Answer: 55
Step-by-step explanation:
126+129= 255
255-200=55
55 students are taking both history and science.
To solve this, we set up the problem as follows: Let H represent the set of students taking history, S represent the set of students taking science, and N represent the total number of seniors. We're given that N = 200, |H| = 126 (the number of students taking history), and |S| = 129 (the number of students taking science). The number of students taking both can be found by adding the number of students in sets H and S and subtracting the total N. This calculation is often represented by the formula |H ∩ S| = |H| + |S| - N, where |H ∩ S| is the number of students taking both history and science.
Using the formula, we calculate: |H ∩ S| = 126 + 129 - 200 = 55. Therefore, 55 seniors are taking both history and science.
on the first day of their 2598-mile trip, the kalsbeeks drove 683 miles. How many more miles do they have to drive to complete their trip?
Answer:
1915 miles more to drive to complete their trip.
Step-by-step explanation:
Given:-
Total distance to travel (D) = 2598 miles.
Distance travelled (d) = 683 miles.
To calculate = remaining distance (r) to complete trip.
Remaining distance = Total distance minus Distance travelled
i.e. [tex]r=D-d[/tex]
[tex]r=2598-683[/tex]
[tex]r=1915\ miles[/tex]
Therefore kalsbeeks have to travel 1915 miles more to complete their trip.
What is the value of -9 r - 7 when r = 2?
Answer:
I thinks its r = 11
Step-by-step explanation:
So you just need to take the number to the r and multipliy it by r So,
9x2=18
then minus it by the other number which would Be 7 so.
18-7=11
Answer:
11
Step-by-step explanation:
(-9 times 2) - 7
18 - 7
11
Tiffany sketched a picture is a car she used the scale 2 inches:12 feet the car in her sketch is 8 inches long what is the length in feet of the actual car
Answer:
The actual length in feet of the car is 48 feet.
Step-by-step explanation:
Given:
Tiffany sketched a picture of a car she used the scale 2 inches : 12 feet.
In her sketch the car is 8 inches long.
Now, to find the length in feet of the actual car.
Let the actual length of car in feet be [tex]x\ feet.[/tex]
And the length of car in her sketch is 8 inches.
Thus, 8 inches is equivalent to [tex]x\ feet[/tex].
So, the ratio of the scale used by Tiffany as given is 2 inches : 12 feet.
Thus, 2 inches is equivalent to 12 feet.
Now, to get the actual length of car by using cross multiplication method:
[tex]\frac{2}{12} =\frac{8}{x}[/tex]
By cross multiplying we get:
⇒ [tex]2x=96[/tex]
Dividing both sides by 2 we get:
⇒ [tex]x=48[/tex]
⇒ [tex]x=48\ feet.[/tex]
Therefore, the actual length in feet of the car is 48 feet.
Given that V= πr^2h. Make r the subject of the formula.
Using the result from the above,find r when V = 81 cm3, π = 4 and h = 9cm
Answer:
The answer is [tex]r=\frac{3}{2}\ cm.[/tex]
Step-by-step explanation:
Given:
V= πr²h.
V = 81 cm3,
π = 4 and
h = 9cm.
Now, making r the subject of the formula using the result from the above, find r.
So, to get the value of r:
[tex]V=\pi r^2h[/tex]
[tex]81=4\times r^2\times 9[/tex]
[tex]81=36r^2[/tex]
Dividing both sides by 36 we get:
[tex]\frac{81}{36} =r^2[/tex]
Using square root on both sides we get:
[tex]\frac{9}{6} =r[/tex]
[tex]\frac{3}{2} =r[/tex]
[tex]r=\frac{3}{2}.[/tex]
Therefore, the answer is [tex]r=\frac{3}{2}\ cm.[/tex]
write a x (-a)x 13 x a x (-a) x 13 in power notation
Answer:
[tex]a\times (-a)\times 13\times a\times (-a)\times 13[/tex] can be written in power notation as [tex]a^{4}\times 13^{2}[/tex]
Step-by-step explanation:
The given expression
[tex]a\times (-a)\times 13\times a\times (-a)\times 13[/tex]
Writing a\times (-a)\times 13\times a\times (-a)\times 13 in power notation:
Let
[tex]a\times (-a)\times 13\times a\times (-a)\times 13[/tex]
= [tex][13\times13][(a\times (-a)\times a\times (-a)][/tex]
As
[tex]13\times13 = 13^{2}[/tex] , [tex]a\times a = a^{2}[/tex] , [tex](-a)\times (-a) = (-a)^{2}[/tex]
So,
[tex]=[13^{2}][a^2\times (-a)^2][/tex]
As
[tex](-a)^2 = a^{2}[/tex]
So,
[tex]=[13^{2}][a^2\times a^2][/tex]
As ∵[tex]a^{m} \times a^{n}=a^{m+n}[/tex]
[tex]=[13^{2}][a^{2+2}][/tex]
As ∵[tex]a^{m} \times a^{n}=a^{m+n}[/tex]
[tex]=13^{2}\times a^{4}[/tex]
[tex]=a^{4}\times 13^{2}[/tex]
Therefore, [tex]a\times (-a)\times 13\times a\times (-a)\times 13[/tex] can be written in power notation as [tex]a^{4}\times 13^{2}[/tex]
Keywords: power notation
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How can the distributive property be used to write equivalent expressions
with an expression like 3x6 you can separate parts of the expression using parentheses like: 3(2+4)
you can find ways to separate a variable (like 6) into a sum of two addends
ex 1+5
0+6
3+3
so a distributive version of 3x6 is 3(2+4) = (3x2) + (3x4)
What is the cube root of 27a^l2?
-3a4
-3a
3a
3a*
Answer:
[tex]3a^4[/tex]
Step-by-step explanation:
What is the cube root of [tex]27a^{12}[/tex]? This is the question.
We can write:
[tex]\sqrt[3]{27a^{12}}[/tex]
We will use the below property to simplify:
[tex]\sqrt[n]{a*b}=\sqrt[n]{a} \sqrt[n]{b}[/tex]
So, we have:
[tex]\sqrt[3]{27a^{12}} =\sqrt[3]{27} \sqrt[3]{a^{12}}[/tex]
We will now use below property to further simplify:
[tex]\sqrt[n]{x} =x^{\frac{1}{n}}[/tex]
Thus, we have:
[tex]\sqrt[3]{27} \sqrt[3]{a^{12}} =3*(a^{12})^{\frac{1}{3}}[/tex]
We know power to the power rule: [tex](a^z)^b=a^{zb}[/tex]
Now, we have:
[tex]3*(a^{12})^{\frac{1}{3}}\\=3*a^{\frac{12}{3}}\\=3a^4[/tex]
This is the correct answer: [tex]3a^4[/tex]
Which Expression Is Equivalent to 1/6 - 3/8 + 1/2
a) 1/6 -(-3/8) + 1/2
b) 1/6 - (-3/8) + (-1/2)
c) 1/6 + (-3/8) + (-1/2)
d) 1/6 + (-3/8) + 1/2
Answer:
d) 1/6 + (-3/8) + 1/2
Step-by-step explanation:
For equivalence, the sign of each term must match the original. Here's how the answer choices stack up:
a) wrong sign for -3/8
b) wrong sign for -3/8 and for 1/2
c) wrong sign for 1/2
d) correct choice
Final answer:
Option (c) 1/6 + (-3/8) + (-1/2) is equivalent to the original expression 1/6 - 3/8 + 1/2 because it accurately reflects the original values and operations without any alterations.
Explanation:
The student's question asks to find an expression equivalent to the arithmetic operation 1/6 - 3/8 + 1/2. To find the equivalent expression, we should look for an option that represents the same operation without any alteration to the values or their signs.
Upon review, option (c) 1/6 + (-3/8) + (-1/2) is the correct equivalent expression because it maintains the original values and their associated signs. The negative signs in front of the fractions in this option simply denote subtraction, which matches the original expression given.
The use of parentheses in the alternative expression is typical in algebra to emphasize operations, but it does not change the value of the expression. Thus, the correct option is c.
What is the value of the expression |x + y| when x = –7 and y = 18? –25 25 –11 11
Answer:
11
Step-by-step explanation:
- 7 + 8 = 11 and the absolute value of 11 is 11
What is the value of f(x) = 9x when x = -2?
Answer:-18
Step-by-step explanation: if f(x)= -9x
And x =2
-9(2)
= -18
Answer:
f(-2)=-18
Step-by-step explanation:
given f(x)=9x...........(1)
put x=-2 in equation (1)
f(-2)=[tex]9\times(-2)[/tex]
f(-2)=-18 answer
What is 4(x−2)=3(2y−1) in standard form?
Answer: 4x-6y=5
Step-by-step explanation: Using the formula, Ax+By=C, write the equation in standard form.
Hope this helps you out! ☺
The equation 4(x-2) = 3(2y-1) can be converted into standard form by first expanding the equation and then rearranging it. The equation in standard form is 4x - 6y = -5.
Explanation:To convert the equation 4(x-2) = 3(2y-1) into standard form, we first expand both sides of the equation. This results in 4x - 8 = 6y - 3. We can then rearrange the equation to bring all variables to one side which yields 4x - 6y = -8 + 3 or 4x - 6y = -5.
However, in standard form, the coefficients of x and y should be integer and the coefficient of x should be positive. Additionally, the constant should be on the right side of the equation. Therefore, we multiply the whole equation by -1 to get -4x + 6y = 5. Multiplying again by -1 to make the coefficient of x positive, we get 4x - 6y = -5 which is the standard form of the given equation.
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3x +15=75 what is the value of x
Answer:
X=20
you subtract 15 from 75 to get 60 then divide 60 by 3 to get 20
What is parentheses one fourth parentheses cubed three
Answer:
(1/4) ^3 = 0.0833333333
In ΔJKL, k = 3.7 cm, ∠K=15° and ∠L=41°. Find the length of j, to the nearest 10th of a centimeter.
Answer:
The length of side j is 11.85cm
Step-by-step explanation:
Given that
In triangle JKL,
[tex]\angle k=15[/tex]
[tex]\angle l=41[/tex]
Side k=LJ=3.7cm
To find side j=KL:
By using sine rule,
We can write as
[tex]\frac{SinK}{LJ} = \frac{SinL}{JK} = \frac{SinJ}{KL} \\\frac{Sin15}{3.7} = \frac{Sin41}{JK} = \frac{SinJ}{KL}[/tex]
Using property of triangle,
[tex]\angle k+\angle l+\angle j=180[/tex]
[tex]15+41+\angle j=180[/tex]
[tex]\angle j=124[/tex]
[tex]\frac{Sin15}{3.7} = \frac{Sin41}{JK} = \frac{Sin124}{KL}\\\frac{Sin15}{3.7} = \frac{Sin124}{KL}\\KL=3.7\frac{Sin124}{Sin15}\\KL=3.7\frac{0.8290}{0.2588}\\KL=11.85cm[/tex]
Thus,
The length of side j is 11.85cm
Answer: 11.9
Step-by-step explanation:
nearest 10th you have to round it
Determine the type and number of solutions of 4x2 − 3x + 1 = 0. A two imaginary solutions B two real solutions C one real solution
Option A
The equation [tex]4x^2 - 3x + 1 = 0[/tex] has two imaginary solutions
Solution:
Given that we have to determine the type and number of solutions of given quadratic equation
[tex]4x^2 - 3x + 1 = 0[/tex]
[tex]\text {For a quadratic equation } a x^{2}+b x+c=0, \text { where } a \neq 0\\\\x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}[/tex]
In a quadratic equation, the discriminant helps tell you the number of real solutions to a quadratic equation
In the case of a quadratic equation [tex]ax^2 + bx + c = 0[/tex], the discriminant is [tex]b^2 -4ac[/tex]
[tex]\text{If } b^{2}-4 a c=0 ;$ then the given quadratic equation has one real root\\\\If b^{2}-4 a c>0,$ then the given quadratic equation has two real roots[/tex]
If [tex]b^2-4ac<0[/tex], then the given quadratic equation has two imaginal roots which are complex conjugates
Given quadratic equation is:
[tex]4x^2 - 3x + 1 = 0[/tex]
Here a = 4 and b = -3 and c = 1
The discriminant is given as:
[tex]b^2 - 4ac = (-3)^2 - 4(4)(1) = 9 - 16 = -7\\\\b^2 - 4ac = -7\\\\b^2-4ac < 0[/tex]
Therefore the given equation has two imaginary solutions
Answer:
two imaginary solutions
Step-by-step explanation:
Can you please help me solve questions 1 and 2
Answer:
see explanation
Step-by-step explanation:
(1)
Given the perimeter then the third side is the perimeter subtract the sum of the 2 given sides, that is
third side
= 4x + 3y - (x - y + x + y)
= 4x + 3y - 2x ← collect like terms
= 2x + 3y
(2)
The area (A) of a triangle is calculated as
A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the height )
Here b = 2x + 6 and h = x - 2, thus
A = [tex]\frac{1}{2}[/tex](2x + 6)(x - 2) ← expand factors using FOIL
= [tex]\frac{1}{2}[/tex](2x² + 2x - 12) ← distribute
= x² + x - 6 ← in standard form
A truck carries apples, grapes, and blackberries in the ratio of 4:3:4 if the apple weighs 160 pounds how much does the truckload of fruit weigh in total
Answer:
440 pounds
Step-by-step explanation:
Ratio is basically "parts".
We have ratio of 4:3:4, that is a total of 4 + 3 + 4 = 11 parts
The apple is 4 parts and total amount is 160 pounds. So each "part" is:
160/4 = 40 pounds
The total pounds of all 3 fruits is 11 parts * 40 pounds per part = 11 * 40 = 440 pounds
hence,
Truckload of fruits weigh at 440 pounds
What is the value of h in the figure below? In this diagram BAD~CBD
Answer:
The correct option is E. 8
The value of h is 8 unit.
Step-by-step explanation:
Given:
Δ BAD ~ Δ CBD
AC = 20
DC = 4
∴ [tex]AD = AC - DC=20-4=16[/tex]
To Find:
h = ?
Solution:
Δ BAD ~ Δ CBD ................Given
If two triangles are similar then their sides are in proportion.
[tex]\frac{BD}{CD} =\frac{AD}{BD} =\frac{BA}{CB}\ \textrm{corresponding sides of similar triangles are in proportion}\\[/tex]
On substituting the given values we get
[tex]\dfrac{BD}{CD} =\dfrac{AD}{BD}[/tex]
[tex]\dfrac{h}{4} =\dfrac{16}{h}\\\therefore h^{2}=64\\\therefore h=8\ unit[/tex]
The value of h is 8 unit.
Answer:
8
Step-by-step explanation:
Which is a factor of 144 − 49x2?
12 - 7x2
72 – 7x2
12 – 7x
72 + 7x
Answer:
(12-7x)
Step-by-step explanation:
144 − 49x²
by observation, we can see that 144 = 12² and 49 = 7²
hence we can rewrite the equation
144 − 49x²
= 12² - 7²x²
= 12² - (7x)²
recall that the expression x² - y² = (x+y)(x-y)
hence,
12² - (7x)²
= (12 + 7x)(12-7x)
(12-7x) appears in the expression above, hence 12 -7x is a factor
Answer:
Answer is C
Step-by-step explanation:
Christian reads 14 book every 23 week.
How many books does Christian read per week?
16
38
223
6 ///////What percent is equivalent to 45 ?
20%
40%
60%
80% /////// Blueberries are on sale for $2.80 per pint. The regular price is $3.50 per pint.
What is the percent of decrease?
Select from the drop-down menu to correctly complete the statement.
The percent of decrease is
Picture 1: The amount of tax for Veena's meal is $1.02
Picture 2: Christian reads [tex]\frac{3}{8}[/tex] books per week.
Picture 3: 80% is equal to [tex]\frac{4}{5}[/tex].
Step-by-step explanation:
Picture 1: Veena ate lunch at a deli. She ordered turkey sandwich for $9.25 and a salad for $4.35. The tax was 7.5%. What is the amount of tax for Veena's meal.
Given,
Price of turkey sandwich = $9.25
Price of salad = $4.35
Total amount = 9.25+4.35 = $13.60
Tax = 7.5%
Amount of tax = 7.5% of total cost
Amount of tax = [tex]\frac{7.5}{100}*13.60[/tex]
Amount of tax = [tex]\frac{102}{100} = \$1.02[/tex]
The amount of tax for Veena's meal is $1.02
Picture 2: Christian reads 1/4 book every 2/3 week. How many books does Christian read per week?
Given,
Books read every 2/3 weeks = 1/4 books
[tex]\frac{2}{3}\ weeks=\frac{1}{4}\ books\\[/tex]
For determining the number of books read per week, we will multiply both sides by [tex]\frac{3}{2}[/tex]
[tex]\frac{3}{2}*\frac{2}{3}\ week=\frac{1}{4}*\frac{3}{2}\ books\\\\1\ week = \frac{3}{8}\ books\\\\[/tex]
Christian reads [tex]\frac{3}{8}[/tex] books per week.
Picture 3: What percent is equivalent to [tex]\frac{4}{5}[/tex]?
We will multiply the given fraction with hundred for calculating the percentage.
[tex]\frac{4}{5}*100\\\\\frac{400}{5}\\\\80\%[/tex]
Therefore,
80% is equal to [tex]\frac{4}{5}[/tex].
Keywords: percentage, division
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Chloe is painting a room she uses 1/4 gallon of paint to cover 1/3 of a wall if the walls are all the same size how much paint will she need to cover one wall
Answer:
3/4 gallon
Step-by-step explanation:
we know that
Chloe uses 1/4 gallon of paint to cover 1/3 of a wall
so
using proportion
Find out how much paint she will need to cover one wall
Let
x ---> paint needed to cover one wall
[tex]\frac{(1/4)}{(1/3)}=\frac{x}{1}\\\\x=\frac{1}{4} :\frac{1}{3}\\\\x=\frac{3}{4}\ gal[/tex]
REALLY NEED HELP ASAP!!!!!!!
Answer: OPTION C
Step-by-step explanation:
There are some transformations for a function f(x). Some of them are shown below:
1. If [tex]f(x)+k[/tex], the function is shifted up "k" units.
2. If [tex]f(x)-k[/tex], the function is shifted down "k" units.
3. If [tex]f(x+k)[/tex], the function is shifted left "k" units.
4. If [tex]f(x-k)[/tex], the function is shifted right "k" units.
In this case you know that the function "g" is the transformation of the function "f".
Observe that the function "f" intersects the y-axis at:
[tex]y=2[/tex]
And the function "g" intersects the y-axis at:
[tex]y=-2[/tex]
Therefore, since both functions are 4 units apart, you can conclude that the function "f" was shifted down 4 units to get the function "g".
Then, the rule that shows that transformation is:
[tex]g(x)=f(x)-4[/tex]
KHAN GEOMETRY QUESTION!!!!!!!!!HELP!!!!!!
Answer:
Arc VU = 44°
Step-by-step explanation:
Given:
Arc SV means ∠SOV = 120°
Arc VU means ∠VOU = ?
We know that, from central angle theorem, central angle made by arc is twice the angle made the same arc at the circumference.
∴ ∠SOU = 2 × ∠STU
⇒ ∠SOU = 2(82°)
⇒ ∠SOU = 164°
Now, from angle addition theorem,
∠SOU = ∠SOV + ∠VOU
⇒ 164° = 120° + ∠VOU
⇒ 164° - 120° = ∠VOU
⇒ ∠VOU = 44°
Therefore, the measure of the arc VU is 44°.
Italy’s time zone is GMT + 1, so if it is 1 PM GMT, it is what time in Italy?
Answer:
Italy Time is in the Central European Time Zone . Central European Standard Time ( CET ) is 1 hours ahead of Greenwich Mean Time ( GMT+1 ).
Step-by-step explanation:
Central European Time Zone
Italy's time zone is one hour ahead of GMT (Greenwich Mean Time), so if it is 1 PM GMT, it would be 2 PM in Italy. This reflects the Time Zone Difference concept.
Explanation:If Italy's time zone is GMT + 1, and it is currently 1 PM GMT, then the time in Italy would be 2 PM. This is due to the fact that Italy is one hour ahead of GMT (Greenwich Mean Time). Therefore, to convert from GMT to Italy's time zone, one simply needs to add one hour. For example, if it was 5 PM in GMT, it would be 6 PM in Italy, and so on. This concept is referred to as Time Zone Difference.
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is y=5x+7 liner, nonlinear, or both
Which of the following statements is needed in order to prove these triangles are congruent using SSS?
A
∠BCA≅∠EFD
B
AC¯¯¯¯¯≅ED¯¯¯¯¯
C
DE¯¯¯¯¯≅BC¯¯¯¯¯
D
AB¯¯¯¯¯≅DE¯¯¯¯¯
To prove congruence by SSS, two statements are needed about equal sides: AC―――― ≅ ED―――― and DE―――― ≅ BC――――. A third unlisted statement equating the other sides is also required.
Explanation:To prove two triangles are congruent using the Side-Side-Side (SSS) Postulate, we need to establish that all three corresponding sides of the triangles are equal in length. Statement B indicates that AC―――― ≅ ED――――, which provides one pair of corresponding sides. Statement C suggests that DE―――― ≅ BC――――, providing a second pair of corresponding sides. Lastly, if we had information that AB―――― = DF――――, not provided in the options but necessary to complete the SSS congruence, then we could establish the congruence of the two triangles. Therefore, the statements needed for SSS congruence proof are options B and C, along with an unlisted statement that equates the third pair of corresponding sides.
how to do this?? give me a solution its confusing me?!!
Answer:
t = 3h
Step-by-step explanation:
Given
h = [tex]\frac{1}{3}[/tex] t
Multiply both sides by 3 to clear the fraction
3h = t
SHOW WORK
WILL MARK BRAINLIEST
Answer:
[tex]\large\boxed{x=\dfrac{5\pi}{4}\ \vee\ x=\dfrac{7\pi}{4}}[/tex]
Step-by-step explanation:
The first step in attachment.
[tex]\sin(x)=-\dfrac{\sqrt2}{2}\to x=-\dfrac{\pi}{4}+2k\pi\ \vee\ x=\dfrac{5\pi}{4}+2k\pi\\\\x\in[0,\ 2\pi)\\\\\text{Therefore}\\\\x=-\dfrac{\pi}{4}+2\pi=\dfrac{7\pi}{4}\ \vee\ x=\dfrac{5\pi}{4}[/tex]
Jordan trolls a fair dice 216 times how many times would Jordan expect to roll a four
Answer:
36
Step-by-step explanation:
since a fair die has 6 sides (i.e 6 possible outcomes),
P (rolls a 4 on 1 roll) = 1/6
hence if he rolls the die 216 times, we would expect to roll a 4 for 1/6 of the time. I.e.
expected number of times to roll a 4
= (1/6) x 216 = 36 times.
Answer:
Answer:
36
Step-by-step explanation:
since a fair die has 6 sides (i.e 6 possible outcomes),
P (rolls a 4 on 1 roll) = 1/6
hence if he rolls the die 216 times, we would expect to roll a 4 for 1/6 of the time. I.e.
expected number of times to roll a 4
= (1/6) x 216 = 36 times.
Step-by-step explanation:
30 points pls help image included