Given:
Three consecutive even numbers have a sum where one half of that sum is between 90 and 105.
Required:
To write an inequality to find the three numbers and to solve the inequality.
Explanation:
(a)
Three consecutive even numbers have a sum where one half of that sum is between 90 and 105.
[tex]90<\frac{1}{2}(n+(n+2)+(n+4))<105[/tex](b)
[tex]undefined[/tex]Rewrite the following equation in slope-intercept form.
10x − 10y = –1 ?
Write your answer using integers, proper fractions, and improper fractions in simplest form.
Answer:
y = x + 1/10
Step-by-step explanation:
Rewrite the following equation in slope-intercept form: 10x − 10y = –1 ?
slope intercept form: y = mx + b so you are solving for y:
10x − 10y = –1
subtract 10x from both sides:
10x − 10y – 10x = –1 – 10x
-10y = –1 – 10x
divide all terms by -10:
-10y/(-10) = –1/(-10) – 10x/(-10)
y = 1/10 + x
rearrange for slope intercept form: y = mx + b
y = x + 1/10
Answer:
[tex]y=x+\dfrac{1}{10}[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}[/tex]
Given equation:
[tex]10x-10y=-1[/tex]
To write the given equation in slope-intercept form, perform algebraic operations to isolate y.
Add 10y to both sides of the equation:
[tex]\implies 10x-10y+10y=10y-1[/tex]
[tex]\implies 10x=10y-1[/tex]
Add 1 to both sides of the equation:
[tex]\implies 10x+1=10y-1+1[/tex]
[tex]\implies 10x+1=10y[/tex]
[tex]\implies 10y=10x+1[/tex]
Divide both sides of the equation by 10:
[tex]\implies \dfrac{10y}{10}=\dfrac{10x+1}{10}[/tex]
[tex]\implies \dfrac{10y}{10}=\dfrac{10x}{10}+\dfrac{1}{10}[/tex]
[tex]\implies y=x+\dfrac{1}{10}[/tex]
Therefore, the given equation in slope-intercept form is:
[tex]\boxed{y=x+\dfrac{1}{10}}[/tex]
Please help me with this problem so my son can better understand I have attached an image of the problem
We have to solve for c:
[tex](c+9)^2=64[/tex]When we have quadratic expressions, we have to take into account that each number has two possible square roots: one positive and one negative.
We can see it in this example: the square root of 4 can be 2 or -2. This is beacuse both (-2)² and 2² are equal to 4.
Then, taking that into account, we can solve this expression as:
[tex]\begin{gathered} (c+9)^2=64 \\ c+9=\pm\sqrt[]{64} \\ c+9=\pm8 \end{gathered}[/tex]We then calculate the first solution for the negative value -8:
[tex]\begin{gathered} c+9=-8 \\ c=-8-9 \\ c=-17 \end{gathered}[/tex]And the second solution for the positive value 8:
[tex]\begin{gathered} c+9=8 \\ c=8-9 \\ c=-1 \end{gathered}[/tex]Then, the two solutions are c = -17 and c = -1.
We can check them replacing c with the corresponding values we have found:
[tex]\begin{gathered} (-17+9)^2=64 \\ (-8)^2=64 \\ 64=64 \end{gathered}[/tex][tex]\begin{gathered} (-1+9)^2=64 \\ (8)^2=64 \\ 64=64 \end{gathered}[/tex]Both solutions check the equality, so they are valid solutions.
Answer: -17 and -1.
The height of a triangle is 3 m
more than twice the length of the
base. The area of the triangle is
76 m2. Find the height of the triangle. Help me!
The triangle has a height of 19 meters.
How to determine the height of a triangle
In this problem we find the area of a triangle, in square meters, and the relationship between its height (h) and its base length (b), both in meters. We must solve the following expression to determine the height:
A = (1 / 2) · b · h
h = 3 + 2 · b
A = 76
Then,
76 = (1 / 2) · b · (3 + 2 · b)
152 = b · (3 + 2 · b)
152 = 3 · b + 2 · b²
2 · b² + 3 · b - 152 = 0
Finally, we find the roots of the polynomial by quadratic formula:
b₁ = 8, b₂ = - 19 / 2
Since, lengths are non-negative real numbers, the only possible solution is b = 8 and the height of the triangle is:
h = 3 + 2 · 8
h = 19
The height of the triangle is 19 meters.
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What are the roots of the function represented by the table?
From the table, the root of the function is a point where y = 0.
Therefore,
The root of the function are ( 4, 0 ) and ( -3, 0 )
Final answer
I and III only Option B
HELP ASAP 15 POINTS Determine which integer will make the equation true.
4x + 7 = 23
S = {3, 4, 5, 6}
3
4
5
6
Answer:
S = 4
Step-by-step explanation:
23-7 = 16
16/4 = 4
4x4+7 = 23
Answer: S = 4
Step-by-step explanation:
23 - 7 = 16
16 / 4 = 4
4 x 4 + 7 = 23
A new shopping mall is gaining in popularity. Every day since it opened, the number of shoppers is 20%, percent more than the number of shoppers the day before. The total number of shoppers over the first 4 days is 671.How many shoppers were at the mall on the first day?Round your final answer to the nearest integer.
if the number of shoppers increases by 20% daily and 671 shoppers had visited over 4 days then let the num ber of shoppers on the first day be x
The numebr of shopperes the next day will be
= x(100 + 20)%
= 1.2x
teh number of shoppers the day after
= 1.2x(100 + 20)%
= 1.44x
the next day, the number
= 1.44x (100 + 20)%
= 1.728x
Given that the total number of people that have shopped after 4 days is 671 then
x + 1.2x + 1.44x + 1.728x = 671
5.368x = 671
x = 671/5.368
= 125
if the number of shoppers increases by 20% daily and 671 shoppers had visited over 4 days then let the num ber of shoppers on the first day be x
The numebr of shopperes the next day will be
= x(100 + 20)%
= 1.2x
teh number of shoppers the day after
= 1.2x(100 + 20)%
= 1.44x
the next day, the number
= 1.44x (100 + 20)%
= 1.728x
Given that the total number of people that have shopped after 4 days is 671 then
x + 1.2x + 1.44x + 1.728x = 671
5.368x = 671
x = 671/5.368
= 125
Parallel and Perpendicular LinesDetermine whether the following lines are parallel, perpendicular, orneither. Write the corresponding letter on the line next to the question.A = parallel, B = perpendicular, or C = neither1. y = }x+6 and y =- *x + 4
One of the criteria for lines being perpendicular is the fact that the slope of the function in a perpendicular line is the inverse of the slope of the first times -1.
And as you can see m (being the slope of the first equation) is the inverse of the second equiation:
[tex]m=\frac{7}{3},m_1=-\frac{1}{m}[/tex][tex]-\frac{1}{m}=-\frac{1}{\frac{7}{3}}=-\frac{3}{7}[/tex]Therefore line 1 is perpendicular to line 2.
how do I know which picture goes with the correct equation
If B is between A and C, but B is not midpoint, then the graph would be
The equation would be
[tex]AC=AB+BC[/tex]On the other hand, if B is between A and C, and B is a midpoint, the graph would be
The equation would be
[tex]AB=BC[/tex]A cookie jar contains 8 oatmeal, 7 peanut butter and 10 sugar cookies. What is theprobability that Ivan will pull a peanut butter cookie from the jar, eats it, then pulls asugar cookie from the jar?A. 17/49B.7/60C. 17/600D. 7/600
Answer:
B. 7/60
Explanation:
Given;
Number of oatmeal cookies = 8
Number of peanut butter cookies = 7
Number of sugar cookies = 10
Total number of cookies = 8 + 7 + 10 = 25
So the probability of Ivan pulling a peanut butter cookie from the jar can be determined as seen below;
[tex]\begin{gathered} P(\text{peanut butter cookie) }=\frac{\text{ number of peanut butter cookies}}{\text{Total number of cookies}} \\ P(\text{peanut butter cookie) }=\frac{7}{25} \end{gathered}[/tex]So if Ivan ate the peanut butter cookie he pulled (he did not replace it), it means that the total number of cookies will be 24, so the probability of pulling a sugar cookie from the jar will now be;
[tex]\begin{gathered} P(sugar\text{ cookie) }=\frac{\text{ number of sugar cookies}}{\text{Total number of cookies}} \\ P(sugar\text{ cookie) }=\frac{10}{24}=\frac{5}{12} \end{gathered}[/tex]So we can determine the probability that Ivan will pull a peanut butter cookie from the jar, eats it, then pulls a sugar cookie from the jar by multiplying the above probabilities;
[tex]P(peanut,sugar)=\frac{7}{25}\times\frac{5}{12}=\frac{7}{5}\times\frac{1}{12}=\frac{7}{60}[/tex]Therefore, the probability is 7/60
Find any domain restrictions on the given rational equation:
X+2
-25
+1=
8x
2x-10
Select all that apply.
A. x = 5
127
B. x = -2
C. X = -5
D. x = 0
The domain restrictions on the rational equation
[tex]\frac{x +2}{x^{2} -25 }+1 =\frac{8x}{2x-10}[/tex] are Options A and C. x = 5 and x = - 5 .
What are domain restrictions?A domain restriction is a prescription or criterion that limits the range of possible values for a function. A domain in mathematics is the collection of all values for which a function produces a result. Domain constraints allow us to create functions defined over numbers that meet our needs.Functions defined in pieces are made up of various functions with distinct domain restrictions. Some functions are not allowed to accept values that would make them undefined.How to find the domain restrictions?
The numbers that makes the denominators zero and the entire expression infinite or undefined are the domain restrictions.
Consider the denominators,
[tex]x^{2}[/tex] - 25 ≠ 0 --(1)
[tex]x^{2}[/tex] ≠ 25
x ≠ 5 and x ≠ -5
2x - 10 ≠ 0 ---(2)
2x ≠ 10
x ≠ 10/2
x ≠ 5
The domain restrictions on the rational equation [tex]\frac{x +2}{x^{2} -25 }+1 =\frac{8x}{2x-10}[/tex] are
x ≠ 5 and x ≠ -5 .
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Complete the equation of the line through (-7,-3) and (-2,4)
If one line passes through the points (x₁, y₁) and (x₂, y), the slope of the line can be calculated using the formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}...(1)[/tex]Additionally, the equation can be expressed in point-slope form as:
[tex]y-y_2=m(x-x_2)...(2)[/tex]From the problem, we identify:
[tex]\begin{gathered} (x_1,y_1)=(-7,-3) \\ \\ (x_2,y_2)=(-2,4) \end{gathered}[/tex]Then, we calculate the slope of the line using (1):
[tex]m=\frac{4-(-3)}{-2-(-7)}=\frac{4+3}{-2+7}=\frac{7}{5}[/tex]Finally, we find the equation of the line using (2):
[tex]\therefore y-4=\frac{7}{5}(x+2)[/tex]PLEASE HELP I WILL GIVE BRAINLYEST!! ALGEBRA 1 HW
Answer:
look below
Step-by-step explanation:
at Frank's auto plaza there are currently 11 new cars, 8 used cars, 12 new trucks and 10 used trucks. frank is going to choose one of these vehicles at random to be the deal of the month. what is the probability that the vehicle that frank chooses is used or is a car?
11 new cars
8 used cars
12 new trucks
10 used trucks
Total vehicles
11+8+12+10 = 41
It is the denominator of the fraction.
The subset "used" + "cars" has 11 (new cars) + 8 (used cars) + 10 (used trucks) = 29 elements.
It is the numerator of the fraction.
P(U or C) = 29/41
PRYZ is a rhombus. If RK=5, RY = 13, and YRZ = 67, find each measure.
The Solution:
The correct answer is 67 degrees.
Given the rhombus below:
We are required to find the measure of angle PRZ.
Considering trianglePRZ, we can apply the law of cosine to the angle of interest, which is, angle PRZ.
[tex]R=\cos ^{-1}(\frac{p^2+z^2-r^2}{2pz})[/tex]In this case,
[tex]\begin{gathered} p=(5+5)=10 \\ z=13 \\ r=13 \\ R=\text{?} \end{gathered}[/tex]Substituting these values in the formula, we get
[tex]R=\cos ^{-1}(\frac{10^2+13^2-13^2}{2(10)(13)})[/tex][tex]R=\cos ^{-1}(\frac{100^{}+169^{}-169^{}}{2(10)(13)})=\cos ^{-1}(\frac{100^{}}{260})=67.380\approx67^o[/tex][tex]m\angle\text{PRZ}\approx67^o[/tex]Therefore, the correct answer is 67 degrees.
True or False: A power has two parts, a base and an exponent. True False
The said statement is true.
A power has two parts, a base and an exponent.
Example
[tex]2^3[/tex]The answer is TRUE
1. The population of Whatville is given by the y=83,000(1.04) where x is the years since 2010.a) What was the population in 2010?b) What is the population in 2020?c) When will the population reach 100,000? Show your work.
ANSWER:
a) 83,000 people
b) 122,860 people
c) 4.75 years
STEP-BY-STEP EXPLANATION:
We have that the population given by the following equation:
[tex]y=83000\cdot\mleft(1.04\mright)^x[/tex]a) What was the population in 2010?
Since no year has passed, the value of x would be 0.
Replacing:
[tex]\begin{gathered} y=83000\cdot(1.04)^0 \\ y=83000 \end{gathered}[/tex]The population in 2010 is 83,000 people
b) What is the population in 2020?
From 2010 to 2020 10 years have passed, therefore the value of x is 10
[tex]\begin{gathered} y=83000\cdot(1.04)^{10} \\ y=122860 \end{gathered}[/tex]The population in 2020 is 122,860 people
c) When will the population reach 100,000?
Since the population is 100,000 people, it is the value of y, therefore we must solve and calculate the value of x
[tex]\begin{gathered} 100000=83000\cdot\mleft(1.04\mright)^x \\ 1.04^x=\frac{100000}{83000} \\ \ln 1.04^x=\ln \frac{100}{83} \\ x\cdot\ln 1.04=\ln \frac{100}{83} \\ x=\frac{\ln \frac{100}{83}}{\ln 1.04} \\ x=4.75 \end{gathered}[/tex]Which means that for the population to be 100,000 people, 4.75 years would have to pass
Hello! I think I'm overthinking this. Could you please help me decipher?
A scatter plot uses dots to represent values for two different values
(16,15)
(20,12)
(14,20)
(15,18)
(19,14)
(18,21)
Where the x value is boys and the y value is girls
can you please solve this practice problem for me I need assistance
The missing angle in the triangle of the left is:
51 + 74 + x = 180
x = 180 - 51 - 74
x = 55°
The missing angle in the triangle of the right is:
55 + 74 + x = 180
x = 180 - 55 - 74
x = 51°
Then, both triangles are similar. This means that their corresponding sides are in proportion. These sides are:
35 in
Use the given information to select the factors of f(x).
ƒ(4) = 0
f(-1) = 0
f(³/²) = 0
options are:
(2x-3)
(2x+3)
(x-4)
(3x-2)
(x-1)
(x+4)
(3x+2)
(x+1)
The factors of f(x) are (x-4), (x+1) and (2x-3) respectively.
How to select the factors of f(x)To select the factors of f(x), we are to pick the functions that satisfy the conditions of the given information.
For f(4) = 0:
The function that evaluates to 0 when x = 4 is (x - 4). That is:
f(x) = (x - 4)
f(4) = (4 - 4) = 0
For f(-1) = 0:
The function that evaluates to 0 when x = -1 is (x + 1). That is:
f(x) = (x + 1)
f(-1) = (-1 + 1) = 0
For f(3/2) = 0:
The function that evaluates to 0 when x = 3/2 is (2x-3). That is:
f(x) = (2x-3)
f(3/2) = (2 × 3/2 - 3) = 0
Therefore, (x-4), (x+1) and (2x-3) are the corresponding factors of f(x)
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Find an equation of the circle having the given center and radius.Center (-3, 3), radius 16
The equation of a circle is given by the next formula:
[tex](x-h)^2+(y-k)^2=r^2[/tex]Where the center is the point (h, k) and r means the radios. Therefore:
[tex]\begin{gathered} (x-(-3))^2+(y-3)^2=(\sqrt[]{6}_{})^2 \\ (x+3)^2+(y-3)^2=6^{} \end{gathered}[/tex]Answer is letter C
on the coordinate plane below
As we can see by the picture below, the school is on the point (5, -2).
A ladder is 12 ft tall, and the base is 4 ft from the house. How high up thehouse does the ladder reach? Round to the nearest tenth of a foot.
ok
t = 12
b = 4
h = ?
[tex]\begin{gathered} \text{ 12}^2=4^2+h^2 \\ \text{ h}^2\text{ = 144 - 16} \\ \text{ h}^2\text{ = 128} \\ \text{ h = }\sqrt[]{128} \\ h\text{ = 11.3 ft} \end{gathered}[/tex]height = 11.3 ft
A farmer is planning on picking 1,000 bell peppers on the first day of the harvest. After picking the first 600, he finds that 70 percent of them are green and 30 percent of them are red. How many of the remaining peppers must he pick must be red in order for exactly half of the total number of peppers picked to be red?
Answer:
320 red bell peppers
Step-by-step explanation:
First, let's calculate how many green and red bell peppers the farmer harvest in the first time:
Green peppers: 600*70/100 = 420
Red peppers: 600*30/100 = 180
If the farmer wants that half (50%) of the pepper harvest are red:
The total number of red peppers harvest have to be:
100*50/100 = 500
For this reason, the amount of remaining red peppers that have to be harvest are:
500 - 180 = 320
Answer: The farmer has to harvest more 320 red bell peppers
Find the coordinates of each point under the given rotation about the origin (-5, 8); 180
As given by the question
There are given that the point, (-5, 8).
Now,
The given coordinate of point (-5, 8) which is lies on the second quadrant.
Then,
According to the question,
Rotate it through 180 degree about the origin
Then,
The given coordinate move from 2nd quadrant to 4th, where the value of x is positive and y is negative
Then,
The new coordinat will be, (5, -8).
Hence, the coordinate is (5, -8).
all you need is in the photo I DON'T WANT STEP BY STEP ANSWER FAST please fdsd
We have the following:
[tex]\begin{gathered} x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ a=5 \\ b=0 \\ c=-80 \end{gathered}[/tex]replacing:
[tex]\begin{gathered} x=\frac{-0\pm\sqrt[]{0^2-4\cdot5\cdot-80}}{2\cdot5}=\frac{\pm\sqrt[]{1600}}{10}=\frac{\pm40}{10}=\pm4 \\ x_1=4 \\ x_2=-4 \end{gathered}[/tex]You roll a die. What is the probability that you’ll get a number less than 3?0.3330.50.6670.75
Recall that the numbers in a die are 1,2,3,4,5,6.
[tex]S=\mleft\lbrace1,2,3,4,5,6\mright\rbrace[/tex]Hence the number of possible outcomes is 6.
[tex]n(S)=6[/tex]We need a number less than 3. Let A be this event.
[tex]A=\mleft\lbrace1,2\mright\rbrace[/tex]The favorable outcome is 2.
[tex]n(A)=\mleft\lbrace1,2\mright\rbrace[/tex]Since there are 1,2 less than 3 in a die.
[tex]P(A)=\frac{Favourable\text{ outcomes}}{\text{Total outcomes}}=\frac{n(A)}{n(S)}[/tex]Substitute n(A)=2 and n(S)=6, we get
[tex]P(A)=\frac{2}{6}=\frac{1}{3}=0.333[/tex]Hence the required probability is 0.333.
Tim and Kevin each sold candies and peanuts for a school fund-raiser. Tim sold 16 boxes of candies and 4 boxes of peanuts and earned $132. Kevin sold 6 boxes of peanuts and 20 boxes of candies and earned $190. Find the cost of each. Cost of a box of candy. Cost of a box of peanuts.
We have the following:
let x cost of a box of candy
let y cost of a box of peanuts
[tex]\begin{gathered} \text{ Tim} \\ 16x+4y=132 \\ \text{ Kevin} \\ 20x+6y=190 \end{gathered}[/tex]resolving the system of equations:
[tex]\begin{gathered} 20x+6y=190 \\ 16x+4y=132\Rightarrow4y=132-16x\Rightarrow y=\frac{132-16x}{4} \\ \text{replacing:} \\ 20x+6\cdot(\frac{132-16x}{4})=190 \\ 20x+198-24x=190 \\ -4x=190-198 \\ x=\frac{-8}{-4} \\ x=2 \end{gathered}[/tex]now, for y
[tex]\begin{gathered} y=\frac{132\cdot16\cdot2}{4} \\ y=25 \end{gathered}[/tex]Therefore the cost of the box of candy is $ 2 and the cost of the box of peanuts is $ 25
Fraction multiplication 5/8 times 2/9 equals 10/72 how to simplify
So,
We're going to multiply:
[tex]\frac{5}{8}\cdot\frac{2}{9}[/tex]Multiplying numerators and denominators together, we obtain:
[tex]\frac{10}{72}[/tex]Now, to simplify, what we're going to do is to reduce the fraction dividing by a common number. Let's begin dividing by 2:
[tex]\frac{10}{72}=\frac{5}{36}[/tex]As you can see, we can't divide by a common number more times, so, the simplified fraction is 5/36.
36. The widths of platinum samples manufactured at a factory are normally distributed, with a mean of 1.3 cm and a standard deviation of 0.3 cm. Find the z-scores that correspond to each of the following widths. Round your answers to the nearest hundredth, if necessary.(a) 1.7 cmz = (b) 0.9 cmz =
Part (a)
Using the formula for the z-scores and the information given, we have:
[tex]\begin{gathered} \text{ z-score=}\frac{\text{ data value }-\text{ mean}}{\text{ standard deviation }} \\ \text{ z-score=}\frac{1.7\text{ cm }-\text{ 1.3 cm}}{0.3\text{ cm}} \\ \text{ z-score=}\frac{0.4\text{ cm}}{0.3\text{ cm}}\text{ (Subtracting)} \\ \text{ z-score=1.33 (Dividing)} \\ \text{The z-score for 1.7 cm is 1.33 rounding to the nearest hundredth.} \end{gathered}[/tex]Part (b)
Using the formula for the z-scores and the information given, we have:
[tex]\begin{gathered} \text{ z-score=}\frac{\text{ data value }-\text{ mean}}{\text{ standard deviation }} \\ \text{z-score=}\frac{\text{ 0.9 cm }-1.3\text{ cm}}{\text{ 0.3 }}\text{ (Replacing the values)} \\ \text{z-score=}\frac{\text{ }-0.4}{\text{ 0.3 }}\text{ (Subtracting)} \\ \text{ z-score= }-1.33 \\ \text{The z-score for 0.9 cm is -1.33 rounding to the nearest hundredth.} \end{gathered}[/tex]Tanvir applies the distributive property to the left-hand side of the equation 1/3(3q+15)=101 Which equation shows the correct application of the distributive property?
1: q+15=101
2:3q+5=101
3:3q+15=101
4:q+5=101
When Tanvir applies the distributive property to the left-hand side of the equation, 1/3(3q+15)=101, the equation that shows the correct application is equation 4: q+5=101.
What is distributive property?The distributive property applies basic mathematical operations, especially in equations.
This property is that when a value is multiplied or divided by a number to a set that will be added or subtracted, the result is the same, notwithstanding if the operation is done before the addition or subtraction.
1/3(3q+15) = 101
(3q/3+15/3) = 101
= q + 5 = 101
q = 96
Check of Distributive Property:
1/3(3q+15) = 101
1/3(3 x 96+15) = 101
= 1 x 96 + 5 = 101
= 96 + 5 = 101
= 101 = 101
Or: 1/3(3q+15) = 101
1/3(3 x 96+15) = 101
= 1/3(288 + 15) = 101
= 1/3(303) = 101
= 101 = 101
Thus, the equation that correctly applies the distributive property is equation 4: q+5=101.
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