Answer:
x = 2
Step-by-step explanation:
→ Work out the area of the first triangle
0.5 × 4 × 7 = 14
→ Set up an equation for the second base
0.5 × x × 14 = 14
→ Simplify
7x = 14
→ Divide both sides by 7
x = 2
Answer:
option B = 2cm
Step-by-step explanation:
[tex]Area \ of \ first \ triangle = \frac{1}{2} \times base_1 \times height_1 \ [ \where base_1 = 4\cm \ height_1 \ = 7cm \ ][/tex]
[tex]=\frac{1}{2} \times 4 \times 7 \\\\= 14 \ cm^2[/tex]
Given area of second triangle is same as first.
[tex]Area \ of \ second \ triangle = \frac{1}{2} \times base_2 \times height_2 \ [ \ where \ height _ 2 = 14cm \ ][/tex]
[tex]14 = \frac{1}{2} \times base_2 \times 14\\\\14 = 7 \times base_2\\\\base_2 = 2 \ cm[/tex]
i need help pleasee
A family uses 15 gallons of milk every 3 weeks. At that rate, about how many gallons of milk will they need to purchase in a year’s time?
Give your answer as a whole number.
ONLY ANSWER IF YOU KNOW THE ANSWER
Answer:
87 gallons
Step-by-step explanation:
5 gallons: 3 weeks = x gallons: 52 weeks
5/3 = x/52
3x = 260
x= 86.6, about 87 gallons
Determine whether the following event is mutually exclusive or not mutually exclusive.
Choosing a student who is a history major or a business major from a nearby university to participate in a research study. (Assume that each student only has one major.)
Answer:
Following are the solution to the given points:
Step-by-step explanation:
Both A and B are exclusive to each other because of P(A and B) = 0.
Therefore, Let A be the major in mathematics and B be the major in philosophy.
Each student is required to only have one major.
No student does have two significant students.
Therefore, the likelihood of both the major pupils being zero.
This is P(A and B) = zero
Therefore, The events are exclusive to each other.
Consider the following statement. For every integer m, 7m + 4 is not divisible by 7. Construct a proof for the statement by selecting sentences from the following scrambled list and putting them in the correct order. Suppose that there is an integer m such that 7m + 4 is divisible by 7.Subtracting 4m from both sides of the equation gives 7 = 4k − 4m = 4(k − m).By definition of divisibility 4m + 7 = 4k, for some integer k.By definition of divisibility 7m + 4 = 7k for some integer k.Dividing both sides of the equation by 7 results in 4 7 = k − m.Dividing both sides of the equation by 4 results in 7 4 = k − m.But k − m is an integer and 7 4 is not an integer.Suppose that there is an integer m such that 7m + 4 is not divisible by 7.But k − m is an integer and 4 7 is not an integer.Subtracting 7m from both sides of the equation gives 4 = 7k − 7m = 7(k − m).
Answer:
A proof for the statement by selecting the given sentences are as follows;
Suppose there is an integer m such that 7·m + 4 is divisible by 7
By definition of divisibility, 7·m + 4 = 7·k for some integer k
Subtracting 7·m from both sides of the equation gives 4 = 7·k - 7·m = 7·(k - m)
Dividing both sides of the equation by 7 results in 4/7 = k - m
But k - m is an integer and 4/7 is not an integer
Therefore, for every integer m, 7·m + 4 is not divisible by 7
Step-by-step explanation:
The given equation can be expressed as follows;
Where 7·m + 4 is divisible by 7, we have;
7·m + 4 = 7·k
Where 'k' is an integer
We have;
7·m + 4 - 7·m = 4 = 7·k - 7·m
∴ k - m = 4/7, where k - m is an integer
∴ k - m cannot be equal to 4/7, from which we have;
7·m + 4 cannot be divisible by 7.
A communications company has developed three new designs for a cell phone. To evaluate consumer response, a sample of n = 120 college students is selected and each student is given all three phones to use for one week. At the end of the week, the students must identify which of the three designs they prefer. The distribution of preference is as follows:
Design 1 Design 2 Design 3
54 38 28
Required:
Do the results indicate any significant preferences among the three designs?
Answer:
There is significant preference among the 3 designs
Step-by-step explanation:
Given :
Design 1 Design 2 Design 3
54 38 28
H0 : no significant preference among the 3 designs
H1 : The preference among the designs are different
To test, we use the Chisquare test for independence ;
χ² = (observed - Expected)² / Expected
The sample size, n = 120
Expected = 120 / number of designs = 120 / 3 = 40
(54-40)^2/ 40 + (38 - 40)² / 40 + (28 - 40)² / 40
= 4.9 + 0.1 + 3.6
= 8.6
The Chisquare critical value at 95% = 5.99
Since ;
|χ² critical| < χ² statistic ; we reject the null and conclude that there is significant preference among the 3 designs
Triangles A B C and D E F are shown. Triangle A B C is rotated to the left about point A and then is shifted up and to the right to form triangle D E F. What are the rigid transformations that will map △ABC to △DEF? Translate vertex A to vertex D, and then reflect △ABC across the line containing AC. Translate vertex B to vertex D, and then rotate △ABC around point B to align the sides and angles. Translate vertex B to vertex D, and then reflect △ABC across the line containing AC. Translate vertex A to vertex D, and then rotate △ABC around point A to align the sides and angles.
Answer:
The answer is D. Translate vertex A to Vertex D, and then rotate triangleABC around point A to align the sides and angles
Translating vertex A to vertex D, and then rotate △ABC around point A to align the sides and angles will bring about a rigid transformation, the correct answer is D.
What are Rigid transformation?The transformations that preserves the Euclidean distance between points. This could be as a result of the any transformation.
Triangle ABC and DEF is shown,
Triangle A B C is rotated to the left about point A and then is shifted up and to the right to form triangle D E F.
To map ΔABC to ΔDEF , the vertex A will be translated to vertex D, and then the triangle is rotated around point A.
This will maintain the distance between the points when vertex A to D.
To know more about Rigid transformation
brainly.com/question/1462871
#SPJ5
Lol, can someone help me please?
Answer:
1. 11/26 because you add all of the numbers together and thats how i got 26 then you simplify 11/26 which is the simplist form.
2. 5/13 because you simplify 10/26 which equals 5/13
3. 5/26 because it is already in the simplist form
Step-by-step explanation:
~ Hope this helped u Kaitilyn :)))))
Answer:
11/26 is red, 10/26 is yellow, and 5/26 is blue
Step-by-step explanation:
So, to find the probabilities, we must figure out the total amount of frequency found. To do this lets add up the frequencies of red blue and yellow:
11+10+5 = 26
So our total is 26.
This will be the denominator of our fractions. The numerator will be the amount of the specific freuqency we are looking at.
So reds would be:
11/26 - Frequency of red over Total frequency = Ratio
10/26 - Frequency of red over Total frequency = Ratio
5/26 - Frequency of red over Total frequency = Ratio
So these are your 3 answers!
Hope this helps!
Convert: (a) 250 liters to kiloliters, (b) 4.5 liters to milliliters.
Answer:
a) 0.25 kl
b) 4500 ml
Step-by-step explanation:
a)
1 kiloliter = 1000 liters
x kiloliters = 250 liters
[tex]x = \frac{250}{1000} = 0.25 \ kiloliters[/tex]
b)
1 liter = 1000 milliliters
4.5 liters = x
[tex]x = 4.5 \times 1000 = 4500 \ milliliters[/tex]
Which expression is equivalent to (st)(6)?
s(t(6))
s(x) × t(6)
s(6) × t(6)
6 × s(x) × t(x)
Answer:
A
Step-by-step explanation
Answer:
the answer is c
Step-by-step explanation:
distributive property
José tiene 30 años menos que su padre y 27 más que su hijo. entre los 3 suman 135 años ¿ cuántos años tiene cada uno?
Answer:
44 años tiene jose . el padre 74 y el hijo 17 años.
Step-by-step explanation:
Find the Diameter of the circle, whose radius is 17 cm.
Answer:
34 cm
Step-by-step explanation:
The radius is half of the diameter, so 17 cm is half of 34 cm.
Diameter = 34 cm
Correct answer plz. 15 points. Reported for wrong answer. Thx
Third option is the right answer:
−2x + 4y ≥ 0
Someone please help T.T I need help ASAP
Step-by-step explanation:
Given that,
The quadratic equation that models the ball's height above the ground h, t seconds after it was thrown is given by :
[tex]h=-16t^2+108t+28[/tex] ...(1)
(a) For maximum height, put dh/dt = 0
So,
[tex]\dfrac{d(h)}{dt}=\dfrac{d}{dt}(-16t^2+108t+28)=0\\\\-32t+108=0\\\\t=\dfrac{108}{32}=3.37\ s[/tex]
Put the value of t in equation (1).
So,
[tex]h=-16(3.37)^2+108(3.37)+28\\\\h=210.24\ ft[/tex]
(b) When the ball reaches the ground,
h = 0
So,
[tex]-16t^2+108t+28=0\\\\t=7\ s[/tex]
So, the ball hits the ground in 7 seconds.
HELP!! I don’t know part c or d and I need to know if part a and b are correct thanksss
Answer:
d=67257
c=93
Step-by-step explanation:
Given that yx is a diameter of V, find mZVX if mYVZ=(15r -1)", mWVX =(8x- 2).mUVW =(7x +15).
and mYVU = 3x + 5).
A 32
B 45°
C 70
D. 134
The girls in Lana’s troop set a goal to sell 1,000 boxes of cookies this year. There are 13 girls in the troop. At least how many boxes of cookies should each girl sell to reach their goal?
Answer:
77 boxes each
Step-by-step explanation:
1,000/13
Answer:
Step-by-step explanation:
1000/13= 76.9 .... Each girl needs to sell 77 boxes
Choose the fraction that is greater than 5/9
===========================================
Convert each fraction shown to decimal form
5/9 = 0.555557/16 = 0.43750 8/15 = 0.53333 6/11 = 0.54545 14/23 = 0.60870With the exception of 7/16 = 0.43750, the other decimal values are approximate.
From that list, we can see the decimal representations of 7/16, 8/15, and 6/11 are all smaller than the decimal version of 5/9. So we rule out choices A, B, and C. The answer must be choice D.
Sure enough, 14/23 = 0.60870 is indeed larger than 5/9 = 0.55555
---------------------
We can show this another way:
First off, assume that 14/23 and 5/9 are equal. We'll cross multiply and show a contradiction happens
14/23 = 5/9
14*9 = 23*5
126 = 115
The contradiction happens since we should get the same value on both sides if the two sides were equal, but they're not equal.
If we replace each equal sign with a greater than sign, then we get,
14/23 > 5/9
14*9 > 23*5
126 > 115
You can think of it like working backwards up the chain.
A metal cube dissolves in acid such that an edge of the cube decreases by 0.53 mm/min. How fast is the volume of the Cube changing when the edge is 6.3 mm?
Answer:
The volume of the cube is decreasing at a rate of 63.1071 cubic millimeters per minute.
Step-by-step explanation:
The volume of a cube is given by:
[tex]V=s^3[/tex]
Implicitly differentiate the equation with respect to time t:
[tex]\displaystyle \frac{dV}{dt}=3s^2\frac{ds}{dt}[/tex]
The edge of the cube decreases by 0.53 mm/min. Therefore, ds/dt = -0.53.
When the edge is 6.3 mm, s = 6.3.
Substitute and evaluate:
[tex]\displaystyle \frac{dV}{dt}=3(6.3)^2\left(-0.53\right)=-63.1071\text{ mm}^3/\text{min}[/tex]
The volume of the cube is decreasing at a rate of 63.1071 cubic millimeters per minute.
Giải phương trình
X^2 +2x-3=?
[tex]\implies {\blue {\boxed {\boxed {\purple {\sf { \:(x - 1)(x + 3) }}}}}}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\orange{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]
[tex] {x}^{2} + 2x - 3[/tex]
[tex] = {x}^{2} + 3x - x - 3[/tex]
Taking [tex]x[/tex] as common from first two terms and 1 from last two terms, we have
[tex] = x(x + 3) - 1(x + 3)[/tex]
Taking the factor [tex](x+3)[/tex] as common,
[tex] = (x - 1)(x + 3)[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{❦}}}}}[/tex]
If f(x) = 2x + 7 and g(x) = 3x - 6, then what is (f + g)(x)?
9514 1404 393
Answer:
(f+g)(x) = 5x +1
Step-by-step explanation:
Substitute the given expressions and simplify.
(f+g)(x) = f(x) +g(x)
(f+g)(x) = (2x +7) +(3x -6) = (2x +3x) +(7 -6)
(f+g)(x) = 5x +1
The original retail of a leather chair is listed at $121.40 and is discounted by 60% in a summer sale. What is the discount and the sale price
Answer:48.56
Step-by-step explanation: 121.40-60%=
Jared has 20 flowers. He wants to plant all of the flowers in equal rows in his garden. What are the different ways Jared can arrange the flowers in equal rows? Solve this problem any way you choose.
Answer:
5 rows of 4 each
4 rows of 5 each
2 rows of 10 each
10 rows of 2 each
1 row of 20
20 rows of 1
Step-by-step explanation:
Solve the inequality 4x – 7 < 5
Answer:
x < 3
Step-by-step explanation:
Given
4x - 7 < 5 ( add 7 to both sides )
4x < 12 ( divide both sides by 4 )
x < 3
If l=10 b=5 and h=2, find the values of 2(lb+bh+lh)
Answer:
160
Step-by-step explanation:
[tex]2((10)(5)+(5)(2)+(10)(2))\\2(50+10+20)\\2(80)\\160[/tex]
[tex]\huge\textsf{Hey there!}[/tex]
[tex]\large\textsf{2(lb + bh + lh)}\\\\\large\textsf{= 2(10(5) + 5(2) + 10(2))}\\\\\large\textsf{10(5) = \boxed{\bf 50}}\\\\\large\textsf{= 2(50 + 5(2) + 10(2))}\\\\\large\textsf{5(2) = \boxed{\bf 10}}\\\\\large\textsf{= 2(50 + 10 + 10(2))}\\\\\large\textsf{50 + 10 = \boxed{\bf 60}}\\\\\large\textsf{= 2(60 + 10(2))}\\\\\large\textsf{10(2) = \boxed{\bf 20}}\\\\\large\textsf{= 2(60 + 20)}\\\\\large\textsf{60 + 20 = \boxed{\bf 80}}\\\\\large\textsf{= 2(80)}\\\\\large\textsf{= \boxed{\bf 160}}\large\checkmark[/tex]
[tex]\boxed{\boxed{\huge\textsf{Answer: \bf 160}}}\huge\checkmark[/tex]
[tex]\large\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Tích các nghiệm của phương trình Log(x-1)²=2 là
Answer:
-99
Step-by-step explanation:
Log(x-1)²=2
Log(x-1)²=Log(100)
(x-1)²=100
x-1=10 and x-1=-10
x₁=11 and x₂=-9
x₁ × x₂ = 11 × (-9) = -99
PLEASEEEEE HELPPPPPPPP
Answer:
f(-5) = -195
Step-by-step explanation:
Given that,
[tex]f(x)=x^3-2x^2+3x-5[/tex] ....(1)
and
[tex]g(x)=x^2+x-1[/tex]
We need to find the value of f(-5).
Put x = -5 in equation (1).
[tex]f(-5)=(-5)^3-2(-5)^2+3(-5)-5\\\\=-195[/tex]
So, the value of f(-5) is equal to (-195).
Amanda only has $30 to buy pens and notebooks. Each pen costs $2. Each notebook coats $3. Which of the following graph represents the possible combinations of pens and notebooks that she may purchase?
Answer:
3p + 8n, 12p + 2n, 9p+4n, 6p+6n
8 columns bar graph.
Step-by-step explanation:
$2 = pen
$3 = notebook
This could be written as a bar graph in multiples of $6.00 along y axes.
3 pens + 8 notebooks. Then 12 pens + 2 notebooks.
Then 9 pens + 4 notebooks . Then 6 pens + 6 notebooks
3p + 8n, 12p + 2n, 9p+4n, 6p + 6n
3p = $6
8n = $24
12p = $24
2n = $6
9p = $18
4n = $12
6p = $12
6n = $18
and so on...
is the function given by G(x) - 1/x-6 continuous over the interval (1, ∞)? Why or why not?
a. No, the function is not continuous at x=
b. Yes, the function is continuous over (1,∞) because lim x>a G(x)= G(a) for all a in (1,∞).
Answer:
No, the function is not continuous at x=
Rotating shapes about the origin by multiples of 90 degrees
Answer:
the rotated point B is then at (3, -7)
Step-by-step explanation:
the specification says a rotation of -90 degrees (counter clockwise) around the point (0, 0).
a turn by 90 degrees in any direction brings it always into the next quadrant, because every quadrant represents 90 degrees.
the rotated point will have the same distance from the center, of course. and the angle of the connection line center to B to the negative x-axis will be then the same as the angle of the connection line to the rotated point to the negative y-axis.
just think about rotating the original graph by -90 degrees. point B stays on the grid were it is and moves with the grid, and we just flip the coordinate axis.
so, it will be (3, -7).
Assume that x and y are both differentiable functions of t and find the required values of dy/dt and dx/dt.
xy = 2
a. Find dy/dt, when x = 4, given that dx/dt = 13.
b. Find dx/dt, when x = 1, given that dy/dt = -9.
Answer:
a. [tex]\frac{dy}{dt} = -\frac{13}{8}[/tex]
b. [tex]\frac{dx}{dt} = \frac{9}{2}[/tex]
Step-by-step explanation:
To solve this question, we apply implicit differentiation.
xy = 2
Applying the implicit differentiation:
[tex]y\frac{dx}{dt} + x\frac{dy}{dt} = \frac{d}{dt}(2)[/tex]
[tex]y\frac{dx}{dt} + x\frac{dy}{dt} = 0[/tex]
a. Find dy/dt, when x = 4, given that dx/dt = 13.
x = 4
So
[tex]xy = 2[/tex]
[tex]4y = 2[/tex]
[tex]y = \frac{2}{4} = \frac{1}{2}[/tex]
Then
[tex]y\frac{dx}{dt} + x\frac{dy}{dt} = 0[/tex]
[tex]\frac{1}{2}(13) + 4\frac{dy}{dt} = 0[/tex]
[tex]4\frac{dy}{dt} = -\frac{13}{2}[/tex]
[tex]\frac{dy}{dt} = -\frac{13}{8}[/tex]
b. Find dx/dt, when x = 1, given that dy/dt = -9.
x = 1
So
[tex]xy = 2[/tex]
[tex]y = 2[/tex]
Then
[tex]y\frac{dx}{dt} + x\frac{dy}{dt} = 0[/tex]
[tex]2\frac{dx}{dt} - 9 = 0[/tex]
[tex]2\frac{dx}{dt} = 9[/tex]
[tex]\frac{dx}{dt} = \frac{9}{2}[/tex]