Answers
Answer:
The correct answer is option C
a = 10√3, b = 5√3, c = 15 and d = 5
Step-by-step explanation:
Points to remember
The angles of a right angled triangle, 30°, 60° and 90° then sides are in the ratio, 1: √3 : 2
To find the value of variables
From the figure we can see 2 right angled triangle with angle 30, 60 and 90
we get, d= 5 then b = 5√3
b = 5√3 the c = 5√3 * √3 = 15
and a = 2 * 5√3 = 10√3
Therefore the correct answer is option C
a = 10√3, b = 5√3, c = 15 and d = 5
Answer:
d.[tex]a=10\sqrt3,b=5\sqrt3,c=15,d=5[/tex]
Step-by-step explanation:
We have to find the value of each variable.
[tex]\frac{P}{H}=sin\theta[/tex]
[tex]\frac{b}{10}=sin 60^{\circ}[/tex]
[tex]\frac{b}{10}=\frac}\sqrt3}{2}[/tex]
[tex]b=10\times \frac{\sqrt3}{2}=5\sqrt3[/tex]
[tex]\frac{d}{10}=cos 60^{\circ}[/tex] ([tex]cos\theta=\frac{base}{hypotenuse}[/tex])
[tex]d=\frac{1}{2}\times 10=5[/tex]
[tex]\frac{b}{a}=sin30^{\circ}[/tex]
[tex]\frac{5\sqrt3}{a}=\frac{1}{2}[/tex]
[tex]a=10\sqrt3[/tex]
[tex]\frac{b}{c}}=tan 30^{\circ}[/tex] ([tex]tan\theta=\frac{p}{b}[/tex])
[tex]\frac{5\sqrt3}{c}=\frac{1}{\sqrt3}[/tex]
[tex]c=5\sqrt3\times \sqrt3=15[/tex]
[tex]a=10\sqrt3,b=5\sqrt3,c=15,d=5[/tex]
Hence, option d is true.
Related Questions
Please help with this problem!!!!! Thank you! I promise to mark brainlest!
Answers
Answer:
D
Step-by-step explanation:
In which direction must the graph of f(x) = x be shifted to produce the graph of g(x) = x - 16?
Answers
Answer: Option C.
Step-by-step explanation:
The equation of the line in slope-intercept form is:
[tex]y=mx+b[/tex]
Where the slope is "m" and the intersection of the line with the y-axis is "b".
Given the function f(x) in the form [tex]f(x)=x[/tex], you can identify that:
[tex]m=1\\b=0[/tex]
This means that the line passes through the origin (0,0)
And from the function g(x) in the form [tex]g(x)=x-16[/tex], , you can identify that:
[tex]m=1\\b=-16[/tex]
This means that the line of the function g(x) and the line of the function f(x) have the same slope, but the line of g(x) passes through the point (0,-16)
Therefore, the graph of f(x) must be shifted 16 units down to produce the graph of g(x)
Factor the expression below by grouping. 3x-6+xy-2y.
A. (x-2)(3+y)
B.(x+2)(3-y)
C.2(x-2(xy-2y)
D.(3x-6)(Cyrus-2y)
Answers
A: (x-2)(3+y)
3x - 6 + xy - 2y
(3x - 6) + (xy - 2y)
3(x - 2) + y(x - 2)
Your two terms are: (3 + y) and (x - 2)
Answer: The correct option is (A). [tex](x-2)(3+y).[/tex]
Step-by-step explanation: We are given to factor the following expression by grouping :
[tex]E=3x-6+xy-2y~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
Since we are given to factorize the expression (i) by grouping, so we will take 3 common from first two terms and y common from last two terms.
The factorization of expression (i) is as follows :
[tex]E\\\\=3x-6+xy-2y\\\\=3(x-2)+y(x-2)\\\\=(x-2)(3+y).[/tex]
Thus, the required factored form of the given expression is [tex](x-2)(3+y).[/tex]
Option (A) is CORRECT.
What value of y makes the system of equations below true?
y = 9x - 7
y = 6x - 4
a.) 2
b.) 1
c.) -1
d.)-2
Answers
Answer:
a) 2
Step-by-step explanation:
9x - 7 = 6x - 4
3x = 3
x = 1
when x = 1
y = 9x - 7 = 9(1) - 7 = 2
or
y = 6x - 4 = 6(1) - 4 = 2
Answer
a) 2
Answer:
The answer is b) 1
Step-by-step explanation:
If you plug in y=9(1)-7= 2
same goes for y=6(1)-4=2
both the same answer
What is the missing value in the equation shown □ x1/10=0.034
Answers
Answer:
0.34
Step-by-step explanation:
Do the inverse operation so;
0.034 / 1/10 = 0.34
Now go back and subsitute,
0.34 * 1/10 = 0.034
In the equation □ x 1/10 = 0.034, the missing value is 0.34 as obtained by isolating □ on one side, i.e., □ = 0.34.
Explanation:The equation presented in the question is □ x 1/10 = 0.034. The missing value is the number that should be multiplied by 1/10 to result in 0.034. To solve for this missing value, we can rearrange the equation using the basic algebraic method. We isolate the missing value (□) on one side by dividing both sides of the equation by 1/10. This results in □ = 0.034 / (1/10), which simplifies further to □ = 0.34. Therefore, the missing value in the equation □ x 1/10 = 0.034 is 0.34.
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Find the unknown: 4:2:3 = x : 18: 27
Answers
Final answer:
To find the unknown values in the given ratios, solve for x by setting up proportions and using cross-multiplication to calculate the missing value.
Explanation:
Find the unknown: 4:2:3 = x : 18: 27
Calculate the ratio of the known values: 4/2 = 2, and 3/2 = 1.5.Set up the proportion: 2 = x/18 and 1.5 = x/27.Solve for x by cross-multiplication: x = 36 for the first ratio and x = 40.5 for the second ratio.The number line is a graph of the
Answers
Answer: real numbers?
Step-by-step explanation:
Answer:
The number line is graph of the or can be graph of any of the following set of numbers.
1. Natural numbers
2. Whole numbers
3. Integers
4.Rational Numbers
5.Irrational numbers
6. Real numbers
We can represent all this set of numbers on the graph of number line.
In equilateral ΔABC, AD, BE, and CF are medians. If BC = 12, then DO =
A) 2 square root 3
B) 3
C) 6
D) 6 square root 3
Answers
Answer:
Option A) 2 square root 3
Step-by-step explanation:
we know that
The equilateral triangle has three equal sides and three equal angles (60 degrees each)
The triangle BOD is a right triangle
we have
<OBD=(60°/2)=30°
BD=12/2=6 units
tan(<OBD)=DO/BD
tan(30°)=DO/6
DO=6*tan(30°)
DO=2√3 units
Answer:
The correct answer is A. 2√3
Step-by-step explanation:
Find the angle between u = i+sqr of 7j and v = -i+9j. Round to the nearest tenth of a degree.
Answers
[tex]\bf ~~~~~~~~~~~~\textit{angle between two vectors } \\\\ cos(\theta)=\cfrac{\stackrel{\textit{dot product}}{u \cdot v}}{\stackrel{\textit{magnitude product}}{||u||~||v||}} \implies \measuredangle \theta = cos^{-1}\left(\cfrac{u \cdot v}{||u||~||v||}\right) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \begin{cases} u=i+\sqrt{7}j\implies &<1,\sqrt{7}>\\\\ v=-i+9j\implies &<-1,9> \end{cases} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf u\cdot v\implies (1)(-1)~+~(\sqrt{7})(9)\implies -1+9\sqrt{7}\implies 9\sqrt{7}-1~\hfill dot~product \\\\[-0.35em] ~\dotfill\\\\ ||u||\implies \sqrt{1^2+(\sqrt{7})^2}\implies \sqrt{1+7}\implies \sqrt{8}~\hfill magnitudes \\\\\\ ||v||\implies \sqrt{(-1)^2+9^2}\implies \sqrt{1+81}\implies \sqrt{82} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf \theta =cos^{-1}\left( \cfrac{9\sqrt{7}-1}{\sqrt{8}\cdot \sqrt{82}} \right)\implies \theta =cos^{-1}\left( \cfrac{9\sqrt{7}-1}{\sqrt{656}} \right) \\\\\\ \theta \approx cos^{-1}(0.8906496638868531)\implies \theta \approx 27.05[/tex]
make sure your calculator is in Degree mode.
Hector surveyed students in his homeroom about how they got to school last Monday and noted whether they arrive on time or late. The data he gathered is shown in the two-way table below.
Answers
The percentage of students surveyed whi didn't take bus to school is 48%.
From the table:
Total number of students surveyed = 10 + 3 + 8 + 4 = 25Number who did not take bus to school = 12The percentage value can be computed thus :
(Number who did not take bus to school / Total number surveyed) × 100%Now we have :
(12 / 25) × 100%
0.48 × 100%
= 48%
Complete Question:
Hector surveyed students in his homeroom about how they got to school last Monday and noted whether they arrive on time or late. The data he gathered is shown in the two-way table below.
According to the data in the table, what percentage of students in Hector’s homeroom did not take the bus to school last Monday?
A transformation T : (x, y) → (x + 3, y + 1). Find the preimage of the point (4, 3) under the given transformation. (7, 4) (1, 2) (4/3, 3) (-1, -2)
Answers
Answer:
(1, 2)
Step-by-step explanation:
Remember that the final shape and position of a figure after a transformation is called the image, and the original shape and position of the figure is the pre-image.
In our case, our figure is just a point. We know that after the transformation T : (x, y) → (x + 3, y + 1), our image has coordinates (4, 3).
The transformation rule T : (x, y) → (x + 3, y + 1) means that we add 3 to the x-coordinate and add 1 to the y-coordinate of our pre-image. Now to find the pre-image of our point, we just need to reverse those operations; in other words, we will subtract 3 from the x-coordinate and subtract 1 from the y-coordinate.
So, our rule to find the pre-image of the point (4, 3) is:
T : (x, y) → (x - 3, y - 1)
We know that the x-coordinate of our image is 4 and its y-coordinate is 3.
Replacing values:
(4 - 3, 3 - 1)
(1, 2)
We can conclude that our pre-image is the point (1, 2).
Final answer:
The preimage of the point (4, 3) under the transformation T : (x, y) → (x + 3, y + 1) is (1, 2), found by reversing the transformation.
Explanation:
The transformation T : (x, y) → (x + 3, y + 1) maps each point in the plane to a new point that is 3 units to the right and 1 unit up from the original point. Finding the preimage of the point (4, 3) means determining which original point would be mapped to (4, 3) by this transformation. To do this, we set up the equations x + 3 = 4 and y + 1 = 3 and solve for x and y. Solving these equations gives us the preimage (1, 2).
Here's the step-by-step math:
Set up the equations based on the transformation T:
x + 3 = 4
y + 1 = 3
Solve for x:
x = 4 - 3 = 1
Solve for y:
y = 3 - 1 = 2
Therefore, the preimage of the point (4, 3) under the given transformation is (1, 2).
Select whether each equation has no solution, one solution, or infinitely many solutions
Answers
Once put into the quadratic formula the numbers in the square root of they are negative no solutions if it is 0 then 1 solution if more then more than one solution
Answer:
Step-by-step explanation:
Use the correct order of operations to solve the problem below. 8 × 9 + 12 ÷ 4 - (5 + 3)
Answers
8•9+12\4-(5+3)
We are gonna use the method PEMDAS (Parenthesis, Exponents, Multiplication/Division, Addition/ Subtraction) to help us solve this equation.
8•9+12/4-8
72+12/4-8
72+3-8
75-8
67
To solve the equation 8 × 9 + 12 ÷ 4 - (5 + 3), apply the order of operations (BIDMAS/PEMDAS): Brackets, Indices, Division/Multiplication (left to right), Addition/Subtraction (left to right). The final answer is 67.
Explanation:The subject of this question is Mathematics and it pertains to the correct order of operations. To solve the provided equation, 8 × 9 + 12 ÷ 4 - (5 + 3), we must follow the order of operations which is popularly known as BIDMAS or PEMDAS. This acronym stands for:
Brackets(or Parentheses in the PEMDAS variant)Indices (or Exponents)Division and Multiplication(in order from left to right)Addition and Subtraction(in order from left to right).Here, we proceed by doing the operations within the brackets. (5+3) equals 8. Now, substitute 8 in the expression and we get 8 × 9 + 12 ÷ 4 - 8. Now according to BIDMAS/PEMDAS, the next step is to do multiplication and division from left to right. The expression now becomes 72 + 3 - 8. Finally, we do addition and subtraction from left to right, so the final result is 67.
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Marco buys a certain brand of shampoo for a supplier $7.25 per bottle he sells it to his customers at a makeup 25% what would the makeup be
Answers
Answer:
Markup= 1.81
Sale price =9.06
Step-by-step explanation:
The markup is the original prices times the markup rate
markup = 7.25 * 25%
= 7.25 * .25
=1.8125
We round this to the nearest cent
=1.81
The new sale price will be the original price + the markup
7.25+1.81
9.06
Answer:
9.06, or real explanation.
Step-by-step explanation:
"Marco buys a certain brand of shampoo for a supplier $7.25 per bottle he sells it to his customers at a makeup 25% what would the makeup be"
I am going to assume makeup is supposed to be markup, but I will answer all there is.
To find how much higher he charges people for the shampoo, we can multiply the original cost by the percent of increase, so in our case 7.25*.25
7.25*.25=1.8125, or $1.81
1.8125 is the total extra he charges people for the soap.
NOW FOR THE TOTAL COST-------------------
For the total cost we take the original + the added cost
1.8125+7.25=9.0625, or 9.06
What’s the distance between (-3,-22) and (-13,-23)
Answers
Answer:
d = sqrt(101)
Step-by-step explanation:
To find the distance between two points, we use the formula
d =sqrt ((x2-x1)^2 + (y2-y1)^2) where (x1,y1) and (x2,x2) are the points
d = sqrt ((-13--3)^2 + (-23--22)^2)
d = sqrt ((-13+3)^2 + (-23+22)^2)
d = sqrt((-10)^2 + (-1)^2)
d = sqrt(100)+1)
d = sqrt(101)
If the best gas mileage is the highest rate, which truck has the BEST gas mileage?
A. Truck A, because for every mile the truck uses 19 gallons.
B. Truck A, because for every gallon the truck goes 19 miles.
C. Truck B, because for every mile the truck uses 18 gallons.
D.Truck B, because for every gallon the truck goes 18 miles.
Answers
A. Truck A , because of every mile the truck uses 19 gallons.
Which statement is true?
is not a logarithmic function because the base is greater than 0.
is not a logarithmic function because the base is a square root.
is not a logarithmic function because the base is equal to 1.
is not a logarithmic function because the base is a fraction.
Answers
3 is correct , base is never equal to 1 cause all of solves of logarithm will be 0
Answer with explanation:
Consider a Logarithmic Function
[tex]y=\log_{a} b\\\\y=\frac{\log b}{\log a}\\\\ \text{if, a=1,then}\\\\y=\frac{\log b}{\log 1}\\\\y=\frac{\log b}{0}[/tex]
which is not defined.
Also,⇒ a∈(0,∞)≠1.
b> 0, that is, b∈(0,∞)
Option C:
is not a logarithmic function because the base is equal to 1.
Which expression is equivalent to (-3y-x)-(5y-8x)
A.-8y-8x
B.-8y+7x
C.2y-7x
D.8y+8x
Answers
Multiply the negative sign into the second bracket and get rid of both brackets
-3y-x-5y+8x
Collect like terms
-8y+7x
Answer:
B: -8y + 7x
Step-by-step explanation:
Start with (-3y-x)-(5y-8x). This is a subtraction problem. Subtract 5y from -3y, obtaining -8y. Next, subtract -8x from -x; this is equivalent to -x - (-8x), or 7x.
Then the difference -x + 8x = 7x.
Combining the x and y results, we get B: -8y + 7x.
How do you do this?please help
Answers
Answer:
10.5 ft.
Step-by-step explanation:
1. Find the radius of the larger circle
4/7 = 3/r --> the ratio should be constant
cross-multiplication: 21 = 4r
Divide: r = 5.25 ft.
2. Find the circumference
Equation: C = 2πr
C = 2π*5.25
C = 10.5π ft.
Mr Johnson, the store owner, ordered 48 boxes of jawbreakers. Each box contained 392 pieces of candy. How many lawbreakers did Mr. Johnson order?
Answers
Answer:
Mr. Johnson would have ordered 18816 jaw breakers.
Step-by-step explanation:
Multiply 392 by 48
Mr. Johnson ordered a total of 18816 jawbreakers by multiplying the number of boxes (48) by the number of pieces of candy per box (392).
The question involves calculating the total number of jawbreakers Mr. Johnson ordered. To do this, we need to multiply the number of boxes ordered by the number of pieces of candy per box.
Step-by-step calculation:
Identify the number of boxes ordered: 48 boxes.
Identify the number of candies per box: 392 pieces.
Multiply the number of boxes by the number of candies per box to find the total: 48 boxes × 392 pieces/box = 18816 jawbreakers.
Therefore, Mr. Johnson ordered a total of 18816 jawbreakers.
PLEASE HELP DETAILS ARE BELOW I WILL RATE BRAINIEST CHORD AND ARCS FIND THE MEASURE OF ARC CD DETAILS BELOW
Answers
Wouldn’t it be 36.7 because that’s the arch am I right?
Answer:
The measure of arc CD is 114.6°.
Step-by-step explanation:
Let the center of the circle be O and OP is perpendicular to CD at point point P.
The perpendicular line from the center of circle divide each chord in two equal parts. so, CP=DP.
[tex]CP=\frac{CD}{2}=\frac{36.7}{2}=18.35[/tex]
In a right angles triangle,
[tex]\sin\theta =\frac{opposite}{hypotenuse}[/tex]
In a right angles triangle OPC,
[tex]\sin\angle POC =\frac{18.35}{21.8}[/tex]
[tex]\angle POC =\sin^{-1} (\frac{18.35}{21.8})[/tex]
[tex]\angle POC \approx 57.3[/tex]
In triangle OPC and OPD,
[tex]OC=OD[/tex] (Radius)
[tex]OP=OP[/tex] (Reflexive property)
[tex]CP=DP[/tex] (Altitude on chord from center)
By SSS postulate
[tex]\triangle OPC\cong \triangle OPD[/tex]
[tex]\angle POC\cong \angle POD[/tex] (CPCTC)
[tex]\angle POC=\angle POD[/tex]
The measure of angle COD is
[tex]\angle COD=\angle POC+\angle POD[/tex]
[tex]\angle COD=2\angle POC[/tex]
[tex]\angle COD=2(57.3)[/tex]
[tex]\angle COD=114.6[/tex]
Therefore the measure of arc CD is 114.6°.
there are two cubes. the smaller cube has a surface area of 24 square units. the larger cube has a surface area that is twice that of the smaller cube. what is the volume, in cubic units, of the larger cube?
Answers
24 times 2 which will be 48
The tax on a property with an assessed value of 90000 is 1200. What is the assessed value of a property if the tax is 2200
Answers
165,000, since 90,000÷1200=75. So 75×2200=165,000.
The assessed value of a property, given a tax amount of $2200, using the proportional ratio obtained from a known property value and tax amount pairing, is $165,000.
Explanation:The subject of your question relates to a simple form of proportionality or ratio. The scenario provided allows us to set up a ratio problem. If the tax on a property valuing $90,000 is $1,200, we can write this ratio as 1200/90000. Now, using that ratio, you want to find the property value for a tax amount of $2,200. Therefore, we can set up the equation 1200/90000 = 2200/x, with x being the property value we're trying to find. Solving for x, we find that x = (90000*2200)/1200 which equals $165,000. Therefore, the assessed value of a property if the tax amounts to $2,200 is $165,000.
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How does the a value affect your sine graph?
Answers
Answer:
Changing value of "a" changes the amplitude of the sine graph.
Step-by-step explanation:
Question says to find about how does the a value affect your sine graph.
General equation of sine function can be given as:
[tex]y=a\cdot\sin\left(b\left(x-h\right)\right)+k[/tex]
There value of "a" gives amplitude.
So changing value of "a" changes the amplitude of the sine graph.
I need help with solving the equation
2x - 5 = x - 7
and i need the steps to solve the problem
Answers
2x - 5 = x - 7
First, let's subtract x from both sides:
2x - x - 5 = x - x - 7
x - 5 = -7
Now, let's add 5 to both sides:
x - 5 + 5 = -7 + 5
x = -2
Answer:
x = -2
Step-by-step explanation:
2x - 5 = x - 7
2x - x - 5 = -7
2x - x = -7 + 5
Now we have isolated x
2x - x = 5 - 7
2x - x = -2
x = -2
the graph of a function never has two diferent points with the same x coordinate because
Answers
It is undefined, meaning it will not pass the vertical line test
A bank offers a 3.7% annual interest rate for a retirement savings account. A worker puts $8,000 into the account. How much will be in the account after a year? $
Answers
The worker will have approximately $8,296.00 in their retirement account after a year.
Explanation:Calculate the interest earned: Multiply the principal amount ($8,000) by the annual interest rate (3.7%): $8,000 * 0.037 = $296.00.
Add the interest earned to the principal: $8,000 + $296.00 = $8,296.00.
Therefore, the worker will have approximately $8,296.00 in their retirement account after one year due to the accrued interest.
If the arithmetic pattern shown continues, what will be the 8th number?
54, 48, 42, 36, ...
Answers
Each time, you are subtracting 6 to get to the next term. The 8th term would be 12.
Help please I can’t solve
Answers
Answer:
Step-by-step explanation:
To solve divide the number of events by the number of possible outcomes.So in this case 60 is the event and 3 is the possible outcome because there is only 3 even numbers out of the 6. So the answer would be 20. Hope the is right. Good luck
9a-14 = 4a+6 solve as equations
Answers
Answer: x=4
Step-by-step explanation: isolate variable using division
=9a-4a=6+14
=5a=20
a=20/5
a=4