Is the ordered pair (-6,3) a solution of the inequality -4x - 8y < 15 ?
A) Yes, the ordered pair is a solution
B) No, the ordered pair is not a solution.
Given:
The inequality is:
[tex]-4x-7y<15[/tex]
To find:
The whether (-6,3) is a solution of given inequality of not.
Solution:
We have,
[tex]-4x-7y<15[/tex]
We need to check the inequality for point (-6,3).
Substitute [tex]x=-6, y=3[/tex] in the given inequality.
[tex]-4(-6)-7(3)<15[/tex]
[tex]24-21<15[/tex]
[tex]3<15[/tex]
This statement is true. It means the point (-6,3) satisfies the given inequality.
Therefore, the correct option is A. Yes, the ordered pair is a solution.
Find the indicated limit, if it exists.
Answer:
[tex]\displaystyle \lim_{x \to -8} f(x) = 1[/tex]
General Formulas and Concepts:
Calculus
Limits
Limit Rule [Constant]: [tex]\displaystyle \lim_{x \to c} b = b[/tex]
Limit Rule [Variable Direct Substitution]: [tex]\displaystyle \lim_{x \to c} x = c[/tex]
Limit Property [Addition/Subtraction]: [tex]\displaystyle \lim_{x \to c} [f(x) \pm g(x)] = \lim_{x \to c} f(x) \pm \lim_{x \to c} g(x)[/tex]
Step-by-step explanation:
*Note:
When you graph the function, the left-hand and right-hand limit does equal the same.
Step 1: Define
[tex]\displaystyle f(x) = \left \{ {{x + 9, x < -8} \atop {-7 - x, x \geq -8}} \right.[/tex]
Step 2: Find Limit
Substitute in function [Limit]: [tex]\displaystyle \lim_{x \to -8} f(x) = \lim_{x \to -8} (-7 - x)[/tex]Evaluate limit [Limit Rule - Variable Direct Substitution]: [tex]\displaystyle \lim_{x \to -8} f(x) = -7 - (-8)[/tex]Simplify: [tex]\displaystyle \lim_{x \to -8} f(x) = 1[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Limits
A cylinder is wight inches high with a radius of three inches.It contains a ball with a diameter of five inches. What volume is left unoccupied in the cylinder?
Complete Question
A cylinder is eight inches high with a radius of three inches.It contains a ball with a diameter of five inches. What volume is left unoccupied in the cylinder?
Answer:
160.74 cubic inches
Step-by-step explanation:
Step 1
Find the volume of cylinder
= πr²h
A cylinder is eight inches high with a radius of three inches.
Height = 8 inches
Radius = 3 inches
Volume of the cylinder = π × 3² × 8
= 226.19 cubic inches
Step 2
Find the volume of sphere
= 4/3 π r³
It contains a ball with a diameter of five inches.
Diameter = Radius /2 = 5/2 = 2.5 inches
Volume of the Sphere = 4/3 × π × 2.5³
= 65.45 cubic inches
Step 3
What volume is left unoccupied in the cylinder?
This is calculated as:
Volume of Cylinder - Volume of sphere
= 226.19 cubic inches - 65.45 cubic inches
= 160.74 cubic inches
Therefore, the volume is left unoccupied in the cylinder is 160.74 cubic inches
The value of the 9 in 901,532 is how many times the value of the 9 in 157,900?
NEED HELP!!!
Answer:
the answer for this question is 1000times.
Step-by-step explanation:
the value for 9 in 157,900 is nine hundred(900).and the value of 9 in 901,532 is nine hundred thousand(900000).
900×1000= 900,000.
The place value of the number 9 in the first number is 1000 times greater than the second number.
What is the standard decimal form of numbers?The standard decimal form of numbers is written in base 10 as there are 10 different numbers from 0 to 9.
Each digit has a face value and a place value.
Given, A number 901,532, So the place value of the number 9 is 900000.
And, In the number 157,900, The place value of 9 is 900.
Therefore, The number of times the value of 9 is greater in 901,532 compared to 157,900 is,
= 900000/900.
= 1000 times.
learn more about face value and place value here :
https://brainly.com/question/27734142
#SPJ2
Help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
24
Step-by-step explanation:
You need to plug in 3 for all of the x-values
That looks like 2(3)^2 + 5(3) - 9
Then if you simplify it is 2(9) + 15 - 9
Then simplify one last time and you get a final answer of 24
[tex]_____________________________________[/tex]
ANSWER:x - intercept:[tex] \\ \tt ( - \frac{ 5 \sqrt{97} }{4} ,0),( - \frac{5 + \sqrt{97} }{4} ,0)[/tex]
y - intercept[tex]\tt(0, - 9)[/tex]
[tex]_____________________________________[/tex]
꧁____YunaKoharuChan____꧂What are complementary and supplementary angles?
Answer:
Complementary angels are basically two angles that add up to 90 degrees. Supplementary angles are two angles that add up to 180 degrees.
Step-by-step explanation:
(self-explanatory)
I hope this helps, have a nice day.
a certain number is added to 9 the result is 5 - the same number what is the number
Answer:
the answer to the question is -2
Step-by-step explanation:
a certain number=x
therefore,x+9=5-x
x+x=5-9
2x= -4
you the divide both sides by2 to gain x
Jen deposits $9,500 into a bank account that pays her 4.5% simple interest for 5 years. How much interesrt will she earn over 5 years?
Answer:
$11838.7
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Simple Interest Rate Formula: [tex]\displaystyle A = P(1 + r)^t[/tex]
P is principle amountr is ratet is timeStep-by-step explanation:
Step 1: Define
Identify variables
P = 9500
r = 4.5% = 0.045
t = 5
Step 2: Find A
Substitute in variables [Simple Interest Rate Formula]: A = 9500(1 + 0.045)⁵(Parenthesis) Add: A = 9500(1.045)⁵Evaluate exponents: A = 9500(1.24618)Multiply: A = 11838.77 - 2x - x4
b) How many terms are there?
c) What is the leading coefficient?
d) What is the constant term?
e) What is the degree of the expression?
Answer: (see explanation)
Step-by-step explanation:
terms: 7, 2x, x4
leading coefficient: 7
constant term: 7
I'm sorry I'm unsure how to solve the last question.
what is the solution of 1
Which of the following expressions is equivalent to 18x + 30y?
A) 3(6x + 30y)
B) 6(3x + 5y)
C) 3xy(6 + 5)
D) 6(3y + 5x)
Answer:
B) 6(3x + 5y)
Step-by-step explanation:
6 times 3 is 18 and 6 times 5 is 30
Which number is equivalent to 2^3x = 10
Answer:
5/4
Step-by-step explanation:
see steps below:)
help now asap ill give brainliest
Answer:
288 square inches
Step-by-step explanation:
since we are not told what to find, we can as well find the volume of the prism
Volume of the prism = BH
B is the base area = 1/2 * 6 * 8
B = 48/2
B = 24 square inches
H is the height of the prism = 12in
Volume of the prism = 24 * 12
Volume of the prism = 288 square inches
Please help the image is attached
Answer:
I tried my best below
Step-by-step explanation:
8. 54
9. 2
Find the total pay for biweekly at $9.50 per hour
how many hours do they work? Please be more spesific
Answer:
The answer is 760
Step-by-step explanation:
If you make $9.50 an hour with 8 hours a day and 40 hours a week you multiply the 9.50 with 40 to get 380. Now, you have the total for one week you can double it to get the pay for two weeks which come out to 760.
4M
+N7
____
123
Determine the value of the missing digits
Answer:
M = 6
N= 7
Step-by-step explanation:
M + 7 = 3
M= 6
6 + 7 = 13, so we get 3 and carry 1
Now 1 + 4 + N = 12
1 + 4 + 7 = 12
So N = 7
Therefore,
46 + 77 = 123
30 POINTS I WILL GIVE U BRAINLIEST AND THANKS AND 5 STARS please help this is very important this is a big part of my grade
Answer:
[tex]1.\:2^x=64, x=\boxed{6},\\2.\:x=\left(\frac{2}{3}\right)^3,x=\boxed{\frac{8}{125}}\\3.\:3\cdot (3^4)=3^x, x=\boxed{5}\\4.\:\frac{16}{25}=x^2,x=\boxed{\frac{4}{5}},[/tex]
Step-by-step explanation:
[tex]1.\\\\2^x=64,\\\log 2^x=\log64,\\x\log 2=\log 64,\\x=\frac{\log 64}{\log 2}=\boxed{6}[/tex]
[tex]2.\\x=\left(\frac{2}{5}\right)^3=\frac{2^3}{5^3}=\boxed{\frac{8}{125}}[/tex]
3. This problem incorporates an exponent property.
Exponent property used: [tex]a^b\cdot a^c=a^{(b+c)}[/tex], yielding an answer of [tex]\boxed{5}[/tex]
[tex]4.\\\\\frac{16}{25}=x^2,\\x=\sqrt{\frac{16}{25}}=\frac{\sqrt{16}}{\sqrt{25}}=\boxed{\frac{4}{5}}[/tex]
Answer:
1. 6
2. 8/25
3. 5
4. 4/5
Step-by-step explanation:
HELP PLEASE I HAVE ONLY TODAY TO SUBMIT
Answer:
Step-by-step explanation:
Find the measure of the arc TDB in the circle P shown below:
[tex]\huge{ \mathfrak{ \underline{ Answer \: \: ✓ }}}[/tex]
The Angle formed by an arc on the centre of the circle is double the angle made by the same arc on the circumference of the circle.
So,
[tex] \boxed{ \mathrm{ \angle TDB = \dfrac{1}{2} \angle TPB }}[/tex]
[tex] \mathrm{\angle TDB = \dfrac{1}{2} \times 90 \degree}[/tex][tex] \mathrm{\angle TDB =45 \degree } [/tex]_____________________________
[tex]\mathrm{☠ \: TeeNForeveR \: ☠}[/tex]
can someone help me solve this question? asap
Answer:
i.x=1 (x,y)=(1,3)
y=3
ii.x=2 (x,y)=(2,4)
y=4
iii.x=3 (x,y)=(3,5)
y=5
iv.x=4 (x,y)=(4,6)
y=6
v.x=5 (x,y)=(5,7)
y=7
Step-by-step explanation:
Describe the relationship between GF and CD when the two lines are perpendicular to AB. Also describe the relationship between GF and CD when CD is not perpendicular to AB . Zoom in or out on the coordinate plane, if needed.
Answer:
See Explanation
Step-by-step explanation:
Given
Lines GF, CD and AB
Required
Relationship between GF and CD
The question is incomplete, as there is no attachment to support the given parameters.
The general solution goes thus:
(a) CD and GF perpendicular to AB
If two lines are perpendicular to another line; then the two lines are parallel to each other.
This means that CD and GF are parallel, and they have the same slope
(b) CD is not perpendicular to AB
Here, we know that GF is perpendicular to AB, CD is not;
This means that GF and AB are not parallel.
More information is needed to determine the actual relationship between GF and AB; but for sure, they are not parallel.
need help on this please
Answer:
5.7
Step-by-step explanation:
7^2- 4^2= 33
[tex]\sqrt{33}[/tex]= 5.7
2x2 = 4 4x 10 = 40 x 32 = ?
Answer:
1280
Hope this helped :D
HELP HELP HELP HELP HELP HELP AHHLIDAKUYSWJG PLEASE
I'm pretty sure it's D
A random number from 1 to 5 is selected
50 times. The number 1 is selected 13 times,
2 is selected 8 times, 3 is selected 14 times, 4
is selected 6 times, and 5 is selected 9 times.
What is the relative frequency of selecting a 2?
3?
Answer:
Relative frequency of selecting a 2 = 8/50 = 0.16
Relative frequency of selecting a 3 = 14/50 = 0.28
Step-by-step explanation:
When we have a given experiment with given outcomes (such that each time that we perform the experiment, one outcome happens) the relative frequency of a given outcome is the quotient between the number of times that that outcome happened, and the total number of times that the experiment was performed.
Here the experiment is selecting a random number between 1 and 5, and it is performed 50 times.
Out of these 50 times, the outcome "2" appears 8 times.
Then the relative frequency of selecting the number 2 is:
f(2) = 8/50 = 0.16
And of these 50 experiments, the outcome "3" appears 14 times.
Then the relative frequency of selecting the number 3 is:
f(3) = 14/50 = 0.28
can someone tell me the points on a graph when you graph y=-5x
Answer:
pls give me brainliest
Step-by-step explanation:
A pizza restaurant is having a contest. The restaurant advertises that one out of every 25 customers will win a small pizza. What is the probability that a customer will win?
The opposite of the integer represented by point A is?
3x + 5y = 23
y = x + 3
Answer:
(1,4)
Step-by-step explanation:
for a smoothie Isaac needs 3 quarts of strawberry puree which is sold in bottles of 1 pint and bottles of 1 cup he already had 1.75 quarts of puree if he wants to buy exactly three bottles in total how many of each bottle should he buy pleasee help its really important
Answer:
There are 2 bottle of 1 pint and 1 bottle of 1 cup.
Step-by-step explanation:
Okay, so first let's look at the conversion factors of these units:
1 quart=2 pints & 1 quart= 4 cups.
Alright well, we already have 1.75 out of 3 quarts of the strawberry puree so all
we need left is 1.25 quarts left. So since 1 pint= .5 quarts and 1 cup=.25 quarts
we need to buy 2 pints and 1 cup to give us our three quarts.
Hence, there are 2 bottle of 1 pint and 1 bottle of 1 cup.
Hope this answer helps you :)
Have a great day
Mark brainliest