The lengths of the sides corresponding to DE and DF in triangle ABC are 3.75cm and 5cm respectively as triangles DEF and ABC are similar and their sides are in proportion.
Explanation:Since triangles DEF and ABC are similar, then their corresponding side lengths are proportional. This means the ratio of the lengths of corresponding sides in both triangles remains constant.
Therefore, the lengths of the corresponding sides in triangle ABC will be in the same ratio as that of the sides in triangle DEF. Since we know the lengths of sides DE and DF in triangle DEF are 6cm and 8cm respectively, we can conclude that the lengths of the sides corresponding to DE and DF in triangle ABC will be in the same ratio as 6 and 8.
The ratio of 6 and 8 can be simplified to 3:4. Therefore, given that the length of side EF in triangle ABC is 5cm, we can apply cross-multiplication to find the lengths of the other sides. For example, using the ratio 3:4 to find the length corresponding to DE in triangle ABC, we would get 5/4 * 3 = 3.75cm. Similarly, "for DF we would get 5/4 * 4 = 5cm".
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The lengths of sides DE and DF in triangle DEF are 6 cm and 8 cm, respectively.
Since triangle DEF is similar to triangle ABC, the corresponding sides of both triangles are proportional. This means that the ratio of any two corresponding sides in the two triangles will be the same. Let's denote the lengths of the corresponding sides in triangle ABC as follows: side AB corresponds to DE, side BC corresponds to EF, and side AC corresponds to DF.
Given that EF is 5 cm, we can set up the following proportion using the corresponding sides of the two triangles:
[tex]\[\frac{DE}{AB} = \frac{EF}{BC} = \frac{DF}{AC}\][/tex]
We know the lengths of DE and DF, so we can express the lengths of AB and AC in terms of the lengths of DE and DF, using the proportion:
[tex]\[\frac{6}{AB} = \frac{5}{BC} = \frac{8}{AC}\][/tex]
From the proportion, we can solve for AB and AC:
[tex]\[AB = \frac{6}{5} \times BC\][/tex]
[tex]\[AC = \frac{8}{5} \times BC\][/tex]
Since we do not have the actual length of BC, we cannot determine the exact lengths of AB and AC. However, we can express them in terms of BC, the corresponding side in triangle ABC. If BC is known, we can simply multiply it by the respective ratios to find AB and AC.
In conclusion, the lengths of sides DE and DF in triangle DEF are 6 cm and 8 cm, respectively, and the lengths of the corresponding sides AB and AC in triangle ABC can be calculated once the length of BC is known, using the ratios derived from the similarity of the triangles.
Which of these four sets of side lengths will form a right triangle? Set 1 6 cm, 7 cm, StartRoot 12 EndRoot cm Set 2 8 in., StartRoot 29 EndRoot in., StartRoot 35 EndRoot in. Set 3 StartRoot 3 EndRoot mm, 4 mm, StartRoot 5 EndRoot mm Set 4 9 ft, StartRoot 26 EndRoot ft, 6 ft Set 1 Set 2 Set 3 Set 4
Answer:
16 cm,7cm, start root 12.
15 subtracted from the product of a number and 4 is -59. Just write equation do not solve please
Answer:
15-x+4=-59
Step-by-step explanation:
The equation of 15 subtracted from the product of a number and 4 is -59 is 4x - 15 = -59.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that 15 is subtracted from the product of a number and 4 is -59. The expression will be written by assuming that the unknown number is x.
The expression is written as,
4x - 15 = -59
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Y = 3x +5
Y = 4x - 2
What is Y?
a hatchling turtle has a shell with a 1-inch diameter. the shell keeps a similar shape as the turtle grows. compare the volume and surface area of the hatchling's shell to the shell when it's diameter is 4 inches
Comparing a hatchling turtle's shell of 1-inch diameter to a 4-inch diameter shell reveals that the volume increases by a factor of about 64, while the surface area only increases by about 16. This difference is due to the way volume and surface area are calculated, with the radius being cubed in the volume formula and squared in the surface area formula.
Explanation:The volume of a sphere (like the turtle's shell) is given by the formula: V = (4/3) * π * r³, and the surface area by A = 4 * π * r², where r is its radius. If a hatchling turtle's shell has a 1-inch diameter, it has a radius of 0.5-inches. If as the turtle grows, its diameter expands to 4-inches, then the radius will be 2-inches. As the radius in each formula is cubed in the volume formula and squared in the surface area formula, the volume will increase far more rapidly than the surface area.
For the smaller turtle, V = (4/3)*π*(0.5)³ = 0.52 cubic inches and A = 4*π*(0.5)² = 3.14 square inches. For the larger turtle, V = (4/3)*π*(2)³ = 33.51 cubic inches and A = 4*π*(2)² = 50.27 square inches. Comparing, the volume increases by a factor of 64 (33.51/0.52) whereas the surface area increases by a factor of roughly 16 (50.27/3.14). This shows that although the turtle's shell maintains the same shape as it grows, the volume increases significantly more than the surface area.
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For Sue’s party, her family rented a bouncy house for $150 plus $2 per child, c.
(1) Write an expression that represents the total cost of the bouncy house for c children to jump.
(2) A total of 15 children attended Sue’s party, including Sue. What was the total cost?
For Sue’s party, her family rented a bouncy house for $150 plus $2 per child, c.
(1) Write an expression that represents the total cost of the bouncy house for c children to jump.
(2) A total of 15 children attended Sue’s party, including Sue. What was the total cost?
For Sue’s party, her family rented a bouncy house for $150 plus $2 per child, c.
(1) Write an expression that represents the total cost of the bouncy house for c children to jump.
(2) A total of 15 children attended Sue’s party, including Sue. What was the total cost?
vFor Sue’s party, her family rented a bouncy house for $150 plus $2 per child, c.
(1) Write an expression that represents the total cost of the bouncy house for c children to jump.
(2) A total of 15 children attended Sue’s party, including Sue. What was the total cost?
For Sue’s party, her family rented a bouncy house for $150 plus $2 per child, c.
(1) Write an expression that represents the total cost of the bouncy house for c children to jump.
(2) A total of 15 children attended Sue’s party, including Sue. What was the total cost?
For Sue’s party, her family rented a bouncy house for $150 plus $2 per child, c.
(1) Write an expression that represents the total cost of the bouncy house for c children to jump.
(2) A total of 15 children attended Sue’s party, including Sue. What was the total cost?
For Sue’s party, her family rented a bouncy house for $150 plus $2 per child, c.
(1) Write an expression that represents the total cost of the bouncy house for c children to jump.
(2) A total of 15 children attended Sue’s party, including Sue. What was the total cost?
vFor Sue’s party, her family rented a bouncy house for $150 plus $2 per child, c.
(1) Write an expression that represents the total cost of the bouncy house for c children to jump.
(2) A total of 15 children attended Sue’s party, including Sue. What was the total cost?
For Sue’s party, her family rented a bouncy house for $150 plus $2 per child, c.
(1) Write an expression that represents the total cost of the bouncy house for c children to jump.
(2) A total of 15 children attended Sue’s party, including Sue. What was the total cost?
v85g5c
1) The expression that represents the total cost of the bouncy house for c children is:Total Cost} = 150 + 2c 2) The total cost for the bouncy house for 15 children is $180.
(1) The expression that represents the total cost of the bouncy house for c children is given by: Total Cost} = 150 + 2c
(2) Given that a total of 15 children attended Sue’s party, including Sue, substitute c with 15 in the expression:
Total Cost} = 150 + 2 * 15
Total Cost} = 150 + 30
Total Cost} = 180
Therefore, the total cost for the bouncy house for 15 children is $180.
area is 20 square units. the length is 4 more than 3 time the width. find the dimension
Write the formula and answer SHOW ALL WORK!
starts with 20 smthing x3 +4 = 20 but what is it ???? hmmmm if you think more you can fiqure it out by just finding random numbers so use ur brain i guess???
Answer:
width: 2
length: 10
Step-by-step explanation:
L = 3W + 4
A = LW = (3W + 4) x W
= 3w² +4w
3w² + 4w = 20
3w² + 4w -20 = 0
(w - 2) (3w + 10) = 0
w = 2 or w = - 10/3 (width is positive) ∴ width = 2
length = 3 x 2 + 4 = 10
New car sales for $25,000 the value of the car decreases by 15% each year what is the approximate value of the car five years after it is purchased
Answer:
approximately $18,984
Step-by-step explanation:
so 15% multiplied by 5 is 75%
25,000 multiplied by .75 is 18,750
3. Roberto wants to reduce a drawing that is 12 inches long by 9 inches wide. If his new drawing is 8 inches long, how wide will it be?
Answer:5 inches wide
Step-by-step explanation:
12-8 (long)=4
9-4 (getting the new drawings length so you subtract)=5
Consider the exponential function f(x) = 2(3)x and its
graph.
Answer:
initial value = 2
base = 3
this function is exponential growth
Step-by-step explanation:
The formula for exponential functions is [tex]f(x) = ab^{x}[/tex]
a = initial value
b = the constant/change factor/fixed base value
x = independent variable
if the function approaches (∞ , ∞) it is positive
Dan and Luck are running in a 20 mile charity benefit race. If Dan runs at 3 mph and Luke runs at 4 mph, how long until their total mileage equals 20 miles?
Answer:
one-fifth of $1,000 is $200; a donation of $30 per charity results in a total of $240 in 1. 32 1/2 2. 30 3. Dan went first and dug 1/9 of the total distance early the next morning.
Step-by-step explanation:
Solve for d.
4d - 4 = 5d - 8
Answer:
Step-by-step explanation:
4d-4=5d-8
add 4 to both sides
4d=5d-4
subtract 5d from both sides
-d=-4
switch so d is positive
d=4
Answer: d = 4
Step-by-step explanation:
4d - 4 = 5d - 8
+8 +8 (Add 8 to both sides)
4d + 4 = 5d
-4d -4d (Subtract 4d from both side)
d= 4
The scale of a map is 1 inch : 10 miles. On the map, Main Street is 0.6 inch long. What is the actual length of Main Street?
A. 6 in.
B. 60 in.
C. 6 mi.
D. 60 mi.
Answer:
option C. 6 mi.
Step-by-step explanation:
Which number is equivalent to -(-2)?
Answer:
2
Step-by-step explanation:
negative times a negative is a positive
In mathematics, a double negative gives a positive result. Therefore, -(-2) equals 2, so the number equivalent to -(-2) is 2.
Explanation:In Mathematics domain, the double negative rule states that the 'negative of a negative is a positive'. It suggests that if you have two negative signs, one turns the other into a positive. So, -(-2) is equals to +2. In simpler terms, if you have a negative number and you negate it, you get the positive version of that number. Therefore, the number that is equivalent to -(-2) is 2
.
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Solve the following linear system of equations using substitution.
y = 3x - 5
y = 2x - 6
A. (3,2)
B. (-5,-6)
C. (-1,-8)
D. (1,-2)
Answer:
Step-by-step explanation:
since both equations are equal to the same thing, y, they are therefore equal to each other
so:
[tex]3x-5=2x-6\\x-5=-6\\x=-1\\[/tex]
substitute x, -1, into either equation to solve for y
[tex]y=3(-1)-5\\y=-3-5\\y=-8[/tex]
or
[tex]y=2(-1)-6\\y=-2-6\\y=-8[/tex]
Therefore, the solution is (-1,-8)
After solving the equations by substitution method the value of x is -1 and the value of y is -8. Hence, option C is correct.
What is an equation?Equations are mathematical expressions that have two algebras on either side of an equal (=) sign. The expressions on the left and right are shown to be equal to one another, demonstrating this relationship. L.H.S. = R.H.S. (left-hand side = right side) is a fundamental simple equation.
As per the given equation from the question,
y = 3x -5 (i)
y = 2x - 6 (ii)
Compare both equations,
3x - 5 = 2x - 6
3x -2x = -6 + 5
x = -1
Substitute x = -1 in equation (i)
y = 3 (-1) - 5
y = -8.
Therefore, both the values are (-1, -8).
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rule: y=x+3
HELPpppppp
Answer:
Step-by-step explanation:
when y=4
x=4-3=1
when y=8
x=8-3=5
when y=5
x=5-3=2
Answer:
[tex]\left[\begin{array}{ccc}x&y\\1&4\\5&8\\2&5\end{array}\right][/tex]
Step-by-step explanation:
x + 3 = y
1 + 3 = 4
5 + 3 = 8
2 + 3 = 5
brainliest?
Timmy drew a triangle that had a 95 degree angle and no congruent sides
Answer:
obtuse scalene triangle
Step-by-step explanation:
I think your question is missed of key information, allow me to add in and hope it will fit the original one.
Timmy drew a triangle with no cogruent sides and a 95° angle. Classify the triangle by the lengths of its sides and measures of its angles. Explain
My answer:
As we know that, the sum of 3 internal angles on a triangle is 180° . In the question, Timmy drew a triangle that had a 95 degree it means that sum of the other two angles is:
180° - 95° = 85 °
Futhurmore, no congruent sides
So his angle will be obtuse scalene triangle, you can have a look at the attached photo
what goes in the blanks
Step-by-step explanation:
2x² + x - 28
= 2x² + ( 8 - 7)x - 28
= 2x² + 8x - 7x - 28
= 2x ( x + 4) - 7( x + 4)
= (x + 4) (2x - 7)
Hope it will help you :)
Four graphs are shown below:
Which graph best shows the line of best fit?
Graph A
Graph B
Graph C
Graph D
Round to the nearest hundredth 4.644
Answer:
4.64
Step-by-step explanation:
the number that comes after the hundreth place(4) is less than 5 so you keep all of the other numbers the same
Find the scale factor of figure A to Figure B.
Answer:
Step-by-step explanation:
The scale factor from figure a to figure b would be 1/16 i believe.
Correct me if im wrong
The scale factor of figure A to figure B is 5/9.
In the given figure, A and B are similar triangles.
What is scale factor?A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).
The basic formula to find the scale factor of a figure is expressed as,
Scale factor = Dimensions of the new shape ÷ Dimensions of the original shape.
Here, 20/36
= 5/9
= 14/25.2
= 2/3.6
= 5/9
Hence, the scale factor of figure A to figure B is 5/9.
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When you declare a function?
Answer:
It is always recommended to declare a function before its use so that we don't see any surprises when the program is run
Step-by-step explanation:
2 more than triple a number is 10.
2 more than triple the number can be expressed as 3x + 2. We want this expression to equal 10, so we can set up the equation as 3x + 2 = 10.
To solve the equation, '2 more than triple a number is 10', we can first translate the sentence into an equation.
Let's assume the number is represented by x.
Triple the number would be 3x. And 2 more than triple the number can be expressed as 3x + 2.
We want this expression to equal 10, so we can set up the equation as follows:
3x + 2 = 10
Now, we can solve for x by isolating it on one side of the equation.
Subtracting 2 from both sides, we get:
3x = 8
Finally, divide both sides by 3 to solve for x:
x = 8/3
The probable question may be:
Formulate a complete mathematical question based on the statement: "2 more than triple a number is 10."
Damon buys lumber worth $562. He gets a 20% contractor’s discount. The sales
tax is 6%. His credit card gives him 2% off. How much does he pay?
*WILL MAKE BRAINLIEST*
which statement about these triangles is true?
a) The dilation is an enlargement.
b) The dilation is a reduction.
c) It is not a dilation.
d) There is not enough information.
Answer:
Not sure, but I would put A
Step-by-step explanation:
i am having a hard time with this page if someone can help me i will appreciate it a lot!!
Answer:
#1 is It could be another girl or it could be a boy
#2 is Its could be another boy or it could be a girl.
The diagram should look like this:
BB. BG
GB GG
#4 is 4
#5 is 1
#6 is there is 1/2 a change the baby can be a girl and a 1/2 change the baby can be a boy. For both of them to be girls; it would be 1/4 chance.
The inverse of G(x) is a function.
A. True
B. False
Answer:
this is false
Step-by-step explanation:
lines that curve can function but if the line that curves hit say "the y is twice it is not a function it is only a function if it does not hit a line twice" this isnt a function because it hits the y axis twice.
Error Analysis A gardener plans to extend the length of a rectangular garden by 7 feet. Let x represent the garden's original length. The expression 6 left parenthesis x plus 7 right parentheses represent the area of the garden, where 6 is the width, in feet, and left parenthesis x plus 7 right parentheses represent the extended length, in feet, of the garden. When asked for the area of the extended portion, the gardener incorrectly said it was 13 square feet. Expand the expression to find the area of the extension. Then describe an error the gardener might have made.
The gardener's expression correctly calculates the area of the entire garden after extension, not just the extension itself. The error was in misinterpreting the question and focusing solely on the extension, leading to the incorrect answer of 13 square feet.
Explanation:Expanding the expression: 6(x + 7) = 6x + 42. This represents the total area of the garden after extending its length by 7 feet.
Error analysis: The gardener likely assumed they needed to calculate the area added by the extension. This could be due to:
Misunderstanding the question and focusing on the 7-foot extension instead of the total area change.
Mistakenly interpreting "area of the extension" as the area of the rectangle formed only by the additional 7-foot length and the original width.
Therefore, while the expression itself is correct, the gardener misinterpreted the question and made an error in interpreting what "area of the extension" referred to.
VERY EASY!!! Find the domain of the graphed function.
Answer:
The answer is c
Step-by-step explanation:
Answer:c
Step-by-step explanation:
Which equation could be used to solve for the length of
XY?
OXY = (22)sin(41°)
O XY = (22)cos(419)
OXY = 22.
cos(41°)
O XY = 22
sin( 41°)
The expressions used to find XY is XY = 22/sin(41)
Trigonometric ratioTrigonometric ratio is used to show the relationship between the sides and angles of a right angled triangle.
Given triangle XYZ with side XY as the hypotenuse. Hence using trigonometric ratios:
sin(41) = 22 / XY
Making XY the subject of the equation:
XY = 22/sin(41)
The expressions used to find XY is XY = 22/sin(41)
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Answer:
D. XY = 22/ (sin) 41
Step-by-step explanation:
I did it on edge
Which type of correlation would you expect between a city's monthly temperature averages and precipitation totals? Why?
A)-1; strong negative correlation between the monthly temperature averages and the amount of precipitation.
B)0; relatively no correlation.
C).98; strong positive correlation between the monthly temperature and the amount of precipitation
D)1; strong positive correlation between the monthly temperature averages and the amount of precipitation
Answer:
B) 0; relatively no correlation.
Step-by-step explanation:
Data tends to not be collinear
The correct statement is,
D)1; strong positive correlation between the monthly temperature averages and the amount of precipitation.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Now, We get;
Based on the general understanding of climate trends, the correct correlation between a city's monthly temperature averages and precipitation totals would be;
⇒ strong positive correlation between the monthly temperature averages and the amount of precipitation.
because in warmer months, the air can hold more moisture, leading to more precipitation. In colder months, there is less moisture in the air, leading to less precipitation.
Thus, as the temperature increases, so does the amount of precipitation, resulting in a strong positive correlation.
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