Congruent triangles have exactly the same three sides and three angles. The triangles may be rotated to see the congruency between them. In other words congruent triangles has corresponding sides equal and corresponding angles equal.
The 2 triangles have equal corresponding
what is f(-2) if f (x)= 1/2xa. -2b. -1c. 0d. 1
EXPLANATION
If x=-2 the f(-2) = (1/2)(-2) = 1
So, f(-2) = 1
The right option is d. 1
In professor Johnson's literature class there are 267 students. At a random check Prof.Johnson notices that 22 students among 59 students did not complete their essays.Can you estimate how many students in Prof. Johnson's class did not finish theiressay?Question 71 pts
We have a class of a total of 267 students.
The professor has a sample of 59 students, where 22 of them did not complete their essays.
This equals a proportion of:
[tex]p=\frac{22}{59}\approx0.373[/tex]If this sample is representative of the class, we can use this proportion to estimate how many students did not complete the essay.
To do that we multiply the total number of students by the proportion we have just calculated:
[tex]X=N\cdot p=267\cdot0.373\approx99.59\approx100[/tex]Answer: it can be estimated that approximately 100 students did not finish their essay.
a boat is heading towards a lighthouse, whose beacon light is 117 feet above the water. the boats crew measures the angle of elevation to tye beacon 3. what is the ships horizontal distnace from the lighthouse( and the shore)? round your answer to the nearest hundreth of a foot if necessary.
So,
We could draw the situation of the problem as follows:
We want to find the horizontal distance, which we will call "x".
To find it, we could use the trigonometric ratio: tan(a).
This ratio relations the opposite side of the angle given (a) and its adjacent side. So, we could write:
[tex]\tan (3)=\frac{117}{x}[/tex]Now, if we solve for x:
[tex]x=\frac{117}{\tan (3)}[/tex]This is, x = 2232.49 ft
Evaluate. Express your answer in scientific notation. 7.94 x 10^-3 6.69 x 10^-4
To solve this question, follow the steps below.
Step 01: Write the numbers to have the same powers.
To do it, choose one number to transform.
Let's choose the number with the greaters power (10⁻³).
To write it with the power -4, multiply 7.94 by 10:
[tex]\begin{gathered} 7.94\times10^{-3}=7.94\operatorname{\times}10*10^{-4} \\ =79.4\operatorname{\times}10^{-4} \end{gathered}[/tex]Step 02: Solve the subtraction.
To solve the subtraction, subtract the decimals.
[tex]\begin{gathered} 79.4\operatorname{\times}10^{-4}-6.69\operatorname{\times}10^{-4} \\ =(79.4-6.69)\operatorname{\times}10^{-4} \\ =72.71\operatorname{\times}10^{-4} \end{gathered}[/tex]Step 03: Rewrite the number in scientific notation.
For a number in scientic notation a x 10ᵇ, 1 ≤ |a| < 10.
Then, divide 72.71 by 10 and multiply the exponent part by 10.
[tex]\begin{gathered} \frac{72.71}{10}\times10^{-4}\times10 \\ 7.271\times10^{-4+1} \\ 7.271\times10^{-3} \end{gathered}[/tex]Answer:
[tex]7.271\cdot10^{-3}[/tex]
Write an equivalent expression by distributing the "-" sign outside the parentheses: -k-(-6.2m +1)
In order to get the required expression you take into account that when you eliminate a prenthesis preceded by a minus sign, terms inside the parenthesis change their sign.
Then, for the following expression, you have:
- k - (-6.2m + 1)
- k + 6.2m - 1 that is, signs inside the parenthesis have changed
In 1960, the world record for the men's mile was 3.91 minutes. In 1980, the record time was 3.81 minutes. a, write the linear model that represents the world record (in minutes) for the men's mile as a function of the number of years, t , since 1960. y=___b, use the model to estimate the record time in 2000 and predict the record time in 2020.2000:___ minutes2020:___ minutes
To first answer this question, we need to find the slope of the linear equation. We have the following information:
x1 = 1960, y1 = 3.91
x2 = 1980, y2 = 3.81
Then
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{3.81-3.91}{1980-1960}=-0.005[/tex]Then, we have that the linear model will be:
[tex]y-y1=m\cdot(x-x1)\Rightarrow y-3.91=-0.005\cdot(x-1960)_{}[/tex]Or
[tex]y=-0.005\cdot(x-1960)+3.91\Rightarrow y=-0.005x+13.71[/tex]This is the linear model.
Then, to use the model to estimate the record time in 2000 and in 2020, we have:
[tex]y=-0.005\cdot(2000)+13.71\Rightarrow y=3.71[/tex]And
[tex]y=-0.005\cdot(2020)+13.71\Rightarrow y=3.61[/tex]Therefore, the linear model is y = -0.005x + 13.71.
The estimation for the record time in 2000 is 3.71 minutes.
The estimation for the record time in 2020 is 3.61 minutes.
This is a linear model.
Question 3 1 Marge is making a chocolate cake to surprise the best nend. She needs 3 1/2cups of four but she only has 1/3cup. How much more flour does she need?
Answer:
19/6 cups
Explanation:
First, we need to transform the mixed number into a fraction as:
[tex]3\frac{1}{2}=\frac{3\cdot2+1}{2}=\frac{7}{2}[/tex]Now, we need to subtract 1/3 from 7/2, so:
[tex]\frac{7}{2}-\frac{1}{3}=\frac{7\cdot3-2\cdot1}{2\cdot3}=\frac{21-2}{6}=\frac{19}{6}[/tex]Therefore, she needs 19/6 cups more
given two numbers 9 * 10 to the 8 power, and 30,000,000, which one is larger and by how much. 3 times larger or 30 times larger
The first number is 9 * 10^8
The second number = 30,000,000 = 3 * 10^7
so, the larger number is 9 * 10^8 because the power of 10 is the larger than the other number
To find how much is larger, divide 9 * 10^8 by 3 * 10^7
so,
so, it is 30 times larger
Triangles ABC and XYZ are similar(pictured below). What is the perimeter 10 points of XYZ (Recall that the perimeter is the total distance around the shape). А Х с B Z 51 unite 21 units 25.5 unite 17 units None of the above
Given: The traingles given are similar to each other
This means that the ratios of similar sides can be taken and then used to obtain the missing sides
comparing similar sides
AB is similar to XY
BC is similar to YZ
AC is similar to XZ
Since we were given XZ = 9, we can find the other sides by comparing XZ with AC
[tex]\frac{Triangle\text{ ZXY}}{\text{Triangle ABC}}\text{ =}\frac{XZ}{AC}=\text{ }\frac{9}{6}\text{ = 1.5}[/tex]This shows that the sides of triangle ZYX are 1.5 times that of ABC
So that YZ = 1.5 x BC= 1.5 x 8 = 12,
YZ = 12
XY = 1.5 x AB= 1.5 x 3 = 4.5,
XY = 4.5
The sides are shown in the diagram below
The perimeter of the triangle XYZ = 9 + 4.5 + 12 = 25.5 units
F(x)=15x+25 find f(1/5)
Given the function:
[tex]f(x)=15x+25[/tex]You need to substitute the following value of "x" into the function:
[tex]x=\frac{1}{5}[/tex]And then evaluate, in order to find:
[tex]f(\frac{1}{5})[/tex]Therefore, you get:
[tex]f(\frac{1}{5})=15(\frac{1}{5})+25[/tex][tex]f(\frac{1}{5})=\frac{15}{5}+25[/tex][tex]\begin{gathered} f(\frac{1}{5})=3+25 \\ \\ f(\frac{1}{5})=28 \end{gathered}[/tex]Hence, the answer is:
[tex]f(\frac{1}{5})=28[/tex]1) What angle relationship/relationships do you see in the below diagram that would help you solve for the missing angle measurements? 2) Write an equation and solve for the measurements of Angle RQS & Angle UQT
The relationship is that the sum of all the angles is 360 degrees.
Because they are angles around a point.
Therefore,
3x + 90 + 4x + 221 = 360
3x+4x+90+221=360
7x+311=360
7x=360-311=49
Hence
x = 49 / 7 =7
Angle RQS = 3x = 3(7) =21 degrees
Angle RQS = 21 degrees
Angle UQT = 4x = 4(7) = 28 degrees
Angle UQT = 28 degrees
Kendra has not completed [tex] \frac{1}{5} [/tex]of the experiment for her science fair project she plans to work on her project over the next few weeks she would like to complete [tex] \frac{1}{4} [/tex]of the remaining experiment next week what fraction of the original experiment will she complete next week
We know that Kendra has not completed 1/5 of the project. To find 1/4 of the remaining part, we just have to multiply.
[tex]\frac{1}{4}\cdot\frac{1}{5}=\frac{1}{20}[/tex]Observe that 1/5 is the remaining part because it's the fraction that represents the not completed part.
Hence, she will complete the 1/20 of the project next week.Find the measure of Z CFD.СF5m + 116T3m + 80D
what is 5.8x10² in standard notation?
Answer:
[tex]5.8\text{ }\times\text{ 10}^2[/tex]Explanation:
Here, we want to write the given number in standard notation
The form we have given, is the scientific notation
To write in the standard form, we consider the scientific notation as they are the same
We have the standard notation as:
[tex]5.8\text{ }\times\text{ 10}^2\text{ = 5.8 }\times\text{ 10}^2[/tex]Ignore c. I only need help with a and b
Part A.
The composition of f ang g is given by
[tex](f\circ g)(x))=f(g(x))=\frac{(3x+7)-7}{3}[/tex]where we have inserted 3x-7 in the place of x in function f. Then, we have
[tex](f\circ g)(x))=f(g(x))=\frac{3x+7-7}{3}=\frac{3x}{3}=x[/tex]Therefore, the answer is
[tex](f\circ g)(x))=x[/tex]Part B
Similarly to the previous case, we have
[tex](g\circ f)(x))=g(f(x))=3(\frac{x+7}{3})-7[/tex]which gives
[tex](g\circ f)(x))=g(f(x))=x+7-7=x[/tex]then, the answer is
[tex](g\circ f)(x))=x[/tex]Part C.
In the first case, x belongs to the domain of g and g(x) belongs to the domain of f. Then, the domain of the composition (fog)(x) is all real numbers.
Similarly, in the second case, x belongs to the domain of f and f(x) belongs to the domain of g. Then, the domain of the composition (gof)(x) is all real numbers. Then, the domains are the same (all real numbers).
TA Write in simplest form (improper not accepted): 7[tex] 7 \frac{7}{14} [/tex]
We are given the following fraction
[tex]\frac{7}{14}[/tex]We are asked to write it in the simplest form.
Notice that the number 14 is a multiple of number 7.
That is 7 times 2 is equal to 14.
Which means that 7 divided by 14 must be equal to 2
So the fraction becomes
[tex]\frac{7}{14}=\frac{1}{2}[/tex]Therefore, the simplest form of the given fraction is 1/2
Please note that the simplest form means that it cannot be further simplified.
a store is having a sale on almonds and Jelly Beans .For 3 pounds of almonds and 8 pounds of jelly beans the total cost is 34 dollars. For 5 pounds of almonds and 2 pounds of jelly beans. the cost is 17 dollars. Find the cost of each pound of almonds and each pound of jelly beans
We have a system of equation problem
x= cost of almonds per pound
y= cost of the jelly beans per pound
For the first equation, we have
3 pounds of almonds
8 pounds of jelly beans
total $34
so the equation is
3x+8y=34
For the second equation we have
5 pounds of almonds
2 pounds of jelly beans
total $17
so the equation is
5x+2y=17
so our system of equation is
[tex]\begin{gathered} 3x+8y=34 \\ 5x+2y=17 \end{gathered}[/tex]In order to solve the system we will multiply the second equation by -4
[tex]-4(5x+2y=17)=-20x-8y=-68[/tex]then we sum the equation above with the first equation
[tex]3x-20x+8y-8y=34-68[/tex]then we sum similar terms and isolate the x to find the value of x
[tex]\begin{gathered} -17x=-34 \\ x=\frac{-34}{-17} \\ x=2 \end{gathered}[/tex]then we substitute the value of x=2 in the first equation and we find the value of y
[tex]\begin{gathered} 3(2)+8y=34 \\ 6+8y=34 \\ 8y=34-6 \\ 8y=28 \\ y=\frac{28}{8} \\ y=3.5 \end{gathered}[/tex]The solution is
x= $ 2 cost of each pound of almond
y= $3.50 cost of each pound of jelly beans
Choose either Yes or No to tell whether there is an angle of the given measure shown in the diagram.
The addition of all angles in the diagram is equal to 360 degrees. Let's call angle x to the unknown angle. Then, we have:
[tex]\begin{gathered} m\angle x+160\degree+40\degree+65\degree+25\degree=360\degree \\ m\angle x=360\degree-160\degree-40\degree-65\degree-25\degree \\ m\angle x=70\degree \end{gathered}[/tex]Therefore, there is an angle that measures 70°.
Combining the angles of 160°, 40°, and 65°, we get a new angle, let's call it y, that measures:
[tex]\begin{gathered} m\angle y=160\degree+40\degree+65\degree \\ m\angle y=265\degree \end{gathered}[/tex]Therefore, there is an angle that measures 265°.
Combining the angles of 160°, 70°, 25°, and 65°, we get a new angle, let's call it z, that measures:
[tex]\begin{gathered} m\angle z=160\degree+70\degree+25\degree+65\degree \\ m\angle z=320\degree \end{gathered}[/tex]Therefore, there is an angle that measures 320°.
Combining the angles of 25°, and 65°, we get a new angle, let's call it a, that measures:
[tex]\begin{gathered} m\angle a=25\degree+65\degree \\ m\angle a=90\degree \end{gathered}[/tex]Therefore, there is an angle that measures 90°.
On the other hand, there is no combination of angles that add up to 225°
Solve the system graphically and check the solution. 2x+y=4. Y-2x=6
Answer:
[tex]\begin{gathered} x\text{ = -0.5} \\ y\text{ = 5} \end{gathered}[/tex]Explanation:
Here, we want to solve the system of linear equations graphically, then we proceed to check for the solution
To do this, we have to plot the graph of the two equations on the same plot, the point at which these lines intersect would be the solution to the system of linear equations
We have the plot shown as follows:
From what we have on the plot, the solution to the system is x = -0.5 and y =5 . The reasonn for this is that it is at this point that both lines intersect
Now, let us check the solution:
We can check the solution by substituting -0.5 for x and 5 for y in both equations
For the first one:
[tex]\begin{gathered} 2(-0.5)\text{ + 5 = 4} \\ -1\text{ + 5 = 4} \\ 4\text{ = 4} \end{gathered}[/tex]We can see that th solution works for the first equation
For the second one, we proceed with the same substitution process
We have this as:
[tex]\begin{gathered} 5-2(-0.5)\text{ = 6} \\ 5\text{ + 1 = 6} \\ 6\text{ = 6} \end{gathered}[/tex]We can see the solution works for the second equation too
I need help with my math
SOLUTION:
Step 1:
An adult's ticket costs $11
A child's ticket costs $6
The number of Adult's tickets sold is x
The number of Children's tickets sold is y
The total number of tickets sold is 60
The total amount of sales made is $460
Step 2:
We need to form two equations based on the information given in the question;
[tex]undefined[/tex]how do you solve 0.27÷0.9?
Given:
[tex]0.27\div0.9[/tex]To divide the decimals, we must take care of the decimal points
So, we will divide it as follows:
[tex]0.27\div0.9=\frac{27}{100}\div\frac{9}{10}=\frac{27}{100}\times\frac{10}{9}=\frac{27}{9}\times\frac{10}{100}=3\times\frac{1}{10}=0.3[/tex]So, the answer will be 0.27 ÷ 0.9 = 0.3
The point (-3, - 5) is on the graph of a function. Which equation must be true regarding the function? A. f(-3) = -5B. f(-3, -5) = -8C. f(-5) = -3D. f(-5, -3) = -2
SOLUTION
The correct option is A
Points with coordinates (x,y) on a graph can also be expressed thus:
[tex]f(x)=y[/tex]So with the above explanation, we can answer the question.
The point (-3,-5) on the graph means that x=-3 and y=-5
So it can be expressed as a function in the form:
[tex]\begin{gathered} f(x)=y \\ x=-3\text{ and y=-5} \\ f(-3)\text{ =-5} \end{gathered}[/tex]The correct option is A
Mrs. Gomez has two kinds of flowers in her garden. The ratio of lillies to daisies is the garden is 5:2 If there are 20 lillies, what is the total number of flowers in her garden? If there are 20 lillies, what is the total number of flowers in her garden?A. 8B. 10C. 15D. 28
The ratio of lilies to daisies is the garden is 5:2
20 Lillies
That means per every 4 lilies there are 2 daisies
4* 5 = 20 lilies
So
2*4 = 8 daisies
_________________
total number of flower are 20 lillies + 8 daisies = 28.
____________________________________
Answer
Option D) 28
Which equation describes the relationship between the tangent and the secant line segments?
Answer:
B. (PQ)² = (PR)(PS)
Step-by-step explanation:
You want the relationship between tangent PQ and the segments of secant PS.
Secant relationThe product of the secant lengths between the point P where it meets the tangent and the two point R and S where it intersects the circle is equal to the square of the tangent from point P.
The relationship is ...
(PQ)² = (PR)(PS)
__
Additional comment
You can eliminate choices C and D because they do not involve segments of PS.
If M is the midpoint of RS, choice A says PQ=PM. Actually PQ < PM, which is clear when RS is a diameter of the circle. This leaves only choice B.
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W XZWhich statement regarding the diagram is true?O mzWXY = mzYXZO mzWXY
Linear pair of angles are formed when two lines intersect each other at a single point.
The angles are said to be linear if they are adjacent to each other after the intersection of the two lines.
The figure shows the line WZ intersected by lines YX and YZ. At X, two adjacent angles are formed at the point where WZ and YX intersect.
This means angles WXY and YXZ are linear angles.
Linear angles always add up to 180°, thus:
m∠WXY + m∠YXZ = 180°
Hello. I’ve attached a photo thank you Find Are and Perimeter.
Given:
Base of the parallelogram, b = 8
Height of the parallelogram, h = 3
Side of the parallelogram, a = 4
Required: Area and Perimeter
Explanation:
The formula to find the area of a parallelogram is
[tex]A=bh[/tex]where b is the base and h is the height.
Plug the given values into the formula.
[tex]\begin{gathered} A=8\cdot3 \\ =24 \end{gathered}[/tex]The formula to find the perimeter is
[tex]P=2a+2b[/tex]Plug the given values into the formula.
[tex]\begin{gathered} P=2\cdot4+2\cdot8 \\ =8+16 \\ =24 \end{gathered}[/tex]Final Answer: Area = 24, Perimeter = 24
Quadratic Functions in Standard FormCaroline wrote these steps to graph f(x) = 2x2 + 4x + 5 on note cards, but they gotmixed up. Help Caroline by re-writing the steps in the correct order. Use the notecards to complete the steps below.
1.- Determine the vertex...
2.- The axis of symmetry...
3.- The y-intercept...
4.- Plot a point...
5.- Plot another point...
The above is the correct order of the cards, now the reason for that first you have to find the vertex. Now, the axis of symmetry is a straight line that passes through the vertex. Later you have to find another 2 points reflected by the symmetry axis and finally construct the graph.
write the equation of the line parallel to y = -5x + 3 with a y - intercept (0,4).
Equation of the line
The equation of a line can be expressed in slope-intercept form as follows:
y = mx + b
Where m is the slope of the line and b is the y-intercept.
We are given the equation of a line:
y = -5x + 3
This line as a slope of m=-5 and the intercept with the y-axis is y=3
We are required to find the equation of another line that is parallel to the given line. Parallel lines have the same slope. Thus the slope of our new line is also m=-5.
We are also given the y-intercept of the new line (0,4). This means the value of b is 4.
Knowing the values of m and b, we can write the equation of the required line as:
y = -5x + 4
This relation map is a student to the English class they are taking… Is this relation a function
Remember that
The data set is a function, if every element of the domain corresponds to exactly one element of the range
In this problem
the element of the domain Andy Rogers, has two different values of the English Class (element of the range)
that means
Is not a function
the answer is NoFind the next three terms of the given sequences below. Type your answer on the blank.1. 12, 18, 24, 30, 36,2.90, 81, 72, 63, 543.100, 90, 80, 70,
We have three arithmetic sequences. Arithmetic sequences have a common difference between each consecutive terms. We just have to calculate the common difference of each sequence and then add to the last term to get the following terms.
item a)
The common difference is
[tex]18-12=6[/tex]The next three terms are
[tex]\begin{gathered} 36+6=42 \\ 42+6=48 \\ 48+6=54 \end{gathered}[/tex]42, 48 and 54.
item b)
The common difference is
[tex]81-90=-9[/tex][tex]\begin{gathered} 54+(-9)=45 \\ 45+(-9)=36 \\ 36+(-9)=27 \end{gathered}[/tex]The next three terms are 45, 36 and 27.
item c)
The common difference is
[tex]90-100=-10[/tex][tex]\begin{gathered} 70+(-10)=60 \\ 60+(-10)=50 \\ 50+(-10)=40 \end{gathered}[/tex]The next three terms are 60, 50 and 40.