Answers
Answer:
[tex]BD=13[/tex]
Step-by-step explanation:
Note that Ray AC bisects ∠A. Therefore, we can use the Angle Bisector Theorem shown below.
Hence:
[tex]\displaystyle \frac{27}{x+5}=\frac{12}{x}[/tex]
Solve for x. Cross-multiply:
[tex]12(x+5)=27(x)[/tex]
Distribute:
[tex]12x+60=27x[/tex]
Subtract 12x from both sides:
[tex]15x=60[/tex]
Divide both sides by 15. Thus:
[tex]x=4[/tex]
BD is the sum of BC and CD:
[tex]BD=BC+CD[/tex]
Substitute:
[tex]BD=x+(x+5)[/tex]
Substitute and evaluate:
[tex]BD=(4)+(4+5)=13[/tex]
Therefore, BD is 13.
Related Questions
Select the correct answer.
What is the solution to this equation?
log3 (4x) – 2log3x =2
A. 36
B. 9/4
C. 4/9
D. 1/36
Answers
9514 1404 393
Answer:
C. 4/9
Step-by-step explanation:
There are a couple of ways you can do this.
[tex]\log_3{4x}-2\log_3{x}=2\\\\\log_3{4}+\log_3{x}-2\log_3{x}=2\\\\\log_3{4}-2=\log_3{x}\\\\4\cdot3^{-2}=x\qquad\text{take antilogs}\\\\\boxed{x=\dfrac{4}{9}}\\\\\textsf{or}\\\\\dfrac{4x}{x^2}=3^2\qquad\text{take antilogs}\\\\\dfrac{4}{9}=x\qquad\text{cancel $x$, multiply by $\dfrac{x}{9}$}[/tex]
oscar is buying soil for his plants. he needs to fill one pot with 8 cups of soil and another pot with 3 gallons of soil. if the price of soil is $2.50 per quart, how much, in dollars, will he pay in all?
PLEASE HELP
Answers
Answer:
Total dollars = 35 dollars.
Step-by-step explanation:
Below is the given values:
Number of cups = 8 cups
Number of gallons = 3 gallons
Price of soil per quart = $2.50
Now convert the cups and gallons into quart.
Total quart = 8 cups + 3 gallons
Total quart = 8 / 4 quart + 3 x 4 quarts
Total quart = 2 quart + 12 quart
Total quart = 14 quart
Total dollars amount = $2.50 per quart x 14 quart
Total dollars = 35 dollars.
Give the domain and range of the quadratic function whose graph is described. Maximum = - 4 at x = 10 The domain of the function is . (Type your answer in interval notation)
Answers
Answer:
it is a parabola with max of -4
so domain (-∞,∞)
Step-by-step explanation:
Write an equation for a line perpendicular to y = -5x - 4 and passing through the point (-5, -4)
Answers
Answer:
Step-by-step explanation:
A perpendicular slope is one that is the opposite reciprocal of the one given. The line given, y = -5x - 4, is a line in slope-intercept form where m is the slope and b is the y-intercept. That means that the slope of the given line is -5; therefore, the perpendicular slope is 1/5. Passing through the point (-5, -4), we have
[tex]y-(-4)=\frac{1}{5}(x-(-5))[/tex] which simplifies a bit to
[tex]y+4=\frac{1}{5}(x+5)[/tex] That's the line in point-slope form, so let's also get it into slope-intercept form, which means that we solve the point-slope form equation for y:
[tex]y+4=\frac{1}{5}x+1[/tex] and
[tex]y=\frac{1}{5}x+1-4[/tex] gives us, finally,
[tex]y=\frac{1}{5}x-3[/tex]
sushil was thinking of a number. sushil halves it and gets an answer of 22.2, what was the original number?
Answers
Answer:
44.4Step-by-step explanation:
Let,
The number thought by Sushil = x
When halved = x/2
We know that,
When the number is halved then it becomes 22.2
Therefore,
The original number is,
[tex] = > \frac{x}{2} = 22.2[/tex]
=> x = 22.2 × 2
=> x = 44.4 (Ans)
In a freshman class of 80 students,22 students take Consumer Education,20 students take French,and 4 students take both.Which equation can be used to find the probability,P, that a randomly selected student from this class takes Consumer Education, French,or both?
A: P = 11/40 + 1/4 + 1/20
B: P = 11/40 + 1/4
C: P = 11/40 + 1/4 - 1/20
D: P = 11/40 + 1/4 - 1/10
Answers
P = 11/40 + 1/4 - 1/20
=========================================================
Explanation:
The formula we use is
P(A or B) = P(A) + P(B) - P(A and B)
In this case,
P(A) = 22/80 = 11/40 = probability of picking someone from consumer educationP(B) = 20/80 = 1/4 = probability of picking someone taking FrenchP(A and B) = 4/80 = 1/20 = probability of picking someone taking both classesSo,
P(A or B) = P(A) + P(B) - P(A and B)
P(A or B) = 11/40 + 1/4 - 1/20
which is why choice C is the answer
----------------
Note: P(A and B) = 1/20 which is nonzero, so events A and B are not mutually exclusive.
How to determine the percentage of total expenses which is allocated to salary ? Please help
Answers
Answer:
(s/t)(100%)
Step-by-step explanation:
Represent salaries by s and total expenses by t. Then the fraction of total expenses allocated to salary is
s
------
t
and so the percentage of total expenses which is allocated to salary is
(s/t)(100%)
Here,
we have to determine the percentage of total expenses which is allocated to salary.
Let,
The salary is denoted by (S)The total expenses value by (T)The percentage of total expenses allocated to salary is,
[tex]\bold{Percentage=\dfrac{salary}{total~expenses}×100 }[/tex] [tex]\sf{Percentage=\dfrac{S}{T}×100 }[/tex]A group of 3 boys is sharing 4 small pans of rice krispie treats. What is the total amount of rice krispie treats each boy will get?
Answers
Answer:
each boy will get 1.33333333333 of a pan
Step-by-step explanation:
Answer:
Each boy in that group would get about 1 and 1 third of a pan of treats or 1.33 repeating
Step-by-step explanation:
To find this you would take the numbers of pans (4) and divide it by the number of boys (3).
4 / 3 = 1.33333
You invest $24,000 at a simple interest rate of 12% for 9 years, and your
investment grows by $25,920. What is the principal?
Answers
Answer:
The principal is $2400
Step-by-step explanation:
Given
[tex]P = \$24000[/tex]
[tex]t = 9[/tex]
[tex]r =12\%[/tex]
[tex]I = \$25920[/tex]
Required
The principal amount
The principal amount is the amount invested.
From the question, we understand that $24000 was invested.
Hence, the principal is $24000
What points does y-4=-2(x-6) go through
Answers
Answer:
(6, 4)
Step-by-step explanation:
y-4=-2(x-6) <=> y-y1 = s(x-x1)
(x1, y1) => (6, 4)
if 6 is added to three quarters of a certain number, the result is 42 . Find the original number
Answers
Answer:
Step-by-step explanation
Hello!
3x/4 + 6=42
3x/4=42-6 = 36
3x = 36*4
3x = 144
x= 144/3 =48
3/4 of 48 = (48*3) / 4 =36
36+6=42
the original number is 48
Answer:
x=48
Step-by-step explanation:
3x/4+6=42
3x/4=42-6
3x/4=36
cross multiply
3x/3=144/3
x=48
A simple random sample of 44 men from a normally distributed population results in a standard deviation of 10.7 beats per minute. The normal range of pulse rates of adults is typically given as 60 to 100 beats per minute. If the range rule of thumb is applied to that normal range, the result is a standard deviation of 10 beats per minute. Use the sample results with a 0.10 significance level to test the claim that pulse rates of men have a standard deviation equal to 10 beats per minute.a. Identify the null and alternative hypotheses.
b. Compute the test statistic; χ2 = ___ .
c. Find the P-value; P-value = ____.d. State the conclusion.
Answers
Answer:
Step-by-step explanation:
The Hypothesis :
H0 : σ = 10
H1 : σ ≠ 10
The Chisquare statistic, χ² ;
χ² = [(n-1) * s²] ÷ σ²
Sample size, n = 44 ; sample Standard deviation, s = 10.7 ; population standard deviation, σ = 10
χ² = [(44 - 1) * 10.7²] ÷ 10²
χ² = [43 * 114.49] ÷ 100
χ² = [4923.07] ÷ 100
χ² = 49.2307
Using the Pvalue from Chisquare calculator :
degree of freedom, df = n - 1 = 44 - 1 = 43
Pvalue = 0.238
1. The arithmetic mean of roots of the quadratic equation x^2- 10x+16=0 is
Answers
Answer:
5
Step-by-step explanation:
x^2 - 10x + 16 = 0
factor
(x - 2)(x - 8) = 0
roots
x = {2, 8}
mean of roots
a = (2 + 8) /2
a = 5
name the plane represented by the back of the box.
I already tried and got it wrong so if you're gonna answer pls explain how you got your answer, thanks
Answers
Answer:
ADH
Step-by-step explanation:
The back of the box is AEDH ( points on the corners)
You need 3 points to name a plane that are not in a line
ADH is one name
ADE is another name
A bicycle shop owner
Answers
Answer:
275, 350, 450, 550, 675
Step-by-step explanation:
Arrange in order
275, 300, 450, 490, 675
range 275 to 675
median 450
mean 438
---------------------------
Raise 300 to 350
Raise 490 to 550
New set of prices
275, 350, 450, 550, 675
range 275 to 675 same
median 450 same
mean 460 increased
What's the Area of the parallelogram
Answers
Answer:
30
Step-by-step explanation:
Area of a parallelogram = base length * height
The parallelogram has a given base length of 10 cm and a given height of 3 cm
Hence, area = 10 * 3 = 30cm^2
The sum
of two consecutive
integers is 8,641.
What is the smallest integer?
Answers
Answer:
sim eu também preciso desta respota
Calculate the area of the following Circle
Answers
Answer:
324
Step-by-step explanation:
Circles are 100% even. If you add another line going opposite direction you would multiply 18x18. You get 324.
Which of the following represents the factorization of the trinomial below?
X2 - 2x - 48
ANSWER
Answers
[tex]\implies {\blue {\boxed {\boxed {\purple {\sf { \: (x + 6)(x - 8)}}}}}}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]
[tex] {x}^{2} - 2x - 48[/tex]
[tex] = {x}^{2} - 8x + 6x - 48[/tex]
Taking [tex]x[/tex] as common from first two terms and 6 from last two terms, we have
[tex] =x \: ( \: x - 8 \: ) + 6 \: ( \: x - 8 \: )[/tex]
Taking the factor [tex](x-8)[/tex] as common,
[tex] = (x + 6)(x - 8)[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{❦}}}}}[/tex]
Answer:
(X+6)(x-8)
Step-by-step explanation:
Each day that a library book is kept past its due date, a $0.30 fee is charged at midnight. Which ordered pair is a viable solution if x represents the number of the days that a library book is late and y represents the total fee?
Answers
Answer:
x + $0.30 = y
Step-by-step explanation:
hope this helps!
Answer:
(x,0.3*x)
Step-by-step explanation:
the equation would be 0.3*x=y where x is days and y is total cost. so the ordered pair would be (x,y). swapping 0.3*x for y is where (x,0.3*x) is derived from. Since there will be no negative days and the fee only applies at midnight x must be positive and an integer.
Put the following equation of a line into slope-intercept form, simplifying all
fractions.
x + y = 3
Answers
Answer:
See below.
Step-by-step explanation:
x + y = 3
Subtract x from both sides:
x - x + y = 3 - x
y = -x + 3 which is slope-intercept form.
please help ill give brainliest I need this answer
Answers
Answer:50
Step-by-step explanation:8+7x =9x-4 2x =12 x =6 so 8+42=50
Answer:
50°
Step-by-step explanation:
These 2 angles are vertically opposite, meaning they equal each other.
This gives the equation 9x-4=7x+8.
Subtracting 7x from both sides gives 2x-4=8.
From there, you want to add 4 to both sides, leaving 2x=12.
In order to isolate the x, divide both sides by 2. This creates a final result of x=6.
We want to find the angle given by 8+7x. Since we know x, we can sub it with its value (6). This makes the equation 8+7×6.
We can then solve this to 8+42, and even further to 50°.
**This content involves transversals and solving algebraic equations, which you may wish to revise. I'm always happy to help!
Jimmy wants to draw a 50° angle. Fill in the missing step to make sure his drawing is completed in the correct order:
Step 1: He draws a ray.
Step 2: He lines up his protractor with the baseline on the ray and the origin of the protractor on the vertex.
Step 3: ________
Step 4: He uses the bottom of the protractor to draw a straight line connecting the mark he made with the vertex.
Step 5: He draws arrows on both ends to make them rays.
Anwsers:
1. He lines up his ruler with the ray and the zero on the ruler.
2. He finds 50° on the protractor and draws a mark on the paper.
3. He lines up his protractor with a straight line and draws a mark on the paper.
4. He draws parallel lines.
Answers
Answer:
2. He finds 50° on the protractor and draws a mark on the paper.
Step-by-step explanation:
Construction is a topic that requires a step wise procedure during the process. In the given question, since Jimmy wish to draw an angle of 50°, he should locate the angle on his protractor and draw a mark on the paper. This is with respect to the previous steps observed.
The essence of the protractor is for Jimmy to accurately measure the angle. Thus he has to determine the angle by the use of a protractor before the construction can be complete.
Therefore the required procedure in step 3 is he finds 50° on the protractor and draws a mark on the paper.
Answer He finds 50° on the protractor and draws a mark on the paper.
5 (v+1) -v = 4 (v-1) +9
Answers
Answer:
All real numbers are solutions.
Step-by-step explanation:
Our goal is to isolate "v" on one side of the equation. Let's do this step by step.
5(v+1)−v=4(v−1)+9
Step 1: Simplify both sides of the equation.
5(v + 1) − v = 4(v−1) + 9
(5)(v) + (5)(1) + −v = (4)(v) + (4)(−1) + 9(Distribute)
5v + 5 + −v = 4v + −4 + 9
(5v + −v) +(5) = (4v) + (−4 + 9) (Combine Like Terms)
4v + 5 = 4v + 5
4v + 5 = 4v + 5
Step 2: Subtract 4v from both sides.
4v + 5 − 4v = 4v + 5 − 4v
5 = 5
Step 3: Subtract 5 from both sides.
5 − 5 = 5 − 5
0 = 0
This means that all real numbers are solutions.
Any real number could be "v."
Hope this helps, please mark brainliest if possible. Have a great day.
Answer:
All numbers are solutions
Step-by-step explanation:
Find the area of the parallelogram in the figure below. Round your final answer to the nearest tenth.
16.8
D
23.2
23.2
12.4
B
Answers
A high school track is shaped as a rectangle with a half circle on either side.
A rectangle has a length of 96 meters and width of 35 meters. 2 semicircles with diameters of 35 meters are on each end of the rectangle.
Jake plans on running four laps. How many meters will Jake run? Use 3.14 for Pi.
301.9 m
823.6 m
1,207.6 m
1,647.2 m
Answers
Answer:
Option (3)
Step-by-step explanation:
Track is shaped as a rectangle with a semicircle on either side.
Therefore, length of the track = 2(Length of rectangle) + perimeter of a complete circle formed by joining the semicircles on each side.
= 2(96) + 2πr
= [tex]192+2\pi (\frac{35}{2})[/tex]
= 192 + 35π
= 192 + 109.9
= 301.9 m
Since, Jake plans to run four laps.
Therefore, distance covered by Jake = 4 × 301.9
= 1207.6 m
Option (3) will be the correct option.
Answer:
C
Step-by-step explanation:
i did the test and got it right :D
Somebody please help me asap
Answers
Answer:
sum of angles in a triangle = 180°
180-(90+21)
= 69
pls am I correct
Am I correct if not plz asap help I have less Than 4 minutes
Answers
what is the solution for 3(x+3)=12
Answers
Answer: 3×4=12
Step-by-step explanation:
Brackets: X=1 , so 1+3=4 and 3+4=12
Mario compares random download times of movies from three different services using the table below.
Service
Download Time
(minutes)
4.9.4.7, 5.0, 4.6, 4.8
Who Knew
Amazing
Prime
4.6. 4.6. 4.8.4.6, 4.9
Peach TV
4.9.4.9, 5.1, 5.0, 5.1
Which service provides the fastest mean download speed?
Answers
Answer:
Who Knew Mean = 4.825
Amazing prime mean =
Peach TV mean = 5.025
Amazing prime wins the fastest speed with 4.75 seconds. Hope this helps!
explanation 4.9-79-638