ANSWER
B. False
EXPLANATION
We want to identify if the statement is true or false.
A function is a type of relation in which each input value is mapped directly to only one output value. In other words, each value of x has only one value of y.
To identify the graph of a function, if a vertical line can be drawn at any value of x such that it connects more than one point on the graph, then, the graph does not represent a function.
From the given graph, we see that a vertical line can be drawn to touch more than one point at several values of x.
This implies that the graph does not represent a function, hence, the statement is false.
The answer is option B.
A new bank customer with $2,500 wants to open a money market account. The bank is offering a simple interest rate of 1.8%.
a. How much interest will the customer earn in 30 years?
b. What will the account balance be after 30 years?
a. The customer will earn $_ in interest.
Using the simple interest formula, the interest will the customer earn in 30 years is $1350, the account balance be after 30 years is $3850 and the customer earn $1350 interest.
In the given given that;
A new bank customer with $2,500 wants to open a money market account.
The bank is offering a simple interest rate of 1.8%.
So the Principal Amout(P)=$2500
Interest Rate(R)=1.8%
(a) So we have to find the interest will the customer earn in 30 years.
So the time (T)=30 years
So the formula of Simple Interest;
I=PRT/100
I=2500*1.8*30/100
I=1350
So the interest will the customer earn in 30 years is $1350.
(b) Now we have to find the account balance be after 30 years.
The account balance = Principal Amount+Interest Amount
The account balance = 2500+1350
The account balance = $3850
(c) Now we have to find the customer will earn $_ in interest.
The customer earn $1350 interest.
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5) Given the following matrices, find the products of LN and MN
Answer:
The products MN and LN are not possible.
Explanation:
Matrix multiplication is only possible when the column number of the first matrix equals the row number of the second matrix.
Now, matrix L is a 2 x 2 matrix and N is a 5 x 2 matrix. Now L has 2 columns and N has 5 rows. Meaning, that columns of L are not equal to the rows of N. Therefore, matrix multiplication is not possible.
Matrix M is 2 x 4 and matrix N is 2 x 2. Since columns of matrix M equal the rows of matrix N, matrix multiplication is possible.
Therefore,
[tex][/tex]If f (x) = -3x - 2, find each value
Given:
The function is given as
[tex]f(x)=-3x-2[/tex]Required:
We want to find the value of
[tex]f(-7)[/tex]Explanation:
[tex]f(-7)=-3(-7)-2=21-2=19[/tex]Final answer:
19
solution of the system of equations.2. (3, 0) 2x+y=-63x + 2y = 94. (-2,3) y =2x+75x+y=-76. (0,-7) 2x -2y = 14X-Y=-7
We can solve these systems of equations as follows:
First CaseWe have:
[tex]\begin{cases}2x+y=-6 \\ 3x+2y=9\end{cases}[/tex]And we can solve this system by substitution as follows:
[tex]\begin{gathered} 2x+y=-6 \\ 2x-2x+y=-6-2x \\ y=-6-2x \end{gathered}[/tex]Now, we can substitute the corresponding value of y into the second equation as follows:
[tex]\begin{gathered} y=-6-2x \\ 3x+2y=9 \\ 3x+2(-6-2x)=9 \\ 3x+(2)(-6)+(2)(-2x)=9 \\ 3x-12-4x=9 \\ 3x-4x-12=9 \\ -x-12=9 \\ -x-12+12=9+12 \\ -x=21\Rightarrow x=-21 \end{gathered}[/tex]Now, we can substitute the value x = -21 into either of the original equations to find the value of y. We will use the first equation:
[tex]\begin{gathered} 2x+y=-6 \\ 2(-21)+y=-6 \\ -42+y=-6 \\ -42+42+y=-6+42 \\ y=36 \end{gathered}[/tex]Therefore, the solution to this first system is (-21, 36).
We can check this result if we substitute both values into the original equations:
[tex]\begin{gathered} \begin{cases}2x+y=-6 \\ 3x+2y=9\end{cases} \\ x=-21,y=36 \\ \begin{cases}2(-21)+36=-6 \\ 3(-21)+2(36)=9\end{cases} \\ \begin{cases}-42+36=-6 \\ -63+72=9\end{cases} \\ \begin{cases}-6=-6\Rightarrow This\text{ is true.} \\ 9=9\Rightarrow This\text{ is true.}\end{cases} \end{gathered}[/tex]Therefore, the solution to the first system of equations is (-21, 36).
Second Case
[tex]\begin{cases}y=2x+7 \\ 5x+y=-7\end{cases}[/tex]We can rewrite the system as follows:
[tex]\begin{cases}-2x+y=7 \\ 5x+y=-7\end{cases}[/tex]And we can solve this system by the elimination method: We have to multiply one of the equations by -1 and then add them algebraically as follows:
[tex]\begin{gathered} \begin{cases}-2x+y=7 \\ -1(5x+y=-7)\end{cases} \\ \begin{cases}-2x+y=7 \\ (-1)(5x)+(-1)(y)=(-1)(-7)\end{cases} \\ \begin{cases}-2x+y=7 \\ -5x-y=7\end{cases} \end{gathered}[/tex]If we add both equations, then we have:
[tex]\begin{gathered} \frac{\begin{cases}-2x+y=7 \\ -5x-y=7\end{cases}}{-7x=14} \\ -\frac{7x}{-7}=\frac{14}{-7} \\ x=-2 \end{gathered}[/tex]And now we can substitute this value in either equation to find y:
[tex]\begin{gathered} y=2x+7 \\ y=2(-2)+7 \\ y=-4+7 \\ y=3 \end{gathered}[/tex]And we got y = 3.
Therefore, the solution to this system is equal to (-2, 3), and we can also check the solutions using the original equations:
[tex]\begin{gathered} \begin{cases}y=2x+7 \\ 5x+y=-7\end{cases} \\ \begin{cases}3=2(-2)+7 \\ 5(-2)+3=-7\end{cases} \\ \begin{cases}3=-4+7 \\ -10+3=-7\end{cases} \\ \begin{cases}3=3\Rightarrow This\text{ is true.} \\ -7=-7\Rightarrow This\text{ is true.}\end{cases} \end{gathered}[/tex]In summary, we have that:
The solution to the first system ---> (-21, 36).
The solution to the second system ---> (-2, 3).
CAN SOMEONE HELP WITH THIS QUESTION?✨
The coterminal angle is 943° .
What is a coterminal angle?Coterminal angles are angles with the starting side on the positive x-axis and a shared terminal side. They are in standard position. Examples include the coterminal nature of the angles 30, -330, and 390. The phrase "coterminal angle" refers to angles with the same starting side and terminal side. If the specified angle is given in radians or degrees, finding coterminal angles is as easy as adding or subtracting 360° or 2 to each angle. It is possible to find all possible coterminal angles. The coterminal angle is described in mathematics as the angle formed by two angles drawn side by side in the same plane. Furthermore, both of them share the same location for their terminal sides. As an illustration, 405 and -315 are the coterminal angles of 45.
1294° = 360° + 934°
So the coterminal angle for 1294° is 934° .
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can you please help me with this question. it's geometry
To find the angle A we need to find first the value of x. To do this we need to use the fact the the addition of the interior angles of any triangle is 180°.
The right side angle is equatl to 4x+4 since its vertically opposite to the one shown in the picture. The upper angle is 100° since it has to be supplementary to the angle of 80° shown in the picture.
With this in mind we have the equation:
[tex](4x+4)+(4x+4)+100=180[/tex]Solving for x we have:
[tex]\begin{gathered} (4x+4)+(4x+4)+100=180 \\ 8x+108=180 \\ 8x=180-108 \\ 8x=72 \\ x=\frac{72}{8} \\ x=9 \end{gathered}[/tex]Once we know the value of x we plug it in the expression for the angle A:
[tex]4(9)+4=40[/tex]Therefore the angle A is 40°.
I need help on 4 please it says find the value of x round each answer to the nearest tenth
The pythagorean theorem is :
[tex]c^2=a^2+b^2[/tex]where c is the hypotenuse
a and b are the legs of the triangle.
From the problem, a = x, b = 19.1 and c = 30.5
Using the formula :
[tex]\begin{gathered} 30.5^2=x^2+19.1^2 \\ 930.25=x^2+364.81 \\ x^2=930.25-364.81 \\ x^2=565.44 \\ x=\sqrt[]{565.44} \\ x=23.779 \end{gathered}[/tex]The answer rounded to the nearest tenth is x = 23.8
A triangle has angle measures of 27 degrees , 50 degrees, and x degrees, use the triangle sum theorem to find the value of x.
ANSWER:
Angle x is 103 degrees
EXPLANATION
The sum of all the angles in a triangle is 180 degrees
Hence, Let angle A = 27 degrees
Angle B = 50 degrees
Angle C = x degrees
Triangle sum theorem state that
50 + 27 + x = 180
77 + x = 180
x = 180 - 77
x = 103 degrees
Pieter sailed his sailboat 1,260 yards in 30 minutes . What is the average number of yards of yards he traveled per minute ? A. 21 B. 30 C. 42
Given:
Distance Pieter sailed = 1260 yards
Time taken to sail = 30 minutes
Let's solve for the average number of yards he traveled per minute.
To find the average number of yards he traveled per minute, apply the formula:
[tex]\begin{gathered} A=\frac{\text{distance in yards}}{time\text{ in minute}} \\ \\ A=\frac{1260}{30}\frac{\text{yards}}{\text{minutes}} \\ \\ A=42\text{ yards per minute} \end{gathered}[/tex]Therefore, the average number of yards he traveled per minute is 42 yards per minute.
ANSWER:
C. 42
Working with special triangles. Find y. I have attached the picture.
In this case, we'll have to carry out several steps to find the solution.
Step :
Data:
diagram:
right triangle
Step 02:
special right triangles:
we must analyze the triangle to find the solution.
special right triangle example:
right triangle:
side y:
[tex]\begin{gathered} 88\text{ = }\sqrt{2}y\text{ } \\ \\ \frac{88}{\sqrt{2}}\text{ = y} \end{gathered}[/tex]That is the full solution.
#1) Write the ratio of 60 km in 28 minutes in simplest form.#2) Is this ratio a rate? Explain your answer using words. [C
1. Expressing 60km per 28 minutes in its simplest form requires us to get it per 1 minute. This, we can easily obtain by:
[tex]\frac{60\operatorname{km}}{28\min}=\frac{15\operatorname{km}}{7\min}=2\frac{1}{7}\frac{km}{\min }[/tex]2.143 km per minute
2. The ratio is a rate. A rate is a measure of a quantity with respect to another, especially with respect to time.
As can be seen, this ratio is speed. Speed is a measure of distance covered per time.
-2x + y = 3 5x - y = -3
we have
-2x + y = 3 -----> equation A
5x - y = -3 -----> equation B
Solve the system of equations
Solve by elimination
Adds equation A and equation B
-2x + y = 3
5x - y = -3
-----------------
-2x+5x=3-3
3x=0
x=0
Find the value of y
substitute the value of x in equation A or equation B
-2(0)+y=3
y=3
therefore
the solution is the point (0,3)Calculate the mean for each set of data round to the nearest tenths
The mean is the average of the numbers.
It is easy to calculate: add up all the numbers, then divide by how many numbers there are
[tex]\bar{x=\frac{\sum ^{\square}_{\text{ of numbers}}}{Number\text{ of items}}\text{ }}[/tex]the numbers given in the question are
[tex]2,11,5,6,13,4,9[/tex]there are 7 numbers in total.
Therefore, the mean will be
[tex]\begin{gathered} \operatorname{mean}=\frac{2+11+5+6+13+4+9}{7} \\ \operatorname{mean}=\frac{50}{7} \\ \operatorname{mean}=7.143 \\ to\text{ the nearest tenths, the mean is} \\ \operatorname{mean}=7.1 \end{gathered}[/tex]Hence,
the mean of the above set of values to the nearest tenth is = 7.1
Pryz is a rhombus. If RK=5, RY=13 and M
Remember that
In a Rhombus
All sides are equal
Diagonals bisect each other perpendicularly
so
Part 22
Find out KY
In the right triangle RYK
Applying the Pythagorean Theorem
RY^2=RK^2+KY^2
substitute given values
13^2=5^2+KY^2
KY^2=13^2-5^2
KY^2=144
KY=12
Part 23
Find out PK
Remember that
Diagonals bisect each other perpendicularly
that means
PK=KY=12
Part 24
mRemember that
Diagonals bisect each other perpendicularly
so
mthat means
m
Part 25
mwe have that
mtherefore
m
Find the next three terms in this sequence: 5120, 1280, 320, 80...-160, -400, -64020, 5, 1.2540, 20, 1076, 72, 68
Given the first four terms of this sequence:
[tex](5120,1280,320,80,\ldots)[/tex]We can see a pattern. To analize this pattern, let's first check the difference between those terms.
[tex]\begin{gathered} 5120-1280=3840 \\ 1280-320=960 \\ 320-80=240 \end{gathered}[/tex]From those differences, we can verify the following equations:
[tex]\begin{gathered} 3840=4(960) \\ 960=4(240) \end{gathered}[/tex]From this, we can write the general rule for this sequence:
[tex]a_n=\frac{5120}{4^{n-1}}[/tex]This sequence gives us:
[tex]\begin{gathered} a_1=5120 \\ a_2=1280 \\ a_3=320 \\ a_4=80 \\ a_5=20 \\ a_6=5 \\ a_7=1.25 \end{gathered}[/tex]Then, we have the following 3 terms. (20, 5, 1.25)
it's under the saying you add an extender different you subtract which a person does this explain
Operations
add → symbol "+"
subtract → symbol "-"
Multiply/divide → symbol "*/÷"
Please Help! An eight foot ladder leans against a building. if the ladder makes an angle of 60 degrees with the ground, haw far from the building is the base of the ladder. Round you answer to the nearest tenth.
The base of the ladder is 4 ft away from the buliding
Here, we want to calculate the distance from the building to the base of the ladder
To properly answer this, an image of the question is needed
We have this as follows;
From the diagram, what we want to calculate is the distance d
To calculate this, we need the appropriate trigonometric identity
Firstly, we need to identify the parts of the triangle present
As we can see, we have the hypotenuse which is the side that faces the right angle and also is the longest side
The side we want to get is the adjacent
Mathematically, the trigonometric ratio that connects the adjacent to the hypotenuse is the cosine
Thus, we have it that;
[tex]\begin{gathered} \cos \text{ 60 = }\frac{d}{8} \\ \\ d\text{ = 8 cos 60} \\ d\text{ = }4.0\text{ ft} \end{gathered}[/tex]the equation below describe the graph of a line on a coordinate planes.y - 2 = -3/2 (x + 1) which graph represents this line ?
The y-intercept is 1/2.
The answer is C. we can use the y-intercept to know the graph. You can see that option C when x = 0 , y is 1/2.
Which of the following options could you do before subtracting the equations so that one variable will be eliminated when you subtract them?
We need to do something to both equations so we can eliminate one variable
We can multiply the first equation by 3 and the second equation by 4
3( 4x-2y = 7) yields 12x -6y = 21
4( 3x-3y = 15) yields 12x -12y = 60
Now when we subtract
12x -6y = 21
-(12x -12y = 60)
---------------------------
12x -6y = 21
-12x +12y = -60
------------------------
6y = 39
The x terms are eliminated
Choice D multiply the top equation by 3 and the bottom equation by 4
Which of the following transformations shows a rotation 270 degrees counterclockwise? *
Explanation:
A rotation 270 degrees counterclockwise happens when the y and x axis value are interchanged and the interchanged y value becomes negative.
When we look at the options given, we look for the image whose rotation is in the positive x axis and negative y axis.
Also the movement will be thrice while moving anticlockwise.
From the options, the one which fits into the description above is B.
There is a movement of counterclockwise
To solve the inequality -7x<24, the inequality sign must be reversed.A. TrueB. False
ANSWER
True
EXPLANATION
To solve the inequality given:
-7x < 24
we have to divide both sides of the inequality by -7.
Dividing both sides of an inequality causes the sign to change direction (or be reversed) and so we will have:
x > -24 / 7
Therefore, it is true that the sign will be reversed.
1. Solve -4x < -3(6x - 2) and sketch the solution set on a number line.
We need to solve the inequality:
[tex]-4x<-3\mleft(6x-2\mright)[/tex]Let's multiply right side out and take variables to one side and numbers to another. The process is shown below:
[tex]\begin{gathered} -4x<-3\mleft(6x-2\mright) \\ -4x<-18x+6 \\ -4x+18x<6 \\ 14x<6 \\ x<\frac{6}{14} \\ x<\frac{3}{7} \end{gathered}[/tex]The solution set is:
[tex]\begin{gathered} x<\frac{3}{7} \\ or \\ x<0.4286 \end{gathered}[/tex]This means that x is less than 3/7, or
x is less than 0.4286
On the number line it looks:
The braking distance of a car is proportional to the square of its speed.17. According to Graham's law, the rate of diffusion of two gases is inverselydproportional to density and is given bywhere ', and r2 are12rates of diffusion of two gases and d, and d2 are their respectivedensities. Which equation represents d, in terms of the other variables?
Ok in this problem you have to take Graham's law which is given to you and manage to write the density d1 as a function of the others. We have:
[tex]\frac{r_1}{r_2}=\sqrt[]{\frac{d_2}{d_1}}[/tex]Since we want to have d1 alone in one side of the equation the first thing we have to do is pass the square root to the other side. Square roots pass as square powers:
[tex](\frac{r_1}{r_2})^2=\frac{d_2}{d_1}[/tex]Then we have to pass d1 multiplying on the other side:
[tex]d_1\frac{r^2_1}{r^2_2}^{}=d_2[/tex]Now we only need to pass both r1 and r2:
[tex]d_1=d_2\frac{r^2_2}{r^2_1}[/tex]This is the same expresion that the one in item B so that is the correct answer
8. If the slope of the equation y = -3/5x + 4 is changed to 3/5 and the y-intercept is changed to -4, which statement best describes this situation? You can use a calculator to graph or create your own graph.*A The new line is perpendicular to the original line. B The new line is parallel to the original line. C The new line and the original line have the same y-intercept. D The new line and the original line have the same x-intercept.
Answer:
Explanation:
Given that the line
[tex]y=-\frac{3}{5}x+4[/tex]is changed to
[tex]y=\frac{3}{5}x-4[/tex]Thelma performed a construction on a quadrilateral.Her work is shown below..EBсDWhich statement is justified by her construction?AD – AEAE - BEAD – BCO ADAD ~ DC
Looking at the image, we can see that the arc created in point E was created with the same radius of segment AD (that is, A is the center of a circle that contains both arcs that pass through points D and E).
From that construction, we can affirm that segments AD and AE are congruent.
Therefore the correct option is the first one.
The product of two factors is x2 – X – 20. If one of the factors is x-5, what is the other factor?
we can rewrite the statement
[tex](x-5)(A)=x^2-x-20[/tex]where A is the missing factor, A must be of the form
[tex](x+a)[/tex]where a is a constant, to obtain "a" we must bear in mind that the multiplication of the two constants must give us the third term and the sum of these must give us the second term
so
[tex]\begin{gathered} -5\times a=-20 \\ -5+a=-1 \end{gathered}[/tex]if we solve any equation, the value of a is 4
so a is 4 and the factor is
[tex](x+4)[/tex][tex](x-5)(x+4)=x^2-x-20[/tex]Translate this sentence into an equation 43 is the difference of Chrissy’s age and 14 Use the variable c to represent Chrissy’s age
When translating into mathematical equations, "is" uses the equal sign and "difference" means that the operation to be used is subtraction.
So, "43 is the difference of Chrissy's age and 14" is written as:
43 = C - 14
Fill in the blanks in the sequence _,29,_,_,_,539, 1083
we are given the following sequence:
[tex]_{}29,,,,539,1083[/tex]To go from 539 to 1083 we multiply 539 by 2 and add 5, like this:
[tex]1083=539\times2+5[/tex]Therefore, for a number in position "n", the formula for its value is:
[tex]a_n=2a_{n-1}+5[/tex]Solving we get:
[tex]a_{n-1}=\frac{a_n-5}{2}[/tex]Replacing the current value for 539 we get:
[tex]a_5=\frac{a_6-5}{2}[/tex][tex]a_5=\frac{539-5}{2}=267[/tex]Now to find the 4th value:
[tex]a_4=\frac{a_5-5}{2}[/tex]Replacing:
[tex]a_4=\frac{267-5}{2}=131[/tex]For the third value:
[tex]a_3=\frac{a_4-5}{2}[/tex]Replacing:
[tex]a_3=\frac{131-5}{2}=63[/tex]The second value is already given as 29, therefore, the first value is:
[tex]a_1=\frac{a_2-5}{2}[/tex]Replacing:
[tex]a_1=\frac{29-5}{2}=12[/tex]Therefore, the sequence is:
[tex]12,29,63,131,267,539,1083[/tex]
|- 1/5| ? |-0.8|what’s the missing inequality symbol?
Given:-
[tex]|-1\frac{1}{5}|,|-0.8|_{}[/tex]To find the correct inequality between the given datas.
So now we simplify. so we get,
[tex]|-1\frac{1}{5}|=|-\frac{6}{5}|=|-1.2|[/tex]So we get,
[tex]\begin{gathered} |-1.2|=1.2 \\ |-0.8|=0.8 \end{gathered}[/tex]So the inequality is,
[tex]1.2>0.8[/tex]What is the perimeter of the isosceles triangle ABC such that angle A= angle C ?
Given angle A=angle C.
The objective is to find the perimeter of the isosceles triangle ABC.
First let's find the value of x.
An isosceles triangle contains two equal sides. Here angle A and angle C are equal. So the sides AB and AC are equal.
[tex]\begin{gathered} AB=BC \\ 5x-1=3x+11 \\ 5x-3x=11+1 \\ 2x=12 \\ x=\frac{12}{2} \\ x=6 \end{gathered}[/tex]Now, find the perimeter of the triangle by adding all the sides of the triangle.
[tex]P=5x-1+3x+11+x+19[/tex]Substittue the value of x =6.
[tex]\begin{gathered} P=5(6)-1+3(6)+11+6+19 \\ P=30-1+18+11+6+19 \\ P=83 \end{gathered}[/tex]Hence, the perimeter of the triangle is 83.
[tex]\begin{gathered} \text{Let's check the whether the obtained x value if correct.} \\ AB=BC \\ 5x-1=3x+11 \\ 5(6)-1=3(6)+11 \\ 30-1=18+11 \\ 29=29 \end{gathered}[/tex]Thus the sides of isoscles triangles are equal. Hence the value of x is correct.