Answers
The measure of side AC from the triangle ABC is 57 units.
Given that, ∠BTC=(3x+3)°, CT=x+8 and TA=x-9.
What is the altitude length?The length of the altitude, often simply called "the altitude", is the distance between the extended base and the vertex. The process of drawing the altitude from the vertex to the foot is known as dropping the altitude at that vertex.
Here, BT is an altitude
The altitude of a triangle is the perpendicular to the opposite side of triangle.
Now,
(3x+3)°=90°
⇒ 3x=87
⇒ x=29
So, CT=x+8
= 29+8=37
TA=x-9
=29-9=20
So, AC=CT+TA
= 37+20
= 57 units
Therefore, the measure of side AC from the triangle ABC is 57 units.
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Related Questions
Tutorial ExerciseSimplify.✓98 + 8Step 1Simplify each term.V 98 + V8 = 172.2 + 237X V2 + V222= 7✓ 2 + 2V 2Submit Skip (you cannot come back)Need Help?Watch it
Answers
Expanding the expressions,
[tex]\sqrt[]{49\cdot2}\text{ +}\sqrt[]{2\cdot2\cdot2}[/tex][tex]\sqrt[]{7^2\cdot2}\text{ + }\sqrt[]{2^3}[/tex][tex]\sqrt[]{7^2}\text{ }\times\sqrt[]{2}\text{ +}\sqrt[]{2^2}\text{ }\times\sqrt[]{2}[/tex][tex]\begin{gathered} 7\times\sqrt[]{2}\text{ +2}\times\sqrt[]{2} \\ 7\sqrt[]{2}\text{ + 2}\sqrt[]{2} \\ =9\sqrt[]{2} \end{gathered}[/tex]Hence, in the boxes where you have the term missed, the correct answer to put there is:
[tex]\sqrt[]{7^2\text{ }}\text{not }\sqrt[]{7}[/tex]A recording company obtains the blank cds used to produce its labels from three compact disk manufacturers: i, ii, and iii. The quality control department of the company has determined that 3% of the compact disks produced by manufacturer i are defective, 4% of those produced by manufacturer ii are defective, and 2% of those produced by manufacturer iii are defective. Manufacturers i, ii, and iii supply 36%, 52%, and 12%, respectively, of the compact disks used by the company. What is the probability that a randomly selected label produced by the company will contain a defective compact disk?.
Answers
The probability that a randomly selected label produced by the company will contain a defective compact disk is 0.034.
How to calculate the probability?In this, it should be noted that there are 3 possible cases in the chosen disc can be from any of the manufacturing companies, so the total probability will be the sum of probabilities of getting a faulty disc from companies 1-3.
The probability from company 1 will be;
= 0.03*0.36
The probability from company 2 will be:
= 0.04*0.52
The probability from company 3 will be:
= 0.02*0.12
The total probability will now be:= (0.36*0.03)+(0.04*0.52)+(0.02*0.12)
= 0.0108 + 0.0208 + 0.0024
= 0.034
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Help my daughter needs to know how to do this she’s asking me I’m lost
Answers
Given:
[tex]\begin{gathered} V=L\times W\times H \\ V=64 \\ L=8 \\ H=4 \end{gathered}[/tex]Solve:
Put the all value then:
[tex]\begin{gathered} V=L\times W\times H \\ 64=8\times W\times4 \\ 64=32\times W \\ W=\frac{64}{32} \\ W=2 \end{gathered}[/tex]So the value of W is 2.
Mr.Wells drew a plan for a rectangular dog run. The vertices are (2 1/3, 7 1/2), (12, 7 1/2),(12, 1) and (2 1/3, 1). What is the perimeter of the dog run?
Answers
Perimeter of rectangular dog run is 32.34 units.
Given,
Vertices of rectangular dog run are [tex](2\frac{1}{3},7\frac{1}{2} ), (12,7\frac{1}{2}), (12,1), (2\frac{1}{3},1 )[/tex]
Let
[tex]A=(2\frac{1}{3},7\frac{1}{2} )=(\frac{7}{3} , \frac{15}{2} } )\\ \\B=(12,7\frac{1}{2})=(12,\frac{15}{2} )\\\\ C=(12,1)\\ \\D=(2\frac{1}{3},1 )=(\frac{7}{3},1)[/tex]
A, B,C and D be the vertices of the rectangular dog run as shown in figure.
In rectangle opposite sides are equal. thus, AB=CD and BC=AD
In this rectangle, AB is length and BC is width.
To find distance of AB and BC use formula,
[tex]Distance=\sqrt{(x2-x1)^2+(y2-y1)^2}[/tex]
[tex]AB=\sqrt{(12-\frac{7}{3} )^2+(\frac{15}{2}-\frac{15}{2} )^2} = \sqrt{(\frac{36-7}{3} )^2} =\frac{29}{3}= 9.67[/tex][tex]Bc=\sqrt{(12-12 )^2+(1-\frac{15}{2} )^2} = \sqrt{(\frac{2-15}{2} )^2} =\sqrt{(\frac{-13}{2})^2} = 6.5[/tex]
To find perimeter of rectangular dog run use formula,
[tex]Perimeter =2(Length + Width)\\\\Perimeter =2(AB+BC)\\\\Perimeter =2(9.67+6.5)\\\\Perimeter=2(16.17)\\\\Perimeter=32.34[/tex]
Hence, perimeter of rectangular dog run is 32.34 units.
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The Matthews’ family paid $265,000 when they bought their house in 2005. It is now worth $319,000. What is the percent increase on the price of the home?
Answers
The percent increase on the price of the home is 20.37%.
What is percent increase?
A percent increase refers to how much a percentage has gone up over time. In order to reach this number, you would need to find the difference between the original value and the final value, subtracting to find the exact total of the decrease.
Formula is given by
New number (value) – original number (value) = increase
Increase / original number (value) x 100 = percent increase
Given ,
initial value of home = $265,000
After few years, the value = $319,000
Increase = $319,000 - 265,000
=54000
Percent increase = 54000/265000× 100
= 20.37%
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Solve by using Substitution: 3x-y=13 2x +2y = -10
Answers
a movie theater is having a special. if a group of four pays $7.25 each for the tickets, each person can get popcorn and a drink for $5.75. use the expression 4(5.75 + 7.25) to find the total cost for 4 friends.
Answers
The total cost for the 4 friends will be $52.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
A group of four pays $7.25 each for the tickets, each person can get popcorn and a drink for $5.75.
Now,
Since, a group of four pays $7.25 each for the tickets, each person can get popcorn and a drink for $5.75.
Hence, We can formulate;
The total cost = 4 (5.75 + 7.25)
= 23 + 29
= 52
Thus, The total cost for the 4 friends will be $52.
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If BD=3, then CD= [blank] −−−−−−.Enter your answer as the number that correctly fills in the blank.
Answers
From the information given,
BA is congruent to AC
AD is common to triangle ABD and ACD
Since the two sides of triangle ABC are congruent, it means that the triangle is an isosceles triangle. Thus,
angle ABD = angle ACD
Triangle ABD and ACD are congruent. Thus, the corresponding sides are congruent
If BD = 3, then
CD = 3
If 1/3 pound of pecans cost $2.25 what is the cost per pound for pecans
Answers
Answer:
$6.75 Per pound
Step-by-step explanation:
2.25 = 1/3
2.25 + 2.25 = 2/3
2.25 + 2.25 + 2.25 = 6.75 / 3/3
11. a $58 video game is on sale for a 14% discount. what is the price with the discount
Answers
As given by the question
There are given that the price of the video games is $58.
Now,
According to the question, there are given that 14% discount on their game price
So,
The price with discount is:
[tex]58\times\frac{14}{100}=8.12[/tex]Then,
[tex]58-8.12=49.88[/tex]Hence, the price with the discount is $49.88
Find the mean, variance, and standard deviation for the data set. 19,11,21,9,15
Answers
Given:
The dataset : 19, 11, 21, 9, 15
Mean
The sum of the values divided by the number of values.
[tex]\begin{gathered} mean\text{ = }\frac{\sum_^x}{n} \\ =\text{ }\frac{19\text{ + 11 + 21 +}9\text{ + 15}}{5} \\ =\text{ }\frac{75}{5} \\ =\text{ 15} \end{gathered}[/tex]The mean is 15
Variance
Variance is a measure of dispersion, meaning it is a measure of how far a set of numbers is spread out from their average value.
[tex]\begin{gathered} variance\text{ = }\frac{\sum^(x-x*)^2}{n-1} \\ =\text{ }\frac{(19-15)^2\text{ + \lparen11-15\rparen}^2+(21-15)^2\text{ +}(9-15)^2\text{ + \lparen15-15\rparen}^2\text{ }}{5-1} \\ =\text{ 26} \end{gathered}[/tex]The variance is 26
Standard deviation
The standard deviation is square root of the variance
[tex]\begin{gathered} \sigma\text{ = }\sqrt{26} \\ =\text{ 5.099} \\ \approx\text{ 5.10} \end{gathered}[/tex]The standard deviation is 5.10
Simplify the expression by combining like terms
36a + 42b - 18a + 6
Answers
The simplified expression, 36a + 42b - 18a + 6 by combining the like terms is 18a + 42b + 6
How to simplify expression?In maths, an expression is a combination of numbers, variables, functions (such as addition, subtraction, multiplication or division etc.).
To simplify an expression means to write an equivalent expression which contains no similar terms.
Therefore, let's simplify the expression by combining the like terms.
36a + 42b - 18a + 6
Like terms can be defined as terms that contain the same variables raised to the same power.
36a + 42b - 18a + 6
combining the like terms
36a - 18a + 42b + 6
Therefore, the simplified expression is 18a + 42b + 6
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Which quadrant includes every points with a positive x-coordinate and a negative y-coordinateA) Quadrant IB) Quadrant IIC) Quadrant IIID) Quadrant IV
Answers
Hello!
Let's write some information about each quadrant:
Quadrant I:
x > 0 and y > 0
Quadrant II:
x < 0 and y > 0
Quadrant III:
x < 0 and y < 0
Quadrant IV:
x > 0 and y < 0
Answer:Alternative D) Quadrant IV
Use the diagram below in the following given information to prove the opposite size of a parallelogram are congruent
Answers
Given:
ABCD is a parallelogram.
To prove:
[tex]AD\cong BC\text{ and AB}\cong CD[/tex]Proof:
[tex]\begin{gathered} \text{ABCD is a parallelogram}\ldots\ldots\text{ given.} \\ DC\parallel AB\text{ and AD}\parallel BC\ldots\ldots..by\text{ definition of parallelogram} \\ \angle\text{DCA congruent to }\angle\text{BAC; }\angle BCA\text{ congruent to }\angle DAC\ldots\ldots\text{.}AI\text{ angles theorem} \\ AC\cong AC\ldots.\text{ reflexive property} \\ \Delta ADC\cong\Delta CBA\ldots.by\text{ ASA} \\ AD\cong BC\text{ and AB}\cong CD\ldots\ldots by\text{ CPCTC} \end{gathered}[/tex]
Hence proved.
What is a Unit Circle?
Answers
The "Unit Circle" is a circle with a radius of 1.
The center is put on a graph where the x axis and y axis cross, so we get this neat arrangement here.
The graph is given by:
Answer:
A unit circle is a circle of unit radius, i.e., of radius 1. The unit circle plays a significant role in a number of different areas of mathematics. For example, the functions of trigonometry are most simply defined using the unit circle.
Step-by-step explanation:
4 1/2 > 1.2x
X >3 3/4
X<3 3/34
X>5 2/5
X<5 2/5
Answers
Answer:
x>3 3/4
Step-by-step explanation:
you need to swap the sides and divide by 1.2
Riddle this: i am a four digit number my thousands digit is 1 more than 0. my hundreds digit is odd, but less than 3.my tens digit is even, but more than 7. my ones digit is 5. who am i? am i an even or odd number?
Answers
Answer:
Step-by-step explanation:
you are 1185 and you are an odd number.
I need the correct answer i have 1 more chance at the question and i must complete 100% mastery to get credit for my homework
Answers
Given:
The equation is
[tex]2x^{\frac{5}{3}}-18x=0[/tex]Required:
Find the non-zero solution to the equation.
Explanation:
The given equation is
[tex]2x^{\frac{5}{3}}-18x=0[/tex]Rewrite the equation as:
[tex]2x^{\frac{5}{3}}=18x[/tex]Divide both sides by 2.
[tex]x^{\frac{5}{3}}=9x[/tex]Take cube on both sides.
[tex]\begin{gathered} (x^{\frac{5}{3}})^3=(9x)^3 \\ x^5=729x^3 \\ x^5-729x^3=0 \end{gathered}[/tex]Take out common x
[tex]x^3[/tex][tex]x^3(x^2-729)=0[/tex]Find the factor by using the formula
[tex]a^2-b^2=(a-b)(a+b)[/tex][tex]\begin{gathered} x^3(x-27)(x+27)=0 \\ x=0,27,-27 \end{gathered}[/tex]Final Answer:
Thus the non-zero solutions to the given equation are x =27, -27.
Donna makes $10.50 each hour she works at her job how much money does she make for 15.75 hours of work round your answer to the nearest cent
Answers
To solve this problem, multiply Donna's earnings per hour by the number of hours of work. This is $10.50 times 15.75.
[tex]10.50\cdot15.75=165.375\approx165.38[/tex]She makes $165.38 for 15.75 hours of work.
Question 13A neighborhood association surveyed its residents regarding marital status and living situation. The results are in the table. What is the probabilitythat a resident is married given that the person owns their home?TotalOwns a Home150Rents a Home17032080250330173SingleMarriedDivorcedWidowedTotal53373201205059087910O050을拉茲结印0
Answers
This question is a conditional probability question
P(B|A) means Event B given Event A
In other words, event A has already happened, now what is the chance of event B?
From the given question
let
B = the event that a resident is married.
A = the event that the person owns their home.
So
Thus
[tex]P(B\text{/A)=}\frac{80}{320}=\frac{1}{4}[/tex]1_<2x-4
1.-5
2.-1
3.7
Which of the following values are solutions to the inequality
Answers
Answer:
VB B.
Step-by-step explanation:
B.
13+v+2v=v+3+4combine like termsmove letters to the leftwhat's left?add or subtract constantwhat's left?divide coefficientanswer
Answers
13+v+2v=v+3+4
Combine like terms
13+3v=v+7
Move letters to the left
13+3v-v =7
13+2v=7
Subtract constant
2v=7-13
2v=-6
divide both side by 2
2v/2 = -6/2
v = -3
If UV = 2x, VW = x + 4, and UW = 10, what is UV?
Answers
ANSWER:
4
STEP-BY-STEP EXPLANATION:
From a graph we can establish the following equation:
[tex]\begin{gathered} UV+VW=UW \\ \\ \text{ We replacing} \\ \\ 2x+x+4=10 \end{gathered}[/tex]We solve for x:
[tex]\begin{gathered} 3x+4=10 \\ \\ 3x=10-4 \\ \\ x=\frac{6}{3} \\ \\ x=2 \\ \\ \text{ Now, for UV} \\ \\ UV=2\cdot2 \\ \\ UV=4 \end{gathered}[/tex]The value of UV is equal to 4
Kim places $1,250 into a bank account that pays 4.25% simple interest. if she does not add or remove any money from the account, how much interest will she earn after 60 months (anwers must be written as money-rounded to the hundred to the place)
Answers
The rule of the simple interest is
[tex]I=P\times R\times T[/tex]P is the initial amount
R is the rate in decimal
T is the time in years
Since Kim places $1250, then
P = 1250
Since the rate is 4.25%, then
[tex]R=\frac{4.25}{100}=0.0425[/tex]Since the time is 60 months, divide it by 12 to change it to years
[tex]\begin{gathered} T=\frac{60}{12} \\ T=5 \end{gathered}[/tex]Substitute them in the rule above
[tex]\begin{gathered} I=1250\times0.0425\times5 \\ I=265.625 \end{gathered}[/tex]Round it to the nearest hundredth
I = $265.63
(e) Cards are 65p each and gift wrap
sheets are 45p each at a gift shop. Owen
buys 21 items from the shop and spends
£11.85. How many cards and how many
gift wrap sheets did Owen buy?
Answers
Owen bought 9 gift wrap sheets.
Given, Cards are 65p each and gift wrap sheets are 45p each at a gift shop.
Owen buys 21 items from the shop and spends £11.85.
Let the number of cards be x,
the number of gift wrap sheets be y
Now, according to question
x + y = 21
0.65x + 0.45y = 11.85
On multiplying the first equation by 0.45, we get
0.45x + 0.45y = 9.45
0.65x + 0.45y = 11.85
On subtracting, we get
0.2x = 2.4
x = 12
On solving, we get
12 + y = 21
y = 9
Hence, Owen bought 9 gift wrap sheets.
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Some of the children at a nursery arrive by car.
. 40% of the children at the nursery are boys.
70% of the boys at the nursery arrive by car.
• 60% of the girls at the nursery arrive by car.
What is the probability that a child chosen at random from the nursery arrives by car?
Answers
Answer:
Will assume that there are 100 kids.
100 x 40% =40 of them are boys
40 x 70% = 28 boys arrive by car.
100 - 40 = 60 - Number of girls in Nursery.
60 x 60% = 36 of them arrive by car.
28 boys + 36 girls = 64 - kids that arrive by car.
64 / 100 = 64% - probability of a randomly picked kid that he/she arrived by car.
2. Booker's father sells computer software and earns a 4.25% commission on every software package he sells. How much commission would he earn on a software package that sold for $15,725? Round to the nearest cent. (Example 1)
Answers
To solve the exercise you can use a rule of three, like this:
[tex]\begin{gathered} \text{\$}15,725\rightarrow100\text{\%} \\ \text{\$}x\rightarrow4.25\text{\%} \\ x=\frac{4.25\text{\%}\cdot\text{ \$15,725}}{100\text{\%}} \\ x=\text{ \$}\frac{4.25\cdot\text{15,725}}{100} \\ x=\text{ \$}\frac{68831.25}{100} \\ x=\text{ \$668.31} \end{gathered}[/tex]Therefore, the commission earned will be $668.31.
help meeeeeeeeee pleasee
Answers
Answer: 19.6 feet
Step-by-step explanation:
Using the Pythagorean theorem,
[tex]x^2 +(x+6)^2 =48^2\\\\x^2 +x^2 +12x+36=2304\\\\2x^2 +12x-2268=0\\\\x^2 +6x-1134=0\\\\x=\frac{-6 \pm \sqrt{6^2 -4(1)(-1134)}}{2(1)}\\\\x \approx 30.8 \text{ } (x > 0)\\\\\implies x+(x+6) \approx 67.6\\\\\therefore (x+(x+6))-48 \approx 19.6[/tex]
Arsenia has 80 movie posters and 40 band posters. She plans to sell 24 movie posters. She says that if she
also sells 24 band posters, the ratio of movie posters to band posters stays the same. Is that true? Why or
why not? Complete the explanation.
Answers
No. Arsenia's statement is not true because if it was true then before and after selling the posters, the ratio have to be same which is 2:1.
Given,
Arsenia has 80 movie posters and 40 band posters
She plans to sell 24 movie posters and 24 band posters.
Number of remaining movie posters =80-24=56
Number of remaining band posters=40-24=16
Ratio of movie posters and band posters before selling,
[tex]80:40=2:1[/tex]
Ratio of movie posters and band posters after selling,
[tex]56:16=7:2[/tex]
Thus, Arsenia's statement is not true because if it was true then before and after selling the posters, the ratio have to be same which is 2:1
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Solve for X: 3. (7x - 1) 125 Submit Question
Answers
Answer:
From the given figure;
[tex](7x-1)^0=125^0[/tex]Reason: Alternate angle.
Solving for x;
[tex]\begin{gathered} 7x-1=125 \\ 7x=125+1 \\ 7x=126 \\ x=\frac{126}{7} \\ x=18 \end{gathered}[/tex]Therefore, the value of x is;
[tex]x=18[/tex]