Assume that the width=w
22=2w+2(w+1)
22=2w+2w+2
22=4w+2
20=4w
w=5
The dimensions are 4 by 5.
The dimensions of the rectangle photograph are 5.5 inches (width) by 6.5 inches (length), calculated by setting the given perimeter equal to twice the sum of the length and the width, and then solving for the width and length.
Explanation:The perimeter of a rectangle is the sum of all its sides. Given that the perimeter of the photograph is 22 inches, you can work out the length and width using algebra. Let's denote the width of the photograph as 'x' (in inches). Thus, the length is 'x + 1' since it is one inch more than the width. Since the rectangle has two equal lengths and two equal widths, its perimeter can be represented as 2*(length + width) or 2*(x + x + 1). Setting this equal to 22 (the perimeter), we get 2*(2x + 1) = 22. Solving for 'x' gives us the width, which is 5.5 inches. The length is therefore 6.5 inches, being 1 inch more than the width. Therefore, the dimensions of the rectangle are 5.5 inches by 6.5 inches.
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What is the midpoint of AB?
The formula of a midpoint:
[tex]\left(\dfrac{x_A+x_B}{2},\ \dfrac{y_A+y_B}{2}\right)[/tex]
We have
[tex]A(-2,\ 5),\ B(3,\ -3)[/tex]
Substitute:
[tex]\dfrac{-2+3}{2}=\dfrac{1}{2}=0.5\\\\\dfrac{5+(-3)}{2}=\dfrac{2}{2}=1[/tex]
Answer: (0.5, 1).
Answer:
The midpoint of AB is (0.5,1).
Step-by-step explanation:
From the given graph it is clear that the vertices of the triangle ABC are A(-2,5), B(3,-3) and C(-4,-1).
If end points of a line segment are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex], then the midpoint of that segment is
[tex]Midpoint=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]
We need to find the midpoint of AB.
[tex]Midpoint=(\frac{-2+3}{2},\frac{5+(-3)}{2})[/tex]
[tex]Midpoint=(\frac{1}{2},\frac{5-3}{2})[/tex]
On further simplification we get
[tex]Midpoint=(\frac{1}{2},\frac{2}{2})[/tex]
[tex]Midpoint=(0.5,1)[/tex]
Therefore the midpoint of AB is (0.5,1).
****BRAINLIEST GOES TO THE FIRST CORRECT ANSWER****
The two equations are vertical angles, which mean they are equal.
Set each equation to equal each other and solve for x.
3x-3 = 6(x-10)
Simplify the right side:
3x-3 = 6x-60
Subtract 3x from each side:
-3 = 3x - 60
Add 60 to each side:
57 = 3x
Divide both sides by 3:
x = 57 / 3
x = 19
What is the slope and y intercept of y= 3
the slope is 0 over 1 and the y-intercept is 3
Simplify the expressions
1a. 6y - 2y = 4y
1b. 6 - 7b + 7b + 3 + b
= 6 + 3 + b
= 9 + b
2a. 10a - 2 + 3 - a
= (10a - a) + (-2 + 3)
= 9a + 1
2b. m · 7 · m · m · m · m · 9
= (7 · 9) · (m · m · m · m · m)
[tex]=63m^{5}[/tex]
3a. 3 + 8(5a + 10)
= 3 + 40a + 80
= 40a + 83
3b. 6v - 8v + 4 + 6v
= (6v - 8v + 6v) + 4
= 4v + 4
4a. s · 1 · s · 3
= (1 · 3) · (s · s)
[tex]= 3s^{2}[/tex]
4b. 6k - 6k
= 0
5a. [tex]10y^{4} (y^{2} )[/tex]
= [tex]=10y^{6}[/tex]
5b. 10x + 7 - 5x
= (10x - 5x) + 7
= 5x + 7
6a. 1v - v + 7 + 9v
= (1v - v + 9v) + 7
= 9v + 7
6b. 6z - 5 + 5 - 6z
= (6z - 6z) + (-5 + 5)
= 0 + 0 = 0
7a. 9w + 5w
= 14w
7b. s · 2s · s · s · s · s
= 2 · (s · s · s · s · s · s)
[tex]= 2s^{6}[/tex]
18x^2-2 factor completely
The factored form of [tex]\(18x^2 - 2\)[/tex] is [tex]\({2(3x - 1)(3x + 1)}\)[/tex].
To factor the expression [tex]\(18x^2 - 2\)[/tex] completely, we first notice that [tex](18x^2\))[/tex] and [tex]\(2\)[/tex] share a common factor of [tex]\(2\)[/tex]. We can factor out this common factor to simplify the expression:
[tex]\[18x^2 - 2 = 2(9x^2 - 1)\][/tex]
Now, we recognize that [tex]\(9x^2 - 1\)[/tex] is a difference of squares. It can be factored as [tex]\((3x)^2 - 1^2\)[/tex], which follows the pattern [tex]\((a^2 - b^2) = (a - b)(a + b)\)[/tex].
So, applying this pattern, we have:
[tex]\[9x^2 - 1 = (3x)^2 - 1^2 = (3x - 1)(3x + 1)\][/tex]
Therefore, the expression \(18x^2 - 2\) factors completely as:
[tex]\[18x^2 - 2 = 2(9x^2 - 1) = 2(3x - 1)(3x + 1)\][/tex]
Triangle ABC has vertices at A(−1 , 2), B(4, 2), and C(3, −1). Classify the triangle according to the side lengths.
A) equilateral
B) isosceles
C) right
D) scalene
Answer:
B) Isosceles
Step-by-step explanation:
The given triangle has vertices at A(-1,2), B(4,2) and C(3,-1).
We must first determine the length of the sides of the triangle, before we can classify it.
We apply the distance formula to find length of the sides.
[tex]|AB|=\sqrt{(4--1)^2+(2-2)^2}[/tex]
[tex]\Rightarrow |AB|=\sqrt{(4+1)^2+(2-2)^2}[/tex]
[tex]\Rightarrow |AB|=\sqrt{5^2+(0)^2}[/tex]
[tex]\Rightarrow |AB|=\sqrt{25}[/tex]
[tex]\Rightarrow |AB|=5 units[/tex].
The length of side BC
[tex]|BC|=\sqrt{(3-4)^2+(-1-2)^2}[/tex]
[tex]\Rightarrow |BC|=\sqrt{(-1)^2+(-3)^2}[/tex]
[tex]\Rightarrow |BC|=\sqrt{1+9}[/tex]
[tex]\Rightarrow |BC|=\sqrt{10}[/tex]
The length of side AC
[tex]|AC|=\sqrt{(3--1)^2+(-1-2)^2}[/tex]
We simplify to obtain;
[tex]|AC|=\sqrt{(3+1)^2+(-3)^2}[/tex]
[tex]\Rightarrow |AC|=\sqrt{(4)^2+(-3)^2}[/tex]
[tex]|AC|=\sqrt{16+9}[/tex]
[tex]|AC|=\sqrt{25}[/tex]
[tex]|AC|=5\:units[/tex]
Since [tex]|AC|=5\:units=|AB|[/tex], the given triangle is an isosceles triangle.
The correct answer is
Answer:
B) isosceles
Step-by-step explanation:
Edward Taylor purchased two shirts for $17.95 and $27.50, a jacket for $94.20, and two ties for $12.30 each. The state tax is 5 percent, the county tax is 1.5 percent, and the city tax is 2 percent. What is the total amount of tax on his purchases?
A. $14.65
B. $12.97
C. $13.96
D. $11.23
Total cost
17.95 + 27.50 + 94.20 + 12.30 + 12.30 = 164.25
tax
164.25 * 5% = 8.21
164.25 * 1.5% = 2.47
164.25 * 2% = 3.28
sum of the tax
8.21 + 2.47 +3.28 =
13.96
your answer is C
Final answer:
To find the total tax on Edward Taylor's purchases, sum the cost of all items ($164.25), multiply by the combined tax rate of 8.5% to get the total tax in dollars ($13.96125), and round to the nearest cent, resulting in $13.96. So, option C is correct.
Explanation:
To determine the total amount of tax on Edward Taylor's purchases, we need to sum up the cost of all items purchased and then calculate the combined sales tax. Edward bought two shirts for $17.95 and $27.50, a jacket for $94.20, and two ties at $12.30 each. Here are the steps taken:
Calculate the sum of the purchases: $(17.95 + 27.50 + 94.20 + 12.30 + 12.30) = $164.25.
Combine the tax rates: (state tax at 5% + county tax at 1.5% + city tax at 2%) = 8.5% total.
Convert the tax rate to a decimal: 8.5% = 0.085.
Multiply the total cost of purchases by the tax rate: $164.25 * 0.085 = $13.96125.
Round the tax to the nearest cent: $13.96.
Therefore, the total amount of tax on his purchases is $13.96. So, option C is correct.
whats the answer for -7x -3x+2= -8x-8
X=5
Add all the Xs together, then get it alone and there’s your anwser
Hope it helps ❤️
[tex]-10x+2=-8x-8[/tex] Combine Like Terms
[tex]-2x+2=-8[/tex] Add [tex]-8x[/tex] on both sides
[tex]-2x=-10[/tex] Subtract [tex]2[/tex] on both side
[tex]x=5[/tex] Divide [tex]-2[/tex] to [tex]-10[/tex]
*(Answer)*= [tex]x=5[/tex]
which expression represents “seventeen more than one-fourth y”
hello again
17-1/49 is your correct answer thank you and have a great day please mark me as brainliest if can
Answer:
Expression which represents “seventeen more than one-fourth y” is:
[tex]\dfrac{1}{4}y+17[/tex]
Step-by-step explanation:
We have to find a expression which represents
“seventeen more than one-fourth y”
one-fourth y= [tex]\dfrac{1}{4}y[/tex]
So, seventeen more than one-fourth y= [tex]\dfrac{1}{4}y+17[/tex]
Hence, expression which represents “seventeen more than one-fourth y” is:
[tex]\dfrac{1}{4}y+17[/tex]
10x=-80
I could us some hlp
10x = -80
Note the equal sign. What you do to one side, you do to the other.
Divide 10 from both sides
10x/10 = -80/10
x = -80/10
x = -8
-8 is your answer for x
---------------------------------------------------------------------------------------------------------------------
~Rise Above the Ordinary, Senpai
answer: x = -8
work:
you're working to solve for x.
this means you want to isolate x, and get it alone.
to do so, divide both sides by 10 to get rid of the 10.
once you divide both sides by 10, x is on its own, and you have the solution to your equation, x = -8!
to check your work you can plug the value for x into the original equation and solve.
10(-8) = -80
-80 = -80
so we can verify this is in fact correct.
i hope this helps, and have a great day! don't hesitate to ask if you need more help with this specific question! ♥ - eviezoom
How much longer is a 1 inch button than a 3 over 8 inch button
Subtract.
1 - 3/8 = 5/8
is 1000 a perfect cube?
Think of a cube with side lengths of 10.
The volume of the cube will be L*W*H = 10*10*10 = 1000
This volume of 1000 is what we consider a perfect cube.
Answer: yes
10*10*10=[tex]10^{3}[/tex]
10*10*10=1,000
1,000 is a perfect cube, because 10^3 is 1,000.
I hope this helps :)
Gabriel needs d more dollars to buy a new video console that coast $156.75. He has saved $98.26. Solve the equation $98.26 + d = $156.75 to find out how much more money Gabriel needs.
Just subtract 98.26 from 156.75. It equals $58.49.
you can use subtraction by doing 156.75 minus 98.26 when you do that the amount he still needs is 58.49
-16+(-28) adding a integer
-44 should be your answer. If you were solving for absolute value and the 28 was positive you would have about 12.
if ( 6^2) ^x =1 what is the value of x
A case of 24 pairs of the same kind of sports shoes costs a little more than $800.Explain whether $28 per pair with tax included is a good estimate.
Answer:
$28 per pair is not a good estimate.
Step-by-step explanation:
Let x represent cost of each pair with tax.
We have been given that a case of 24 pairs of the same kind of sport shoes cost a little more than $800.
The cost of 24 pairs would be [tex]24x[/tex].
[tex]24x>800[/tex]
[tex]\frac{24x}{24}>\frac{800}{24}[/tex]
[tex]x>33.33[/tex]
Since the cost of each pair is greater than $33.33, therefore, $28 is not a good estimate.
What is triple the sum of 45 and 55
the answer is 300 because 55+45=100 and 100*3 is 300
What is triple the sum of 45 and 55
First, add 45 and 55
45 + 55 = 100
Next, triple the sum. Multiply 3 with the number gotten
3(100) = 300
300 is your answer
hope this helps
~Rise Above the Ordinary
What is f(–3) for the function f(a) = –2a2 – 5a + 4?
Answer:
The value of f(-3) is 1.
Step-by-step explanation:
Given expression,
[tex]f(a)=-2a^2-5a+4----------(1)[/tex]
For finding the value of f(-3),
Put a = - 3 in equation (1),
We get,
[tex]f(-3)=-2(-3)^2-5(-3)+4[/tex]
[tex]=-2(9)+15+4[/tex]
[tex]=-18+19[/tex]
[tex]=1[/tex]
Hence, the value of f(-3) is 1 for the given function.
Evaluate the algebraic expression for the given variable
-x- -3,x=-5
Evaluate –4 – w for w = –7
i think the answer might be 3
The answer is 3. Have a great day!
Please help. Thanks!
B. The equation of this line is x = 3.
E. This graph is not a function because the value x = 3 is assigned to more than one y-value.
Sole the equation for the indicated variable.
zm= a+b/a, for a
zm= a+b/a, for a
Switch sides to have a on left side
a+b/a=zm
Now multiply both sides by a
A+b= zm(a)
A+b= ama
Now subtract azm both sides
A+b-azm=0
Subtract b both sides
A-azm= -b
Factor out a from ask
A(1 -zm)= -b
Divide each term by 1 - zm to get
A= - b/1-zm
The points (0, 1), (1, 5), (2, 25), (3, 125) are on the graph of a function. Which equation represents that function? f(x) = 2x f(x) = 3x f(x) = 4x f(x) = 5x
Answer:
Option D is the correct answer.
Explanation:
The points (0, 1), (1, 5), (2, 25), (3, 125) are on the graph of a function.
We need to find f(x)
Checking each options.
a) f(x) = [tex]2^x[/tex]
For (0,1)
f(0) = [tex]2^0=1[/tex]
For (1,5)
f(1) = [tex]2^1=2[/tex], given that f(1) = 5, so option A is wrong.
b) f(x) = [tex]3^x[/tex]
For (0,1)
f(0) = [tex]3^0=1[/tex]
For (1,5)
f(1) = [tex]2^1=3[/tex], given that f(1) = 5, so option B is wrong.
c) f(x) = [tex]4^x[/tex]
For (0,1)
f(0) = [tex]4^0=1[/tex]
For (1,5)
f(1) = [tex]4^1=4[/tex], given that f(1) = 5, so option C is wrong.
d) f(x) = [tex]5^x[/tex]
For (0,1)
f(0) = [tex]5^0=1[/tex]
For (1,5)
f(1) = [tex]5^1=5[/tex]
For (2,25)
f(2) = [tex]5^2=25[/tex]
For (3,125)
f(3) = [tex]5^3=125[/tex]
So all values are satisfied Option D is the correct answer.
Please help on these questions and explain please!!
The median is 8 I beliwve because of the 12
a rock fell from a cliff at 108 feet high and landed on an embankment feet from the ground. find the amount if time it would have taken the rock to fall.
To solve this problem we will directly use the formula:
[tex]h=\frac{1}{2}gt^2[/tex]..........Equation 1
where symbols have their usual meanings.
Here g=32.2 ft/s^2 and h=108 feet
Therefore, from Equation 1 we will get:
[tex]t=\sqrt{\frac{2h}{g}}[/tex]....Equation 2
Plugging in the values in Equation 2 we get:
[tex]t=\sqrt{\frac{2\times 108}{32.2}}\approx 2.59[/tex] seconds.
Therefore, the amount of time it would have taken the rock to fall is 2.59 seconds.
Which statement is true about a line and a point? (1 point)
Select one:
a. A point and a line have length as a dimension to measure.
b. A point is a location and a line has many points located on it.
c. A line and a point cannot lie on the same plane.
d. A line and a point cannot be collinear.
x intercept and y intercept
x + 8y = 0
x - intercept when y = 0:
x + 8(0) = 0
x + 0 = 0
x = 0
y - intercept when x = 0:
0 + 8y = 0
8y = 0 |:8
y = 0
Answer:
The x-intercept is 0
The y-intercept is 0
I am very confused lol... So I'm doing a worksheet for Algebra 1 (highschool) and we're doing division and multiplication with fractions at the moment to review what we learned last year and I'm stuck. Right now I'm doing #1 and ended up getting 7 1\2... so I ended up doing this as my equation..
[tex]3 \frac{3}{4} \div \frac{1}{2} [/tex]I have no idea if I'm supposed to do division with this but I tried division and multiplication and got 7 1\2 Everytime I did it. And I know the answer is 1 7/8 cause I may have found a cheat sheet online but I still need to know how to do it. Anyways this is what I did:
[tex]3 \frac{3}{4} \div \frac{1}{2} [/tex]
[tex] \frac{15}{4} \times \frac{2}{1} = \frac{30}{4} [/tex]
[tex] \frac{30}{4} = \frac{15}{2} = 7 \frac{1}{2} [/tex]
I don't understand what I'm doing wrong lol.
OK first change 3 3/4 to an improper fraction and that will give you 15/4. so you got that part right. Next, change the division sign to multiplication. then flip the 1/2 to 2/1. Then multiply 15 times 2 and that will give you 30. Then multiply 4 times 1 and that will give you 4. then you will have an answer of 30/4. Finally, since you a have a big number over a small number you divide 30 by 4 and that will give you 7 1/2. So it turns out that your little cheat sheet is wrong because when you check your answer you should go on Math-way to check it. Also, a little background about me is that I am in 8th grade and I am taking algebra 1 too.
Choose the graph below that correctly represents the equation 2x + 4y = 24.
A. line through the points 0 comma 6 and 12 comma 0
B. line through the points 0 comma negative 6 and 12 comma 0
C. line through the points 0 comma negative 12 and 6 comma 0
D. line through the points 0 comma 12 and 6 comma 0
a line through the point (0, 6 )
to find a point on the line, choose any value of x , substitute into the equation and solve for y
x = 0 : 0 + 4y = 24 ( divide both sides by 4 )
y = [tex]\frac{24}{4}[/tex] = 6
hence line goes through (0, 6 )
The correct graph that represents the equation 2x + 4y = 24 is option A, which shows a line through the points (0, 6) and (12, 0).
Explanation:The equation 2x + 4y = 24 can be rearranged to y = -0.5x + 6. This means that the equation represents a linear function with a slope of -0.5 and a y-intercept of 6.
Option A, which shows a line through the points (0, 6) and (12, 0), is the correct graph since it satisfies the equation. The slope is -0.5 and the y-intercept is 6.
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The lateral surface area of cone A is equal to the lateral surface area of cylinder B.
True or false
Answer:
TRUE
Step-by-step explanation:
Lateral area of cone is given by: πrl
where r is the radius and l is the slant height
Here r=r and l=2h
Hence, lateral area of cone A= π×r×2h
= 2πrh
Lateral area of cylinder is given by: 2πrh
where r is the radius and h is the height
Lateral area of cylinder B=2πrh
Clearly, both the lateral areas are equal
Hence, the statement that:The lateral surface area of cone A is equal to the lateral surface area of cylinder B. is:
True