Answers
Answer:
C
Step-by-step explanation:
To make it easy let's start by organizing our information :
AC=12 AND BD=8 ABCD is a rhombus K and L are the midpoints of sides AD and CD we notice that the rhombus ABCD is divided into four right trianglesWhat do you think of when you hear a right triangle ?
The pythagorian theorem !AC and BD are khown so let's focus on them .
If we concentrated we can notice that AB and BD are cossing each other in the midpoints . why ?
Simply because they are the diagonals of a rhombus .
ow let's apply the pythagorian theorem :
(AC/2)² + (BD/2)² = BC² 6²+4²=52BC²= 52⇒[tex]\sqrt{52}[/tex]=BCNow we khow that : AB=BC=CD=AD=[tex]\sqrt{52}[/tex]
This isn't enough . Let's try to figure out a way to calculate the length of KL wich is the base of the triangle
KL is parallel to AC k is the midpoint of AD and L of DCI smell something . yes! Thales theorem
KL/AC=DL/DC=DK/AD WE4LL TAKE OLY ONE KL/12=[tex]\sqrt{52}[/tex]/2*[tex]\sqrt{52}[/tex] KL/12=1/2⇒ KL=6Now we have the length of the base kl
Now the big boss the height :
notice that you khow the length of KL BD crosses kl from its midpoint and DL = [tex]\sqrt{52}[/tex] /2What I want to do is to apply the pythgorian thaorem to khow the lenght of that small part that is not a part of the height of the triangle . I will call it D
DL²=(KL/2)²+D²52/4= 9+ D² D² = 52/4-9 +4 SO D=2now the height of the trigle is H= BD-D= 8-2=6
NOw the area of the triangle is :
A=(KL*H)/2 ⇒ A= (6*6)/2=18THE ANSWER IS 18 SQ.UN
Related Questions
there were 7 little cherries for every 2 big cherries. if there were 630 cherries in the box, how many little cherries were there? (please also answer the question in the picture)
Answers
Answer:
1)2205little cherries
2)0.5.
Step-by-step explanation:
1)7little=2big
?=630big
7×630=2205little cherries
2
2)²/5x=¹/10what is the value of 10x-2
first find the value of x that is ¹/10÷²/5=¼
so x is ¼
insert the value ie 10×¼-2
=2.5-2
=0.5
For the diagram shown, which pairs of angles are vertical angles? Select all that apply. Angle1 and Angle3 Angle2 and Angle4 Angle2 and Angle3 Angle5 and Angle7 Angle5 and Angle8 Angle8 and Angle6
Answers
Answer:
2 & 4
1 & 3
5 & 7
8 & 6
Vertical angles are formed in a set of intersecting lines. They are two differrent angles that are opposite of eachother but have the same angle.
Angle pairs that are vertical angles in the diagram shown when a transversal intersects two parallel lines are:
<1 and <3
<2 and <4
<5 and <7; and
<8 and <6
Recall:
Angles that are regarded as pairs of vertical angles share the same vertex and are directly opposite each other at the point of intersection of two straight lines.
From the image given,<1 and <3 are directly opposite each other and share same vertex.
<1 and <3 are therefore are a pair of angles that are vertical angles.
In the same vein, the following pairs:<2 and <4; <5 and <7; and <8 and <6 are all directly opposite each other. They are vertical angles pair.
Therefore, angle pairs that are vertical angles in the diagram shown when a transversal intersects two parallel lines are:
<1 and <3
<2 and <4
<5 and <7; and
<8 and <6
Learn more here:
https://brainly.com/question/2889556
Which statement illustrates the distributive property?
3 (4 + 5) = 3 (4) + 5
3 (4 + 5) = 3 (4) + 3 (5)
3 left-bracket (4) (5) right-bracket = 3 (4) + 3 (5)
3 left-bracket (4) (5) right-bracket = Left-bracket 3 (4) right-bracket + Left-bracket 3 (5) Right-bracket
Answers
Answer:
B. 3(4 + 5) = 3(4) + 3(5)
3 left-bracket (4) (5) right-bracket = 3 (4) + 3 (5)
3 left-bracket (4) (5) right-bracket = Left-bracket 3 (4) right-bracket + Left-bracket 3 (5) Right-bracket
Step-by-step explanation:
Distributive property of multiplication over addition:
a(b + c) = ab + ac
You have
3(4 + 5), so following the pattern above, you should get:
3(4 + 5) = 3(4) + 3(5)
Answer:
b
Step-by-step explanation:
I took the test
2. Solve 4(3c + 10) < 12c + 40.
use photo for Choices
Answers
Answer:
no solution
Step-by-step explanation:
4 (3c + 10) < 12c + 4012c +40 < 12c +4012c- 12c < 40 -40 0 < 0Left and right sides are equal so no solution
Answer:No solution
Step-by-step explanation: I got it right on the test :)
An equilateral triangle has sides 8 units long. An equilateral triangle with sides 4 units long is cut off at the top, leaving an isosceles trapezoid. What is the ratio of the area of the smaller triangle to the area of the trapezoid? Express your answer as a common fraction.
Answers
Answer:
1:3
Step-by-step explanation:
Please study the diagram briefly to understand the concept.
First, we determine the height of the isosceles trapezoid using Pythagoras theorem.
[tex]4^2=2^2+h^2\\h^2=16-4\\h^2=12\\h=\sqrt{12}\\ h=2\sqrt{3}$ units[/tex]
The two parallel sides of the trapezoid are 8 Inits and 4 units respectively.
Area of a trapezoid [tex]=\dfrac12 (a+b)h[/tex]
Area of the trapezoid
[tex]=\dfrac12 (8+4)*2\sqrt{3}\\=12\sqrt{3}$ Square Units[/tex]
For an equilateral triangle of side length s.
Area [tex]=\dfrac{\sqrt{3}}{4}s^2[/tex]
Side Length of the smaller triangle, s= 4 Units
Therefore:
Area of the smaller triangle
[tex]=\dfrac{\sqrt{3}}{4}*4^2\\=4\sqrt{3}$ Square units[/tex]
Therefore, the ratio of the area of the smaller triangle to the area of the trapezoid
[tex]=4\sqrt{3}:12\sqrt{3}\\$Divide both sides by 4\sqrt{3}\\=1:3[/tex]
Matt has c baseball cards, and Jen has 9 fewer than 5 times as many cards as Matt. Jen gives Matt 14 cards. How many cards does Jen have now?
Answers
Answer:
Jen has 5c -23 cards now
Step-by-step explanation:
Matt has c baseballs.
Jen has 9 fewer than 5 times as Matt.
Mathematically, what Jen has will be 5c -9 baseballs
Now, Jen gives Matt 14 cards. This means that she lost 14 of her cards and we are going to subtract.
The number of cards she has now is thus 5c-9-14 = 5c -23 cards
factorise this expression as fully as possible 2x^2+6x
Answers
Answer:
(Factor out 2x from the expression)
2x (x +3)
which of the following shows the correct steps to find the value of 8^1/3? (1 point)
Answers
Answer:
8 to the power of 1 over 3 equals 2 to the power of 3 whole to the power of 1 over 3 equals 2 to the power of 3 multiplied by 1 over 3 equals 2
Step-by-step explanation:
Options are below
8 to the power of 1 over 3 equals 4 to the power of 3 whole to the power of 1 over 3 equals 4 to the power of 3 multiplied by 1 over 3 equals 4
8 to the power of 1 over 3 equals 2 to the power of 3 whole to the power of 1 over 3 equals 2 to the power of 3 multiplied by 1 over 3 equals 2
8 to the power of 1 over 3 equals 2 to the power of 4 whole to the power of 1 over 3 equals 2 to the power of 4 multiplied by 1 over 3 equals 16
16 to the power of 1 over 4 equals 8 to the power of 2 whole to the power of 1 over 4 equals 8 to the power of 2 multiplied by 1 over 4 equals 8
Given:
8^1/3
if a power is raised to a power, we simplify it by multiplying the exponents; this will create a whole number exponent
if 8 can be rewritten as a number to the 3rd power.
We have
8 = 2*2*2 = 2³
Therefore,
8^1/3=(2^3)^1/3
=2^3×1/3
=2^3/3
=2^1
=2
HELP please!!
“Find the volume of the sphere rounded to the nearest hundredth
Answers
Answer:
904.32 cm^3
Step-by-step explanation:
The formula for the volume of a sphere is V=4/3πr³. Since r is given, we can plug that in for r. I'm assuming that we are using 3.14 for pi, so when we plug in all the values in the equation we get V = 4/3*3.14*6³, which solves out to 904.32.
Find the nth term -1 8 19 32 47
Answers
[tex]\bold{\text{Answer:}\quad \text{Recursive formula:}\ a_n=a_{-1}+2n+5}\\.\qquad \qquad \ \text{Explicit formula:}\ a_n=2n^2+3n-6[/tex]
Step-by-step explanation:
-1 → 8 = +9
8 → 19 = +11
19 → 32 = +13
32 → 47 = + 15
a₁ = -1
d = 2n + 5
Recursive formula is: the previous term plus the difference (d)
[tex]\large\boxed{a_n=a_{n-1}+2n+5}[/tex]
Explicit formula is the first term plus the product of d and n-1:
[tex]a_n=a_1+d(n-1)\\a_n=-1+(2n+5)(n-1)\\a_n=-1+2n^2-2n+5n-5\\\large\boxed{a_n=2n^2+3n-6}[/tex]
SNOG HELP OR SOMEONE THANK YOUUUU
Which unit rate is equivalent to 14 miles per gallon?
two gallons over thirty two miles
thirty two miles over two gallons
three gallons over forty two miles
forty two miles over three gallons
Answers
Answer:
forty two miles over three gallons
Step-by-step explanation:
2 gallons over 32 miles simplifies to 1 gallon over 16 miles, or 1 gallon per 16 miles. This is not the desired result, so we know the first choice is incorrect.
32 miles over 2 gallons simplifies to 16 miles over 1 gallon, or 16 miles per gallon. Again, this is not the desired result, so we know the second choice is also incorrect.
3 gallons over 42 miles simplifies to 1 gallon over 14 miles, or 1 gallon per 14 miles. While this may look correct, note that 1 gallon per 14 miles and 14 miles per gallon are not the same thing, so we know that the third answer is also incorrect.
By process of elimination, we know that the correct answer must be the last option, but let's still simplify it. 42 miles over 3 gallons simplifies to 14 miles over 1 gallon, or 14 gallons per mile. This is in fact the desired result, so we know that the correct answer is the last option. Hope this helps!
Which one of the following numbers is divisible by 11?
A. 924711
B. 527620
C. 320793.
D. 435854
Answers
Answer:
320793
Step-by-step explanation:
320793 / 11 = 29163
Ice is placed around a bowl of water to lower the temperature. The equation D=−75t+22 shows the time, t, measured in minutes and temperature, D, measured in degrees Celsius. Which statement is correct?
Answers
Answer:
d) Before cooling begins, the temperature of the water is 22°C
Step-by-step explanation:
Option A
If t=7 minutes
D=-7/5t+22
=-7/5(7)+22
=-49/5+22
=-49+110/5
=61/5
=12.2°C
Change in temperature=12.2°C-22°C
=-9.8°C
Option B
If t=5 minutes
D=-7/5t+22
=-7/5*5+22
=-7+22
=15°
Change in temperature=15°-22°
=-7°
Option C
The temperature of the ice must be less than 22°C
Option D
D=-7/5t+22
When ice is not placed, t=0
D=-7/5t+22
=-7/5(0)+22
=0+22
=22
Temperature of the water before cooling=22°
Answer:
D
Step-by-step explanation:
The radius of a circle is 2 feet. What is the area of a sector bounded by a 180° arc?
Answers
Answer:
[tex]\boxed{Area = 3.14 ft^2}[/tex]
Step-by-step explanation:
Radius = r = 2 feet
Angle = θ = π/2 (In radians) = 1.57 radians
Area of Sector = [tex]\frac{1}{2} r^2 \theta[/tex]
Area = [tex]\frac{1}{2} (4)(1.57)[/tex]
Area = 2 * 1.57
Area = 3.14 ft²
Answer:
[tex]\bold{2\pi\ ft^2\approx6,28\ ft^2}[/tex]
Step-by-step explanation:
360°:2 = 180° so the area of a sector bounded by a 180° arc is a half of area of a circle of the same radius.
[tex]A=\frac12\pi R^2=\frac12\pi\cdot2^2=\frac12\pi\cdot4=2\pi\ ft^2\approx2\cdot3,14=6,28\ ft^2[/tex]
Anyone know please help!!
Answers
Answer:
only the inverse is a function
If x-14=y+196 and y is 14 times of x then x=WHAT??
Answers
Answer:
x is 226.154…
Step-by-step explanation:
1) x-14=y+196
x=y+196+14
x=y+210
2)x=14y
3) 14y=y+210 collect like terms together
14y-y=210
13y=210 divide both sides by 13
y=16.154
4)x=y+210 meaning:
x=16.154+210
=226.154
This isosceles triangle has two sides of equal length, a, that are longer than the length of the base, b. The perimeter of the triangle is 15.7 centimeters. The equation can be used to find the side lengths.
If one of the longer sides is 6.3 centimeters, what is the length of the base?
cm
Answers
Answer:
b=3.1 cm
Step-by-step explanation:
Both of the longer sides will be equal so you can set up the equation (6.3+6.3)+b=15.7. Simplified you get 12.6+b=15.7, subtracting 12.6 from both sides you get that b=3.1 cm. This can be checked because it is also shorter than 6.3 and works correctly in the perimeter.
Please answer this question in two minutes
Answers
Answer:
work is shown and pictured
Evaluate: m - 12 when m = 23.
Answers
Answer:
11
Step-by-step explanation:
sub 23 with m
23 - 12 = 11
What are the solutions to the quadratic equation below? x^2+34x-72=0
Answers
Answer:
( x + 36 ) ( x - 2 ) = 0
Step-by-step explanation:
x^2 + 36x - 2x -72 = 0
x ( x + 36 ) - 2 ( x + 36 ) = 0
( x + 36 ) ( x - 2 ) = 0
The diagram represents 6x2 – 7x + 2 with a factor of 2x – 1. A 2-column table with 2 rows. First column is labeled 2 x with entries 6 x squared, negative 4 x. Second column is labeled negative 1 with entries negative 3 x, 2. Both rows are labeled with a question mark. What is the other factor of 6x2 – 7x + 2? 3x – 2 3x – 1 3x + 1 3x + 2
Answers
Answer:
( 3x -2)
Step-by-step explanation:
6x^2 – 7x + 2
We know that the constant only has factors of 1 and 2
Since the middle term is negative we know that that we are subtracting
A negative times a negative is positive for the final term
A negative plus a negative is negative for the middle term
( -1 ) ( -2)
We have to determine how to break up 6x^2
1x * 6x
2x*3x
3x*2x
6x*1x
We are given that one factor is 2x-1
( 2x -1 ) ( -2)
That means the other factor of 6x^2 is 3x ( 2x*3x)
( 2x -1 ) ( 3x -2)
Answer:
3x-2
Step-by-step explanation:
6x² – 7x + 2= 6x² -3x- 4x + 2= 3x(2x-1)- 2(2x-1)= (2x-1)(3x-2)Factors are:
2x-1 and 3x-2--------------
3x – 2 correct3x – 1 incorrect3x + 1 incorrect3x + 2 incorrect. Find the measure of angle A.
A
160°
Answers
Answer:
20°
Step-by-step explanation:
A= 360°- (160°+2*90°)= 20°
17. The length of a swing is 2.1 m. If the length
of the arc that is made by the swing
4.4 m, calculate the angle swept by the
swing
Answers
Answer:
dose it tell you want angle the arc is at?
Step-by-step explanation:
Find the value of x. Round the length to the nearest tenth.
Answers
Answer:
[tex] x = 5.1 yd [/tex]
Step-by-step Explanation:
Angle of depression is congruent to angle of elevation.
Therefore, angle of elevation of the given figure, which is opposite to x is 25°.
Adjacent length = 11 yd
Opposite length = x
Trigonometric ratio formula for finding x is shown below:
[tex] tan(25) = \frac{opposite}{adjacent} [/tex]
[tex] tan(25) = \frac{x}{11} [/tex]
Multiply both sides by 11 to solve for x
[tex] 11*tan(25) = x [/tex]
[tex] 5.129 = x [/tex]
[tex] x = 5.1 yd [/tex] (to the nearest tenth)
Suppose the lengths of the pregnancies of a certain animal are approximately normally distributed with mean mu equals 247 days and standard deviation sigma equals 16 days. Complete parts (a) through (f) below.
Answers
Answer:
The answer is given below
Step-by-step explanation:
a) What is the probability that a randomly selected pregnancy lasts less than 242 days
First we have to calculate the z score. The z score is used to determine the measure of standard deviation by which the raw score is above or below the mean. It is given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
Given that Mean (μ) = 247 and standard deviation (σ) = 16 days. For x < 242 days,
[tex]z=\frac{x-\mu}{\sigma}=\frac{242-247}{16}=-0.31[/tex]
From the normal distribution table, P(x < 242) = P(z < -0.3125) = 0.3783
(b) Suppose a random sample of 17 pregnancies is obtained. Describe the sampling distribution of the sample mean length of pregnancies.
If a sample of 17 pregnancies is obtained, the new mean [tex]\mu_x=\mu=247,[/tex] the new standard deviation: [tex]\sigma_x=\sigma/\sqrt{n} =16/\sqrt{17} =3.88[/tex]
c) What is the probability that a random sample of 17 pregnancies has a mean gestation period of 242 days or less
[tex]z=\frac{x-\mu}{\sigma/\sqrt{n} }=\frac{242-247}{16/\sqrt{17} }=-1.29[/tex]
From the normal distribution table, P(x < 242) = P(z < -1.29) = 0.0985
d) What is the probability that a random sample of 49 pregnancies has a mean gestation period of 242 days or less?
[tex]z=\frac{x-\mu}{\sigma/\sqrt{n} }=\frac{242-247}{16/\sqrt{49} }=-2.19[/tex]
From the normal distribution table, P(x < 242) = P(z < -2.19) = 0.0143
(e) What might you conclude if a random sample of 49 pregnancies resulted in a mean gestation period of 242 days or less?
It would be unusual if it came from mean of 247 days
f) What is the probability a random sample of size 2020 will have a mean gestation period within 11 days of the mean
For x = 236 days
[tex]z=\frac{x-\mu}{\sigma/\sqrt{n} }=\frac{236-247}{16/\sqrt{20} }=-3.07[/tex]
For x = 258 days
[tex]z=\frac{x-\mu}{\sigma/\sqrt{n} }=\frac{258-247}{16/\sqrt{20} }=3.07[/tex]
From the normal distribution table, P(236 < x < 258) = P(-3.07 < z < 3.07) = P(z < 3.07) - P(z < -3.07) =0.9985 - 0.0011 = 0.9939
CD=17 AM=5 CD=? I've tried everything but I can't figure it out.
Answers
Answer:
We can prove that ΔTMB ≅ ΔTMD and ΔTMA ≅ ΔTMC by ASA. This means that BM = MD = BD / 2 = 8.5 and that AM = CM = 5 which means that CD = MD - CM = 8.5 - 5 = 3.5.
The points (-2,4), (0,8), (1,10), and (3,14) are on a line. Which of the following statements are true?
Answers
Answer: y = 2x+8
Check out this graph I supplied you with!
Find the values of the variables and the measures of the angles
Answers
Answer:
Add each given variable
(6x + 10) + (x + 2) + x = 8x + 12
The sum of all the angles equals 180ᴼ
8x + 12 = 180
Subtract 12 from both sides
8x = 168
Divide by 8 on both sides
x = 21
Now plug in 21 for each x to find the measure of each angle.
(6[21] + 10) = 126 + 10 = 136ᴼ
(21 + 2) = 23ᴼ
x = 21ᴼ
ASAP! A boat travelling at top speed upstream moves at 15km/hr. When it travels downstream, again at top speed< it moves at 25km/hr. What is the boat's top speed in still water?
Answers
Answer: 20km/h
Step-by-step explanation:
20km/h. Simply average 15 and 25 by doing (15+25)/2
Hope it helps <3
A company borrows 60,000 for 10 years at a simple interest rate of 8.5%. Find the interest paid on the loan and the total amount paid.
Answers
Answer: 51,000 ; 111,000
Step-by-step explanation:
The formula to calculate the simple interest is: PRT/100
where,
P = principal = 60,000
R = rate = 8.5%
T = time = 10 years
Simple interest =(60000 × 8.5 × 10)/100
= 5100000/100
= 51,000
Total Amount Paid= Principal + Interest
= 60,000 + 51,000
= 111,000