By using the ASA Congruence Theorem, Delta PQR is congruent to Delta TSR.
We can prove this by using the fact that triangle PQR and triangle TSR are both right triangles and that R is the midpoint of overline PT and overline PQ is congruent to overline TS. Since R is the midpoint of overline PT, it follows that overline PR is congruent to overline TR (by the midpoint theorem).
Since PQR is a right triangle, and R is the right angle, it follows that angle PQR is congruent to angle TSR (by the definition of a right angle). Since overline PQ is congruent to overline TS, it follows that angle PQS is congruent to angle TSR (by the definition of congruence). Together, these congruences imply that triangle PQR is congruent to triangle TSR by the ASA congruence theorem.
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Given that y varies indirectly as x and that x = 15 when y = 3, then the value of k is
Answer:
Step-by-step explanation:
the equation of this function has the form y = k/x, and when x = 15 and y = 3, the value of k can be calculated as follows:
3 = k/15, or (by multiplying both sides by 15) k = 45
Then y = 45/x
PLEASE HELP DUE IN 1 HOUR, AND PLEASE DON'T PUT THOSE LINKS OR ELSE I WILL REPORT YOU.
Answer:
h ≤ 16
Step-by-step explanation:
If he plans to cook 16 of less hotdogs, h is going to be equal to or less than 16. The circle is closed because he could cook 16.
Answer:
For the first question it would be answer 4
Since they ask you "at most 16 hot dogs," that means that it has to be less than or equal to 16.
For the second question, you would put the endpoint on 16 and make the arrow going left.
Use a calculator to simplify: N (-8 - 92.5) / -32
Answer:
3.14
Step-by-step explanation:
-8 - 92.5 = -100.5, and then -100.5/(-32) = 3.14
Alternatively, type in (-8 -92.5)/(-32)
Pete borrowed $400 for one year. He paid back a total of $440. What was the interest rate per year?
A cylindrical water tank of height 4 m is used to fill containers with dimensions 20 cm X 30 cm X 50 cm. If the tank can fill exactly 200 of these containers, find its base radius. (Take Pi = 3.14)
Answer:
0.35cm
Step-by-step explanation:
Step 1
We find the volume of the container.
The formula = Length × Width × Height
Length = 20cm
Width = 30cm
Height = 50cm
The volume of the tank = 20cm × 30cm × 50cm
= 30000 cm³
Step 2
We are told that:
The tank can fill exactly 200 of these containers
We have to find the volume that 1 cylinder will contain
Hence,
200 containers = 30000 cm³
1 container = x
Cross Multiply
200 × x = 30000cm³
x = 30000cm³/200
x = 150cm³
Step 3
We find the base radius of the cylindrical tank
Height = 4m
Convert to cm
1m = 100cm
4m = x
Cross Multiply
x = 4 × 100cm = 400cm
Volume of the cylinder = πr²h
Radius = √V/πh
Radius = √150/π × 400
Radius = 0.35 cm
Therefore, base radius = 0.35cm
A construction company plans to lean a 15ft ladder against a building from 7ft away. How far up the building will if reach?
Answer:
8 Feet
Step-by-step explanation:
15 feet subtract 7 feet is 8 feet
What is the modulus of 2 - 3i?
Oi
O √√√5
O
1-√√5
O√13
The modulus of 2 - 3i is √13. So, the correct option is d.
What is modulus?Modulus is a mathematical operation used to find the remainder when dividing two numbers. This is called a percent sign (%) and is represented by a single number such as 12. Used to determine if two numbers are divisible (no remainder). You can also use the modulus to compare two numbers to see which is greater or lesser. Additionally, this module can be used to calculate the distance between two points on the coordinate plane.
It is computed by taking the square root of the sum of the squares of the real and imaginary components, so √(2^2 + (-3)^2) = √13. The modulus of a complex number, also called absolute value, is a measure of distance from the origin.
Let z = -2 - 3i
z = (-2) + (-3)i
Modulus of z = √((-2)² + (-3)²)
√(4 + 9) = √13
Modulus of z = √13
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Change the following mixed numbers to improper fractions
a) 4 3/8 b) 2 1/3 c) 5 2/5
Answer:
A.35/8
B.7/3
C.27/5
those r the improper fractions of the mixed fractions
Someone help me out my grade are bad
Answer:
-26Step-by-step explanation:
x - 4y =
-2 - (6 x 4) =
-2 - (24) =
-2 - 24 =
-26
Hope that helps! :)
-Aphrodite
For what value of k the given equation 4 K X² 2k 4 x+ 8k+ 1 0 is a perfect square?
For k=0 or k=3, the given equation will be a perfect square.
Note: we are taking the equation to be: (4−k) X^2+(2k+4) x+8k+1=0
Taking,
(4−k) X2+(2k+4) x+8k+1=0
Here, a=4+k, b=2k+4, c=8k+1
The given equation will be a perfect square, When D= 0
We know, D = b^2−4ac [A perfect square trinomial is an expression that can be generated from the square of a binomial equation. If an equation has the formula ax^2 + bx + c and meets the requirement b^2 = 4ac, it is referred to as a perfect square trinomial. The formula for the perfect square has the following variations: ax2 + 2abx + b2 = (ax + b). When b^2 = 4ac, we know that an equation is a perfect square.]
b2−4ac=0
(2k+4)2−4(4−k) (8k+1) =0
4k2+16+16k−4(32k−8k2+4−k) =0
K2+4+4k−32k+8k2−4+k=0
9k2−27k = 0
K2−3k = 0
k(k−3) =0
k=0 or k=3
Hence for k=0 or k=3, the given equation will be a perfect square.
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The population of a town is 20,000. It decreases at a rate of 9% per year. In about how many years will the population be fewer than 13 2007
In 5 years the population will be fewer than 13000.
What is percentage ?
A percentage is a figure or ratio stated as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent symbol, "%," is frequently used to indicate it. A % is a number without dimensions and without a standard measurement.
In essence, percentages are fractions with a 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. Percentage, a relative value showing hundredth parts of any amount, is a relative measure that indicates how many questions on a test you correctly answered out of 100 (75/100). Since one percent (symbolized as 1%) is equal to one hundredth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified percentage.
20000( 1 - 9% )^5
≈ 12481
12481 < 13000
ie 5 years
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The measurement of angle DBE is 0.1x-33 and the measurement of angle CBE is 0.3x-39 what's the value of x
Answer:
x = 405
Step-by-step explanation:
DBE is 0.1x-33 and the measurement of angle CBE is
The sum of both angles form a right angled triangle ;
DBE + CBE = DBC
DBC = RIGHT angled triangle = 90°
(0.1x-33) + (0.3x - 39) = 90°
0.1x - 33 + 0.3x - 39 = 90°
0.1x + 0.3x - 33 - 39 = 90
0.4x - 72 = 90
0.4x = 90 + 72
0.4x = 162
x = 162 / 0.4
x = 405
Factor completely.
6y^2 — 30y
Answer:
6y² - 30y= 6y (y-5)
Step-by-step explanation:
Write the number 100 as a product of its prime factors in the same way,
Write the factors in order, from smallest to largest.
Answer:
100 = 4×25
= 1×2×2×5×5
.......
The difference between ( -7×-7) + -(7×7) is
A)98. B)28
C)0. D)-28
To find the difference between (-7*-7) + -(7*7), we first need to calculate the values of each expression.
(-7*-7) = 77 = 49
-(77) = -49
The difference between these two values is 49 - (-49) = 49 + 49 = 98.
Therefore, the answer is A) 98.
The Correct answer is Option (A) = 98.
We need to determine the value of each part and calculate their difference. after that.
Here, (-7*-7)= 49
and, -(7*7) = -49
Now, their difference is to be calculated as follows:
=49 - (-49)
= 49+ 49
= 98.
So, the answer is 98.
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please help quickly
The polygons are similar. x = ___ Write your answer as a decimal
By using the fact that the two images are similar, we can write and solve a linear equation to get x = 3/2.
How to find the value of x?We know that the two figures are similar, then, if we take the quotient between the adjacent sides for both figures, these quotients should give the same value.
Thus, we can write the equation:
14/10 = (x + 9)/(x + 6)
Now we can solve that equation for x, if we multiply both sides by (x + 6) we will get:
(14/10)*(x + 6) = x + 9
Now we can multiply both sides by 10 to get:
14*(x + 6) = 10*(x + 9)
14x + 84 = 10x + 90
Now we can solve this linear equation for x.
14x - 10x = 90 - 84
4x = 6
x = 6/4
x = 3/2
That is the value of x.
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Combine the like terms to create an equivalent expression: 5n + 6 +(-7n) - 9
Answer:
-2n - 3
Step-by-step explanation:
5n + 6 + (-7n) - 9
5n + 6 - 7n - 9
5n - 7n + 6 - 9
-2n - 3
Given square ABCD, what is the length of AD?
What is the perimeter?
Help plz...And No links!! I repeat No links!!
Answer:
36mm
Step-by-step explanation:
12^2 + 9^2 = c^2
144 + 81 = c^2
225 = c^2
[tex]\sqrt{225}[/tex] = 15
c = 15mm
12+9+15 = 36
4 of 7
June rolls a fair dice 234 times.
How many times would June expect to roll a one?
Answer: 39 times
Step-by-step explanation: A fair dice has 6 sides with each side having a different number between 1 and 6. Therefore, the probability of rolling a 1 is 1/6. To find out how many times June would expect to roll a 1 after rolling the dice 234 times, you must multiply 234 by 1/6 to get the answer of 39.
HELP MEEEEEEEE PLEASEEEEEEEE
Answer: 75p
Step-by-step explanation:
So, if one kilogram of bacon is £1.50, then half a kilogram would cost half of that, so 75p
jaxon is ordering a taxi from an online service. the taxi charger 4$ just for the pickup and then an additional $0.75 per mile driven. how much would a taxi ride cost that is m miles long?
Answer:
i think you asking for a equation if so here
hope it helps brainiest?
Step-by-step explanation:
x=total cost
x=0.75m+4
Please help! No links! Thanks!!
Answer: 30
Step-by-step explanation:
3 times 2 is 6 and divided by 2 is 3 and 3 times 10 is 30
Which point represents the value of –(–2) on the number line?
A number line has points A, negative 3, B, blank, 0, blank, C, 3, D.
Point A
Point B
Point C
Point D
The point that is -2 on the number line is point B. Option B
What is the number line?We know that the number line can be taken as a representation of the numbers. We ought to know that the numbers that we find on the number line are the numbers that are increasing to the right as shown.
In the question that we have, the task that is before us is that we should be able to locate the point on the number line that has been labelled as -2 on this the point B non the line. This is the point that is read off as -2.
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PLSSSSS HELP ME PLSSSSS I NEED TO EXPLAIN
Joules and calories are two different units of energy. The equation j=0. 239c relates the measures, where c stands for calories and j stands for joules. Complete the table
To complete the table, we can simply multiply the number of calories by 0.239 to find the equivalent amount of Joules.
The equation relates Joules to calories as j = 0.239c, where c stands for calories and j stands for joules. For example, 1 calorie is equal to 0.239 Joules, 2 calories is equal to 0.478 Joules, and so on.
Joules (j) Calories (c)
0.239c 1
0.478c 2
0.717c 3
0.956c 4
1.195c 5
1.434c 6
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The auditorium seated 375, but this was enough for only 30% of those who wanted a seat. How many wanted a seat but couldn't get one?
Answer: 875 people
Step-by-step explanation:
The 375 people seated represent 30% of the total number of people who wanted seats but these ones got them.
This means that the number of people who wanted seats is 70% of the number of people who wanted seats.
Assume the number of people who wanted seats is x:
30% * x = 375
x = 375 / 30%
x = 1,250 people wanted seats.
Those who wanted seats but couldn't get:
= 1,250 * 70%
= 875 people
I need help plz no links
Answer:
Step-by-step explanation:
5x+8+6x-6=90
11x+2=90
11x=88
x=8
angle BOC = 6x-6 = 48-6 = 42 degrees
PLS HELP ASAP 50 POINTS!!!!
Triangle ABC is congruent to triangle PDF. Dude AC corresponds to what side in triangle PDF
Answer:
PF
Step-by-step explanation:
Since the triangles are congruent, meaning they are the same shape, we can just match the lines between the two triangles. In triangle ABC, the line AC is the hypotenuse of the triangle. So, we need to find the hypotenuse of the triangle PDF. Looking, we can see the hypotenuse of the triangle PDF is the line, or side, PF.
Hope this helped!
In the right triangle shown, mZA = 45° and AB = 12.
B
12
45
How long is BC?
Answer:
6sqrt(2)=8.5
Step-by-step explanation:
Using pythagoras theorem
The measure of BC is 8.486 unit.
What is Trigonometry?Trigonometry is the branch of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six popular trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and acronyms (csc).
Given angle is 45 degree.
Hypotenuse = 12 unit
Now, using Trigonometry
sin 45 = P/ H
sin 45 = BC / 12
0.707 = x/ 12
x = 8.486 unit
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