7x - 2 = 2y 3x = 2y - 1
Solve the system of equations by substitution.
(3/4, 13/8), (1/4, -1/8), no solution, coincident
Answer:
7x - 2 = 2y
7x = 2y + 2
so
7x = 2y + 2
3x = 2y - 1
----------------subtract
4x = 3
x = 3/4
7x - 2 = 2y
7(3/4) - 2 = 2y
21/4 - 2 = 2y
21/4 - 8/4 = 2y
13/4 = 2y
so
y = 13/4 * 1/2
y = 13/8
answer
(3/4, 13/8)
Step-by-step explanation:
What two numbers multiply to 12 and add to negative 4?
The two numbers that multiply to 12 and add to negative 4 are -6 and 2.
To find the two numbers, we need to solve the system of equations:
1. xy = 12 (Equation 1)
2. x + y = -4 (Equation 2)
From Equation 2, we can express y in terms of x:
y = -4 - x (Equation 3)
Now, we substitute Equation 3 into Equation 1:
[tex]\( x(-4 - x) = 12 \)\\ \( -4x - x^2 = 12 \)\\ \( x^2 + 4x - 12 = 0 \)[/tex]
We can factor this quadratic equation:
[tex]\( (x + 6)(x - 2) = 0 \)[/tex]
Setting each factor equal to zero gives us two possible solutions for x:
[tex]\( x + 6 = 0 \) or \( x - 2 = 0 \)[/tex]
So, [tex]\( x = -6 \) or \( x = 2 \)[/tex].
Using Equation 3 to find the corresponding y values:
If ( x = -6 ), then ( y = -4 - (-6) = 2 ).
If ( x = 2 ), then ( y = -4 - 2 = -6 ).
Therefore, the two pairs of numbers that satisfy both conditions are (-6, 2) and (2, -6). Since the question asks for two numbers, and both pairs contain the same numbers, the answer is -6 and 2.
Molly walked four more miles than Tim. Together, they walked ten miles. How many miles did each walk? The replacement set is {1, 2, 3, 4}.
a. Define the variable, and write expressions for the number of miles each person walked.
b. Write an equation that represents the problem.
c. Solve the equation. (Be sure to try every element in the replacement set and to show all of your work.)
d. Answer the question. (Remember, answers to word problems have units.)
A) Variable = x ( miles Tim walked )
B) Tim walked X miles, Molly walked 4+x miles ( 4 more than Tim)
Equation: x + x+4 = 10
C) x +x+4 = 10
2x+4 = 10
2x =6
x = 3
D)
Tim walked 3 miles, Molly walked 7 miles
The sum of twice a first number and five times a second number is 78. If the second number is subtracted from five times the first number the result is 33. Find the numbers.
The leg of a right triangle is 3 units and the hypotenuse is 7 units. What is the length, in units, of the other leg of the triangle?
4
Square root of 40
Square root of 58
10
Answer:
square root of 40
Step-by-step explanation:
a^(2)+b^(2)=c^(2)
3^(2)+b^(2)=7^(2)
9+b^(2)=49
9-9+b^(2)=49-9
b^(2)=40
sqr b^(2)=sqr 40
b=6.32455532034
therefore,the square root of 40 is the answer
I need the steps to this, please. It says solve for x. Each figure is a parallelogram. Show your work.
in how many ways can jasmine draw a blue or yellow marble from the jar containing 28 blue marbles and 7 yellow marbles
Bob has some 10 lb weights and some 3 lb weights. Together, all his weights add up to 50 lbs. If x represents the number of 3 lb weights and y represents the number of 10 lb weights, which equation can be used to find the number of each type of weight Bob has?
3x - 7 = 14 implies that 3x = 21
What is the slope intercept form of 6x + 2y = 24?
What is vertex on a graph
Plot the inequality on the number line.
−7≤x≤−2
Choose the proper tool with the correct endpoints then click and drag the endpoints to the correct location.
Notice the trash can is available if an error is made.
Plot the inequality on the number line. the graph is attached below.
Use the tool that has solid dots at both ends
Explanation :
Plot the inequality on the number line.
−7≤x≤−2
We start plotting the point at -7. we use closed circle at -7 because we have less than or equal to sign at -7
Now we plot another point at -2. here also we use closed circle that is solid circle .
Now shaded the region between -7 and -2 because x lies between -7 and -2
The graph of number line is attached below
The tool uses here is a line with solid dot at both ends
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The rule (x,y)→(2x,2y) maps △DEF to △D′E′F′.
Which statement correctly describes the relationship between △DEF and △D′E′F′ ?
The triangles are not congruent because △D′E′F′ is a translation of △DEF , and a translation is not a rigid motion.
The triangles are congruent because △D′E′F′ is a rotation of △DEF , and a rotation is a rigid motion.
The triangles are not congruent because △D′E′F′ is a dilation of △DEF , and a dilation is not a rigid motion.
The triangles are congruent because △D′E′F′ is a reflection of △DEF , and a reflection is a rigid motion.
Answer:
The triangles are not congruent because △D′E′F′ is a dilation of △DEF , and a dilation is not a rigid motion.
Step-by-step explanation:
The rule we have is (x, y)→(2x, 2y). This means that each x-coordinate and each y-coordinate are multiplied by 2. This is a dilation by a factor of 2.
This will stretch the image by a factor of 2; this means the sides will be twice as long. This means they will not be congruent.
Answer: The triangles are not congruent because △D′E′F′ is a dilation of △DEF .
Step-by-step explanation:
Rigid motions form congruent figures, the common rigid motions are:
1) translation (moves figure about some distance)
2) reflection (creates mirror image)
3) rotation (rotate figure about some degrees)
Dilation : It does not create congruent images. It creates an image that is the exactly same shape as the original, but have a different size with the help of a scale factor k .
Given : The rule (x,y)→(2x,2y) maps △DEF to △D′E′F′.
Here the coordinates of the image are increased by using a scale factor 2.
So △D′E′F′ must be an enlargement of △DEF.
⇒△D′E′F′ is a dilation of △DEF
It means : The triangles are not congruent because △D′E′F′ is a dilation of △DEF , and a dilation is not a rigid motion.
An item is regularly priced at $40. she bought it at a discount of 35% off the regular price. How much did she pay?
If m<3 is five times the measure of its supplement (<4), then determine the measure of each angle.
explain how you can solve 40 × 16 by breaking apart the numbers.
what are the steps for using a compass and a straightedge to construct a line perpendicular to a given line through a point not lying on the given line?
Answer:
As mention in the explanation steps.
Step-by-step explanation:
Te following steps may be helpful for using a compass and a straightedge to construct a line perpendicular to a given line through a point not lying on the given line (as shown in the figure).
Step - 1. Draw a line (line AB)
Step- 2. Take a point (point P), that do not lie on the line AB.
Step - 3. Assume point p as a center an draw as arc which intersect the line AB at two point (point C and point D).
Step - 4. Now draw a line XY that is the perpendicular bisector of line segment CD. This recurred line XY is the line perpendicular to a given line (line AB) through a point not lying on the given line.
The formula k=c+273.15k=c+273.15 converts temperatures from celsius cc to kelvin kk.
a. solve the formula for cc. c=c=
b. convert 300 kelvin to celsius. write your answer using decimals. 300k=300k= ∘c
a. We are given that the formula for Celsius (c) to Kelvin (k) is:
k = c + 273.15
Now to solve for the formula for c, simply subtract 273.15 from both sides, so that:
k – 273.15 = c + 273.15 – 273.15
k – 273.15 = c
Rearranging:
c = k – 273.15
b. We are given that k = 300 Kelvin, therefore find for c:
c = k – 273.15
c = 300 – 273.15
c = 26.85°C
The formula to convert temperature from Kelvin to Celsius is c = k - 273.15. When you use this formula to convert 300 Kelvin to Celsius, the answer is 26.85°C.
Explanation:The formula k = c + 273.15 is used to convert temperatures from Celsius to Kelvin. To solve for 'c' (Celsius), you would subtract 273.15 from both sides of the equation which gives c = k - 273.15.
If you have a temperature of 300 Kelvin and you want to convert this to Celsius using the formula c = k - 273.15, you would substitute 300 in place of k. This gives: c = 300 - 273.15, which equals 26.85°C.
Learn more about Temperature Conversion here:https://brainly.com/question/30451535
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Five times the sum of a number (x) and three is equal to the sum of that number (x) and fifteen.
I just need to know how to put this from Word-Form into Number form and solve for the
x. Please help.
What angle measures larger than 180 degrees, but less than 360 degrees?
Answer:
reflex
Step-by-step explanation:
Prove or disprove: if p and q are prime numbers then pq - 2 is also a prime number.
Counterexample:
[tex] p=2\\
q=3\\\\
pq-2=2\cdot3-2=4 [/tex]
4 is not a prime number. So, it's false.
Factor this expression completely.
ab + 4 + a + 4b
Is it possible for a line ax+by=c to lack a y-intercept? To lack an x-intercept
Can someone help me write an equation for this problem?
Felicity put down $800 on a used car. She took out a loan to pay off the balance of the cost of the car. Her monthly payment will be $175. After 9 months how much will she have paid for the car?
which of the following statement are false? o vertical angles are congruent. o angles with measures between 0 and 90 are complementary. o straight angles are supplementary. o angles with measures between 90 and 180 are obtuse
Suppose FLX =ZAQ Which other congruency statements are correct
As a salesperson, you are paid $100 per week plus $3 per sale. This week you want your pay to be at least $160. Write an inequality for the number of sales you need to make, and describe the solutions. A) 100 - 3s ≤ 160; s ≤ 20 B) 100 + 3s ≥ 160; s ≥ 18 C) 100 - 3s ≤ 160; s ≤ 18 D) 100 + 3s ≥ 160; s ≥ 20
Answer:
The answer is D. Hope it helps!
Allen's boat used 6 gallons of gas in 5 hours. at this rate, how many gallons of gas will the boat use in 12 hours?
How do you find the amount of nuetrons in an atom?
which angle is included angle forJL and KL