Find the solution of the system by graphing.-x - 4y=4y=1/4x-3Part B: The solution to the system,as an ordered pair,is
Answers
Solution
-x -4y = 4
y= 1/4 x -3
Replacing the second equation in the first one we got:
-x -4(1/4x -3) =4
-x -x +12= 4
-2x = 4-12
-2x = -8
x= 4
And the value of y would be:
y= 1/4* 4 -3= 1 -3= - 2
And the solution would be ( 4,-2)
Related Questions
I need help on this i tried and it was wrong
Answers
Given the Division:
[tex]420\div10[/tex]You can identify that have to divide 420 by 10. This means that you need to move the Decimal Point 1 place to the left. Notice that, if you do this, you get:
[tex]=42.0[/tex]Notice that now the digit that was placed in the Ones Place, is in the Tenths Place. Therefore, each original digit was shifted one place to the right.
Hence, the answer is:
Silvergrove Hardware kept an inventory of 517,110 lawnmowers in the past. With a change inmanagement, the hardware store now keeps an inventory of 70% more lawnmowers. Howmany lawnmowers is that?
Answers
879,087.
EXPLANATION
To find the number of lawnmowers, we need to first find 70% of the number of lawnmowers that was kept in the past. Then add the to the number of lawnmowers kept in the past.
From the given question;
Number of lawnmowers kept in the past = 517, 110.
70% of lawnmowers kept in the past = 70% of 517 110
[tex]\begin{gathered} =\frac{70}{100}\times517\text{ 110} \\ \\ =361\text{ 977} \end{gathered}[/tex]Number of lawnmowers now kept in store = number of lawnmowers kept in the past + 70% of lawnmowers kept in the past
= 517 110 + 361 977
= 879,087.
How many -digit even numbers are possible the digit cannot be zero?
Answers
Answer:
45,000
Step-by-step explanation:
Hey! Let's help you with your question here!
So, let's think about this logically. The only limit we have here is that the leftmost digit cannot be zero. This makes sense because there would be no five-digit number if the leftmost is zero. In order to find the possible amount of even numbers, we need to take the possible numbers of each digit and have them multiplied to each other to get the total. (I will explain this soon).
First Digit:
Since, the rules state that the leftmost digit cannot be zero, this would be the digit that the rule affects. From here, we can have a possibility of the numbers 1 through 9 here. So, for the first digit, we have the possibility of 9 numbers that can be here.
Second, Third, Fourth Digit:
Now you're probably wondering as to why I've grouped up these 3 digits and not the last or the first one. We'll get to the last one in the next explanation, but we exclude the first digit because the rule that affects the first digit, does not affect these digits nor the last digit. With these 3 digits, we don't have that rule of it cannot be zero, so now our possibilities for what the numbers can be is 0 through 9. If we include 0 as a number too, then we have a possibility of 10 numbers that can be within these digits.
Fifth (Last) Digit:
For this last digit, there is an implicit rule being stated for the last digit. The question asks how many five-digit even numbers are possible if the leftmost digit cannot be zero. This rule affects the last digit only as that allows the whole five-digit number to be even and zero is included in this. So, the even numbers are 0, 2, 4, 6, and 8. In this case, we only have 5 possible numbers to choose from for the very last digit.
Answer Explanation:
Before I begin answering, back in the very first paragraph, I said we need to take the possible numbers of each digit and multiply them altogether to get the total amount of possible values. Why do we do this? This is the idea of possibility combination. We multiply because we are taking in account all of the possible values whereas if we just add, we're only taking in account the maximum possible value of each possibility. So, let's calculate the answer now! For the first digit, we have a possibility of 9 numbers being there (1-9). For the Second, Third, and Fourth digit, we have a possibility of 10 numbers being there (0-9). And finally for the last digit, we have a possibility of only 5 numbers (0, 2, 4, 6, and 8). So, the total possible combination is:
[tex]9*10*10*10*5[/tex]
[tex]=45,000[/tex]
Therefore, we get 45,000 total possible five-digit even numbers where the leftmost digit cannot be zero.
in the diagram segment AD and AB are tangent to circle C solve for x
Answers
A property ostates that if two lines that are tangent to the circle intersect in an external point, they are congruent, i.e. they have the same length.
[tex]\begin{gathered} AD=AB \\ x^2+2=11 \end{gathered}[/tex]From this expression we can determine the possible values of x. The first step is to equal the expression to zero
[tex]\begin{gathered} x^2+2-11=11-11 \\ x^2+2-11=0 \\ x^2-9 \end{gathered}[/tex]The expression obtained is a quadratic equation, using the queadratic formula we can determine the possible values of x:
[tex]\begin{gathered} f(x)=ax^2+bx+c \\ x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \end{gathered}[/tex]For our expression
[tex]x^2+0x+-9[/tex]The coefficients are
a=1
b=0
c=-9
Replace them in the formula
[tex]\begin{gathered} x=\frac{-0\pm\sqrt[]{0^2-4\cdot1\cdot(-9)}}{2\cdot1} \\ x=\frac{0\pm\sqrt[]{36}}{2} \\ x=\frac{0\pm6}{2} \end{gathered}[/tex]Now calculate both possible values:
Positive:
[tex]\begin{gathered} x=\frac{+6}{2} \\ x=3 \end{gathered}[/tex]Negative:
[tex]\begin{gathered} x=\frac{-6}{2} \\ x=-3 \end{gathered}[/tex]The possible values of x are 3 and -3
Segment RS is translated by (x+1, y-2) and then reflected over the x-axis. The resulting segment R" S" has coordinates R" (7,3) and
S" (2,7). What are the coordinates of the segment RS?
can someone pls help meee
Answers
Answers:
R = (6, -1)
S = (1, -5)
==========================================================
Explanation:
R'' is located at (7,3)
Reflect this over the x axis to get R'(7,-3). We flip the sign of the y coordinate while keeping the x coordinate the same. The rule is [tex](x,y) \to (x,-y)[/tex]
Then we apply the inverse of (x+1, y-2) which is (x-1, y+2). Notice the sign flips.
Let's apply this inverse transformation to determine the coordinates of point R.
[tex](\text{x},\text{y})\to(\text{x}-1,\text{y}+2)\\\\(7,-3)\to(7-1,-3+2)\\\\(7,-3)\to(6,-1)\\\\[/tex]
Therefore, point R is located at (6, -1)
-------------------
Point S'' is at (2,7)
It reflects over the x axis to get to (2,-7)
Then we apply that inverse transformation to get
[tex](\text{x},\text{y})\to(\text{x}-1,\text{y}+2)\\\\(2,-7)\to(2-1,-7+2)\\\\(2,-7)\to(1,-5)\\\\[/tex]
Point S would be located at (1, -5)
30-28-25-21-16 next number
Answers
Answer:
10
Step-by-step explanation:
30 -2
28 -3
25 -4
21 -5
16 -6
= 10
Answer:
10
Step-by-step explanation:
Given the sequence 30, 28, 25, 21, 16, you want to know the next number.
DifferencesFirst differences between successive terms are ...
28 -30 = -2
25 -28 = -3
21 -25 = -4
16 -21 = -5
These are not constant, so this is not an arithmetic sequence. However, we notice the second differences are constant:
-3 -(-2) = -1
-4 -(-3) = -1
-5 -(-4) = -1
ApplicationThis observation tells us the next second difference is ...
-5 +(-1) = -6
And the next number in sequence is ...
16 +(-6) = 10
The next number is 10.
__
Additional comment
When a sequence of numbers is described by a polynomial or exponential, looking at differences (and their differences) can help determine the degree of the polynomial, or the common ratio of the exponential.
Here, the second differences are constant, so a second-degree (quadratic) polynomial will describe the sequence. The polynomial describing this sequence is ...
a(n) = 31 -(n)(n+1)/2
HELP PLEASEEEEE!!!!!!
Answers
-1 3/4, 14/8, 1.125 and -0.875 correspond to points 1, 8, 6 and 4 respectively on the number line.
How can we match -1 3/4, 14/8, 1.125 and -0.875 on the number line?Looking at the number line, there are 8 divisions between two points e.g 0 to 1.
To know the value of 1 division, we divide the value of the distance between two points by the number of divisions:
= 1/8 = 0.125
To find the locations, we just divide the value of the locations with the value of 1 division:
-1 3/4 / 0.125 = -14 (Count 14 divisions to the left of 0) = point 1
14/8 / 0.125 = 14 (Count 14 divisions to the right of 0) = point 8
1.125/ 0.125 = 9 (Count 9 divisions to the right of 0) = point 6
-0.875 / 0.125 = -7 (Count 7 divisions to the left of 0) = point 4
Therefore, the positions of -1 3/4, 14/8, 1.125 and -0.875 on the number line are points 1, 8, 6 and 4 respectively.
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Circumference of a circleThe radius of a circle measures 16 m. What is the circumference of the circle?Use 3.14 for, and do not round your answer. Be sure to include the correct unit in your answer.
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Solution:
Given:
[tex]\text{radius of a circle, r = 16m}[/tex]The circumference (C) of a circle is given by;
[tex]\begin{gathered} C=2\pi r \\ \text{where;} \\ C\text{ is the circumference of the circle} \\ r\text{ is the radius} \end{gathered}[/tex]Hence,
[tex]\begin{gathered} r=16m \\ \pi=3.14 \\ C=\text{?} \end{gathered}[/tex]Thus,
[tex]\begin{gathered} C=2\pi r \\ C=2\times3.14\times16 \\ C=100.48m \end{gathered}[/tex]Therefore, the circumference of the circle is 100.48m
the width of a rectangle is 8 inches less than its length, and the area is 9 square inches. what are the length and width of the rectangle?
Answers
The given situation can be written in an algebraic way:
Say x the width of the rectangle and y its height.
- The width of a rectangle is 8 inches less than its length:
x = y - 8
- The area of the rectangle is 9 square inches:
xy = 9
In order to find the values of y and x, you first replace the expression
x = y - 8 into the expression xy = 9, just as follow:
[tex]\begin{gathered} xy=9 \\ (y-8)y=9 \end{gathered}[/tex]you apply distribution property, and order the equation in such a way that you obtain the general form of a quadratic equation:
[tex]\begin{gathered} (y-8)y=9 \\ y^2-8y=9 \\ y^2-8y-9=0 \end{gathered}[/tex]Next, you use the quadratic formula to solve the previous equation for y:
[tex]y=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]here you have a = 1, b = -8 and c = 9. By replacing these values you obtain:
[tex]\begin{gathered} y=\frac{-(-8)\pm\sqrt[]{(-8)^2-4(1)(-9)}}{2(1)}=\frac{8\pm\sqrt[]{64+36}}{2} \\ y=\frac{8\pm\sqrt[]{100}}{2}=\frac{8\pm10}{2}=\frac{8}{2}\pm\frac{10}{2}=4\pm5 \end{gathered}[/tex]Hence, you have two solutions for y:
y1 = 4 + 5 = 9
y2 = 4 - 5 = -1
You select only the positive solution, because negative lengths do not exist in real life. Hence, you have y = 9.
Finally, you replace the value of y into the expression x = y - 8 to obtain x:
[tex]\begin{gathered} x=y-8 \\ x=9-8 \\ x=1 \end{gathered}[/tex]Hence, the width and length of the given recgtangle are:
width = 1 in
length = 9 in
I need help with this question involving the Cartesian plane will post pic
Answers
The graph of f(x) is a parabola with "arms up"
The vertex of the parabola is (0,-3)
Then we can know all the problem ask us:
increasing: (-3, infinity)
decreasing: (minus infinty, -3)
DNE maximum, beacuase it's arbitrarily large.
The minimum is the vertex: minimum of -3 at x = 0
The domain is all real numbers
The range is [-3, infinity)
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To know the shape of a parabola you want to look 2 things. The standar formula of a parabola is:
[tex]f(x)=ax^2+b[/tex]We focus on a and b. Always will be a squared x, but a and b vary. a lot
A tell us if the parabola has it's arms up or down. If is positive, has arms up. If it's negative, arms down.
Also, this isn't something "strictly mathematical" but can tel you is the parabola is thin or fat.
Now b tells us what happends when x=0. If b is positive, the vertex will be "rised up". If b is negative, the vertex will be "pulled down"
When you get relatively confident, you can watch a and b, and based on their sign and how big they are, you can make a really good idea how the graphic is.
All the information the problem ask, you can get it by those numbers.
To know how wide is a parabola, you need to look at a. Let's supose a = 100. This is a very big number, si if I plug in an x, the function will square it and multiply it by 100 right? Then the function will be very thin. For an x very low, the function will be very great. Example: f(x)=100x^2 if I put x = 1 then I have to square it, and multipli it by 100: 1^2*100=100
Now let's copare this with an smaller a. Suppose a =2. Then if I plug x = 1 I get:
[tex]2x^2\text{ at x =1 }\Rightarrow f(1)=2\cdot1^2=2[/tex]For the same value of x, the first function is 100 and the second 2
Read the problem below and find the solution. Use a model or act the
problem out to help solve it.
A group of 24 students have recess together. They are making teams to play
a game. Each team has to have exactly 5 players, and no one can be on more
than one team. How many teams can they make? (It is possible that not
everyone can be on a team.)
Answers
Answer:
possible
Step-by-step explanation:
Victoria and her children went into a grocery store and she bought $9 worth of applesand bananas. Each apple costs $1.50 and each banana costs $0.50. She bought a totalof 8 apples and bananas altogether. Determine the number of apples, x, and thenumber of bananas, y, that Victoria bought.Victoria boughtapples andbananas.
Answers
We will determine the solution as follows:
*First: From the text, we have the following expressions:
[tex]x+y=8[/tex]&
[tex]1.50x+0.5y=9[/tex]Here x represents apples and y represents bananas.
*Second: From the first expression, we solve for either x or y, that is [I will solve for ]:
[tex]x+y=8\Rightarrow x=8-y[/tex]*Third: Now, using the value for x, we replace in the second expression and solve for y, that is:
[tex]1.50x+0.5y=9\Rightarrow1.50(8-y)+0.5y=9[/tex][tex]\Rightarrow12-1.50y+0.5y=9\Rightarrow-y=-3[/tex][tex]\Rightarrow y=3[/tex]*Fourth: We replace the found value of y on the first expression and solve for x:
[tex]x+y=8\Rightarrow x+3=8[/tex][tex]\Rightarrow x=5[/tex]So, the number of apples was 5 and the number of bananas was 3.
I have 5 digits in my number. I do not have any tens. My digits add upto the product of 2 and 6. My biggest place has a value of 30,000. Myhundreds and thousands place adds up to three. The value of mythousands place is bigger than my hundreds. I only have one 0 in mynumber. The sum of my ten thousands, thousands, and hundredsequals the value of my ones place.
Answers
Let's begin by listing out the information given to us:
I have 5 digits in my number means the number is XXXXX (10,000 - 99,999)
No tens: the place value of 'tens' is zero
My digits add up to the product of 2 and 6: 2 * 6 = 12
[tex]\begin{gathered} \Sigma X=2\cdot6=12 \\ \Sigma X=12 \end{gathered}[/tex]My biggest place has a value of 30,000: this restricts the number to lie between 10,000 - 30,000
My hundreds and thousands place adds up to three: this can either be 2 + 1 or 1 + 2 or 0 + 3 or 3 + 0
The value of my thousands place is bigger than my hundreds: this implies that it is 2 + 1 or 3 + 0
I only have one 0 in my number: this cannot be in the 'ten thousands' place, it is the 'tens' place value (I do not have any tens)
The sum of my ten thousands, thousands, and hundreds equals the value of my ones place: the value of the 'ones' place is 6, the value of the 'ten thousands' is 2, the value of the 'thousands' is 3, the value of the 'hundreds' is 1
Hence, the number is 23,106 (remember that "My biggest place has a value of 30,000")
At an appliance store, if 63 stereos were sold during a one-month period, which of the following must be true?A. At least one stereo was sold on each day of the monthB. Exactly two stereos were sold on the same day during the monthC. At least one stereo was sold on either Monday, Wednesday, or Friday during the monthD. At least three stereos were sold on one day of the month.
Answers
Answer:
Alternative D. At least three stereos were sold on one day of the month.
Explanation:
Now, let's evaluate the options:
A. At least one stereo was sold on each day of the month
It is false.
We can not affirm that. For example, all the stereos can be sold on only one day of the month
B. Exactly two stereos were sold on the same day during the month
It is false.
Same explanation as A.
C. At least one stereo was sold on either Monday, Wednesday, or Friday during the month
It is false.
We can not affirm that too. The explanation is the same as for alternative A.
D. At least three stereos were sold on one day of the month.
It is true.
If two stereos are sold every day, for a month of 30 days, 60 stereos are sold. So, on some days 3 or more stereos are sold.
Also, if all the stereos are sold on the same day, more than 3 stereos were also sold.
So, alternative D is correct.
A volleyball drops 8 meters and bounces up 2 meters.
Use the expression |-8 + 2 to find the total distance
the volleyball travels. The total distance the volleyball travels is
✓meters.
Answers
The volleyball travelled a total distance of 10 meters
How to determine the total distance travelled by the volleyball?From the question, the given parameters are
Initial height = 8 meters
Height of bounce = 2 meters
The expression of the total distance is represented as
Total distance = |-8| + 2
Remove the absolute symbol
Total distance = 8 + 2
Evaluate the sum
Total distance = 10
Hence, the total distance travelled by the volleyball is 10 meters
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v+1.6>-5.5
nnnnnnnnnnnn
Answers
Answer:
v > -7.1
Step-by-step explanation:
PR and SU are parallel lines. Which angles are corresponding angles?
Answers
Given
PR and SU are parallel lines.
To find the pair of corressponding angles.
Explanation:
From, the figure,
Since PR and SU are parallel and the corressponding angles lie in the same corner.
Then,
[tex]\begin{gathered} \angle PQO,\angle STQ \\ \text{are corressponding angles.} \end{gathered}[/tex]Hence, the answer is Option c).
A lab assistant needs to create a 1000 ML mixture that is 5% hydroelectric acid. The assistant has solutions of 3.5% and 6% in supply at the lab. Using the variables x and y to represent the number of milliliters of the 3.5% solution and the number of milliliters of the 6% solution respectively, determine a system of equation that describes the situation the situation.Enter the equations below separated by a comma How many milliliters of the 3.5% solution should be used?How many milliliters of 6% solution should be used?
Answers
Given:
A lab assistant needs to create a 1000 ML mixture that is 5% hydroelectric acid.
The assistant has solutions of 3.5% and 6% in supply at the lab.
let the number of milliliters from the solution of 3.5% = x
And the number of milliliters from the solution of 6% = y
so, we can write the following equations:
The first equation, the sum of the two solutions = 1000 ml
So, x + y = 1000
The second equation, the mixture has a concentration of 5%
so, 3.5x + 6y = 5 * 1000
So, the system of equations will be as follows:
[tex]\begin{gathered} x+y=1000\rightarrow(1) \\ 3.5x+6y=5000\rightarrow(2) \end{gathered}[/tex]Now, we will find the solution to the system using the substitution method:
From equation (1)
[tex]x=1000-y\rightarrow(3)[/tex]substitute with (x) from equation (3) into equation (2):
[tex]3.5\cdot(1000-y)+6y=5000[/tex]Solve the equation to find (y):
[tex]\begin{gathered} 3500-3.5y+6y=5000 \\ -3.5y+6y=5000-3500 \\ 2.5y=1500 \\ y=\frac{1500}{2.5}=600 \end{gathered}[/tex]substitute with (y) into equation (3) to find x:
[tex]x=1000-600=400[/tex]So, the answer will be:
Enter the equations below separated by a comma
[tex]x+y=1000,3.5x+6y=5000[/tex]How many milliliters of the 3.5% solution should be used?
400 milliliters
How many milliliters of 6% solution should be used?
600 milliliters
See photo for problem
Answers
The distance, x, from one corner to another corner three corners away is 4. 70cm
The distance, y, from one corner to another corner two corners away is 4. 07cm
How to determine the valueIt is important to note that the image shown is a hexagon and each of the interior angles of a hexagon has a value of 120 degrees
Also note that the have the trigonometric identities;
sinecosinetangentcotangentsecantcosecantUsing the cosine identity, we have;
sin θ = adjacent/ hypotenuse
substitute the values
cos 60 = 2.35/x
cross multiply
x = 2. 35/cos 60
x = 2. 35/ 0. 5
x = 4. 7 cm
Then, we have,
sin 60 = y/ 4. 7
y = sin 60 × 4.7
y = 0. 8660 × 4. 7
y = 4. 07cm
Hence, the values are 4. 7cm and 4. 07cm
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Solve the triangle for the missing sides and angles. Round all side lengths to the nearest hundredth. (Triangle not to scale.)
Answers
The Law of Cosines
Let a,b, and c be the length of the sides of a given triangle, and x the included angle between sides a and b, then the following relation applies:
[tex]c^2=a^2+b^2-2ab\cos x[/tex]The triangle shown in the figure has two side lengths of a=4 and b=5. The included angle between them is x=100°. We can find the side length c by substituting the given values in the formula:
[tex]c^2=4^2+5^2-2\cdot4\cdot5\cos 100^o[/tex]Calculating:
[tex]c^2=16+25-40\cdot(-0.17365)[/tex][tex]\begin{gathered} c^2=47.946 \\ c=\sqrt[]{47.946}=6.92 \end{gathered}[/tex]Now we can apply the law of the sines:
[tex]\frac{4}{\sin A}=\frac{5}{\sin B}=\frac{c}{\sin 100^o}[/tex]Combining the first and the last part of the expression above:
[tex]\begin{gathered} \frac{4}{\sin A}=\frac{c}{\sin100^o} \\ \text{Solving for sin A:} \\ \sin A=\frac{4\sin100^o}{c} \end{gathered}[/tex]Substituting the known values:
[tex]\begin{gathered} \sin A=0.57 \\ A=\arcsin 0.57=34.7^o \end{gathered}[/tex]The last angle can be ob
Describe the translation:A) 4 units right and 6 units downB) 4 units left and 6 units upC) 6 units left and 4 units upD) 6 units right and 4 units down
Answers
To describe the transfer we will review what the points of the blue and red triangle are.
Blue triangle
I = (-2, 8)
I' = (4, 4)
First, we will determine the x-axis translation
[tex]\begin{gathered} \Delta x=x2-x1 \\ \Delta x=4-(-2) \\ \Delta x=6 \end{gathered}[/tex]6 units right
Now let's calculate the y-axis transfer
[tex]\begin{gathered} \Delta y=y2-y1 \\ \Delta y=4-8 \\ \Delta y=-4 \end{gathered}[/tex]4 units down
The answer would be 6 units right and 4 units down
You got 84 of 100 questions on the test correct. What percent did you get correct?Answer: 84%100%16%8.4%11/100 is equal to what percent?Answer: 110%10%89%11%3 out of 4 students in your class are girls. What percent of the class are girls?Answer: 3%4%75%25%
Answers
Recipe A calls for 2 cups of sugar and makes 48 cookles. Recipe B calls for 3 cups of sugar and makes 54 of the same sized cookies. Determine which recipe contains more sugar in each cookle. Use complete sentences to explain your reasoning.
Answers
we are given two recipes for cookies and we are asked which of the two contains more sugar. To do that we need to find the amount of sugar per cookie for each recipe.
For recipe A we have:
[tex]2cups\rightarrow48cookies[/tex]This means:
[tex]\frac{2cups}{48cookies}=\frac{1}{24}\frac{cups}{cookies}[/tex]For recipe B we have:
[tex]3cups\rightarrow54\text{cookies}[/tex]This means:
[tex]\frac{3\text{cups}}{54\text{cookies}}=\frac{1}{18}(\frac{cups}{cookies})[/tex]Since 1/18 is greater than 1/24, this means that there is more sugar per cookie in recipe B than in recipe A.
tell whether the fractions are equivalent
Answers
Step 1:
Equivalent fractions are fraction that are equal in ratio.
1/3 is equivalent to 4/12
4/12 can be simplify to 1/3 because 4 is a highest common factor of 4 and 12
When you divide by numerator ( 4) and denominator (12) by 4, the fraction result to 1/3.
Hence, 1/3 is equivalent to 4/12.
Final answer
[tex]\frac{1}{3}\text{ = }\frac{4}{12}[/tex]
The sides of an equilateral triangle are 8 units long. What is the length of the altitude of the triangle? N O svē units O 4/3 units 10,5 units O 165 units M
Answers
The all the sided of the equlatral triangle have the same lentgth. All the angles of the triangles are 60 degrees.
The expression for the hight of a equlatral triangle is,
[tex]\sin (60^0)=\frac{h}{l}_{}[/tex]Here, ''
g(x) = 2x - 5f(x) = 4x + 2Find g(f(x))
Answers
Explanation
Step 1
Let
[tex]\begin{gathered} g(x)=2x-5 \\ \text{and} \\ f(x)=4x+2 \end{gathered}[/tex]then
[tex]\begin{gathered} g(f(x))= \\ g(x)=2x-5 \\ g(f(x))=2(4x+2)-5 \\ \text{apply distributive property} \\ g(f(x))=8x+4-5 \\ g(f(x))=8x-1 \end{gathered}[/tex]I hope this helps you
Can someone help me with this?
Answers
x to the zeroth power - 3x +5
A parent is buying two types of chocolate truffles for the children. The oldest child likes white chocolate (W), the younger two like dark chocolate (D) and the spouse likes white chocolate (W). Four white chocolate truffles (W) cost the same as three dark chocolate truffles (D). If the parent bought 8 white chocolate truffles(W) and 10 dark chocolate truffles (D), and spent $50.00, how much was each dark chocolate truffle?2.422.343.13
Answers
SOLUTION
Given the information on the question tab;
[tex]Let\text{ the price for a white chocolate truffle be W, and the price for a dark chocolate truffle be D;}[/tex][tex]\begin{gathered} From\text{ the statements made in the question;} \\ 4W=3D-----(1) \\ 8W+10D=50----(2) \end{gathered}[/tex][tex]\begin{gathered} From\text{ equation \lparen1\rparen;} \\ W=\frac{3D}{4}-----(3) \\ substituting\text{ W=}\frac{3D}{4}\text{ into equation \lparen2\rparen} \end{gathered}[/tex][tex]\begin{gathered} 8\times\frac{3D}{4}+10D=50 \\ 6D+10D=50 \\ 16D=50 \\ D=\frac{50}{16} \\ D=3.125\approx3.13 \end{gathered}[/tex]Final answer:
Each dark chocolate truffle costs $3.13
Divide the polynomial by the monomial (63xy^3+ 56x^2y^4)/(7xy)
Answers
ANSWER
9y² + 8xy³
EXPLANATION
To divide this polynomial by the given monomial, we can distribute the denominator into the sum,
[tex]\frac{63xy^3+56x^2y^4}{7xy}=\frac{63xy^3}{7xy}+\frac{56x^2y^4}{7xy}[/tex]Then, each coefficient simplifies with the coefficient of the monomial, since both are multiples of 7. Also, in the first term, x cancels out, and we have to subtract 1 from the exponent of y. In the second term, we subtract 1 from both the exponents of x and y,
[tex]\frac{63xy^3}{7xy}+\frac{56x^2y^4}{7xy}=9y^2+8xy^3[/tex]Hence, the result is 9y² + 8xy³.
how do I write down the values of each letters without measuring it?
Answers
Given the graph of parallel lines and a transversal
There is an angle = 90
This means the transversal is perpendicular to the parallel lines
So, All the angles are right angles
So, the measure of all angles = 90
So,
[tex]\begin{gathered} m\angle g=90\degree \\ m\angle h=90\degree \\ m\angle i=90\degree \end{gathered}[/tex]