Final answer:
To solve the system of equations, use the method of substitution. Solve one equation for one variable and substitute the value in the other equation. Simplify and solve for the variable, then find the value of the other variable. The solution to the system is x = 7 and y = 2.
Explanation:
To determine the solution to the system of equations, we can use the method of substitution or elimination. Let's use the method of substitution.
Step 1: Solve one equation for one variable
From the first equation, we can isolate x: x = 1 + 3y
Step 2: Substitute the value of the variable in the other equation
Substitute x = 1 + 3y into the second equation: 3(1 + 3y) - 5y = 11
Step 3: Simplify and solve for y
Expand the equation and simplify: 3 + 9y - 5y = 11
Combine like terms: 9y - 5y = 11 - 3
Simplify: 4y = 8
Solve for y: y = 2
Step 4: Find the value of the other variable
Substitute the value of y into the first equation: x - 3(2) = 1
Simplify and solve for x: x - 6 = 1
x = 7
Therefore, the solution to the system of equations is x = 7 and y = 2.
The price of an item has been reduced by 70%. The original price was $31. What is the price of the item now?
Answer:
$9.3 dollars.
Step-by-step explanation:
To solve this question, you will need to begin by finding the percentage left of the original value:
100%-70%= 30% left.
Now, to find the exact value of the discounted item, you will solve for 30% (0.3) of $31:
0.3×31= $9.3 dollars.
The length of a rectangle is 7 inches longer than its width. If the area of the
rectangle is 144 square inches, what are the dimensions?
The dimensions of the rectangle are 9 inches (width) and 16 inches (length) as obtained from solving the quadratic equation derived from the facts provided.
Explanation:To solve this problem, let's denote the width of the rectangle as x in inches. Since we know that the length of the rectangle is 7 inches longer than its width, we can write it as x + 7 inches. The area of a rectangle is calculated by multiplying its length by its width. Here, it's given as 144 square inches.
Setting up the equation for the area, we get x(x + 7) = 144.
Solving this quadratic equation, we find that x = 9. As a result, the width is 9 inches and the length, being 7 inches longer, is 16 inches. Therefore, the dimensions of the rectangle are 9 inches by 16 inches.
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Brianna’s teacher asks her which of these three expressions are equivalent to each other.
Expression A:
9
x
−
3
x
−
4
Expression B:
12
x
−
4
Expression C:
5
x
+
x
−
4
Brianna says that all three expressions are equivalent because the value of each one is
−
4
when
x
=
0
.
Brianna’s thinking is incorrect.
Answer:
Expression A and C are correct because 9x - 3x = 6x and 5x + x = 6x, then -4
After simplification, Expression A (6x - 4) and Expression C (6x - 4) are equivalent to each other, but Expression B (12x - 4) is not equivalent to the other two.
The student's teacher presented a problem to determine the equivalence of three algebraic expressions: Expression A (9x - 3x - 4), Expression B (12x - 4), and Expression C (5x + x - 4).
Brianna incorrectly states that all three expressions are equivalent simply because they all evaluate to -4 when x = 0. However, this is a misinterpretation, as equivalence between algebraic expressions means that they yield the same result for all values of x, not just a single value.
To correct this, we simplify each expression:
Expression A: 9x - 3x - 4 simplifies to 6x - 4.
Expression B: 12x - 4 remains the same.
Expression C: 5x + x - 4 simplifies to 6x - 4.
After simplification, we see that Expression A is equivalent to Expression C, both simplifying to 6x - 4. However, Expression B remains different, with the term 12x - 4.a
11. The measure of an angle formed by two tangents to a circle is 90. If the radius of the circle
is 8 centimeters, how far is the vertex of the angle from the center of the circle?
Vertex of the angle is 11.31 cm far from the center of the circle.
Given in the question,
Measure of angle formed by two tangents of the circle (∠PVQ) = 90°Measure of the radius (OP)= 8 cmIn ΔOPV and ΔOQV,
OP ≅ OQ (Radii of the circle)
PV ≅ QV (Tangents from a point outside the circle)
OV ≅ OV (Reflexive property)
ΔOPV ≅ ΔOQV (SSS property of congruence)
Therefore, m∠PVO = m∠QVO = 45°
By triangle sum theorem,
m∠POV + m∠PVO + m∠OPV = 180°
m∠POV + 45° + 90° = 180°
m∠POV = 45°
Hence, ΔOPV is an isosceles triangle.
OP = PV = 8 cm
By applying Pythagoras theorem in ΔOPV.
OV² = OP² + PV²
OV² = 8² + 8²
OV = √128
OV = 11.31 cm
Therefore, vertex V is 11.31 cm from the center of the circle.
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The distance from the vertex of the angle to the center of the circle is 0 centimeters.
Explanation:In this problem, we have two tangents to a circle, and we are given that the angle between them is 90 degrees. We need to find the distance from the vertex of the angle to the center of the circle.
Since the angle between the tangents is 90 degrees, the tangents are perpendicular to each other. This means that the vertex of the angle is located on the circumference of the circle, and it forms a right triangle with the center of the circle and one of the points where the tangents intersect the circle.
Using the Pythagorean theorem, we can find the distance from the vertex to the center of the circle. Let's call this distance x. We know that the radius of the circle is 8 centimeters, so one leg of the right triangle is 8 centimeters. The other leg is x centimeters, and the hypotenuse is the radius of the circle plus x centimeters.
Applying the Pythagorean theorem, we have:
x^2 + 8^2 = (8 + x)^2
Simplifying the equation, we get:
x^2 + 64 = 64 + 16x + x^2
Cancelling out x^2 terms, we have:
64 = 64 + 16x
Subtracting 64 from both sides, we get:
0 = 16x
Dividing both sides by 16, we get:
x = 0
Since we cannot have a distance of 0, the equation does not have a solution. This means that the vertex of the angle is located at the center of the circle, and the distance is 0 centimeters.
HELP ASAP GIVING BRAINLIST AND A LOT OF POINTS!!!!!
Tara starts with $20, in which she buys 2 items for d amount. Subtract 2d from the total for your answer.
1) 20 - 2d
To find the average distance, add all the numbers together, and divide by the amount of numbers there are:
3) (t + w)/2
~
13 out of 19 students said they were attending the football game. About how many students out of 500 would you expect to attend the football game? *
1 point
13
730
342
19
Step-by-step explanation:
The answer is 342
Because when we divide 19 by 13 = 1.46
Then when we divide 500 by 1.46 = 342
A golfer is standing on a tee with a green in a valley below. If the tee is 43 yards higher
than the green and the direct distance from the green to the hole is 177 yards, find the
angle of depression from the tee to the green.
Answer:
[tex]13.65^0.[/tex]
Step-by-step explanation:
Given,
Height of tee, H = 43 yard
Direct distance of the hole is, D = 177 yards
Now, Angle of depression of tee
[tex]\tan \theta = \dfrac{H}{D}[/tex]
[tex]\tan \theta = \dfrac{43}{177}[/tex]
[tex]\tan \theta =0.2429[/tex]
[tex]\theta = 13.65^\circ[/tex]
Hence, angle of depression from tee to the green is [tex]13.65^0.[/tex]
8y - 1-/2 ( 4y - 16)
Answer:
6y +8
Step-by-step explanation:
8y - 1-/2 ( 4y - 16)
Distribute
8y - 1/2*4y - 1/2 *-16
8y -2y +8
Combine like terms
6y +8
What is the name of this polygon?
A. rectangle
B. square
C. trapezoid
D. rhombus
Answer:
That is a rhombus.
Brainliest is greatly appreciated
Answered by: Skylar
5/20/2020
1:37 PM (Eastern Time)
Answer:
This is a rhombus because it has 4 verticles, 4 edges and 2 lines of symmetry.
I know I'm late but hope this helps!!
What is the power of 1^5
Answer:
1x1x1x1x1
Step-by-step explanation:
1^5 is the same as 1x1x1x1x1 because a power multiplies a number by itself
Answer:
1x1x1x1x1
Step-by-step explanation:
1^5 = 1x1x1x1x1 = 1
(happy to help!!!)
can u help me please
Answer:
C
Step-by-step explanation:
8x^2 - 8x + 2
=2(4x^2 - 4x + 1)
=2(2x - 1)^2
Evaluate the following
expression if x = 6.
3x
Answer:
3x would equal 18 is x was 6
Step-by-step explanation:
x=6
3*6=18
3x would equal 18
Two ice skaters push against each other. The skater on the left has a mass of 70.0 kg and the skater on the right has a mass of 90.0 kg. If the skater on the left experiences a force of 250 N, how many Newtons of force is experienced by the skater on the right?
Answer:250 N
Step-by-step explanation:
Given
mass of skater on left side [tex]m_l=70\ kg[/tex]
mass of skater on right side [tex]m_r=90\ kg[/tex]
If the skater on the left experience a force of [tex]250\ N[/tex]
If they push against each other then they must experience an equal force according to newtons third law
Thus [tex]F_l=F_r[/tex]
Thus skater on right experience [tex]250\ N[/tex] force
Using Newton's third law, if the first skater pushes off with a force of 250 N, the second skater will experience an equal but opposite force of 250 N. This occurs irrespective of the skaters' masses.
Explanation:The subject of this question is physics, specifically Newton's third law of motion, which states that for every action, there is an equal and opposite reaction. In this case, the action is the first skater pushing off the second skater, and the reaction is the force experienced by the second skater.
The amount of force experienced by the first skater is 250 N. Because of Newton's third law, this means the second skater is also experiencing a force of 250 N. The direction of the force, however, is in the opposite direction to the force experienced by the first skater.
The force experienced by an object is independent of its mass. Therefore, despite the second skater having a mass of 90.0 kg versus the first skater's 70.0 kg, the force experienced remains the same.
In conclusion, the second skater experiences a force of 250 N.
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A rectangle has an area of (x2 - 17x + 72) square units. Since the area of a rectangle is determined using the formula, A =
lw, what could be the length and width of the rectangle?
length = (x - 8) units and width = (x - 9) units
length = (x + 9) units and width = (x + 8) units
length = (x - 6) units and width = (x - 12) units
length = (x + 12) units and width = (x + 6) units
O
Answer:
Step-by-step explanation:
x² - 17x + 72 = 0
Sum = -17
Product = 72
Factor = 8 , 9
x² - 17x + 72 = 0
x² - 8x -9x + (-8)*(-9) = 0
x(x - 8) -9(x -8) = 0
(x - 8 ) (x - 9) = 0
Length = (x - 8) units
Width = (x - 9) units
For breakfast, Sarah can choose eggs, granola, or oatmeal as a main course, and orange juice or milk for a drink. How many possible outcomes are there in the sample space?
Answer:
6 outcomes
Step-by-step explanation:
3 (main courses) x 2 (drinks) = 6 outcomes
eggs - orange juice
granola - orange juice
oatmeal - orange juice
eggs - milk
granola - milk
oatmeal - milk
Solve the inequality: –3(–3x – 4) < 66
To solve the inequality -3(-3x - 4) < 66, first distribute the -3, then isolate the variable term resulting in 9x < 54 and divide by 9 to find x < 6 as the solution set.
Explanation:Solving the Inequality
To solve the inequality -3(-3x - 4) < 66, we first distribute the -3 across the terms within the parentheses, which gives us 9x + 12 < 66.
Next, we subtract 12 from both sides to isolate the term with the variable, resulting in 9x < 54. Finally, we divide both sides by 9 to solve for x, which yields x < 6.
Thus, the solution set to the inequality is all real numbers less than 6.
James charles was buying beauty products at Ikea while T-posing cause he can. He got lost at Ikea for 24 hours, how many minutes are in 24 hours?
Answer:
1440 minutes
Step-by-step explanation:
24 hours a day x 60 minutes an hour = 1440 minutes on a day
Help ASAP!! Which pair of ratios are proportional?
A.7/14 and 20/40
B.25/100 and 5/150
C.18/24 and 16/12
D.6/21 and 2/42
Answer:
A
Step-by-step explanation:
This can be easily seen. 7/14 simplified is 1/2. When 20/40 is simplified, it's also 1/2
Mrs. Cho wrote the following problem on the board.
Problem: StartFraction 1 Over x squared EndFraction minus StartFraction 2 Over y EndFraction divided by y minus 2 x squared
Step 1: StartFraction y Over x squared y EndFraction minust StartFraction 2 x squared Over x squared y EndFraction divided by y minus 2 x squared
Step 2: StartFraction y minus 2 x squared Over x squared y EndFraction divided by StartFraction y minus 2 x squared Over 1 EndFraction
Step 3: StartFraction y minus 2 x squared Over x squared y EndFraction times StartFraction 1 Over y minus 2 x squared EndFraction
What should Mrs. Cho do next?
Answer:
Multiply the numerators and the denominators.
Step-by-step explanation:
Problem: [tex]\dfrac{1}{x^2}- \dfrac{2}{y}\div y-2x^2[/tex]
Step 1: [tex]\dfrac{y}{x^2y}- \dfrac{2x^2}{x^2y}\div y-2x^2[/tex]
Step 2: [tex]\dfrac{y-2x^2}{x^2y} \div \dfrac{y-2x^2}{1}[/tex]
Step 3: [tex]\dfrac{y-2x^2}{x^2y} X \dfrac{1}{y-2x^2}[/tex]
The next step would be to multiply the numerators and the denominators.
Step 4: [tex]\dfrac{y-2x^2}{(x^2y)(y-2x^2)}[/tex]
Since [tex]y-2x^2[/tex] is common in the numerator and denominator, it divides itself, thus our result is:
[tex]\dfrac{1}{x^2y}[/tex]
Find the pre-image given the image and scale factor. Scale factor: n = 2 Identify the coordinates of the image. A'(–2, –4) B'(2, 1) Divide the coordinates by the scale factor. The pre-image of B' is B(1, 1 2 ). What is the pre-image of A'?
Answer: the answer is -1, -2
Step-by-step explanation:
If you know a length in a scale drawing and its corresponding length in the original drawing, how can you determine the relationship between the areas of the drawings? Explain. (Lesson 13,14 & 15 of module 4)
Answer:
If the scale factor is represented by , then the area of the scale drawing is [tex]k^{2}[/tex] times the corresponding area of the original drawing.
Step-by-step explanation:
If the scale factor is represented by , then the area of the scale drawing is [tex]k^{2}[/tex] times the corresponding area of the original drawing.
For example:
Given a scale factor of 25%, would the quotient of the area of the scale drawing to the area of the original drawing be?
Answer:
The quotient of the areas would be equal to the square of the scale factor. Therefore, the quotient of the scale drawing to the original in this example would be equal to [tex](\frac{1}{4}) ^{2}[/tex]
Hope it will find you well.
25*10^-6 in standard form
Answer:
.000025
Step-by-step explanation:
25*10^-6
The negative means we move the decimal point to the left
The 6 means move it 6 places
25.
6 places to the left
Add the number of zeros as required
000025
.000025
Answer:
0.000025
Step-by-step explanation:
25 × 10^-6
25/10⁶
25/1000000
0.000025
If you toss a coin 4 times, what is the probability of landing heads, heads, tails, heads and then heads?
Answer: 0%
Step-by-step explanation:
if you toss a coin 4 times you cant get 5 results.
PLEASE HELP ME!! LIKE I NEED IT NOW!!
A DJ charges $150 for set-up and transportation, plus $65 per hour to entertain at a party. Which equation represents the relationship between the cost, y (in dollars), and the number of hours, x, for which the DJ is hired?
A DJ charges $150 for set-up and transportation, plus $65 per hour to entertain at a party. Which equation represents the relationship between the cost, y (in dollars), and the number of hours, x, for which the DJ is hired?
A. y= 150+65x
B. y= 65+150x
C. y=215x
D. y=65x
Answer:
A. y= 150+65x
Step-by-step explanation:
65 is the only number that changes. The 150 will be the same no matter what.
Find the surface area
A gaming console that is $300 plus 8% tax. What is the final cost of the console? (Round to the nearest cent) Please explain :)
Answer: $324
Explanation: I changed the 8% to 0.08 and multiplied that by 300 and got 24. Then I added 300+ 24 to get $324.
Answer:
324
Step-by-step explanation:
final cost = (100+8)% of 300 = 324
What is the arc measure of CD in degrees?
Answer:
An arc is a segment of a circle. An arc measure is the measure of an angle that the arc creates in the center of a circle, while an arc length is the span of the arc. This measure can be given in degrees or radians. We can easily convert between the two using the fact that pi radians = 180 degrees.
Step-by-step explanation:
PLease help, I need this in 2 minutes!
y÷2.3+5.69=7.58
Answer:
y=4.347
Step-by-step explanation:
To solve for y in the equation:
[tex]\dfrac{y}{2.3}+5.69 =7.58[/tex]
First, subtract 5.69 from both sides
[tex]\dfrac{y}{2.3}+5.69-5.69 =7.58-5.69\\\dfrac{y}{2.3}=1.89\\$Cross Multiply\\y=1.89 X 2.3\\y=4.347[/tex]
Please help me!! Will give brainliest!!
Answer:
A) 53
B) 53%
C) 37%
D) 63%
E) Yes.
Step-by-step explanation:
A) 53 people did not get headaches at all.
B) To solve for the percentage of participants that reported they did not get a migraine headache, you will need to divide out of the TOTAL number of people:
53/100= .53 --> Convert to percentage--> .53×100 = 53%.
C) To find this value, you will need to divide out of the amount of people that took MEDICINE and got a headache:
22/60≈0.367--> Convert to percentage --> 0.367×100≈37%
D) This percentage will be found out of who did NOT take the medicine:
25/40= 0.625 --> Convert to percentage --> 0.625×100≈63%
E) The medicine did help prevent migraine headaches because the percentage that got migraines with the medicine is lower than the percentage that got migraines WITHOUT the medicine.
Amelia wants to put wood shavings in her ferret's cage. The floor of the cage measures 1 yard wide by 9 feet long. One bag of shavings covers 5 square feet. How many bags will Amelia have to buy to cover the floor of the cage?
Answer:
6 bags
Step-by-step explanation:
1 yard is 3 feet, so the area of the cage is ...
A = LW
A = (9 ft)(3 ft) = 27 ft^2
At 5 square feet per bag, the number needed is ...
(27 ft^2)/(5 ft^2/bag) = 5.4 bags
We assume that Amelia can only buy whole bags, so ...
Amelia will have to buy 6 bags to cover the floor of the cage.