the phrase which i believe is correct is A. 7 more than 2 times m
ABC and ACD are triangles.
a) Show that AC = 11.4 cm, correct to 3 significant figures.
А
17 cm
76°
429
D
13 cm
83
B В-
с
b) Calculate BC.
Answer:
a) 11.4
Step-by-step explanation:
cos42=0.74
d²=c²+a²-2caCosD
d²=17²+13²-2×17×13×Cos42
d²=17²+13²-328.47
d²=289+169-328.47
d²=458-328.37
d=√129.63
d=11.4
The length of AC is 11.4 cm and the length of BC is 30.9 cm after solving through trigonometric ratios.
What are trigonometric ratios?Trigonometric ratios deal with the sides and angles in a right angled triangle. sin, cos, tangent ,cosecant ,secant and cotangent are trigonometric ratios.
How to find the length of side of triangle?ABC and ACD are triangle,
The value of AC will be:
According to cosine formula:
[tex]AC^{2} =AD^{2} +AC^{2} -2AD*AC*Cos D.[/tex]
[tex]AC^{2} =17^{2} +13^{2} -2*17*13* cos 42[/tex]
[tex]AC^{2} =[/tex]289+169-328.47
[tex]AC^{2}[/tex]=129.52
AC=11.4 cm
The value of BC will be as under:
using the sine rule
BC/sin A=CA/sin B=AB/sinC
BC/sin76=11.4/sin 21=AB/sin83
from the first 2 in equal to form
BC/sin 76=11.4/sin 21
BC=30.9
Hence the length of AC=11.4 cm and BC=30.9 cm.
Learn more about trigonometry at https://brainly.com/question/24349828
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prove that (n+5)^2-(n+3)^2 is a multiple of 4 for all positive integer values of n
Answer:
Proved
Step-by-step explanation:
Given
[tex](n+5)^2-(n+3)^2[/tex]
Required
Show that [tex](n+5)^2-(n+3)^2[/tex] is a multiple of 4
Expand each bracket
[tex](n+5)(n+5)-(n+3)(n+3)[/tex]
Open brackets
[tex]n^2 + 5x + 5x + 25 - (n^2 + 3x + 3x + 9)[/tex]
[tex]n^2 + 10x + 25 - (n^2 + 6x + 9)[/tex]
Open bracket
[tex]n^2 + 10x + 25 - n^2 - 6x - 9[/tex]
Collect Like Terms
[tex]- n^2 + n^2 - 6n + 10n + 25 - 9[/tex]
[tex]- 6n + 10n + 25 - 9[/tex]
[tex]4n + 25 - 9[/tex]
[tex]4n + 16[/tex]
Factorize
[tex]4(n + 4)[/tex]
Hence, the multiples of [tex](n+5)^2-(n+3)^2[/tex] are [tex]4[/tex] and [tex](n + 4)[/tex]
Evaluate if a = 2 , b = 3, and c = -4 :
ab +3c-b
Answer:
Evaluate if a = 2 , b = 3, and c = -4 :
Step-by-step explanation: that the answer
The square ABCD has side length 20 cm,
E is the midpoint of BC,
20 cm
20 cm
Work out the length of AE,
Give your answer correct to one decimal place.
Answer:
AE=22.4
Step-by-step explanation:
BE is 1/2 of BC
BC is 20 cm All sides of a square are equal
BE = 1/2 BC Property of a midpoint.
BE = 10
Now just use Pythagorus
AB^2 + BE^2 = AE^2
AE^2 = 20^2 + 10^2 Perform the sqrs
AE^2 = 400 + 100 Add the terms
AE^2 = 500 Take the square root of both sides
√AE^2 = √500
AE = 22.36
AE ≈ 22.4
WILL GIVE YOU BRAINLIEST
In the coordinate plane, the point X (3, -2) is translated to the point X'(2, - 4). Under the same translation, the points Y (7, 1) and Z (-1, 2) are
translated to Y' and Z', respectively. What are the coordinates of Y' and Z'?
Answer:
The coordinates of Y' and Z' are, respectively Y'(6,-1) Z'(-2,0)
Step-by-step explanation:
Translations
A given point A(x,y) when translated by the rule (h,k) maps to A'(x+h,y+k).
We are given the point X(3,-2) and its image at X'(2,-4). The rule for the translation used is:
(h,k)=(2,-4)-(3,-2)=(2-3,-4+2)=(-1,-2)
If we apply the same translation to the point Y(7,1) we get the image Y'(7-1,1-2)=Y'(6,-1).
If we apply the same translation to the point Z(-1,2) we get the image Z'(-1-1,2-2)=Z'(-2,0).
The coordinates of Y' and Z' are, respectively Y'(6,-1) Z'(-2,0)
Help me with this please worth 40 points!!!
find the product of (−x−3)(2x2+5x+8)
Find the missing angle.
Answer:
[tex]m\angle XYV=135^{\circ}[/tex]
Step-by-step explanation:
Notice that [tex]m\angle XYV=m\angle XYW+m\angle VYW[/tex].
The diagram already marks [tex]m\angle VYW=80^{\circ}[/tex], so we just need to find [tex]m\angle XYW[/tex].
[tex]\angle TYU[/tex] and [tex]\angle XYW[/tex] are vertical angles, which means they are equal in measure.
Therefore,
[tex]m\angle TYU=m\angle XYW=6x+7[/tex]
Since there are [tex]180^{\circ}[/tex] on each side of a line, we have the following equation:
[tex]m\angle XYW+m\angle VYW+m\angle UYV=180^{\circ},\\6x+7+13+4x+80=180,\\10x+20=100,\\10x=80,\\x=8[/tex].
Plugging in [tex]x=8[/tex], we have:
[tex]m\angle XYW=6(8)+7=55^{\circ}[/tex].
Therefore,
[tex]m\angle XYV=55^{\circ}+80^{\circ},\\m\angle XYV=\fbox{$135^{\circ}$}[/tex].
Write an equivalent expression in standa
form and collect like terms.
2x - (x + 8) - 4
The diameter of the circle above is 20 cm. What is the circumference of the circle? (Use = 3.14.)
Step-by-step explanation:
diameter=20/2,radius=10
circumference of circle=2×pi×radius
circumference of circle=2×3.14×10
circumference of circle=62.8
find the unit rate (constant of proportionality) for bobby
Answer:
Plss this question is Soo blurry I can't read it can u retake this plss?
Please help it's due by 11 59 i will make as brainliest, thanks, and 5.0 for those who give actual and proper answers
Orange colors - Why are the locations of the police station and fire department congruent?
blue colors - Why are the locations of the restaurant and bank congruent?
Answer:
Step-by-step explanation:
Congruent are angles that are in identical angles. For example the orange colors are congruent because both of the angles are across each other, and because of them being crossed they are both the same degrees making the congruent, same with the blue but instead of being across eachother they are in the angle to the left of the parallel lines that are the same degrees as well.
please help me asap!!!
Answer:
230
Step-by-step explanation:
Add the other angles for a total of 130 degrees there is a total of 360 degrees in the interior angle of a quadrilateral subtract 130 from 360.
Answer:
m< CDF = 58°
Step-by-step explanation:
Key skills needed: Congruent Triangles
1) We can use Triangle Congruence Rules to prove that Triangle EDF and Triangle CDF are congruent triangles.
2) Since both triangles have 1 right angle, they are both triangle triangles.
3) Both triangles share the same hypotenuse (DF)
Also, it gives us EF is 36, and FC is 36 --> This means that EF ≅ FC
Since both are Right Triangles, we can use Right Triangle HL Congruence to prove it
HL means Hypotenuse-Leg
This rule can only be applied to right angle triangles. In order to use this rule, a hypotenuse and a leg of the triangles need to proven congruent.
4) Since ΔEDF ≅ ΔCDF with Right triangle HL, we can say that < CDF is congruent to < EDF. These are corresponding parts of the triangle.
--> To say that < CDF is congruent to < EDF, we can use the theorem:
If Δs are ≅, then all corresponding parts are ≅.
5) Therefore, <CDF ≅ <EDF (which means the measures of the angles are the same value)
Since <EDF is 58°, <CDF would also be 58°
Hope you understood and have a nice day!! :D
Assume that Q, R, and S are the angles of a triangle, with opposite sides q, r, and s respectively. Select all of the following that represent the law of cosines. q2 = r2 + s2 – 2rscos(Q) . q2 = r2 + s2 – 2qscos(R) . r2 = q2 + s2 – 2qscos(Q) . r2 = q2 + s2 – 2qscos(R) .s2 = q2 + r2 – 2qrcos(S)
Answer:
A. q2 = r2 + s2 – 2rscos(Q)
D. r2 = q2 + s2 – 2qscos(R)
E. s2 = q2 + r2 – 2qrcos(S)
Step-by-step explanation:
The following relation represent the law of cosines.
[tex]q^{2}=r^{2}+s^{2} -2rscos(Q) \\\\r^{2}=q^{2}+s^{2} -2qscos(R) \\\\s^{2}=r^{2}+q^{2} -2rqcos(S)[/tex]
Law of cosines:The law of cosine states that the square of any one side of a triangle is equal to the difference between the sum of squares of the other two sides and double the product of other sides and cosine angle included between them.
It is given that, Q, R, and S are the angles of a triangle, with opposite sides q, r, and s respectively.
A diagram is attached below,
From cosines law,
[tex]q^{2}=r^{2}+s^{2} -2rscos(Q) \\\\r^{2}=q^{2}+s^{2} -2qscos(R) \\\\s^{2}=r^{2}+q^{2} -2rqcos(S)[/tex]
Above relation represent law of cosines.
Learn more about the Law of cosines here:
https://brainly.com/question/4372174
Casandra earned 520$ this month by walking her neighbors dog . This is a 30% increase from amount she earned last month
Answer: last week she earned $364.
Step-by-step explanation:
-44 x -44 × -44 × -44 =
Answer:
3748096
Step-by-step explanation:
Let X, denote the weight of a randomly selected prepackaged one-pound bag of carrots. Of course, one pound bags of carrots won't weigh exactly one pound. In fact, history suggests that Xi is normally distributed with a mean of 1.18 pounds and a standard deviation of 0.07 pound. Now, let W denote the weight of randomly selected prepackaged three-pound bag of carrots. Three pound bags of carrots won't weigh exactly three pounds either. In fact, history suggests that Wis normally distributed with a mean of 3.22 pounds and a standard deviation of 0.09 pound. Selecting bags at random, what is the probability that the sum of three one-pound bags exceeds the weight of one three-pound bag?
Answer:
0.9830 = 98.30% probability that the sum of three one-pound bags exceeds the weight of one three-pound bag
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Three one pound bags:
3 one pound mags, which have mean 1.18 and standard deviation of 0.07. The mean is 1.18 multiplied by 3, and the standard deviation will be 0.07 multiplied by the square root of 3. So
[tex]\mu_{1} = 3*1.18 = 3.54[/tex]
[tex]\sigma_{1} = 0.07\sqrt{3} = 0.1212[/tex]
Three pound bags:
Mean 3.22, standard deviation 0.09. So
[tex]\mu_{2} = 3.22, \sigma_{2} = 0.09[/tex]
What is the probability that the sum of three one-pound bags exceeds the weight of one three-pound bag?
Here, we work with the subtraction of the normal variables. The mean is the subtraction of the means, and the standard deviation is the square root of the sum of the variances. So
[tex]\mu = \mu_{1} - \mu_{2} = 3.54 - 3.22 = 0.32[/tex]
[tex]\sigma = \sqrt{\sigma_{1}^2 + \sigma_{2}^2} = \sqrt{0.1212^2+0.09^2} = 0.151[/tex]
This is the probability of the subtraction being positive, that is, 1 subtracted by the pvalue of Z when X = 0. Then
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{0 - 0.32}{0.151}[/tex]
[tex]Z = -2.12[/tex]
[tex]Z = -2.12[/tex] has a pvalue of 0.0170
1 - 0.0170 = 0.9830
0.9830 = 98.30% probability that the sum of three one-pound bags exceeds the weight of one three-pound bag
Question 2 of 10
What is the center of the circle shown below?
A. 7.8
В. ЈК
C. K
D. J
Answer:
its 100% JK
Step-by-step explanation:
i need help plz
State the coordinates of the point.
Answer:
(-5,8)
Step-by-step explanation:
Hope this helps ;)
help please. I need
Answer:
the slope is= 3/2
y= (3/2)x + (-4)
can anyone help me pls
Answer:
405 calories
Step-by-step explanation:
All we have to do is:
9 × 45
I hope this helps!
18 = 0.29 so 20 = ???
Answer:
x=29/90 or 0.3222222
Step-by-step explanation:
ok, rewrite the question as a ratio
18/0.29=20/x, cross multiply
18x=.29*20, evaluate x
18x=5.8
x=29/90 or 0.3222222
29
Step-by-step explanation:
29/90
I will give a brainlist if someone could answer this problem with a explanation:)
Answer:
It would be ASA
Step-by-step explanation:
Those two triangles are congregant so it would be A. ASA
maurice read 10 pages that is 50 percent of the paper lenght what i the paper lenght
Answer:
Would it not be 20?
Step-by-step explanation:
Answer:
The answer is 20
Step-by-step explanation:
If 10 pages is 50% of the paper length, to make it equal 100% you just multiply 10X2 or add 10+10 and that equals 20.
1) Which of these are equivalent to - ? Choose ALL that apply.
PLEASE ANSWER ASAP !!!!
*ANSWERS ON PIC*
Sherry uses the steps below to solve the equation x + (negative 8) = 3 x + 6.
Step 1 Add 1 negative x-tile to both sides and create zero pairs
Step 2 Add 8 positive unit tiles to both sides and create zero pairs.
Step 3 Divide the 14 unit tiles evenly among the 2 x-tiles.
Step 4 The solution is x = 7
What is Sherry’s error?
In step 1, she should have added 3 negative x-tiles to both sides.
In step 2, she should have added 6 negative unit tiles to both sides.
In step 3, she did not divide the tiles evenly.
In step 4, she should have found the solution x = negative 1.
Step-by-step explanation:
The given equation :
x + (negative 8) = 3 x + 6.
or
x+(-8) = 3x+6
Step 1.
Add (-3x) to both sides of the equation.
x+(-8) + (-3x) = 3x+6 +(-3x)
x-8 = 3x +6
Step 2.
Add 8 positive unit tiles to both sides and create zero pairs.
x-8+8 = 3x +6 +8
x = 3x +14
Step 3.
x-3x = 14
-2x = 14
x = -7
Hence, step 1 is incorrect as she should have added 3 negative x-tiles to both sides.
Answer:
Step 2
Step-by-step explanation:
pls help u dont have to explain that much
Answer:
k = -7
Step-by-step explanation:
Given
x² - x - 42 = (x + k)(x + 6)
Required
Find k
x² - x - 42 = (x + k)(x + 6)
Expand the left hand side
x²-7x + 6x - 42 = (x + k)(x+ 6)
Factorize
x(x - 7) + 6(x- 7) = (x + k)(x+ 6)
Further factorize
(x - 7)(x + 6) = (x + k)(x + 6)
By comparison
x + k = x - 7
Subtract x from both sides
k = -7
Write the equation of the line in slope-intercept form (y = mx +b): 3y - 12x = 15
Answer:
y = 4x + 5
Step-by-step explanation:
3y - 12x = 15
Add 12x to both sides.
3y = 12x + 15
Divide by 3 to isolate y.
y = 4x + 5
Answer:
ACTUALLY IT'S, y=4x-5
Step-by-step explanation:
12x-3y=15 - Get y alone
-12x =12x
-3y=-12x+15
-3y=-12x+15 - Divide.
__________
-3 -3
y=12/3x-15/3 - Distribute division. Negative over a negative is positive. Positive over a negative is a negative.
y=4x-5 - Reduce fractions.
You deposit $60 in an account earning simple interest at an annual rate of 5% after 12 years what is your new balance
Answer:
The total amount accrued, principal plus interest, from simple interest on a principal of $60.00 at a rate of 5% per year for 12 years is $96.
Step-by-step explanation:
Given
Principle P = $60
Rate r = 5% = 5/100 = 0.05
Time period t = 12 years
To determine
New Balance A = ?
Using the formula
A = P(1 + rt)
A = 60(1+(0.05×12))
A = $96.00
Therefore, the total amount accrued, principal plus interest, from simple interest on a principal of $60.00 at a rate of 5% per year for 12 years is $96.
a) 17
b) 15
c) 18
d) 16
^ Which one ?
Answer:
15
Step-by-step explanation:
if one side is 9, another is C, based on the angle tilt would have to be 15.
Hope its helps.