Similar triangles are triangles that have the same interior angles and the corresponding sides are proportional, that is, for triangles STU and XYZ we have the proportion:
[tex]\frac{ST}{XY}=\frac{TU}{YZ}=\frac{SU}{XZ}[/tex]The corresponding sides are congruent only if the proportion rate is 1, but that is not always true and it's not necessary.
Therefore the correct option is B: False
If the corresponding sides are congruent, the triangles are congruent.
An employee makes $10.51 per hour but is getting a 3% increase. What is his new wage per hour to the nearest cent?
First, we find 3% of $10.51.
[tex]0.03\cdot10.51=0.32[/tex]Then, we add this increase to $10.51.
[tex]10.51+0.32=10.83[/tex]Hence, the new wage per hour is $10.83.The temperature is recorded in 65 cities on a given day in California the average temperature is 74ﾟF with a standard deviation 4ﾟ what is the Z score for temperature of 71ﾟ
the z-score is equal to
z=(74-71)/4
z=0.75
answer is 0.75A student cafeteria has 24 tables, tables X has 4 seats each, tables Y has 6 seats each, and tables Z has 10 seats each. The total seating capacity of the cafeteria is 148. For a student meeting, half of tables X, 1/4 of tables Y, and 1/3 of tables Z will be used, for a total of 9 tables. Determine X, Y, and Z. ( Answer the final answer in a full sentence. )
Answer: For a meeting, half of x, 1/4 of y, and 1/3 of z will be used for a total of 9 tables:
[tex]\begin{gathered} x+y+z=9 \\ \\ \\ \\ \frac{1}{2}x=\frac{4}{2}=2 \\ \\ \frac{1}{4}y=\frac{6}{4}=\frac{3}{2} \\ \\ \frac{1}{3}z=\frac{10}{3} \\ \\ \text{ Since we have a total of 9 tables therefore we have:} \\ \\ 3x+3y+3z\Rightarrow\text{ Total number of chairs.} \\ \\ 3(2)+3(\frac{3}{2})+3(\frac{10}{3})=6+\frac{9}{2}+10 \\ \\ \\ \text{Therefore:} \\ \\ ------------------------------- \\ \\ x=6 \\ \\ y=\frac{9}{2} \\ \\ z=10 \end{gathered}[/tex]Therefore the x = 6 and y = 9/2 and z = 10 is the answer.
The graph of a function is shown on the coordinate plane below. Which relationship represents a function with the same slope as the function graphed?
If (x_1, y_1) and (x_2, y_2) are points of a line, its slope is given by:
[tex]m=\frac{y_2-y_1}{x_2-x_1}\text{.}[/tex]From the graph of the function, we see that the line passes through the points:
• (x_1, y_1) = (-1, 6),
,• (x_2, y_2) = (0, 1).
The slope of the line is:
[tex]m=\frac{1-6}{0-(-1)}=-5.[/tex]A) Using the points:
• (x_1, y_1) = (-2, 0),
,• (x_2, y_2) = (2, 10).
We find that the slope of this line is:
[tex]m=\frac{10-0}{2-(-2)}=\frac{10}{4}=2.5.[/tex]This function has not the same slope as the line of the graph.
B) The general equation of a line is:
[tex]y=m\cdot x+b\text{.}[/tex]Where m is the slope and b is the y-intercept.
Comparing the general equation with the equation:
[tex]y=-5x+3,[/tex]we see that the slope of the line of this equation is m = -5.
This function has the same slope as the line of the graph.
C) Using the points:
• (x_1, y_1) = (-4, 8),
,• (x_2, y_2) = (0, 5).
We find that the slope of this line is:
[tex]m=\frac{5-8}{0-(-4)}=-\frac{3}{4}=-0.75.[/tex]This function has not the same slope as the line of the graph.
D) Comparing the general equation with the equation:
[tex]y=-\frac{5}{4}x+2.[/tex]we see that the slope of the line of this equation is m = -5/4.
This function has not the same slope as the line of the graph.
Answer
B. y = -5x + 3
4(3y-7)=-3(-2y) - 4
What is the y
Answer:
y=4
Step-by-step explanation:
first we have to distribute
4(3y)+(4)(-7)=-3(-2y)-4
12y-28=6y-4
6y-28=-4
6y=24
y=4
Hopes this helps please mark brainliest
Find the circumference of a circle with an area of 95.03 m^2. Round the answer to the nearest tenth.
The area of a circle with radius r is given by the following formula:
[tex]A=\pi r^2[/tex]The circumference of that circle is given by:
[tex]C=2\pi r[/tex]Finding the answerWe are given the area of the circle. With this data and the first formula we can construct an equation for the radius r. Once we find the radius of the circle we can use it to find its circumference. So first of all we take the first formula and we equalize it to 95.03:
[tex]95.03=\pi r^2[/tex]We can divide both sides by π:
[tex]\begin{gathered} \frac{95.03}{\pi}=\frac{\pi r^2}{\pi} \\ r^2=\frac{95.03}{\pi} \end{gathered}[/tex]Now we apply a square root to both sides:
[tex]\begin{gathered} \sqrt{r^2}=\sqrt{\frac{95.03}{\pi}} \\ r=\sqrt{\frac{95.03}{\pi}} \end{gathered}[/tex]And that's the radius of the circle. Then we can use this value in the formula of the circumference C:
[tex]C=2\pi *\sqrt{\frac{95.03}{\pi}}=34.6[/tex]AnswerThen the answer is 34.6 m.
1,1,2,2,2,5,5,8,9,10,11
In order to calculate the median the data should be arranged in order from least to greatest.
According to this question we have the following number:
1,1,2,2,2,5,5,8,9,10,11
So, we would proceed to arrange the number as follows:
1, 1, 2, 2, 2, 5, 5, 8, 9, 10, 11
As we have a total of number of 11, then that means that the median would be the central score of it.
Therefore, in this case the central score
Dave wants to borrow $22,000 from first finance bank. the bank will give him a 15 year loan at an interest rate od 4.85 % how mich will he pay the bank in interest over the life of the loan? Round to the nearest hundred dollar ?
Problem 7:
We determine the time as follows:
*We can proceed using the following expression:
[tex]t=\frac{\ln (\frac{m}{p})-\ln (\frac{m}{p}-\frac{r}{n})}{n\ln (1+\frac{r}{n})}[/tex]Here, t is the time it will take to pay, m is the maximum she can afford to pay each month, p is the base loan value, r is the interest rate, n is the number of periods. Now we replace:
[tex]t=\frac{\ln(\frac{500}{20000})-\ln(\frac{500}{20000}-\frac{0.071}{12})}{12\ln(1+\frac{0.071}{12})}\Rightarrow t\approx3.8[/tex]So, she will take approximately 3.8 years to pay up the loan.
Problem 8:
We determine the time he has as follows:
We use the expression:
[tex]t=\frac{\ln (\frac{m}{p})-\ln (\frac{m}{p}-\frac{r}{n})}{n\ln (1+\frac{r}{n})}[/tex]Here, t is the time it will take to pay, m is the maximum he can afford to pay each month, p is the base loan value, r is APR, n is the number of periods. Now we replace:
[tex]t=\frac{\ln(\frac{400}{14000})-\ln(\frac{400}{14000}-\frac{0.068}{12})}{12\ln(1+\frac{0.068}{12})}\Rightarrow t\approx3.3[/tex]So, he will take approximately 3.3 years to pay the loan.
Problem 10:
We determine the amount he will have to pay as follows:
*We use the following expression:
[tex]V=P(1+n)^t[/tex]Here V is the value to obtain, P is the original amount, n is the interest rate and t is the number of periods, now we replace:
[tex]V=(22000)(1-0.0485)^{15}\Rightarrow V\approx44766.09[/tex]So, after 15 years he will have to pay approximately $44766.09.
Two fifths of the instruments in the marching band are brass
A 4/15 fraction of the band's instruments are woodwinds.
What is a fraction?It describes how many parts of a certain there are. The foundations of fractions explain the top and bottom numbers in a fraction. It represents a numerical value that expresses a part of a whole. The whole can be any specific value or a particular number. A fraction has two parts. The figure above the line is known as the numerator and the number below the line is termed the denominator.
Given, two-fifths of the marching band is brass. And one-third of them are percussion.
Multiply 2/5 by 3 we get, 6/15
And multiply 1/3 by 5 we get, 5/15
Given, that the rest are woodwind instruments,
Then, 1-(6/15)-(5/15)=4/15
4/15 fraction of the band's instruments are woodwinds
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The complete question is:
"Two-fifths of the instruments in the marching band are brass, one-third are percussion, and the rest are woodwinds. What fraction of the band is woodwinds?"
Use quadratic formula to find the roots of x^2+2x-7
Okay, here we have this:
[tex]x^2+2x-7=0[/tex]We will solve using the general formula, then we obtain:
[tex]\begin{gathered} x_{1,2}=\frac{-2\pm\sqrt[]{2^2-4\cdot1\cdot(-7)}}{2\cdot1} \\ =\frac{-2\pm\sqrt[]{4+28}}{2} \\ =\frac{-2\pm\sqrt[]{32}}{2} \\ =\frac{-2\pm4\sqrt[]{2}}{2} \end{gathered}[/tex]Let's separate the solutions:
[tex]\begin{gathered} x_1=\frac{-2+4\sqrt[]{2}}{2} \\ =\frac{2(-1+2\sqrt[]{2})}{2} \\ =-1+2\sqrt[]{2} \end{gathered}[/tex][tex]\begin{gathered} x_2_{}=\frac{-2-4\sqrt[]{2}}{2} \\ =\frac{2(-1-2\sqrt[]{2})}{2} \\ =-1-2\sqrt[]{2} \end{gathered}[/tex]Finally we obtain that the roots are: -1+2√2 and -1-2√2.
I need help with this question... the correct answer choice
Given:
P(2,-4) to point P'(-2,1)
[tex]P(2-4,-4+5)=P^{\prime}(-2,1)[/tex][tex](x,y)\rightarrow(x-4,y+5)[/tex]3rd option is the correct answer.
Describe how the graph of the function is a transformation of the original function f.y=f(x+16)This results in a Answer shift to the graph Answer units Answer.
When we add a constant to the argument of a function, we are shifting the graph horizontally. If the constant is positive, the graph gets shifted to the left, if it's negative, the graph gets shifted to the right.
With this in mind we can solve the problem. The constant "16" was added to the argument of the function "f(x)". This results in a "horizontal" shift to the graph "16" units "to the left".
If a savings account of $19,400 is compounded semiannually at 5,07% annual interest, how much will the account be worth in 32 months? Round your answer to thenearest cent, if necessary. Note: 365 days in a year and 30 days in a month.
From the question, we are provided with the following information:
[tex]\begin{gathered} \text{Principal, P=\$19,400} \\ \text{Rate, r=5.07\%} \\ r=\frac{5.07}{100}=0.0507 \\ \text{Time, t(in years)=}\frac{32}{12}=2.67years \\ N\text{umber of times interest applied per time period, n=2(semi-annually)} \end{gathered}[/tex]The required parameter we are to find is the Amount, A.
Amount of a compound interest is given by the formula:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Thus, we have:
[tex]\begin{gathered} A=19,400(1+\frac{0.0507}{2})^{2\times2.67} \\ A=19400(1+0.02535)^{5.34} \\ A=19400(1.02535)^{5.34} \\ A=19400\times1.143 \\ A=\text{ \$22,174.76} \end{gathered}[/tex]Hence, the account will be worth $22,174.76 in 32 months
A car with a 15-gallon gas tank can go 22 miles on 1 gallon of gas. If the tank is full at the beginning of a 377-mile trip, how many times does the driver have to refill the gas tank?
Consider that the car can go 22 miles on 1 gallon of gas, therefore the amount of gas required for the 377 mile trip is calculated as,
[tex]\frac{377}{22}\approx17.136[/tex]So the car needs 17.136 gallons of gas to complete the trip.
Since the capacity of the tank is 15 gallons, so the driver has to fill the tank two times.
First time for the full 15 gallons refill, and the second tme for the remaining 2.136 galllons fuel refill.
Thus, the driver has to refill the gas tank 2 times, to complete the trip.
Reasoning Use the Distributive Property to solve the equation below. Use pencil and paper. Explain why the Distributive Property makes it possible to solve this equation. 44 - (2c + 3) = 4(C+5) + C The solution of the equation is
ANSWER and EXPLANATION
The distributive property involves simplifying expressions to make them easier to solve.
It is possible to solve the equation with distributive property because it allows us to break down equations into simpler forms of addition or subtraction.
The equation we are given is:
44 - (2c + 3) = 4(c + 5) + c
Using the distributive property, we have:
44 - 2c - 3 = 4c + 20 + c
Collect like terms:
-2c - 4c - c = 20 - 44 + 3
-7c = -21
Divide through by -7:
c = -21 / -7
c = 3
The equation has been solved.
Which of the following transformations accurately describes the relationship between the two trapezoids?A. Dilate the blue trapezoid by a scale factor of ½ to obtain the red trapezoid.B. Dilate the red trapezoid by a scale factor of 2 to obtain the blue trapezoid.C. Dilate the red trapezoid by a scale factor of ½ to obtain the blue trapezoid.D. Dilate the blue trapezoid by a scale factor of 3 to obtain the red trapezoid.
Given: Two trapezoid as shown in the image
To Determine: The transformation that relates the two trapezoids
Solution
Let us determine the coordinates of the two trapezoid as shown below
We can relate the blue trapezoid to the red trapezoid
[tex]\begin{gathered} (3,1.5)\rightarrow(6,3) \\ (4.5,1.5)\rightarrow(9,3) \\ (3,3)\rightarrow(6,6) \\ (4.5,4.5)\rightarrow(9,9) \end{gathered}[/tex]It can be observed that the transformation rule that relates the blue trapezoid to the red trapezoid is
[tex](x,y)\rightarrow(2x,2y)[/tex]It can be observed that the blue trapezoid is enlarged by a scale factor to get the red trapezoid. So, we dilate the blue trapzoid by a scale factor of 2 to get the red trapezoid.
From the options provided, the best answer related the red trapezoid to the blue trapezoid, which is a reduction by a scale factor of 1/2
Hence, the correct option is
Dilate the red trapezoid by a scale factor of 1/2 to obtain the blue trapezoid, OPTION C
A sun is a distant of galaxy what is the distance
We would divide the mass of the sun by the mass of the earth. From the information given,
mass of earth = 5.972 x 10^24
mass of sun = 1.61244 x 10^31
Number of earths = 1.61244 x 10^31/5.972 x 10^24 = 2.7 x 10^6
It will take 2.7 x 10^6 to equal the mass of the sun
Estimate the sum of the decimals below by rounding to the nearest whole number. Enter your answer in the space provided gym
Given:
[tex]5.029,8.315,5.284[/tex]Required:
Find the estimated sum of the given decimals to the nearest whole number.
Explanation:
The estimated sum by rounding to the nearest whole number is 19.
Final Answer:
The estimated sum of the given decimals by rounding to the nearest whole number is 19.
70% of what is 35 ???
We calculate the 70% of the number that is 35 as follows:
[tex]x=\frac{35\cdot100}{70}\Rightarrow x=50[/tex]So, the number which 70% is 35 is 50.
Please help me with #1Please help me on my hw
The given expression is,
[tex](2x^2)^3[/tex]According to the law of exponents,
[tex]\begin{gathered} (xy)^m=x^my^m\text{ ---(a)} \\ (x^m)^n=x^{mn}\text{ ---(b)} \end{gathered}[/tex]Applying the law of exponents to the given expression,
[tex]\begin{gathered} (2x^2)^3=2^3(x^2)^3\text{ (using law (a))} \\ =8x^{2\times3}\text{ (using law (b))} \\ =8x^6 \end{gathered}[/tex]Therefore, the correct expression is
[tex](2x^2)^3=8x^6[/tex]
Which ratio represents the ratio 6 cups to 4 quarts in simplest form? ●3 to 8 ●6 to 16 ●3 to 4 ●3 to 2
Simplift the ratio of 6 cups to 4 quarts.
[tex]\begin{gathered} \frac{6}{4}=\frac{2\times3}{2\times2} \\ =\frac{3}{2} \end{gathered}[/tex]So in simplest form ratio is 3 to 2.
x^2- 20x = -2x – 80In (x+a)^2=b form please hurry
Completing Squares
It's given the following equation:
[tex]x^2-20x=-2x-80[/tex]We are required to express the equation in the form:
[tex](x+a)^2=b[/tex]The first step is sending all the variables to the left side of the equation.
Adding 2x:
[tex]\begin{gathered} x^2-20x+2x=-80 \\ \\ \text{Simplifying:} \\ x^2-18x=-80 \end{gathered}[/tex]To complete squares, we need to recall the following identity:
[tex]p^2+2pq+q^2=(p+q)^2[/tex]The expression on the left side is missing the third term to be a perfect square. Note that comparing
p=x
2pq = -18x
This means that
q = -18x/2p
q = -18x/2x
q = -9
Now we know the value of the second term, we need to add q^2=81:
[tex]x^2-18x+81=-80+81[/tex]The left side of the equation is the square of x-9, and the right side can be calculated:
[tex](x-9)^2=1[/tex]Now we have the required expression, where a=-9 and b = 1
-------------------
1/2 to 3rd power1/2 to the 3rd power
Let's begin by identifying key information given to us:
[tex]\begin{gathered} (\frac{1}{2})^3=\frac{1}{2}\cdot\frac{1}{2}\cdot\frac{1}{2}=\frac{1}{8} \\ \Rightarrow(\frac{1}{2})^3=\frac{1}{8} \end{gathered}[/tex]Mr. Abraham, a married man, works a 40 hour work week, 48 wooks each yoor, His hourly rate of pay is $36.60 por hour. Aftor tax deductions for his two exemptions, his bl-wookly taxablo wagos were 12,410.77. How much is deducted from each paycheck for fodoral income tax? Noto: Porcontage mothod for calculation: For taxablo bi-wooklywages over 5066, but not over $2,698 - 366,40, plus 18% of excess over $068.$200,00$278.56$283.32$294.70None of these choices are correct.
We know that the biweekly tax is equal to $65.40 plus 15% of excess over $958. In this case the excess is:
[tex]2410.77-958=1452.77[/tex]Then for this excess the tax is:
[tex]0.15\cdot1452.77=217.92[/tex]Hence the total tax is:
[tex]217.92+65.40=283.32[/tex]Therefore the answer is the third option.
How do I solve the role of zero?f(x) = (x - 2)^5 (x + 4)^3
ANSWER
2 and -4
EXPLANATION
We are given the function:
f(x) = (x - 2)^5 (x + 4)^3
We simply need to find the zeros of the function and to do that, we need to find the values of x such that the function will be 0.
The function has already been factorised and so, we simply need to identify the zeros.
There are two zeros for the function and they are 2 and -4.
This is because when x is either 2 or -4, the function resolves to 0.
When x = 2:
[tex](2-2)^5(2+4)^3=0(6)^3\text{ = 0}[/tex]and when x = -4:
[tex](-4-2)^5(-4+4)^3=(-6)^50\text{ = 0}[/tex]And so, the zeros of the function are 2 and -4.
Supposed that the mean systolic blood pressure for women I’ve age seventy is 131mmHg ( millimeters of mercury), with a standard deviation of 9 mmHg. Supposed that the blood pressure are normally distributed. Complete the following statements ( choose correct answers 68%,75%,95%,99.7%)
To answer the question, having a z-table with you will help. We can also use the 68-95-99.7 rule.
The rule states that 68.27% of a normally distributed data set is within one standard deviation of the mean, 95.45% is within two standard deviations, and 99.73% is with three standard deviations.
Given that the mean is 131 mmHg and the standard deviation is 9 mmHg, we can calculate the boundaries which are 3 standard deviations away from the mean by adding and subtracting three times the standard deviation.
[tex]\begin{gathered} 131-(3\times9)=104 \\ \\ 131+(3\times9)=158 \end{gathered}[/tex]Therefore, approximately 99.7% of women over seventy have blood pressures between 104 mmHg and 158 mmHg.
Now let's find out how many standard deviations away 122 mmHg and 140 mmHg are from the mean.
[tex]\begin{gathered} z=\frac{122-131}{9}=-1 \\ \\ z=\frac{140-131}{9}=1 \end{gathered}[/tex]122 and 140 mmHg are within 1 standard deviation of the mean. Using the 68-95-99.7 rule, we know that approximately 68.27% of women over seventy have blood pressures between 122 mmHg and 140 mmHg.
use basic trigonometric identities to simplify the expression: -tan (-x) cot (-x) = ?
-1
Explanation
let's remember the indentities
[tex]\begin{gathered} tan\theta=\frac{sen\text{ \lparen x\rparen}}{cos\text{ \lparen x\rparen}} \\ cot\theta=\frac{cos(x)}{sin(x)} \end{gathered}[/tex]so
Step 1
let the expression
[tex]-tan(-x)cot(-x)=?[/tex]rewrite the expression:
replace using the identity
[tex]\begin{gathered} -tan(-x)cot(-x)=? \\ -tan(-x)cot(-x)=-\frac{\sin(-x)}{cos(-x)}*\frac{cos(-x)}{\sin(-x)} \\ -tan(-x)cot(-x)=-\frac{\sin(-x)}{sin(-x)}\frac{cos\left(-x\right)}{\sin(*x)} \\ -tan(-x)cot(-x)=-1*1 \\ -tan(-x)cot(-x)=-1 \end{gathered}[/tex]therefore, the answer is
-1
I hope this helps you
△ABC has a right angle at C, BC=7.7 centimeters, and m∠A=41∘. What is CA ? Enter your answer rounded to the nearest tenth in the box.
The length of the side CA is 11.84cm when the triangle is ABC and the right angle is at ∠C and the length of BC is 7.7 cm and angle A is 41°.
Given that,
The triangle is ABC and the right angle is at ∠C.
The length of BC is 7.7 cm and angle A is 41°.
We have to find the length of CA.
Take the side CA as x.
Take the trigonometric ratio.
TanA =Opposite side/ adjacent side.
Tan 41° = 7.7/ x
0.65= 7.7/x
x= 7.7/0.65
x= 11.84 cm.
Therefore, The length of the side CA is 11.84cm when the triangle is ABC and the right angle is at ∠C and the length of BC is 7.7 cm and angle A is 41°.
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2) Joe has a cube of cheese that measures 4 inches on each edge. He cuts out a 1-inch cube of
cheese from each of the eight corners, as shown below. What percentage of the cheese does
Joe cut out from the original cube of cheese? Express your answer as a decimal.
The percentage of the cheese cut off by Joe from the original cube of cheese is 12.5% by application of the formula for finding the volume of a cube.
Volume of a cubeThe volume of a cube is defined as the total number of cubic units occupied by the cube. The formula is given as V = a³ where "a" is the length of edge or sides.
Given that the cube of cheese has 4inches of length on its edges, then volume;
V = 4³inches
V = (4×4×4) inches
V = 64inches
the total volume cut off by Joe from the original cube of cheese;
V = 1inch × 8edges of the cube cheese
V = 8inches
Therefore, the percentage of the cube cheese cut off by Joe from the original cheese is derived as;
(8/64) × 100 = 12.5% by simplification.
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Convert the repeated decimal 0.47 into a fraction using infinite geometric series.
Answer:
47/99
Explanation:
Given the repeated decimal 0.4747...
This can be splitted into;
0.47 + 0.0047 + 0.000047 + ...
On rewriting;
47/100 + 47/10000 + 47/1000000 + ...
The given series is a geometric progression
The sum to infinity of a geometric progression is expressed as;
[tex]S\infty\text{ = }\frac{a}{1-r}[/tex]a is the first term
r is the common ratio
From the sequence;
a = 47/100
r = (47/10000)/(47/100)
r = 47/10000 * 100/47
r = 1/100
Substitute;
[tex]\begin{gathered} S\infty\text{ = }\frac{\frac{47}{100}}{1-\frac{1}{100}} \\ S\infty\text{ = }\frac{\frac{47}{100}}{\frac{99}{100}} \\ S\infty\text{ = }\frac{47}{100}\cdot\frac{100}{99} \\ S\infty\text{ = }\frac{47}{99} \end{gathered}[/tex]Henec the repeated fraction to decimal is 47/99