Answer:
[tex] \boxed{\bold{\boxed{ \sf{x = - 3}}}}[/tex]Step-by-step explanation:
[tex] \sf{2(6x - 1) = - 38}[/tex]
Distribute 2 through the parentheses
⇒[tex] \sf{12x - 2 = - 38}[/tex]
Move constant to right hand side and change it's sign
⇒[tex] \sf{12x = - 38 + 2}[/tex]
Calculate
⇒[tex] \sf{12x = - 36}[/tex]
Divide both sides of the equation by 12
⇒[tex] \sf{ \frac{12x}{12} = \frac{ - 36}{12} }[/tex]
Calculate
⇒[tex] \sf{x = - 3}[/tex]
Hope I helped!
Best regards!!
For one of their science experiments students needed 10 1/2 liters of water. If there were 7 groups
doing the same experiment, how much water did they need for all of the groups?
Answer:
73.5 liters of water
Step-by-step explanation:
10 1/2× 7= 73.5
The amount of water that they need for all of the groups will be 73.5 liters.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
For one of their scientific tests, understudies required 10 ¹/₂ liters of water. Assuming there were 7 gatherings doing likewise analysis.
The amount of water that they need for all of the groups will be calculated as,
⇒ (10 ¹/₂) x 7
Simplify the expression, then we have
⇒ (10 ¹/₂) x 7
⇒ (10 + ¹/₂) x 7
⇒ (21/2) x 7
⇒ 147/2
⇒ 73.5 liters
The amount of water that they need for the gatherings will be all 73.5 liters.
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A consignment of fodder can feed 1000 sheep
20 days. Assuming that all the sheep consume
fodder at the same rate, how many consignmen
of fodder are needed to feed 550 sheep for 400 days?
Answer: 11 consignmen
Step-by-step explanation:
Given that a consignment of fodder can feed 1000 sheep 20 days. Assuming that all the sheep consume
fodder at the same rate, then
1000 × 20 = 20000 for 1 consignment
to feed 550 sheep for 400 days, that is
550 × 400 = 220000
The consignment that will be needed will be
220000 / 20000 = 11
Therefore, 11 consignment fodder are needed to feed 550 sheep for 400 days.
kevin has 70 cents in his pocket. one coin is a quarter, and the others are nickels. how many nickels does he have?
Answer:
Step-by-step explanation:
25 +5+5+5+5+5+5+5+5+5=70
Answer: 9nickels
Find the exact area of the shaded region. A. 16π−8 cm² B. 42.3 cm² C. 92.5 cm² D. 84.6 cm2
Answer:
A = (16π - 8) cm^2
Step-by-step explanation:
The shaded area is trhe area of the circle minus rthe area of the truiangle,.
A = πr^2 - bh/2
A = π(4 cm)^2 - (4 cm)(4 cm)/2
A = 16π cm^2 - 8 cm^2
A = (16π - 8) cm^2
The exact area of the shaded region is (16π - 8) [tex]cm^{2}[/tex].
Option (A) is correct.
To find the shaded area.
What is circle?
A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “center”.
Given that:
Height of triangle is same as that of base because is equal to radius of circle.
The shaded area is area of the circle minus the area of the triangle.
A = π[tex]r^2 - bh/2[/tex]
A = π[tex]4^{2}[/tex] - (4 cm)*(4 cm)/2
A = (16π - 8 )[tex]cm^{2}[/tex]
A = (16π - 8) [tex]cm^{2}[/tex]
The exact area of the shaded region is (16π - 8) [tex]cm^{2}[/tex].
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Given that El bisects ZCEA, which statements must be
true? Select three options,
mZCEA = 90°
mZCEF = m ZCEA + m ZBEF
mZCEB = 2(m ZCEA)
ZCEF is a straight angle.
ZAEF is a right angle.
Question: Given that BE bisects ∠CEA, which statements must be true? Select THREE options.
(See attachment below for the figure)
m∠CEA = 90°
m∠CEF = m∠CEA + m∠BEF
m∠CEB = 2(m∠CEA)
∠CEF is a straight angle.
∠AEF is a right angle.
Answer:
m∠CEA = 90°
∠CEF is a straight angle.
∠AEF is a right angle
Step-by-step explanation:
Line AE is perpendicular to line CF, which is a straight line. This creates two right angles, <CEA and <AEF.
Angle on a straight line = 180°. Therefore, m<CEA + m<AEF = m<CEF. Each right angle measures 90°.
Thus, the three statements that must be TRUE are:
m∠CEA = 90°
∠CEF is a straight angle.
∠AEF is a right angle
The correct statements from the given diagram is m∠CEA = 90°, m∠CEF = m∠CEA + m∠BEF and m∠CEB = 2(m∠CEA)
Lines and anglesFrom the given diagram, we have the following information
∠CEF is a straight angle.
∠AEF is a right angle.
Line AE is perpendicular to line CF, which is a straight line. This creates two right angles, <CEA and <AEF.
Since the angle on a straight line is 180 degrees, hence;
<CEA + m<AEF = m<CEF
Hence, the three statements that must be TRUE are m∠CEA = 90°, ∠CEF is a straight angle and ∠AEF is a right angle
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A jogger leaves his house runs 15 km on a straight track in a North westerly direction to a lake. The lake is 2.9 km north of the joggers house. find the bearing of the lake from the joggers house correct to the nearest degree
Answer: 281.1 degree
Step-by-step explanation:
Given that a jogger leaves his house runs 15 km on a straight track in a North westerly direction to a lake. The lake is 2.9 km north of the joggers house.
Using pythagorean theorem to find the third side, which is 14.72
The angle at the lake side will be achieved by using sine rule.
Please find the attached file for the solution and explanation.
A function f(x) has range {yer 1-50}. Explain why reflecting the function vertically would not affect the range
Answer:
For the reflection property, we have;
For reflection vertically, which is equivalent to reflection across the y-axis, we have;
Let the location or point of the pre-image before, reflection be (x, y), then, the location or point of the image after reflection will be (-x, y)
Therefore, the y-coordinates remains the same
Given that the range of the function is the value of f(x) or y from 1 - 50, which are the y-coordinate values of the function, it will not be affected by the vertical reflection of the function.
Step-by-step explanation:
Help needed ASAP will give brainliest.
Answer:
0.22, 15%, 1/7, 12%, 1/9
Step-by-step explanation:
Showing all given numbers in decimal form rounded to hundredths:
12% = 0.121/9 = 0.110.221/7 = 0.1415%= 0.15Putting them in the order from the greatest to least:
0.22, 0.15, 0.14, 0.12, 0.11Same order with original numbers:
0.22, 15%, 1/7, 12%, 1/9Matching with answer choices:
The third one from the top or C is the correct choice3.
Which of the following equations does not have a real solution?
(A) x + x = 1
(B) x + x=0
(C) x*x=0
(D) x*x=-1
Answer:
I think the right answer is d
Answer:
The last equation (D): doesn't have a real solution
Step-by-step explanation:
Notice that equation A has for solution x = 1/2
Equation B has for solution x = 0
Equation C has for solution x = 0
There is no real number that multiplied by itself can render a negative value.
6. Christopher can make enough iced coffee for one
person by mixing two teaspoons of espresso
with 4 ounces of water. How many tablespoons
of espresso would he need to make enough iced
coffee for 24 people? (3 teaspoons =
1 tablespoon
A) 12
B) 16
C) 48
D) 144
R
Answer:
B) 16
Step-by-step explanation:
Espresso required for one person:
2 teaspoonsEspresso required for 24 people:
2*24 = 48 teaspoons3 teaspoons = 1 tablespoon
48 teaspoons = 48/3 = 16 tablespoons
Christopher needs 16 tablespoons of espresso.
Correct answer choice: B) 16
Please Help. I really don’t get this concept, if you could explain it in detail it would be very appreciated
=================================================
Explanation:
Sine is given to be negative, and so is tangent. This only happens in quadrant Q4
Recall that y = sin(theta), so if sin(theta) < 0, then we're below the x axis.
If tan(theta) < 0, then this means cos(theta) > 0
So we have y < 0 and x > 0 which places the angle somewhere in Q4.
--------------------------
Draw a right triangle as shown below in the attached image. We have AC = 25 and BC = 7. Use the pythagorean theorem to find that AB = 24
So this is what your steps may look like
a^2+b^2 = c^2
7^2+b^2 = 25^2
b^2+49 = 625
b^2 = 625-49
b^2 = 576
b = sqrt(576)
b = 24
So because AB = 24, we know that the cosine of the angle is adjacent/hypotenuse = 24/25
---------------------------
As an alternative, you could use the trig identity
sin^2(x) + cos^2(x) = 1
and plug in the given value of sine to solve for cosine. The cosine value result will be positive since we're in Q4.
So,
sin^2(x) + cos^2(x) = 1
(-7/25)^2 + cos^2(x) = 1
(49/625) + cos^2(x) = 1
cos^2(x) = 1 - (49/625)
cos^2(x) = (625/625) - (49/625)
cos^2(x) = (625-49)/625
cos^2(x) = 576/625
cos(x) = sqrt(576/625)
cos(x) = sqrt(576)/sqrt(625)
cos(x) = 24/25
This is effectively a rephrasing of the previous section since the pythagorean trig identity is more or less the pythagorean theorem (just in a trig form)
The density of Venus, compared to Earth having a density of 1,
is 0.943. The density of Mercury is 0.983, compared to the
density of Earth. Which planet has a greater density, Venus or
Mercury?
Answer:
Mercury
Step-by-step explanation:
We'll translate this into ratios.
First, V:E = 0.943:1
Then, M:E = 0.983:1
We already have their density in terms earth's density. They are in the same unit. So, we can compare them directly, with greater ratio means greater density. It's clear that Mercury has the greater density.
6=2(y+2) what does y equal ?
Answer:
1
Step-by-step explanation:
1. expand the terms on the right side of the equation: 6=2y+4
2. subtract 4 from both side: 2=2y
3. divide both side by 2: 1=y
Answer:
y=1
Step-by-step explanation:
2(y+2)=6
2y+4=6
2y=6-4
2y=2
y=2/2
y=1
Alice has 2 dogs, ollie and taffy, ollie eats 2/3 of a tin of dog food every day and taffy eats 2/5 of a tin everyday, Alice buys a crate of 24 tins. How many whole days should the crate last?
Answer:
Step-by-step explanation:
2/3 + 2/5 = 10/15 + 6/15 = 16/15 tins per day
24 tins divided by 16/15 = 24/1 divided by 16/15
To divide one fraction by another, take reciprocal of the other and then multiply.
24/1 x 15/16 = 360/16 = 22 1/2 days
A number minus 4 equals 19. Which equation fits this statement?
A 4-X=19
BX-4 = 19
C 4 = X-19
D 19 - X=4
If A = {1, 2, 3} and B = {1, 2, 2, 3}, is B ⊆ A? If so, is A = B?
Answer:
yes, yes
Step-by-step explanation:
B={1,2,3} it doesn't matter if it has ten 2's or one!
so A=B and A⊆B
Solve the formula 4x + 7y = 5 for y.
Answer:
39x
Step-by-step explanation:
Just multiply 7 by 5 and that equals-35
now you just add 4x by 35 and that equals-39x
In Niagara-on-the-Lake, you can ride a horse-drawn carriage for a fixed price plus a variable amount that depends on the length of the trip. The variable cost is $10/km and a 2.5-km trip costs $40. a) Determine the equation relating cost, C, in dollars, and distance, d, in kilometres. b) Use your equation to find the cost of a 6.5-km ride. c) Graph this relation. d) Use the graph to find the cost of a 6.5-km ride.
Answer:
Step-by-step explanation:
a) The cost of a product is given as:
Cost = a + bx
Where a is the fixed cost, b is the variable cost, x is the independent variable.
In this case, the independent variable is the distance(d), therefore:
Cost (C) = a + bd
C = a + bd
But the variable cost is $10/km, therefore:
C = a + 10d
A 2.5 km trip cost $40, therefore:
40 = a + 10(2.5)
40 = a + 25
a = 40 - 25 = 15
The fixed cost is $15. Therefore the equation for cost is:
C = 15 + 10d
b) C = 15 + 10d
For 6.5 km ride:
C = 15 + 10(6.5) = 15 + 65 = 80
It would cost $80 for a 6.5 km drive.
Find the least number which should be subtracted from 500 to make it a perfect square
Answer: 16
Step-by-step explanation:
A perfect square is basically some number multiplied by itself. For example, 4 is a perfect square because 2x2=4.
22 x 22 = 484 (under 500)
23 x 23 = 529 (over 500)
Therefore, the perfect square must be 484.
Subtract 484 from 500:
500 - 484 = 16
16 is the answer :)
Two students were asked to use estimation strategies to find a reasonable solution to this question: Darrell has $1,990 saved and wants to buy a motorcycle. He earns $10 per hour and he works for 39 hours. Estimate how much money, Darrell has left after buying a $2,200 motorcycle. From the choices below, select the student with a more reasonable solution.
Answer:
1990+(10h)-2200
or
1990+(10x39)-2200
Step-by-step explanation:
he already has 1990
He earns $10 per hour
he works for 39 hours
$2,200 needed for a motorcycle
1990+(10h)-2200
or
1990+(10x39)-2200
Write this number in expanded form. 268,741
Answer:
200000+60000+8000+700+40+1
Step-by-step explanation:
268,741
2 is in the hundred thousands place 200000
2 is in the ten thousands place 60000
8 is in the thousands place 8000
7 is in the hundreds place 700
4 is in the tens place 40
1 is in the one place 1
Add these together
200000+60000+8000+700+40+1
Answer:
[tex](2\times100000)+(6\times10000)+(8\times 1000)+(7\times100)+(4\times10)+(1\times1)[/tex]
Step-by-step explanation:
So we want to write 268,741 in expanded form.
To do so, first take a look at what each digit means starting from the right.
268,741
This means 1 1s.
268,741
This means 4 10s.
268, 741
This means 7 100s.
268,741
This means 8 1000s.
268,751
This means 6 10,000s.
and 268,751.
This means 2 100,000s.
Therefore, 268,741 is 2 100,000s plus 6 10,000s plus 8 1000s plus 7 100s plus 4 10s plus 1 1s.
In expression form, this would be:
[tex](2\times100000)+(6\times10000)+(8\times 1000)+(7\times100)+(4\times10)+(1\times1)[/tex]
a way to make a approximation to a given number by using fewer digits is called.
Answer:
Rounding
Step-by-step explanation:
Rounding is a way to make an approximation to a given number by using fewer digits.
Answer:
Rounding
Step-by-step explanation:
A way to make a approximation to a given number by using fewer digits is called rounding
How you round:If the next smallest place value is greater than or equal to five (5, 6, 7, 8, or 9), you increase the value of the digit you're rounding to by one (+1). Any remaining digits before the decimal point become zeros, and any that are after the decimal point are dropped.please help :) Write the number shown in standard notation. 6.6 x 10 to the 5 power A. 6,600 B. 660,000 C. 66,000 D. 6,600,000
Answer: Hi!
The equation given is 6.6 * 10^5.
First, we will solve the exponent.
10^5 = 100,000
Next, we will multiply 100,000 by 6.6.
100,000 * 6.6 = 660,000
Therefore, your answer is b), 660,000.
Hope this helps!
what fraction is equivlant to 2/6
Answer:
1/3
Step-by-step explanation:
The simplest form of 2/6 is 1/3. You can do 2/6*.5/.5 to get 1/3
You can do other fractions such as 4/12, 8/24, as long as it the numerator maintains a ratio of 1:3
six times the difference of x and 22
Answer:
6(x-22) or 6x-132
Step-by-step explanation:
translate into english : it says 6 times difference of x and 22, so you would need to do the subtraction first before you multiply by 6 which you get 6(x-22)!
Answer:
-4
Step-by-step explanation:
6*x-22
keep 6x on the LHS and -22 on the RHS
leave x in LHS and divide -22 with 6 on the RHS
the answer will come -4
How many solutions does the system have?
Answer:
Infinitely many solutions.
You basically have just one equation.
The top equation is the bottom equation times 5.
Step-by-step explanation:
Answer: C. Infinite many solution
Step-by-step explanation:
#1 simplify the first equation: 20x-5y=5
since the GCF in it is 5, we factor out 5
4x-y=1
#2 compare the first and the second equation
[tex]\left \{ {{4x-y=1} \atop {4x-y=1}} \right.[/tex]
we can see that both equation are same, which means they present the same line.
Thus, they overlap and they have infinite many solution
translating verbal expression: 1/2 of a m
Answer: (1/2) m
Step-by-step explanation:
1/2 of a m=(1/2) m
If you want to make it more comprehensive, I am going to provide you with some examples
1/2 of 8=1/2(8)=41/2 of 40=1/2(40)=20Applying [m] goes with the same pattern
Hope this helps!! :)
Please let me know if you have any question
A store polled its customers about the fit of jeans they preferred. the two-way frequency table shows the result of the poll.
doing this because its already answered and I need points. But to be safe, Itds the second option going to the right. (aka the top right option)
Step-by-step explanation:
The two-way frequency table shows the result of the poll is in option "B".
What is frequency table?Frequency refers to the number of times an event or a value occurs. A frequency table is a table that lists items and shows the number of times the items occur.
According to the question
A store polled its customers about the fit of jeans they preferred.
The two-way frequency table shows the result of the poll.
As the frequency table have 4 columns and 3 rows
In which columns have : Regular , Slim , Bootcut , Total
In which rows have : Male , Female ,Total
To check which option is correct we will check whether total is correct for column is row or not
Option A :
This option is incorrect
1st column is not correct as total should be 1 but it is 0.5 .
Option B:
This option is correct as total is correct for column and row .
Option C:
This option is incorrect as total of column Bootcut is not correct .
Option D:
This option is incorrect as total of all columns are incorrect .
Hence, the two-way frequency table shows the result of the poll is in option "B".
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Calculate the area of this diagram
[tex]A=\frac{1}{2}\cdot a\cdot b\cdot \sin\angle AB\\\\A=\frac{1}{2}\cdot6\cdot6\cdot\sin38^\circ\\\\A=18\cdot0.616\\\\\boxed{A=11.0819}[/tex]
b. Simplify (1-3) (⅓+√3), leaving your answer in the form P+Q√3
Answer:
6
Step-by-step explanation: