Answer:
The area of cardboard required is 40750 cm².
Step-by-step explanation:
Given:
Length (L) = 25 cm
Width (W) = 5 m = 5 × 100 = 500 cm
Height (H) = 15 cm
Area of the cardboard is same as the total surface area of the closed rectangular box.
Total surface area of the rectangular box is given as:
[tex]SA=2(LW+WH+LH)\\\\SA=2(25\times 500+500\times 15+15\times 25)\\\\SA=2(12500+7500+375)\\\\SA=2\times 20375=40750\ cm^2[/tex]
So, the area of cardboard required is 40750 cm².
1. In quadrilateral QUAD shown below, point R is the midpoint of diagonal QA. What are
the coordinates of point Q?
R(-2, 10)
A (12,6)
A. (-16,14)
B. (-12, 16)
C. (-14,4)
D. (-7,2)
Answer:
Option A. (-16,14)
Step-by-step explanation:
we know that
The formula to calculate the midpoint between two points is equal to
[tex]M(\frac{x1+x2}{2},\frac{y1+y2}{2})[/tex]
In this problem we have that
[tex]point\ Q(x1,y1)\\point\ A(x2,y2)[/tex]
[tex](-2,10)=(\frac{x1+12}{2},\frac{y1+6}{2})[/tex]
so
[tex]\frac{x1+12}{2}=-2[/tex] ---> [tex]x1=-4-12=-16[/tex]
[tex]\frac{y1+6}{2}=10[/tex] ---> [tex]y1=20-6=14[/tex]
therefore
The coordinates of point Q are (-16,14)
The coins in Diego’s pocket are worth 150% of a dollar. How much are they worth (in dollars)?
Answer:
In Diego’s pocket are worth $1.5.
Step-by-step explanation:
Given:
The coins in Diego’s pocket are worth 150% of a dollar.
Now, to find the worth in dollars in Diego's pocket.
So, as given the coins in Diego’s pocket are worth 150% of a dollar.
That means 150% of $1. As a dollar expresses 1$.
Thus, 150% of 1$.
[tex]=\frac{150}{100} \times 1[/tex]
[tex]=1.5\times 1[/tex]
[tex]=\$1.5.[/tex]
Therefore, in Diego’s pocket are worth $1.5.
Diego's coins are worth 150% of a dollar, which means they are worth $1.50. This was calculated by converting 150% to a decimal (1.50) and multiplying it by 1 dollar.
The question involves calculating the value of coins in terms of dollar amounts, which falls under the subject of Mathematics, specifically dealing with percentages and conversion of values.
Diego has coins in his pocket worth 150% of a dollar. To find out how much this is in dollars, we need to convert the percentage to a decimal by dividing by 100, which gives us 1.50. Therefore, the coins in Diego's pocket are worth $1.50. This is because 150% of 1 dollar is 1.5 times 1, which equals 1.5 or $1.50.
Remember, in math, percentages over 100% mean that you have more than the whole. So, 150% represents 1 whole (100%) plus half of another whole (50%), which in terms of dollars, translates to $1.50.
Solve the triangle. B = 73°, b = 15, c = 10
Incomplete Question, the complete question is
Solve the triangle.
B = 73°, b = 15, c = 10
A. C = 39.6°, A = 67.4°, a ≈ 14.5
B. Cannot be solved
C. C = 44.8°, A = 62.4°, a ≈ 14.5
D. C = 39.6°, A = 67.4°, a ≈ 20.3
Answer:
The Answer is the option A
A. C = 39.6°, A = 67.4°, a ≈ 14.5
Step-by-step explanation:
Given:
In Δ ABC,
∠B = 73°
b = 15
c = 10
To Find:
∠A = ?
∠B = ?
a = ?
Solution:
IN Δ ABC, Sine Rule says that
[tex]\dfrac{a}{\sin A}= \dfrac{b}{\sin B}= \dfrac{c}{\sin C}[/tex]
Substituting the given values we get
[tex]\dfrac{15}{\sin 73}= \dfrac{10}{\sin C}\\\\\sin C=0.6375\\\therefore C=39.6\°[/tex]
Triangle sum property:
In a Triangle sum of the measures of all the angles of a triangle is 180°.
[tex]\angle A+\angle B+\angle C=180\\\\73+39.6+\angle A=180\\\therefore m\angle A =180-112.6=67.4\°[/tex]
∴ [tex]\dfrac{a}{\sin A}= \dfrac{b}{\sin B}[/tex]
Substituting the given values we get
∴ [tex]\dfrac{a}{\sin 67.4}= \dfrac{15}{\sin 73}\\\\\therefore a=14.48\approx14.5[/tex]
Therefore,
A. ∠C = 39.6°, ∠A = 67.4°, a ≈ 14.5
YOUR TURN
9. Out of the 25 students in Mrs. Green's class, 19 have a per. Wh
of the students in Mrs. Green's class have a pet?
Answer:
[tex]\frac{19}{25}[/tex] or [tex]76%[/tex]
Step-by-step explanation:
As a fraction: [tex]\frac{19}{25} \\[/tex] it can't be simplified further
As a percentage: [tex]\frac{19}{25} =0.76[/tex]
find the scale factor.
The scale factor is 1.5. The dilation rule is : (x,y)-------(.15x,1.5y)
Step-by-step explanation:
Dilation is a transformation that maps an object to an image of the same shape as the original object to form a different size image.When a larger image is produced it's called an enlargement where as when a small image is produced, it's called a reduction.
The rule of dilation, with center as the origin follows;
(x,y)------(sx,sy) where s is the scale factor. To find the scale factor, select one of the vertices of the object and of the image at divide the coordinate of image with that of object.
Taking O(2,16) and O'(3,24), the scale factor will be;
s*2=3
2s=3
s=3/2 =1.5
or
s*16=24
16s=24
s=24/16=3/2=1.5
The scale factor is 1.5, hence the dilation rule is;
(x,y)-------(.15x,1.5y)
Learn More
Dilation:https://brainly.com/question/10945890
Keywords: dilation, vertices, origin, scale factor, translation
#LearnwithBrainly
Find the length of the third side of each triangle
Answer:Where is the picture?
Step-by-step explanation:
twice a number x,minus 19
Answer:
2x - 19
Step-by-step explanation:
"Twice a number x" means the (missing) number is called x. Write "2x" which means multiply "x" by 2.
"Minus 19" is -19.
Together, the expression is 2x - 19.
Write an equation for the line that is parallel to y =
-2x and passes through the point (0, -7).
Answer:
y=-2x-7
Step-by-step explanation:
y=-2x
y-y1=m(x-x1)
y-(-7)=-2(x-0)
y+7=-2(x)
y+7=-2x
y=-2x-7
What is 86 as a fraction in simplest form
A baseball player recorded 60 hits in 186 at-bats.What is the ratio of hits to at-bats?
Answer:
10:31
Step-by-step explanation:
Given: A baseball player recorded [tex]60[/tex] hits in [tex]186[/tex] at-bats.
To Find: ratio of hits to at-bats.
Solution:
Total number of hits recorded by baseball player [tex]=60[/tex]
Total number of at-bats [tex]=186[/tex]
Now,
ratio of hits to at-bats [tex]=\frac{\text{total number of hits recorded}}{\text{total number of at-bats}}[/tex]
putting values,
ratio of hits to at-bats [tex]=\frac{60}{186}[/tex]
[tex]=\frac{10}{31}[/tex]
[tex]=10:31[/tex]
Hence the ratio of hits to at-bats is [tex]10:31[/tex]
solve the inequality 4y+3>2y+14
Step-by-step explanation:
Step 1. subtract 2Y from both sides
4y+3-2y>+14-2y 2y+3>14
step 2. subtract 3 from both sides
2y+3-3>14-3 2y>11
step 3. divide both sides by 2
2÷2y>11÷2 y>11÷2
answer is: y>11/ 2
The given inequality (4y + 3 > 2y + 14) is reduced to y > 5.5 and this can be evaluated by using the arithmetic operations.
Given :
Inequality -- 4y + 3 > 2y + 14
The following steps can be used to evaluate the given inequality:
Step 1 - Write the given inequality.
4y + 3 > 2y + 14
Step 2 - Subtract 3 from both sides in the above inequality.
4y + 3 - 3 > 2y + 14 - 3
4y > 2y + 11
Step 3 - Subtract 2y from both sides in the above inequality.
4y - 2y > 2y + 11 - 2y
Step 4 - Simplify the above inequality.
2y > 11
Step 5 - Divide by 2 on both sides in the above inequality.
y > 5.5
For more information, refer to the link given below:
https://brainly.com/question/15137133
The function g is defined by g(x)=cx-3, where c is a constant. Find c if the value of g(x) at x=0.5 is equal to -1
Answer:
c = 4
Step-by-step explanation:
In g(x)=cx-3 when x is set to 0.5 , g(x)= -1.
We can solve for "c" when it is the only variable in the equation.
Substitute x for 0.5 and g(x) for -1. Isolate "c" to solve by doing reverse operations.
g(x) = cx - 3
g(0.5) = 0.5c - 3 Substitute x=0.5
-1 = 0.5c - 3 Substitute g(0.5) = -1
-1 + 3 = 0.5c - 3 + 3 Add 3 to both sides to start isolating c
2 = 0.5c
2/0.5 = 0.5c/0.5 Divide both sides by 0.5 to isolate c
4 = c Value of c
c = 4 Standard formatting puts the variable on the left side
Therefore the value of c if g(0.5)=-1 is 4.
Answer:
c = 4.
Step-by-step explanation:
Substitute the given values x = 0.5 and g(x) = -1:
-1 = c(0.5) - 3
0.5c = -1 + 3 = 2
c = 2/0.5
c = 4.
The sum of two consecutive integers is 131
Answer:
65 and 66
Step-by-step explanation:
x + (x+1) = 131
2x + 1 = 131
2x = 131 - 1 = 130
x = 65
x + 1 = 66
A line includes the points (10,1) and (a,-5) has a slope of 1/3. What is the value of a?
For this case we have that by definition, the slope of a line is given by:
[tex]m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}}[/tex]
Where:
[tex](x_ {1}, y_ {1})\ and\ (x_ {2}, y_ {2})[/tex]are two points through which the line passes.
According to the statement we have:
[tex](x_ {1}, y_ {1}) :( 10,1)\\(x_ {2}, y_ {2}) :( a, -5)\\m = \frac {1} {3}[/tex]
Substituting we have:
[tex]\frac {1} {3} = \frac {-5-1} {a-10}\\\frac {1} {3} = \frac {-6} {a-10}\\a-10 = \frac {-6} {\frac {1} {3}}\\a-10 = -18\\a = -18 + 10\\a = -8[/tex]
Thus, the value of a is -8.
Answer:
[tex]a = -8[/tex]
Complete the inequality.
6 gal ___ 24 qt
Answer:
equal to.
Step-by-step explanation:
1 gallon would equal 4 quarts, So if 6 gallons were presnt multiply 6 and 4 and you get 24 quarts
The quantity in the inequality is the same for both sides, so you would use the equals sign. According to unit conversion, 6 gallons is equal to 24 quarts.
Explanation:The inequality you are trying to solve involves comparing the two quantities in gallons and quarts. One gallon is equivalent to 4 quarts. Therefore, we can multiply 6 gallons by 4 to convert it to quarts:
6 gal * 4 qt/gal = 24 qt
Therefore, the inequality would be: 6 gal = 24 qt
Learn more about Unit Conversion here:https://brainly.com/question/32030244
#SPJ2
Simplify to create an equivalent expression.
8(10 - 69q) +3(-7q - 2)
Choose 1 answer:
-69q + 78
-55q + 74
-69q + 74
69q + 74
Answer:
-573q+74
Step-by-step explanation:
8(10-69q)+3(-7q-2)
80--552q-21q-6
80-573q-6
-573q+74
Answer:
the other guys i wrong completely the actual answer is −69q+74 i just did it and i am tring to help more people
Step-by-step explanation:
Fill in the using table this function rule y=-10x+2
HELP I WILL MARK YOU AS A BRAINLIEST!!
John earns $10.26 an hour. How much will he earn if he works for 6.6 hours?
Answer:
he will earn 67.71 dollars, or more precisely 67.716 dollars in 6.6 hours
Step-by-step explanation:
Answer:
$67.72 or 67.71 (depends if you are taking the first 2 decimal points or if you are rounding
Step-by-step explanation:
10.26*6.6
This is done because we have how much he earns per hour and the number of hour he works so we have to multiple them together
The end result would be: 67.716 dollars. The answer varies like I said above
an amount of $41,000 is borrowed for 7 years at 6.75% interest, compounded annually. If the loan is paid in full at the end of that year, how much must be paid back?
Answer:
We must pay back US$ 64,767.70 for the loan after 7 years.
Step-by-step explanation:
1. Let's review the data given to us for answering the question:
Loan amount = US$ 41,000
Duration of the loan = 7 years
Interest rate = 6.75% compounded annually
2. Let's find the future value of this loan after 7 years, using the following formula:
FV = PV * (1 + r) ⁿ
PV = Loan = US$ 41,000
number of periods (n) = 7 (7 years compounded annually)
rate (r) = 6.75% = 0.0675
Replacing with the real values, we have:
FV = 41,000 * (1 + 0.0675) ⁷
FV = 41,000 * (1.0675) ⁷
FV = 41,000 * 1.5797
FV = US$ 64,767.70
We must pay back US$ 64,767.70 for the loan after 7 years.
A bedroom has the shape shown. The homeowner is upgrading by putting in new crown molding. How many feet of crown molding does she need?
Answer: D.
Step-by-step explanation: Add all of the sides' lengths together. The rest of the wall beneath where "5 ft." is measures as 6 ft. Add that to the 5 ft of the rest of the wall and you'll have 11 for the whole right wall. Add 11 to 8, 10 and 12, and you'll have 41 which is close to the last choice so you're safest bet is D.
The homeowner needs 48 feet of crown molding.
Explanation:To determine how many feet of crown molding she needs, the homeowner needs to find the perimeter of the room. The room has four sides, each measuring 12 feet, so the perimeter is 4 * 12 = 48 feet. Therefore, the homeowner needs 48 feet of crown molding.
Trent lifts weights 7 days a week. He spends 18 minutes lifting weights on Monday, 29 minutes on Tuesday, 40 minutes on Wednesday, and 51 minutes on Thursday. If this pattern continues, how many minutes will Trent lift weights on Saturday?
Answer:
73 minutes
Step-by-step explanation:
Find a pattern in the sequence.
The sequence is 18, 29, 40, 51.
29 - 18 = 11
40 - 29 = 11
51 - 40 = 11
The pattern is add 11 each day.
If 51 is Thursday, 51 + 11 is Friday.
51 + 11 + 11 is Saturday.
51 + 11 + 11 = 73
Therefore Trent will lift weights for 73 minutes.
Calculate the median of: 4.6, 3, 8.1, 9, 12,3, 9, 3.5, 7.3.
A. 5.8
B. 9
C. 3
D. 6.22
Answer: 7.3
Step-by-step explanation: The median is the middle number in the data set when the data set is written from least to greatest.
Least to greatest ⇒ 3, 3, 3.5, 4.6, 7.3, 8.1, 9, 9, 12
So the median will be the middle number or 7.3.
Answer:
5.8
Step-by-step explanation:
First put all the numbers in order from least to greatest.
3, 3, 3, 3.5, 4.6, 7, 8.1, 9, 9, 12
There are two middle numbers, 4.6 and 7. Average them to get 5.8.
What is the value of Negative 3 m n + 4 m minus 3 when m = 2 and n = negative 4?
Answer:
Answer is D
Step-by-step explanation:
engenuity 2022
Answer:
29
Step-by-step explanation:
Which expressions are equivalent to 35+30s-45t35+30s−45t35, plus, 30, s, minus, 45, t?
Answer:
The correct option is B. [tex]5(7+6s-9t)[/tex] and C. [tex](-35-30s+45t)\times (-1)[/tex].
Step-by-step explanation:
Consider the provided expression.
[tex]35 + 30s - 45t[/tex]
Option (A): [tex]7\cdot(5+30s-45t)[/tex]
Open parenthesis.
[tex]35+210s-315t[/tex]
Which is not equal to the provided expression.
Option (B) [tex]5(7+6s-9t)[/tex]
Open parenthesis.
35+30s-45t
Which is equal to the provided expression.
Option (C) [tex](-35-30s+45t)\times (-1)[/tex]
Open parenthesis.
[tex]35+30s-45t[/tex]
Which is equal to the provided expression.
Option (D) [tex]10\times(3.5+3s-4.5)[/tex]
[tex]35+30s-45[/tex]
Which is not equal to the provided expression.
Option (E) [tex](\frac{35}{2}- 15s + \frac{45t}{2}) \cdot(-2)[/tex]
Open parenthesis.
[tex]-35+30s-45t[/tex]
Which is not equal to the provided expression.
Hence, the correct option is B. [tex]5(7+6s-9t)[/tex] and C. [tex](-35-30s+45t)\times (-1)[/tex].
Given f(x) = 364-27, what is the value of f(16)
Answer:
f(16)=337
Step-by-step explanation:
Ron walked 3 3/4 km on monday,4 1/3 km on Wednesday. What distance did he walk in all
Answer:
Ron walked a total of 8 1/12 km
Step-by-step explanation:
Answer:
[tex]8\frac{1}{12} \; km[/tex]
Step-by-step explanation:
Distance walked by Ron on Monday = [tex]3\frac{3}{4} \; km[/tex]
Distance walked by Ron on Wednesday = [tex]4\frac{1}{3} \; km[/tex]
Now we will convert the given mixed fractions into improper fractions.
As we know that, a mixed fraction is composed of a whole number and a proper fraction.
Now,.
[tex]3\frac{3}{4} =\frac{3\times4+3}{4}=\frac{15}{4}[/tex]
[tex]4\frac{1}{3} =\frac{4\times3+1}{3} =\frac{13}{3}[/tex]
So, distance walked by Ron on Monday = [tex]\frac{15}{4}\; km[/tex]
Distance walked by Ron on Wednesday = [tex]\frac{13}{3} \; km[/tex]
Now, to find the total distance walked by Ron, we will add the distances walked by him on Monday and Wednesday.
So,
[tex]3\frac{3}{4} +4\frac{1}{3} =\frac{15}{4}+ \frac{13}{3}[/tex]
Now, we will find the LCM of the denominators of the given fractions.
The prime factorisation of 4 and 3 is,
4 = 2 × 2
3 = 3
So, LCM (3, 4) = 2 × 2 × 3 = 12
Now, we will convert each of the given fractions into their equivalent fractions with denominator 12.
[tex]\frac{15}{4}=\frac{15\times3}{4\times3}=\frac{45}{12}[/tex]
[tex]\frac{13}{3}=\frac{13\times4}{3\times4}=\frac{52}{12}[/tex]
So,
[tex]\frac{15}{4}+\frac{13}{3}=\frac{45}{12} +\frac{52}{12}=\frac{45+52}{12}=\frac{97}{12}[/tex]
Now, we will convert [tex]\frac{97}{12}[/tex] into improper fraction.
Now, 97 = 96 + 1 = 12 × 8 + 1
So, when '97' is divided by '12', then we get '8' as the quotient and '1' as the remainder.
So,
[tex]\frac{97}{12} = 8\frac{1}{12}[/tex]
Hence, Ron walked a total distance of [tex]8\frac{1}{12}[/tex] km in both the days.
WORTH 8 POINTS
What is the area of a rectangle with side lengths of 6/8 meter and 4/ 10 meter?
Answer:
3/10 (see picture for work)
Correction:I meant to write down [tex]a=l*h[/tex], not [tex]a=b*w[/tex].The area of a rectangle with side lengths of 6/8 meter and 4/10 meter is calculated by multiplying the lengths together after simplifying them to 3/4 and 2/5, respectively. The resulting area is 0.3 m².
Explanation:To calculate the area of a rectangle, you multiply the length by the width. The question provides the side lengths as 6/8 meter and 4/10 meter. First, you may want to simplify these fractions to make multiplication easier. The fraction 6/8 simplifies to 3/4 after dividing both the numerator and the denominator by 2. The fraction 4/10 simplifies to 2/5 after dividing both the numerator and the denominator by 2.
Now, you multiply the simplified side lengths together to get the area:
Area = length × width
Area = (3/4) m × (2/5) m
Area = (3 × 2) / (4 × 5) [tex]m^2[/tex]
Area = 6 / 20 [tex]m^2[/tex]
Area = 3 / 10 [tex]m^2[/tex]
Area = 0.3 [tex]m^2[/tex]
The area of the rectangle is 0.3 [tex]m^2[/tex] (square meters).
Learn more about Area of a Rectangle here:https://brainly.com/question/15218510
#SPJ2
A pipe that is 12 - feet long is cut into pieces that are 2 feet long. Which step below would give the
number of pieces into which the pipe is cut?
Answer:
Step-by-step explanation:
Number of pieces= total length/ length of one piece
= 12/2 = 6 pieces
What is the equation in standard form of the line that passes through the point (1, 24) and has a slope of -0.6.
Answer:
y= -0.6x + 123/5
Step-by-step explanation:
Start with the slope.
Given the slope is -0.6, the equation must be in the form of y=-0.6x+b, where b is the y-intercept.
Now, substitute your values of a and b inside the equation. 24=-0.6+b. given this, b=24.6, which is 123/5.
The function c=3x-y is minimized at the vertex point of the feasible region at (4,5). What is the minimum value
(x,y)=(4,5)
c = 3x-y = 3(4) - 5 = 7
Answer: 7
Final answer:
The minimum value of the function c=3x-y at the vertex point (4,5) of the feasible region is 7.
Explanation:
The question provided by the student involves finding the minimum value of a function of two variables, given by c=3x-y, at a certain point in the feasible region. Since the minimum is achieved at the vertex point (4,5), we can directly substitute these values into the function to find the minimum value.
To calculate the minimum value of the function c=3x-y at the point (4,5), we substitute x=4 and y=5 into the equation:
c = 3×4 - 5
c = 12 - 5
c = 7
Therefore, the minimum value of the function is 7 at the vertex point (4,5).