(x_1+x_2)=-b/a=18/3=6
x_1x_2=c/a=-21/3=-7
So
(x_1+x_2)²-2x_1x_2=x_1^2+x2²x1²+x2²=(6)²-2(-7)=36+14=50(x_1-x_2)²
x1²+x2²-2x_1x250+1464x_1-x_2=8
Answer:
[tex]x{_1}^2+x{_2}^2=50[/tex]
[tex]|x_1-x_2|=8[/tex]
Step-by-step explanation:
Given equation:
[tex]3x^2-18x-21=0[/tex]
Factor to find the roots:
[tex]\implies 3(x^2-6x-7)=0[/tex]
[tex]\implies x^2-6x-7=0[/tex]
[tex]\implies x^2+x-7x-7=0[/tex]
[tex]\implies x(x+1)-7(x+1)=0[/tex]
[tex]\implies (x-7)(x+1)=0[/tex]
Therefore:
[tex]\implies (x-7)=0 \implies x=7[/tex]
[tex]\implies (x+1)=0 \implies x=-1[/tex]
Therefore, the roots of the quadratic equation are:
[tex]x = 7,\quad x = -1[/tex]
Let [tex]x_1 = 7[/tex]
Let [tex]x_2 = -1[/tex]
[tex]\implies x{_1}^2+x{_2}^2=7^2+(-1)^2=50[/tex]
[tex]\implies |x_1-x_2|=|7-(-1)|=8[/tex]
Your friend has t marbles. You have 11 marbles. You and your friend have a total of 29 marbles. Write an equation that you can use to find t
Answer:
t + 11 = 29
Step-by-step explanation:
Since you are combining your total and your friend's total marbles together, this will be an addition equation.
t + 11 = 29
25
24.
What is the value of x?
(4x + 1)
F 9.5
G 18
(2x - 19)
H 33
J 81
Answer:
33 degrees
Step-by-step explanation:
(4x+1) and (2x-19) add up to 180 degrees
[tex](4x+1)+(2x-19)=180\\6x-18=180\\6x=198\\x=33[/tex]
Arturo is
putting 18 erasers into equal rows. He
says there will be more erasers in 2 equal
rows than in 3 equal rows Is Arturo
correct?
Answer:
Yes
Step-by-step explanation:
When there are 2 rows
Number of erasers per row = No. of erasers / No. of rowsNumber of erasers per row = 18/2Number of erasers per row = 9When there are 3 rows
Number of erasers per row = No. of erasers / No. of rowsNumber of erasers per row = 18/3Number of erasers per row = 6Therefore, there will be more erasers per row in 2 equal rows than in 3 equal rows.
HELPPPPPPP! DUE TOMORROW
Answer: Check the step by step
Step-by-step explanation:
Measure of <2 = 37.3 because opposite sides of a line are congruent. To find < 1, you have to add that plus <2 ( 37.3 ) to equal 180. 180 -37.3 = 142.7
For <3, it is also gonna be 142.7 ( as said before, opposite sides are congruent. ) and for <4, it is gonna be 79.4. Hope this helps! If you have any other questions, let me know! :D
I need help finding the slope and what m=
Find the length of the segment that joins the points (-5,2) and (4,-3).
Answer:
10.2956
Step-by-step explanation:
formula:
d = √((x2-x1)2 + (y2-y1)2)
(x1, y2) and (x2, y2)
(-5,2) and (4,-3).
Find the difference between coordinates:
(x2-x1) = (4 - -5) = 9
(y2-y1) = (-3 - 2) = -5
Square the results and sum them up:
(9)2 + (-5)2 = 81 + 25 = 106
Now Find the square root and that's your result:
Exact solution: √106 = √106
Approximate solution: 10.2956
Write an equation for the translation of y=6/x that has the asymptotes x = 4 and y = 5
Answer:
[tex]\displaystyle y=\frac{30x}{6(x-4)}[/tex]
Step-by-step explanation:
Keep in mind that a rational function with a vertical asymptote at [tex]x=4[/tex] means the denominator must be 0 when [tex]x=4[/tex] is plugged in.
This means we have [tex]\displaystyle y=\frac{6}{x-4}[/tex] so far.
To account for the horizontal asymptote at [tex]y=5[/tex], we need to adjust the numerator and denominator so that they are the same degree and that the leading coefficients have a ratio of 5. We can do this by multiplying the numerator by 5x and the denominator by 6.
This leaves us with [tex]\displaystyle y=\frac{30x}{6(x-4)}[/tex] as the translated equation since the end behavior of the function is [tex]\displaystyle y=\frac{30x}{6x}=5[/tex]. See attached graph.
Find the missing value (x)
Answer:
y=14; x=72
Step-by-step explanation:
y=(21×2)/3; x=(48×21)/14
find the height of a right circular cone if the slant height is 4 units and the radius is 2 units
The slant height of the right circular cone will be [tex]l=2\sqrt5}[/tex]
What is slant height of cone?The formula for the slant height of the cone is given as:
[tex]l^2=r^2+h^2[/tex]
Here we have
r=2 units
h=4 units
By putting the values we will get
[tex]l=\sqrt{4^2+2^2[/tex]
[tex]l=\sqrt{16+4[/tex]
[tex]l=\sqrt{20}[/tex]
[tex]l=2\sqrt{5}[/tex]
Hence the slant height of the right circular cone will be [tex]l=2\sqrt5}[/tex]
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OC is perpendicular to AB. What is the length of AB?
A. 8.8 units
B. 4.4 units
C. 13.2 units
D. 2.2 units
Answer:
A.8.8 units
Step-by-step explanation:
Answer:
The correct answer is 8.8 units
Step-by-step explanation:
I just got it correct.
Find the area of the kite shown.
A) 20 cm²
C) 42 cm²
B) 40 cm²
D) 84 cm²
Answer:
A
Step-by-step explanation:
the area (A) of a kite is calculated as
A = [tex]\frac{1}{2}[/tex] × d₁ × d₂ ( d₁ and d₂ are the diagonals )
here d₁ = 2 + 2 = 4 and d₂ = 3 + 7 = 10 , then
A = [tex]\frac{1}{2}[/tex] × 4 × 10 = 2 × 10 = 20 cm²
Answer:
A) 20 cm^2
Step-by-step explanation:
Area of a kite is the product of the 2 diagonals divided by 2.
= (4*10)/2
= 20
find the quantities of 18% of 50
Answer:
9
Step-by-step explanation:
18%of 50
18/100×50
0.18×50= 9
Answer:
9
Step-by-step explanation:
18% of 50
We can rewrite it as,
% = 1/100of = *(into)> 18/100 * 50
Solving,
18/100 * 5018/10 * 518/29Hence,18% of 50 = 9
plssssssssss help meeeeeeeeeeeeeeeee
Answer:
The A graph applies to the first and fourth statement
The B graph applies to the second and third statement
The number of ducks in a pond increasing is a 100% bar with an extra 40% added to it (looks like graph A from the previous question)
The number of mosquitos decreasing by 80% is a bar within the already existing 100% (looks like graph B from the previous question)
Step-by-step explanation:
none further needed
what is blank % of 18 = 9
Answer:
50 percent, trust me.
Answer: 50%
Step-by-step explanation: 50/100 x 18 = 9
50/100 can also be written as 0.5
0.5 x 18 = 9
of = multiply
I need help(!) I appreciate a good explanation so I can understand it too (!)
The ranges values of the function f(x) are: {-89,-9,7} - Option D.
Domain and RangeThe domain of a function is the set of input values for which the function is real and defined. In the other words, when you define the domain, you are indicating for which values x the function is real and defined.
While the domain is related to the values of x, the range is related to the possible values of y that the function can have.
Here, you need to replace the domain values in the given equation.
f(x)=-2x²+9
For x=-3f(x)=-2*(-3)²+9
f(x)=-2*9+9
f(x)=-18+9=-9
For x=1f(x)=-2*(1)²+9f(x)=-2*1+9f(x)=-2+9=7For x=7f(x)=-2*(7)²+9f(x)=-2*49+9f(x)=-98+9=-89Learn more about the range here:
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a magnifying glass makes objects appear 2.54 times largers than their actual size. How large does a 6-millimeter seed appear in the magnifying glass
Answer:
15.24 millimeters
Step-by-step explanation:
6 * 2.54 = 15.24 mm.
Answer: should be 15.24
Step-by-step explanation: quick maths
IF UR GOOD WITH MATHS THIS ONES FOR U SURELY HELP :) ILL BRAINLIST I PROMISE THIS IS SO DIFFICULT IM GONNA RAGE.
Answer:
[tex] d = sin(39) \times 30[/tex]
A farmer has hens, this hen composes 2500 eggs every month. A farmer has 2500 eggs a month, 25% of these eggs are sold in restaurant. How much is the total number of eggs sold in the restaurant, if 35 eggs are sold in the restaurant.
Answer:
625 eggs are sold in a restaurant
2500-100%
x- 25%
62500=100x
x=625 eggs
Answer:
21875
Step-by-step explanation:
25% x 35 x 2500
= 0.25 x 35 x 2500
=21875
Wyatt has a loyalty card good for a discount at his local hardware store. To find the
total he has to pay, before tax, he multiplies the prices by 0.8. What percent discount
does the card give?
Answer:
80%
Step-by-step explanation:
You multiple .8 by 100 to find percentage, giving you 80%.
Answer:
i don’t know
Step-by-step explanation:
I don’t know
Find (a) the range and (b) the standard deviation of the data set 141,116,117,135,126,121. round to the nearest hundredth if necessary.
a) The range of the given data set is 25.
b) The standard deviation of the given data set is 10.1.
The given data set is 141, 116, 117, 135, 126, 121.
a) The range is the difference between the highest and lowest values within a set of numbers.
Range = Highest value - Lowest value
= 141-116
= 25
So, the range is 25.
b) Set up the formula for sample standard deviation. The standard deviation of a set of values is a measure of the spread of its values.
[tex]s=\sqrt{\frac{(x_i-\bar x)^2}{n-1} }[/tex]
Here, mean ([tex]\bar x[/tex]) = [tex]\frac{141+116+117+135+126+121}{6}[/tex]
= 126
[tex]s=\sqrt{\frac{(141-126)^2+(116-126)^2+(117-126)^2+(135-126)^2+(126-126)^2+(121-126)^2}{6-1}}[/tex]
[tex]s=\sqrt{\frac{(15^2+(-10)^2+(-9)^2+(9)^2+(0)^2+(-5)^2}{5}}[/tex]
[tex]s=\sqrt{\frac{(225+100+81+81+25)}{5}}[/tex]
[tex]s=\sqrt{\frac{512}{5}}[/tex]
s=10.1
So, the standard deviation is 10.1.
Therefore,
a) The range of the given data set is 25.
b) The standard deviation of the given data set is 10.1.
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How many solutions does the following equation have? 14(8x −4) = 2x + 1
Write the standard form of the equation
Answer:B
Step-by-step explanation:
Using the following figure select all statements that are TRUE. (Write the number of the statement and separate them with a comma)
Answer:
3
Step-by-step explanation:
Which graph shows the solution to the system of linear inequalities?
2x – 3y <12
y < –3
On a coordinate plane, 2 lines are shown. The first dashed straight line is horizontal to the y-axis at y = negative 3. Everything below the line is shaded. The second solid line has a positive slope and goes through (0, negative 4) and (3, negative 2). Everything below the line is shaded.
On a coordinate plane, 2 lines are shown. The first dashed straight line is horizontal to the y-axis at y = negative 3. Everything above the line is shaded. The second solid line has a positive slope and goes through (0, negative 4) and (3, negative 2). Everything above the line is shaded.
On a coordinate plane, 2 lines are shown. The first dashed straight line is horizontal to the y-axis at y = negative 3. Everything below the line is shaded. The second solid line has a positive slope and goes through (0, negative 4) and (3, negative 2). Everything above the line is shaded.
On a coordinate plane, 2 lines are shown. The first dashed straight line is horizontal to the y-axis at y = negative 3. Everything above the line is shaded. The second solid line has a positive slope and goes through (0, negative 4) and (3, negative 2). Everything below the line is shaded.
Since the graph was not given, answer will be subjective. The graph that shows the solution to the system of linear inequalities of 2x – 3y <12 y < –3 is the one that has It is option B.
What is linear inequalities?A linear inequality is said to be a kind of an inequality that entails a linear function.
Note that a linear inequality is said to be made up of one of the symbols that connote inequality. It is the one that depicts the data that is not equal on a graph.
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Answer:
The correct answer is Graph B
Step-by-step explanation:
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Which is wrong? Question is below in link.
In simplifying the given expression, the error made was in Step 4. 7c - 41 is wrong. The correct answer should be -c - 59.
How to Simplify Expressions?In simplifying expressions, like the one given, first apply the distributive property to clear out the bracket.
Next is to combine like terms. In step 4, there was an error in the calculation while combining like terms.
-6c - 3c + 10c should give us -c NOT 7c.
Also, 3 - 12 - 50 should give us -59 not -41.
Therefore, the correct answer should be:
-c - 59.
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what is the volume of a cone with a diameter of 30 feet and height of 60 feet? use 3.14 for pi. enter your answer in the box
Answer:
volume = 14,137
Step-by-step explanation:
radius is the diameter divided by 2
30÷2=15
radius = 15 then square
15^2 = 225
formula of volume of a cone is 1/3*pi*raduis^2*the height
1/3(3.14)(225)(60)= 14,137
The volume of a cone with a diameter of 30 feet and a height of 60 feet is 14130.
What is the volume of a cone?The volume of the cone is given by;
[tex]\rm Volume \ of \ cone=\dfrac{1}{3}\pi r^2h\\\\Where;\ r = radius \ and \ h = height[/tex]
The volume of a cone with a diameter of 30 feet and a height of 60 feet.
The radius of the cone is;
[tex]\rm Radius =\dfrac{Diameter}{2}\\\\Radius=\dfrac{30}{2}\\\\Radius=15[/tex]
Substitute all the values in the formula
[tex]\rm Volume \ of \ cone=\dfrac{1}{3}\pi r^2h\\\\ Volume \ of \ cone=\dfrac{1}{3}\times 3.14 \times 15^2 \times 60\\\\Volume \ of \ cone=14130[/tex]
Hence, the volume of a cone with a diameter of 30 feet and height of 60 feet is 14130.
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The difference between a number and three fourths of itself is 15. Find the number.
Answer:
60
Step-by-step explanation:
lets say the number is X so:
X-3/4X=15
then multiple both sides by 4 then you will get
4X-3X=60
SO:X=60
Answer:
60Step-by-step explanation:
let x be the number that we are trying to figure out.
the statement “The difference between a number and three fourths of itself is 15” means x + (3/4)x = 15
then
(1/4)x = 15
Then
x = 4 × 15
Then
x = 60
Leah bought a bicycle for $118 that was originally priced at $472. What is the discount
percentage?
Write your answer using a percent sign (%).
Answer:
75%Step-by-step explanation:
the discount percentage :
[tex]\frac{472-118}{472} \times100 = 75 \%[/tex]
The percentage decrease ( discount percentage ).
Solution:[tex]\large\boxed{\sf{formula = 100 \times \frac{(final - initial)}{initial} }}[/tex]
We'll have to subtract 472 ( initial value ) from 118 ( final value).
[tex]472 - 118[/tex]
[tex] = 354[/tex]
Now, we'll have to divide 354 ( difference ) by 118 ( initial value ) and multiply by 100.
[tex] 100 \times \frac{354}{118} [/tex]
[tex]\large\boxed{\sf{ = 75\% }}[/tex]
Hence, the discount percentage is 75.
What is the probability that a person who is above 35 years old has a hemoglobin level of 9 or above? a. 0.357 b. 0.313 c. 0.531 d. 0.343 e. 0.432
Using it's concept, it is found that the probability that a person who is above 35 years old has a hemoglobin level of 9 or above is of 0.247.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
Researching the problem on the internet, we find a table, which says that there are 162 participants above 35 years old, and 40 have hemoglobin levels of 9 and above, hence the probability is given by:
p = 40/162 = 0.247.
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Answer:
Actually, its option C when the hemoglobin level is of 9 or above
Step-by-step explanation:
C. 0.531
Group the terms with variables on one side of the equal sign, and simplify.
8t −15 = 32t
Answer:
[tex] \implies \boxed{\rm t = \frac{ - 5}{8} }[/tex]
Step-by-step explanation:
8t-15=32t
Group the terms then subtract:
=>8t-32t=15
=>-24t=15
Divide both sides by -24:
[tex] \implies \rm \cfrac{ - 24t}{ - 24} = \cfrac{15}{ - 24} [/tex]
[tex] \rm \implies \: t = \cfrac{ - 5}{8} [/tex]