Solve the system by the elimination method.
x + y - 6 = 0
x - y - 8 = 0
When you eliminate y , what is the resulting equation?
2x = -14
2x = 14
-2x = 14
Answers
Answer: The answer is b, 2x=14
Step-by-step explanation:
You add the equations...
2x-14=0
Move -14 over...
2x=14
Answer: The correct option is
(B) 2x = 14.
Step-by-step explanation: We are given to solve the following system of equations by the method of Elimination :
[tex]x+y-6=0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\x-y-8=0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]
Also, to select the resulting equation when we eliminate y.
Adding equations (i) and (ii), we get
[tex](x+y-6)+(x-y-8)=0+0\\\\\Rightarrow 2x-14=0\\\\\Rightarrow 2x=14~~~~~~~~~~[\textup{this is the resulting equation}]\\\\\Rightarrow x=\dfrac{14}{2}\\\\\Rightarrow x=7.[/tex]
From equation (i), we get
[tex]7+y-8=0\\\\\Rightarrow y-1=0\\\\\Rightarrow y=1.[/tex]
Thus, the required solution is (x, y) = (-1, 7) and the resulting equation while eliminating y is 2x = 14.
Option (B) is CORRECT.
Related Questions
Which value of x is a solution of the inequality?
4x+7≥35
x = 6
x = 7
x = 3
x = 0
Answers
Answer:
x = 7
Step-by-step explanation:
Just try all the choices and see which one gives a valid answer
4x+7≥35
x = 6 : 4 (6) + 7 = 31 is NOT ≥35 (not valid)
x = 7 : 4 (7) + 7 = 35 IS ≥35 (valid) (ANSWER)
x = 3 : 4 (3) + 7 = 19 is NOT ≥35 (not valid)
x = 0 : 4 (0) + 7 = 7 is NOT ≥35 (not valid)
Answer:
x = 7
Step-by-step explanation:
Just try all the choices and see which one gives a valid answer
4x+7≥35
x = 6 : 4 (6) + 7 = 31 is NOT ≥35 (not valid)
x = 7 : 4 (7) + 7 = 35 IS ≥35 (valid) (ANSWER)
x = 3 : 4 (3) + 7 = 19 is NOT ≥35 (not valid)
x = 0 : 4 (0) + 7 = 7 is NOT ≥35 (not valid)
in everyday English, interpret the financial meaning of the
y-intercept in the equation y=0.10x+9.50
Answers
Final answer:
The y-intercept in the equation y=0.10x+9.50 represents an initial financial value of $9.50, such as a fixed charge or baseline cost, before any variable amounts are factored in.
Explanation:
In everyday English, the financial meaning of the y-intercept in the equation y=0.10x+9.50 refers to the initial amount or fixed cost that does not depend on the quantity represented by x. In other words, when x, which might represent the quantity of goods sold or the number of hours worked, is zero, the y-intercept indicates a starting value of $9.50. This could be a baseline charge, a fixed fee, or some kind of initial cost before any additional variables are added to the equation.
Factor the polynomial expression x6 – x3 – 20
Answers
Answer:
x6 − x3 − 20 = (x3)2 − x3 − 20 = (x3 + 4)(x3 − 5)
Step-by-step explanation:
In this trinomial, the exponent of the first term, 6, is double the exponent in the second term, 3. And, the third term contains no variables. So, we can factor the expression as we would a quadratic, but treating x3 as if it were x:
Answer:
(x³ - 5)(x³ + 4)
Step-by-step explanation:
Consider the factors of the constant term (- 20) which sum to give the coefficient of the x³ term (- 1)
The factors are - 5 and + 4, since
- 5 × 4 = - 20 and - 5 + 4 = - 1, hence
[tex]x^{6}[/tex] - x³ - 20 = (x³ - 5)(x³ + 4)
What are the points for f(x)=3^(x-1)-2
Answers
Answer: (0, -1 [tex]\frac{2}{3}[/tex]), (1, -1), (2, 1)
Step-by-step explanation:
Set the exponent equal to zero - that is your anchor point.
Then choose an x-value less than and greater than the anchor point.
[tex]\left\begin{array}{c|c|l}&\underline{\quad x\quad }&\underline{\qquad \qquad f(x)\qquad \qquad \qquad \quad }\\\text{less than anchor}&0&3^{0-1}-2=3^{-1}-2=\frac{1}{3}-2 = -1\frac{2}{3}}\\\\anchor\ point&1&3^{1-1}-2=3^{0}-2=1-2 = -1}\\\\\text{greater than anchor}&2&3^{2-1}-2=3^{1}-2=3-2 = 1}\end{array}\right[/tex]
Mateo is constructing an equilateral triangle inscribed in a circle with Center p . he draws the diameter of the circle through centerpiece using the Straight Edge next he opend his compass to a width equivalent to the radius of the circle what is his next step
Answers
Answer:
Step-by-step explanation:
Next he marks the circumference of the circle with 6 equal marks that also equal the radius.
He numbers the points consecutively.
He joins points 2 4 6 2 or 1 3 5 1 (The last point gets him back to where he started.
That's his equilateral triangle using just a straight edge and compass.
What is -a^-2 if a = -5? (PLEASE HELP WILL MARK BRAINLIEST!!!)
Answers
Answer:
-1/25
Step-by-step explanation:
-a^-2
-(-5)^-2
=-1/25
Find the x-intercepts of the parabola with
vertex (-3,-14) and y-intercept (0,13).
Write your answer in this form: (x1,y1),(X2,y2).
If necessary, round to the nearest hundredth.
Answers
Answer:
(-0.84, 0) and (-5.16, 0).
Step-by-step explanation:
Help me I need to pass so I can go on to the next thing plz someone help me
Answers
Answer:
i cant see the picture
Step-by-step explanation:
Answer:
5
Step-by-step explanation:
The scale factor is the ratio of the corresponding sides of the image to the original, that is
scale factor = [tex]\frac{CA'}{CA}[/tex] = [tex]\frac{4+16}{4}[/tex] = [tex]\frac{20}{4}[/tex] = 5
Square T was translated by the rule (x + 2, y + 2) and then dilated from the origin by a scale factor of 3 to create square T″. Which statement explains why the squares are similar?
A. Translations and dilations preserve side length; therefore, the corresponding sides of squares T and T″ are congruent.
B. Translations and dilations preserve orientation; therefore, the corresponding angles of squares T and T″ are congruent.
C. Translations and dilations preserve betweenness of points; therefore, the corresponding sides of squares T and T″ are proportional.
D. Translations and dilations preserve collinearity; therefore, the corresponding angles of squares T and T″ are congruent.
Answers
Answer: OPTION C.
Step-by-step explanation:
It is important to know the following:
Dilation:
Transformation in which the image has the same shape as the pre-image, but the size changes. Dilation preserves betweenness of points. Angle measures do not change.
Translation:
Transformation in which the image is the same size and shape as the pre-image. Translation preserves betweenness of points. Angle measures do not change.Therefore, since the Square T was translated and then dilated to create Square T'', we can conclude that the statement that explains why they are similar is:
Translations and dilations preserve betweenness of points; therefore, the corresponding sides of squares T and T″ are proportional.
Answer:
C. Translations and dilations preserve betweenness of points; therefore, the corresponding sides of squares T and T″ are proportional.
Step-by-step explanation:
Use the property of exponents to rewrite the expression
(-4qr)(-4qr)(-4qr)(-4qr)
Answers
Answer:
(-4qr)^4
Step-by-step explanation:
(-4qr)(-4qr)(-4qr)(-4qr)
There are 4 sets of -4qr being multiplied together
(-4qr)^4
Substitute t=3 and t=5 to determine if the two expressions are equivalent. 4(t+3) 4t+12 Which statements are true? Check all that apply. The value of both expressions when t=3 is 32. The two expressions are not equivalent. The value of both expressions when t=5 is 15. The value of both expressions when t=5 is 23. The two expressions are equivalent. The value of both expressions when t=3 is 24.
Answers
Answer:
Answers are:
The value of both expressions when t=3 is 32.
The the value of both expressions when t=3 is 24.
The two expressions are equivalent.
Step-by-step explanation:
These answers are 100% correct. I just finished my quiz. I hope this helps
Please mark me brainlyest :)
The correct statements are that, both the equations are equivalent when the value of t is taken 3 and The value of both the equations is 24 when t is taken as 3.
So, the correct options that match the statement above are E and F.
Simplification of expressions. Taking the value of t as 3 in both the equations, we get,[tex]4(t+3)\\\\4(3+3)\\\\\\4\ \rm x\ 6=24[/tex]Now, in the second expression, [tex]4t+12\\\\4\ \rm x\ 3+12\\\\12+12=24[/tex] Whereas, when the value of t is taken as 5 the values obtained are as 23 and 32 respectively.Hence, the correct options are E and F that the equations are of both the values when t is 3 is obtained as 24. And both the expressions are equivalent when t is taken as 3.
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The equation y2/100+x2/4 =1 represents an ellipse. Which points are the vertices of the ellipse? (−10, 0) and (10, 0) (−2, 0) and (2, 0) (0, −10) and (0, 10) (0, −2) and (0, 2)
Answers
The vertices of the ellipse (10, 0), (-10, 0), (0, 10), and (0, -10) can be determined using the center and major axes of the ellipse.
Explanation:The vertices of the ellipse are at (10, 0), (-10, 0), (0, 10), and (0, -10). To find the vertices of an ellipse, you use the major and minor axes that pass through the center of the ellipse. In this case, the center is (4.619, 5.425), and the major axes are inclined at an angle of 128° 51' to the x-axis.
What is the measure of angle D?
52o
54o
57o
126o
Answers
A trapezoid has a total of 360 degrees, so when you add up the degrees we are given we end up with 308 degrees. If you add 52 degrees you get 360.
For a given trapezium ABCD, measure of angle [tex]D = 52\°[/tex].
What is an angle?" An angle is defined as when two rays meet at a common point known as vertex."
According to the question,
Given trapezium ABCD,
Measure of angle [tex]BAD= 128\°[/tex]
Measure of angle [tex]ABC= 126\°[/tex]
Measure of angle [tex]BCD= 54\°[/tex]
Sum of all the interior angles in a trapezium is equal to [tex]360\°[/tex].
Therefore,
[tex]\angle ABC + \angle BCD +\angle CDA + \angle DAB = 360\°\\\\\implies 126\°+54\°+ \angle CDA + 128\°=360\°\\\\\implies \angle CDA = 360\° - 308\°\\\\\implies \angle CDA = 52\°[/tex]
Hence, Option (A) is the correct answer.
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7. If the value of x varies directly with the value of y, and x = 3 when y = 21. What is the valu
y, and x = 3 when y = 21. What is the value of x when y =
105?
Answers
Answer:
15
Step-by-step explanation:
Because x=y÷7
i.e,105÷7=15
When x = 3 , y= 21
3/21 = x/105
What number times 21 is equal to 105?
21* 5 = 105
So 3* 5 = 15
When x= 15, y= 105
Hope this helps!
Help ASAP please! Thanks in advance.
In which set are ALL of the numbers solutions to the inequality x < -3?
Answers
Step-by-step explanation:
The second one, of course. Because the inequality means that x must be smaller than -3. So in negative numbers, numbers are getting smaller when they go far from 0. So [tex]-8\frac{2}{3},-6,-4, -3,5[/tex] are smaller than -3 because the distance between 0 and these numbers are more than he distance between zero and -3. Good luck :)
Find measure of angle A
Round to the nearest degree
Answers
To solve this question, we must use the cosine rule:
cos(A) = (b^2 + c^2 - a^2)/2bc, where A is the angle you want to find, a is the side opposite that angle, and b and c are the other two sides of the triangle.
Given that we know that a = 6, b = 12, c = 14, we can substitute these values into the formula to get:
cos(A) = (12^2 + 14^2 - 6^2)/2(12)(14)
cos(A) = (144 + 196 - 36)/336
cos(A) = 304/336
cos(A) = 19/21
A = cos-1(19/21)
A = 25° (to the nearest degree)
Two cylinders with different radii have the same
volume.
Which statement is true?
A.
The bases of the two cylinders must have the
same areas.
B.
The cylinder with the smaller radius must be
taller.
C.
The cylinder with the larger radius must be
taller.
D.
The heights of the two cylinders must be
equal.
Answers
Which of the following is the equation for a circle with a radius of rand center
at (h, v)?
Answers
Answer:
[tex]\large\boxed{(x-h)^2+(y-v)^2=r^2-\bold{Standard\ form}}\\\boxed{x^2+y^2-2hx-2vy+h^2+v^2-r^2=0-\bold{General\ form}}[/tex]
Step-by-step explanation:
[tex](x-h)^2+(y-v)^2=r^2\qquad\text{use}\ (a-b)^2=a^2-2ab+b^2\\\\x^2-2hx+h^2+y^2-2vy+v^2=r^2\qquad\text{subtract}\ r^2\ \text{from both sides}\\\\x^2+y^2-2hx-2vy+h^2+v^2-r^2=0[/tex]
There are 6 cupcakes shared equally between 10 people. What fraction of a cupcake does each person receive?
A- six tenths cupcake
B- one tenth cupcake
C- ten sixths cupcake
D- one sixth cupcake
Answers
Answer:
six tenths cupcake
Step-by-step explanation:
6/1 ÷ 10/1
6/1 × 1/10 = 6/10
The fraction of a cupcake does each person receive will be [tex]\frac{6}{10}[/tex] i.e. option A, i.e. six tenths of cupcake.
What is fraction?The fraction is numerical representation of the numbers in the form of numerator and denominator.
We have,
Total cupcakes = 6
Total people = 10
So,
To get equal share of the cupcake divide it by total number of people,
i.e.
Equal share [tex]=\frac{Total\ cupcake}{Total\ people}[/tex]
So,
Equal share for 10 people [tex]=\frac{6}{10}[/tex]
So,
Everyone gets six tenths of cupcake.
Hence, we can say that the fraction of a cupcake does each person receive will be [tex]\frac{6}{10}[/tex] i.e. option A, i.e. six tenths of cupcake.
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Please please help me
Answers
Answer:
multiply 2/5 by 4
Step-by-step explanation:
When we divide fractions, we use copy dot flip
2/5 ÷ 1/4
Copy dot flip
2/5 * 4/1
For this case we must find the quotient of the following expression:
[tex]\frac {\frac {2} {5}} {\frac {1} {4}} =[/tex]
Applying double C we have:
[tex]\frac {2 * 4} {5 * 1} = \frac {8} {5}[/tex]
This is equivalent to multiplying the following: [tex]\frac {2} {5} * 4 = \frac {8} {5}[/tex]
Answer:
OPTION A
prove that (x-2)is factor of p (x)=2x³-3x²-17x+30
Answers
Answer:
P(2)=0 then x-2 is a factor of P(x)
Step-by-step explanation:
To see if (x-2) is a factor just plug in 2 for x into the polynomial expression.
2(2)^3-3(2)^2-17(2)+30
2(8)-3(4)-34+30
16-12-34+30
4-34+30
-30+30
0
Since P(2)=0 then x-2 is a factor
eh best describes the range of the function
Which best describes the range of the function f(x)=2(1/4)x
after it has been reflected over the y-axis?
Answers
Answer:
(0,∞)
Step-by-step explanation:
The problems tells us to find the range of the function
f(x)=2*(1/4)^x
after it has been reflected over the y-axis
This means
g(x) = 2*(1/4)^(-x)
To quickly find the answer, we can plot the equation and examine the range in the graph.
The range of both functions is the same
(0,∞)
See attached picture
A pair of shoes coats $25 to make. This means that you need to charge a price of atleast __ just to cover you Options : A:$25 B:$10 C:$50
Answers
Answer:
25
Step-by-step explanation:
Because they cost $25 to make so in order to cover the cost they would need to charge at least 25, but out of those choices if they wanted to make a profit they'd need to charge the $50
Solve: In 2x + In 2 =0
Answers
Answer:
x = [tex]\frac{1}{4}[/tex]
Step-by-step explanation:
Using the rules of logarithms
• log x + log y ⇔ log(xy)
• [tex]log_{b}[/tex] = n ⇔ x = [tex]b^{n}[/tex]
Given
ln 2x + ln 2 = 0
ln(2x × 2) = 0
ln 4x = 0
4x = [tex]e^{0}[/tex] = 1 ( divide both sides by 4 )
x = [tex]\frac{1}{4}[/tex]
A hockey goalie blocks 75% of shots at the goal. How many shots can the goalie predict she or he will block in 75 tries
Answers
Answer:
56
Step-by-step explanation:
75% of 75 tries = 0.75×75 = 56.25
Rounding, he can expect to block 56 shots.
Helaine graphed the equation 12x - 4y = 3. What was the slope of Helaine's line?
The slope of the graph is
Answers
Answer:
The slope of this line is 3.
Step-by-step explanation:
Solve 12x - 4y = 3 for y to obtain the equation in slope-intercept form:
Add 4y to both sides, obtaining 12x = 3 + 4y
Subtract 3 from both sides: 12x - 3 = 4y
Finally, divide all terms by 4: y = 3x - 3/4
The slope of this line is 3.
Answer: The slope of the graph is 3.
Step-by-step explanation:
The equation of a line in slope intercept for is given by :-
[tex]y=mx+c[/tex], where m is the slope of the line.
The given equation of the line graphed by Helaine = [tex]12x - 4y = 3[/tex]
Now, rewrite the above equation in slope-intercept form by adding 4y and subtracting 3 from both sides , we get
[tex]4y=12x-3[/tex]
Divide 4 on both sides , we get
[tex]y=3x-\dfrac{3}{4}[/tex] which is the slope-intercept form.
[tex]\Rightarrow\text{Slope}=3[/tex]
Hence, the slope of Helaine's line =3
A triangle ABC has two side lengths of 28 ft. and 24 ft. If angle C is 91°, what's the measurement of angle B?
Answers
Answer:
B = 58.9
Step-by-step explanation:
We are given that a triangle ABC has two side lengths of 28 ft. and 24 ft. with angle C measuring 91°. We are to find the measure of angle B.
AB = 28 ft
AC = 24 ft
For this, we will use the sine formula:
[tex]\frac{sin B}{24} = \frac{sin91}{28}[/tex]
[tex]sin B = \frac{sin91 \times 24}{28}[/tex]
[tex] sin B = 0 . 8 5 7 [/tex]
[tex] B = sin' 0 . 8 5 7 [/tex]
B = 58.9
What’s 0.85 in simplest form
Answers
Answer:
17/20
Step-by-step explanation:
To find the simplest form of 0.85 you need to turn it into a fraction.
To turn it into a fraction you put 85 over 100 since 0.85 is in the hundredths place.
85/100 can be simplified to 17/20 because 85/5 is 17 and 100/5 is 20
Answer:
17/20
Step-by-step explanation:
The simplest form of a number is a fraction. .85 as a fraction is 85/100. Simplifying this into 17/20 puts it into its simplest form.
please help i don know how to do this
thanks
Answers
Answer
The answer to this question is not one of your answer choices, but the answer is 240.1413932 square centimeters.
Step-by-step explanation:
A=πr(r+√h² + r²) [radical wrapped around h² + r²]
What is the solution to this Logarithmic Equation?
(Those are L's infront of the N)
ln x + ln x = 0
Answers
Answer:
x = 1
Step-by-step explanation:
ln x + ln x = 0
2ln x = 0
ln x = 0
recall ln x = [tex]log_{e}[/tex]x
so equation becomes
[tex]log_{e}[/tex]x = 0
or [tex]e^{0}[/tex]=x
since anything raised to the power of zero = 1
x = 1
Answer:
x = 1
Step-by-step explanation:
We are to find the solution of the following logarithmic equation:
[tex] ln ( x ) + l n ( x ) = 0 [/tex]
We will add the similar elements to get:
[tex] 2 l n ( x ) = 0 [/tex]
Dividing both sides by 2 and simplify to get:
[tex] \frac { 2 l n ( x ) } { 2 } = \frac { 0 } { 2 } [/tex]
[tex]ln(x)=0[/tex]
Applying the rule [tex]a=log_b(b^a)[/tex] to get:
[tex]0=ln(e^0)=ln(1)[/tex]
[tex]ln(x)=ln(1)[/tex]
Here the logs have the same base, so:
x = 1