Answer:
(C)Determine the principal square root of both sides of the equation.
Step-by-step explanation:
Given: Isosceles right triangle XYZ (45°–45°–90° triangle)
To Prove: In a 45°–45°–90° triangle, the hypotenuse is [tex]\sqrt{2}[/tex] times the length of each leg.
Proof:
[tex]\angle XYZ$ is 90^\circ$ and the other 2 angles are 45^\circ. \\\overline{XY} = a, \overline{YZ}= a, \overline{XZ}= c.\\[/tex]
Because triangle XYZ is a right triangle, the side lengths must satisfy the Pythagorean theorem, [tex]a^2 + b^2 = c^2[/tex]
Since a=b in an isosceles triangle:
[tex]a^2 + a^2 = c^2\\$Combining like terms\\2a^2 = c^2\\$Determine the principal square root of both sides of the equation.\\\sqrt{c^2}=\sqrt{2a^2} \\\\c=a\sqrt{2} \\[/tex]
Therefore, the next step is to Determine the principal square root of both sides of the equation.
Answer: C and hoped this helped and please mark as brainlest.
Please answer correctly !!!!!!!!! Will mark brainliest !!!!!!!!!!!!!!!
Answer:
(x-3)^2 = 4
Step-by-step explanation:
2 ( x-3) ^2 +6 = 14
Subtract 6 from each side
2(x-3)^2 = 8
Divide each side by 2
(x-3)^2 = 4
Take the square root of each side
x-3 = ±2
Add 3 to each side
x = 3±2
x =1 x = 5
A trapezoid has an area of 20 cm2 and a height z cm. The lengths of the parallel sides are (2z + 3) cm and (6z – 1) cm. Find the height, z, of the trapezoid. In your final answer, include all of the formulas and calculations necessary.
Answer: 2.11cm
Step-by-step explanation:
Given the following :
The lengths of the parallel sides are (2z + 3) cm and (6z – 1) cm
The area of trapezoid is calculated using the formula:
1/2(a + b) × h
Where ;
a = Length of side 1
b = length of side 2
h = height
Take a = (2z + 3) and b = (6z – 1), h = z
Therefore ;
1/2 (2z + 3 + 6z - 1) × z
Opening the bracket
(z + 1.5 + 3z - 0.5) × z
(4z + 1 ) × z = 20cm^2
4z^2 + z = 20cm^2
Using Quadratic formula:
4z^2 + z - 20 = 0
a = 4, b = 1, c = - 20
(-b±√b^2 -4ac) / 2a
Z = 2.11 or - 2.364
z cannot be negative, therefore,
Z = 2.11 cm
** FOR 30 POINTS**
what is the height of the triangular prism shown above?
Please answer correctly !!!! Will mark brianliest !!!!!!!!!
Answer:
(−8x+1)(x+2)
Step-by-step explanation:
Factor −8x2−15x+2
−8x2−15x+2
=(−8x+1)(x+2)
Apply the rule (-x, y - 2) to the following point, what is the result?
(-3, 5)
a. (-3, 7)
b. (3, 3)
c. (-5, -5)
d.(-5, 3)
(Please Help!!)
Which of these Nets can be folded into a cube.
Answer:
b
Step-by-step explanation:
I DID THIS !!
The Options 3rd and 4th are the correct options that be folded into a cube.
What is a cube?A cube is a three-dimensional representation of a square. it has 6 faces 2 on the bottom and top, 4 on the sides faces.
In the given figure of the cube, if we open up the formation then we get to know that only options 2nd and options 4th can be folded into a cube.
The third figure form a pyramid and 1st option could not able to make the cube when folded.
Learn more about cubes;
https://brainly.com/question/15420947
A cylindrical container with a radius of 6 cm and a height of 10 cm is filled with water to a depth of 6 cm. A sphere with a radius of 3 cm is placed at the bottom of the container.
a) What is the volume of the water to the nearest tenth?
b) What is the volume of the sphere to the nearest tenth?
c) How much higher does the water level rise in the container, to the nearest tenth, after the
sphere is placed inside?
Answer:
a. 452.4 cm³ to the nearest tenth b. 113.1 cm³ to the nearest tenth
c. 5.0 cm to the nearest tenth
Step-by-step explanation:
a. The volume of the water V₁ = πr²h since it is in a cylindrical container. r = 6 cm and h = 10 cm - 6 cm = 4 cm (since it is filled to a depth of 6 cm measuring from the top, so we have a height from the bottom of 10 cm - 6 cm = 4 cm).
So, V₁ = πr²h
= π × (6 cm)² × 4 cm
= 452.39 cm³
= 452.4 cm³ to the nearest tenth
b. The volume of the sphere V₂ = 4πr³/3 where r = radius of sphere = 3 cm.
V₂ = 4πr³/3
= 4π(3 cm)³/3
= 113.1 cm³ to the nearest tenth
c. When the sphere is placed in the container, the new volume of water in the container would be V = V₁ + V₂
So V = 452.4 cm³ + 113.1 cm³ = 565.5 cm³
Since the volume of water is still the volume of a cylinder, its height h is
h = V/πr²
= 565.5 cm³/π(6 cm)²
= 5.0 cm to the nearest tenth
WILL GIVE BRAINLIEST TO ANYONE WHO ANSWERS!!
Quadrilateral OPQR is inscribed inside a circle as shown below. What is the measure of angle P? You must show all work and calculations to receive credit. (10 points) Circle N is shown with an inscribed quadrilateral labeled OPQR. O is labeled 2x degrees. P is labeled y degrees. Q is labeled 2
Answer:
The measure of angle P is 43°
Step-by-step explanation:
If a quadrilateral is inscribed inside a circle, the sum of opposite angles are always equal to 180 degrees.
The angle POR is opposite to the angle PQR, and the angle OPQ is opposite to the angle ORQ.
So we have that:
mOPQ + mORQ = 180°
y + 3y + 8 = 180
4y = 172
y = 43°
So the measure of angle P is 43°.
To qualify for the car race, Christine needed to drive 100 miles under 43 minutes. She completed the first lap in 412 minutes. At this rate, what will be her total time for the 100-mile qualifying distance?
Answer: 41,200 minutes
Step-by-step explanation: 412 x 100 is 41,200, so she need 41,200 minutes to comeplete the 100-mile drive.
What's the answer to this I just need the numbers to these boxes (9th Grade Math)
Answer:
Pennies = 80
Nickels = 160
Step-by-step explanation:
Two equations representing the relation between numbers of pennies and nickels have been given.
0.01p + 0.05n = 8.80 ---------(1)
n = 2p -----(2)
By substituting the value of n from equation (2) in equation (1).
0.01p + 0.05(2p) = 8.80
0.01p + 0.1p = 8.80
0.11p = 8.80
p = [tex]\frac{8.8}{0.11}[/tex]
p = 80
By equation (2)
n = 2×80
n = 160
In "Pokemon Go", pokeballs cost $0.99 per 100 poke balls and great balls cost $0.99 per
50 great balls.
1. Mr. Underwood loves his "Pokemon Go". He wants to be the very best, like no one
ever was. He bought 200 pokeballs for the upcoming event. He bought 50 more
pokeballs than great balls. How many great balls did he buy?
2. What is the ratio of pokeballs to great balls that he bought?
Answer:
150 greatballs 200 pokeballs. Ratio is 4:3
Step-by-step explanation:
Fifteen percent of the students at Central High take Spanish, 12% take French, and 4% take both. If a student is selected at random, what is the probability that the student takes Spanish or French?
This question is incomplete because it lacks the appropriate options
Complete Question
Fifteen percent of the students at Central High take Spanish, 12% take French, and 4% take both. If a student is selected at random, what is the
probability that the student takes Spanish or French?
A 31%
B. 27%
C. 23%
D. 19%
Answer:
C. 23%
Step-by-step explanation:
At Central High
From the question, we are told that:
Spanish = 15%
French = 12%
Spanish and French = 4%
French or Spanish = unknown
Therefore, the probability that a student at random takes Spanish or French
= P(Spanish) + P(French) - P(Spanish and French)
= 15% + 12% - 4%
= 27% - 4%
= 23%
what is 3n+2(−2n−1)
Answer:
-n-2
Step-by-step explanation:
First, you need to distribute the 2 on the -2n and -1. So multiply the 2 by -2n and -1. You get = -4n-2.
You still have the 3n, so the equation will now look like: 3n-4n-2.
Combine like terms. 3n-4n= -1n or just -n.
Now you have -n-2.
In Act III, scene ii of Julius Caesar, who gave their reasons for why Caesar was killed ?
Answer:
Brutus
Step-by-step explanation:
He was the one who killed him, because he didn't fancy Caesar's ambition.
6(5r-11) - (5 - r) A: 30r - 71 B: 31r - 71 C: 29r - 71 D: 31r- 61 please help asap
Answer:
31r-71
Step-by-step explanation:
=> 6(5r-11)-(5-r)
=> 30r-66-5+r
=> 30r+r-66-5
=> 31r-71
Answer:
B
Step-by-step explanation:
6(5r-11) - (5 - r)
Expand.
30r-66 - 5 + r
Rearrange.
30r + r - 66 - 5
31r - 66 - 5
Factor negative sign.
31r - (66+5)
Add.
31r - (71)
What is the equatation of the line that is parallel to y=6x-1 and passes through the point (-3,4)? The equatation will be in slope-intercept form.
Answer:
work is shown and pictured
Ricky is making diamond shapes in different sizes from pieces of wire. The diamonds will be used to decorate a barn for a barn dance. How many inches of wire will Ricky need to make a diamond with sides that are 9 inches long?
Answer:
Step-by-step explanation:
The volume of a right-rectangular prism is 15 cubic feet. The prism is 2½ feet wide and has a height of ½ foot. How long, in feet, is the rectangular prism?
Answer:
12 feet
Step-by-step explanation:
To get the volume of a rectangular prism, you must multiply the height, width, and length of the prism. So to get your answer, you must multiply 2 1/2 and 1/2, then divide 15 feet by the answer. 2 1/2 × 1/2 × 12 = 15
Which graph displays a rate of change of 2.5?
On a coordinate plane, a line with negative slope goes through points (negative 2, 0) and (negative 1, negative 2).
On a coordinate plane, a line with negative slope goes through points (0, negative 3) and (2, 2).
On a coordinate plane, a line with positive slope goes through points (0, 1) and (2, 2).
Answer:
in edg is B
Step-by-step explanation:
Answer:
It's B
Step-by-step explanation:
What is the range of the function represented by this graph?
y 10
-8
-10
-8
-6
4
-2
2
4
6
8
10
-2
4
-6
-8
1-10
Answer:
Chose10-8 2
Step-by-step explanation:
Add.
6x -5x +3
+
3x2 + 7 x-8
A. 9x2 - 2x + 5
B. 9x2 + 2x-5
C. 9x2 + 12x-5
D. 9x2 + 2x + 11
Please help me solve this problem
Answer:
~120.4 cm
Step-by-step explanation:
Applying the Pythagorean theorem:
height^2 + 127^2 = 175^2
=> height^2 = 175^2 - 127^2
=> height^2 = 14496
=> height = sqrt(14496) = ~120.4 cm
Hope this helps!
This graph shows the amount of money Abdul earns from tutoring compared with the number of hours he works. Select the correct statement about the graph
The graph shows that for every hour the earnings are $!8.
Option D is the correct answer.
What are coordinates in a graph?The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.
The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.
We have,
Some of the coordinates from the graph are:
(1, 18), (2, 36), and (3, 54)
Now,
The rate of change between (1, 18), and (2, 36).
Slope = (36 - 18) / (2 - 1) = 18
The rate of change between (2, 36), and (3, 54).
Slope = (54 - 36) / (3 - 2) = 18
This means,
That for every hour there is an earning of $18.
Thus,
The graph shows that for every hour the earnings are $!8.
Learn more about coordinates here:
https://brainly.com/question/13118993
#SPJ2
If there are 25 students in a math class in which 16 of them are male . If there are 1500 students in the school how many of them are male and how many other or females
Mercury and Alcohol are two common liquids used in thermometers. The boiling point of MERCURY is 357 degree C, while its freezing point is -39 degree C; For ALCOHOL, the boiling point is 78 degree C and the freezing point is -80 degree C; It is required in a laboratory to make measurements which are in the region of -60 degree C. Which type of thermometer would be more suitable? (ASSET)
Answer:
Alcohol
Step-by-step explanation:
Alcohol would be more suitable for making measurements in a -60 degree laboratory, since its boiling point is 78 degrees and its freezing point is -80 degrees, meaning alcohol will not freeze in a -60 degree environment.
Mercury on the other hand, has a freezing point of -39. Thus, it will freeze in a -60 degree environment, making it not suitable for use in this laboratory.
I need help with this question ;w;
Answer:
XZ = 16.25 cm
QR = 6.8 cm
Step-by-step explanation:
A) Taking the proportion of similar sides
=> [tex]\frac{7.2}{6.5} = \frac{18}{XZ}[/tex]
Cross Multiplying
=> 7.2 XZ = 18*6.5
=> XZ = 117/7.2
=> XZ = 16.25 cm
B) Taking proportion of similar sides
=> [tex]\frac{18}{17}=\frac{7.2}{QR}[/tex]
Cross Multiplying
=> 18 QR = 17*7.2
=> QR = 122.4/18
=> QR = 6.8 cm
A student earned a grade of 80% on a math test that had 20 problems. How many problems on this test did the student answer correctly?What is the value of (0.3)4 ?
Answer: 16 questions
Step-by-step explanation:
To find how many problems the student correctly answered on the test, we can turn 80% into a fraction.
[tex]\frac{80}{100} =\frac{16}{20}[/tex]
The student answered 16 questions correctly.
The value of (0.3)^4 is 0.0081.
Unless you mean 0.3*4, then it is 1.2.
In the system of equations
4x + 2y = 4
8x - 7y = -58
If the value of y = 6, Find the value of x and show your work.
Step-by-step explanation:
4x+2y=4
soln
4×x+2×6=4
4x+ 12=4
4x=12-4
4÷4x=8÷4
x=2
What is the formula for Pythagorean therom??
Answer:
[tex]c=\sqrt{a}^{2}+b^{2}[/tex]
Step-by-step explanation:
Answer:
The formula is a^2+b^2=c^2
what is the answer to 97% of 345m
Answer:
334.65
Step-by-step explanation:
97% of 345 = 334.65