An equation that can be used to determine the value of x is x² + 5x - 36 = 0.
To answer the question, we need to know what equations are
What is an equation?An equation is an expression which shows the relationship between two variables.
Given that the x represents the length of side of the square picture and the rectangular sheet poster leaving a border around the picture of 2 inches on the bottom and 1 inch on each remaining sides.
Then,
The width of the rectangular poster is W = x + 2 + 1 = x + 3. The length of the rectangular poster is L = x + 1 + 1 = x + 2So, the area of the rectangular sheet poster is A = LW
= (x + 2)(x + 3)
Since the rectangular sheet poster has an area of 42 square inches, A = 42 in².
So, (x + 2)(x + 3) = 42
x² + 3x + 2x + 6 = 42
x² + 5x + 6 - 42 = 0
x² + 5x - 36 = 0
So, an equation that can be used to determine the value of x is x² + 5x - 36 = 0.
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2. What are the x-intercepts of the graph of the function defined by (x - 2)(2x + 1)? A. (2,0) and (-1,0) B. (2,0) and (1,0) C. (-2,0) and (1,0) D. (-2,0) and (-1,0)
The x-intercepts of the graph of the function defined by (x - 2)(2x + 1) will be at (2,0) and (0.5,0).
what is a quadratic equation?The polynomial having a degree of two or the maximum power of the variable in a polynomial will be 2 is defined as the quadratic equation and it will cut two intercepts on the graph at x-axis.
Here we are having an equation:-
(x-2)(2x+1)=0
2x²+x-4x-2=0
2x²-3x-2=0
2x²-4x+x-2=0
2x(-1)(x-2)=0
x=2 x=0.5
Hence the x-intercepts of the graph of the function defined by (x - 2)(2x + 1) will be at (2,0) and (0.5,0).
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Find the nth term of the following sequence;
-5, -2, 3, 10, 19
Answer:
n= -5+ 7(n-1)
Step-by-step explanation:
Using the image above, what is the measure of side GF?
The measure of side GF is solved to be
1.73 How to find the measure of side GFToo side GF we use trigonometry tan, in the formula
tan x = opposite / adjacent
Where x is the given angle and opposite and adjacent are the legs of the right triangle
In this case, opposite = EF = 3, and adjacent = GF, x = 60 degrees
tan 60 = 3 / GF
Isolating GF results to
GF = 3 / tan 60
GF = 1.73205080757
GF = 1.73
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Select all the expressions that are equivalent to 6x + 1 - (3x - 1)
A medicine is effective for 80% of patients. The table shows 30 randomly generated numbers from 0 to 999. Use the table to estimate the probability that the medicine is effective on fewer than two of the next three patients. Let the digits 1 through 8 represent the medicine being effective.
463 013 231 898 139
365 492 565 188 465
438 751 961 646 598
045 241 940 901 467
151 774 538 380 509
251 924 401 549 859
Answer:
1/2 and 1/10 is your answer
Which of the following is equivalent to x + 1/y ÷ g + 1/h
x + 1 / y ÷ h / g + 1
x + 1 / y · h / g + 1
y / x+1 ÷ g + 1 / h
x/y · h/g
Answer:
say what now?
Step-by-step explanation:
How many minutes did Todd use in October
Answer:
100 minutes cost Todd $24. He had extra bill of 26.38 - 24 = $2.38
$2.38 = 238 cents
7 cents billed for 1 extra minute
1 cents billed for 1/7 extra minute
238 cents billed for 238/7 = 34 extra minutes
total minutes = 134 minutes
Plsss help.
How do poets use rhythm to support the meanings in their poems?
they put lots of harsh-sounding words in their poems
they repeat sounds at the end of each line
they put words together in a way that sounds like what the poem means
they make up a musical score for playing an instrument while reading the poem
Answer:
they put words together in a way that sounds like what the poem means.
Which of these functions has the same graph but shifted to the left?
Step-by-step explanation:
the second and the 6th options keep the same graph but shift it to the left.
the other options :
the first option changes the graph (the factor -2 stretched and flips the graph).
the third and the 5th options shift the graph up and down. but not to the left.
the 4th option shifts it to the right.
when you add a constant inside the x terms, you shift to the left.
when you subtract a constant inside the x terms, you shift to the right.
e.g. when having f(x+2), then everything, that should happen at x+2 happens already at x. 2 units earlier, and therefore a shift to the left.
in the other direction, f(x-2) makes everything that should have happened at x-2 happen finally at x. so, everything shifts 2 units to the right.
Find an explicit function rule for the following sequence defined over the natural numbers: –7, –1, 9, 23, . . .
A. an=9n²+2
B. an=2n²+9
C. an=9n²-2
D. an=2n²-9
===========================================================
Reason:
Replace n with 1 in choice A to get
[tex]a_n = 9n^2 + 2\\\\a_1 = 9(1)^2 + 2\\\\a_1 = 11\\\\[/tex]
Choice A says the first term is 11, but this contradicts the fact that the first term should be -7 instead. Therefore, we cross choice A off the list.
You should find that choice B is the exact same story, so it must be eliminated as well.
Choice C has n = 1 get us [tex]a_1 = 7[/tex] which is close, but we want the result to be negative 7 instead of positive. Choice C is eliminated as well.
The only thing left is choice D. Sure enough, plugging in n = 1 does lead to the first term of -7. If you tried n = 2, then it would get you -1 as the second term, and so on. This confirms choice D is the correct answer.
6.501 +5.25y + 1850 258)
Answer:
Answer is in attachment
Mark brainliest :)
The garden shown at right is divided into two section by a fence. If the quadrilateral section is a square, what is the square area? (6ft : 8ft)
The area of the triangle is 24 ft² while the area of the square is 64 ft²
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Area of triangle = (1/2) * base * height = 0.5 * 8 * 6 = 24 ft²
Area of square = 8 ft * 8 ft = 64 ft²
The area of the triangle is 24 ft² while the area of the square is 64 ft²
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need help on math problem please
Answer:
parallel
Step-by-step explanation:
the slope of both is 1/3
x2 + 5x + 6
x2 + 8x + 12
y2-7y + 12
y? - 11y + 28
x2 - 3x - 40
here I hope this helps you. Always have 2 bracket when factoring trinomials and know you prime factors
A.point 1
B.point 2
C.point 3
D.point 4
E.point 5
Answer: Point 2, because Point B will have shrunk slightly if dilated by a factor that is a fraction.
the difference of two numbers is 9 and they are in the ratio 4:7.find The numbers
[tex]\huge\underline{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}[/tex]
Given - the difference between two numbers is 9 and the numbers are in the ratio of 4:7To find - the numbersLet the number be 4x and 7x respectively !
Then ,
[tex]\bold{7x - 4x = 9} \\ \\ \bold{\longrightarrow \: 3x = 9} \\ \\ \bold{\longrightarrow \: x = \cancel\frac{9}{3}} \\ \\ \bold{\longrightarrow \: x = 3}[/tex]
therefore ,
first number = 4x = 4 × 3 = 12
second number = 7x = 7 × 3 = 21
hope helpful ~
The difference of two numbers is 9 and they are in the ratio 4 : 7. Find the numbers.
❖ Explanation -:In this question we are provided with the ratio of two numbers that is 4 : 7 and it is also given that the difference between two numbers is 9. We are asked to calculate the two numbers.
[tex] \small \purple{ \underline{ \underline{\rm{ First \: we \: will \: form \: an \: equation }}}}[/tex]
Let us assume the number as 4x and 7x.
It is given that the difference is 9
According To Question
[tex] \small \blue{\sf{7x - 4x = 9}}[/tex]
[tex] \small \green{ \underline{ \underline{\rm{ Now \: we \: will \: solve \: this \: equation \: and \: find \: the \: value \: of \: x}}}}[/tex]
Let us solve this equation
[tex] \small\sf{7x - 4x = 9} [/tex]
[tex]⟹ \small\rm{3x = 9} [/tex]
[tex]⟹ \small\rm{x = \dfrac{ \cancel{9} \: \: 3}{ \cancel{3}} } [/tex]
[tex] \small\sf{x = 3} [/tex]
Substitute the value of x = 3
7x = 7 × 3 = 21
4x = 4 × 3 = 12
Hence the two numbers are 21 and 12.
Write the quadratic equation in standard form:
-3x^2-16=-3x
Standard form ax²+bx+c
-3x²-16=-3xMultiply - on both sides
-(-3x²-16)=-(-3x)Simplify
3x²+16=3xConvert
3x²-3x+16=0I don’t have a question
Answer:
thats cool imma use this for a challenge now
A wheel has a radius of 4 inches and travels as it spins. How far does the wheel travel
in one revolution? Round your answer to the nearest inch.
Use the pi (T) on the calculator.
Use formula for circumference to figure out the answer: C = 277 (or) C = ad
The distance a tire travels is equal it it’s circumference.
circumference = pi x radius x 2
Circumference = 25.13 inches
Rounded to nearest inch = 25 inches
pls help
pls
pls
it's very hard
Answer:
Simplest Form. 2/3 * 3 3/5 = 125 = 2 25 = 2.4. Spelled result in words is twelve fifths (or two and two fifths).
Answer 12/5
Step-by-step explanation:
If i am wrong sorry :(
The probability that mary picks a yellow marble out of a bag of marbles is 0.35. there are 500 marbles in the bag. work out how many yellow marbles there are.
Answer:
175
Step-by-step explanation:
500*.35
Billy’s medical bills have been sent to a collection agency. He’s been stressed out for the past few days because agents have been calling him in the early hours of the morning and warning him they’ll have to report him because he has committed a crime. What do you tell Billy? Do you have any advice on what he can do?
Answer:
First of all, I could inform Billy that collection agencies cannot falsely claim that he had committed a crime or say that he will be arrested if he does not repay the money he owes. Failing to repay a medical bill in a timely manner would not land him in prison.
The law also states that debt collectors are not allowed to harass debtors. They are not permitted to call in the early hours of the morning and call repeatedly. Billy can actually order collectors to stop contacting him.
Next, as his account/medical debt had already been sold to collections, he should contact the collection agency to work out payment arrangements. If he is unable to pay the debt in full, some collection agencies may offer a settlement amount. Once he has paid off the account, the collection agency will notify the credit reporting companies it reports to that the account should be updated to note it has been paid in full. He should check to see how his account is appearing by ordering a copy of his report from each of the three credit reporting agencies.
After all these, Billy should then work on rebuilding his credit score.
Step-by-step explanation:
giving brainliest!!!!
A is the answer
all equalateral triangles' angles = 60
70 - 10 = 60 Y
55 + 5 = 60 X
Answer:
y = 70 degrees
x = 55 degrees
Step-by-step explanation:
y-10 = 60
x+5 = 60
y = 70
x = 55
A angles equal 60 degrees if equalateral!
Which statement is true about the solutions for the equation 4y + 6 = −2? (5 points) Hint: If you are solving for ONE variable, how many solutions will you have? a It has infinitely many solutions. b It has two solutions. c It has one solution. d It has no solution.
Answer: C) has one solution
That solution is y = -2
=======================================
Work Shown:
4y + 6 = -2
4y = -2-6
4y = -8
y = -8/4
y = -2
I first subtracted 6 from both sides (step 2), then I divided both sides by 4 (in step 4) to fully isolate y. We get one solution here.
Check:
4y + 6 = -2
4(-2) + 6 = -2
-8+6 = -2
-2 = -2
The solution is confirmed.
I'm taking a test and don't know how to solve this problem :')
The triangle PSQ is an isosceles triangle, and the area of the triangle PSQ is 1360.62 square units
How to determine the area?The given parameters are:
PS = SQ
Perimeter, P = 50
SQ - PQ = 1
The perimeter is calculated using:
PS + SQ + PQ = 50
This gives
2SQ + PQ = 50
Make SQ the subject in SQ - PQ = 1
SQ = 1 + PQ
So, the equation 2SQ + PQ = 50 becomes
2(1 + PQ) + PQ = 50
Expand
2 + 2PQ + PQ = 50
Evaluate like terms
3PQ = 48
Divide by 3
PQ = 16
Substitute PQ = 16 in SQ - PQ = 1
SQ - 16 = 1
So:
SQ = 17
The area is then calculated using:
A = √[P * (P - PS) * (P - SQ) * (P - PQ)]
This gives
A = √[50 * (50 - 17) * (50 - 17) * (50 - 16)]
Evaluate
A = 1360.62
Hence, the area of the triangle PSQ is 1360.62 square units
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Mr. Perez brought his daughter and her friends to
the drive-in movie theater. He purchased all the
tickets and spent $28.75 for snacks at the
concession. If he spent a total of $60.00 between
the 5 tickets and concession, how much did each
ticket cost?
Answer: $6.25
Step-by-step explanation:
First, we will find out how much money was spent on tickets.
$60 - $28.75 = $31.25
Now, we will divide the money spent on tickets by the number of tickets bought. This will give us the answer to your problem.
$31.25 / 5 = $6.25
Each ticket cost $6.25.
y=7x
y= 9x²
At how many points in the xy-plane do the graphs of the given equations intersect?
Answer:
2
Step-by-step explanation:
A line and a parabola will intersect at one point if and only if that point is a point of tangency.
__
Here, we know there is one point of intersection at x=0, but the line has a slope of 7, not 0. It is not a tangent to the parabola, so there must bet two points of intersection.
find the length of the arc.Round your answer to the nearest tenth
Find the circumference:
Circumference = 2 x pi x radius
Circumference = 2 x 3.14 x 9 = 56.52 inches
the arc length is 45 degrees/360 degrees of the circumference.
Marc length = 56.52 x 45/360 = 7.065 inches
Rounded to the nearest tenth = 7.1 inches
Does anybody know this?Find the area of the shaded region if PA=7 inches and PB=4 inches
Hi Student!
The first step that we must take before attempting to solve the problem is to gather important information. Looking at the problem we are given two lengths, PA and PB. These two lengths make up the radius of two different circles which we will need to find the area for both of them. The other important information that we must take in is that we are trying to determine the area of the shaded region.
Now that we have our important information concluded, let's move onto solving the problem. We know that we are trying to determine the area of the shaded region which means that we will need to do some subtraction between the total area of the larger circle and the total area of the smaller circle.
Area of a Circle Formula
[tex]A=\pi*r^2[/tex]Plug in the information
[tex]Shaded\ Region = Larger\ Circle - Smaller\ Circle[/tex][tex]Shaded\ Region = (\pi *PA^2)-(\pi*PB^2)[/tex][tex]Shaded\ Region = (\pi *(7\ in)^2)-(\pi*(4\ in)^2)[/tex]Simplify the exponents
[tex]Shaded\ Region = (\pi *49\ in^2)-(\pi*16\ in^2)[/tex]Subtract
[tex]Shaded\ Region = 49\ in^2*\pi-16\ in^2*\pi[/tex][tex]Shaded\ Region = 33\ in^2*\pi[/tex]Therefore, our final answer would be that the shaded region is 33 inches squared times pi which is best described in Option D. We got this after subtracting the area of the smaller circle from the area of the larger circle which provides us with the area of the shaded region.
Divide £350 in the ratio 3:11
Answer:£75, £275
Step-by-step explanation:
The division of the numbers £350 will be £25 and £275.
What is the solution to the equation?The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.
Divide £350 in the ratio of 3:11.
Let the division in the form of variables be x and y. Then the equation will be
x + y = 350 ...1
x / y = 3 / 11
x = (3/11)y ...2
Put the equation2 in equation 1, then we have
(3/11)y + y = 350
3y + 11y = 3850
14y = 3850
y = 275
Then the value of x will be
x = (3/11) x 275
x = 25
Then the division of the number £350 will be £25 and £275.
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