To find the y-intercept, we have to make x=0 and solve for y:
[tex]\begin{gathered} 3x-2y=12 \\ x=0 \\ \Rightarrow3\cdot0-2y=12 \\ \Rightarrow-2y=12 \\ \Rightarrow y=\frac{12}{-2}=-6 \\ y=-6 \end{gathered}[/tex]Now, to find the x-intercept, we make y=0 and do the same as the previous case:
[tex]\begin{gathered} y=0 \\ \Rightarrow3x-2\cdot0=12 \\ \Rightarrow3x=12 \\ \Rightarrow x=\frac{12}{3}=4 \\ x=4 \end{gathered}[/tex]therefore, the y-intercept is the point (0,-6) and the x-intercept is the point (4,0)
HURRRYYY Given that AD is congruent to DC , find the length of XC.
The length of XC is 20
What does congruence of triangle mean?Triangles are said to be congruent if the three angles and three sides of a triangle are equal to the corresponding angles and sides of another triangle.
To be congruent, two triangles must have the same size and shape. The two triangles under consideration must overlap. If you rotate, flip, and/or move the triangle, its position and appearance will look different. In this case, we need to identify the six parts of one triangle and the corresponding parts of the other triangle.
For the triangles ΔAXD and ΔCXD
AD = DC ( congruent sides)
∠XDA = ∠XDC = 90° ( XD is perpendicular to AC)
XD is the common side.
This proves that triangles ΔAXD and ΔCXD are congruent
So it concludes, that XD = XC
2m + 10 = 4m
10 = 4m - 2m
10 = 2m
m = [tex]\frac{10}{2}[/tex]
m = 5
XC = 4m
XC = 4 × 5 = 20
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The segments shown below could form a triangle.
9
A
C
C
B
4
B
A
15
True or false
No/False - there is a rule that state that the sum of two sides of a triangle must be greater than the 3rd side.
In light of the question -In geometry, a triangle is a closed two-dimensional figure with three sides, three corners, and three vertices.Triangles are considered polygons with the fewest sides. In this article, we will discuss in detail what a triangle is, its types, properties and formulas.Learn more about triangles here. In geometry, a triangle is a type of polygon with three sides and three vertices. A triangle is considered a three-sided polygon.The sum of the three angles of a triangle is 180°. A triangle is contained in a single plane. There are six types of triangles based on their side and angle measurements.A triangle has only three sides joined by corners. Therefore, no matter what kind of triangle it is, it always has three sides.CalculationNo - there is a rule that state that the sum of two sides of a triangle must be greater than the 3rd side.
While 9+15 >4
and 4+15 >9
9+4 is not greater than 15 - so this triangle cannot be made.
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Graph the equationy = 6
Since the equation has only the variable y and it is a constant value, that means this equation is represented by a horizontal line (the line contains all values of x and always the value of y is 6).
In order to graph this equation, we can graph two points that are on the line (for example, (0, 6) and (1, 6)) and then draw the line that passes through both of them.
So we have:
Write this ratio as a fraction in simplest form without any units. 25 days to 5 weeks
Given:
There are given the statement:
25 days to 5 weeks.
Explanation:
To find the ratio, first, we need to convert the value of days into the week.
So,
To convert days into the week, we need to divide by 7.
So,
[tex]\frac{25}{7}week[/tex]Now,
The ratio as a fraction is:
[tex]\frac{25}{\frac{7}{5}}=\frac{25}{7\times5}[/tex]Then,
[tex]\begin{gathered} \frac{25}{\frac{7}{5}}=\frac{25}{7\times5} \\ =\frac{5}{7} \end{gathered}[/tex]Final answer:
Hence, the ratio as a fraction is shown below:
[tex]\frac{5}{7}[/tex]How would I solve this and what would be the answer?
Solution
(1). Domain
Since the graph is a polynomial, thus
The domain is all the elements of the set of Real Number
[tex]DOMAIN=(-\infty,\infty)[/tex](2) . Range
Notice that the graph is on the x - axis and above the x - axis throughout
The range will be
[tex]Range=\lbrack0,\infty)[/tex](3). x - intercept
We check where the graph touch the x - axis ( we have two)
That is at
[tex]\begin{gathered} x=-1 \\ \text{and} \\ x=2 \end{gathered}[/tex](4). y - intercept
We also check where the graph touch the y - axis
That is at
[tex]y=4[/tex](5). End Behaviour
First from the graph
[tex]x\rightarrow\infty,f(x)\rightarrow\infty[/tex]Second from the graph
[tex]x\rightarrow-\infty,f(x)\rightarrow\infty[/tex]What percentage of 3436 is 20
Let x percent of 3436 be 20.
Recall, percentage is expressed in terms of 100. This means that
x/100 * 3436 = 20
34.36x = 20
Dividing both sides of the equation by 34.36, we have
34.36x/34.36 = 20/34.36
x = 0.582%
Thus, 0.582% of 3436 is 20
Blank 1: 2/5Question 8 (1 point)Point - (4-7)Point B - (B. 1)mBlank 1:
We have to use the slope formula.
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Let's replace the given points.
[tex]m=\frac{1-(-7)}{8-4}=\frac{1+7}{4}=\frac{8}{4}=2[/tex]Hence, the slope is 2.Consider the function f(x)= log5 xComplete the following and then graphx= 1/5 f(x)?x=1 f(x)? x=5 f(x)?x=25 f(x)?
Given:
[tex]f(x)=\log_5x[/tex]Required: Function values at x = 1/5, 1, 5, and 25.
Explanation:
Use the logarithmic properties
[tex]\log_b1=0,\log_b\frac{A}{B}=\log_bA-\log_bB,\log_bb=1,\log_bb^n=n[/tex]To find f(1/5), substitute 1/5 for x into f(x).
[tex]\begin{gathered} f(\frac{1}{5})=\log_5(\frac{1}{5}) \\ =\log_51-\log_55 \\ =0-1 \\ =-1 \end{gathered}[/tex]To find f(1), substitute 1 for x into f(x).
[tex]\begin{gathered} f(1)=\log_51 \\ =0 \end{gathered}[/tex]To find f(5), substitute 5 for x into f(x).
[tex]\begin{gathered} f(5)=\log_55 \\ =1 \end{gathered}[/tex]To find f(25), substitute 25 for x into f(x).
[tex]\begin{gathered} f(25)=\log_525 \\ =\log_55^2 \\ =2\log_55 \\ =2 \end{gathered}[/tex]
Enter the value of the expression using the Order of Operations. (4 x 3) + 23 x 4-3
Starting with the expression:
[tex](4\times3)+23\times4-3[/tex]Solve parenthesis first. Since 4 times 3 equals 12, then the expression is equal to:
[tex]12+23\times4-3[/tex]Next, solve for multiplications. In this case, solve 23 times 4:
[tex]12+92-3[/tex]Finally, solve additions and substractions from left to right:
[tex]\begin{gathered} 12+92-3=104-3 \\ =101 \end{gathered}[/tex]Therefore:
[tex](4\times3)+23\times4-3=101[/tex]OWhat is the image point of (-4, 6) after the transformation r y=x 0 Rotation of 180 degrees
Given the point (-4,6).
So, The rule for a rotation by 180° about the origin is (x,y)→(−x,−y). Therefore, the new point is:
(-4,6) --> ( - ( - 4), - (6) ) --> (4, - 6)
Answer: ( 4, - 6 )
Jupiter's orbital speed is approximately 52 kilometers in 4 seconds. At this rate, how many kilometers will Jupiter travel in 5 seconds?
Jupiter's orbital speed is approximately 52 kilometers in 4 seconds.
In 4 seconds, she travel = 52km
i.e. in 1 minute she travel = 52/4
In one minutes she travel = 13 km
Distance travel in 5 seconds =
5 x 13 km = 65 km
At this rate Jupitar will travel 65 km in 5 seconds
Answer : Jupitar will travel 65 km in 5 seconds
if a pound of almonds cost eight dollars how many ounces can be bought for $3.80
Proportions
A pound of almonds is said to cost 8 dollars.
But one pound is equivalent to 16 ounces, therefore:
16 ounces cost 8 dollars
Dividing by 8 we get that
2 ounces of almonds cost 1 dollar
Thus, for $3.80 we can buy 2*3.80 = 7.60 ounces of almonds
a. If Links printing store will make a 150 copies for the cost of $15.00, then what is theunit rate of price per copy?
ANSWER
$0.10
EXPLANATION
We have that 150 copies are made for a total cost of $15.00
The unit rate of price per copy is the price of each copy of the printing.
To find the unit rate of price per copy, we have to divide the total price by the total number of copies.
So, we have:
[tex]\frac{15}{150}\text{ = \$0.10}[/tex]This means that the unit rate of price per copy is $0.10
what happens to F(x) when x is negative but approaches zero for the function F(x)=1/x whose graph is show below?*PHOTO*
We have the following function:
[tex]F(x)=\frac{1}{x}[/tex]According to the graph, the function tends to minus infinity when x takes negative values close to zero.
Answer: B. F(x) is a negative number
I think I have the right answer but I would still like to be 100% sure that I understand i also have to show my work
To solve this inequality, we can proceed as follows:
First: multiply both sides of the inequality by 9:
[tex]9\cdot\frac{x}{9}\leq9\cdot1\Rightarrow x\leq9[/tex]Then, the answer is x <= 9. In interval notation, we have that the answer is:
(-infinity, 9 ]. Or graphically:
In the quadrilateral below. “Angle WXZ is congruent to Angle YZX." If Ricardo's conjecture is true, which of the following must be true for Quadrilateral WXYZ to be a parallelogram?
Answer:
∠YXZ ≅ ∠WZX
Explanation:
Given that “Angle WXZ is congruent to Angle YZX."
The angles are shown in the diagram below.
This means that angles WXZ and YZX are alternate angles and thus,
• WX is parallel to ZY.
Consider the diagram below:
Angles YXZ and WZX are congruent by alternate angles, and thus:
• WZ is parallel to XY.
So, we have shown that the opposite sides of the quadrilateral are parallel.
Therefore, in order for quadrilateral WXYZ to be a parallelogram, Angles YXZ and WZX must be congruent.
The first option (∠YXZ ≅ ∠WZX ) is correct.
$75.00 is shared among 3 people in the ratio 2:4:9 how much is the largest share?
The ratio is 2:4:9, so we can consider the total parts we are dividing the total as 2+4+9 = 15.
Then, the first person receives 2/15, the second receives 4/15 and the third receives 9/15.
As the total is 75, we can calculate each part as:
[tex]\begin{gathered} p_1=75*\frac{2}{15}=10 \\ \\ p_2=75*\frac{4}{15}=20 \\ \\ p_3=75*\frac{9}{15}=45 \end{gathered}[/tex]Then, the largest share correspond to the third person and is $45.00.
Answer: $45.00
A small restaurant was purchased for 316000 with no down payment and a 6.6% loan for 10 year. Find the monthly payment
We will have the following:
First, we calculate the total payment per year:
[tex]p_y=316000\cdot0.066\Rightarrow p_y=20856[/tex]Now, we calculate the monthly payment:
[tex]316000=\frac{p}{0.0055}(1-\frac{1}{(1+0.066)^{120}})\Rightarrow1738=p(0.9995331951\ldots)[/tex][tex]\Rightarrow p=\frac{1738}{(1-\frac{1}{(1+0.066)^{120}})}\Rightarrow p=1738.811686[/tex]So, the monthly payment will be approximately $1738.811686.
The slope of the line is 2 and goes through the point (-8,6)
Given:
Slope m=2
The point,
[tex](x_1,y_1_{})=(-8,-6)[/tex]Using point-slope formula,
[tex]y-y_1=m(x-x_1)[/tex]Therefore, we get the equation,
[tex]y-(-6)=2(x-(-8)_{})[/tex]Determine whether the event below is mutually exclusive. Then find the probability. Round to the nearest tenth of a percent, if necessary. Rolling a pair of dice and doubles or a sum of 6 is rolled.Not mutually exclusive.
The given event is not mutually exclusive.
Remember that mutually exclusive events are those events that can't be both true, that is, if one event is true, then the other is false.
The probability of this event would be
[tex]P=\frac{6+5-1}{36}=\frac{10}{36}=\frac{5}{18}\approx0.28[/tex]Therefore, the probability is 0.28, or 28%, approximately.Please help!
1.) You are the crew chief of the Algebra 2 formula racing team. Your current task is to
determine fuel consumption of both cars. Car A travel x² + 3x miles and Car B travels 2x + 8 miles. Based upon tire wear (x), the cars will use x² + 4x gallons of fuel.
a.) What is the mileage
(miles/gallons) for each car?
Car A:
Car B:
b.) What is the total mileage for both cars in simplified form? (3 points)
Total:
2.)Solve for x: (5 points)
3r+3=−x+6
The mileage of Car A, Car B, and the average of is (x+3)/(x+4), 2/x and [tex]\frac{x^{2} +5x +8 }{x^{2} +4x}[/tex]
It is given that the distance traveled by the car A = x² + 3x
And the distance traveled by car B = 2x + 8
The mileage is given by mile/gallon.
So, the mileage of Car A = distance traveled by car A/gallons of fuel used.
Then,
Mileage of Car A = [tex]\frac{x^{2} +3x }{x^{2} +4x} =\frac{x(x +3)}{x(x+4)} = \frac{x+3}{x+4}[/tex] miles /gallons
Similarly, the mileage of Car B = distance traveled by car B/gallons of fuel used.
Then,
Mileage of Car B = [tex]\frac{2x+8}{x^{2} +4x} = \frac{2(x+4)}{x(x+4)} =\frac{2}{x}[/tex] miles/gallons
Now, the total mileage of A and B is the average of car A and car B,
Mileage of Car A + Mileage of Car B = [tex]\frac{x^{2} +3x }{x^{2} +4x} + \frac{2x+8}{x^{2} +4x} = \frac{x^{2} +5x +8 }{x^{2} +4x}[/tex]
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Simplify the following expression. Leave your answer in the form a^b.3^19/3^13= ___
Given the expression:
[tex]\frac{3^{19}}{3^{13}}[/tex]To simplify the expression, we will use the following rule of the exponents:
[tex]\frac{a^m}{a^n}=a^{m-n}[/tex]The answer will be:
[tex]\begin{gathered} \frac{3^{19}}{3^{13}}=3^{19-13}^{} \\ \\ =3^6 \end{gathered}[/tex]you will write the answer as 3^6
A U.S. dime has a diameter of about millimeters. What is the area of one side of a dime to the nearest square millimeter? Use as an approximation for .The area of one side of a U.S. dime is approximately blank square millimeters.The solution is
A US dime has a diameter of 18 millimeters. That makes the radius 9 millimeters, because
[tex]\begin{gathered} \text{radius}=\frac{\text{diameter}}{2} \\ \text{radius}=\frac{18}{2} \\ radius=9 \end{gathered}[/tex]The area of the dime (which is circular in shape) is given by the formula;
[tex]\begin{gathered} \text{Area of a circle} \\ A=\pi\times r^2 \\ r=9,\pi=3.14 \\ A=3.14\times9^2 \\ A=254.34mm^2 \end{gathered}[/tex]The area of one side of the dime is 254 square millimeters (approximated to the nearest square millimeter)
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The equation of the parabola in the vertex form with vertex (6,-6) and passing through (8,6) is y = 3(x - 6)² - 6 , the correct option is (b) .
In the question ,
it is given that ,
the parabola passes through the point (8,6) .
the vertex of the parabola = (6,-6) .
We know that the equation of parabola in the vertex form with vertex (h,k) is
(y - k) = C.(x - h)²
we substitute the vertex and the point passing ,
we get ,
6 - (-6) = C.(8 - 6)²
6 + 6 = C(2)²
12 = 4C
C = 12/4
C = 3
So , the equation is (y - (-6)) = 3.(x - 6)²
y + 6 = 3(x - 6)²
y = 3(x - 6)² - 6
Therefore , The equation of the parabola in the vertex form with vertex (6,-6) and passing through (8,6) is y = 3(x - 6)² - 6 , the correct option is (b) .
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how do I write 1 9/10 as dollars and cent
PLEASE HELP! I WILL GIVE BRAINLIEST The sales tax rate is 50%. How much will it cost to buy a $7.59 panther figureine? (Panther $7.59 plus tax) $11.95$0.57$12.52$11.39
The sale tax of the product will be:
0.5(7.59)=3.795
then the final price for the panther figurine (with taxes) will be:
7.59+3.795=$11.39
okay I think your name was Mrs Huggins can you please help me with the rest of this fraction I'm really struggling and I accidentally signed off because of a network error I'm really sad please
In a previous session we worked on the subtraction of the mixed numbers 2 1/8 and 1 7/8 and reached the following result:
[tex]2\frac{1}{8}-1\frac{7}{8}=\frac{17}{8}-\frac{15}{8}=\frac{2}{8}[/tex]This fraction 2/8 can be simplified. Both values 2 and 8 are divisible by 2, so to simplify the fraction you have to divide the numerator and denominator of the fraction by 2:
[tex]\frac{2\div2}{8\div2}=\frac{1}{4}[/tex]solve each inequality graph and check the solution (JUST NUMBER 8)
ANSWER
p ≤ -3
EXPLANATION
To solve this inequality first we have to subtract 5 from both sides:
[tex]\begin{gathered} 2-5\ge5-5+p \\ -3\ge p \end{gathered}[/tex]That's the solution, but we can flip it to see it more clearly:
[tex]p\le-3[/tex]To graph this, we have to draw a line from -3 to the left. Usually we have to draw a filled circle on -3, to indicate that that value is included in the solution.
Please help me help help me please help help me
When we are given a polynomial of the form:
[tex]ax^n+bx^{n-1}+cx^{n-2}+..+d^{}[/tex]Then the number that is multiplied by no variable or contains no variables is called the constant of the polynomial. In the above example, it would be "d".
Therefore, in the given polynomial we have:
[tex]3x^9+4x+129[/tex]Therefore, the constant of the polynomial is 129.
If the radius of circle M is 7, and LK = 18, find JK
Answer:
JK = 24
Explanation:
If the radius of circle M is 7, we can say that MJ = 7 and ML = 7
So, the length of MK will be equal to:
MK = ML + LK
MK = 7 + 18
MK = 25
Now, we have a right triangle JMK, and we know the length of one leg MJ = 7 and the length of the hypotenuse MK = 25. Using the Pythagorean theorem, we can find the length of the other side JK, so
[tex]\begin{gathered} JK=\sqrt[]{MK^2-MJ^2^{}} \\ JK=\sqrt[]{25^2-7^2} \\ JK=\sqrt[]{625-49} \\ JK=\sqrt[]{576} \\ JK=24 \end{gathered}[/tex]Therefore, the value of JK is 24.