Answer:
The dimensions of the garden are
Length [tex]25.5\ ft[/tex] and Width [tex]16.5\ ft[/tex]
Step-by-step explanation:
Let
x----> the length of the rectangular garden
y ---> the width of the rectangular garden
Aw ----> the area of the walkway
we know that
[tex]x=y+9[/tex] ----> equation A
[tex]Aw=(x+8)(y+8)-xy[/tex]
[tex]Aw=400\ ft^{2}[/tex]
so
[tex]400=(x+8)(y+8)-xy\\400=xy+8x+8y+64-xy[/tex]
[tex]400=8x+8y+64[/tex] ----> equation B
Substitute equation A in equation B
[tex]400=8(y+9)+8y+64[/tex]
[tex]400=8y+72+8y+64[/tex]
[tex]400=16y+136[/tex]
[tex]16y=400-136[/tex]
[tex]y=16.5\ ft[/tex]
Find the value of x
[tex]x=16.5+9=25.5\ ft[/tex]
therefore
The dimensions of the garden are
Length [tex]25.5\ ft[/tex]
Width [tex]16.5\ ft[/tex]
jim works h hours in a week. to find his weekly pay he multiplies his hours by his pay of $10 per hour and adds $50 for his sales bonus. he's decided that he wanted to take one-tenth of his weekly pay and place it in his savings. Which simplified expression represents the amount that will go into his savings each week?
Answer:
Step-by-step explanation:
Take home pay = 10*h + 50 I assume the 50 is a flat rate.
Savings = 1/10 of the take home pay.
Savings = (10*h + 50)/10
Determine the axis of symmetry for the function f(x)=-2(x+3)^2-5
Answer:
x=-3
Step-by-step explanation:
f(x)=-2(x+3)^2-5
The equation is in the form
f(x) = a(x-h)^2 -k
where (h,k) is the vertex
The h value is also the axis of symmetry
f(x)=-2(x--3)^2-5
The vertex is (-3,-5)
so the axis of symmetry is x=-3
Which of the following is not a real number?
Answer:
D
Step-by-step explanation:
by definition, the square root of an negative number is known as an imaginary number. i.e Not a real number
[tex]\sqrt{-2}[/tex] = [tex]\sqrt{2}[/tex][tex]\sqrt{-1}[/tex] = [tex]\sqrt{2}[/tex]i (imaginary number)
The [tex]\sqrt{-2}[/tex] is not a real number.
The following information should be considered with respect to the real number:
The numbers should be found in the number line. It should be in fractions, whole, naturals, rational, irrational. But it can't be in imaginary numbers.Therefore, the first three options are considered to be the real number.
Thus we can conclude that the [tex]\sqrt{-2}[/tex] is not a real number.
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The figure shows a parallelogram inside a rectangle outline:
What is the area of the parallelogram?
A) 1/25 square feet
B) 11/25 square feet
C) 3/25 square feet
D) 4/25 square feet
A = base x height
A = (3/5 - 1/5) x 2/5
A = 2/5 x 2/5
A = (2/5)²
A = 2²/5²
A = 4/25
The answer is D) 4/25 square feet.
Which equation represent the line that is perpendicular to the line 5x-2y=-6 and passed through the point (5,-4)?
To find the equation of a line perpendicular to 5x - 2y = -6 and passing through (5, -4), first determine the slope of the given line and then find the negative reciprocal of that slope. Using point-slope form with the new slope and the given point, the equation is y = - (2/5)x - 2.
To find the equation of the line that is perpendicular to the given line 5x - 2y = -6 and passes through the point (5, -4), follow these steps:
Step 1: Find the slope of the given line
Rewrite the given line in slope-intercept form (y = mx + b):
5x - 2y = -6
-2y = -5x - 6
y = (5/2)x + 3
The slope (m) of the given line is 5/2.
Step 2: Find the slope of the perpendicular line
The slope of the line perpendicular to another is the negative reciprocal. Thus, the slope of the perpendicular line is -2/5.
Step 3: Use the point-slope form
Using the point (5, -4) and the slope -2/5 in the point-slope form (y - y1 = m(x - x1)):
y - (-4) = - (2/5)(x - 5)
y + 4 = - (2/5)x + 2
y = - (2/5)x - 2
Therefore, the equation of the line that is perpendicular to 5x - 2y = -6 and passes through the point (5, -4) is y = - (2/5)x - 2.
What is the simplest form of this expression?
2x(x2 – 3) – 6x2
Answer:
-6x - 6x² + 2x³
Step-by-step explanation:
Match each like-term to end up with the above answer.
I hope this helps.
What is the length of segment AB?
Consider the diagram.
7,9,18,25
Answer:
9
Step-by-step explanation:
It is congruent to the other side.
What number line represents the solution set for the inequality -1/2 greater
than or equal to 4
Answer:
[8, inifinity sign)
Step-by-step explanation:
(2)/1 x -1/2 (greater than or equal to sign) 4(2), You need to get rid of the fraction so times 2 on both sides.
So the fraction cancels out and your answer is x (greater than or equal to) 8
The open side of the sign always is facing the bigger number so like this > so x is positive.
Since i can't show the number line i'll try to explain it if it's a greater than sign its a closed dot on the 8 going right. The 8 is in a bracket and the infinity is with a parenthesis. like this [8, infinity sign)
My teacher may have taught me different but it should be about the same.
Hope my answer has helped you and if not i'm sorry.
What is the slope of the line that passes through the points (3, 1) and (8,3)
Please help I need this before it hits 12
Answer:
2/5
Step-by-step explanation:
Rise over run
Difference of y over the difference in x
Answer:
The slope is 2/5
Step-by-step explanation:
The slope formula is delta y over delta x. If you insert the coordinates the equation is 1-3 / 3-8 = -2/-5 = 2/5. The slope is 2/5
An international equity mutual funds includes, american stock ,japanese stock,german. Stock , british stock in the ratio of 27:19:14:11 respectively. If its current holdings of german stocks are valued at us$238 millions what are the values of its holdings in the securities of other 3 countries
Give me BRAINLIEST please
let's say the total holdings for the company, or namely the total quantity for the ratios is say hmmm "x", and we were to split "x" in quantities of 27:19:14:11 ratio, what we do is, we simply divide "x" by (27+19+14+11), and then distribute accordingly.
so, if we divide the total amount like that, we end up with fragments of the total, and each ratio gets so many fragments.
so, we know the German stock or that ratio gets $238 millions, and in those 238, since it's on a 14 ratio, there are 14 of those fragments of the total, how much is a fragment anyway? well, simply how many times does 14 go into 238? 238 ÷ 14 = 17.
well, since we know the whole total of the holdings was split in fragments of 17, let's simply distribute accordingly.
[tex]\bf \stackrel{American}{27(17)}~~:~~\stackrel{Japanese}{19(17)}~~:~~\stackrel{German}{14(17)}~~:~~\stackrel{British}{11(17)} \\\\\\ \stackrel{American}{459}~~:~~\stackrel{Japanese}{323}~~:~~\stackrel{German}{238}~~:~~\stackrel{British}{187}\qquad \textit{in millions}[/tex]
PLEASE HELP ASAP.
Which graph has a correlation coefficient between the variables closest to 0?
what is the equation of (4,10),(6,11) in standard form?
ANSWER
The standard form is:
[tex]x - 2y = - 16[/tex]
EXPLANATION
The given line passes through (4,10)and (6,11).
The slope of this line is
[tex]m = \frac{11 - 10}{6 - 4} [/tex]
[tex]m = \frac{1}{2} [/tex]
The equation is given by the formula,
[tex]y-y_1=m(x-x_1)[/tex]
We plug in the first point and the slope to get.
[tex]y-10= \frac{1}{2} (x-4)[/tex]
[tex]2y - 20 = x - 4[/tex]
[tex]x - 2y = - 20 + 4[/tex]
[tex]x - 2y = - 16[/tex]
The standard form is
[tex]x - 2y = - 16[/tex]
2 1/3 divided by 1/4
Answer:
20/3 or 6 2/3
Step-by-step explanation:
Please mark brainliest and have a great day!
Answer: 28/3
7/3 x 4
=28/4
= 9&1/3
PLEASE ANSWER QUICKLY Carmen uses 2/7 of a bag of flour to make 1/2 of a batch of her special homemade cookies how many bags of flour does it take to make 3 batches of the cookies
Answer:
1 5/7 bags of flour to make three batches of cookies
Step-by-step explanatio
12/7 bag of the flour is required to make 3 batches of cookies
What's the equation defining?Mathematics written statement indicating the equality of 2 expressions. this consists of the sequence of the symbols that is split in to left or right sides joined by the equal sign. For example, 2 + 4 + 5 = 11 is an equation.
Do equations always contain terms?When equality holds, the total weight on the each side is the same. Equations often contain terms other than a unknowns. These other terms, which is assumed to be known, is usually known as constants, coefficients and parameters
From the question;
2/7 bag of flour makes 1/2 of a batch of cookies
x bag of flour will make 3 batches of cookies
Mathematically, we cross multiply
2/7 * 3 = 1/2 * x
6/7 = x/2
2 * 6 = 7 * x
12 = 7x
x = 12/7 bag of flour
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What is the value of x? Will give brainliest!
Answer:
75 degrees
Step-by-step explanation:
This is because all the angles in a triangle are supplementary which means they add up to 180 degrees. This means that you subtract 180 from the other two angles
Please give Brainliest!!! Thanks! :D
Answer:
C. 75 degrees
Step-by-step explanation:
The angles in a triangle add up to 180 degrees.
You already know the degree of two angles: 70 & 35.
Now, subtract those numbers from 180 to find the degree of the missing angle.
180 - 70 - 35 = 75
So, the answer is C. 75 degrees.
I hope this helps!
Use the diagram below to solve for x and y.
Answer:
Option A. x=30,y=42
Step-by-step explanation:
we know that
If two triangles are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent
In this problem
Triangles ABC and ZYX have three congruent interior angles
therefore
Triangles are similar
step 1
Find the value of x
[tex]\frac{ZY}{AB}=\frac{ZX}{AC}[/tex]
substitute the values
[tex]\frac{20}{x}=\frac{12}{18}[/tex]
[tex]x=20*18/12=30\ units[/tex]
step 2
Find the value of y
[tex]\frac{ZY}{AB}=\frac{XY}{CB}[/tex]
substitute the values
[tex]\frac{20}{30}=\frac{28}{y}[/tex]
[tex]y=30*28/20=42\ units[/tex]
A shirt originally cost $50.97, but it is on sale for $40.78. What is the percentage decrease of the price of the shirt? If necessary, round to the nearest percent.
Answer:
20% decrease.
Step-by-step explanation:
difference over original
50.97-40.78= 10.19
diff/orig=sales tax
10.19 / 50.97= 19.99..
19.99 is approximately 20.
Identify the vertex of the graph Tell whether it is a minimum or a maximum
Answer:
(1,2) maximum
Step-by-step explanation:
The vertex is the the point on the graph where the graph does a "u-turn".
this point can either represent the maximum value or the minimum value depending on which way the graph is facing.
In this case, the graph looks like an "n" (as opposed to a "u").
We can clearly see that the point where the graph makes a U-turn is (1, 2)
we can also see that no part of the graph extends above this point, hence this point represents the maximum value which y could possibly be.
Hence (1,2) is maximum
Find the difference 28y-16y
Answer:
12y
Step-by-step explanation:
28y - 16y
Factor out a y
y(28-16)
y(12)
The difference is 12y
56 coins = $9.80. how many are quarters how many are nickels
Answer:
So there are 35 quarters and 21 nickels.
Step-by-step explanation:
So I guess that is all we have is quarters and nickels.
Quarters are worth .25
Nickels are worth .05
Let x represent the number of quarters
Let y represent the number of nickels
x+y=56
.25x+.05y=9.8
We are going to solve this system.
I'm going to use substitution. I will solve the first equation for y and then plug that into the second equation.
y=56-x
.25x+.05(56-x)=9.8
.25x+2.8-.05x=9.8
.20x+2.8=9.8
.2x = 7
x=7/(.2) or 7*5=35
y=56-x
y=56-35=21
So there are 35 quarters and 21 nickels.
Answer:
A) n + q = 56
B) .05n + .25q = 9.80
We multiply A) by -.25
A) -.25n -.25q = -14 then add it to equation B)
B) .05n + .25q = 9.80
-.2n = -4.20
nickels = 4.20 / .20 = 21
quarters = 35
Step-by-step explanation:
A person alive for x 3(2x-3)+4(2-x)=0 ..
A. 1/2
B. 17/10
C. -17/2
Split 90 into two parts so that one part is four times the other part.
Answer:
can you help me with my answer when your done on my page? vvvvv
Step-by-step explanation:
1. **Separating 90 into Two Parts:**
- The smaller part is [tex]\( 18 \)[/tex] and the larger part is [tex]\( 72 \)[/tex].
2. **Sum of Three Consecutive Integers:**
- The three integers (in order) are [tex]\( 17, 18, \)[/tex] and [tex]\( 19 \)[/tex].
1. **Separating 90 into Two Parts:**
- Let's denote the smaller part as [tex]\( x \)[/tex] and the larger part as [tex]\( 4x \)[/tex].
- According to the problem, the sum of these two parts equals 90: [tex]\( x + 4x = 90 \)[/tex].
- Combine like terms: [tex]\( 5x = 90 \)[/tex].
- Divide both sides by 5 to solve for [tex]\( x \): \( x = 18 \)[/tex].
- So, the smaller part is [tex]\( 18 \)[/tex] and the larger part is [tex]\( 4 \times 18 = 72 \)[/tex].
2. **Sum of Three Consecutive Integers:**
- Let's denote the smallest integer as [tex]\( x \)[/tex].
- The next two consecutive integers would be [tex]\( x + 1 \)[/tex] and [tex]\( x + 2 \)[/tex].
- According to the problem, the sum of these three integers equals 54: [tex]\( x + (x + 1) + (x + 2) = 54 \)[/tex].
- Combine like terms: [tex]\( 3x + 3 = 54 \)[/tex].
- Subtract 3 from both sides: [tex]\( 3x = 51 \)[/tex].
- Divide both sides by 3 to solve for [tex]\( x \): \( x = 17 \)[/tex].
- So, the three consecutive integers are [tex]\( 17, 18, \)[/tex] and [tex]\( 19 \)[/tex].
The complete question is here:
Separate 90 into two parts so that one part is four times the other part. What are the sizes of the two parts? The smaller part is _____ and the larger part is ____.
The sum of three consecutive integers is 54. Find the three integers. The three integers (in order) are ____, ____, and ____.
Which graph shows the solution to the system of linear inequalities below? Y>-2x+2 Y<2x-1
Answer:
That would be B. Graph A.
Step-by-step explanation:
The graph y < 2x - 1 is a dotted line which rises to the right with a slope of 2 and passes through y = -1 and is shaded below the line. The graph y > -2 x + 2 rises to the left and passes through y = 2 and is shaded above the line.
which of the following statements best describes midpoint of a line segment? 1. point at end of line segments 2. a point halfway between the endpoints of a line segments 3. it its any point on a line segments 4. it is the x-coordinate of any point on a line segment.
The answer is:
2. A point halfway between the endpoints of a line segment.
Why?The midpoint of a line segment, is a point that divides the line segment into two equal length sides, no matter the length of the segment, the midpoint will always cut the segment into two equal length sides
The midpoint is an ordinary point located in the middle of the line segment. The x-coordinate of the midpoint is halfway between the x-coordinates of the beginning and the end of the segment. The y-coordinate of the midpoint is halfway between the y-coordinates of the beginning and the end of the segment.
Hence, the correct option is:
2. A point halfway between the endpoints of a line segment.
Have a nice day!
Midpoint refers to point in the mid. The midpoint of a line segment is given as: Option 2: A point halfway between the endpoints of a line segment.
What does a midpoint mean?Midpoint, as the word suggests, means the point which lies in the middle of something. Midpoint of a line segment means a point which lies in the mid of the given line segment.
What is a line segment?A line segment is a straight line with finite length, and thus, have to endpoints(points on either ends).
If you walk halfway between the endpoints of a line segment, you'll reach to its mid, and thus, the midpoint of a line segment can be reached by walking halfway between its end points.
Thus,
The midpoint of a line segment is given as: Option 2: A point halfway between the endpoints of a line segment.
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The graph of the equation y=|x+5| is shifted 2 units up and 6 units to the right. Rewrite the equation of the new graph for the values x>1, without using absolute value.
Answer:
Step-by-step explanation:
To move the graph 6 units to the right, subtract 6 in the absolute value.
y=|x+5-6|
To move it up, add 2 outside the absolute value.
y=|x+5-6|+2
Now remove the absolute values since x>1.
y=x+5-6+2
y=x+1
What are the possible steps involved in solving the equation shown? Check all that apply.
3.5 + 1.2(6.3 – 7x) = 9.38
Add 3.5 and 1.2.
Distribute 1.2 to 6.3 and –7x .
Combine 6.3 and –7x .
Combine 3.5 and 7.56.
Subtract 11.06 from both sides.
Divide both sides by 9.38.
Answer:
B) Distribute 1.2 to 6.3 and –7x
D) Combine 3.5 and 7.56
E) Subtract 11.06 from both sides
Answer:
b, d, and e :)
15 points
Line AB←→ passes through the points A(3,−1) and B(1,7).
Which lines are parallel to AB←→?
THIS IS MULTIPLE CHOICES
y=−4x
y=−4x+8
y=4x
y−1=2(x+2)
y+1=−4(x+1)
y=4x+7
y=2x−3
y−6=−4(x−3)
Lines that are parrellell presume to have the same slope.
So if we just calculate the slope of a function or a line we should be good.
[tex]s=\dfrac{\Delta{y}}{\Delta{x}}=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
Now put in the data from the coordinates of the points [tex]A(3,-1)\wedge B(1,7)[/tex]
[tex]s=\dfrac{7-(-1)}{1-3}=\dfrac{8}{-2}=\underline{-4}[/tex]
The form of a function now looks like: [tex]
f(x)\vee y=-4x+n[/tex]
From here we are no longer required to calculate anything more. Leave n alone.
The solutions are the equations of the form above.
That would mean:
[tex]
y=-4x \\
y=-4x+8 \\
y+1=-4(x+1) \\
y-6=-4(x-3)
[/tex]
Hope this helps.
Johnny has 19 bottles of dish soap and he gives Jeina 5. How much dish soaps will he have now?
Answer:
14 dish soaps
Step-by-step explanation:
Johnny has 19 bottles of dish soap and he gives 5 to Jeina
19 - 5 = 14
Answer:
14
Step-by-step explanation:
Johnny has 19 bottles of dish soap and he gives 5 to Jeina
19 - 5 = 14
S, & nequalties:Question 2
Expand the following expression 5x(3 - 7y)
Select one:
0 152 - 3577
o 152-7
0 20xy
0
152 – 35
Answer:
15 x - 35 x y
Step-by-step explanation:
5 x (3-7 y)
5 * 3 x - 7 * 5 x y
= 15 x - 35 x y
What is the equation of the line that passes through (7,4) and (4,-2)?
O y= 2x - 10
O y=-2x - 10
O y=-2x + 18
y= 2x + 18
Answer:
y = 2x - 10
Step-by-step explanation:
First, we find the slope.
m = slope = (y2 - y1)/(x2 - x1) = (-2 - 4)/(4 - 7) = -6/(-3) = 2
Now we use the slope in the slope-intercept form of the equation of a line.
y = mx + b
y = 2x + b
We use the coordinates of one of the given points for x and y, and we solve for b. Let's use the point (7, 4), so we have x = 7 and y = 4.
4 = 2(7) + b
4 = 14 + b
Subtract 14 from both sides.
-10 = b
Now we replace b with -10.
y = 2x - 10
Answer: y = 2x - 10