vegetables = $ 2.40
fruit = $2.40 + X
= 2.40 ÷ 2
= 1.2
therefore 2.40 + 1.2
=$3.6 (For fruits )
= $3.6 + $2.40 + $2.40
= $ 8.4
Hope this helps .Plzz mark me brainliest
The total cost of the meat, vegetables and fruit is $8.4.
What is the ratio?The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.
Given that, the costs of the meat, vegetables and fruit are in the ratio meat : vegetables : fruit = 2:2:3.
The cost of the meat is $2.40.
Let the total cost of the meat, vegetables and fruit be x.
Now, 2+2+3=7
So, 2/7 ×x=2.40
2x=2.40×7
2x=16.8
x=8.4
Therefore, the total cost of the meat, vegetables and fruit is $8.4.
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Which number line represents the solution set for the given inequality?
x + 1 ≤ -3 or -4x < -8
The solution to the system of equations is x≤ -4 and x > 2. Find the number line attached below:
Given the set of inequalities expressed as;
x + 1 ≤ -3 or -4x < -8
For the inequality expression x + 1 ≤ -3
x ≤ -3 - 1
x ≤ -4
For the inequality expression:
-4x < -8
Divide both sides by -4
-4x/-4 > -8/-4
x > 2
Hence the solution to the system of equations is x≤ -4 and x > 2. Find the number line attached below:
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10+10= hhihihhhiihihihih
Answer:
10+10=1010
Step-by-step explanation:
brainliest?
Answer:
20 lol
And hi!
HELLP MEEEEEE
PLEASE
Answer:
x = [tex]\frac{5}{4} + \frac{ \sqrt{5} }{4}[/tex]
x = [tex]\frac{5}{4} - \frac{ \sqrt{5} }{4}[/tex]
Step-by-step explanation:
Quadratic equation:
[tex]x = \frac{-b +- \sqrt{b^2 - 4ac} }{2a}[/tex]
The equation is:
[tex]4x^2 - 10x + 5 = 0\\[/tex]
So:
a = 4
b = -10
c = 5
Plug the variables into the quadratic equation:
[tex]x = \frac{-(-10) +- \sqrt{(-10)^2 - (4 * 4 * 5)} }{(2 * 4)}[/tex]
[tex]x = \frac{\sqrt{10 +- \sqrt{100 - 80} } }{8}[/tex]
[tex]x = \frac{10 + \sqrt{20} }{8}[/tex]
Divide both sides by 8:
10 ÷ 8 = [tex]\frac{5}{4}[/tex]
[tex]\sqrt{20}[/tex] ÷ 8 = [tex]\frac{\sqrt{5}}{4}[/tex]
[tex]\frac{5}{4}[/tex] +- [tex]\frac{\sqrt{5}}{4}[/tex]
This means that the solutions that satisfy the equation is:
x = [tex]\frac{5}{4} + \frac{ \sqrt{5} }{4}[/tex]
x = [tex]\frac{5}{4} - \frac{ \sqrt{5} }{4}[/tex]
Hope this helps!
What is the coefficient of the term of degree 4 in the polynomial?
6x3 + 2x - 5x3 + x²
the coefficient of term 4 is 2
Someone please help me!
Answer:
Look when angle 3= angle B
It would make AD parallel to BC
Step-by-step explanation:
So go with
AD//BC
#BeBrainly
Someone help me please
Answer:
2,4
Step-by-step explanation:
Question
Need help rn
Use the figure to find the measures of the numbered angles.
∠1 = °
∠2 = °
Answer:
m∠1 = 107 degrees
m∠2 = 73 degrees
Step-by-step explanation:
1. ∠1 and the angle with 107 degrees are corresponding angles, which are located in the same relative position. They're congruent in measures, so m∠1 = 107 degrees.
2. ∠1 and ∠2 are a linear pair, meaning their angle measures add up to 180 degrees. Given m∠1 = 107 degrees, we just have to subtract 107 from 180 to get m∠2.
[tex]180-107[/tex] [tex]73[/tex]Therefore, m∠2 = 73 degrees.
Please help!!! Write 4x^2=12 in standard form?
Answer:
[tex]x = \sqrt{3} [/tex]
Step-by-step explanation:
4x^2=12
x^2=12/4
x= root 3
Can y'all help me this question ASAP this all I need