Answer:
The width is 7 inches and the length is 9 inches
Step-by-step explanation:
So we can divide 32 by 2 because we know perimeter is 2(l*w)
So it becomes 16, and it is now (l*w)
We know that the length is 2 inches longer so we subtract 2 from 16.
It then becomes 14 inches so therefore we can then divide it by 2.
14 divided by 2 is 7 and therefore we add 2 because we subtracted the two from earlier temporarily.
Therefore the width is 7 and the length is 9.
Final answer:
To find the dimensions of the picture frame with a perimeter of 32 inches and length 2 inches more than its width, equations based on the rectangle's perimeter formula are used. The width is found to be 7 inches, leading to a length of 9 inches.
Explanation:
To determine the dimensions of a rectangular picture frame where the perimeter is 32 inches and the length is 2 inches longer than the width, we can set up two equations based on the properties of a rectangle's perimeter. The perimeter (P) of a rectangle is given by the formula P = 2l + 2w, where l is the length and w is the width. Let's denote the width of the frame as w inches; thus, the length will be w + 2 inches since the length is 2 inches longer than the width.
Now, since the perimeter is 32 inches, we plug in our expressions for length and width into the perimeter formula: 2(w + 2) + 2w = 32. Simplifying this, we get 2w + 4 + 2w = 32. Combining like terms, we have 4w + 4 = 32. Subtracting 4 from both sides, we get 4w = 28. Dividing both sides by 4, we find w = 7 inches.
Therefore, the width of the frame is 7 inches, and the length, being 2 inches longer, is 7 + 2 = 9 inches. So the dimensions of the frame are 7 inches by 9 inches.
Which time is faster 2/3, 11/12, 5/6 or 7/12
Answer:
Correct choice is 11/12.
Step-by-step explanation:
Given numbers are 2/3, 11/12, 5/6 and 7/12.
Now we need to find about which time is faster among 2/3, 11/12, 5/6 and 7/12.
To find that we need to make denominators equal.
2/3, 11/12, 5/6, 7/12
Common denominator is 12 so let's multiply by suitable numbers to get equal denominator.
8/12, 11/12, 10/12, 7/12
Now we see that largest numerator is 11.
Hence correct choice is 11/12.
Answer:
11/12 is the answer
Step-by-step explanation:
Can you help me please
The answer to this question is 10. The working out is shown in the image attached.
*** Sorry instead of writing 170 I wrote 270 for the big angle.. other than that it's correct
or another way to solve this is....
we know that a straight line is 180 degrees and the angle APD is 170 all we need to do is subtract 170 from 180 to get the answer of DPB
Hope this helped
Write an equation of the direct variation that includes the point (5,1)
Answer:
y = 1/5k
Step-by-step explanation:
y = kx
1= k(5)
1/5 = l
Which of the following is true about the expression radical 3 times radical 12
There is nothing here, but I do know that the answer is 6⃣.
Answer:
It represents the product of two irrational numbers and is equivalent to a rational number.
How much ice cream can fit in a chocolate cone with a height of 7 inches and a diameter of 4 inches?
87.92in^3 or 29.3in^3
Answer:
29.3 in³
Step-by-step explanation:
1. Volume of cone: V = ¹/₃ * πr²h
2. Find r: r = d/2 = 4/2 = 2 in
3. Plug in: V = ¹/₃ * π(2)²*7
4. Powers: V = ¹/₃ * π * 4 * 7
5. Multiply: V = ²⁸/₃π in³ ≈ 29.3 in³ (excluding outside of the cone)
Final answer:
Approximately 29.3 cubic inches of ice cream can fit in the chocolate cone.
Explanation:
To find the amount of ice cream that can fit in a chocolate cone, we need to calculate the volume of the cone. The volume of a cone is given by the formula V = (1/3)πr^2h, where r is the radius (half the diameter) of the base of the cone and h is the height of the cone. In this case, the diameter is 4 inches, so the radius is 2 inches. The height of the cone is 7 inches. Plugging these values into the formula, we get V = (1/3)π(2^2)(7) = (4/3)π(7) = 28/3π ≈ 29.3 cubic inches. Therefore, approximately 29.3 cubic inches of ice cream can fit in the chocolate cone.
What is 40.99 times 2.1
Answer:
86.079
Step-by-step explanation:
40.99*2.1
The Answer Is 86.079.
The equation 2x = 3y - 5 when written in slope-intercept form is:
Answer:
y=2/3x+5/3
Step-by-step explanation:
The equation written in slope intercept form will be y = (2/3)x + 5/3.
What is the slope intercept form?When you know the slope of the line (m) to be investigated and the point of y-intercept (0,c) is also given, you utilize the slope intercept formula.
Slope intercept formula:
y = mx + c
m is the slope
c is the y intercept
Given equation in the question is
2x = 3y - 5
3y = 2x + 5
y = (2/3)x + (5/3)
Now if we compare this equation to slope intercept form we will get m = 2/3 and c = 5/3.
Hence the slope intercept form of the equation is y = (2/3)x + (5/3).
Learn more about slopes on:
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Which triangle always has 1 right angle and 2 sides the same length?
a. acute isosceles
B. right isosceles
c. right equilateral
D. acute scalene
Answer:
The Answer is B
Step-by-step explanation:
Answer:
Step-by-step explanation:
Isosceles tells you that two sides of a triangle (in this case) are equal. The two non hypotenuse sides are both the same size. Each of the angles opposite the equal sides are equal and are 45o.
A right angle takes up the other 90o.
Please help me with the first one
Answer:
5:3
Step-by-step explanation:
it would be 5:3 because it is the ratio of consonant to vowels
the median of the data set is 18 what number is missing 12,17,21,13,25
Answer:
19
Step-by-step explanation:
The area of a rectangle is x^2-5x+6 Which of the following could be one of the dimensions?
A)(x + 3)
B)(x - 2)
C)(x - 1)
D)(x + 6)
Answer:
B)(x - 2)
Step-by-step explanation:
Given that the area of a rectangle is [tex]x^2-5x+6[/tex].
Now we need to find about which of the given choices could be one of the dimensions. Where given choices are:
A)(x + 3)
B)(x - 2)
C)(x - 1)
D)(x + 6)
We know that area of rectangle = (length) x (width)
So basically we need to factor the given area of rectangle to find the corresponding dimensions.
[tex]x^2-5x+6[/tex]
[tex]=x^2-2x-3x+6[/tex]
[tex]=(x-2)(x-3)[/tex]
Hence B)(x - 2) is the correct choice.
Answer:
x-2
Step-by-step explanation:
Help on this question
The answer is the third one
The answer is C it’s pretty easy
Elvaluate b^-3 for b=3
A. 27
B. 1/9
C. 1/27
D. -27
Answer:
C
Step-by-step explanation:
Using the rule of exponents
• [tex]b^{-m}[/tex] ⇔ [tex]\frac{1}{b^{m} }[/tex], thus
[tex]3^{-3}[/tex] = [tex]\frac{1}{3^{3} }[/tex] = [tex]\frac{1}{27}[/tex] → C
Answer: C 1/27
b^-3 and b=3
So we have 1/b^3= 1/3^3= 1/27
If you put $2,000 into an interest bearing account, where interest is compounded quarterly (4 times a year) at 6%, how long will it take for your money to triple?
Answer:
[tex]18.4\ years[/tex]
Step-by-step explanation:
we know that
The compound interest formula is equal to
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
in this problem we have
[tex]t=?\ years\\ P=\$2,000\\ r=0.06\\n=4\\A=\$6,000[/tex]
substitute in the formula above
[tex]\$6,000=\$2,000(1+\frac{0.06}{4})^{4t}[/tex]
[tex]3=(1.015)^{4t}[/tex]
Applying log both sides
[tex]log(3)=4tlog(1.015)[/tex]
[tex]t=log(3)/[4log(1.015)][/tex]
[tex]t=18.4\ years[/tex]
a 7cm × 5cm rectangle sits inside a circle with radius 6cm. what is the area of the shaded region
Answer:
The area of the shaded region is [tex](36\pi-35)\ cm^{2}[/tex]
Step-by-step explanation:
we know that
The area of the shaded region is equal to the area of the circle minus the area of the rectangle
so
[tex]A=\pi r^{2}-a*b[/tex]
we have
[tex]a=7\ cm[/tex]
[tex]b=5\ cm[/tex]
[tex]r=6\ cm[/tex]
substitute the values
[tex]A=\pi (6)^{2}-(7)*(5)[/tex]
[tex]A=(36\pi-35)\ cm^{2}[/tex]
Answer:
78.1
Step-by-step explanation:
11/33 in lowest terms
Answer:
1/3
Step-by-step explanation:
Both 11 and 33 are divisible by 11
11/11 =1
33/11 =3
11/33 = 1/3
The answer is 1/3. I hope this helps!
23. How many solutions are there to the system of equations below?
y = x2 + 3x – 7
y – 5x + 8 = 0
A. There are exactly 4 solutions
B. There are exactly 2 solutions
C. There is exactly 1 solution
D. There are no solutions.
D
When you add 2+3 which equals 5 so it’ll be y=5x-7. And plug in y into the other equation. 5x-7-5x+8=0. -7-8=0, -7-8 =-1 therefore there is no solution because-7-8= -1 not 0.
Answer:
There are exactly 4 solutions
Step-by-step explanation
Given the two equation
y = x² + 3x – 7 ... (1)
y – 5x + 8 = 0 ...(2)
From equation 2,
y - 5x = -8
y = -8+5x ...(3)
Substituting equation 3 into 1
-8+5x = x²+3x-7
Moving -8+5x to the other side of the equation, we have:
x²+3x-7+8-5x = 0
x²+3x-8x-7+8= 0
x²-5x+1 = 0
Since the resulting equation is quadratic, we will get two solutions as our x and substituting both value of x in equation 2 to get y will give us two solutions for our y variable making a total of 4 solutions.
Therefore in the system of equation given, there are exactly 4 solutions
Parallelogram CARD has vertices (5, -2), (-1, -2), (1, 2), and (7, 2), respectively. The diagonals, CR and AD intersect at Point T. What is the length of CT? What is the length of DT?
Complete your work in the space provided or upload a file that can display math symbols if your work requires it. If necessary, round lengths to the nearest hundredth of a unit.
Answer:
a) T(3,0)
b) |CT|=2.83
c) |DT|=4.47
Step-by-step explanation:
The given parallelogram CARD has vertices (5, -2), (-1, -2), (1, 2), and (7, 2)
The diagonals of a parallelogram bisect each other.
Find the midpoint of one diagonal, that gives us the point of intersection of the diagonals T.
The midpoint of C(5,-2) and (1,2) is
[tex]T(\frac{5+1}{2},\frac{-2+2}{2} )[/tex]
[tex]T(3,0)[/tex]
b) To find the length of CT, we use the distance formula; where C(5,-2) ahd T(3,0).
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]d=\sqrt{(3-5)^2+(-2-0)^2}[/tex]
[tex]d=\sqrt{4+4}[/tex]
[tex]d=\sqrt{8}[/tex]
[tex]d=2\sqrt{2}=2.83[/tex]
The length of CT is 2.83 to the nearest hundredth
c) To find the length of DT, we use the distance formula; where D(7,2) ahd T(3,0).
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]d=\sqrt{(3-7)^2+(2-0)^2}[/tex]
[tex]d=\sqrt{16+4}[/tex]
[tex]d=\sqrt{20}[/tex]
[tex]d=2\sqrt{5}=4.47[/tex]
The length of DT is 4.47 to the nearest hundredth
8 + 4 - 3 using pemdas
Answer:
You can alternatively apply PEMDAS as schools do today: Simplify everything inside the parentheses first, then exponents, then all multiplication and division from left to right in the order both operations appear, then all addition and subtraction from left to right in the order both operations appear.
Step-by-step explanation:
PEMDAS is an acronym for the words parenthesis, exponents, multiplication, division, addition, subtraction. Given two or more operations in a single expression, the order of the letters in PEMDAS tells you what to calculate first, second, third and so on, until the calculation is complete.
so 8+4 =12 12-3=9
the correct answer would be 9
If DEF is similar to PRY, what is the measure of PY?
The measure of PY is 24 centimeters, found using the properties of similar triangles and the correct option is C.
To solve this problem, we can use the following steps:
Identify the corresponding sides of the two similar triangles.
Write down the proportion for the corresponding sides of the two triangles.
Cross-multiply to solve for the unknown side.
In this case, the corresponding sides of the two triangles are:
AD = AP
DE = PR
EF = RY
We can write down the following proportion:
AD/DE = AP/PR
We know that AD = 6 cm and AP = 16 cm. We also know that PR = 8 cm. We can substitute these values into the proportion and solve for DE:
6/DE = 16/8
DE = 6 * 8 / 16
DE = 3 cm
Now that we know the length of DE, we can use the following proportion to solve for PY:
DE/EF = PR/PY
3/9 = 8/PY
PY = 8 * 9 / 3
PY = 24 cm
Therefore, the measure of PY is 24 centimeters.
So, the correct option is C.
For such more questions on triangles
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Which reaction takes place in a nuclear fission reactor?
Image below
Answer:
The reaction that takes place in a nuclear fission reactor is answer D.
Step-by-step explanation:
Nuclear fission reactions involves the process by which large atomic nuclei are bombarded with energetic particles and release of an enormous amount of nuclear energy, which mainly ends up as heat energy.
So now, consider the nuclear reaction from D, after the uranium nucleus absorbs the neutron its split into two smaller nuclei (often radioactive themselves), Krypton and Barium and releases more neutrons (or energy).
Which is the equation in slope intercept form for the line that passes through (-3,3) and is parallel to 3x + y= 7?
A y= 3x + 12
B y= 1/3x y = 4
C y= -3x -6
D y= -1/3x + 3
The equation of the line parallel to 3x + y = 7 and passing through (-3,3) is y = -3x + 12 (Option A) because parallel lines have identical slopes and using the point-slope formula provides us with the y-intercept.
To find the equation of a line parallel to 3x + y = 7 and passing through the point (-3,3), we need two pieces of information:
The slope of the parallel line
The coordinates of a point it passes through
First, let's rewrite the given equation in slope-intercept form to find the slope. Slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.
y = -3x + 7
So, the slope m is -3. Because parallel lines have the same slope, our new line will also have a slope of -3.
Using the slope (-3) and the given point (-3,3), we apply the point-slope formula:
y - y1 = m(x - x1)
y - 3 = -3(x - (-3))
y - 3 = -3x - 9
y = -3x + 12
Thus, the equation in slope-intercept form for the line that passes through (-3,3) and is parallel to 3x + y= 7 is y = -3x + 12 which corresponds to Option A.
Find the volume of the cylinder.
Either enter an exact answer in terms π or use 3.14 for π
Answer:
160π units³
Step-by-step explanation:
The volume (V) of a cylinder is calculated using the formula
V = πr²h ( r is the base radius and h the height )
here r = 4 and h = 10, thus
V = π × 4² × 10 = 160π units³ ← exact value
what is the unit rate for the cost of a salad at the salad bar?
Answer:
C.) $2.00 per pound
Hope This Helps! Have A Nice Day!
$2.00 per pound, the answer would be letter C
10011 lower 2 x 11 lower 2 ?
ANSWER
[tex] 10011_{2} \times 11_{2}= 111001_{2}[/tex]
EXPLANATION
We want to multiply:
[tex] 10011_{2} \times 11_{2}[/tex]
in base 2
One can choose to convert everything to base 10
This gives 19×3=57
We then convert 57 to base two to get
[tex]57 = 111001_{2}[/tex]
Or perform the multiplication in base 2 straight forward.
10011
× 11
10011
+10011
111001
------------
[tex]10011_{2} \times 11_{2} = 111001_{2}[/tex]
What is the measure of the missing angle?
60°
80°
100
180°
Answer: 80
Step-by-step explanation:
After selling some lemonade and cookies, Vivian and her brother Gil had 7-one dollar bills, 8 quarters and 6 dimes.They agreed to divide the money equally. What is the total amount of money that Vivian and Gil earned? Explain.
Answer:
They earned $9.60 they will each get $4.80. Give or take.
Step-by-step explanation:
9.60÷2=4.80
If the perimeter of a square garden is 84 ft, what is the area of the garden?
Answer:
Step-by-step explanation:
7056
express 0.009238 to 3 significant figures
The number 0.009238 is expressed correctly to 3 significant figures as 0.00924
To express 0.009238 to 3 significant figures, we need to consider the first three non-zero digits from the left.
Identify the first three non-zero digits from the left: 9, 2, and 3.
Since the digit after the third significant figure (8) is greater than or equal to 5, we round up the last significant figure.
Therefore, the number rounded to 3 significant figures is 0.00924.
The complete question is : express 0.009238 to 3 significant figures
Please help!!! Is this correct????
Answer:
yes
Step-by-step explanation:
Weight appears to be the independent variable, so will be graphed on the horizontal axis. Cost is the dependent variable, so will be graphed on the vertical axis.