In converse, a segment is divided into two congruent portions if a line bisects it.
What is converse?A line bisects a segment if it can be divided up into two congruent portions. A line does not cut a section in half if it is not separated into two equal parts.A line is split into two equal parts by a bisector. Therefore, when we refer to a perpendicular bisector of a line segment AB, we mean that it bisects or divides AB into two equal halves. It is perpendicular to AB or at right angles to it. The distance between each point on the perpendicular bisector from points A and B is equal.Contrarily, if two segments are congruent, they have the same length. Inverse: Two segments have different lengths if they are not congruent.To learn more about line bisector refer to :
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how do I know where which choices below go into the correct blanks for number 2, 3, 4?
For 2, we have the following triangle:
Using sine and cosine we have the following:
[tex]\begin{gathered} \cos (45)=\frac{x}{10\sqrt[]{2}} \\ \Rightarrow x=\cos (45)\cdot10\sqrt[]{2}=(\frac{1}{\sqrt[]{2}})\cdot10\sqrt[]{2}=10 \\ \sin (45)=\frac{y}{10\sqrt[]{2}} \\ \Rightarrow y=\sin (45)\cdot10\sqrt[]{2}=(\frac{1}{\sqrt[]{2}})10\sqrt[]{2}=10 \end{gathered}[/tex]Therefore, the remaining sides are y= 10 and x = 10
Midpoint: 8, -2 Endpoint: 3,10 find other point
The midpoint coordinates are: (8,-2)
We can label this coordinates as follows
[tex]\begin{gathered} x_m=8 \\ y_m=-2 \end{gathered}[/tex]The coordinates for one of the endpoints are: (3,10)
We label this coordinates as follows:
[tex]\begin{gathered} x_1=3 \\ y_1=10_{}_{} \end{gathered}[/tex]We are looking for the other endpoints with the coordinates (x2,y2).
We use the formulas to find the midpoint:
[tex]\begin{gathered} x_m=\frac{x_1+x_2}{2}_{} \\ y_m=\frac{y_1+y_2}{2} \end{gathered}[/tex]But, since we need x2 and y2, we solve for then in the equations:
[tex]\begin{gathered} 2x_m-x_1=x_2_{} \\ 2y_m-y_1=y_2 \end{gathered}[/tex]And we substitute our values into the equations:
For x2:
[tex]\begin{gathered} 2(8)-3=x_2 \\ 16-3=x_2 \\ 13=x_2 \end{gathered}[/tex]For y2:
[tex]\begin{gathered} 2(-2)-10=y_2 \\ -4-10=y_2 \\ -14=y_2 \end{gathered}[/tex]Answer: (13,-14)
For a small plane, v , the angle of depression of a sailboat is 21 degrees. The angle of depression of a ferry on the other side of the plane is 52 degrees. The plane is flying at an altitude of 1650m how far apart are the boats, to the nearest meter?
Answer:
5,588 m
Explanation:
In the diagram:
[tex]\begin{gathered} \angle\text{UVX}=90\degree-21\degree=69\degree \\ \angle\text{XVW}=90\degree-52\degree=38\degree \end{gathered}[/tex]The distance between the two boats is UW and:
[tex]UW=UX+XW[/tex]In right triangle UXV:
[tex]\begin{gathered} \tan V=\frac{UX}{VX} \\ \implies\tan 69\degree=\frac{UX}{1650} \\ \implies UX=1650\times\tan 69\degree \end{gathered}[/tex]Similarly, in the right triangle WXV:
[tex]\begin{gathered} \tan V=\frac{XW}{VX} \\ \implies\tan 38\degree=\frac{XW}{1650} \\ \implies XW=1650\times\tan 38\degree \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} UW=UX+XW \\ =(1650\times\tan 69\degree)+(1650\times\tan 38\degree) \\ =5587.52m \\ \approx5,588m \end{gathered}[/tex]The boats are 5,588 meters apart (correct to the nearest meter).
8−6÷2+3×5= 7×3−15÷5= 8+2(1+12÷2)^2=
Recall that the order of the operations PEMDAS
1. Parenthesis
2. Exponents.
3. Multiplication.
4. Division.
5. Addition.
6. Subtraction.
1. Given expression is
[tex]8-6\div2+3\times5[/tex]Multiply 3 and 5, we get
[tex]8-6\div2+3\times5=8-6\div2+15[/tex]Divide 6 by 2, we get
[tex]=8-3+15[/tex]Subtract 3 from 8, we get
[tex]=5+15[/tex]Add 5 and 15, we get
[tex]=20[/tex]The answer is
[tex]8-6\div2+3\times5=20[/tex]2.Given expression is
[tex]7\times3-15\div5[/tex]Multiply 7 and 3, we get
[tex]7\times3-15\div5=21-15\div5[/tex]Divide 15 by 5, we get
[tex]=21-3[/tex]Subtract 3 from 21, we get
[tex]=18[/tex]The answer is
[tex]7\times3-15\div5=18[/tex]3. Given expression is
[tex]8+2(1+12\div2)^2[/tex]First, we need to solve inside the parenthesis, divide 12 by 2, we get
[tex]8+2(1+12\div2)^2=8+2(1+6)^2[/tex]Add 1 and 6, we get
[tex]=8+2(7)^2[/tex]Solve exponent.
[tex]=8+2(49)[/tex]Multiply 2 and 49, we get
[tex]=8+98[/tex]Add 8 and 98, we get
[tex]=106[/tex]The answer is
[tex]8+2(1+12\div2)^2=106[/tex]What is the probability of either event occurring when you spina spinner with the numbers 1 through 4 which are all evenlyrepresented?Event A: Spinning an odd numberEvent B: Spinning a 4
We are given an experiment, and we are asked about the probability that either event happens. Therefore, we use the addition rule of probability, which states that if A and B are two events in a probability experiment the probability that either one of the events to happen is:
[tex]P(A\text{ }or\text{ }B)=P(A)+P(B)\text{ - }P(A\text{ }and\text{ }B)[/tex]Therefore, in our specific case, we have that the probability of A is 1/2, since we have 2 odd numbers out of possible 4 outcomes. The probability of B is 1/4, since we have a number 4 out of 4 possible outcomes. The probability of A and B is 0, because obtaining a 4 and an odd number are two mutually exclusive events. Therefore we have that our probability simply is the sum of our two probabilities:
[tex]P(A\text{ }or\text{ }B)=\frac{1}{2}+\frac{1}{4}=\frac{2}{4}+\frac{1}{4}=\frac{3}{4}[/tex]Therefore, our answer is 3/4
help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answer:
7 would be the closest meter when rounded 7 times 3 is 21 so its one-off but the closest you can get so the answer is 7 meters
Step-by-step explanation:
I divided 22 by three because the way to solve for the area is length times width so it'd be area divided by width for length
(2x²+4-5x)-(-8x+2+x²) is a what kind of polynomial
Answer:
The degree of the polynomial is the greatest of its various terms' exponents (powers). This is a seconds degree polynomial.
Step-by-step explanation:
2x^2 - 3x^5 + 5x^6.
We observe that the above polynomial has three terms. Here the first term is 2x^2, the second term is -3x^5 and the third term is 5x^6.
Now we will determine the exponent of each term.
(i) the exponent of the first term 2x^2 = 2
(ii) the exponent of the second term 3x^5 = 5
(iii) the exponent of the third term 5x^6 = 6
Since the greatest exponent is 6, the degree of 2x^2 - 3x^5 + 5x^6 is also 6.
Therefore, the degree of the polynomial 2x^2 - 3x^5 + 5x^6 = 6.
Easy peasy, hope you understand now.
NSWERVariableType ofvariableQuantitative(a) Temperature (in degrees Fahrenheit)Level ofmeasurementNominalOrdinalIntervalRatioCategoricalQuantitative(b) Dosage (in milligrams) of medicationNominalOrdinalIntervalRatioCategoricalQuantitative(C) Exchange on which a stock is traded(NYSE, AMEX, or other)NominalOrdinalIntervalRatioCategorical
We are looking at what type of variables are given. Let's analyze it one by one to check which one suits it best.
(a) Temperature
Temperature is measured by numbers, hence, this is categorized as a quantitative variable. Temperature does not have a non-finite value since it changes as time goes by, hence, the level of measurement for this type of variable is ratio.
Answer: Quantitative and ratio
(b) Dosage of the medication
The dosage of medication is measured in milligrams, which means we are dealing with numbers, hence, this is a quantitative variable. In the case of dosage, we are dealing with fixed values, hence, the level of measurement for this type of variable is interval.
Answer: Quantitative and interval
(c) Stock exchange
Stock exchanges are types of group variables. These are represented as categories, hence, this variable is classified as categorical. The exchanges are ranked in some specific order. When dealing with categorical variables that have rank order, we have ordinal variables.
Answer: Categorical and ordinal
The equations in elimination method are written in the standard form as _______________.ax - by = cax + by + c = 0Ax + By = Cax - by - c = 0
Step 1
Given; The equations in the elimination method are written in the standard form as ____
Step 2
Simultaneous linear equations can be solved using the elimination method. First of all, make sure that the equations are written in the standard form either Ax+By=C or Ax+By+C=0. In this method, we multiply both the equations with a non-zero number to make the coefficients of any one variable equal.
Thus the answer is; The equations are written in standard form as seen below
[tex]Ax+By=C[/tex]Write these numbers in order of size, starting with the smallest?
0.45
4.5
0.045
0.405
4.05
Answer:
0.045, 0.405, 0.45, 4.05, 4.5
Step-by-step explanation:
So, we have 0.045 before 0.405 because the second number (0) in the first one is lower than the second number (4) in the second one. We have 0.405 before 0.45 because the third numbers don't match up. The lower one is 0, while the higher one is 5. Next, 4.05 is smaller than 4.5 because of the second number. The second number in the smaller one is 0, while the bigger one, its second number is 4.5.
May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!
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Answer: Width = 3.4 meters, Length = 6.4 meters
Step-by-step explanation:
If the width is [tex]w[/tex], then the length is [tex]w+3[/tex].
[tex]w(w+3)=22\\\\w^2 +3w=22\\\\w^2 +3w-22=0\\ \\ w=\frac{-3 \pm \sqrt{3^2 -4(1)(-22)}}{2(1)}\\\\w \approx 3.4 \text{ } (w > 0)\\\\\implies w+3 \approx 6.4[/tex]
in 2000, the total population of the u.s. was 281.4 million people. in 2010, it was 308.7 million people. (source: www.census.gov) what is the average rate of change in the total population over this time period?
The average rate of change is 2,73,000.
The average rate of change is calculated using the formula -
Average rate of change = change in population ÷ change in time
Keep the values in formula to find the rate of change of population over given time period
Average rate of change = (308.7 - 281.4) million ÷ (2010 - 2000)
Performing subtraction in numerator and denominator on Right Hand Side of the equation
Average rate of change = 2730000 ÷ 10
Performing division on Right Hand Side of the equation
Average rate of change = 2,73,000
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A remote-controoled car is traveling at a speed of 4 feet per second. use this rate to complete the equation, where d is the distance in feet that the car travels in t seconds. use equation to find the distance in feet that the car travels in t=8 seconds
Distance travelled by remote controlled car is 32 feet in 8 sec
What is speed ?Speed is the rate and direction of an object's movement, whereas speed is the scalar at which an object moves along a path in time. Velocity is a vector, whereas speed is a scalar integer.
Calculationspeed = 4 feet/sec
distance = d feet
time = t sec
4 = d / t
t = 8 sec
d = 4 *8
d = 32 feet
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a model rocket is launched with an initial upward velocity of 175 ft/s the rocket's height is represented by h (in feet) after t seconds is given by the followingh = 175t - 16t^2find all values of t for which the rockets height id 85 feetand i need to round the answer to nearest hundredth
Given relation between height and time is:
[tex]h=175t-16t^2[/tex]Now put the value of h=85 ft in given relation:
[tex]85=175t-16t^2[/tex]Solving it for t:
[tex]\begin{gathered} 16t^2-175t-85=0 \\ t=\frac{175\pm\sqrt[]{(-175)^2-4\times16\times85}}{2\times16} \\ t=\frac{175\pm\sqrt[]{30625-5440}}{32} \\ t=\frac{175\pm\sqrt[]{25185}}{32} \\ t=\frac{175\pm158.6}{32} \\ t=0.51\text{ or }10.43\text{ second} \end{gathered}[/tex]Write the equation of the line that passes through the points (9,-1)(9,−1) and (-7,4)(−7,4). Put your answer in fully simplified form, unless it is a vertical or horizontal line.
The equation for lines will be y = -5/16 x + 29/16
What is equation straight line?
Y = mx + c is the general equation for a straight line, where m denotes the line's slope and c the y-intercept. It is the version of the equation for a straight line that is used most frequently in geometry. There are numerous ways to express the equation of a straight line, including point-slope form, slope-intercept form, general form, standard form, etc. A straight line is a geometric object with two dimensions and infinite lengths at both ends. The formulas for the equation of a straight line that are most frequently employed are y = mx + c and axe + by = c. Other versions include point-slope, slope-intercept, standard, general, and others.
The equation of the right line is [tex]\frac{(y+1)}{(x-9)} =m \frac{(4+1)}{(-7-9)}[/tex]
[tex]\frac{(y+1)}{(x-9)} = \frac{(4+1)}{(-7-9)}[/tex]
[tex]\frac{(y+1)}{(x-9)} = -5/16[/tex]
16y+16 =-5x +45
16y = -5x +29
y = -5/16 x + 29/16
Hence the equation for lines will be y = -5/16 x + 29/16
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You have $6,000 to invest in a savings account for 15 years and you have hvo account options to choose from. You can invest in an account that offers 8% simple interest or you can invest in an account that offers 6% interest compounded once a year. Complete the table and write an equation for each situation Simple interest & Compound Interest. Will you choose simple or compound interest? Why?
Problem
You have $6,000 to invest in a savings account for 15 years and you have hvo account options to choose from. You can invest in an account that offers 8% simple interest or you can invest in an account that offers 6% interest compounded once a year. Complete the table and write an equation for each situation Simple interest & Compound Interest. Will you choose simple or compound interest? Why?
Solution
Case 1: Simple interest
We can use the formula:
y= 6000 + 6000(0.08 x)= 6000+ 480x
And replacing we got:
X Y
__________
0 6000
1 6480
2 6960
5 8400
10 10800
15 13200
__________
Case 2: Compound interest
We can use the following formula:
Y= 6000 (1+0.08)^x =6000 (1.08)^x
And replacing we got:
X Y
__________
0 6000
1 6480
2 6998.4
5 8815.97
10 12953.55
15 19033.01
__________
The angle measures in a triangle are (3x+4), (5x), and (7x-4). What is the measure of the largest angle in the triangle?12 degrees40 degrees60 degrees80 degrees
Answer:
80 degrees
Explanation:
The sum of the measures of angles in a triangle is 18 degrees.
Given that the angle measures in a triangle are (3x+4), (5x), and (7x-4), then:
[tex](3x+4)+(5x)+(7x-4)=180^0[/tex]First, we solve the equation for x.
[tex]\begin{gathered} 3x+5x+7x+4-4=180^0 \\ 15x=180^0 \\ x=\frac{180^0}{15} \\ x=12^0 \end{gathered}[/tex]Therefore, the measures of the angles are:
[tex]\begin{gathered} 3x+4=3(12)+4=40^0 \\ 5x=5(12)=60^0 \\ 7x-4=7(12)-4=80^0 \end{gathered}[/tex]The measure of the largest angle in the triangle is 80 degrees.
12. Jayden sold 103 tickets for the school play. Student tickets cost $9 and adult tickets cost $14. Jayden's sales totaled $1127. How many adult tickets and how many student tickets did Jayden sell?
The total number of student tickets which are sold is 63 and the total number of adult tickets which are sold is 40.
Let the students' tickets sold by Jayden be x. Then, the number of adult tickets which are sold be 103-x.
Now, one student ticket costs $9.
Total cost of student tickets which are being sold = $9x
Similarly, one adult ticket costs $14.
Total cost of adult tickets which are being sold = $14×(103-x)
Total sales done by Jayden = $1127
∵ $9x + $14×(103-x) = $1127
⇒ 9x + 14×(103-x) = 1127
⇒ 9x + 1442 - 14x = 1127
⇒ 14x - 9x = 1442 - 1127
⇒ 5x = 315
∴ x = 63
⇒ 103 - x = 103 - 63 = 40
Hence, the total number of student tickets which are sold is 63 and the total number of adult tickets which are sold is 40.
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WXYZ~EFGD.13WXYZ26EFGDWhat is the similarity ratio of WXYZ to EFGD?Simplify your answer and write it as a proper fraction, improper fraction, or whole number
STEP - BY - STEP SOLUTION
What to find?
The similarity ratio of WXYZ to EFGD.
Given:
The ratio of WXYZ to EFGD can be determine by taking the ratio of any of the simila side of WXYZ to EFGD.
That is;
[tex]Similarity\text{ ratio=}\frac{WZ}{ED}[/tex]Since EFGD is a rectangle, using the property of the rectangle that state " opposite sides are congruent, we can deduce that ED = EG = 6
Hence,
[tex]similarity\text{ ratio=}\frac{WZ}{ED}=\frac{3}{6}=\frac{1}{2}[/tex]ANSWER
1/2
The value of x equals the number of cubic units in a box that is 4 units high, 4 units deep, and 4 units wide. Which equation can be used to determine the value of x?Math item stem image3x=644x=64x−−√=4x−−√3=4
The value of x equals the number of cubic units in a box that is 4 units high, 4 units deep, and 4 units wide.
Recall that the volume of a cube is given by
[tex]V=l\cdot w\cdot h[/tex]Where l is the length, w is the width, and h is the height of the cube.
We are given that all three sides are 4 units.
So, the volume is
[tex]\begin{gathered} V=4\cdot4\cdot4\; \\ V=64\; \; cubic\; \text{units} \end{gathered}[/tex]x must be equal to this volume
[tex]x=64[/tex]Take cube root on both sides of the equation
[tex]\begin{gathered} \sqrt[3]{x}=\sqrt[3]{64} \\ \sqrt[3]{x}=\sqrt[3]{4^3} \\ \sqrt[3]{x}=4 \end{gathered}[/tex]Therefore, the correct equation is the last option.
[tex]\sqrt[3]{x}=4[/tex]The function f(x) = 4x − 6 is shown in the table below. Identify the domain and range of function f. Enter the numbers in order from least to greatest.
x −5 −2 1 5
y −26 −14 −2 −14
The domain and the range of the function are {−5, −2, 1 ,5} and {−26, −14, −2} respectively
How to determine the domain and the range?From the question, we have the following parameters that can be used in our computation:
Function: f(x) = 4x - 6
Table of values
x −5 −2 1 5
y −26 −14 −2 −14
The set of x values is the domain
So, we have
Domain = {−5 −2 1 5}
Rewrite as
Domain = {−5, −2, 1 ,5}
The set of y values is the range
So, we have
Range = {−26 −14 −2 −14}
Rewrite as
Range = {−26, −14, −2}
Hence, the range is {−26, −14, −2}
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Hi can I have some help on number 12 please
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given functions
[tex]\begin{gathered} f(x)=x^2 \\ g(x)=-(x+2)^2-3 \end{gathered}[/tex]STEP 2: Describe the transformations
Translation to the left/right: Horizontal translation refers to the movement toward the left or right of the graph of a function by the given units. The shape of the function remains the same. It is also known as the movement/shifting of the graph along the x-axis.
To shift, move, or translate horizontally, replace y = f(x) with y = f(x + c) (left by c) or y = f(x - c) (right by c).
Translations up/down: The graph of a function can be moved up, down, left, or right by adding to or subtracting from the output or the input. Adding to the output of a function moves the graph up. Subtracting from the output of a function moves the graph down.
To translate the function up and down, you simply add or subtract numbers from the whole function. If you add a positive number (or subtract a negative number), you translate the function up. If you subtract a positive number (or add a negative number), you translate the function down.
STEP 3: Define the first transformation
[tex]\begin{gathered} x^2\Rightarrow(x+2)^2 \\ \text{This shows an horizontal transformation to the left by 2 units according to the description in step 2} \end{gathered}[/tex]STEP 4: Define the vertical transformation
[tex]\begin{gathered} f(x)\Rightarrow f(x)-3 \\ This\text{ shows a vertical transformation downwards by 3 units} \end{gathered}[/tex]STEP 5: Define the final transformation
[tex]\begin{gathered} f(x)\Rightarrow-f(x) \\ This\text{ shows a reflection over the x-axis} \end{gathered}[/tex]Hence, the transformations of f(x) to g(x) are:
Translated 2 units left
Translated 3 units down
Reflected over the x-axis (yes)
hi I need to solve for X and Y in this
In this question, we are given two similar triangles ABC and DEF.
Similar triangles:
The triangles are similar if they have congruent corresponding angles and the corresponding sides of triangles are in proportion.
Therefore, the proportion of all sides should be the same. To proportion (k) can be found using:
k = Side AB / side DE
k = 9/6
or
k = 3/2
Similarly, the 'k' should be the same for side BC and side EF. Therefore,
k = side BC/ side EF
Now, put the values in the equation
[tex]\frac{3}{2}=\frac{4x-1}{10}[/tex][tex]3\cdot10\text{ = 2}\cdot(4x-1)[/tex][tex]30\text{ = 8}x-2[/tex][tex]30+2\text{ = 8}x[/tex][tex]32\text{ = 8}x[/tex][tex]x\text{ = }\frac{32}{8}[/tex][tex]x\text{ = 4}[/tex]Therefore, the value of x would be 4.
Which graph has a slope of ? A coordinate plane with a straight line. The line starts at (negative 5, negative 4) and passes through points at (0, 1) and (4, 5). A coordinate plane with straight line. The line starts at (negative 5, negative 2) and passes through points at (negative 1, 0) and (4, 5). A coordinate plane with straight line. The line starts at (negative 5, negative 1) and passes through points at (negative 2, 0) and (3, 2). A coordinate plane with straight line. The line starts at (negative 4, negative 5) and passes through points at (0, 0) and (4, 5).
Answer: B
Step-by-step explanation:
a rectangle field is four times as long as it's wide if the length is decreased by 10 ft and the width is increased by 2 ft the perimeter will be 80 ft find the dimensions of the original field the original dimensions are blank feet long by blank feet wide
Let the width of the field = w
∵ The length is four times as the width
∵ The width = w
∴ The length = 4w
∵ The length is decreased by 10 feet
∴ The new length = 4w - 10
∵ The width is increased by 2 feet
∴ The new width = w + 2
The new perimeter is 80 feet
∵ The perimeter of the rectangle = 2(length + width)
[tex]\therefore P=2(4w-10+w+2)[/tex]Let us simplify it
[tex]\begin{gathered} P=2(4w+w-10+2) \\ P=2(5w-8) \\ P=2(5w)-2(8) \\ P=10w-16 \end{gathered}[/tex]Now equate it by 80
[tex]10w-16=80[/tex]Add 16 to both sides
[tex]\begin{gathered} 10w-16+16=80+16 \\ 10w=96 \end{gathered}[/tex]Divide both sides by 10
[tex]\begin{gathered} \frac{10w}{10}=\frac{96}{10} \\ w=9.6 \end{gathered}[/tex]The length is 4 times the width
[tex]\begin{gathered} l=4(9.6) \\ l=38.4 \end{gathered}[/tex]The length is 38.4 feet and the width is 9.6 feet
help please what is 3x plus 94 if x equals 27
Answer: To do that, we divide both sides by 3. Thus, the answer to "3 times what equals 27?" is 9. To double-check our work, multiply 9 by 3 to see that it equals 27.
Step-by-step explanation:
Answer: 175
Step-by-step explanation:
3(27)+94 =
81 + 94 = 175
2. Alonzo built a rectangular sign that measured 2 3/4 feet in length by 1 1/2 feet in width. a. What is the area of the sign?
Area of a rectangle = Length x Breadth
[tex]\begin{gathered} \text{Length = 2}\frac{3}{4} \\ \text{ = }\frac{11}{4} \\ \text{Breadth = 1}\frac{1}{2} \\ \text{ = }\frac{3}{2} \\ \\ \text{Area of a rectangle = }\frac{11}{4}\text{ x }\frac{3}{2} \\ \text{ = }\frac{33}{8} \\ \text{ = 4}\frac{1}{8}feet^2 \end{gathered}[/tex]Write a quadratic equation in standard form with the given roots. -4, 6
Answer:
Below
Step-by-step explanation:
With roots -4 and 6
the equation is a * (x+4)(x-6) = 0
'a' can be any real number (I'll choose '1')
Expand to x^2 -2x - 24 = f(x)
Which of the following would solve the equation below for x in onestep?10=x-15A. Adding 15 to both sides of the equationB. Adding 10 to both sides of the equationC. Subtracting 15 to both sides of the equationD. Subtracting 10 to both sides of the equation
In order to solve the equation for x, we need to look at the side where the variable is, then, we apply the contrary operations to this operation on both sides.
In this case, x is being subtracted by 15, then we need to eliminate this 15 by adding 15 on both sides
[tex]\begin{gathered} 10+15=x-15+15 \\ 25=x \end{gathered}[/tex]Answer:
A. Adding 15 to both sides of the equation
please help me. I think I have it figured out but I just wanted to double check.
Let's consider triangle ABC
Length AB can be obtained using Pythagoras
[tex]\begin{gathered} AB^2=x^2+y^2 \\ AB\text{ = }\sqrt[]{x^2+y^2} \\ \end{gathered}[/tex]Similarly, we can consider triangle ACD, so that length AD will be obtained through Pythagoras
[tex]\begin{gathered} AD^2=x^2+z^2 \\ AD\text{ = }\sqrt[]{x^2+z^2} \end{gathered}[/tex]Considering triangle ABD, with BD being the hypotenuse
[tex]\begin{gathered} BD^2=AD^2+AB^2 \\ (y+z)^{2\text{ }}=(x^2+z^2)+(x^2+y^2\text{)} \end{gathered}[/tex]Expanding the parentheses
[tex]\begin{gathered} y^2+2yz+z^2=x^2+z^2+x^2+y^2 \\ \\ y^2-y^2+z^2-z^2+2yz=2x^2 \\ 2yz=2x^2 \\ \end{gathered}[/tex]Divide both sides by 2
[tex]\begin{gathered} \frac{2yz}{2}=\text{ }\frac{2x^2}{2} \\ yz=x^2 \\ \\ x^2\text{ =yz} \\ \\ x\text{ = }\sqrt[]{yz} \end{gathered}[/tex]Option A is correct
Answer:
Let's consider triangle ABCLength AB can be obtained using PythagorasSimilarly, we can consider triangle ACD, so that length AD will be obtained through PythagorasConsidering triangle ABD, with BD being the hypotenuseExpanding the parentheses Divide both sides by 2Option A is correct
Step-by-step explanation: