个HS: Math II North Carolina High School Math II [M] (Prescripti8. Which statement is true?O OIf two figures are congruent, then they have the same shape but nOIf two figures are congruent, then they are similar.OIf two figures are similar, then they are congruent.OIf two figures are similar, then corresponding sides must be congru
![HS: Math II North Carolina High School Math II [M] (Prescripti8. Which Statement Is True?O OIf Two Figures](https://brainimage.s3.us-east-005.backblazeb2.com/contents/attachments/UKKqKY2JYzJYXsPp9RMt4CVko7SlnuZj.jpeg)
Answers
For two triangles to be similar, it is enough if two angles of one triangle are equal to two angles of the other triangle.
If two figures are congruent, the corresponding sides must be equal and also the corresponding sides.
Therefore, the answer is:
If two figures are congruent, then they are similar
Related Questions
use the angle shown to determine if the line are parallel
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If the lines were parallel then
angle H would be corresponding to angle L and then
[tex]\measuredangle H\cong\measuredangle Z.[/tex]Since angles H and Z are a linear pair then if the lines were parallel angle H, Z and L would have to be right angles. Since the problem never states that those angles are right angles, then the lines are not necessarily parallel.
Answer: No.
Right Triangle ABC is pictured below.Which equation gives the correct value for BC?Option 1: sin(32) = BC/8.2Option 2: cos(32) = BC/10.6Option 3: tan(58) = 8.2/BCOption 4: sin(58) = BC/10.6
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Given the image, we are asked which equation gives the correct value for BC?
Explanation
From the image;
[tex]\begin{gathered} A+B+C=180 \\ 32+B+90=180 \\ B=180-90-32 \\ B=58^0 \end{gathered}[/tex]Therefore,
[tex]tan58^0=\frac{opposite}{Adjacent}=\frac{8.2}{BC}[/tex]Answer: Option three
Write the ordered pair with no spaces (x,y) of point C for j(x).
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This problem is about functions.
In this case, we don't have function j(x) defined in order to find its ordered pairs.
However, assuming that function j(x) is a function of f(x), we can deduct that points C is
[tex]C(0,0)[/tex]21/x=48/96. 70/b=20/80. 50/20=x/72
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In summary, the respective values of the unknown variables in the equations are 42, 280, and 1800.
which calculation does not show the surface area of the cube?
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Given: A cube with side 6.5 cm
Required: Which calculation does not show the surface area of the cube.
Explanation:
Surface area of cube with side a is 6a².
So here the surface area of cube is
[tex]6(6.5)^2[/tex]Oprion 2, 3 and 4 reflects the calculation correctly.
But option A is actually the volume of the cube, it is not a correct way to show surface area of the cube.
Final Answer: option A is correct.
Factor the following expression using the GCF.5dr - 40rr(5 dr - 40)5 r( d - 8)r(5 d - 40)5( dr - 8 r)
Answers
The greatest common factor (GCF) is: 5r
You multiply 5r by d to get the first term and multiply 5r by -8 to get the second term, then the factors are:
[tex]5r(d-8)[/tex]Answer: 5r(d-8)4. Identify the properties that are always true for the given quadrilateral by placing an X in the appropriate box. Property Parallelogram Rectangle Rhombus Square Isosceles Trapezoid Kite a. Opposite sides are parallel. b. Only one pair of opposite sides is parallel C. Opposite sides are congruent Side Relationships d. Only one pair of opposite sides is congruent e. All sides are congruent. f. 2 pairs of consecutive sides are congruent.
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There is quadrilateral, means it has 4 lines
Is a rhombus
The volume of the right cone below is 36π units ^3. Find the value of x
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The formula to find the volume of a cone is:
[tex]\begin{gathered} V=\frac{1}{3}\pi r{}{}^2h \\ \text{ Where} \\ V\text{ is the volume} \\ r\text{ is the radius} \\ h\text{ is the heigth} \end{gathered}[/tex]Then, we replace the know values in the above formula and solve for h.
[tex]\begin{gathered} V=36\pi \\ r=\frac{\text{ diameter}}{2}=\frac{6}{2}=3 \\ h=x \end{gathered}[/tex][tex]\begin{gathered} V=\frac{1}{3}\pi r^2h \\ 36\pi=\frac{1}{3}\pi(3)^2x \\ 36\pi=\frac{9\pi x}{3} \\ 36\pi=3\pi x \\ \text{ Divide by }3\pi\text{ from both sides} \\ \frac{36\pi}{3\pi}=\frac{3\pi x}{3\pi} \\ 12=x \end{gathered}[/tex]AnswerThe value of x is 12 units.
Square ABCD is inscribed in a circle with radius 20 m . What is the area of the part of the circle outside of the square
Answers
ANSWER:
456 square meters
STEP-BY-STEP EXPLANATION:
The first thing is to represent the problem in the following figure:
To calculate the area of the part of the circle outside of the square, we must calculate the area of the circle and subtract the area of the inscribed square.
To calculate the area of the square, we plant the following, taking into account that the diagonal of the square is equal to twice the radius and the sides equal to the radius times the root of two, like this:
Knowing the value of the side of the square, we can directly calculate the area of the part of the circle outside of the square, subtracting the corresponding areas like this:
[tex]\begin{gathered} A=A_C-A_S_{} \\ A=\pi\cdot r^2-\mleft(r\cdot\sqrt{2}\mright)^2 \\ \text{replacing} \\ A=3.14\cdot20^2-\mleft(20\cdot\sqrt{2}\mright)^2 \\ A=1256-800 \\ A=456 \end{gathered}[/tex]The area of the part of the circle outside of the square is equal to 456 square meters
WXYZ is a kite. Use the figure below to fill in the blanks below.
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We can assume the kite is simetrycal along line WY, as such
[tex]ZW=XW=10[/tex][tex]m\angle\text{XSW}=90[/tex]because the diagonals of a kite are perpendicular.
Since m∠XSW is 90°, triangle WSX is a right triangle. Thus
[tex]m\angle WXZ=m\angle WXS=180-90-46=44[/tex]By the symmetry we discussed earlier,
[tex]m\angle WYZ=m\angle WYX=18[/tex]And finally
[tex]m\angle XYZ=m\angle WYZ+m\angle WYX=18+18=36[/tex]PLEASE ANSWER ASAP1. The length of a bookshelf is 5 ft. The length of a model of this bookshelf is 3 ft. Find the scale of the model to the bookshelf. Enter your answer in the box.2. A rectangular garden has a length of 8 ft and a width of 4 ft. A smaller garden was made, using a scale of 3:4 . Find the dimensions of the smaller garden. Enter your answers in the boxes.
Answers
1.
The scale factor would be:
[tex]3\colon5[/tex]2.
Divide each original dimension by 4 and then multiply by 3, as following:
[tex]\begin{gathered} \frac{8ft}{4}\cdot3=6ft \\ \\ \frac{4ft}{4}\cdot3=3ft \end{gathered}[/tex]The smaller garden has a length of 6 ft and a widht of 3 ft
triangle OPQ is similar to triangle RST. Find the measure of side RS. Round your answer to the nearest tent if necessary
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To answer this question, we have that, if two triangles are similar, they maintain the same proportion on their corresponding sides.
We have that the corresponding sides are QP and TS, OP and RS, and QO and TR, so we can write:
[tex]\frac{TS}{QP}=\frac{RS}{OP}=\frac{TR}{QO}[/tex]Then, since we have the values for QP, TS, and OP, we can find RS using the above proportion:
[tex]\frac{TS}{QP}=\frac{RS}{OP}\Rightarrow\frac{41.4}{11}=\frac{RS}{8}\Rightarrow RS=\frac{41.4\cdot8}{11}=\frac{331.2}{11}\Rightarrow RS=30.109090\ldots[/tex]Then, we have that we can round this value to 30.11 units, and if we round the answer to the nearest tenth, we finally have that RS = 30.1 units.
Answer:
x = 30.1 (round 30)
Step-by-step explanation:
being similar we can solve with a simple equation
11 : 8 = 41.4 : x
x = 8 × 41.4 : 11
x = 331,2 : 11
x = 30.1 (round 30)
Which probem situation can be represented by the equation below?3x +3 <11F Joe and Hannah together got less than 11 questions correct on their quizzes. Joe got 3 more questions correct than Hannah. What is x, the number of quiz questions Hannah got 3 correct?G A coin collection of dimes and quarters has less than 11 coins. The collection has more than 3 times as many quarters as dimes. How many dimes, x, is in the collection?H Two numbers have a sum that is less than 11. The larger number is 3 more than twice he smaller number. What s the smaller number, x?J The length of a rectangle is 3 inches more than the width, x. Three times the length is less than 11. What is the width of the rectangle?
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Let x be correct questions of Joe and y be correct quiz question of Joe. The in equality for Joe and Hannah together questions is,
[tex]x+y<11[/tex]Joe got 3 more questions correct than Hannah, means equaltion is,
[tex]y=x+3[/tex]So inequality obtained is,
[tex]\begin{gathered} x+x+3<11 \\ 2x+3<11 \end{gathered}[/tex]Thus option F is incorrect.
Let x be number of dimes and y be number of quarters. So inequality for collection of coins is,
[tex]x+y<11[/tex]The number of quarters are,
[tex]y=3x[/tex]So resultant inequality is,
[tex]\begin{gathered} x+3x<11 \\ 4x<11 \end{gathered}[/tex]Thus option G is incorrect.
Let larger number be y. So sum of numbers is less than 11, means
[tex]x+y<11[/tex]The equation of larger number in terms of smaller number is,
[tex]y=2x+3[/tex]Substitute the value of y in the inequality to obtain the desired inequality.
[tex]\begin{gathered} x+2x+3<11 \\ 3x+3<11 \end{gathered}[/tex]Thus inequality obtained is 3x + 3 < 11.
Thus option H is correct.
Correct option : Two numbers have a sum that is less than 11. The larger number is 3 more than twice he smaller number. What s the smaller number, x?
the product of 4 and the diference of 9 and 2 find the value of your expression
Answers
Answer:
28
Step-by-step explanation:
4(9-2)
4(7)
28
help me pleaseeeeeeeee
Answers
Answer:
A. 200
B. 500
Step-by-step explanation:
1000x²
R(x) = --------------
x² + 4
x = years
A. the first year = 1
1000(1)²
R(1) = --------------
(1)² + 4
1000
R(1) = --------------
1 + 4
1000
R(1) = --------------
5
R(1) = 200
B. years = 2
1000(2)²
R(2) = --------------
(2)² + 4
1000(4)
R(2) = --------------
4 + 4
4000
R(2) = --------------
8
R(2) = 500
I hope this helps!
Write 5^-15 with a positive exponent
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Given:
[tex]5^{-15}[/tex]To change a negative exponent to a positive exponent, the variable will change from numerator to denominator and vice versa.
For example:
[tex]\begin{gathered} P^{-1}\text{ = }\frac{1}{P} \\ \\ We\text{ know that:} \\ 5^{-15}=5^{(15)-1} \\ \\ 5^{(15)-1}\text{ = }\frac{1}{5^{15}} \end{gathered}[/tex]Therefore, we have:
[tex]5^{-15}\text{ = }\frac{1}{5^{15}}[/tex]ANSWER:
[tex]\frac{1}{5^{15}}[/tex]ive tried to do this question multiple times but i just cant seem to understand it
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The domain of the function which is the entire x values during the strike is
[tex]0\leq x\leq230[/tex]Please help, disregard the option I chose because I'm not sure it's right :)
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Consider that the graph of f(x) is the graph of a cubic function, that is, the graph of a 3 degree polynomial. If you apply first derivative to such a polynomial, the result is another polynomial of degree 2.
Now, take into account that the graph of a polynomial of degree 2 is a parabola. The parabola can open up or down. It depends of the leadding coefficient of the polynomial. In this case, due to the graph of f(x), the leadding coefficient is positive, which means that the parabola of f'(x) opens up.
Hence, you can conclude that the graph of f'(x) is option C.
How do I solve it and what would be the answer
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The quotient is x² + 4x + 3
Yes, (x - 2) is a factor of x³ + 2x² - 5x - 6
Explanation:[tex](x^3+2x^2\text{ - 5x - 6) }\div\text{ (x - 2)}[/tex][tex]\begin{gathered} x\text{ - 2 = 0} \\ x\text{ = 2} \\ \\ \text{coefficient of }x^3+2x^2\text{ - 5x - 6:} \\ 1\text{ 2 -5 -6} \\ \\ We\text{ will divide the coefficients by 2} \end{gathered}[/tex]Using synthetic division:
[tex]\begin{gathered} (x^3+2x^2\text{ - 5x - 6) }\div\text{ (x - 2) = }\frac{(x^3+2x^2\text{ - 5x - 6)}}{\text{(x - 2)}} \\ \frac{(x^3+2x^2\text{ - 5x - 6)}}{\text{(x - 2)}}\text{ = quotient + }\frac{remai\text{ nder}}{\text{divisor}} \\ \\ The\text{ coefficient of the quotient = 1 4 3} \\ \text{The last number is zero, so the remainder = 0} \end{gathered}[/tex][tex]\begin{gathered} \frac{(x^3+2x^2\text{ - 5x - 6)}}{\text{(x - 2)}}=1x^2\text{ + 4x + 3 + }\frac{0}{x\text{ - 2}} \\ \text{quotient }=\text{ }x^2\text{ + 4x + 3} \end{gathered}[/tex]For a (x - 2) to be a factor of x³ + 2x² - 5x - 6, it will not have a remainder when it is divided.
Since remainder = 0
Yes, (x - 2) is a factor of x³ + 2x² - 5x - 6
5. a) Look at the number grid below. Shade the Multiples of 4, 1 2 3 4 5 6 7 00 8 9 10 11 12 13 14 15 16 17 17 18 19 20
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We need to find the multiples of 4 using the next given set:
The multiples of 4 are given by
4*1 =4
4*2 = 8
4*3= 12
4*4=16
4 *5 =20
Then:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20.
In ATUV, the measure of ZV=90°, TV = 28, UT = 53, and VU = 45. What ratiorepresents the cosecant of ZU?
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cosecant = hypotenuse / opposite side
hypotenuse = 53
opposite side = 28
cosecant U = 53/28
find the percent notation 7/10
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A notation is a way of communicating through symbols or signs, or it might be a brief written message. A chemist notating AuBr for gold bromide is an illustration of a notation. A quick list of things to accomplish is an illustration of a notation.
Explain about the percent notation?Since one percent (symbolized as 1%) is equal to one hundredth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified.
A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The sign "%" is used to denote it.
When expressing a fraction as a percentage, we multiply the provided fraction by 100.7/10, which is 70%.
To learn more about percent notation refer to:
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6. ΔABC is mapped onto ΔA'B'C' by a dilation at D. Complete the statement: The dilation of 4/3 is _____. a. a reduction b. an enlargement
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Dilation involves adjusting the size of an object or a figure, without altering its shape.
The object can be increased or decreased depending on its scale factor.
A scale factor less than 1 results in a figure of reduced dimensions whereas, a scale factor greater than 1 results in a figure or an object of enlarged dimensions.
In the ΔABC, a dilation of 4/3, which is greater than 1, will thus result into an enlargement.
The correct option is B.
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Answer:
[tex]\large \text{$f^{-1}(x) = 3x -6$}[/tex]
Graphs attached
Step-by-step explanation:
Your inverse function is correct. So not sure what additional information you need
I am not familiar with the graphing tool you have been provided with. My graph is attached. I used a free online graphing tool
You can use a calculator to approximate the logarithm. Round to four decimal place
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This is a simple question to solve when we use the calculator (as the question allows us to use it).
For this problem when we have :
[tex]\log \pi[/tex]It can be read as "log base 10 of pi", and using a calculator we find:
And that is the final answer.
NOTE: this result means that:
.
what is the slope of the line which goes through the points (-2, -9) and (2, 11) the slope of the line is___
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We know the equation of a line is given by:
[tex]y=mx+b[/tex]where m is its slope and b its interpcetion with y - axis.
We know the slope equation is
[tex]\begin{gathered} m=\frac{\Delta y}{\Delta x} \\ =\frac{y_2-y_1}{x_2-x_1} \end{gathered}[/tex]If (x₁, y₁) = (-2, -9) and (x₂, y₂) = (2, 11) then replacing in the slope equation
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ =\frac{11-(-9)}{2-(-2)} \\ =\frac{11+9}{2+2} \\ =\frac{20}{4}=5 \end{gathered}[/tex]Answer: the slope of the line is 5Plot the x-intercept(s), y-intercept, vertex, and axis of symmetry of this function:h(x) = (x − 1)^2− 9.
Answers
The function is
[tex]h(x)=(x-1)^2-9[/tex]1) x-intercept(s)
The x-intercepts refer to the points on which the function intercepts with the x-axis, in other words, when y=h(x)=0
So, given that condition, we get
[tex]\begin{gathered} h(x)=0 \\ \Rightarrow(x-1)^2-9=0 \\ \Rightarrow x^2-2x+1^{}-9=0 \\ \Rightarrow x^2-2x-8=0 \\ \Rightarrow(x-4)(x+2)=0 \end{gathered}[/tex]Therefore, there are two x-intercepts, and those are the points
[tex](4,0),(-2,0)[/tex]2) y-intercepts
The y-intercepts happen when x=0. So,
[tex]\begin{gathered} x=0 \\ \Rightarrow h(0)=(0-1)^2-9=1-9=-8 \end{gathered}[/tex]So, there is only one y-intercept and it's on the point (0,-8)
3) Vertex
The general equation of a parabola is
[tex]y=f(x)=a^{}x^2+bx+c[/tex]There is another way to express the same function, which is called the 'vertex form':
[tex]\begin{gathered} y=f(x)=a(x-h)^2+k \\ \Rightarrow y=ax^2-2ahx+ah^2+k \end{gathered}[/tex]What is particularly useful of this vertex form is that the vertex is the point (h,k)
So, transforming h(x) into vertex form:
[tex]\begin{gathered} h(x)=(x-1)^2-9=a(x-h)^2+k \\ \Rightarrow\begin{cases}a=1 \\ h=1 \\ k=-9\end{cases} \end{gathered}[/tex]Therefore, the vertex is the point (h,k)=(1,-9)
4) Axis of symmetry
In general, the equation of the axis of symmetry is given by
[tex]x=-\frac{b}{2a};y=f(x)=ax^2+bx+c[/tex]Therefore, in our particular problem,
[tex]\begin{gathered} h(x)=x^2-2x-8=ax^2+bx+c \\ \Rightarrow\begin{cases}a=1 \\ b=-2 \\ c=-8\end{cases} \\ \end{gathered}[/tex]Thus, the equation of the line that is the axis of symmetry is
[tex]x=-\frac{b}{2a}=-\frac{(-2)}{2\cdot1}=-\frac{(-2)}{2}=1[/tex]Then, the axis of symmetry is the line x=1.
Summing up the information in the four previous steps, we get
you are 5 feet and 4 inches tall and cast a shadow 6 feet long. At the same time , a nearby tree cast a shadow 40 feet 6 inches long. Find the heigh of the tree.
Answers
The height of the tree is such that it cast a shadow 40 feet 6 inches long and maintains the given ratio will be 36 feet.
What are the ratio and proportion?The ratio is the division of the two numbers.
For example, a/b, where a will be the numerator and b will be the denominator.
As per the given question,
The height of a person is 5 feet and 4 inches.
Since 1 feet = 12 inches so 4 inches = 1/3 feet
Therefore,height of a person = 5 + 1/3 = 16/3 feet
Its shadow length = 6 feet
The ratio of the height to shadow length = (16/3)/6
Now, the shadow of the tree = 40 feet and 6 inches so 40.5 feet
Let's say its length was x feet.
Then x/40.5 = (16/3)/6
x = 36 feet
Hence "The height of the tree is such that it cast a shadow 40 feet 6 inches long and maintains the given ratio will be 36 feet".
For more information about ratios and proportions,
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Multiplying Polynomials 5y[tex] ({5y}^{2} + y + 3)(x - 2)[/tex]
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Let's distribute those factors, and expand this:
[tex]\begin{gathered} (5y^2+y+3)\mleft(x-2\mright) \\ 5xy^2-10y^2+xy-2y+3x-6 \\ \end{gathered}[/tex]There's no further way beyond that. Either we pick the factored form or the expanded version of that polynomial. As this is not an equation we stop it here.
Endpoint 19,-10) Midpoint (4,8).What is the other endpoint
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Let the first end point be x1 y1 and the second x2 y2 the midpoint would be
x1 + x2 / 2 y1 + y2 / 2
Hence
(19 + x2)/2 = 4
19 + x2 = 8
x2 = 8 -19
x2 = -11
(-10 + y2)/2 =8
- 10 + y2 = 8
y2 = 8 + 10
= 18
The other end point is (-11, 18)
