For a triangle to be possible with 3 given lengths, the largest side must be lower than the sum of the two remaining sides.
Let L be the length of the third side. There are two cases:
If L is the largest side, then:
[tex]\begin{gathered} L<24+52 \\ \Rightarrow L<76 \end{gathered}[/tex]If L is not the largest side, then the largest side has a measure of 52 and:
[tex]\begin{gathered} 52<24+L \\ \Rightarrow52-24Since both conditions should meet for a triangle to be formed, then:[tex]28Therefore, the range of possible values for L is:[tex]undefined[/tex]Gabe made a scale drawing of a neighborhood park. The scale of the drawing was 1 millimeter : 6 meters. If the actual length of the volleyball court is 18 meters, how long is the volleyball court in the drawing?
Line g passes through the points (-2.6,1) and (-1.4.2.5), as shown. Find theequation of the line that passes through (0,-b) and (c,0).
The blue line passes through the points
(-2.6, 1) and (-1.4, 2.5)
I will label the coordinates as follows for reference:
[tex]x_1=-2.6,y_1=1,x_2=-1.4,y_2=2.5[/tex]Step 1: Find the slope of the blue line
The slope between two points is calculated with the formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]We substitute the values and we get that the slope of the blue line is:
[tex]m=\frac{2.5-1}{-1.4-(-2.6)}=\frac{1.5}{1.2}=1.25[/tex]The slope m of the blue line is 1.25.
step 2: With that slope, calculate b (the intercept of the blue line with the y axis).
For this we use the point - slope equation:
[tex]y=m(x-x_1)+y_1[/tex]Where we will use the sane x1 and x2 as in the previous step, so we get
[tex]\begin{gathered} y=1.25(x-(-2.6))+1 \\ y=1.25(x+2.6)+1 \\ y=1.25x+3.25+1 \\ y=1.25x+4.25 \end{gathered}[/tex]We compare this with the slope-intercept equation
[tex]y=mx+b[/tex]And we can see that the incercept b is 4.25
[tex]b=4.25[/tex]step 3: Find the value of c.
to find the value of c, we need to know at which point the blue line crosses the x axis.
Since we already have the equation of the blue line y=1.25x+4.25, and the line crosses the x axis at y=0, we substitute this to find the x value that is equal to c:
[tex]\begin{gathered} 0=1.25x+4.25 \\ -4.25=1.25x \\ \frac{-4.25}{1.25}=x \\ -3.4=x \end{gathered}[/tex]The blue line crosses the x axis at (-3.4,0), thus we can conclude that
[tex]c=-3.4[/tex]Step 4: Define the two point where the orange line passes through.
We know from the picture that the orange line passes through (c,0) and (0,-b)
Since we have the values of c = -3.4 and b=4.25, we can say that the orange line passes through (-3.4, 0) and (0, -4.25)
Step 5: Calculate the slope of the orange line.
the orange line passes through (-3.4, 0) and (0, -4.25), so we define:
[tex]undefined[/tex]Select the expressions that are equivalent to 7(7f)1. 49f2. 7(f+6f)3. f+144. f+49
ANSWER :
49f and 7(f + 6f)
EXPLANATION :
From the problem, we have :
[tex]7(7f)[/tex]When multiplied, it will be 49f
When breaking it down, 7f is equal to f + 6f. Then it will be 7(f + 6f)
The next options f + 14 and f + 49 has two terms, so it will not be equivalent to the given expression with one term.
So the only expressions that are equivalent to the given expression are 1 and 2
The science class is taking a trip to the science center. there are 20 students and an unknown number of adult chaperones going. the bus holds at most 35 people.what is the greatest number of adults who can chaperone? I know the answer is 15. however, what they want us to do is create an equation using inequalities (<, >, etc..) That's what I don't know how to do with this problem. I'm trying to explain it to my daughter but I don't know how to do it myself.
We are given that there are 20 students and an unknown number of adult chaperones.
Let x denotes the unknown number of adult chaperones.
The bus holds at most 35 people
We know that 20 students plus x number of adult chaperones should be at most 35
at most 35 means equal or less than 35
So we can write
[tex]20+x\le35[/tex]Now we can easily solve for x
[tex]\begin{gathered} 20+x\le35 \\ x\le35-20 \\ x\le15 \end{gathered}[/tex]Two towns are 1050 miles apart, a group of hikers start from each town and walk the trail toward each other. They meet after a total hiking time of 200 hours. If one group travels 1 1/2 miles Per hour faster than the other group, find the rate of each group
Answer:
Rate of the faster group = 3.38 miles per hour
Rate of the slower group = 1.88 miles per hour
Explanation:
Let x = rate of the slower group
Therefore the rate of the faster group will be x + 1 1/2 = x + 3/2 = x + 1.5
From the question, we're told that the two groups traveled for a total hiking time of 200 hours.
We know that distance = rate x time
So the distance of the slower group will be = 200x
And the distance of the faster group will be = 200(x + 1.5)
So if the distance between each town is 1050, we can then solve of x as shown below;
[tex]\begin{gathered} 200x+200(x+1.5)=1050 \\ 200x+200x+300=1050 \\ 400x=750 \\ x=\frac{750}{400} \\ x=1.88\text{ mph} \end{gathered}[/tex]Therefore the rate of the faster group = 1.88 + 1.5 = 3.38 mph.
A swim team consists of 5 boys and 5 girls. A relay team of 4 swimmers is chosen at random from the team members. What is the probability that 3 boys are selected for the relay team given that the first selection was a girl? Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
In order to find the probability start the construction of the possible relay team, if the team is made by any 4 swimmers then
[tex]10\cdot9\cdot8\cdot7=5040[/tex]if the first member is a girl and the other three needs to be boys, the number of possibilities are
[tex]1\cdot5\cdot4\cdot3=60[/tex]then, divide in order to find the probability
[tex]\frac{60}{5040}=\frac{1}{84}[/tex]Subtracting algorithm
Using subtracting algorithm, we have 69,000 - 42,547 = 26,453 and 152,681 - 34,820 = 117,861.
According to the question,
We have the following expressions:
_ _ , 0 0 0
-4 2, _ _ _
_________
2 6 , 4 5 3
Now, we will first solve this.
The spaces has to be filed with the digits from 0 to 9 and in both the questions, no digit has to be repeated.
Now, we will solve it from the right hand side.
(Note that we will solve each row that is we will solve vertically.)
0 is given, then we have blank, and in result we have 3.
It is clear that no number can be subtracted from 0. So, we have to regroup it from other digits. So, it will be 10.
Now, 10-3 = 7
So, this blank will be 7.
Now, come to next one.
We have 0 and a blank and then 5 in the result.
Now, it should be 9 because 1 was taken away from it.
So, 9-5 = 4
This blank has to be filled with 4.
Now, we will solve next one.
We have 0, a blank and then 4 in the result.
Now, this 0 will make 9.
9-4 = 5
This blank has to be filled with 5.
Now, we have a blank, 2 and 6 in the result.
1 has been carried from this digit.
So, we have:
6+2+1 = 9
This blank has to be filled with 9.
Next, we have a blank, 4 and 2 in the result.
4+2 = 6
This has to be filled with 6.
Now, we will solve the second question like this.
_ 5 2, 6 8 1
- _ 4, _ _ _
__________
1 1 7, 8 6 1
Now, moving from right to left vertically:
We have 1, a blank and 1 in the result.
1-1 = 0
Blank = 0
We have 8, a blank and 6 in the result.
8-6 = 2
Blank = 2
We have 6, a blank and 8 in the result.
Now, 8 can not be subtracted from 6. So, it has to be 16.
16-8 = 8
Blank = 8
Now, next one is complete.
So, we have next one.
We have 5, a blank and 1 in the result.
We will subtract 1 from 4 because 1 was carried away from 5.
4-1 = 3
Blank = 3
Now, we have a blank and 1 in the result.
Blank = 1
Hence, the answers would be 69,000 - 42,547 = 26,453 and 152,681 - 34,820 = 117,861.
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What is the probability that a random selected yard will have fewer than 6 trees
Based on the given histogram on yards and the number of trees they have, the probability that a random selected yard will have fewer than 6 trees is 60%
How to find the probability?The probability that in a random yard, the number of trees would be less than 6 trees can be found by the formula:
= Proportion of yards with 0 - 2 trees + Proportion of yards with 2 - 4 trees + Proportion of yards with 4 - 6 trees
The probability that a random yard would have fewer than six trees is therefore:
= 0.35 + 0.20 + 0.05
= 0.60
= 60%
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5. Noah is solving an equation and one of his moves is unacceptable. Hereare the moves he made. Which answer best explains why the "divide eachside by x step is unacceptable? *2(3+6) - 4= 8 + 6321 + 12 - 4= 8 + 612.1 + 8 = 8 + 6.120 = 602 = 6original equationapply the distributive propertycombine like termssubtract 8 from both sidesdivide each side by IO When you divide both sides of 2x = 6x by x you get 2x^2 = 6x^2.When you divide both sides of 2x = 6x by x it could lead us to think that there is nosolution while in fact the solution is x = 0..aWhen you divide both sides of 2x = 6x by x you get 2 = 6x.aOWhen you divide both sides of 2x = 6x by x it could lead us to think that there is nosolution while in fact the solution is x = 3..
SOLUTION
Write out the original equation
[tex]2(x+6)-4=8+6x[/tex]Then, Apply the distributive property on the left hand side of the equation
[tex]\begin{gathered} 2x+12-4=8+6x \\ 2x+8=8+6x \end{gathered}[/tex]Then combine trhe like terms subtracting 6x from both side
[tex]\begin{gathered} 2x+8-6x=8+6x-6x \\ 2x-6x+8=8 \end{gathered}[/tex]Subtract 8 from both sides of the last equation
[tex]\begin{gathered} 2x-6x+8-8=8-8 \\ 2x-6x=0 \\ -4x=0 \\ \end{gathered}[/tex]hence
Divide both sides by -4, we have
[tex]\begin{gathered} -\frac{4x}{-4}=\frac{0}{-4} \\ \text{Then} \\ x=0 \end{gathered}[/tex]Therefore, the solution is x=0
Hence
When we divide both sides of the equation by x, we have
[tex]\begin{gathered} \frac{2x}{x}=\frac{6x}{x} \\ 2=6 \\ \text{which implies thier is no solution} \end{gathered}[/tex]While the solution is x=0
Therefore
When we divide the equation by 2x=6x by x it could lead us to think that there is no solution while the solution is x=0
Answer; The second option is right
Graph transformation of the following line given the transformation: g(x)= -f(x) -2
Transformation of a Function
We are given the function:
[tex]y=f(x)=\frac{2}{3}x+8[/tex]And it's required to find another function g(x) according to the transformation:
g(x) = -f(x) - 2
First, we calculate the negative of f(x):
[tex]-f(x)=-(\frac{2}{3}x+8)=-\frac{2}{3}x-8[/tex]And now we subtract 2 to find g(x):
[tex]g(x)=-\frac{2}{3}x-8-2=-\frac{2}{3}x-10[/tex]The equation above is in the slope-intercept form where the slope is m=-2/3 and the y-intercept = -10
Answer:
[tex]g(x)=-\frac{2}{3}x-10[/tex]Find the missing length of the triangle. 22 cm 17.6 cm The missing length is centimeters.
Question 10
Answer:
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A tyre made of rubber (density 1.2 g/cm³) has a mass of 3.6 kg.
Find its volume.
(Use ^sign from the computer's keyboard to express the power of the units for the volume
Question 11
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What percentage of the grid is shaded?
PFlag question
1.volume = mass*density
v = 1.2 * 3.6 = 4.32 cm3
The density of a substance quantifies how tightly its molecules are packed, which affects how heavy or light it is.
Density is calculated as follows: density=mass/volume. Most often, mass is measured in grams or kilograms. Most often, volume is measured in cubic centimeters (cm3), cubic meters (m3), or millileters (mL).
How can you find mass from density?
multiply the volume by the density.
Mass per unit volume is the definition of density.
ρ = m V
This can be rearranged to yield the mass expression.
m = ρ × V
Example:
What mass of the liquid is present if 500 mL of it has a density of 1.11 g/mL
m = ρ × V = 500 mL × 1.11 g
1 mL = 555 g
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Rebecca must complete 15 hours of volunteer work. She does 3 hours each day.
For the linear equation that represents y, the hours Rebecca still has to work after x days, what does the y-intercept represent?
The y-intercept represents the hours Rebecca must work.
How to represent linear equation?Linear equation can be represented in slope intercept from, point slope form and standard form.
Therefore, in slope intercept form it can be represented as follows:
Hence,
y = mx + b
where
m = slopeb = y-interceptShe must complete 15 hours of volunteer work. She does 3 hours each day. Let's represent Rebecca situation in linear form.
where,
y = hours Rebecca still has to work
x = the number of days
Therefore,
y = 15 - 3x
The y-intercept is 15 which implies the number of hours she must complete.
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The number of hours Rebecca must work is represented by the y-intercept in the linear equation.
What is the linear equation?An equation is said to be linear if the power output of the variable is consistently one.
The linear equation is y = mx + c, where m denotes the slope and c is its intercept.
Given that she is required to put in 15 hours of volunteer work. Each day, she works three hours.
As per the given situation,
If x represents the number of days and y represents the number of hours she must work
So the linear representation shows Rebecca's situation will be:
y = 15 - 3x
Therefore, the number of hours Rebecca must work is represented by the y-intercept in the linear equation.
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Use quadratic regression to find the equation of a quadratic function that fits the given points. x 0 1 2 3. Y. 49 50.4 39.5. 21
The regression Quadratic equation y = 49 + 7.55x - 6.15x².
What is Regression Equation?The technique of finding the equation of a parabola that most closely matches a collection of data is known as quadratic regression. The graph points that make up the parabola-shaped shape of this set of data are given. The parabola's equation is written as y = ax² + bx + c, where a never equals zero.
For data presented as ordered pairs, you can calculate the model's degree by identifying differences between dependent values. The model will be linear if the initial difference has the same value. The model will be quadratic if the second difference has the same value as the first.
As, we know the Quadratic model
Quadratic model, y = a + bx + cx²
Now, value of
a = 49
b = 7.55
c = -6.15
Then, the Regression Quadratic model is
y = 49 + 7.55x - 6.15x²
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if you're lonely then be lonely with me but I need your help
Let's use distributive property to simplify:
[tex]-35-5x+2\frac{5}{6}x=0[/tex]Now we add up the x's and take number to another side:
[tex]\begin{gathered} -5x+2\frac{5}{6}x=35 \\ -2\frac{1}{6}x=35 \end{gathered}[/tex]We make 2 and one-sixth into improper fraction and divide to get x:
[tex]\begin{gathered} -\frac{13}{6}x=35 \\ x=\frac{35}{-\frac{13}{6}} \\ x=35\cdot-\frac{6}{13}=-\frac{210}{13} \end{gathered}[/tex]x is "minus 210 over thirteen"
find the volume and total surface area of a right circular cone whose base diameter is 10 cm and whose altitude is 20 cm.
SOLUTION
Given the question in the question tab, the following are the solution steps to calculate the required measurements.
Step 1: write the given parameters
[tex]\begin{gathered} \text{diameter}=10\operatorname{cm},\text{altitude}=\text{height}=20\operatorname{cm} \\ r=\frac{d}{2}=\frac{10}{2}=5\operatorname{cm} \end{gathered}[/tex]Step 2: Calculate the volume of the right circular cone
[tex]\begin{gathered} V=\frac{\pi r^2h}{3} \\ V=\frac{\pi\times5\times5\times20}{3} \\ V=\frac{500\pi}{3}=523.5987756 \\ V\approx523.5988\operatorname{cm}^3 \end{gathered}[/tex]Step 3: Calculate the total surface area of the right circular cone
[tex]\begin{gathered} \text{TSA}=\pi r(r+\sqrt[]{h^2+r^2)} \\ \text{TSA}=\pi(5)(5+\sqrt[]{20^2+5^2)} \\ \text{TSA}=5\pi(5+\sqrt[]{400+25)} \\ \text{TSA}=5\pi(5+\sqrt[]{425})=5\pi(5+20.61552813) \\ \text{TSA}=5\pi(25.615528134) \\ \text{TSA}=402.3677749 \\ \text{TSA}\approx402.3678cm^2 \end{gathered}[/tex]Hence, the volume and the total surface area of the given right circular cone are approximately 523.5988cm³ and 402.3678cm² respectively
A company plans a major investment and theamount of profit is uncertain, but researchersgive the following estimate for the distribution.1.5210Profit(inmillions)Probability0.10.20.40.20.1What is the expected value of the profit?[?] million dollars
The expected value is the return you expect from some kind of investment/action.
When we are presented with probabilty of an action, we can take the expected value of the whole table [investment] by taking the sum of the products of probability and the action.
Here, we want products of "probability" and "profit". Then we sum it. Shown below:
[tex]\begin{gathered} E=(0.1)(1)+(0.2)(1.5)+(0.4)(2)+(0.2)(4)+(0.1)(10) \\ E=3 \end{gathered}[/tex]Expected value of profit = 3 million dollarsThe shorter leg of a right triangle is 9cm shorter than the longer leg. The hypotenuse is 9cm longer than the longer leg. Find the side lengths of the triangle.Length of the shorter leg: _ cmLength of the longer leg:__ cmLength of hypotenuse __ cm
Explanation:
let the longer leg = x
The shorter leg = 9cm shorter than the longer leg
The shorter leg = x - 9
hypotenuse = 9cm longer than the longer leg
hypotenuse = x + 9
Using pythagoras theorem:
hypotenuse² = shorter leg² + longer leg²
(x + 9)² = x² + (x - 9)²
Expanding:
x² + 9x + 9x + 81 = x² + x ² - 9x -9x + 81
x² + 18x + 81 = 2x² -18x + 81
collect like terms:
18x + 18x + 81 - 81 = 2x² - x²
36x + 0 = x²
x² - 36x = 0
x(x - 36) = 0
x = 0 or (x - 36) = 0
x = 0 or x = 36
if x = 0
shorter side = x - 9 = 0 - 9 = -9
Since the length cannot be negative, x = 36
The longer leg = x = 36 cm
The shorter leg = x - 9 = 36 - 9
The shorter leg = 27cm
The hypotenuse = x + 9 = 36 + 9
The hypotenuse = 45 cm
Select the correct answer..What is the value of i^ if the remainder of 4 is 2?OA. -i'OB.-1Ос. іOD. 1ResetNext
1) Considering that for that complex number we have the following pattern:
[tex]\begin{gathered} i^1=i \\ i^2=-1 \\ i^3=-1\cdot i=-i \\ i^4=-1\cdot-1=1 \end{gathered}[/tex]2) And that, the question asks us about the what number must be that exponent so that the remainder is 2, we can write out:
[tex]\frac{n}{4}=4d+2[/tex]which d is the divisor, so if the remainder is 2 then we can state:
[tex]i^n=i^2=-1[/tex]For the two numbers listed find two factors of the first number such that their product is the first number and there sum is the second number
Given:
Product of two numbers is 24
Sum of two numbers is -11
-8 and -3 are the two numbers.
Using the origin as the center of dilation and a scale factor of k=1/2 find the coordinates of the vertices of the image of the polygon below
Given
Using the scale of 1/2
This means we divide each coordinate by 2
[tex]\begin{gathered} (0,3)=(0,1.5) \\ (-4,0)=(-2,0) \\ (2,0)=(1,0) \\ (0,-3)=(0,-1.5)_{} \end{gathered}[/tex]Which is an example of a survey?A- collecting the cholesterol readings of a group of elderly people in a small townB- interviewing college students to find what percentage expect a job immediately after graduationC- testing the effectiveness of a hair product by allowing one group to use it and comparing results against a control groupD- testing the effectiveness of a mouthwash by allowing one group to use it and comparing results with those of a group that doesn't use ot
Answer: B- interviewing college students to find what percentage expect a job immediately after graduation
Surveys are meant to collect data that can be used to analyze a population as ahwole. This option analyzes the perspective of college students as a whole, whereas option A only focuses on a minority group of elderly. Additionally, options C and D are moreso experiments and not surveys that can be applied on a larger scale.
What is the value of the expression 2c( a + b) when a = 2, b = 5, and c = 4
The given expression is
2c(a + b)
From the information given,
a = 2
b = 5
c = 4
By substituting these values into the expression, it becomes
2 * 4(2 + 5)
= 8(7)
= 56
The value of the expression is 56
Write the equation for a line that is perpendicular to the given line and contain the following points. 12. X=-11Contains the point (-5, -7)equation:____
Purple line is perpendicular to given line (x = -11), and the equation for this lines is y = -7
Martin Brothers Moving rents moving vans by the hour. The company charges a flat fee of $17.99, plus an additional $19.99 per hour. One customer pays $57.97 for her rental. How long was her rental?
Let h be the number of hours that the customer rented the van, then we can set the following equation:
[tex]19.99h+17.99=57.97.[/tex]Subtracting 17.99 from the above equation we get:
[tex]\begin{gathered} 19.99h+17.99-17.99=57.97-17.99, \\ 19.99h=39.98. \end{gathered}[/tex]Dividing by 19.99 we get:
[tex]\begin{gathered} \frac{19.99h}{19.99}=\frac{39.98}{19.99}, \\ h=2. \end{gathered}[/tex]Answer: 2 hours.
find the coordinates of point P that lies on the line segment MQ, M(-9,-5) , Q(3,5), and partitions the segment at a ratio of 2 to 5
PMark for Review 1 Harold spent the summer working at a diner. He now pays for a monthly subscription to a magazine. The equation y -35x + 180 can be used to represent this situation, where y is the amount of money Harold has remaining after x months of paying for his monthly magazine subscription. Which statement best describes the amount of money Harold has, given this equation? - A) Harold started with $35 and he spends $180 per month on his magazine subscription. B) Harold started with $180 and he gets paid $35 per month. C) Harold started with owed $180 for magazines and he continues to spends $35 per month on his magazine subscription. D) Harold started with $180 and he spends $35 per month on his magazine subscription.
the option D is the correct answer
the equation is
y = 35x +180
that means he started with 180 $ and his monthly subscription is 35 $.
The graph of a toy car's speed y
over time x is a parabola that
shows a minimum speed of 2 m/s
after 3 seconds. After 5 seconds,
the car's speed is 3 m/s. What is
the equation in vertex form of the
parabola?
The equation in vertex form of the parabola is y=-1/30(x+23/2)²+529/120
Y axis represends the toy car's speed
X axis represents time
y=ax²+bx+c
c=0
y=ax²+bx
2=9a+3b multiplied with -5
-10 = -45a -15b........equation 1
3=25a+5b multiplied with 3
9 = 75a + 15b............equation 2
adding equation 1 and 2
9-10=75a-45a+15b-15b
30a=-1
a=-1/(30)
2=9×(-1/30)+3b
3b=2+3/10=23/10
b=23/30
y=-1/30 x²+23/30=-1/30(x²+23x+(23/2)²)+1/30 ×(529/4)
y=-1/30(x+23/2)²+529/120
Therefore, the equation in vertex form of the parabola is y=-1/30(x+23/2)²+529/120
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Given the median QR and trapezoid MNOP, what is the value of X?M3.8033Rکد 73PA. 6B. 19(C. 2D, 5E 7F. Cannot be determined
SOLUTION
Consider the diagram below
Applying the rule in the diagram above, we have
[tex]|QR|=\frac{1}{2}(|ON|+|PM|)[/tex]Recall from the questions
[tex]\begin{gathered} |QR|=33 \\ |ON|=3x-8 \\ |PM|=7x+4 \end{gathered}[/tex]Then we substitute the parameters above into the expression above
[tex]\begin{gathered} 33=\frac{1}{2}(3x-8+7x+4) \\ \text{ Multiply both sides by 2} \\ 66=3x-8+7x+4 \\ \text{rerrange the terms and simplify } \\ 66=10x-4 \\ \text{collect like terms } \\ 66+4=10x \end{gathered}[/tex]simplify further
[tex]\begin{gathered} 70=10x \\ \text{divide both sides by 10} \\ x=\frac{70}{10} \\ \text{then} \\ x=7 \end{gathered}[/tex]Therefore the value of x is 7
Therefore the right option is E
Solve the equation. Check your solution.20x - 4= 50x + 2x=(Simplify your answer. Type an integer or a simplified fraction.)
20x - 4 = 50x + 2
Solve for x
20x - 50x =
