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If both triangles are similar, it means that the ratio of the corresponding sides is proportional. It also means that the corresponding angles are congruent
By comparing both triangles,
2x - 10 = 30
2x = 30 + 10
2x = 40
x = 40/2
x = 20
Related Questions
The following data set represents the math test scores for a class of 20 students.90, 85, 95, 100, 100, 90, 100, 70, 100, 85, 80, 95, 80, 100, 85, 75, 100, 90, 90, 75How many outliers are in this data set?Enter your answer as a number.Provide your answer below:
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Given:
The data set represents the math test scores for a class of 20 students.
As shown most of the scores are between 80 and 100
The outlier will be the score that is more or less of most of the data
The least score = 70
So, the answer will be:
the number of the outliers = 1
During the first year of opening a law firm , a lawyer served 46 clients .in the second year, his number grew to 58 . If the linear trend continue, write an equation that gives the number of clients (c) the lawyer will have have (t) years after beginning the firm
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The equation of a line with slope m and y-intercept b in slope-intercept form is:
[tex]y=mx+b[/tex]The slope represents the rate of change of the variable y with respect to the variable x, and the y-intercept represents the initial value of y when x=0.
In this case, let c represent the number of clients as a function of time, and let t represent time in years.
Then, c=46 when t=1 and c=58 when t=2.
Use the slope formula to find the slope of the line that passes through the points (1,46) and (2,58) in a c vs t graph:
[tex]\begin{gathered} m=\frac{c_2-c_1}{t_2-t_1} \\ =\frac{58-46}{2-1} \\ =\frac{12}{1} \\ =12 \end{gathered}[/tex]Replace 12 for the slope and substitute a pair of corresponding values of c and t into the equation to find the initial value. For instance, substitute t=1 and c=46:
[tex]\begin{gathered} c=12t+b \\ \Rightarrow46=12(1)+b \\ \Rightarrow46-12=b \\ \Rightarrow34=b \\ \therefore b=34 \end{gathered}[/tex]To find the equation that gives the number of clients the lawyer will have as a function of time, replace 12 for the slope and 34 for the initial value:
[tex]c=12t+34[/tex]We can verify that we obtain the correct values for c when t=1 and t=2:
[tex]\begin{gathered} c_1=12(1)+34=12+34=46 \\ c_2=12(2)+34=24+34=58 \end{gathered}[/tex]Therefore, the equation that gives the number of clients (c) the lawyer will have (t) years after beginning the firm, is:
[tex]c=12t+34[/tex]
A spherical storage tank has a length of radius of 2 ft. What is the surface area (in square feet) of the storage tank? Use the calculator value of . (Round your answer to two decimal places.)ft2The storage tank needs to be painted, and you can only purchase full pints of rust-proofing paint. Determine the number of pints of paint that must be purchased to paint the tank if 1 pint covers approximately20 ft2.(Round your answer up to the nearest whole number.)pt
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The formula for the surface area (A) of a sphere is,
[tex]A=4πr^2[/tex]Given:
[tex]r=2ft[/tex]Therefore,
[tex]A=4\pi(2)^2=50.26548\approx50.27(2\text{ decimal places\rparen}[/tex]Hence, the surface area of the sphere is 50.27ft².
Given that
[tex]\begin{gathered} 1pint=20ft^2 \\ \therefore50.27ft^2=\frac{1pint\times50.27}{20}=\frac{50.27pint}{20}=2.5135\approx3pt \end{gathered}[/tex]Therefore, you need to purchase 3pints.
Solve t/−5=−7.What is t?
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Use permutations to solveThe student activity club at the college has 25 members. In how many different ways can the club select a president, a vice president, a treasurer, and a secretary?Substitute values into the formula for251P,=(25 - 4)There aredifferent ways that the offices can be filled
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the question is a permutation question
the formular for permutation is
nPr = n!/(n-r)!
in this case,
n = 25
r = 4
so,
nPr = 25!/(25 - 4)!
nPr = 25!/21!
nPr = 25 x 24 x 23 x 22 x 21!/21!
nPr = 303600
therefore,
its 303600 ways
What is the greatest common factor of 40a^2b and 48ab^2?
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Answer:
The greatest common factor GCF is;
[tex]8ab[/tex]Explanation:
Given the terms;
[tex]\begin{gathered} 40a^2b \\ \text{and} \\ 48ab^2 \end{gathered}[/tex]Let us expand each of the terms;
[tex]\begin{gathered} 40a^2b=2\times2\times2\times5\times a\times a\times b \\ 48ab^2=2\times2\times2\times2\times3\times a\times b\times b \\ \end{gathered}[/tex]then we will write out the greatest common factor;
[tex]\begin{gathered} \text{GCF}=2\times2\times2\times a\times b=8ab \\ \text{GCF}=8ab \end{gathered}[/tex]Therefore, the greatest common factor GCF is;
[tex]8ab[/tex]
Question 2: * A swimming pool is 50 meters long, 15 meters wide, and 3 meters deep. What is the volume of the pool? 0 4,500 cubic meters O 2,250 cubic meters 900 cubic meters O 750 cubic meters
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A swimming pool is 50 meters long, 15 meters wide, and 3 meters deep. What is the volume of the pool.
Length of the pool = 50 m
Width of the pool = 15 m
Depth of pool = 3 m
Volume of cuboid = Length x Width x Depth
For, the volume of the pool substitute the value of Length, Width and depth
Volume of Pool = 50 x 15 x 3
Volume of pool = 2250 m³
Volume of pool is 2250m³
Answer : B) 2250 cubic meter
what is the midpoint of (4,-5) and (10,3)
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The formula for the midpoint of the given coordinate is,
[tex](x,y)=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]Now, applying the formula to the given coordinate,
[tex]\begin{gathered} (x,y)=(\frac{4+10}{2},\frac{-5+3}{2}) \\ (x,y)=(\frac{14}{2},\frac{-2}{2}) \\ (x,y)=(7,-1) \end{gathered}[/tex]So, the required mid point is (7,-1).
The missing sequence (I tried to many times not getting it)
Answers
Answer
Missing term in the sequence = 36
Explanation
Looking at the sequence, we can see that it is a geometric progression.
And the general form for the nth term of an geometric progression is
aₙ = a (rⁿ⁻¹)
where
aₙ = nth term = 3rd term
a = first term = 4
n = number of terms = 3
r = common ratio = ratio of consecitive terms = (second term)/(first term) = (fifth term)/(fourth term) = (12/4) = (324/108) = 3
For the third term now,
aₙ = a (rⁿ⁻¹)
a₃ = 4 (3³⁻¹)
a₃ = 4 (3²)
a₃ = 4 (9)
a₃ = 36
Hope this Helps!!!
The players drew screws to see who would start 1st. There were 6 short straws & 1 long straw. Santa drew 1st. What is the probability of his picking the long straw & going 1st?
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The probability is given by the ratio between the amount of long straws and the total amount of straws. Since we have 6 short straws and 1 long starw, the total is
[tex]6+1=7[/tex]Then, the probability is
[tex]\frac{1}{7}[/tex]Two companies modeled their profits for one year.Company A used the function P(t)= 1.8(1.4)" to represent its monthly profit, P(t), inhundreds of dollars, after t months, where 0 < < 12.Company B used the data in the table to write a linear model to represent its monthly profits.Which statement describes the relationship between the profits, predicted by the models, of thetwo companies?
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Given:
[tex]undefined[/tex]FIND SIDE a. Round to the nearest tenth.A. 36.9B. 31.3C. -18.1D. 13.3
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Side a= BC =?
Then
BC /34 = Cos 23°
BC = 34 • Cos 23°
. = 31.29
rounded it gives
SOLUTION IS
OPTION B) 31.3
The total cost of a jacket and a tie was $70.71. If the price of the jacket was $5.09 less than the tie, what was the price of the jacket? Express your answer as a simplified fraction or a decimal rounded to two places.
Answers
Let:
x = cost of the jacket
y = Cost of the tie
The total cost of a jacket and a tie was $70.71 so:
[tex]x+y=70.71[/tex]the price of the jacket was $5.09 less than the tie, so:
[tex]\begin{gathered} x=y-5.09 \\ so\colon \\ y=x+5.09 \end{gathered}[/tex]Replace y into the original equation:
[tex]\begin{gathered} x+(x+5.09)=70.71 \\ 2x+5.09=70.71 \\ solve_{\text{ }}for_{\text{ }}x\colon \\ 2x=70.71-5.09 \\ 2x=65.62 \\ x=\frac{65.62}{2} \\ x=32.81 \end{gathered}[/tex]Answer:
$32.81
5 What is the measure of ZA? B 53 X 105° C A
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We are asked to find the measure of ∠A
First, we have to find the measure of ∠C
Recall the straight-line angle property
[tex]\angle C+105\degree=180\degree[/tex]Let us solve for angle ∠C
[tex]\begin{gathered} \angle C+105\degree=180\degree \\ \angle C=180\degree-105\degree \\ \angle C=75\degree \end{gathered}[/tex]Now recall that the sum of all three angles of a triangle must be equal to 180°
[tex]x+53\degree+75\degree=180\degree[/tex]Let us solve for angle x
[tex]\begin{gathered} x+53\degree+75\degree=180\degree \\ x=180\degree-53\degree-75\degree \\ x=52\degree \end{gathered}[/tex]Therefore, the measure of ∠A is 52°
Solve the equationb + 15 = 4b = ??
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b+15= 4
Subtract 15 from both sides of the equation:
b+15-15 = 4 -15
b= -11
Find the area of the quadrilateral with the given coordinates A(-2, 4), B(2, 1),C(-1, -3), D(-5, 0).25 square units20 square units10 square units50 square units
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Determine the length of side AB.
[tex]\begin{gathered} AB=\sqrt[]{(-2-2)^2+(4-1)^2} \\ =\sqrt[]{16+9} \\ =5 \end{gathered}[/tex]Determine the length of BC.
[tex]\begin{gathered} BC=\sqrt[]{(-1-2)^2+(-3-1)^2} \\ =\sqrt[]{9+16} \\ =5 \end{gathered}[/tex]Determine the length of CD.
[tex]\begin{gathered} CD=\sqrt[]{(-5+1)^2+(0+3)^2} \\ =\sqrt[]{16+9} \\ =5 \end{gathered}[/tex]Determine the length of side DA.
[tex]\begin{gathered} DA=\sqrt[]{(-2+5)^2+(4-0)^2} \\ =\sqrt[]{9+16} \\ =5 \end{gathered}[/tex]All sides of quadilateral are equal. So quadilateral is a square or rhombus with side of 5 units.
Determine the length of diagonal AC and BD.
[tex]\begin{gathered} AC=\sqrt[]{(-1+2)^2+(-3-4)^2} \\ =\sqrt[]{1+49} \\ =\sqrt[]{50} \end{gathered}[/tex][tex]\begin{gathered} BD=\sqrt[]{(-5-2)^2+(0-1)^2} \\ =\sqrt[]{49+1} \\ =\sqrt[]{50} \end{gathered}[/tex]Diagonals are equal so quadilateral is a square.
Determine the area of square with side 5.
[tex]\begin{gathered} A=5\cdot5 \\ =25 \end{gathered}[/tex]So area is 25 square units.
Graph the solution to the following inequality on the number line.x(x-7) <0.
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The solution is from - 1 to 8
something like this
What does Cofer use to symbolize a lack of freedom in "Primary Lessons"?speaking Spanishthe gypsy lifestylethe cool New Jersey apartmentcolor coding on the island
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1) To find the solution, we have to substitute the values in the equation.
2) Substituting x = 1
[tex]\begin{gathered} 2x-4\ge2 \\ 2\cdot1-4\ge2 \\ -2\ge2\text{ - FALSE} \end{gathered}[/tex]3) Substituting x = 2
[tex]\begin{gathered} 2x-4\ge2 \\ 2\cdot2-4\ge2 \\ 4-4\ge2 \\ 0\ge2-\text{FALSE} \end{gathered}[/tex]4) Substituting x = 3
[tex]\begin{gathered} 2x-4\ge2 \\ 2\cdot3-4\ge2 \\ 6-4\ge2 \\ 2\ge2-\text{TRUE} \end{gathered}[/tex]5) Substituting x = 4
[tex]\begin{gathered} 2x-4\ge2 \\ 2\cdot4-4\ge2 \\ 8-4\ge2 \\ 4\ge2-TRUE \\ \end{gathered}[/tex]6) The solutions are x = 3 and x = 4.
Alternative C - {3,4}.
Answer:
color coding on the island
Step-by-step explanation:
For each pair of figures below, choose how they are related. rs Translation Translation O Translation O Reflection Reflection Reflection
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The first one is ROTATION
the second one is REFLECTION
1 3/4 converted into percents
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Given:
[tex]1\frac{3}{4}[/tex]The decimal number is:
[tex]\begin{gathered} \frac{3}{4}=0.75 \\ 1\frac{3}{4}=1+0.75=1.75 \end{gathered}[/tex]To turn this to percent, we know that:
1 = 100%
and
[tex]\frac{3}{4}=0.75*100=75[/tex]3/4 = 75%
Therefore:
[tex]1\frac{3}{4}=(1+0.75)*100=100+75=175[/tex]The answer is: 175%.
Match the correct value with each expression. Answers may be used more than once. (-8) – 2 (-8) + 2 (-2)-(-8) 11 (-2) + (-8) (-8) - (-2) :: -16 :: -10 :: 10 * 16
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The values of the expression can be determined as,
[tex]\begin{gathered} (-8)-2=-8-2=-10 \\ (-8)+2=-8+2=-6 \\ (-2)-(-8)=-2+8=6 \\ (-2)+(-8)=-2-8=-10 \\ (-8)-(-2)=-8+2=-6 \end{gathered}[/tex]Thus, the above expression gives the required values.
SAT scores were originally scaled so that the scores for each section were approximately normally distributed with a mean of 500 and a standard deviation of 100. Use the empirical rule to estimate the probability that a randomly-selected student gets a section score between 400 and 700.
Answers
Given:
a.) SAT scores were originally scaled so that the scores for each section were approximately normally distributed with a mean of 500 and a standard deviation of 100.
b.) Use the empirical rule to estimate the probability that a randomly-selected student gets a section score between 400 and 700.
How tall are you in centimeters? (Start with feet and inches and then convert to centimeters) . Round to two decimal places.(1cm = 0.3937in; 12in = 1ft)**My height is 5’11
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Based on the question, your height is 5 ft and 11 inches. Let's convert the numbers first to inches then centimeters.
Let's start with 5ft. Let's convert 5ft to inches first.
[tex]5ft\times\frac{12in}{1ft}=60in[/tex]Therefore, your height is 60 inches + 11 inches = 71 inches.
Let's convert 71 inches to cm.
[tex]71in\times\frac{1\operatorname{cm}}{0.3937in}=180.34\operatorname{cm}[/tex]Therefore, your height in cm is approximately 180.34 cm.
What is the domain ?A.All real NumbersB Y≥-4C. Y>-4D X≤4
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x ≤4
1) The Domain is the set of entries, a function is defined.
Examining the graph we can state the Domain is:
Note there are three ways to represent, formally this set Domain:
D =(-∞, 4] or ]-∞, 4] or {D ∈ R :-∞
Simply put
x ≤4
The fat cat weighs twice as much as the tiny dog.There are two unknowns in this problem, the weight of the cat and the weight of the dog,Both unknowns need to be described with the same variable. Do not use two differentletters. Give the variable to the unknown we know the least about, then use the given info tocreate an expression for the second unknown using the same variable.1. We know least about the weight of the dog, so let x equal the weight of the dog. Definethe weight of the cat in terms of x. See earlier examples if you need help.2. Write the simplified expression that models the combined weight of the cat and the dog.
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From the instructions on point number 1, let x be the weight of the dog.
Since the cat weighs twice as much as the dog, then the weight of the cat is equal to 2x.
The combined weight of the cat and the dog is the sum of their individual weights. Therefore, it is equal to 2x+x, which is equal to 3x.
please just give me the answer is homework please help1)vertex 2)axis of symmetry 3)x-intercepts 4)maximum or minimum 5)max/min value 6)y-intercept please help I really needed heeeeelp
Answers
Answer:
See explanations below
Explanation:
Vertex of a graph is the lowest point on the curve. The vertex occurs at (1.75, -2.5)
The axis of symmetry is the point on the x axis of the line that cuts through the minimum point. The axis of symmetry occurs at x = 1.75
x intercept is the point where the curve cuts the x axis. The x intercept occurs at x = 0 and x = 2.5
To get the minimum, we will use the formula;
c - b^2/4a
The equation of the curve is expressed as;
(x-0)(x-2.5)
= x (x-2.5)
= x^2 - 2.5x
a = 1, b = -2.5, c = 0
minimum = 0 - (-2.5)^2/4(1)
minimum = -6.25/4
minimum = -1.5625
Minimum value occurs at the base of the parabola. The minimum value of the function is -2.5
y intercept is the point where the curve cuts the y axis. The y-intercept occurs at y = 0.
Write the function that describes the transformation from Figure KLMN to Figure K'L'M'N'.
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Dilation centered at the origin whose scale factor is k=1/2
1) We need to locate two points from each figure, the pre-image and the image.
2) So, let's locate them:
K(0,11) K' (0, 5.5)
L (-9,3) L' (-4.5, 1.5)
3) As we can see the pre-image is larger than the image. And so, the scale factor of this Dilation has to be lesser than 1.
4) Therefore, the answer is:
Dilation centered at the origin whose scale factor is k=1/2
To show me similarity to this statement, how can it be done?
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We start with the expression at the left of the equation.
We can combine the terms as:
[tex]\begin{gathered} \frac{2+\sqrt[]{3}}{\sqrt[]{2}+\sqrt[]{2-\sqrt[]{3}}}-\frac{2-\sqrt[]{3}}{\sqrt[]{2}-\sqrt[]{2-\sqrt[]{3}}} \\ \frac{2+\sqrt[]{3}}{\sqrt[]{2}+\sqrt[]{2-\sqrt[]{3}}}\cdot\frac{(\sqrt[]{2}-\sqrt[]{2-\sqrt[]{3}})}{(\sqrt[]{2}-\sqrt[]{2-\sqrt[]{3}})}-\frac{2-\sqrt[]{3}}{\sqrt[]{2}-\sqrt[]{2-\sqrt[]{3}}}\cdot\frac{(\sqrt[]{2}+\sqrt[]{2-\sqrt[]{3}})}{(\sqrt[]{2}+\sqrt[]{2-\sqrt[]{3}})} \\ \frac{(2+\sqrt[]{3})\cdot(\sqrt[]{2}-\sqrt[]{2-\sqrt[]{3}})-(2-\sqrt[]{3})\cdot(\sqrt[]{2}+\sqrt[]{2-\sqrt[]{3}})}{(\sqrt[]{2}+\sqrt[]{2-\sqrt[]{3}})(\sqrt[]{2}-\sqrt[]{2-\sqrt[]{3}})} \end{gathered}[/tex]We can now apply the distributive property for the both the numerator and denominator. We can see also that the denominator is the expansion of the difference of squares:
[tex]\begin{gathered} \frac{(2+\sqrt[]{3})\cdot(\sqrt[]{2}-\sqrt[]{2-\sqrt[]{3}})-(2-\sqrt[]{3})\cdot(\sqrt[]{2}+\sqrt[]{2-\sqrt[]{3}})}{(\sqrt[]{2})^2-(\sqrt[]{2-\sqrt[]{3}}))^2} \\ \frac{(2+\sqrt[]{3})\cdot(\sqrt[]{2}-\sqrt[]{2-\sqrt[]{3}})+(\sqrt[]{3}-2)\cdot(\sqrt[]{2}+\sqrt[]{2-\sqrt[]{3}})}{2^{}-(2-\sqrt[]{3})^{}} \\ \frac{\sqrt[]{2}\cdot(2+\sqrt[]{3})-\sqrt[]{2-\sqrt[]{3}}\cdot(2+\sqrt[]{3})+\sqrt[]{2}\cdot(\sqrt[]{3}-2)+\sqrt[]{2-\sqrt[]{3}}\cdot(\sqrt[]{3}-2)}{2-2+\sqrt[]{3}} \\ \frac{\sqrt[]{2}(2+\sqrt[]{3}+\sqrt[]{3}-2)+\sqrt[]{2-\sqrt[]{3}}(-2-\sqrt[]{3}+\sqrt[]{3}-2)}{\sqrt[]{3}} \\ \frac{\sqrt[]{2}(2\sqrt[]{3})+\sqrt[]{2-\sqrt[]{3}}(-4)}{\sqrt[]{3}} \\ 2\sqrt[]{2}-4\frac{\sqrt[]{2-\sqrt[]{3}}}{\sqrt[]{3}} \end{gathered}[/tex]We then can continue rearranging this as:
A local small business will donate money to the student Use the graph to complete the table council based on the number of carnival tickets sold. The Tickets sold Money donated points shown on the graph represent the model. 10 a 25 b 10 20 30 10 40 d 10 15 20 25 30 35 40 a = b = Number of tickets sold c d= 5 10 5 20 Intro Done
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As we can see in the graph, for 10 tickets sold ( x-axis) we donate $5 (y-axis) the point is (10,5)
So; a = 5
To donate $10 (y-axis) we have to sell 20 tickets ( x-axis)
The point is ( 20,10)
So, b = 20
For 30 tickets sold (x-axis) the money donated is 15 (y-axis)
The point is : ( 30,15)
c= 15
For 40 tickets sold (x-axis) the money donated is 20 ( y-axis)
Point: (40,20)
d=20
Find the product of 1. 2x2 - 8x + 2 and 5x2 + 4x - 1 Your answer 2. (x3 - 12x2 + 33x-8) + (x - 8)Algebra II