In order to determine whether P is a right angle, we will apply the Pytyhagoras theorem.
The formula is,
\(\text{Hypotenuse}^2=Opposite^2+Adjacent^2\)where,
\(\begin{gathered} Hypotenuse=QR=29inches \\ \text{Opposite}=PR=21\text{inches} \\ \text{Adjacent}=PQ=20\text{inches} \end{gathered}\)Therefore,
\(29^2=21^2+20^2\)Simplify
\(\begin{gathered} 841=400+441 \\ 841=841 \end{gathered}\)Hence, the correct answer is
\(20^2+21^2=29^2\text{ (OPTION 4)}\)Use the quadratic formula to solve the equation.
-X^2+7x=8
Answer:
\( x = \frac{ - ( - 7) + - \sqrt{( - 7) {}^{2} } - 4 \times 1 \times 8}{ 2 \times 1} \)
\(x = \frac{7 + - \sqrt {49 - 32} }{ 2} \)
\( x = \frac{ 7 + - \sqrt{17} }{2} \)
\(x 1= \frac{7 + \sqrt{17} }{2} \)
\(x 2= \frac{ 7 - \sqrt{17} }{2} \)
Use the relationship represented in this Venn diagram to identify the true statement.
A. All trapezoids are rhombuses
B. All rhombuses are trapezoids
C. No trapezoids are rhombuses
D. No rhombuses are trapezoids
The true statement based on the relationship depicted in the Venn diagram is that no rhombuses are trapezoids (option D).
To identify the true statement using the relationship represented in the Venn diagram, we need to analyze the overlapping regions and the properties of the shapes involved.
A trapezoid is a quadrilateral with at least one pair of parallel sides, while a rhombus is a quadrilateral with all sides of equal length. Let's evaluate the options:
A. All trapezoids are rhombuses: This statement is not true based on the diagram. The overlapping region between the trapezoids and rhombuses shows that there are trapezoids that are not rhombuses. Therefore, option A is incorrect.
B. All rhombuses are trapezoids: This statement is true based on the diagram. The entire region representing rhombuses is also included within the region representing trapezoids. Every rhombus can be considered a trapezoid because it has at least one pair of parallel sides. Thus, option B is correct.
C. No trapezoids are rhombuses: This statement is not true based on the diagram. The overlapping region indicates that there are trapezoids that are indeed rhombuses. Therefore, option C is incorrect.
D. No rhombuses are trapezoids: This statement is true based on the diagram. There is no overlap between the regions representing rhombuses and trapezoids, implying that no rhombus can be considered a trapezoid. Hence, option D is correct.
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A farmer needs to fence a rectangular piece of land. She wants the length of the field to be 80 feet longer than the width. If she has 1080 feet of fencing material, what should be the length and width of the field?
The width of the field is 230 feet and the length is 310 feet.
Let's denote the width of the field as "x" feet.
The length of the field is 80 feet longer than the width, so it can be represented as "x + 80" feet.
To find the total amount of fencing material needed, we sum up the lengths of all four sides of the rectangular field:
2(length) + 2(width) = perimeter
Substituting the given values:
2(x + 80) + 2(x) = 1080
2x + 160 + 2x = 1080
4x + 160 = 1080
4x = 920
x = 920/4
x = 230
Therefore, the width of the field is 230 feet.
Now we can find the length by adding 80 feet to the width:
Length = Width + 80 = 230 + 80 = 310 feet.
So, the width of the field is 230 feet and the length is 310 feet.
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Question 4 of 17
Rewrite 50.82 : 1.1 to make the divisor a whole number. Select the answer
choice that shows the correct setup for long division and answer.
O A. 11)50.82 = 46.2
B. 11)508 2 = 42.6
O C. 11)508.2 = 46.2
D. 11)50.82 = 4.62
Help
Answer:
I think it is A OR D
solve [ 2x - 2 ] _> 6
x ≥ 4 which means that x must be greater than or equal to 4.
What is inequality?An Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.
Given inequality as :
⇒ 2x - 2 ≥ 6
Divided by 2 both sides of the inequality,
⇒ x - 1 ≥ 3
Add the 1 on both sides of the inequality,
⇒ x - 1 + 1 ≥ 3 + 1
⇒ x ≥ 4 or
⇒ x ∈ [4, ∞ )
So, the solution of 2x - 2 ≥ 6 is x ≥ 4
Therefore, x must be greater than or equal to 4.
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Can someone help awnser this
Answer:
A) Bicycle: Circumference: 188.4cm
Distance of 100 Turns: 18840cm
Diameter: 60
B) In-line skate: Circumference: 25.12cm
Distance of 100 Turns: 2512cm
Diameter: 8
C) Skateboard: Circumference: 15.7cm
Distance of 100 Turns: 1570cm
Diameter: 5
Step-by-step explanation:
The circumference would be one turn. So, you simply multiply the circumferences by 100.
A) 188.4 x 100 = 18840
B) 25.12 x 100 = 2512
C) 15.7 x 100 = 1570
What is the total weight of the bags that weighed /8 pound each?
The total weight of Rice that Mark buys is given as follows:
2.5 pounds.
How to obtain the total weight?The total weight of Rice that Mark buys is obtained applying the proportions in the context of the problem.
The weight of each bag is given as follows:
5/8 pounds = 0.625 pounds.
The number of bags is given as follows:
4 bags.
Hence the total weight of Rice that Mark buys is given as follows:
4 x 0.625 = 2.5 pounds.
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can someone help me please
Answer:
i think its b
Step-by-step explanation:
the 7th-grade class wants to collect empty soda pop cans to earn $50.00. If pop cans earn $0.25 per pound how many cans will they need to collect to earn the $50.00?
200 pounds need to collect to earn the $50.00. Divide the cost per pound from the total amount needed, \(\frac{50.00}{0.25}\)= 200 pounds.
Is the British pound?The official money of the U.k. and its regions is the GBP, or British pound sterling. The Pound is the earliest currency that is still accepted as legal tender in the entire world. The GBP, represented by pound sign (£), has one of the greatest trade volumes worldwide.
What makes something a "pound"?The development of the pounds sterling -The Latin word "libra," which means balance and weight, is where the name "pound sterling" comes from. During the years, the pound banknotes underwent various revisions before being initially printed by the Bank of England and over 300 years ago.
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The chart shows the ratio of water to pancake mix used in a pancake recipe.
Water Pancake Mix
29
4
7
13
?
O
21
2
How many cups of pancake mix are used with 1 cup of water?
(Write the answer as a fraction.)
Answer:
Doing the math, it should be 7.25/1
623-3=
What is 623 divided by 3
can somebody give me the answers to the whole thing please?
Find the value of (27) to the - 2/3
Answer: Yes. For example: (27)^2/3 would be 3^2 which = 9.
Step-by-step explanation: Hopefully this help :D ask for more help if you need!
helpppp meeeeee
Which expression represents the following statement? Add 8 to 6 times the quotient of 21 and 3.
6 x (21 ÷ 3) + 8
6 + 8 − (21 ÷ 3)
21 ÷ 3 − (8 + 6)
6 x (21 + 3) + 8
Answer:
(a) 6 x (21 ÷ 3) + 8
Step-by-step explanation:
The first step in translating English to math is to understand the English.
Parsing itThe quotient of 21 and 3 is written (21 ÷ 3). Six times that quotient is ...
6×(21÷3)
When 8 is added to this, it becomes ...
6 × (21 ÷ 3) + 8
Find the area of the circle, given the square has an area of 144 cm^2. Leave your answer in terms of pi.
A) 36pi cm^2
B) 24pi cm^2
C) 144pi cm^2
In the figure the area of circle is obtained as option C: 144π cm².
What is area?
An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure.
The area of the square is = 144 cm².
The formula for area of square is - (side)²
The equation is -
Area = (side)²
Substitute the value into the equation -
144 = (side)²
side = √144
side = 12 cm
The side of the square is the radius of the circle.
The area of circle is given as -
Area = πr²
Substitute the value into the equation -
Area = π(12)²
Area = 144π cm²
Therefore, the area of circle is 144π cm².
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Given: AAEB and ADFC, ABCD, AE || DF, EB || FC, AC = DB
Prove: AEAB AFDC
By proving that ΔEAB and ΔFDC have congruent corresponding angles and proportional corresponding sides, we can conclude that ΔEAB ≅ ΔFDC.
Proving that Triangles are EqualGiven:
- Triangle ΔAEB and ΔDFC
- Line ABCD is straight (implies AC and BD are collinear)
- AE is parallel to DF
- EB is parallel to FC
- AC = DB
To prove: ΔEAB ≅ ΔFDC
Recall that:
AE || DF
EB || FC
AC = DB
AE || DF, EB || FC (Parallel lines with transversal line AB)
Corresponding angles are congruent:
∠AEB = ∠DFC (Corresponding angles)
∠EAB = ∠FDC (Corresponding angles)
Corresponding sides are proportional:
AE/DF = EB/FC (Corresponding sides)
AC/DB = BC/DC (Corresponding sides)
AC = DB
BC = DC (Equal ratios)
ΔEAB ≅ ΔFDC (By angle-side-angle (ASA) congruence)
∠EAB = ∠FDC
∠AEB = ∠DFC
AC = DB, BC = DC
Therefore, by proving that ΔEAB and ΔFDC have congruent corresponding angles and proportional corresponding sides, we can conclude that ΔEAB ≅ ΔFDC.
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A family is planning their vacation to Disney World. They will drive from a small town outside New Orleans,
Louisiana, to Orlando, Florida, a distance of 700 miles. They plan to average a rate of 55 mph. How long will this
trip take?
The time taken for the trip will be 12.7 hours.
How to calculate the value?It should be noted that time taken is calculated as:
Time = Distance / Speed
Distance = 700 miles
Speed = 55 mph
Time = 700/55
Time = 12.7 hours.
Therefore, the time taken for the trip will be 12.7 hours.
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A line with a slope of 5 passes through the point (6, 12). Write the equation for this line.
Step-by-step explanation:
Hi have a great day!! This is our answer. If it is wrong, apologies from our side.
Suppose that the functions p and q are defined as follows.
p(x)=x² +6
q (x)=√x+9
Find the following.
(pg) (7) =
(9 °p) (7) = [
X
0/0
5
Answer:
Step-by-step explanation:
Xavier is buying fencing to surround his garden if his garden has a perimeter of 30 yards and fencing cost six dollars a yard how much money will he need for the fencing
Answer:
$180
Step-by-step explanation:
If the perimeter is 30 yards and each yard costs $6 you times 30 and 6 and you get $180
Elijah's puppy weighs 35 ounces if he weighed 19 ounces at the last visit to the veterinarian's office what is the percent increase in the puppy's weight rounded to the nearest whole number
Answer:
To find the percent increase in the puppy's weight, we can use the formula:
% increase = ((current value - initial value) / initial value) * 100
% increase = ((35 - 19) / 19) * 100
% increase = (16 / 19) * 100
% increase = 84.21%
So, Elijah's puppy has increased 84.21% in weight. Rounded to the nearest whole number is 84%.
Step-by-step explanation:
Complete the model to find-9 + 3 Show your work
Answer:
Answer is 0. If you have to owe someone 9 dollars and they give you nine back it is 0. You can also rearrange the problem to 9-9 (same thing) which is 0
Bridget has 13 gallons of gasoline to use for her lawnmowing business. She uses gasoline in the lawnmower at a consistent rate. Let X represent the number of lines mode and Y represent the amount of gasoline remaining. Look at the graph of the function construct the function for this scenario.
The linear function that models this scenario is given as follows:
y = -0.25x + 13.
How to define the linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
The slope m represents the rate of change.The intercept b represents the initial amount.Bridget has 13 gallons of gasoline to use for her lawnmowing business, hence the intercept b is given as follows:
b = 13.
From the graph, when x increases by 20, y decays by 5, hence the slope m is given as follows:
m = -5/20
m = -0.25.
Hence the function is given as follows:
y = -0.25x + 13.
Missing InformationThe problem is given by the image presented at the end of the answer.
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Can someone please explain what this is?! None of my parents understand it and neither do I!
Answer:
given below
Step-by-step explanation:
the column if multiplied shall give 12 as product. two sides are given.
multiply the given ones and divide it by 12.
What is the area of the composite figure?
O 262 cm2
O 264 cm2
O 266 cm
O 268 cm2
5.
20 am
Answer:
B: 264 cm squared
Step-by-step explanation:
got it right
We can write the volume of the cylinder as 48π cubic feet.
What is Area?Area is a collection of two - dimensional points enclosed by a single dimensional line. Mathematically, we can write -
V = ∫∫F(x, y) dx dy
Given is to find the area of the given composite figure.
It is given to find the area of the given composite figure. We can write the area of the figure as -
Area = Area of square + Area of trapezoid + Area of rectangle
Area = {side x side} + {1/2(a + b) x h} + {L x B}
Area = {10 x 10} + {1/2(14 + 8) x 4} + {20 x 6}
Area = 100 + 44 + 120
Area = 264 square centimeter
So, it can be concluded that the area of the figure is 264 square centimeter.
Therefore, we can write the the area of the figure is 264 square centimeter.
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need help with this one
Answer:
triangle 2.854e55
Step-by-step explanation:
A bag contains 10 green,8 blue, and 2 white balls. Naomi seclets 2 balls from the bag at random, one at a time, without replacing them. What is the probability that she selects all two white balls?
E.) 2/95
F.) 1/95
G.) 1/190
H.) 1/380
To find the probability that Naomi selects both white balls, we need to consider the total number of possible outcomes and the number of favorable outcomes.
Total number of outcomes:
Naomi selects 2 balls without replacement, so the total number of outcomes is the number of ways she can choose 2 balls out of the total number of balls in the bag. This can be calculated using combinations:
Total outcomes = C(20, 2) = (20!)/(2!(20-2)!) = (20 * 19)/(2 * 1) = 190
Number of favorable outcomes:
Naomi needs to select 2 white balls. There are 2 white balls in the bag, so the number of favorable outcomes is the number of ways she can choose 2 white balls out of the 2 white balls in the bag:
Favorable outcomes = C(2, 2) = 1
Probability = Favorable outcomes / Total outcomes = 1/190
Therefore, the correct answer is (G) 1/190.
NEED HELP ASAP!
Samantha says that 5x and 5y are like terms. Is she correct? Explain.
Answer:
No
Step-by-step explanation:
They are not because since 5 is being multiplied by x, that is not the same thing as 5 being multiplied by y. Don't get confused by the 5. Have a wonderful day! <3
please help me with this !
9514 1404 393
Answer:
(a) 30%
Step-by-step explanation:
The number in the section marked "car" is 15.
The total of the numbers in all sections is (working CW) ...
15 + 10 + 5 + 20 = 50
Then the fraction that come by car is ...
car/total = ...
15/50 = 30/100 = 30%
10% of what number is 3005% of what number is 72
1)
Given that 10 % of a number is 300.
Let x be the required number.
\(10\text{\% of x is 300}\)\(10\text{\% }\times x=\text{ 300}\)\(\frac{10}{100}\times x=\text{ 300}\)\(\frac{1}{10}\times x=\text{ 300}\)Multiplying 10 on both sides, we get
\(\frac{1}{10}\times x\times10=300\times10\)\(x=3000\)Hence 10 % of 3000 is 300.
2)
Given that 5 % of a number is 72.
Let x be the required number.
\(5\text{\% of x is 7}2\)\(5\text{\% }\times x=\text{ 7}2\)\(\frac{5}{100}\times x=72\)\(\frac{1}{20}\times x=72\)Multiplying 20 on both sides, we get
\(\frac{1}{20}\times x\times20=72\times20\)\(x=1440\)Hence 5% of 1440 is 72.