Answer:
In interval notation, the solution of |3 x-2|<7 is [tex]$-\frac{5}{3} < x < 3$[/tex] or [tex]$\left\{-\frac{5}{3}, 3\right\}$[/tex].
Step-by-step explanation:
The given absolute value function is |3 x-2|<7.
It is required to solve the inequality and express the solution using interval notation. -B<x-A<B and solving them separately for x
Step 1 of 3
Given absolute value equation is |3 x-2|<7.
It can be written as -7<3 x-2<7.
To solve for the equality, 3x-2=7 and
[tex]$$3 x-2=-7$$[/tex]
First, solve the equation 3x-2=7, then add 2 on both sides.
[tex]$$\begin{aligned}&3 x=7+2 \\&3 x=9\end{aligned}$$[/tex]
Step 2 of 3
Simplify 3x=9 further, by dividing each side with 3 .
[tex]$$\begin{aligned}&\frac{3 x}{3}=\frac{9}{3} \\&x=3\end{aligned}$$[/tex]
Step 3 of 3
Similarly, 3x-2=-7
From the above term 3x-2=-7,
Add 2 on each side.
[tex]$$\begin{aligned}&3 x=-7+2 \\&3 x=-5\end{aligned}$$[/tex]
Simplify $3 x=-5$ further, by dividing each side with 3 .
[tex]$$\begin{aligned}&\frac{3 x}{3}=-\frac{5}{3} \\&x=-\frac{5}{3}\end{aligned}$$[/tex]
Therefore, the solution is [tex]$-\frac{5}{3} < x < 3$[/tex] or [tex]$\left\{-\frac{5}{3}, 3\right\}$[/tex]
A researcher who wishes to study the effects of a prenatal breastfeeding education program on the length of time African-American inner-city women breastfeed infants learns that 70% of women in the target population are unmarried. To achieve stratified random sampling in a sample of 50 subjects, the researcher will:
Select a random sample of 35 unmarried and 15 married subjects
A researcher who wishes to study the effects of a prenatal breastfeeding education program on the length of time African-American inner-city women breastfeed infants learns that 70% of women in the target population are unmarried.
To achieve stratified random sampling in a sample of 50 subjects, the researcher will:
Select a random sample of 35 unmarried and 15 married subjects.
hence, Select a random sample of 35 unmarried and 15 married subjects.
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show that,t for any triangle abc, even if b or c is an obtuse angle, a = b cos c + c cos b. use the law of sines to deduce the "addition formula" sin (b + c) = sin b cos c + sin c cos b.
For the triangle ABC, if B or C is an obtuse angle, then a = b cos C + c cos B according to the law of sines and the addition formula.
What is the law of sines states?For a triangle ABC with angles ∠A, ∠B, and ∠C and with sides a, b, and c
Thus, we can write,
sinA/a = sinB/b = sinC/c
or
a/sinA = b/sinB = c/sinC
Calculation:It is given that in a ΔABC,
The ∠B or ∠C is an obtuse angle.
So, ∠A = 180° - (B + C)
⇒ sin A = sin (180° - (B + C))
⇒ sin A = sin (B + C) (since we know that sin(180° - θ) = sinθ)
From the addition formula,
sin (B + C) = sin B cos C + sin C cos B
⇒ sin A = sin (B + C)
⇒ sin A = sin B cos C + sin C cos B
From the law of sines,
a/sinA = b/sinB = c/sinC = K
⇒ aK =sin A, bK = sin B, cK = sin C
On substituting,
⇒ sin A = sin B cos C + sin C cos B
⇒ aK = bK cos C + cK cos B
⇒ K(a) = K(b cos C + c cos B)
∴ a = b cos C + c cos B
Hence it is proved.
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i dont understand how to do this problem. Someone please assist me
Answer:
The unknown length = 12 units.
Step-by-step explanation:
The small and large triangles are similar because of the parallel lines.
So
6 / (6+4) = x / 20
10x = 120
x = 12.
ik this is a lot but pls helpp. thank you so much if you would help! this is due tomorrow
1. Five groups at summer camp have a total of 27 boxes of popsicles to share. How many boxes will each group recieve?
2. If 16 is divided by 5 what fraction would represent the remainder?
3. Suppose four friends want to share five cookies equally. How many cookies would each friend recieve?
4. If there are 90 minutes in a race and 4 teams of runners share this time equally, how many minutes will each team run?
5. Ten soccer teams are sharing 3 boxes of bottled water. How much of a box will each team get?
6. Dan has $695 in the bank. He wants to take out 2/5 of money. How much money should he take out?
7. You have 7 packs of paper share betweem you and 3 of your friends. If you share the paper equally, how much paper does each student get?
8. Four friends are taking a road trip. They want to share the driving equally. If the trip takes 6 hours, how long should each friend drive?
9. If 9 people want to share a 50-pound box of apples equally by weight, how many pounds of apples should each person get?
How many terms are in (3x^2-3)(3x^2+3)
The number of terms in the expression given is; 2.
How many term are in the expression given?It follows from the task content that the expression given is; (3x^2-3)(3x^2+3).
It therefore follows the converse of law regarding difference of two squares that the expression given can be rewritten as;
= 9x⁴ -9
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A group of students tossed coins and recorded 167 tails and 179 heads.
What is the experimental probability of heads?
Answer:
29893
Step-by-step explanation:
167 x 179
Part A
Simplify (6-2) (3-3)(3-6).
Answer:
0
Step-by-step explanation:
First, lets solve what's in the parentheses.
(6-2) = 4
(3-3) = 0
(3-6) = -3
Now, we put that into the equation.
4*0*-3
We get 0
Find the missing the side of the triangle. 19New A. 73‾√ in B. 72‾√ in C. 75‾√ in D. 77‾√ in
By applying Pythagorean's theorem, the missing side of this right-angled triangle is: A. 7√3 inches.
How to find the missing side?By critically observing the triangle shown in the image attached below, we can logically deduce that it is a right-angled triangle. Thus, we would find the missing side by applying Pythagorean's theorem:
z² = x² + y²
Also, the sides of this right-angled triangle are:
Hypotenuse = 14 inches.Opposite side = x inches.Adjacent side = 7 inches.Substituting the given parameters into the formula, we have;
14² = x² + 7²
196 = x² + 49
x² = 196 - 49
x² = 147
x = √147
x = √49 × √3
x = 7√3 inches.
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Answer:
A.) 7√3 in
Step-by-step explanation:
I got it correct on founders edtell
Choose the correct classification of 5x 3x4 − 7x3 10 by number of terms and by degree. third degree polynomial fourth degree polynomial sixth degree polynomial first degree binomial
The correct classification of the expression 5x + 3x⁴ - 7x³ + 10, is that it is the fourth-degree polynomial.
The degree of a polynomial is the highest power of the variable in the expression.
In the expression 5x + 3x⁴ - 7x³ + 10, there are 4 terms, and the term 3x⁴ involves the highest power = 4.
Therefore, the degree of the polynomial is 4.
Hence, we can say that the correct classification of the expression 5x + 3x⁴ - 7x³ + 10, is that it is the fourth-degree polynomial.
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7x-9y-6x+2y simplify
Answer:
x-7y
Step-by-step explanation:
7x-9y-6x+2y
Combine like terms
7x -6x -9y +2y
x -7y
x-7y
Answer:
x -7y
Step-by-step explanation:
7x - 9y - 6x + 2y
Rearrange so like terms are together (these are terms that are similar such as 5b and 7b; 7 and 1)
7x - 6x - 9y + 2y
Group into brackets one-by-one and solve
(7x-6x) -9y + 2y
x -9y + 2y
x (-9y + 2y)
x -7y
Note that 1x, 1b, 1z etc are simply written as their variable eg x, b and z
A third-grade teacher is introducing the concept of multiplication using manipulatives, pictures, and arrays. Last year several parents asked why their child wasn't learning to multiply the same way that they did. What should the teacher do in order to address potential questions this year
Answer:
The 3rd-grade teacher should say that the school systems and ways of teaching get updated each year.
Step-by-step explanation:
Children's parent's schools would have probably taught different techniques and ways of learning a topic. As years go by, more efficient ways of learning that topic are presented and selected.
If the parent would like the child to learn that way, they may teach them at home, but the school has decided on a system for at-school learning that seems to have worked the best.
Hopefully, that should answer the parent's questions!
pls and thank you if you help out
Answer: x = 80°
Step-by-step explanation:
Hi,
Since the angle is bisected, that means it is split in half and that both sides equal each other.
Therefore,
50 = 1/2x + 10
subtract 10 from both sides
40 = 1/2x
divide 40 by 1/2
x = 80°
Hope this helped :)
Which graph shows a system of equations with a solution at (2, -1)?
Graph fourth shows a system of equations with a solution at (2, -1) option fourth is correct.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
The question is incomplete.
The complete question is
Which graph shows a system of equations with a solution at (2,-1)?
The graph is in the picture, please refer to the attached picture.
As we can see in the graph there are two graphs of a function shown.
The first one is a parabola and the second one is a linear graph.
From the graph, the intersection point of the two groups is at (2, -1)
The intersection point is shown in graph fourth.
Thus, graph fourth shows a system of equations with a solution at (2, -1) option fourth is correct.
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Answer:
Graph 4
Step-by-step explanation:
Help pls I don’t understand WILL GIVE BRAINLIEST FOR FIRST ANSWER
Step-by-step explanation:
sin if -7.2 = -0.79 approximately -0.8
Hope you understand and hope this helps.
Good luck ✅.
The number of visitors to the homepage of an online magazine can be modeled by the equation y = 1100.74x − 1976.47, where x = 5 represents the year 2005 and y represents the total number of visitors.
The function y = 1100.74x - 1976.47 represent the total number of visitors x years after 2005.
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Let y represent the total number of visitors x years after 2005. Hence:
y = 1100.74x - 1976.47
The function y = 1100.74x - 1976.47 represent the total number of visitors x years after 2005.
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Which function has zeros at x = -2 and x = 5?
O f(x) = x2 + 2x - 10
• f(x) = x2 - 2x - 10
O f(x) = X2 + 3x - 10
® f(x) = x2 - 3x - 10
Answer:
f(x)=x²-3x-10
Step-by-step explanation:
\begin{gathered}f(x) = x {}^{2} - 3x - 10 \\ to \: find \: x \: intercept \:o r \: zero \: substitute \: f(x) = 0\: \\ 0 = x {}^{2} - 3x - 10 \\ x {}^{2} - 3x - 10 = 0 \\ x {}^{2} + 2x - 5x - 10 = 0 \\ x(x + 2) - 5x - 10 = 0 \\ x(x + 2) - 5(x + 2) = 0 \\ (x + 2).(x - 5) = 0 \\ x + 2 = 0 \\ x - 5 = 0 \\ x = - 2 \\ x = 5\end{gathered}
f(x)=x
2
−3x−10
tofindxinterceptorzerosubstitutef(x)=0
0=x
2
−3x−10
x
2
−3x−10=0
x
2
+2x−5x−10=0
x(x+2)−5x−10=0
x(x+2)−5(x+2)=0
(x+2).(x−5)=0
x+2=0
x−5=0
x=−2
x=5
therefore the zeros of the equation are x₁=-2,x₂=5
select all the con
Choose the graphs that indicate equations with no solution.
+
3x + 2 = −6(-ª)
y
A
4 -2
4+
2
-2-
2 4
4
+x+
8(-a)
-4 -2
HE
H
у
14
2.
2.
-2-
-4-
-4 -2
-2x + 4
4
4 =
y
4
2
2
+x
A
2
4
+2
3+1=
-4 -2
4
2.
12
x +
4
++++
-4
2
52 + 1 = 7(-z)
y
-2
5(-) + 2
4
TE
t
4
2-
14
+
+X
2
4
Hx
Answer:
Top leftBottom rightStep-by-step explanation:
For there to be no solution, the graphs must never intersect.
An equation is formed of two equal expressions. The graphs that indicate that the equation has no solution are the first graph from the top row and the last graph from the second row.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
The solution of a pair of equations is the point at which the graph of the two functions intersects each other. The number of times the two graphs intersect is the number of solutions to the pair of equations.
Since there are only two graphs where the graphs do not intersect.
Thus, the graphs that indicate that the equation has no solution are the first graph from the top row and the last graph from the second row.
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Find the distance between (-4,3,-6) and the origin ((X,Y,Z) Graph)
The distance between (-4,3,-6) and the origin is [tex]\sqrt{61[/tex]
How to determine the distance?The point is given as:
(x, y, z) = (-4,3,-6)
The origin is
(x, y, z) = (0,0,0)
The distance between the point and the origin is calculated as:
[tex]d = \sqrt{x^2 + y^2 + z^2[/tex]
So, we have:
[tex]d = \sqrt{(-4)^2 + (3)^2 + (-6)^2[/tex]
Evaluate
[tex]d = \sqrt{61[/tex]
Hence, the distance between (-4,3,-6) and the origin is [tex]\sqrt{61[/tex]
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y=3x + 4
x=3y + 4
x-4= 3y
how do divide x-4 by 3?
Answer:
x = 3y + 4
Step-by-step explanation:
add 4 to both sides
simplify
Given: ΔABC is isosceles; AB ≅ AC
Prove: ∠B ≅ ∠C
Triangle A B C is shown. Sides B A and A C are congruent.
We are given that ΔABC is isosceles with AB ≅ AC. Using the definition of congruent line segments, we know that .
Let’s assume that angles B and C are not congruent. Then one angle measure must be greater than the other. If m∠B is greater than m∠C, then AC is greater than AB by the .
However, this contradicts the given information that . Therefore, , which is what we wished to prove.
Similarly, if m∠B is less than m∠C, we would reach the contradiction that AB > AC. Therefore, the angles must be congruent.
AB = AC, they are equivalent. Since an isosceles triangle has the congruent angle property, mB = mC cannot be shown until AB=AC.
What is Isosceles triangles?Generally, Isosceles triangles are those that have two sides that are equal in length and two angles that are also equal in size.
Hence The sides and angles theorem for triangles., and the side AB is equal to the other side AC,
In conclusion, Assuming that the base angles, mB, and mC, are of equal measure, the triangle sides and angles theorem states that segment AC is larger than AB. The bigger angle of a triangle is always opposite to the longer side, according to the theorem.
AB is congruent to AC cannot be proven unless AB=AC then,
m<B = m<C because the isosceles triangle has the congruent angle property
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Answer:
AB = AC
Triangle parts relationship theorem
side AB is congruent to side AC
angle B is congruent to angle c
Step-by-step explanation:
Circle a is centered at point p, and point q lies on the circle. what other points also lie on circle a?
All the points which are at the distance of PQ from the center of the circle will be located on the circle.
What is a circle?A circle is a closed shape created by following a moving point on a plane while maintaining a constant distance from another point.
According to the given question, the circle named A has it's center at the point P and has a point Q on the circumference of the circle, so any point at the distance of PQ from the center of the circle will lie on the circumference of the circle.
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Answer:
Points S, T, and W
Hope this helps!
Step-by-step explanation:
Please help
The question is:
Which shows how to find the value when x = (-2) and y = 5?
I attached the equation & choices
Answer:
i believe the answer is 3^2(-2)^6/ 5^4
Step-by-step explanation:
solve for the missing variable 9 4 and x pls help need in 2 hours
Answer:
81/4
Step-by-step explanation:
By the Pythagorean theorem, the length of the altitude drawn from the hypotenuse is
[tex] \sqrt{65} [/tex]
This means that by the geometric mean theorem, that out of the two segments the hypotenuse is split into, the one with unknown length has length 65/4.
Thus, x = 65/4 + 4 = 81/4.
The times of all 15 year olds who run a certain race are approximately normally distributed with a given mean mu = 18 sec and standard deviation sigma = 1.2 sec. what percentage of the runners have times less than 14.4 sec?
The percentage of runners that have times less than 14.4 seconds that is P(x<14.4) is 0.0013499 which is approximately = 0.15%.
What is standard deviation?The standard deviation of a data set is defined as how the data is dispersed in relation to the mean.
From the question,
The raw time given (X) = 14.4 sec
The mean value(m) = 18sec
The standard deviation(d) = 1.2 sec
Using the formula,
z = X - m/ d
z= 14.4- 18/1.2
z = -3.6/1.2
z= -3
Using a Z table to find the percentage equivalent of P(x<14.4) is 0.0013499 which is approximately = 0.15%.
Therefore, the percentage of runners that have times less than 14.4 seconds that is P(x<14.4) is 0.0013499 which is approximately = 0.15%.
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What is the answer to this?
Answer: J
Step-by-step explanation:
Corresponding sides of similar triangles are proportional, so
[tex]\frac{3x-9}{x+8}=\frac{45}{30}=\frac{3}{2}\\\\2(3x-9)=3(x+8)\\\\6x-18=3x+24\\\\3x-18=24\\\\3x=42\\\\x=14\\\\\implies YX=14+8=22[/tex]
help please!!! i dont get it
The amount of money in the account if compounded quarterly at 6% after 9 years is $22,217
Compound interestPrincipal, P = $13,000Time, t = 9 yearsInterest rate, r = 6% = 0.06Number of periods, n = 4A = P(1 + r/n)^nt
= 13,000(1 + 0.06/4)^4×9
= 13,000(1 + 0.015)^36
= 13,000(1.015)^36
= 13000(1.709)
= $22,217
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help me please n^2, when n = 3
Answer: 9
Step-by-step explanation:
Given:
n², n = 3
Plug-in:
(3)²
Square 3:
3 * 3 = 9, so (3)² = 9
Simplify:
9
Esto es una división por favor ayuda
El resultado de esta división es 0.010
¿Cómo solucionar la operación matemática?Para solucionar la operación matemática debemos realizar los siguientes pasos:
Como el 81 es menos que el 7593, debemos poner un cero en el cociente y agregarle un cero al 81, entonces quedaría 810 dividido 7593.Como el 810 sigue siendo menor que el 7593, añadimos coma (,) y otro cero en el 810, entonces quedaría 8100 dividido 7593.Una vez tenemos el 8100 dividido 7593 realizamos la división, en este caso vemos cuántas veces cabe 7593 en 8100 y lo multiplicamos por ese número de veces (1).Una vez tenemos estos números a 8100 le restamos 7593 y obtenemos como resultado 507.Nuevamente, 507 es menos que 7593, entonces debemos agregar otro cero en el cociente para conocer las siguientes cifras decimales que falta.Ahora debemos averiguar cuántas veces cabe 7593 en 50700. Este número cabe 6 veces, entonces lo multiplicamos por 6 y luego restamos 50700 - 7593.Para conocer las siguientes cifras decimales debemos ir agregando un número cero en el resto para poder realizar las restas y seguir la división.Aprenda más sobre división en: https://brainly.com/question/24592547
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A survey was conducted to determine which type of lunch was most popular among the school's football team. How many more players prefer salad lunches than hot dog lunches?
Chart:
pizza- 15
hot dog-8
chicken-5
salad-10
burger-12
A. 3
B. 4
C. 2
D. 5
Answer:
ok this is pretty simple we just have to look at the chart
8 like hot dog
10 like salad
10-8=2
Hope This Helps!!!
Answer:B.2
Step-by-step explanation:
Find the area of the triangle
Answer:
12 yd^2 (c)
Step-by-step explanation:
A=1/2bh
= 1/2 x 8 x 3
=12 yd^2
Hope it helps!!!
Answer: 12 yd^2
Step-by-step explanation:
Area=[tex](1/2) *base*height\\[/tex]
here
base= 8yd
height =3 yd
putting values
area=(1/2)*(8)*(3)
area=12 yd^2