Which number line shows all the values of x that make the inequality -3x + 1 < 7 true
Answers
After solving the equation (work shown in image) your answer would be x > -2. I drew an image of how the number line should look at least similar to, using the solution.
*whenever you divide or multiply with a negative number reverse/flip the sign
< or > signs will always have an open circle
≥ or ≤ signs will have a closed/filled in circle
TIP: To know which way the arrow should point, look at the sign and think of it as an arrow.
< would have the arrow on the number point
this way: <-
or > which would have the arrow on the number line point this way: ->
Related Questions
Which to integers is Sqrt 58
between?
A. 7 and 8
B. -8 and -7
C.-6 and -5
D. 5 and 6
Answers
Option A
Solution:First, let's find the square root of 58.The square root of 58 is equivalent to:√58≈7,62 (approximately equal to)Now, which two integers is 7.62 between?Is it between 7 and 8? Yes.Is it between -8 and -7? No. 7.62 is positive.Is it between -6 and -5? No.Is it between 5 and 6? No.Therefore, √58 is between 7 and 8.Hope it helps.
Do comment if you have any query.
5. A population has a normal distribution with a mean of 50 and a standard deviation of
10. If a random sample of size 9 is taken from the population, then what is the
probability that this sample mean will be between 48 and 54?
a. 0.060
b. 0.228
c. 0.385
d. 0.399
e. 0.611
Answers
Using the normal distribution and the central limit theorem, it is found that the probability is given by:
e. 0.611
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].In this problem, the parameters are given as follows:
[tex]\mu = 50, \sigma = 10, n = 9, s = \frac{10}{\sqrt{9}} = 3.3333[/tex]
The probability that this sample mean will be between 48 and 54 is the p-value of Z when X = 54 subtracted by the p-value of Z when X = 48, hence:
X = 54:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{54 - 50}{3.3333}[/tex]
Z = 1.2
Z = 1.2 has a p-value of 0.885.
X = 48:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{48 - 50}{3.3333}[/tex]
Z = -0.6
Z = -0.6 has a p-value of 0.274.
0.885 - 0.274 = 0.611, hence option e is correct.
More can be learned about the normal distribution and the central limit theorem at https://brainly.com/question/24663213
In circle K with \text{m} \angle JKL= 82^{\circ}m∠JKL=82 ∘ , find the angle measure of minor arc \stackrel{\Large \frown}{JL}. JL⌢ .
Answers
Answer:
M< JKL = 82°Solution: UP
The angle measure of the minor arc JL equals 82°.
What is Arc of a Circle?An arc of a circle is defined as the part of the boundary of a circle. The straight line drawn joining the two end points of the arc is called chord of the circle.
If we mark any two points on the circle, by joining those points along the circle, we get two arcs. The smaller arc is called the minor arc and the longer arc is called the major arc. If the length of the arc exactly equals the half length of the circle, then the arc is called semicircular arc.
An arc can be measured in two ways : By finding the measure of the angle of arc and finding the length of the arc.
Here we are asked to find the measure of the minor arc which is the measure of the angle of the arc JL.
Measure of the angle of the arc equals the angle formed at the center of the circle by joining the end points of the arc to the center of the circle.
We have ∠JKL = 82°
∴ measure of arc JL = 82°
Hence, the measure of the minor arc JL equals 82°.
To learn more about Arc of the Circle, click:
https://brainly.com/question/18741430
#SPJ2
When three squares are joined at their vertices to form a right triangle, the combined area of the two smaller
squares is equal to the area of the largest square. Which three squares support this statement?
5 cm
3 cm
Answers
Answer:
Top right (one what has 16cm^2 and 9cm^2)
Step-by-step explanation:
The one in the top right and even though I cannot see what the area is of the biggest square, I can tell what it should be the two smaller squares combined
Hope this helps :)
In the figure shown below, cos 0 =
Answers
[tex]\cos \theta = \dfrac{\text{Base}}{\text{Hypotenuse}}\\ \\\\~~~~~~~=\dfrac{3}{\sqrt{3^2 +2^2}}~~~~~~~;[\text{Pythagorean theorem.}]\\\\\\~~~~~~~=\dfrac{3}{\sqrt{9+4}}\\\\\\~~~~~~~=\dfrac{3}{\sqrt{13}}[/tex]
help pls with these two about surface area
Answers
Answer:
6) 152.6
7) 348.4
Step-by-step explanation:
For question number 6, calculate the surface area of the two triangles first. And then, calculate each of the surface area for the rectangles. Finally, total up the area of the two triangles and the rectangles.
[tex](6.6 \times 9) + (4 \times 9) + (5.2 \times 9) \times (\frac{1}{2} \times 5.2 \times 4) = 152.6[/tex]
For question number 7, given that the area of a triangle is 28.4. Hence calculate the area of the three rectangles. Lastly, total up the area of two triangles and three rectangles.
[tex]28.4 + 28.4 + 3(12 \times 8.1) = 348.4[/tex]
Hope this helps =)
The number of students in sixth grade is 1.03 times the number of students in seventh grade. What percent is equivalent to 1.03?
Answers
1.03 —-> 103%
What do we do to both sides of this equation to solve?
x/3 =5
Question 4 options:
Add 3 to both sides
Subtract 3 from both sides
Multiply both sides by 3
Divide both sides by 3
Answers
Answer:
Multiply both sides by 3
Step-by-step explanation:
x/3 = 5
x/3 × 3 = 5×3
x = 15
Answer:
multipy both sides by 3
Step-by-step explanation:
Find the volume of the rectangular prism
Answers
Answer:
336
Step-by-step explanation:
V=whl=8·7·6=336
Domain and range for y=x^2+5x-6
Answers
Step-by-step explanation:
domain is all real numbers since its quadratic: (-infinity, infinity)
Range is from -6 to positive infinity or [-6, infinity)
List three solutions for the inequality x≥5 and give one example of a number that is not a solutions.
Answers
Answer:
Many simple inequalities can be solved by adding, subtracting, multiplying or dividing both sides until you are left with the variable on its own. But these things will change direction of the inequality: Multiplying or dividing both sides by a negative number. Swapping left and right hand.JUST FOLLOW THE TEXT TO GET THE ANSWER OF THE INEQUALITY ×>5
Simplify. (In the problems where you combine fractions with unlike denominators leave the denominators in factored form.)
Answers
Answer:
[tex] \dfrac{a}{a - 4} [/tex]
Step-by-step explanation:
You are subtracting fractions, so as usual with fraction subtraction, you need a common denominator. To get a common denominator, you need to factor each denominator.
[tex] \dfrac{3a}{a + 4} - \dfrac{2a^2 - 16a}{a^2 - 16} = [/tex]
Factor the right denominator. It is a difference of two squares.
[tex] = \dfrac{3a}{a + 4} - \dfrac{2a^2 - 16a}{(a - 4)(a + 4)} [/tex]
The left denominator is (a + 4). The right denominator is (a - 4)(a + 4). The LCD is (a - 4)(a + 4), so multiply the left fraction by (a - 4)/(a - 4).
[tex] = \dfrac{3a}{a + 4} \times \dfrac{a - 4}{a - 4} - \dfrac{2a^2 - 16a}{(a - 4)(a + 4)} [/tex]
[tex] = \dfrac{3a^2 - 12a}{(a - 4)(a + 4)} - \dfrac{2a^2 - 16a}{(a - 4)(a + 4)} [/tex]
Be careful when you do the subtraction of the numerators, 3a² - 12a minus 2a² - 16a. 3a² - 12a - (2a² - 16a). The minus of the subtraction changes each sign inside the parentheses, so you end up with 3a² - 12a - 2a² + 16a. Be especially careful with the +16a.
[tex] = \dfrac{3a^2 - 12a - (2a^2 - 16a)}{(a - 4)(a + 4)} [/tex]
[tex] = \dfrac{3a^2 - 12a - 2a^2 + 16a}{(a - 4)(a + 4)} [/tex]
[tex] = \dfrac{a^2 + 4a}{(a - 4)(a + 4)} [/tex]
[tex] = \dfrac{a(a + 4)}{(a - 4)(a + 4)} [/tex]
[tex] = \dfrac{a}{a - 4} [/tex]
What is the domain of the function y = √√x+6-7?
x>_-7
x>_-6
x>_6
x>_7
Answers
the domain is
[tex]x \geqslant - 6[/tex]
Find the length of the segment indicated. Round your answer to the nearest tenth if necessary.
See picture for full problem. Please and thank you so very much!
Answers
Answer:
Step-by-step explanation:
a. Convert 5x^2 + 55x + 140 from standard to vertex form
b. Describe the transformation.
Answers
Answer:
The transformation will be 5
Step-by-step explanation:
Answer:
See below.
Step-by-step explanation:
5x^2 + 55x + 140 ---> required
Coefficients a=5, b=55, c=140 yield
[tex]h=\frac{-h}{2*a} =\frac{-(55)}{2*5} =\frac{-55}{10} =-5.5[/tex]
Thus, the x-coordinate of the vertex is [tex]\boxed{h = -5.5 }[/tex]
Plugging x=-5.5 into the given equation yields:
[tex]k=5*(-5.5)^{2} +55*-5.5+140=-11.25[/tex]
Thus, the y-coordinate of the vertex is [tex]\boxed{k = -11.25 }[/tex]
Altogether, the vertex of the given parabola is
[tex]\boxed{ (h,k)=(-5.5,-11.25) }[/tex]
Plugging (h,k)=(−5.5,−11.25) into the vertex formula
[tex]\boxed{ y=(x-h)^2+k }[/tex]
yields the vertex form of the parabola
[tex]\boxed{ y=(x+5.5)^2-11.25 }[/tex]
To find the vertex of a parabola in standard form, first, convert it to the vertex form y=a(x−h)2+k y = a ( x − h ) 2 + k .Hello, I am a little confused on how to do this problem. If anyone can help and explain also that will be awesome.
Answers
Answer:
4(5x-2)= 6(x+8)
20x-8=6x+48
20x-6x=48+8
14x=56
[tex]x = \frac{56}{14} [/tex]
x=4
Step-by-step explanation:
hope this helps you!!
XXITSCHOCOLOVERXX
Answer:
x = 4
Step-by-step explanation:
[tex]\frac{5x-2}{6}=\frac{x+8}{4} < == cross\ multiply\\\\4(5x-2)=6(x+8) < ==distribute\\\\4(5x)+4(-2)=6(x)+6(8)\\\\20x-8=6x+48 < ==subtract\ 6x\ from\ both\ sides\\-6x\ \ \ \ -6x\\\\14x-8=48 < == add\ 8\ to\both\ sides\\\ \ \ +8 \ \ \ \ \ \ \ +8\\\\14x=56 < ==divide\ both\ sides\ by\ 14\\/14 \ \ \ /14\\\\x=4 < ==final\ answer[/tex]
Check your answer:
[tex]\frac{5x-2}{6}=\frac{x+8}{4}\\\\\frac{5(4)-2}{6}=\frac{4+8}{4}\\\\\frac{20-2}{6}=\frac{12}{4}\\\\\frac{18}{6}=\frac{12}{4}\\\\3=3[/tex]
This statement is correct
Hope this helps!
What is the least natural number which when divided by 3,5,6,8,10 and 12 leaves in each case remainder 2 but when divided by 13 leave no remainder.
Answers
Answer:
962
Step-by-step explanation:
MMM for step by step its kinda just plug and check
962/3 = 320 R2
962/6 = 160 R2
962/8 = 120 R2
962/10 = 96 R2
962/12 = 80 R2
and finally 962/13 = 74
The Hernandez family built a backyard patio .
Area = 150 square feet
What could be the dimensions of the
patio?
A 100 feet long by 50 feet wide
B
50 feet long by 25 feet wide
15 feet long by 10 feet wide
D
10 feet long by 5 feet wide
Answers
Find the missing
information.
Arc length-1.5 ft
Radius-?
Central angle-pie/4 rad
Round to the nearest thousandth.
Answers
Answer:
1.91 ft
Step-by-step explanation:
Formula
l = rαwhere :
l = arc lengthr = radiusα = central angleSolving for r
l = rαr = l/αr = 1.5/(π/4)r = 6/πr = 1.90985932 ftr = 1.91 ft (nearest thousandth)The graph below shows the cost, in
dollars, per notebook at the school store.
Which equation represents the total cost, T, per n notebooks?
Answers
Answer:
t = 2.4n
Step-by-step explanation:
y = mx + c
t = mn + c
c = y-intercept (where the graph line crosses the cost line)
c = 0
mx/mn= gradient ( rise/run, up/across)
mn= 12/5 ( you could have picked any point in the graph )
mn= 2.4
the m is unnecessary now so we discard it
t = 2.4n + 0
Did this for a test and that is what I put
what is the total EXACT area of the composite figure made up of two triangles, a rectangle, and a semicircle.
Answers
Answer:
637
Step-by-step explanation:
rectangle =
12*16*2 = 384
triangle = 12*16/2
= 96
semi circle = pie*hyp^2/2
= pie * (sqrt(12^2+16^2))^2/2
=157
Ana y Maria vieron 2 hombres robar una joyería y también vieron como alcanzaron a salir. cuando fueron interrogadas por la policía, las jóvenes dieron información sobre la placa del auto que vieron alejarse: constaba de dos letras seguidas de cuatro dígitos. María aseguraba que la segunda letra era una O o una Q y que el último dígito era un 3 a un 8. Y Ana dijo que la primera letra era una C o una G y que el primer dígito de la definitivamente un 7. ¿Cuántas placas diferentes tendrá que verificar la policía para dar a conocer el auto que vieron Ana y María?
Answers
have a government
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Step-by-step explanation:
yan napo lahat answer
Prove that equation ax^2+2hxy+by^2 always represent a pair of straight lines passing through the origin
Answers
2/3a-1/6=1/3 what is the solution
Answers
Here is your Answer:
3/4
pleeeaaasseeee help (questions in photo) will mark brainliest
Answers
Answer:
a. 0.8727rad
b. 5.585rad
that should be correct, if not, i apologize T_T
Classify each polynomial by degree and number of terms. 1. Quartic monomial v 5x? - 7x + 9 2. Cubic binomial 2x3 + 3 < 3. Quadratic trinomial < 8x4 4. Quintic quadnomial
Answers
The degree of a polynomial is categorized by its highest power of its leading variable.
Degree and number of terms of a polynomial
Given the following polynomial functions, we are to classify them based on their degrees and the number of terms
For the polynomial function 5x^4 - 7x + 9
The degree is 4 being quartic and there are three terms in the expression
For the polynomial 2x3 + 3 < 3, the degree is 3 (cubic) with three terms in the expression.
For a Quintic quadnomial, the degree of the polynomial is 5.
Learn more on polynomials here: https://brainly.com/question/4142886
Is the following shape a square?, How do you know?
Answers
Answer:
C. No, because the sides aren't congruent
Step-by-step explanation:
Connor filled his 150 gallon pool with water in 6.25 hours. How many gallons per hour did he use?
Answers
Answer:
24 gallons per hour
Step-by-step explanation:
Connor filled his 150-gallon pool with water in 6.25, to find out how many gallons per hour he used, we have to divide the amount of gallons into every hour. Therefore:
150/6.25
24 gallons per hour.
f(x)=x^2. What is g(x)?
A. g(x)=-4x^2
B. g(x)=-x^2-4
C. g(x)=x^2+4
D. g(x)=x^2-4
Answers
Answer:
g(x)=(-x²-4)
Step-by-step explanation:
[tex] - {x}^{2} - 4 \: is \: th \: requied \: equation[/tex]
On a standardized exam, the scores are normally distributed with a mean of 300 and a standard deviation of 20. Find the z-score of a person who scored 270 on the exam.
Answers
Answer:
z = -1.5
Step-by-step explanation:
To Find z-score
z = (X - μ) / σX = Test scoreμ = Mean σ = Standard DeviationGiven
X = 270μ = 300σ = 20Solving
z = 270 - 300 / 20z = -30/20z = -1.5