Answer:
Below.
Step-by-step explanation:
2x+4 = (x²)²÷2
2x + 4 = x^4/2
x^4 = 4x + 8
x^4 - 4x - 8 = 0
We can try trial an error to solve this
Looks like x = 2 fits it:
2^4 - 4(2) - 8
= 16 -8 -8 = 0
so x = 2 is one solution.
I can't find any other solution among other integers.
To find the other solutions you can draw a graph manually or by using software.
There will be either 1 or 3 more real solutions.
I used software to draw the graph and found one other solution:
x = -1.296
possible
An unusually wet spring has caused the size of a mosquito population in some city to increase by 6% each
day. If an estimated 230,000 mosquitoes are in the city on May 12, find how many mosquitoes will inhabit the
city on May 26. Use y = 230,000(1.06)* where x is number of days since May 12.
Answer:
about 520,000
Step-by-step explanation:
Following directions, we evaluate the equation by putting the value where the variable is and doing the arithmetic.
__
The value of x will be the number of days between May 26 and May 12. That value is ...
x = 26 -12 = 14
Then the number of mosquitos is estimated to be ...
y = 230,000(1.06^14) ≈ 520,008
About 520,000 mosquitos will inhabit the city on May 26.
_____
Additional comment
Typically, an "estimate" is one or two significant figures. So, 520,000 is a reasonable estimate. 520,008 has more precsision than can be justified.
1. A triangular garden is being formed with stones. The three sides measure 4 meters
by 6 meters by 7 meters. Which of the following is a true statement about the side
lengths of the triangle?
A The side lengths will nptform a triangle because 6 + 4 > 7
B. The side lengths will form a triangle because 4 + 6+ 7
C. The side lengths will not form a triangle because 7 + 4 < 6
D. The side lengths will form a triangle because 6 + 7 > 4
Answer:
The side lengths will form a triangle because 6+4 > 7
Step-by-step explanation:
For side lengths, the two smallest sides (ex. 6 and 4) must have a greater sum than then highest side length. Since 6+4 is greater than 7, it creates a triange. If it would have been 5+2 it would not have worked because it needs to be greater than, not less than or equal to.
Are the following functions exponential growth or decay?
Graphing Exponentials
a) f(x)=10(2)x
is this exponential growth? or exponential decay?
b) f(x)=2(0.5)x
is this a exponential growth? or exponential decay?
Answer:
a) growth b) decay
Step-by-step explanation:
In the function f (x) = b^x when b > 1, the function represents exponential growth.
In the function f (x) = b^x when 0 < b < 1, the function represents exponential decay.
a)b=2 > 1 this function growth
b)b=0.5 < 1 this function decay
What past paper is this, can you please put a link to the question paper that this question came from :
danil, gabriel and hadley share some money in the ratios 3:5:9 the difference between the amount of money that gabriel receives and the amount of money that hadley receives is 196 euros. work out the amount of money that danil receives
Using proportions, considering the ratios, it is found that Danil receives 65.33 euros.
What is a proportion?A proportion is a fraction of a total amount.
Danil, gabriel and hadley share some money in the ratios 3:5:9. Hence, the fraction of the total amount that Danil and Hadley receive are given by:
[tex]D = \frac{3}{17}n[/tex]
[tex]H = \frac{9}{17}n[/tex]
The amount of money that hadley receives is 196 euros, hence the total amount is found as follows.
[tex]196 = \frac{9}{17}n[/tex]
[tex]n = \frac{196 \times 17}{9}[/tex]
n = 370.22.
Hence, the amount received by Danil is given by:
[tex]D = \frac{3}{17}n = \frac{3}{17} \times 370.22 = 65.33[/tex]
More can be learned about proportions at https://brainly.com/question/24372153
#SPJ1
What is the line of the equation PARALLEL to the line y=3x+4 and through the y-intercept of -6?
Answer:
y = 3x - 6
Step-by-step explanation:
The line here is parallel
Slope remains the sameY-intercept is now -6Equation of line
y = mx + c [where m = slope and c = y-intercept]y = 3x - 6sin C = AB/??
BA
AC
BC
AB
Answer:
Step-by-step explanation:
Melissa weighed 14 packages. Their mean weight was 3 pounds. What was the total weight of the 14 packages?
pounds
The total weight of the 14 packages that Melissa weighed is gotten as; Total weight = 42 pounds
How to calculate mean?We are given;
Mean weight = 3
Now,formula for mean is;
Mean = total/sample size
We are given;
Sample size = 14
Thus;
3 = total/14
Total = 3 * 14
Total weight = 42 pounds
Read more about Mean average at; https://brainly.com/question/20118982
#SPJ1
Collect like terms
3
x
2
+
x
+
2
x
2
Answer:
x+10
Step-by-step explanation:
surface area of this right prism
[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
[tex] \textsf{Let's calculate the surface area of given right prism} [/tex]
[tex] \textbf{Area of Triangles :} [/tex]
[tex] \sf{\dfrac{1}{2}\cdot 16\cdot 12} [/tex][tex] \sf{8×12} [/tex][tex] \sf96 \: \: cm {}^{2} [/tex][tex] \textsf{Since there are two triangles, } [/tex]
[tex] \textsf{Area of Triangles = 96 × 2 = 192 cm²} [/tex]
[tex] \textbf{Now, calculate the Areas of rectangles :} [/tex]
[tex] \textsf{Area - 1 = 12 × 10 = 120 cm²} [/tex][tex] \textsf{Area - 2 = 16 × 10 = 160 cm²} [/tex][tex] \textsf{Area - 3 = 20 × 10 = 200 cm²} [/tex][tex] \textsf{Now add them all :} [/tex]
[tex] \textsf{120 + 160 + 200 + 192} [/tex][tex] \textsf{672 cm²} [/tex]
Answer:
Step-by-step explanation:
(16+12+20)*10+16*12= 48*10+192+480+192=672 c.m. squared
In the function y = 4x + 3, what is the value of the dependent variable if the value of the independent variable is 3?
Hannah made a table to show
the number of paragraphs in her
essays based on the number of
hours it took to write the essays.
Her data set is shown in the
table.
The equation of the line of best fit of Hannah's dataset represented by the graph is y = 1.25x - 1
How to determine the equation of the line of best fit?From the given figure, we have the following points on the line of best fit:
(x,y) = (2,1.5) and (4,4)
Start by calculating the slope (m) using:
[tex]m = \frac{y_2 -y_1}{x_2 -x_1}[/tex]
So, we have:
[tex]m = \frac{4 -1.5}{4 - 2}[/tex]
Evaluate the differences
[tex]m = \frac{2.5}{2}[/tex]
Divide
m = 1.25
The equation is then calculated using:
y = m(x - x₁) + y₁
So, we have:
y = 1.25(x - 2) + 1.5
Open the bracket
y = 1.25x - 2.5 + 1.5
Evaluate
y = 1.25x - 1
Hence, the equation of the line of best fit is y = 1.25x - 1
Read more about linear regression at:
https://brainly.com/question/17844286
#SPJ1
x - 9y = -19 What is thr slope intervept form and answer
Answer:
[tex]y=\frac{1}{9}x+19/9[/tex]
Step-by-step explanation:
First get y by itself.
[tex]x-9y=-19\\-9y=-x-19\\[/tex]
Then variable y itself
[tex]y=(-x-19)*-1/9\\y=\frac{1}{9}x+19/9[/tex]
2 ( x - 8 ) + 2 ( 12 ) how do i solve it?
What is the area of the figure below?
3 5/6in 6in
Answer:
120
Step-by-step explanation:
Are my answer correct? If not explain why.
Answer:
Step-by-step explanation:
a)
First I will calculate the equation of the line that goes trough the points
C (0, 0) and (-4, 3).
y= mx + b
y = [(3-0)/ (-4 -0) ] x + 0
y = (-3/4)x →the slope of tis line is (-3/4)
The slope of line l is the negative reciprocal of (-3/4) the slop of line that goes trough points C (0, 0) and (-4, 3) because the lines are ⊥.
Slope of line l is 4/3
b)
The equation of l is
y= (4/3)x + b
for point (x= -4, y = 3) that belongs to the line l, we have
3 = (4/3) (-4) + b
3 = (-16/3) + b
3 + (16/3) = b
(9+16)/3 = b
25/3 = b
The equation of the line l in slope intercept form is :
y = (4/3)x + (25/3)
c)
The radius of circle C is the distance between C (0, 0) and (-4, 3).
d² = (x2-x1)² +(y2-y2)²
d = √(-4-0)² +(3-0)²
d = √16+ 9
d = 5 → the radius of the circle C is 5
d)
Line l intersects the y-axis at (25/3) as we previously found out.
The radius is 5.
...therefore the distance between the line l's y-intercept and the circumference of the circle is
(25/3 ) - 5 = (25 - 5·3)/3 = 10/3
Find the volume of this rectangular prism.
6 cm
16 cm
1 cm
Answer:
The answer is 96
Step-by-step explanation:
Just write (16 x 6) x 1 = v and solve it by doing 16 x 6 and the answer would be 96 cm for the volume.
During a sale, a store offered a 15% discount on a TV that originally sold for
$540. After the sale, the discounted price of the TV was marked up by 15%.
What was the price of the TV after the markup? Round to the nearest cent.
0.765 (100) + .06 (.0765 x 100)
76.5 + .06 (76.5)
76.5 + 4.59 = 81.09 Chris will pay $81.09
A better way ( if you don't care to know the tax just the bottom line of what it will cost) would be to do:
0.765x x 1.06 = 76.5 x 1.06 = $81.09 too.
Why the 1 in front of the .06? The one includes the price of the coat so you don't have to add the tax on after.
Think about it like this. When you buy something you pay (even with an employee
discount) for all of it (100%) + the tax (in this case, it's 6%) So you pay 106% of the cost of the item. 106% = 1.06
A 15-foot ladder is set up 5 feet from the base of a building. How far up the building does the ladder reach? Round your answer to the nearest tenth of a foot
Answer:
20 feet up
Step-by-step explanation:
its quite simple really, just add 15+5 and you get 20
A triangular prism. The rectangular sides are 6 centimeters by 10 centimeters, 10 centimeters by 5 centimeters, and 10 centimeters by 5 centimeters. The 2 triangular bases have a base of 6 centimeters and height of 4 centimeters.
What is the surface area of the triangular prism shown?
32 square centimeters
120 square centimeters
184 square centimeters
1,560 square centimeters
\
Answer:
d
Step-by-step explanation:
1. Which indicates the dilation of a figure in the coordinate plane?
A. (x,y) —> (kx,ky)
B. (x,y) —> (-y,x)
C. (x,y) —> (-x,-y)
D. (x,y) —> (x+h,y+v)
Answer:
A. [tex](x,y)[/tex] ⇒ [tex](kx, ky)[/tex]
Step-by-step explanation:
Because that's the dilation equation or formula
8
300
60°
y
Find the value of y.
Solve for x 10(2x-4)=100x
A.x=7
B. x=3
C.x=1/2
D.x=-1/2
Answer:
The value of x = -1/2
Step-by-step explanation:
=> 10(2x-4)=100x
=> 20x - 40 = 100x
=> -40 = 100x - 20x
=> -40 = 80x
=> -40/80 = x
=> -1/2 = x
There are 5 white pencils and 6 red pencils in a box. One pencil is selected at random and not replaced. Another pencil is randomly selected from the remaining pencils. Determine whether this event is independent or dependent. Explain your answer.
A. Independent; the first pencil does not affect the sample space for the second one.
B. Independent; there are fewer pencils to choose from the second time.
C. Dependent; the first pencil does not affect the sample space for the second one.
D. Dependent; there are fewer pencils to choose from the second time.
Answer:
D
Step-by-step explanation:
You have 5 + 6 pencils, which is 11 pencilsThe probability you will get white is 5/11Prob you get red is 6/11If you pick up a pencil and do not replace it, you now only have 10 pencils leftThe prob you get a red or a white is dependent on what you picked up firststate the slope of the line perpendicular to the line -2x+5y=12
Answer:
- 5/2
Step-by-step explanation:
Arrange this line equation into y = mx + b form m = slope
y = 2/5x + 12/5
then perpindicular line = - 1/m = - 1/ (2/5) = - 5/2
Your local garden shop has plants on sale for $1.50 each. You are planning a vegetable
garden. You have $20 to spend on tomato plants
a.) write an inequality to find the greatest number of plants you can buy.
60 points please helppp
The inequality that can be used to find the greatest number of plants you can buy is p ≤$20 / 1.50.
What inequality can be used to find the greatest number of plants you can buy?Here are inequality signs and what they mean:
> means greater than
< means less than
≥ means greater than or equal to
≤ less than or equal to
The inequality sign that would be used in this question is ≤.
(cost of plant x number of plants) ≤ total spending money
$1.50p ≤ $20
p ≤ $20 / 1.50
To learn more about inequality, please check: https://brainly.com/question/5031619
Question 1
4 pts
Rewrite each equation so that the expression on one side could be graphed and the x-
intercepts of the
graph would show the solutions to the equation.
a. 3r? = 81
b. (x-1)(x+1)-9=5x
Cr? - Sx + 10 = 32
d. 6x(x-8)=29
The equations will be re-written such that the expression on one side can be graphed and the x-intercepts of the graph would indicate the solution.
What are the re-written equations?A) 3X² = 81
Rewritten, we have 3X² - 81 = 0
This is also = 3(X² - 27) = 0
B) (X - 1)(X + 1) - 9 = 5X
Open the brackets and we have X² - 1 - 9 - 5x = 0
Simplified, we have X² - 5X - 10 = 0
C) X² - 9x + 10 = 32
Collect like terms and we have:
X² - 9X - 22 = 0
D) 6x(x - 8) = 29
Expand the bracket and collect like terms such that the equation is equal to zero and we have
6X² - 48x - 29 = 0
Using Desmos Graphing, the following results can be obtained showing that x intercepts at:
(a) (-5.196, 0) & (5.196, 0)
(b) (-1.531, 0) & (6.531, 0)
(c) (-2, 0) & (11, 0)
(d) (-0.564, 0) & (8.564, 0)
Learn more about graphed equations at:
https://brainly.com/question/14323743
Hi, can you please help me answer this direct proportion question?
Somehow I keep getting it wrong and so I'd really appreciate some help. Please don't offer joke answers and possibly show me any workings out.
Thank you :)
Answer:
X = 100
Step-by-step explanation:
In proportion questions, they want you to multiply one of the sides by a variable, (i usually represent it with K) and then change the proportion sign to an equal.This is because proportional means they have a ratio between them, with one side increasing by "k" for each increase in the other side.Multiply the left by k, so [tex]y = \frac{k}{\sqrt{x} }[/tex]we know that y= 5, for x = 36, so sub this in the equation[tex]5 = \frac{k}{\sqrt{36} }[/tex]simplify[tex]5 = \frac{k}{6 }[/tex]re-arrange for k, k = 5*6 = 30now we know k, we can create the real equation, [tex]y = \frac{30}{\sqrt{x} }[/tex]sub in 3 as y[tex]3 = \frac{30}{\sqrt{x} }[/tex]x = 100What is the volume of the figure below if a = 4.3 units, b = 5.3 units, and c = 3 units?
a x a x c = 3.9 * 3.9 * 3 =45.6345.63 * 2 = 91.26a x b x c = 3.9 * 5.7 * 3 = 66.6966.69 + 91.26 = 157.95 cubic units
100 POINTS AND BRAINLIEST TO WHOEVER SOLVES IT
The edge length, s, of a regular tetrahedron is approximately given by , where V is the volume of the terahedron. Use a graphing calculator to graph the function. Estimate the volume of a regular tetrhedron with an edge length of 4 inches.
Volume of a tetrahedron with edge s
[tex]\\ \rm\Rrightarrow V=\dfrac{s^3}{6\sqrt{2}}[/tex]
According to question
s=4in[tex]\\ \rm\Rrightarrow V=\dfrac{4^3}{6\sqrt{2}}[/tex]
[tex]\\ \rm\Rrightarrow V=\dfrac{64}{6\sqrt{2}}[/tex]
[tex]\\ \rm\Rrightarrow V=\dfrac{32}{3\sqrt{2}}[/tex]
[tex]\\ \rm\Rrightarrow V=\dfrac{32}{4.2426406871192}[/tex]
[tex]\\ \rm\Rrightarrow V\approx 7.5425in^3[/tex]
Answer:
See below ~
Step-by-step explanation:
Volume of a tetrahedon
V = s³ / 6√2s = edge lengthSolving for V
V = (4)³ / 6√2V = 64 / 6√2V = 32 / 3√2V = 32√2 / 6V = 16√2 / 3V = 7.54 cubic inchesGraph
Ms. Rivera created two dot plots to compare the results of her recent science quiz for 1st period students compared to 7th period students. The dot plots are displayed to the right. Use this information to answer the questions below.
The dot plots is an illustration of charts and graphs
The average score of period 7 is greater than the average score of period 1
How to determine the period with the higher average?From the dot plots in the complete question, we have the following frequency tables
Period 1 Period 7
Score Students Score Students
55 1 65 1
70 1 75 3
75 6 80 5
80 6 85 6
85 2 90 3
90 3 95 2
95 1
The average is calculated using:
[tex]\bar x = \frac{\sum fx}{\sum f}[/tex]
For period 1, we have:
[tex]\bar x_1 = \frac{55 * 1 + 70 * 1 + 75 * 6 + 80 * 6 + 85 * 2 + 90 * 3 + 95 * 1}{1 + 1 + 6 + 6 + 2 + 3 + 1}[/tex]
Evaluate the sum
[tex]\bar x_1 = \frac{1590}{20}[/tex]
Evaluate the quotient
[tex]\bar x_1 = 79.5[/tex]
For period 7, we have:
[tex]\bar x_7 = \frac{65 * 1 + 75 * 3 + 80 * 5 + 85 * 6 + 90 * 3 + 95 * 2}{1 + 3 + 5 + 6 + 3 + 2}[/tex]
Evaluate the sum
[tex]\bar x_7 = \frac{1660}{20}[/tex]
Evaluate the quotient
[tex]\bar x_7 = 83[/tex]
By comparison, 83 is greater than 79.5
Hence, the average score of period 7 is greater than the average score of period 1
Read more about dot plots at:
https://brainly.com/question/12276901