Match the inequality to the graph of its solution.
a. c + 7 ≤ 3
b. c - 3 > 1
c. c - 7 < 3
case a) [tex]c+7 \leq 3[/tex]
[tex]c+7 \leq 3\\ c\leq3-7\\c\leq -4[/tex]
the solution is the interval-------> (-∞,-4]
the answer case a) in the attached figure
case b) [tex]c-3 > 1[/tex]
[tex]c-3 > 1\\c > 1+3\\c> 4[/tex]
the solution is the interval-------> (4,∞)
the answer case b) in the attached figure
case c) [tex]c-7< 3[/tex]
[tex]c-7< 3\\ c<3+7\\ c< 10[/tex]
the solution is the interval-------> (-∞,10)
the answer case c) in the attached figure
Inequalities are used to represent unequal expressions.
Graph (b) represents [tex]\mathbf{c + 7 \le 3}[/tex]Graph (c) represents [tex]\mathbf{c - 3 > 1}[/tex]Graph (a) represents [tex]\mathbf{c - 7 < 3}[/tex][tex]\mathbf{(a)\ c + 7 \le 3}[/tex]
Subtract 7 from both sides
[tex]\mathbf{c \le -4}[/tex]
The above means that:
The graph points leftThe graph starts at -4, with a closed circleHence, graph (b) represents [tex]\mathbf{c + 7 \le 3}[/tex]
[tex]\mathbf{(b)\ c - 3 > 1}[/tex]
Add 1 to both sides
[tex]\mathbf{c > 4}[/tex]
The above means that:
The graph points rightThe graph starts at 4, with an open circleHence, graph (c) represents [tex]\mathbf{c - 3 > 1}[/tex]
[tex]\mathbf{(c)\ c - 7 < 3}[/tex]
Add 7 to both sides
[tex]\mathbf{c < 10}[/tex]
The above means that:
The graph points leftThe graph starts at 10, with an opened circleHence, graph (a) represents [tex]\mathbf{c - 7 < 3}[/tex]
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If m∠1 = 68°, what is y?
What is the length, in units, of the hypotenuse of a right triangle if each of the two legs is 2 units?
4 units
2 units
Square root of 6 units
Square root of 8 units
Answer:
square root of 8
Step-by-step explanation:
because it is 8 squared
The length of the hypotenuse of a right triangle with legs of 2 units each is the square root of 8 units.
Explanation:In a right triangle, the length of the hypotenuse can be found using the Pythagorean theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the other two sides. If each of the two legs is 2 units, then the length of the hypotenuse can be found as follows:
hypotenuse2 = leg12 + leg22
hypotenuse2 = 22 + 22
hypotenuse2 = 4 + 4
hypotenuse2 = 8
Therefore, the length of the hypotenuse is the square root of 8 units.
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A package delivery company has determined that they can meet their schedules if they have 4 drivers for every 30 square miles of area they cover. If they want to offer service to a county of 75 square miles, how many drivers must they have?
A. 9 drivers
B. 10 drivers
C. 15 drivers
D. 12 drivers
Please explain your answer! : )
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Maddie plays 16 Games of tennis. Her went to loss ratio is 10 to 6. She is expected to play 12 more games during the season. How many do you expect her to win
every months, a man deposit in his bank account a savings of php 5,000 , in how many years would he have saved php 250,000?
Assume the ball passes through the points (3,8), (5,20/3), and (6,5) . Use this data to set up a system of three equations and three unknowns (a, b, and c) that will allow you to find the equation of the parabola. Write the system in the space provided.
To solve this question:
First, we need to know the standard equation of a parabola.Then, with the three points given, we can build a system of three equations.Doing this, we get that the system is, with the 3 equations:
[tex]9a^2 + 3b + c = 8[/tex]
[tex]75a + 15b + 3c = 20[/tex]
[tex]36a + 6b + c = 5[/tex]
Equation of a parabola:
A parabola is a second degree polynomial, having an standard equation of:
[tex]y = ax^2 + bx + c, a \neq 0[/tex]
Point (3,8)
This means that when [tex]x = 3, y = 8[/tex]. So
[tex]y = ax^2 + bx + c, a \neq 0[/tex]
[tex]8 = a\times3^2 + 3b + c[/tex]
[tex]9a^2 + 3b + c = 8[/tex]
Thus, [tex]9a^2 + 3b + c = 8[/tex] is the first equation.
(5,20/3)
This means that when [tex]x = 5, y = \frac{20}{3}[/tex]. Thus
[tex]y = ax^2 + bx + c, a \neq 0[/tex]
[tex]\frac{20}{3} = a\times5^2 + 5b + c[/tex]
[tex]25a + 5b + c = \frac{20}{3}[/tex]
[tex]75a + 15b + 3c = 20[/tex]
Thus, [tex]75a + 15b + 3c = 20[/tex] is the second equation.
(6,5)
This means that when [tex]x = 6, y = 5[/tex]. Thus
[tex]y = ax^2 + bx + c, a \neq 0[/tex]
[tex]5 = a\times6^2 + 6b + c[/tex]
[tex]36a + 6b + c = 5[/tex]
Thus, [tex]36a + 6b + c = 5[/tex] is the third equation.
After all, the system of equations is:
[tex]9a^2 + 3b + c = 8[/tex]
[tex]75a + 15b + 3c = 20[/tex]
[tex]36a + 6b + c = 5[/tex]
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im pretty sure somone answered this but
Rosemary left a 15% tip for a meal that cost $39.
What was the amount of the tip?
If y varies directly with x in the following table problem, find the constant of variation (k) and write the equation x 6,9,12,15 Y 10,15,20,25
On a tour of an old gold mine, you find a nugget containing 0.82 ounce of gold. gold is worth $1566.80 per ounce. how much is your nugget worth?
Since the gold is worth $1566.80 per ounce, then the nugget is worth $1284.776.
Worth of gold per ounce = $1566.80 per ounceAmount of gold that the nugget contains = 0.82 ounces of goldThis is a question relating to multiplication. Therefore, in order to know the worth of the nugget, we've to multiply 0.82 by $1566.80. This will be:
= 0.82 × $1566.80
= $1284.776
Therefore, the value of the nuggets is $1284.776.
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Can someone clearly explain and workout Q19? Much appreciated
Find the total area of the solid figure with the length, 3 width 5, and height 6
What is the equation of a line that passes through the point (4, 2) and is perpendicular to the line whose equation is y=x/3−1 ?
What are the intercepts of the line 4x+3y=24?
For carlees birthday her mother is baking cupcakes for her 12 friends at daycare. the recipe calls for
[tex]3\frac{1}{3} [/tex]
cups of flour. this recipe makes
[tex]2 \frac{1}{2} dozen \: cupcakes[/tex]
carlees mother only has 1 cup of flour. is there enough flour for each of her friends to get a cupcake
A college student borrows $3,000 for 3 months to pay for a semester of school. If the interest is $61.88 find the monthly payment
The student must make monthly payments of $1,020.63 to repay the $3,000 loan with $61.88 in interest over 3 months.
The student has borrowed $3,000 for 3 months and the interest incurred on this loan is $61.88. To find the monthly payment, we need to add the total interest to the principal borrowed and then divide it by the number of payments (which is 3 in this case).
The total repayment amount is calculated as $3,000 principal + $61.88 interest = $3,061.88.
Now, we divide the total repayment amount by the number of monthly payments:
Monthly Payment = Total Repayment Amount / Number of Payments
Monthly Payment = $3,061.88 / 3
Monthly Payment = $1,020.63
Therefore, the student will need to make monthly payments of $1,020.63 to repay the $3,000 loan over 3 months.
please help, I am really bad at algebra
Answer:
a, b, c
Step-by-step explanation:
f(x) = 3(1/4)^x
a. (-2, 48)
f(-2) = 3(1/4)^(-2) = 3(4)^2 = 3 * 16 = 48
(-2, 48) is on the graph.
b. (0, 3)
f(0) = 3(1/4)^(0) = 3(1) = 3
(0, 3) is on the graph.
c. (2, 3/16)
f(2) = 3(1/4)^(2) = 3(1/16) = 3/16
(2, 3/16) is on the graph.
d. (12, 0)
f(12) = 3(1/4)^(12) = 3(0.000000596)
f(12) does not equal zero.
(12, 0) is not correct
A train leaves chicago and travels east at 60 mph. another train at the same depot leaves at the same time and travels west at 72 mph. how long before the two trains are 330 miles apart?
The two trains will be 330 miles apart after 2.5 hours.
Explanation:To find how long it takes for the two trains to be 330 miles apart, we can apply the formula for relative velocity:
Relative velocity = sum of their speeds
The first train is moving east at 60 mph, and the second train is moving west at 72 mph. So their relative velocity is 60 mph + 72 mph = 132 mph.
To find the time it takes for the trains to be 330 miles apart, we can use the formula:
Distance = speed × time
330 miles = 132 mph × time
Solving for time, we have:
Time = 330 miles / 132 mph = 2.5 hours
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Write an expression describing all the angles that are coterminal with 141°.
How many times larger is 2 x 10-6 than 2 x 10-11?
Ohhhhhhh! I have a Brainliest
You deposit $1,000 in a savings account that earns 0.5% each month. Assuming you do not deposit or withdraw any money from the account, how much will you have in the account after 3 years?
If you shift the quadratic parent function, f(x) = x2, right 12 units, what is the equation of the new function?
A. g(x) = (x – 12)2
B. g(x) = (x + 12)2
C. g(x) = x2 – 12
D. g(x) = x2
Answer:
A. [tex]f(x) = (x-12)^2[/tex]
Step-by-step explanation:
The parent function [tex]f(x) = x^2[/tex] can be shifted 12 units to the right by moving its vertex 12 units to the right. The parent function has a vertex at (0,0) since [tex]f(0) = 0^2=0[/tex]. It will shift to (12,0) so [tex]f(12) =(12-a)^2=0[/tex]. The only value of a which will make it 0 is 12. So the equation is [tex]f(x) = (x-12)^2[/tex]
Which pair of triangles are congruent by ASA ?
The pair of triangles that are congruent by ASA is [tex]\boxed{\bf option (d)}[/tex].
Further explanation:
Triangles are congruent when all the corresponding sides and interior angles are equal.
There are four theorems by which we say that the triangles are congruent.
1. Side-Side-Side(SSS)
If all the three sides of a triangle are equal to the corresponding sides of the other triangle, then the two triangles are congruent by SSS theorem.
2. Angle-Side-Angle(ASA)
If any two angles and the included side between the angles of one triangle are equal to the corresponding two angles and the included side between the angles of the second triangle then the two triangles are congruent by ASA theorem.
3. Side-Angle-Side(SAS)
If any two sides and angle between the sides of one triangle are equal to the corresponding two sides and angle between the sides of the second triangle then the two triangles are congruent by SAS theorem.
4. Hypotenuse Leg (HL)
If the hypotenuse and side of a right angled triangle is equal to the hypotenuse and a side of the other right angled triangle then the triangles are congruent by HL theorem.
Option (a)
The first figure shows one side is included between the two angles but the second figure shows two angles and one side as shown in below attachment.
Both the figures don’t have a single property from the above mentioned properties.
Therefore, option (a) is incorrect.
Option (b)
The first figure shows one angle between the two sides and the second figure also shows one angle between the two sides as shown in below attachment.
Both have the same property.
Therefore, the triangles are congruent by SAS rule not by ASA.
Thus, option (b) is incorrect.
Option (c)
The first figure shows one angle between the two sides and the second figure also shows one angle between the two sides as shown in below attachment.
Both have the same property.
Therefore, the triangles are congruent by SAS rule not by ASA rule.
Thus, option (c) is incorrect.
Option (d)
The first figure shows two angles and one side is included between them and the second figure shows two angles and one side is included between them as shown in below attachment.
Both have the same property.
Therefore, the triangles are congruent by ASA rule.
Thus, option (d) is correct.
Hence, the [tex]\boxed{\bf option (d)}[/tex] is correct as the triangles are congruent by ASA rule.
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Answer details:
Grade: Middle school
Subject: Mathematics
Chapter: Angles and Triangles
Keywords: Triangles, angles, sides, congruent triangles, similar triangles, SAS theorem, ASA theorem, SSS theorem, HL theorem, geometry, translation, rotation, reflection, mirror image.
The pair of triangles that are congruent by the Angle-Side-Angle Congruent Theorem (ASA) are the pairs that have two corresponding angles and an included side that are congruent to each other which is: Option D.
Recall:
The Angle-Side-Angle Congruent Theorem (ASA) states that two triangles are considered congruent if they have two corresponding angles that are congruent and an included side that are congruent to each other.
The included side is the side that is lie between the two congruent angles in each of the triangles.
Thus, form the pairs of angles given, the pair in option d has two corresponding angles and an included side that are congruent to each other in each triangle.
Therefore, the pair of triangles that are congruent by the Angle-Side-Angle Congruent Theorem (ASA) are the pairs that have two corresponding angles and an included side that are congruent to each other which is: Option D.
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Solve - ( c - 3) = 6
Simplify. 4^3 x 4^4/ 4^9
A. 4^16
B. 4^2
C. 1/4^2
D 1/4
The sum of two numbers is 90. if twice the smaller number is subtracted from the larger number, the result is 12. find the two numbers.
Solve the compound inequality 2x > –10 and 3x < 24
5 > x > –8
5 > x < –8
–5 < x < 8
–5 < x > 8
Answer: Third option is correct.
Step-by-step explanation:
Since we have given that
[tex]2x>-10---------------------------(1)[/tex]
and
[tex]3x<24------------------------------(2)[/tex]
From eq(1), we have
[tex]\dfrac{2x}{2}>\dfrac{-10}{2}\\\\x>-5[/tex]
From eq(2), we have
[tex]3x<24\\\\\dfrac{3x}{3}<\dfrac{24}{3}\\\\x<8[/tex]
So, compound inequality becomes
[tex]-5<x<8[/tex]
Hence, Third option is correct.
How do you find a literal equation for d=rt,
solve for t.
Answer: [tex]\frac{d}{r} = t[/tex]
Step-by-step explanation: To solve for t in the equation d = rt, all we have to do is get t by itself on the right side of the equation.
Since t is being multiplied by r, we simply divide both sides of the equation by r. On the right, the r's cancel and we are left with r.
On the left side of the equation we have [tex]\frac{d}{r}[/tex].
Therefore, our answer is [tex]\frac{d}{r} = t[/tex].
How many different primes are in the prime factorization of 20! or 20 factorial?