Answer:
Second statement 2x2 + 8x – 24 = 0 Is true for the given conditions. When x = -6 2x2 + 8x – 24 = 0 Becomes 2(-6)2 + 8(-6) – 24 = 0 2(36) - 48 - 24 = 0 72 - 48 - 24 = 0 0 = 0 Which is true. When x = 2 2x2 + 8x – 24 = 0 Becomes 2(2)2 + 8(2) – 24 = 0 2(4) + 16 - 24 = 0 8 + 16 - 24 = 0 0 = 0 Which is true. So 2x2 + 8x – 24 = 0 will be answer.
The characteristics of the solutions of the polynomials are listed below:
The polynomial has two distinct real roots.The polynomial has two conjugated complex roots.The polynomial has two distinct real roots.The polynomial has two conjugated complex roots.Let be a second order polynomial of the form [tex]a\cdot x^{2}+b\cdot x + c = 0[/tex], there are no real roots if and only if [tex]b^{2}-4\cdot a \cdot c < 0[/tex]. Now we proceed to determine the nature of the roots of each polynomial:
1) [tex]x^{2} = 49[/tex]
This expression is equivalent to the polynomial [tex]x^{2}-49 = 0[/tex], then the discriminant is:
[tex]d = 0^{2}-4\cdot (1)\cdot (-49)[/tex]
[tex]d = 196[/tex]
The polynomial has two distinct real roots.
2) [tex]2\cdot x^{2} = -128[/tex]
This expression is equivalent to the polynomial [tex]2\cdot x^{2} +128 = 0[/tex], then the discriminant is:
[tex]d = 0^{2} - 4\cdot (2)\cdot (128)[/tex]
[tex]d = -1024[/tex]
The polynomial has two conjugated complex roots.
3) [tex]3\cdot x^{2}-16 = 32[/tex]
This expression is equivalent to the polynomial [tex]3\cdot x^{2}-48 = 0[/tex], then the discriminant is:
[tex]d = 0^{2}-4\cdot (3) \cdot (-48)[/tex]
[tex]d = 576[/tex]
The polynomial has two distinct real roots.
4) [tex]x^{2}+x+1 = 0[/tex]
The discriminant of this expression is:
[tex]d = 1^{2}-4\cdot (1)\cdot (1)[/tex]
[tex]d = -3[/tex]
The polynomial has two conjugated complex roots.
Nota - The original statement reports typing mistakes. Corrected form is presented below:
Select all the equations that do not have a real solution:
[tex]x^{2} = 49[/tex] [tex]2\cdot x^{2} = -128[/tex] [tex]3\cdot x^{2} - 16 = 32[/tex] [tex]2\cdot x^{2} + 36 = 18[/tex] [tex]x^{2}+x + 1 = 0[/tex]
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How do you do scientific notation with the number 0.2058
Answer:
2.058 x 10 to the -1st
Step-by-step explanation:
2×103 find the value
Answer:
206.
Step-by-step explanation:
100x2 = 200
3x2 = 6
200+6 = 206
Answer:
206
Step-by-step explanation:
multiplying anything by 2 is basically adding the exact same number to the original number. So basically: 103 +103
which equals 206
Please help me it’s due in a hour! I’ll do brainiest to the first right person and please explain how to.
Answer:
you got to draw a line cutting the shapes in half, then add the permiters or area of both squares
Step-by-step explanation:
The number of campers who sign up for archery each week is listed in the table. If the relationship is proportional, how many campers will sign up for archery in Week 3?
Archery Sign Up Total Campers
Week 1 36 120
Week 2 45 150
Week 3 ? 130
A. 54
B. 40
C. 41
D. 39
Answer:
[tex]\boxed{39}[/tex]
Step-by-step explanation:
[tex]\begin{array}{rcc}& \textbf{Archery Sign Up} & \textbf{Total Campers}\\\textbf{Week 1} & 36 & 120\\\textbf{Week 2} & 45 & 150\\\textbf{Week 3} & ? & 130\\\end{array}[/tex]
Let x = Total campers
and y = Archery sign up
In a direct proportionality,
y = kx
1. Calculate the value of k
Substitute a pair of values for x and y
150 = k × 45
Divide each side by 45
k = 150/45 = 10/3
2. Calculate the value of x in Week 3
[tex]\begin{array}{rcl}130& = & \dfrac{10}{3}x\\\\390 & = & 10x\\x & = & \mathbf{39}\\\end{array}[/tex]
[tex]\boxed{\textbf{39 campers}} \text{ will sign up for archery in Week 3}[/tex]
The diagram is a graph of your proportionality. It shows that y = 130 when x = 39.
2 + 2 divided by 2 is 3 why?
please help me
500+150+20+6=
In the figure below, the arc x is formed on the unit circle by angle θ . What is the measure of angle θ in radians? A x B π−x C π/2 D π
Answer:
A. x radians
Step-by-step explanation:
The circumference of the unit circle is
[tex]2\pi r=2\pi \cdot 1=2\pi[/tex]
The full rotation angle has the measure [tex]2\pi[/tex] radians.
So,
[tex]\begin{array}{cc}\text{Angle}&\text{Arc length}\\ \\2\pi &2\pi \\\theta &x\end{array}[/tex]
Write a proportion:
[tex]\dfrac{2\pi }{\theta}=\dfrac{2\pi }{x}[/tex]
Cross multiply:
[tex]2\pi x=2\pi \theta\\ \\\theta=x[/tex]
Ar which root does the graph of P(x) = (x + 4)(x + 7) cross the x-axis?
Answer:
(-4,0)(-7,0)
Step-by-step explanation:
The x axis is crossed when y = 0.
That happens in two places.
x +4=0 is one place
x = - 4 when it does.
x + 7 =0 is the other.
x = - 7
The sum of two consecutive numbers is 535
Answer:
267 and 268Step-by-step explanation:
[tex]n,\ n+1-\text{two consecutive numbers}\\\\535-\text{the sum}\\\\\bold{EQUATION:}\\\\n+(n+1)=535\\\\n+n+1=535\\\\2n+1=535\qquad\text{subtract 1 from both sides}\\\\2n+1-1=535-1\\\\2n=534\qquad\text{divide both sides by 2}\\\\\dfrac{2n}{2}=\dfrac{534}{2}\\\\n=267[/tex]
Bailey drove 290 miles in 4 hours. Find the miles per hour.
Answer:
72.5 miles/hour
Step-by-step explanation:
When we say "miles per hour" in English this just is simply the question "If Bailey drove for only one hour, how far did she go?". Now mathematically we can find this very easily by simply dividing 290 by 4, which is equal to 72.5. So Bailey travels 72.5 miles every hour.
If it is confusing about why we do this, think about splitting up 290 miles evenly between 4 hours, how many miles does each hour 'get'. Each would 'get' 72.5 miles. So for every hour Bailey drives she travels 72.5 miles which is the same as saying that she drove at 72.5 miles per hour.
Hope this helps!
Raj is mixing different colors of paint. The table shows the amount of each color paint Raj uses for each mixture. Select the two mixtures that will create the same color.
Answer:
Mixture 1 and Mixture 2 will create the same color
Step-by-step explanation:
we know that
If two mixtures create the same color, then the proportion of the painting in the mixtures must be the same
Let
x ----> the ounces of a red paint in the mixture
y ----> the ounces of a blue paint in the mixture
Verify the proportion of the paints in each mixture
Mixture 1) x=2, y=1
[tex]\frac{2}{1}=2[/tex]
Mixture 2) x=7, y=3.5
[tex]\frac{7}{3.5}=2[/tex]
Mixture 3) x=4.5, y=2
[tex]\frac{4.5}{2}=2.25[/tex]
Mixture 4) x=5.5, y=2.5
[tex]\frac{5.5}{2.5}=2.2[/tex]
therefore
Mixture 1 and Mixture 2 will create the same color, because have the same ratio
Answer:
Mixture 1 and Mixture 2
Step-by-step explanation:
It is given that Raj is mixing different colors (blue and red) of paint to make a new color.
If two mixtures have same ratio of red and blue color, then that will create the same color.
The ratio of red and blue color in each mixture is shown below:
Mixture 1: [tex]\frac{Red}{Blue}=\frac{2}{1}=2:1[/tex]
Mixture 2: [tex]\frac{Red}{Blue}=\frac{7}{3.5}=\frac{2}{1}=2:1[/tex]
Mixture 3: [tex]\frac{Red}{Blue}=\frac{4.5}{2}=\frac{9}{4}=9:4[/tex]
Mixture 4: [tex]\frac{Red}{Blue}=\frac{5.5}{2.5}=\frac{11}{5}=11:5[/tex]
From the above calculation it is clear that the ratio of red and blue color in mixture 1 and mixture 2 is same.
Therefore, Mixture 1 and Mixture 2 will create the same color.
A rectangle strip of land is 2 1/2 miles wide its area is 5/6 square mi.² what is the length of the strip of land
Answer:
1/3 mile
Step-by-step explanation:
Answer:
1/3 mile
Step-by-step explanation:
A rectangle strip of land is 2 1/2 miles wide its area is 5/6 square mi.² what is the length of the strip of land
what are the first four terms of the geometric sequence an=2 an-1 and a1=3
Answer:
3, 6, 12, 24
Step-by-step explanation:
This is a recursive formula which allows the next term in a sequence to be found from the previous term in the sequence
Given
[tex]a_{n}[/tex] = 2[tex]a_{n-1}[/tex] with a₁ = 3, then
a₂ = 2 × a₁ = 2 × 3 = 6
a₃ = 2 × a₂ = 2 × 6 = 12
a₄ = 2 × a₃ = 2 × 12 = 24
Thus the first 4 terms are 3, 6, 12, 24
Answer:
B.[tex]3,6,12,24[/tex]
Step-by-step explanation:
We are given that
[tex]a_n=2a_{n-1}[/tex]
[tex]a_1=3[/tex]
We have to find the first four terms of G.P
Substitute n=2
[tex]a_2=2a_1=2(3)=6[/tex]
Substitute n=3
[tex]a_3=2a_2=2(6)=12[/tex]
Substitute n=4
[tex]a_4=2a_3=2(12)=24[/tex]
Hence, the first four terms of G.P are given by
[tex]3,6,12,24[/tex]
Option B is true.
One day last week, 6 teachers joined 5/7 of the members of the running club in an after-school run. Priya counted a total of 31 people running that day. How many members does the running club have?
Answer:
The running club has 35 members
Step-by-step explanation:
Let
x ----> the total members of the running club
we know that
The total members of the running club multiplied by 5/7 plus 6 must be equal to 31 people
so
[tex]\frac{5}{7}x+6=31[/tex]
Solve for x
[tex]\frac{5}{7}x=31-6[/tex]
[tex]\frac{5}{7}x=25[/tex]
[tex]x=25(7)/5[/tex]
[tex]x=35\ members[/tex]
therefore
The running club has 35 members
Probability of a male having a blood circulation problem, given he's a smoker, is approximately 0.6667.
Step 1:
Identify the given probabilities:
Let [tex]\( P(A) \)[/tex] be the probability that a randomly chosen male has a blood circulation problem, which is [tex]\( 0.25 \)[/tex].
Let [tex]\( P(B|A) \)[/tex] be the probability that a male is a smoker given that he has a blood circulation problem, and it's twice the probability of being a smoker given not having a blood circulation problem.
Step 2:
Calculate [tex]\( P(B|\neg A) \)[/tex]:
Since males with blood circulation problems are twice as likely to be smokers as those without, \( P(B|\neg A) \) is half of [tex]\( P(B|A) \)[/tex], which is [tex]\( \frac{1}{2} \)[/tex].
Step 3:
Apply Bayes' theorem:
[tex]\[ P(A|B) = \frac{P(B|A) \times P(A)}{P(B)} \][/tex]
Step 4:
Calculate \( P(B) \):
[tex]\[ P(B) = P(B|A) \times P(A) + P(B|\neg A) \times P(\neg A) \][/tex]
Step 5:
Substitute values into Bayes' theorem and solve:
[tex]\[ P(A|B) = \frac{(2 \times P(B|\neg A)) \times P(A)}{(2 \times P(B|\neg A)) \times P(A) + P(B|\neg A) \times (1 - P(A))} \]\[ P(A|B) = \frac{(2 \times \frac{1}{2}) \times 0.25}{(2 \times \frac{1}{2}) \times 0.25 + \frac{1}{2} \times (1 - 0.25)} \]\[ P(A|B) = \frac{0.25}{0.25 + 0.125} \]\[ P(A|B) = \frac{0.25}{0.375} \]\[ P(A|B) \approx 0.6667 \][/tex]
Thus, the probability that a male has a blood circulation problem, given that he is a smoker, is approximately 0.6667.
Write and simplify an expression for 6 to the third power
Answer:
6 x 6 x 6
Step-by-step explanation:
Six to the third power means to multiply 6 by itself 3 times.
The standard exponential function is expressed as y = ab^x. The value for the simplified form of 6 to the third power is 216
Exponential functionsThe standard exponential function is expressed as y = ab^x
Given the following parameters
6 to the third power
This can be expressed as 6^3
6^3 = 6 * 6 * 6
6^3 =36 *6
6^3 = 216
Hence the value for the simplified form of 6 to the third power is 216
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What values could be substituted for x to make a true number sentence in x + 4 = x + 8
Carly and Gina read the following problem in their math class:
Seven cereal bars were shared equally by 3 children. How much did each child receive?
Carly and Gina solve the problem differently. Carly gives each child 2 whole cereal bars and then divides the remaining cereal bar among the 3 children. Gina divides all the cereal bars into thirds and shares the thirds equally among the 3 children.
a. Illustrate both girls’ solutions.
b. Explain why they are both right.
Answer:
Part a) and Part b) see the explanation
Step-by-step explanation:
Part a) Illustrate both girls’ solutions
Carly
Carly gives each child 2 whole cereal bars and then divides the remaining cereal bar among the 3 children
so
1) Each child receive first 2 whole cereal bars
the remaining is
[tex]7-(2+2+2)=7-6=1\ cereal\ bar[/tex]
2) Divides the remaining cereal bar among the 3 children
Each child receive 1/3 cereal bar
3) Each child receive in total
[tex]2+\frac{1}{3}=2\frac{1}{3}\ cereal\ bar[/tex]
Gina
Gina divides all the cereal bars into thirds and shares the thirds equally among the 3 children.
so
1) Divide the total bars by 3
Each child receive
[tex]\frac{7}{3}\ cereal\ bar[/tex]
Part b) Explain why they are both right
Compare the results
Carly ----> [tex]2\frac{1}{3}\ cereal\ bar[/tex]
Gina ----> [tex]\frac{7}{3}\ cereal\ bar[/tex]
Convert mixed number to decimal number
[tex]2\frac{1}{3}\ cereal\ bar=2+\frac{1}{3}=\frac{2*3+1}{3}=\frac{7}{3}\ cereal\ bar[/tex]
so
[tex]2\frac{1}{3}\ cereal\ bar=\frac{7}{3}\ cereal\ bar[/tex]
therefore
Carly and Gina are right
(A) Write an expression for a number that is five
times greater than two
I need help please?!!!
What is the inverse of the function f(x) = x +3?
h(x) = one-thirdx + 3
h(x) = one-thirdx – 3
h(x) = x – 3
h(x) = x + 3
Answer:
C. [tex]h(x)=x-3[/tex]
Step-by-step explanation:
We have been given a function [tex]f(x)=x+3[/tex]. We are asked to find the inverse of the given function.
First of all, we will replace [tex]f(x)[/tex] by y as:
[tex]y=x+3[/tex]
Now, we will interchange x and y variables as:
[tex]x=y+3[/tex]
Solve for y:
[tex]x-3=y+3-3[/tex]
[tex]x-3=y[/tex]
Switch sides:
[tex]y=x-3[/tex]
Therefore, the inverse function for the given function would be [tex]h(x)=x-3[/tex].
Answer:
C
Step-by-step explanation:
What’s the algebraic expression of ? Twice the sum of a number n and 2 ?
A 2(n+2)
B n+2•2
C 2n+2
D 2+(n+2)
Answer:
A is the answer. 2(n+2)
Answer:
A
Step-by-step explanation:
The sum of a number n and 2 is n + 2
Twice this sum is
2(n+ 2) → A
What is the answer for A?
Answer:
a=2B/d-l
Step-by-step explanation:
da-la=2B
1) Factor out an a from (da-la):
a(d-l)=2B
2) Divide both sides by (d-l):
a=2B/d-l
what is the value of x?
Answer: 36
Step-by-step explanation:
5x has to equal 180 and 180 divided by 5 equals 36. This means that x=36 and 4x=144
Answer: B. 36
Step-by-step explanation:
Look at the answer choices. The one that is an obtuse angle, 144, is going to be divided by 4. Your answer is B. 36
Use rounding to estimate the product
Question: 4 3/4 * 7 2/17
A. About 28
B. About 32
C. About 35
D. About 40
Answer:
The estimate of the product is about 35 answer C
Step-by-step explanation:
- We use rounding to estimate the product of two fractions
- The mixed number has whole number and fraction
- To round the mixed number we look to the fraction
- If the numerator is half or greater than half the denominator, then we
add the whole number by 1 and cancel the fraction
- If the numerator is less than half the denominator, then we keep the
whole number as it and cancel the fraction
- Ex: If the mixed number is [tex]2\frac{3}{4}[/tex], 3 is more than
half 4 then we will add 2 by 1 and cancel the fraction part, the
mixed number [tex]2\frac{3}{4}[/tex] after rounding is 3
- Ex: If the mixed number is [tex]5\frac{1}{4}[/tex], 1 is less than
half 4 then we will keep 5 as it and cancel the fraction part, the
mixed number [tex]5\frac{1}{4}[/tex] after rounding is 5
* Lets solve the problem
∵ In the part [tex]4\frac{3}{4}[/tex] 3 is more than half 4
∴ The rounding value of [tex]4\frac{3}{4}[/tex] is 5
∵ In the part [tex]7\frac{2}{17}[/tex] 2 is less than half 17
∴ The rounding value of [tex]7\frac{2}{17}[/tex] is 7
∴ [tex]4\frac{3}{4}*7\frac{2}{17}=5*7=35[/tex]
* The estimate of the product is about 35
he equation sin (40 degree) equals StartFraction b Over 20 EndFraction can be used to determine the length of line segment AC.
Triangle A B C is shown. Angle A C B is a right angle. The length of side A C is b and the length of hypotenuse A B is 20 centimeters.
What is the length of ? Round to the nearest tenth.
Answer:
The value of b is 12.9 cm
The value of a is 15.3 cm
Step-by-step explanation:
see the attached figure to better understand the problem
Find the value of b
we know that
in the right triangle ABC
The function sine of angle of 40 degrees is equal to divide the opposite side to the angle of 40 degrees (AC) by the hypotenuse (AB)
so
[tex]sin(40\°)=AC/AB[/tex]
Solve for AC
[tex]AC=(AB)sin(40\°)[/tex]
substitute the given value
[tex]AC=(20)sin(40\°)[/tex]
[tex]AC=12.9\ cm[/tex]
therefore
The value of b is 12.9 cm
Find the value of a
we know that
in the right triangle ABC
The function cosine of angle of 40 degrees is equal to divide the adjacent side to the angle of 40 degrees (BC) by the hypotenuse (AB)
so
[tex]cos(40\°)=BC/AB[/tex]
Solve for BC
[tex]BC=(AB)cos(40\°)[/tex]
substitute the given value
[tex]BC=(20)cos(40\°)[/tex]
[tex]BC=15.3\ cm[/tex]
therefore
The value of a is 15.3 cm
In the problem 5 divided 3/5 instead of dividing 5 by 3/5 we can find the answer by multiplying 5 by what number
Answer:
5/3
Step-by-step explanation:
If you do 5/ 3/5 what youre really doing is just doing two division problems which by the way equals 5/0.6 or 8.3333333
But one thing i realized when i was doing division by fractions is that if you flip the fraction then you can multiply and you get the same exact answer. SO lets try: 5/3 = 1.6666
1.6666*5=8.3333333
So you can use that trick when dividing a whole number by fractions. It makes it a lot easier.
The official answer is instead of dividing 5 by 3/5 you can instead multiply 5 by 5/3 and get the same answer!
Katie collects stamps. She has stamps from Canada, the U.S.A, and the rest of the world in a ratio of 1: 1.2: 1.5. She has 135 stamps from the rest of the world.
a) How many stamps are from Canada?
b) How many stamps are from the U.S.A?
c) What is the total number of stamps in Katie's collection?
(Please explain and show how you got those answers.)
Answer:
Step-by-step explanation:
: I got A)90
B)108
C)333
Hope that's right. I checked it 4 times.
Answer:
Step-by-step explanation:
A) 90
B) 108
C)333
-2(2x+1)=1 define x and explain why
Answer:
x=-3/4
Step-by-step explanation:
Use the distributive property a(a+b)= ab+bc:
-4x-2=1
Add a 2 to both sides:
-4x=3
Divide both sides by -4:
x=3/-4
This can be rewritten as -3/4
Someone plzzz help I’m lost :(
Answer:
j = (h-4) / k
Step-by-step explanation:
Unless there is more information given about this question somewhere else in the assignment, I'm assuming you are being asked to solve this equation for j.
If so, then its just a matter of rearranging the equation so that it is in the form
j = (expression containing other variables)
(h-4) / j = k (multiply both sides by j)
(h-4) = jk (divide both sides by k)
j = (h-4) / k
what is 3 divde by 3/4
[tex]\bf 3\div \cfrac{3}{4}\implies \cfrac{3}{1}\div\cfrac{3}{4}\implies \cfrac{~~\begin{matrix} 3 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{1}\cdot \cfrac{4}{~~\begin{matrix} 3 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\implies 4[/tex]