Answer:
The measure of angle z is 30
Step-by-step explanation:
The angles of a triangle all add up to 180. So we can set these measures equal to 180 and solve for the unknown.
60 + 90 + z = 180
150 + z = 180
z = 30
Expand the following logs:
[tex]log_{2} \sqrt{ab^{3} }[/tex]
SHOW ALL WORK.
Answer:
[tex]\log_2(ab^3)^{\frac{1}{2}}=\frac{1}{2}[\log_2(a)+3\log_2(b)][/tex].
Step-by-step explanation:
The given logarithmic expression is [tex]\log_2\sqrt{ab^3}[/tex].
We rewrite the radical as an exponent to obtain;
[tex]\log_2(ab^3)^{\frac{1}{2}}[/tex].
Recall that; [tex]\log_a(M^n)=n\log_a(M)[/tex]
We apply this rule to obtain;
[tex]=\frac{1}{2}\log_2(ab^3)[/tex].
We now use the rule: [tex]\log_a(MN)=\log_a(M)+\log_a(N)[/tex]
This implies that;
[tex]=\frac{1}{2}[\log_2(a)+\log_2(b^3)][/tex].
We again apply: [tex]\log_a(M^n)=n\log_a(M)[/tex]
[tex]=\frac{1}{2}[\log_2(a)+3\log_2(b)][/tex].
The coffee Lily likes is composed of 97.3% water and 2.7% cocoa. The coffee John likes is composed of 96% water and 4% cocoa. How many ounces of water, x, should be added to 30 ounces of coffee that John likes to make the coffee that Lily likes?
30 ounces of the coffee John likes consists of
[tex]0.96\cdot30=28.8[/tex] ounces of water[tex]0.04\cdot30=1.2[/tex] ounces of cocoaTo this mixture we're adding [tex]x[/tex] ounces of water, so that the new mix has a total volume of [tex]30+x[/tex] ounces and matches the composition of the coffee Lily likes. This means it would consist of
[tex]0.973\cdot(30+x)=28.8+x[/tex] ounces of water[tex]0.027\cdot(30+x)=1.2[/tex] ounces of cocoa (same amount of cocoa as before because pure water is being added)Solve for [tex]x[/tex]:
[tex]0.973(30+x)=28.8+x\implies29.12+0.973x=28.8+x[/tex]
[tex]\implies0.39=0.027x[/tex]
[tex]\implies x\approx14.4[/tex]
###
Just to confirm: the new mixture consists of
[tex]28.8+14.4=43.2[/tex] ounces of water[tex]1.2+0=1.2[/tex] ounces of cocoagiving a total volume of [tex]43.2+1.2=44.4[/tex] ounces of coffee, and [tex]\dfrac{43.2}{44.4}\approx0.973[/tex], as required.
In triangle ABC, c is the hypotenuse, 0=25°, and b =3, Find the length of c ?
Answer:
[tex]\large\boxed{c\approx3.31}[/tex]
Step-by-step explanation:
Use cosine:
[tex]cosine=\dfrac{adjacent}{hypotenuse}[/tex]
[tex]\cos\theta=\dfrac{b}{c}[/tex]
We have:
[tex]\theta=25^o\to\cos25^o\approx0.9063\\\\b=3[/tex]
Substitute:
[tex]\dfrac{3}{c}=0.9063[/tex]
[tex]\dfrac{3}{c}=\dfrac{9063}{10000}[/tex] cross multiply
[tex]9063c=30000[/tex] divide both sides by 9063
[tex]c\approx3.31[/tex]
Do the following lengths form a right triangle?
Answer:
22, no: 24, yes
Step-by-step explanation:
22 wouldn't be a triangle because when you square both sides
8^2+6^2= 81 (but 9^2 is 81) the 2 values surpasses 81
24 would be a triangle because
8^2+6^2=10^2
64+36=100
At a new exhibit in the Museum of Science, people are asked to choose between 73 or 175 random draws from a machine. The machine is known to have 98 green balls and 61 red balls. After each draw, the color of the ball is noted and the ball is put back for the next draw. You win a prize if more than 70% of the draws result in a green ball. [You may find it useful to reference the z table.] a. Calculate the probability of getting more than 70% green balls. (Round your intermediate proportion values and “z” value to 2 decimal places, and final answer to 4 decimal places.) b. Would you choose 73 or 175 draws for the game?
Answer:
Probability of winning first situation: 0.0793
Probability of winning second situation: 0.0146
You should go with the first option
Step-by-step explanation:
See attached photo for answers. For this situation you need to identify p-hat, p, q and n.
P-hat, p, and q all stay the same for both situations, only n changes.
p-hat is the proportion of green balls we want, which is 0.7
p = 98/159 = 0.62
q = 0.38 because q = 1 - p, which in this case is q = 1 - 0.62 = 0.38
n = 73 for the first situation, and n = 175 for the second situation
Using the normal probability distribution and the central limit theorem, it is found that:
a)
With 73 draws, there is a 0.0808 = 8.08% probability of getting more than 70% green balls.
With 175 draws, 0.015 = 1.5% probability of getting more than 70% green balls.
b)
Due to the higher probability of getting more than 70% green balls, 73 draws should be chosen.
Normal Probability Distribution
In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.Central Limit Theorem
It states that the sampling distribution of the sample means with size n can be approximated to a normal distribution. For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]Item a:
98 green balls out of 158, thus [tex]p = \frac{98}{158} = 0.6203[/tex]
Out of 73 draws:
[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.6203(0.3797)}{73}} = 0.0568[/tex]
The probability of more than 70% green balls is 1 subtracted by the p-value of Z when X = 0.7, thus:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.7 - 0.6203}{0.0568}[/tex]
[tex]Z = 1.4[/tex]
[tex]Z = 1.4[/tex] has a p-value of 0.9192.
1 - 0.9192 = 0.0808
With 73 draws, there is a 0.0808 = 8.08% probability of getting more than 70% green balls.
Out of 175 draws:
[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.6203(0.3797)}{175}} = 0.0367[/tex]
Then:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.7 - 0.6203}{0.0367}[/tex]
[tex]Z = 2.17[/tex]
[tex]Z = 2.17[/tex] has a p-value of 0.985.
1 - 0.985 = 0.015.
With 175 draws, 0.015 = 1.5% probability of getting more than 70% green balls.
Item b:
Due to the higher probability of getting more than 70% green balls, 73 draws should be chosen.
A similar problem is given at https://brainly.com/question/24663213
Which sentence best describes the function below? F(x) = x^3 - x^2 -9x + 9 A. It fails the vertical line test B. It is a one-to-one function C. It is not a function D. It is a many-to-one function
Answer:
D
Step-by-step explanation:
This function graphed as the picture attached below show is a function. It passes the vertical test. However, it does not pass the horizontal line. This means the function is not one-to-one but many-to -one.
Parallelogram abcd is divided into two triangles along diagonal ac. if you know the area of the parallelogram, how do you find the area of triangle abc
Answer :- Just try area/2 or half the area of the triangle
Answer:
Step-by-step explanation:
The area of triangle abc would be half the area of the parallelogram. The two triangles are of equal area.
WILL THANK, GIVE FIVE STARS, AND BRAINLIEST!!!!!
(a) Let the function [tex]$f$[/tex] be defined on the complex numbers as [tex]$\[f(z) = (1+i)z.\]$[/tex] Prove that the distance between [tex]$f(z)$[/tex] and [tex]$0$[/tex] is a constant multiple of the distance between [tex]$f(z)$[/tex] and [tex]$z$[/tex], and find the value of this constant.
(b) Let the function [tex]$g$[/tex] be defined on the complex numbers as [tex]$\[g(z) = (a + 2 i)z\]$[/tex] for some real value of [tex]$a$[/tex]. Then if [tex]$g(z)$[/tex] is equidistant from [tex]$0$[/tex] and [tex]$z$[/tex] for all [tex]$z$[/tex], what is [tex]$a$[/tex] equal to?
Answer:
(a) √2
(b) 1/2
Step-by-step explanation:
(a) The ratio of distances will be the magnitude of the ratio f(z)/(f(z) -z), so will be ...
|(1+i)z/((1+i)z -z)| = |(1+i)/i| = |1-i| = √(1+1) = √2
___
(b) You want |g(z) -0| = |g(z) -z|, so you have ...
|(a +2i)z -0| = |(a +2i)z -z|
|(a +2i)|·|z| = |a-1 +2i|·|z|
Dividing by the magnitude of z and squaring both sides, we have ...
a^2 +4 = (a-1)^2 +4
0 = -2a +1 . . . . . . subtract a^2+4 and simplify
1/2 = a . . . . . . . . . divide by -2, add 1/2
given the two sets, which statement is true?
A = {1, 2}
B = {1, 2, 3, 4}
a. B c A
b. 3 c A
c. 4 c A
d. A c B
e. none of the above
Answer:
[tex]\large\boxed{A\subset B}[/tex]
Step-by-step explanation:
[tex]A=\{1,\ 2\},\ B=\{1,\ 2,\ 3,\ 4\}\\\\A\subset B,\ \text{because all elements of the set A are the elements of the set B.}[/tex]
1.5 horas para realizar un afinamiento; 0,2 horas para limpiar la bateria; 0,75 horas para cambiar el aceite y el filtro del motor; 1,45 horas para cambiar y alinear luces; y 1,3 horas para reparar el sistema de aire acondicionado. Por hora de trabajo cobra 32,8 soles; ?Cuánto cuesta la reparación del automóvil?
El costo total por concepto de la reparación del automóvil es de 170,56 soles.
¿Cómo calcular el costo total de la reparación de un automóvil?
En este problema se debe determinar el costo total por concepto de la reparación de un automóvil. Dimensionalmente hablando, se tiene que el costo total se determina mediante la siguiente fórmula:
C = c · Δt
Donde:
c - Costo unitario por hora de trabajo, en soles por hora. Δt - Tiempo, en horas.C - Costo total, en soles.A continuación, el costo total se calcula según la información suministrada por el enunciado de la pregunta:
C = (32,8 soles / hora) · (1,5 horas + 0,2 horas + 0,75 horas + 1,45 horas + 1,3 horas)
C = 170,56 soles
A kite is designed on a rectangular grid with squares that measure 1cm by 1 cm. A hexagonal piece within the kite will be reserved for the company logo. Use the grid to identify the perimeter and area of the space reserved for the logo.
Answer:
The answer is the first answer
P = 8 + 8√17 cm
A = 96 cm²
Step-by-step explanation:
* Lets study the figure
- Its a kite with two diagonals
- The shortest one is 12 cm
- The longest one is 26 ⇒ axis of symmetry of the kite
* To find the area reserved for the logo divide
the hexagonal piece into two congruent trapezium
- The length of the two parallel bases are 4 cm and 8 cm and
its height is 8 cm
- The length of non-parallel bases can calculated by Pythagoras rule
∵ The lengths of the two perpendicular sides are 2 cm and 8 cm
- 8 cm is the height of the trapezium
- 2 cm its the difference between the 2 parallel bases ÷ 2
(8 - 4)/2 = 4/2 = 2 cm
∴The length of the non-parallel base = √(2² + 8²) = 2√17
* Now we can find the area of the space reserved for the logo
- The area of the trapezium = (1/2)(b1 + b2) × h
∴ The area = (1/2)(4 + 8) × 8 = (1/2)(12)(8) = 48 cm²
∵ The space reserved for the logo are 2 trapezium
∴ The area reserved for the logo = 2 × 48 = 96 cm²
* The area of the reserved space for the logo = 96 cm²
* The perimeter of the reserved space for the logo is the
perimeter of the hexagon
∵ The lengths of the sides of the hexagon are:
4 cm , 4 cm , 2√17 cm , 2√17 cm , 2√17 cm , 2√17 cm
∴ The perimeter = 2(4) + 4(2√17) = 8 + 8√17 cm
* The perimeter of the reserved space for the logo = 8 + 8√17 cm
A right triangle has legs measuring 4.5 meters and 1.5 meters. The length of a second triangle are proportional to the lengths of the legs of the first triangle. Which could be the length of the legs of the second triangle? A) 6m and 2m B) 8m and 5m C) 7m and 3.5m D) 10m and 2.5m E) 11.25 and 3.75m
Answer:
A. 6m and 2m
E. 11.25m and 3.75m
Step-by-step explanation:
we know that
If two figures are similar, then the ratio of its corresponding sides is proportional
so
Verify each case
case A) 6m and 2m
[tex]\frac{6}{4.5}=\frac{2}{1.5} \\ \\6(1.5)=2(4.5)\\ \\9=9[/tex]
therefore
The legs are proportional
case B) 8m and 5m
[tex]\frac{8}{4.5}=\frac{5}{1.5} \\ \\8(1.5)=5(4.5)\\ \\12\neq22.5[/tex]
therefore
The legs are not proportional
case C) 7m and 3.5m
[tex]\frac{7}{4.5}=\frac{3.5}{1.5} \\ \\7(1.5)=3.5(4.5)\\ \\10.5\neq15.75[/tex]
therefore
The legs are not proportional
case D) 10m and 2.5m
[tex]\frac{10}{4.5}=\frac{2.5}{1.5} \\ \\10(1.5)=2.5(4.5)\\ \\15\neq11.25[/tex]
therefore
The legs are not proportional
case E) 11.25m and 3.75m
[tex]\frac{11.25}{4.5}=\frac{3.75}{1.5} \\ \\11.25(1.5)=3.75(4.5)\\ \\16.875=16.875[/tex]
therefore
The legs are proportional
Please help me out................
Answer: 90 Degrees
Step-by-step explanation:
I believe the answer is 90° because the diagonals of a rhombus, just like a square form right triangles. in reality, a rhombus is just a square that was pulled to the side a bit.
A good source to play with rhombuses is on mathisfun. It can help you build a study guide and further your understanding of the subject.
how much tax is owned or how much refund is expected tax due 1324 and tax withheld 678
the proper term is tax LIABILITY ( i e what you would owe if you had not paid in anything ).
then because the liability is greater than the w/h ; 1374 - 678 = owed
Hope this helps!
The tax due is $1,324 and the tax withheld is $678. By subtracting the tax withheld from the tax due, we find that an additional $646 is owed and no refund is expected.
Tax is due or the expected refund, you need to compare the total tax owed to the amount of tax withheld. In this scenario, the tax due is $1,324, and the tax withheld is $678.
First, subtract the tax withheld from the tax due: $1,324 (tax due) - $678 (tax withheld) = $646.
If the result is positive, as it is in this case, it means that you owe $646 more in taxes. If the result were negative, it would indicate an expected refund of that amount.
Therefore, no refund is expected because the tax withheld does not cover the total amount of tax due. The individual will owe an additional $646.
will mark brainliest !!!!!!
The base of the middle triangle is 3 and the base of the larger one is 6, so the larger triangle is twice the size of the middle one.
Multiply the height of the middle one by 2 to get the height of the larger one, which is labeled n.
n = 5 x 2 = 10
in the symbol AB, the letter A represents a(n) ANSWERS : a.) segment b.) ray c.) point d.)plane
It would have to be C. point.
Since it says AB that marks two points and a line in between them. If only talking about A, it would be a point.
Option: C is the correct answer.
c.) Point
Step-by-step explanation:In the symbol AB:
AB represents a line segment which connects point A to point B.
If there would be an arrow over this with right arrow then it would represent a ray which originates at point A an it extends to infinity from the other direction.
Hence the letter A will represent a : Point.
Help with this question, please! I don't understand it!
Answer:
18 cm
Step-by-step explanation:
The area (A) of a kite is
A = [tex]\frac{1}{2}[/tex][tex]d_{1}[/tex][tex]d_{2}[/tex], that is
[tex]\frac{1}{2}[/tex] × 8 × [tex]d_{2}[/tex] = 72
4 × [tex]d_{2}[/tex] = 72 ( divide both sides by 4 )
[tex]d_{2}[/tex] = 18 cm
If angle one and angle five a vertical angles and angle one equals 55° then angle five will equal _____?
55º
vertical angles are congruent
In Cherokee County, the fine for speeding is $17 for each mile per hour the driver is traveling over the posted speed limit. In Cherokee County, Kirk was fined $221 for speeding on a road with the posted speed limit of 30mph. Kirk was fined for traveling at what speed, in miles per hour? Explain you answer in 3 sentences. (2 points)
Answer:
43 miles per hour
Step-by-step explanation:
We know that in Cherokee County, the speed tickets amounts are calculated on the basis of $17 for each mile above the speed limit.
Since Kirk was fined $221, we can easily calculate the excess speed he was caught at by dividing $221 by $17/mile, which gives us 13 miles.
Since he was caught in a zone where the posted speed limit was 30, and that he exceeded it by 13 miles per hour... we know he was going at 43 miles per hour.
Is an elevation of -10 feet closer or farther from the surface of the ocean than an elevation of -8 feet?
Answer:
farther
Step-by-step explanation:
The negative sign means that it is 10 feet down while -8 is only 8 feet down
An elevation of -10 feet is farther from the surface of the ocean than - 8 feet.
What is something else that can not be negative?Time can not be negative as we can not go to past.Time is unidirectional.
According to the given question we have to determine Is an elevation of -10 feet closer or farther from the surface of the ocean than an elevation of -8 feet.
We know that -10 is less than -8 as it is present in the left of -8 in the number line that is one case.
But here we are measuring elevation which is length and we know length can not be negative so going by the idea of length an elevation of -10 feet is farther from the surface of the ocean we are diving 10 feet below here so more distance.
learn more about these type of problems here :
https://brainly.com/question/8725611
#SPJ2
Which will have a higher effective interest rate — a payday loan for $1900 that is due in 14 days with a fee of $80, or a payday loan for $1900 that is due in 12 days with a fee of $80?
A. A payday loan for $1900 that is due in 12 days with a fee of $80, since it has the longer period
B. A payday loan for $1900 that is due in 14 days with a fee of $80, since it has the shorter period
C. A payday loan for $1900 that is due in 14 days with a fee of $80, since it has the longer period
D. A payday loan for $1900 that is due in 12 days with a fee of $80, since it has the shorter period
Answer:
It's D.
Step-by-step explanation:
The shorter period loan has the same total interest for the same loan amount, so it has the higher effective interest rate: 80/12 is higher than 89/14.
A payday credit for $1900 that is expected in 12 days with an expense of $80, since it has the less limited time frame. Then the correct option is D.
What is the loan?When buying or recovering proposals in a common asset, a financial backer may be paid a business fee or commission. Deals with fees can be set up in a variety of ways.
Banks and insurance providers may offer their clients a grace period, which allows them to postpone payment for a predetermined amount of time after the time limit (after the payment deadline).
A payday credit for $1900 that is expected in 14 days with a charge of $80 or a payday credit for $1900 that is expected in 12 days with a charge of $800.
A payday credit for $1900 that is expected in 12 days with an expense of $80, since it has the less limited time frame. Then the correct option is D.
More about the load link is given below.
https://brainly.com/question/20039214
#SPJ2
A polynomial function has roots – 6 and 2. Which of the following could represent this function?
f(x) = (x + 6)(x + 2)
f(x) = (x – 6)(x – 2)
f(x) = (x – 6)(x + 2)
f(x) = (x + 6)(x – 2)
Answer:
f(x) = (x + 6)(x – 2)
Step-by-step explanation:
The roots of a polynomial are the solutions to its factors. This means you can set the factors equal to 0 and the roots are the solution. Working backwards, if the roots are x = -6 and x = 2 then they must have resulted from factors x + 6 and x - 2. This is true since x + 6 = 0 has solution x = -6. And x-2 = 0 has solution x = 2.
So the polynomial has factors (x+6)(x-2). The solution is f(x) = (x + 6)(x – 2).
Answer:
the answer is 4
Step-by-step explanation:
just did it on edge.
your welcome
Write ln 2x + 2x ln x -ln 3y as a single logarithm.
Answer: option c.
Step-by-step explanation:
To solve this problem you must keep on mind the properties of logarithms:
[tex]ln(b)-ln(a)=ln(\frac{b}{a})\\\\ln(b)+ln(a)=ln(ba)\\\\a*ln(b)=ln(b)^a[/tex]
Therefore, knowing the properties, you can write the expression gven in the problem as shown below:
[tex]ln2x+2lnx-ln3y=ln2x+lnx^2-ln3y\\\\=ln(2x)(x^2)-ln3y\\\\=ln(\frac{2x^3}{3y})[/tex]
Therefore, the answer is the option c.
Answer:
C
Step-by-step explanation:
We can use 3 properties here to write this as single logarithm:
1. Log (a^b) = b Log a
2. Log x + Log y = Log (x*y)
3. Log x - Log y = Log (x/y)
We can use property #1 first to write:
[tex]ln2x+2lnx-ln3y\\=ln2x+lnx^2-ln3y[/tex]
Now we can use property #2 and property #3 to write this as single logarithm:
[tex]ln2x+lnx^2-ln3y\\=ln(\frac{(2x)(x^2)}{3y})\\=ln(\frac{2x^3}{3y})[/tex]
Answer choice C is right.
(Q8) The graph of an exponential function is given. Which of the following is the correct equation of the function? (Picture Provided)
Answer:
b. [tex]y=3.9^x[/tex]
Step-by-step explanation:
Remember that the standard exponential function is [tex]y=ab^x[/tex]
where
[tex]a[/tex] is the coefficient
[tex]b[/tex] is the base
If [tex]b>0[/tex], the function is growing
If [tex]0<b<1[/tex] the graph is decaying
We can infer from the graph that the function is growing, so we can discard [tex]y=0.45^x[/tex] and [tex]y=0.73^x[/tex].
Now, to evaluate our tow remaining equations, we are using the test values [tex]x=0[/tex] and [tex]x=1[/tex]:
For [tex]y=1.8^x[/tex]
For [tex]x=0[/tex]
[tex]y=1.8^0[/tex]
[tex]y=0[/tex]
For [tex]x=1[/tex]
[tex]y=1.8^1[/tex]
[tex]y=1.8[/tex]
The graph passes through the points (0,1) and (1, 1.8)
For [tex]y=3.9^x[/tex]
[tex]x=0[/tex]
[tex]y=3.9^0[/tex]
[tex]y=0[/tex]
[tex]x=1[/tex]
[tex]y=3.9^1[/tex]
[tex]y=3.9[/tex]
The graph passes through the points (0,1) and (1, 3.9)
We can see in the graph when [tex]x=1[/tex], [tex]y[/tex] is almost 4, so we can conclude that the correct equation is [tex]y=3.9^x[/tex]
Which polynomial identity will prove that 64+27=91?
A. Difference of Squares
B. Difference of Cubes
C. Sum of Cubes
D. Square of a Binomial
Answer:
Sum of cubes. I just did this test.
Step-by-step explanation:
Honestly I have no real explanation other than a sum would be adding, whereas difference would be subtracting.
Hence, the polynomial identity shows the sum of cubes.
What is the polynomial?
Polynomials are sums of terms of the form [tex]kx^n[/tex], where [tex]k[/tex] is any number and [tex]n[/tex] is a positive integer.
Here given that,
[tex]64+27=91[/tex]
Addition of two values gives us the third number.It is representing the sum of cubes.
Hence, the polynomial identity shows the sum of cubes.
To know more about the polynomial
https://brainly.com/question/11154053
#SPJ5
Henley could draw 12 sketches in 5 hours . How many sketches could she draw in 3 hours
Henley can draw 7.2 sketches in 3 hours based on the proportion of 12 sketches in 5 hours; however, when rounding to the nearest whole number, she can complete 7 sketches.
The problem at hand is a simple proportion problem where we want to find out how many sketches Henley can make in 3 hours given that she can make 12 sketches in 5 hours. To solve this, we set up a ratio that relates her drawing rate to the time spent drawing:
12 sketches x sketches
----------- = ------------
5 hours 3 hours
We can solve for x by cross-multiplying and then dividing by the coefficient of x:
12 sketches [tex]\times[/tex] 3 hours = 5 hours [tex]\times[/tex] sketches
x = ([tex]12 sketches \times 3 hours[/tex]) / 5 hours
x = 7.2 sketches
Therefore, Henley can draw 7.2 sketches in 3 hours. However, since one cannot draw a fraction of a sketch, we round down to the nearest whole number. Henley can thus draw 7 sketches in 3 hours assuming a consistent drawing speed.
Noah has 5 meters of rope. How many pieces of rope of length 1/2 meter can he cut from it?
Answer:
10
Step-by-step explanation:
We are taking 5m and dividing by 1/2 m
5 ÷ 1/2
Copy dot flip
5 * 2/1
10
We can get 10 pieces from the rope
10 pieces of rope of length 0.5 meter can be cut from the rope of total length 5 meters.
Given :
Total length of Rope = 5 m.
Division is about breaking something into many pieces. The number you are dividing is called the dividend. The number you are "dividing by" is the divisor. The answers to your division problems are called quotients.
Number of pieces of rope of length 0.5 meter will be calculated as follows:
[tex]=\dfrac{5}{0.5}[/tex]
[tex]=10[/tex]
10 pieces of rope of length 0.5 meter can he cut from it.
For more information, refer the link given below
https://brainly.com/question/25028413
I need help on this please guys, thank you.
1. Add or subtract. Show your work for each problem by using boxes, circles, colored underlines, OR grouping
to identify the like terms before you simplify.
4 points each (1 point for correct answer, 3 points for showing ALL work.)
a. (−2x
^2 −4x+ 13)+ (12x
^2 + 2x −25) b. (7x
^2 + 4x − 26)− (−7x^
2 − 3x + 15)
2. Multiply. Show all your work including boxes, circles, colored underlines, distributing, OR grouping to identify
the like terms before you simplify.
6 points (1 point for correct answer, 5 points for showing ALL work)
(5x − 1)(6x
^2 + 3x + 7)
3. Find the roots. Show your work. List your steps correctly.
6 points (2 points for correct answer, 2 points for showing ALL work, 2 points for writing the steps of the
problem)
(n) = n
^2 − 6n − 16
Answer:
The solutions to your three problem question are:
1.
a. 10x^2 −2x -12
b. 14x^2 + 7x -41
2. 30x^3 + 9x^2 + 32x - 7
3.
n1 = 8
n2 = -2
Step-by-step explanation:
1. First problem
We need to Add or subtract the expressions to find the equivalent terms
a) (−2x^2 −4x + 13)+ (12x^2 + 2x −25)
We add together the terms with the same exponent
= (−2x^2 + 12x^2 ) + (−4x + 2x) + (13 - 25)
= (10x^2 ) + (−2x) + (-12)
= 10x^2 −2x -12
b) (7x^2 + 4x − 26)− (−7x^2 − 3x + 15)
= (7x^2 + 4x − 26) + (7x^2 + 3x - 15)
We add together the terms with the same exponent
= (7x^2 + 7x^2 ) + (4x + 3x) + (- 26 -15)
= (14x^2 ) + (7x) + (-41)
= 14x^2 + 7x -41
2. Second problem
(5x − 1)(6x^2 + 3x + 7)
We need to multiply to find the equivalent expression\
(5x − 1)(6x^2 + 3x + 7) = (5x)*(6x^2 + 3x + 7) + (-1)*(6x^2 + 3x + 7)
= [(5x)*(6x^2 + 3x + 7)] + [-6x^2 - 3x - 7]
= [(5x*6x^2) + (5x*3x) + (5x*7)] + [-6x^2 - 3x - 7]
= [(30x^3) + (15x^2) + (35x)] + [-6x^2 - 3x - 7]
We add together the remaining terms
= [(30x^3) + (15x^2 - 6x^2) + (35x - 3x) - 7]
= (30x^3) + (9x^2) + (32x) - 7
= 30x^3 + 9x^2 + 32x - 7
3. Third problem
f(n) = n^2 − 6n − 16
We need to find the roots for the polynomial f(n)
That is, the values of n for which f(n) = 0
We can find an analysis of the function in the images below.
Lets use the quadratic formula
Let y = ax2 + bx + c
a = 1
b = -6
c = -16
x = -b/(2*a) ± sqrt(b^2 -4ac)/(2*a)
x = 3 ± 10/2 = 3 ± 5
roots
n1 = 8
n2 = -2
13) Convert 300 seconds to minutes. There are 60 seconds in 1 minute. A) 5 minutes B) 15 minutes C) 30 minutes D) 150 minutes
Answer:
5 minutes
Step-by-step explanation:
300 seconds / x minutes = 60 seconds / 1 minute
300 = 60x; divide both sides by 60 to get x; 5 = x
Each shape has 1 whole. What fraction greater than 1 names the parts that are shaded
Answer:
THERE IS NO PICTURE OR VISUAL REPRESENTATION
Step-by-step explanation: