1 pointUse the distributive property to solve the following equation:z + 4(2z + 3) = 15АZ=41Z=Bz=3DZ=-1
Answers
We have the following:
\(z+4\mleft(2z+3\mright)=15\)solving for z:
\(\begin{gathered} z+8z+12=15 \\ 9z=15-12 \\ z=\frac{3}{9} \\ z=\frac{1}{3} \end{gathered}\)The answer is B. z = 1/3
Related Questions
Find the polar coordinates of rectangular coordinates (-√2,1). Limit θ to the interval [0,2pi) and round 2 dceimal places if needed
Answers
The point (-√2,1) can also be represented as (√3, 5.18) in polar coordinates.
To find the polar coordinates of the rectangular coordinates (-√2,1), we can use the following formulas:
r = √(x² + y²)
θ = tan^⁻1(y/x)
Plugging in the given values of (-√2,1), we get:
r = √((-√2)² + 1²) = √(2 + 1) = √3
θ = tan^⁻1(1/(-√2)) ≈ 2.0344 radians
Note that since the point (-√2,1) is in the second quadrant, we need to add π to the value of θ obtained from the inverse tangent in order to obtain an angle in the interval [0,2π). Thus, we have:
θ ≈ 2.0344 + π ≈ 5.1779 radians
Rounding to 2 decimal places as needed, we get the polar coordinates of (-√2,1) as (r,θ) ≈ (√3, 5.18).
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Twelve cards are numbered from 1 to 12 and placed in a box. One card is selected at random and not replaced. Another is randomly selected. What is the probability of selecting two even numbers?
Answers
In this case, we are to determine the probability of selecting two even numbers. This can be solved as follows:There are six even numbers: {2, 4, 6, 8, 10, 12}.We can use the concept of conditional probability since the first event affects the probability of the second event. This can be expressed as follows:
In this case, P(A) represents the probability of selecting an even number, and P(B|A) represents the probability of selecting an even number given that the first card selected was even. P(A) = 6/12 = 1/2 (there are six even numbers and twelve cards in total)P(B|A) = 5/11 (there are five even numbers left in the box after the first even number is selected, and eleven cards are left in total).
The probability of selecting two even numbers can be found by multiplying these probabilities: P(A) x P(B|A) = (1/2) x (5/11) = 5/22Therefore, the probability of selecting two even numbers is 5/22.Answer: 5/22
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Construct the indicated confidence interval for the population mean using the t-distribution. Assume the population is normally distributed.
picture of question below
Answers
Using the t-distribution, it is found that the confidence interval is (14.2, 14.8).
What is a t-distribution confidence interval?The confidence interval is:
\(\overline{x} \pm t\frac{s}{\sqrt{n}}\)
In which:
\(\overline{x}\) is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 18 - 1 = 17 df, is t = 2.1098.
The other parameters are given by:
\(\overline{x} = 14.5, s = 0.68, n = 18\).
Hence, the bounds of the interval are given by:
\(\overline{x} - t\frac{s}{\sqrt{n}} = 14.5 - 2.1098\frac{0.68}{\sqrt{18}} = 14.2\)
\(\overline{x} + t\frac{s}{\sqrt{n}} = 14.5 + 2.1098\frac{0.68}{\sqrt{18}} = 14.8\)
The confidence interval is (14.2, 14.8).
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I need help with this problem, what is x for this problem
Answers
Answer:
(5x-5)°=90°
5x-5=90
5x=90+5
=95
x=95÷5
=19
angle BCD=19+12
=31°
Simplify -16x^8/-8x^9
Answers
An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
The final expression of -16\(x^{8}\) / -8\(x^{9}\) is 2/x.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
-16\(x^{8}\) / -8\(x^{9}\)
= (-16/-8)\(x^{8 - 9}\)
= 2 \(x^{-1}\)
= 2/x
Thus,
The final expression of -16\(x^{8}\) / -8\(x^{9}\) is 2/x.
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Find the perimeter of the equilateral triangle.
9x16
8-3x
The perimeter is
Answers
The perimeter of the equilateral triangle will be 27x - 48.
How to calculate the perimeter?It should be noted that the perimeter of an equilateral triangle is the addition of all its sides or multiplying by three since they're equal.
Therefore, the perimeter of the equilateral triangle will be:
= 3(9x - 16)
= 27x - 48
Therefore, the perimeter of the equilateral triangle will be 27x - 48.
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Find the perimeter of the equilateral triangle.
9x - 16
What is the equation of the line that passes through the points (-5,1) and (5,5)
Answers
Answer:
The first one is -4 because pretend you had 5 green toy bears and 1 blue toy bears and you bring one of the bears and they fell down the mountain and then all you have is 4,4 means a negative so you have a -4,the second one is 0 and just do the same but don't use green toy bears because green toy bears stand for negative and blue toy bears stand for positive.I hope this helped.
Step-by-step explanation:
The histogram below gives the distribution of test scores for a sample of
students in a school in Alaska. Approximately how many students received a
score between 70.5 and 80?
Answers
Answer:
The correct answer is B.
Approximately 200 students received a test score between 70.5 and 80.
Which expression is equivalent to StartRoot 8 x Superscript 7 Baseline y Superscript 8 Baseline EndRoot? Assume x greater-than-or-equal-to 0.
x y squared StartRoot 8 x cubed EndRoot
2 x cubed y cubed StartRoot x y squared EndRoot
2 x cubed y Superscript 4 Baseline StartRoot 2 x EndRoot
4 x cubed y Superscript 4 Baseline StartRoot x EndRoot
Answers
The expression that is equivalent to StartRoot \(8 x^7 y^8\) EndRoot is (\(2 x^3 y^4\) StartRoot 2 x EndRoot)^2.
To understand why this is the case, let's break down each expression and simplify them step by step:
StartRoot \(8 x^7 y^8\) EndRoot:
We can rewrite 8 as \(2^3\), and since the square root can be split over multiplication, we have StartRoot \((2^3) x^7 y^8\) EndRoot. Applying the exponent rule for square roots, we get StartRoot \(2^3\) EndRoot StartRoot \(x^7\) EndRoot StartRoot \(y^8\) EndRoot.
Simplifying further, we have 2 StartRoot \(2 x^3 y^4\) EndRoot StartRoot \(2^2\) EndRoot StartRoot \(x^2\) EndRoot StartRoot \(y^4\) EndRoot. Finally, we obtain 2 \(x^3 y^4\) StartRoot 2 x EndRoot, which is the expression in question.
(\(2 x y^2\) StartRoot 8 x^3 EndRoot)^2:
Expanding the expression inside the parentheses, we have \(2 x y^2\)StartRoot \((2^3) x^3\) EndRoot. Applying the exponent rule for square roots, we get \(2 x y^2\) StartRoot \(2^3\) EndRoot StartRoot \(x^3\) EndRoot.
Simplifying further, we have \(2 x y^2\) StartRoot 2 x EndRoot. Squaring the entire expression, we obtain (\(2 x y^2\) StartRoot 2 x EndRoot)^2.
Therefore, the expression (\(2 x^3 y^4\) StartRoot 2 x EndRoot)^2 is equivalent to StartRoot \(8 x^7 y^8\) EndRoot.
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to earn an A in a course, a boy must have a final average of at least 88%. on the first four examinations, he as grades of 85%, 91%, 81%, and 83%. if the final examination counts as two grades, what must be get on the final to earn an A in the course?
Answers
He must get at least 97% on the final examination to earn an A in the course.
What must be get on the final to earn an A in the course?To earn an A in a course, a boy must have a final average of at least 88%. On the first four examinations, he had grades of 85%, 91%, 81%, and 83%. If the final examination counts as two grades, the final grade must be at least 91% to earn an A in the course. The total of all five grades must be equal to or greater than 88%. To calculate this, the four grades must first be added together to get the total of the first four grades. In this case, the total is 340. The final grade must then be calculated to get the total of all five grades to equal or exceed 88%.To find the final grade, the 340 must be divided by five, since the final counts as two grades. The result of this calculation is 68. This number must then be added to the final grade to reach a total of 88%. The final grade must therefore be at least 20 points higher than the 68, so 91% or higher. Therefore, to earn an A in the course, the boy must get at least 91% on the final examination, since this counts as two grades.To learn more about weighted average refer to:
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y Elizabeth buys a jar of 100 dog treats. In one month, she gives her dog
80 of the treats. What percent is this? What fraction is this? Draw a model to
support your answers.
Answers
Answer:
As Fraction: 80/100
As percentage: 80%
Step-by-step explanation:
I can't draw but could maybe explain; 80 out of 100 can be converted to 80/100 or 80%.
A container is in the form of a cuboid 20cm long, 3cm wide and 14cm high. Find, in
liters, the capacity of the container.
Answers
Answer:
840cm^3
Step-by-step explanation:
Given data
Length= 20cm
Width= 3cm
Height= 14cm
The expression for the volume/capacity of the container is
Volume= L*W*H
Volume= 20*3*14
Volume= 840cm^3
The average annual cost (in dollars) of tuition and fees at a 2 -year college for selected years is shown in the given table, where year 0 represents 2004. The data can be approximated by the equation y=83.66x+3915 . Predict the average annual cost in 2014 to the nearest dollar.
Answers
The average annual cοst in 2014 is $4751.6.
What is equatiοn?The definitiοn οf an equatiοn in algebra is a mathematical statement that demοnstrates the equality οf twο mathematical expressiοns. Fοr instance, the equatiοn 3x + 5 = 14 cοnsists οf the twο equatiοns 3x + 5 and 14, which are separated by the 'equal' sign.
Here the given equatiοn that represent the annual cοst in dοllars.
=> y = 83.66x+3915
Where x= number οf years
In 2004 , t = 0 years
Sο , In 2014 , t = 2014-2004 = 10 years.
Then average annual cοst in 2014 is,
=> y=83.66(10)+3915
=> y=836.6+3915
=> y = $4751.6.
Hence the average annual cοst in 2014 is $4751.6.
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Please I’ll give brainliest
A Ferris wheel reaches a maximum height of 60 m above the ground and takes twelve minutes to complete one revolution. Riders have to climb a m staircase to board the ride at its lowest point.
(a) [4 marks] Write a sine function for the height of Emma, who is at the very top of the ride when t = 0.
(b) [2 marks] Write a cosine function for Eva, who is just boarding the ride.
(c) (2 marks] Write a sine function for Matthew, who is on his way up, and is at the same height as the central axle of the wheel.
Answers
If Riders have to climb a m staircase to board the ride at its lowest point.
a. sine function for the height of Emma, who is at the very top of the ride when t = 0 is: h(t) = 60 sin(π/6 t).
b. a cosine function for Eva, who is just boarding the ride is: h(t) = m + 60 cos(π/6 t).
c. a sine function for Matthew is: h(t) = 30 sin(π/6 t).
What is the sine function for the height of Emma?(a) Let's assume that the Ferris wheel completes one full revolution in 12 minutes. The height of the Ferris wheel can be modeled by a sine function as it moves up and down periodically. When the Ferris wheel completes one revolution, it returns to its original position, so the period of the sine function is 12 minutes.
The maximum height of the Ferris wheel is 60 m, so the amplitude of the sine function is 60 m. When t = 0, Emma is at the very top of the ride, which means she is at the maximum height of the Ferris wheel. Therefore, the sine function for Emma's height, h(t), can be written as:
h(t) = 60 sin(2π/12 t)
Simplifying this equation, we get:
h(t) = 60 sin(π/6 t)
(b) Eva is just boarding the ride, which means she is at the lowest point of the ride when t = 0. The cosine function is ideal for modeling this situation, as it starts at its maximum value and reaches its minimum value after one-fourth of the period. Therefore, the cosine function for Eva's height, h(t), can be written as:
h(t) = m + 60 cos(2π/12 t)
Simplifying this equation, we get:
h(t) = m + 60 cos(π/6 t)
where m is the height of the staircase that Eva has to climb to board the ride.
(c) Matthew is at the same height as the central axle of the Ferris wheel, which means he is halfway between the maximum and minimum height of the ride. Therefore, the sine function for Matthew's height, h(t), can be written as:
h(t) = 30 sin(2π/12 t)
Simplifying this equation, we get:
h(t) = 30 sin(π/6 t)
Therefore sine function for the height of Emma, who is at the very top of the ride when t = 0 is: h(t) = 60 sin(π/6 t).
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Graph the parabola.
Plot five points on the parabola: the vertex, two points to the left of the vertex, and two points to the right of the vertex. Then click on the graph-a-function button.
Answers
The graph of the parabola is added as an attachment
The vertex is (0, 0)The points to the right are (1, 1) and (2, 4)The points to the left are (-1, 1) and (-2, 4)How to graph the parabola?From the complete question (added at the end of the solution), the equation of the parabola is given as
y = x²
When a parabola has the form of y = x², then the vertex of the parabola is
Vertex = (0, 0)
Set x > 0 to determine the points to the right
When x = 1
y = 1² = 1
When x = 2
y = 2² = 4
Set x > 0 to determine the points to the left
When x = -1
y = -1² = 1
When x = -2
y = -2² = 4
So, the points are
(1, 1), (2, 4), (-1, 1) and (-2, 4)
While the vertex is (0, 0)
Next, we plot the graph of the parabola using a graphing calculator
See attachment for the graph
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Complete question
Graph the parabola y = x²
Plot five points on the parabola: the vertex, two points to the left of the vertex, and two points to the right of the vertex. Then click on the graph-a-function button.
100 pts!!
Thanh rents a car. He has a fixed rate of $49.00 weekly, pays $14.00 per week for the optional insurance, and he spends $12.00 weekly on gas. What will Thanh's cost be per month (four weeks)?
Answers
Thanh's cost per month (four weeks) will be $300.00.The given fixed rate for Thanh is $49.00 per week. Thanh also pays $14.00 per week for the optional insurance and $12.00 weekly on gas.
To find Thanh's cost per month (four weeks), we need to multiply his weekly cost by 4.We can use the formula below to calculate Thanh's monthly cost.
Total weekly cost = Fixed rate + Insurance cost + Gas cost
Total weekly cost = $49.00 + $14.00 + $12.00
Total weekly cost = $75.00
The cost for Thanh per month (four weeks) = Total weekly cost × 4
Cost for Thanh per month (four weeks) = $75.00 × 4
Cost for Thanh per month (four weeks) = $300.00
Therefore, Thanh's cost per month (four weeks) will be $300.00.
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25 + 14 ÷ ( 5 - 3 )
its urgent please
Answers
Answer:
Step-by-step explanation:
25 + 14 / (5-3)
25 + 14 / 2
25 + 7
32
Select the correct answer.
It costs $480.00 to rent an apartment on the Gold Coast for a weekend. Last year it cost $400.00.
What method below shows how you would calculate the % increase?
Answers
The method is: Find the increase and find the ratio of the increase and the old price.
The percentage increase is 20%
What method below shows how you would calculate the percentage increase?A percentage is defined as the ratio that can be expressed as a fraction of 100.
The method below shows how you would calculate the % increase.
First step: Find the increase:
increase = 480 - 400 = $80
Second step: Find the ratio of the increase and the old price and multiply by 100 to express in percentage:
80/400 * 100 = 20%
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Merrisa is booking a holiday costing £660.
She needs to pay a deposit of of the total cost of the booking
How much does she pay?
Answers
The amount of money she will have to pay for booking of the holidays would be = £220
How to calculate the amount ofr deposit?The total amount of money that will cost Merrisa for booking of holidays = £660
The fraction of the total cost that she needs to deposit = 1/3
Therefore, the actual amount that she needs to deposit = 1/3 of £660
= 1/3× 660
= £220
Therefore, in conclusion, Merrisa would have to pay a total of £220 for booking of the holidays. This total amount is ⅓ of total cost of booking.
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what are the answers? thank you.
Answers
Answer:
176.78cm squared,23.57cm,Step-by-step explanation:
inorder to solve the area of the shaded area;°/360ñRsquared
arc length you use ;°/360ñD
Here's a graph of a linear function. Write the
equation that describes that function.
xpress it in slope-intercept form.
Answers
Answer:
the slope intercept form is y = (1/2)x - 1
Step-by-step explanation:
The slope-intercept form is, y = mx + b
We see from looking at the graph that,
at x = 0, y = -1
So, from this we find that b = -1
at x = 2, y = 0,
now, we find the slope m,
using,
\(m = \frac{y_{2} -y_1}{x_2-x_1}\)
Using x_2 = 2, y_2 = 0,
x_1 = 0, y_1 = -1, we get,
m = (0-(-1))/(2-0)
m = 1/2
So, the slope intercept form is,
y = (1/2)x - 1
Horizon Financial Inc. was organized on February 28. Projected selling and administrative expenses for each of the first three months of operations are as follows:
March $114,900
April 106,900
May 97,300
Depreciation, insurance, and property taxes represent $24,000 of the estimated monthly expenses. The annual insurance premium was paid on February 28, and property taxes for the year will be paid in June. 75% of the remainder of the expenses are expected to be paid in the month in which they are incurred, with the balance to be paid in the following month.
Prepare a schedule of cash payments for selling and administrative expenses for March, April, and May.
Answers
Answer:
Hey bro
Step-by-step explanation:
Determine if triangle XYZ with coordinates x (1, 1), y (5,6) and z (6,2) is a right triangle
Answers
Answer:
No(im not totally sure though because its slanted.)
Step-by-step explanation:
desmos.
16) Solve for side AB.
AB-
Round your answer to the nearest hundredth.
A) 5.45
B) 6.45
C) 7.45
Answers
Answer:
AB= 7.45
Anwer C)
Step-by-step explanation:
Cos (angle) = Nearest side / Huypothenuse
Cos(20) = 7 / AB
Cos(20) * AB = (7 /AB) * AB
Cos (20) * AB = 7
(Cos(20) *AB) / Cos(20) = 7 / Cos(20)
AB = 7 / cos(20)
AB= 7.45
In order to find the hypotenuse, we can use the trigonometric function “cosine”,
since.
Cosine =
Adjacent side (which is 7) / hypotenuse
Cos(50) = 7 / AB
AB = 7 / Cos(50)
AB = 10.89006678802289
AB ≈ 10.89
Have a good day ^^
NO LINKS! PLEASE help me with this problem 2f
Answers
\(u_1 = 43, \ d = 3\)
=======================================================
Work Shown:
a = \(u_1\) = first term
d = common difference
Let's start off plugging in n = 20 and then isolating the variable 'a'
\(u_n = u_1 + d(n-1)\\\\u_{20} = a + d(20-1)\\\\100 = a + 19d\\\\a = 100-19d\\\\\)
We'll come back to it later.
Now plug in n = 25
\(u_n = u_1 + d(n-1)\\\\u_{25} = a + d(25-1)\\\\115 = a + 24d\\\\a+24d = 115\\\\\)
Let's replace each copy of 'a' with 100-19d, because of the equation we solved for earlier.
\(a+24d = 115\\\\100-19d+24d = 115\\\\100+5d = 115\\\\5d = 115-100\\\\5d = 15\\\\d = 15 \div 5\\\\d = 3\\\\\)
Now we can finally determine 'a'
\(a = 100-19d\\\\a = 100-19*3\\\\a = 100-57\\\\a = 43\\\\\)
which is the first term.
To quickly list out the terms, I recommend using a spreadsheet. That way you can confirm the answers.
-----------------------
Another way to check the answer is to plug n = 20 into \(u_n = 43 + 3(n-1)\) and you should get \(u_{20} = 100\). Also, plugging n = 25 into that formula should yield \(u_{25} = 115\). These two facts fully confirm the answer. I'll let you perform this check.
Answer:
\(\textsf{c)} \quad u_1=43, \quad d=3\)
Step-by-step explanation:
General formula of an arithmetic sequence
\(\boxed{u_n=u_1+(n-1)d}\)
where:
uₙ is the nth term.u₁ is the first term.d is the common difference between terms.n is the position of the term.Given terms:
u₂₀ = 100u₂₅ = 115Substitute the given terms into the formula to create two equations:
\(\begin{aligned}\implies u_{20}=u_1+(20-1)d&=100\\u_1+19d&=100\end{aligned}\)
\(\begin{aligned}\implies u_{25}=u_1+(25-1)d&=115\\u_1+24d&=115\end{aligned}\)
Subtract the first equation from the second equation to eliminate u₁:
\(\begin{array}{rrclcl}& u_1 &+ &24d &= &115\\-& (u_1 &+ &19d& =& 100)\\\cline{2-6}&&&5d &=& \phantom{1}15\end{array}\)
Solve for d:
\(\implies 5d=15\)
\(\implies \dfrac{5d}{5}=\dfrac{15}{5}\)
\(\implies d=3\)
Substitute the found value of d into one of the equations and solve for u₁:
\(\implies u_1+19(3)=100\)
\(\implies u_1+57=100\)
\(\implies u_1=43\)
Therefore:
u₁ = 43d = 3What is the equation of the line that passes through the point (-4, 4) and has a
slope of -2:
Answers
Answer:
y=-2x-4
Step-by-step explanation:
Slope of line -2
Point (-4,4)
Equation :
(y-4) = -2(x+4)
y-4=-2x-8
y=-2x-4
name the quadrilateral with 2 pairs of consecutive congruent sides with diagonals that meet at a right angle
Answers
The quadrilateral you're describing is a Kite. A kite is a quadrilateral with two pairs of consecutive congruent sides, and its diagonals meet at a right angle.
Pablo Picasso is making one color version of all his paintings. He uses the colors in the following order and then starts over from the begining red, blue, pink, green, and purple. What color is painting 27
Answers
Answer:
The answer is blue
Step-by-step explanation:
There are five colors. So count by fives until you hit 25.
red, blue, pink, green, and purple. 5
red, blue, pink, green, and purple. 10
red, blue, pink, green, and purple. 15
red, blue, pink, green, and purple. 20
red, blue, pink, green, and purple. 25
Then count to 27.
red, blue. 27
So it is blue.
This question is determined by using simple mathematics tricks . Therefore, the color is blue on painting 27.
Given:
The order of painting begin from the red, blue, pink, green, and purple.
We need to determined the color of 27 painting.
According to question,
There are five colors for painting, count by fives until you hit 25.
Now, count the colors,
red, blue, pink, green, and purple - 5
red, blue, pink, green, and purple - 10
red, blue, pink, green, and purple - 15
red, blue, pink, green, and purple - 20
red, blue, pink, green, and purple - 25
Now at 26 there is red and at 27 there is blue color.
Therefore, the color is blue on painting 27.
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What is the absolute value of -8.35
Answers
Answer:
8.35
Step-by-step explanation:
To get absolute value, just make it the opposite
Answer: |-8.35| = 8.35
Step-by-step explanation: |-8.35| = 8.35
A rectangle is 27 in tall and 18 in wide. If
it is reduced to a height of 3 in, then how
wide will it be?
Answers
Answer: 2in
Step-by-step explanation: 27 divided by 3 is 9, then 18 divided by 9 is 2