Respuesta:
1
Explicación paso a paso:
Para completar el cuadrado tendremos que sumar la mitad del cuadrado del coeficiente de x a la expresión;
Coeficiente de x = -2
Mitad del coeficiente = (-2/2) = -1
Tomando el cuadrado del resultado = (-1) ^ 2 = 1
Por lo tanto, el número que se debe sumar para obtener un cuadrado perfecto es 1.
If ABC~ ADEF and the scale factor from AABC to A DEF is 2, what are the
lengths of DE, EF, and DF, respectively?
E
B
4
2
6
A А
A. 4, 8, 12
B. 2, 8, 12
C. 8, 16, 24
D. 1, 2, 3
Answer:
A. 4, 8, 12
Step-by-step explanation:
there is a scale factor f=2 to "go" from one triangle to the other.
that means all sides of the target triangle are created out of their corresponding side of the source triangle by multiplying them by the scale factor.
so,
2×f = 2×2 = 4
4×f = 4×2 = 8
6×f = 6×2 = 12
The lengths of DE, EF, and DF are 4, 8 and 12 respectively, (option 1)
What are similar triangles?Two triangles are said to be similar if their corresponding sides are in equal ratio and corresponding angles are congruent.
Given that, Δ ABC~ Δ DEF and the scale factor from Δ ABC to Δ DEF is 2
Since, the scale factor is 2, therefore each side of Δ ABC is increased by 2 in Δ DEF
Therefore,
DE = 2AB
EF = 2BC
DF = 2AC
Therefore,
DE = 4
EF = 8
DF = 12
Hence, the lengths of DE, EF, and DF are 4, 8 and 12 respectively, (option 1)\
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You buy a 1:10000 scale model of the One World Trade Center during a trip to New York City. The height of the model is 5.41 centimeters. Find the actual height x (in meters) of the One World Trade Center.
Answer:
541m
Step-by-step explanation:
The scale given 1 represents the height of the model and 10000 represents the actual height,place the 5.41 in line with the one and an unknown letter in line with the 10000 inorder to calculate the actual height
1:10000
5.41:x
cross multiply and solve for x,which will be 54100cm
but since the answer has to be in meters convert the 54100cm to a meter by dividing it by 100..
Which statements are true about the result of simplifying this polynomial?
+ (8 + 9t) – (t2 + 4)(+2 – 3t)
The simplified expression has four terms.
The simplified expression is a polynomial.
The simplified expression has a constant term.
The simplified expression is cubic.
a
The simplified expression is a trinomial.
Answer:
The simplified expression has four terms.
The simplified expression has a constant term.
The simplified expression is cubic.
The simplified expression is a trinomial.
The statements that are true about the result of simplifying this polynomial are:
b. The simplified expression is a polynomial.
c. The simplified expression has a constant term.
What are polynomials?Sums of terms of the form k x xⁿ, where k is any number and n is a positive integer, make up polynomials. For instance, the polynomial 3x+2x-5. A description of polynomials.
All other options are false. As it is not cubic because it is degree 4, and it does not have four terms as it has five terms. And it is not trinomial as it has five terms, not three.
The full solution is;
t³(8 + 9t) - (t² + 4)(2 - 3t)
8t³ + 9t⁴ - (2t² - 3t³ + 8 - 12t)
8t³ + 9t⁴ - 2t² + 3t³ - 8 + 12t
9t⁴ + 11t³ - 2t² + 12t - 8
Therefore, the correct options are a, and b.
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Solve for x. Round to the nearest tenth, if necessary. Calculating Sin or Cos or Tan
Answer:
x = 3.6
Step-by-step explanation:
[tex]Cos \theta = \frac{adjacent}{hypotenuse} \\\\ \ where \ \theta = 69^\circ , \ adjacent = TS = x ,\ Hypotenuse = SU = 10[/tex]
[tex]cos \ 69 = \frac{x}{10}\\\\x = 10 \times cos \ 69\\\\x = 10 \times 0.3584\\\\x= 3.584 \\\\x = 3.6[/tex]
What is the answer to this
Answer:
Step-by-step explanation:
Peter owned a juice shop. He sold a cup of lemon juice for $1.25 and a cup of apple juice for $2.50. If Peter sold a total of 155 cups of juice and collected a total of $256 approximately, how many cups of each type did he sell?
The number of cup of lemon juice is 105 cups and number of cup of apple juice is 50 cups.
What is a system of equation?A system of equations is a set or collection of equations that you deal with all together at once. For a system to have a unique solution, the number of equations must equal the number of unknowns.
For the given situation,
Peter sold a cup of lemon juice = $1.25
Peter sold a cup of apple juice = $2.50
Total number of cups sold = 155 cups
Total amount = $256
Let number of cup of lemon juice be x and
let number of cup of apple juice be y
The equations for the above statements are
[tex]x + y = 155 ------- (1)\\1.25x +2.50y = 256 ------- (2)[/tex]
From equation 1,
⇒ [tex]x=155-y[/tex]
Now substitute x in equation 2,
⇒ [tex]1.25(155-y)+2.50y=256[/tex]
⇒ [tex]193.75-1.25y+2.50y=256[/tex]
⇒ [tex]1.25y=256-193.75[/tex]
⇒ [tex]1.25y=62.25\\[/tex]
⇒ [tex]y=\frac{62.25}{1.25}[/tex]
⇒ [tex]y=49.8[/tex] ≈ [tex]50[/tex]
Now substitute y in equation 1,
⇒ [tex]x=155-50[/tex]
⇒ [tex]x=105[/tex]
Hence we can conclude that the number of cup of lemon juice is 105 cups and number of cup of apple juice is 50 cups.
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The volume of the sphere is
500
-n cubic units.
3
What is the value of x?
O4 units
O 5 units
O 8 units
O 10 units
Answer:5 units!
Step-by-step explanation:
.
The value of x will be 5 units for the sphere that has the volume of (500/3)π cubic units.
From the formula of the volume of sphere,
volume of sphere = 4/3 πr³
where, r is the radius
in our case,
volume = (500/3)π
radius = x
substituting the given values
(500/3)π = (4/3)π *x³
x³ = 125
x= 5 units
Therefore, the value of x will be 5 units.
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Complete question:
The volume of the sphere is 500/3 π cubic units.
What is the value of x?
4 units
5 units
8 units
10 units
Which of the following CANNOT be assumed from this image?
Answer:
that he lines are not going strait
Step-by-step explanation:
Two square based pyramids are joined, total volume is 2700mm, perpendicular height 16mm on top pyramid and 20mm on the other, joint base has length and width of x, find x. Please help me..
Answer:
15 mm
Step-by-step explanation:
Since both pyramids are joined together, this means that the base of the pyramid which is a square have the same dimensions.
Let the length and width of the base be x, hence the dimension of the base is x mm by x mm.
For the first pyramid, the volume is:
V₁ = a²h₁/3; where a is the length of the square base, h₁ is the height.
Since the pyramid has a height of 16 mm, hence:
V₁ = 16x²/3
the second pyramid, the volume is:
V₂ = a²h₂/3; where a is the length of the square base, h₂ is the height.
Since the pyramid has a height of 20 mm, hence:
V₂ = 20x²/3
Since the total volume (V) of the pyramid is 2700 mm³, hence:
V = V₁ + V₂
V = 16x²/3 + 20x²/3
2700 = 16x²/3 + 20x²/3
2700 = 36x²/3
36x² = 8100
x² = 225
x = 15 mm
Choose the appropriate word or phrase from the drop down menu to complete the sentences: The mean of the quantitative variable of interest in the population is called the [ Select ] . The mean of the quantitative variable of interest in the sample is called the [ Select ] . The standard deviation of the quantitative variable of interest in the population is called the [ Select ] . The standard deviation of the quantitative variable of interest in the sample is called the [ Select ] .
Answer:
1. Population mean
2. Sample mean
3. Population standard deviation
4. Sample standard deviation
Step-by-step explanation:
Required
Complete the gaps
The answer is self-explanatory.
All you need to do in this question is to look for the keywords (mean/standard deviation) and (population/sample).
In addition, the symbol of the parameters are:
1. Population mean [tex]\mu[/tex]
2. Sample mean [tex]\bar x[/tex]
3. Population standard deviation [tex]\sigma[/tex]
4. Sample standard deviation [tex]\sigma_x[/tex]
What’s the answer 3y+5<10
Answer:
y < 5/3
Step-by-step explanation:
3y + 5 < 10
Let's subtract 5.
3y < 5
Okay. We have something manageable. Let's divide by 3.
y < 5/3
That's our answer.
What is the slope, m, and y-intercept for the line that is plotted on the fried below…?
Determine the solution on the following equation
Answer:
x = 3
Step-by-step explanation:
Step-by-step explanation:
3(8x-8)/2=64
3(8x-8)=64×2
24x-24=128
24x=128+24
24x=152
24x/24=152/24
x=6.3
NEED ANSWER ASAP GIVING BRAINLIEST
Answer:
(-1,1)
Step-by-step explanation:
(x,y), and X is one unit to the left (negative, or -), while Y is one unit up
I will mark brainliest!!
A class conduct an experiment in biology. They place a number of 1 m by 1 m square grids on the playing field and count the number of plants in each grid. The results obtained are given below.
6 3 2 1 3 2 1 3 0 1
0 3 2 1 1 4 0 1 2 0
1 1 2 2 2 4 3 1 1 1
2 3 3 1 2 2 2 1 7 1
(a)
Calculate the mean number of plants.
Step-by-step explanation:
their mean is....
6+3+2+1+3+2+1+3+0+1/10=2.1
3+2+1+1+4+0+1+2+0/10=1.4
1+1+2+2+2+4+3+1+1+1/10=1.8
2+3+3+1+2+2+2+1+7+1/10=2.4
the means are 2.1,1.4,1.8,2.4
the average mean is
21+14+18+24/40
32+45/40
77/40=1.925
the average mean is 1.925
15 POINTS AND BRANLIEST!!!
y = ?x + ?
Answer:
y = -x - 6
Step-by-step explanation:
Parallel lines have same slope
y = -x + 9 {y = mx + c}
m = -1
(x₁, y₁) = (7 , -13)
Equation: y - y₁ = m(x -x₁)
y - [-13] = -1(x -7)
y+ 13 = -x + 7
y = - x + 7 - 13
y = -x - 6
HELP PLS!!
Find the value of x and the value of y.
A. x = 16, y = 9√2
B. X= 7, y = 16√2
C. x = 6√2, y=7√2
D. X= 7√3, y = 16
Answer:
A
Step-by-step explanation:
Thanks to the given angle, we can say that the triangle formed by tracing another height has two congruent legs
So
x = 9 + 7 = 16
y = √2 * 9^2 = 9√2
Answer:
A
Step-by-step explanation:
Completing the rectangle formed by legs 9 and 7 , gives us a right triangle on the left.
Using the sine ratio and the exact value sin45° = [tex]\frac{1}{\sqrt{2} }[/tex] , then
sin45° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{9}{y}[/tex] = [tex]\frac{1}{\sqrt{2} }[/tex] ( cross- multiply )
y = 9[tex]\sqrt{2}[/tex]
Using the tan ratio in the right triangle and the value tan45° = 1 , then
tan45° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{9}{adj}[/tex] = 1
adj = 9
Then
x = 9 + 7 = 16
Details
A movie theater has a seating capacity of 205. The theater charges $5.00 for
children, $7.00 for
students, and $12.00 of adults. There are half as many
adults as there are children. If the total ticket sales was $ 1482, How many
children, students, and adults attended?
Answer:
94 children, 64 students, and 47 adults attended the movie theater.
Step-by-step explanation:
Let; a be for adults, s for students, and c for children.
Make a system to solve for the amount of people.
c/a = 2
a + 2a + s = 205
3a + s = 205
Simplify.
s = 205 - 3a
s = 205 - 3a
c = 2a
Plug it in.
5c + 7s + 12a = 1482
10a + 7(205 -3a) + 12a = 1482
10a + 1435 - 21a + 12a = 1482
a + 1435 = 1482
a = 47
Substitute.
c = 2(47)
c = 94
Solve.
s = 205 - 3(47)
s = 64
out of 1300 students in a school , only 60% passed . find the number of students failed .
Hi there!
»»————- ★ ————-««
I believe your answer is:
520 students.
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
60% of the 1300 students passed. This means that 40% of the students failed.
⸻⸻⸻⸻
[tex]1300 * 0.4= 520[/tex]
⸻⸻⸻⸻
520 students failed school.
⸻⸻⸻⸻
[tex]\boxed{\text{Another way to find this...}}\\\\\text{Take 60}\% \text{ of 1300:}\\\\1300 * 0.6 = 780\\\\\text{780 students passed school.}\\\\\text{Subtract 780 from 1300:}\\\\1300 - 780 = \boxed{520}[/tex]
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
In circle B with m \angle ABC= 74m∠ABC=74 and AB=12AB=12 units find area of sector ABC. Round to the nearest hundredth.
Answer:
92.99
Step-by-step explanation:
The value of area of sector ABC is,
Area = 93.05 square units.
What is mean by Circle?The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.
Given that;
In circle B;
⇒ m ∠ABC = 74° and AB = 12 units
Hence, We can formulate;
The value of area of sector ABC is,
Area = (angle / 360) π r²
Area = (74/360) × 3.14 × 12²
Area = 93.05 square units.
Thus, The value of area of sector ABC is,
Area = 93.05 square units.
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5 + 3bc =
9a + b =
cd + bc =
Answer:
You can't answer these questons
sorry
Hope This Helps!!!
2/3(x+6)=-18 what is the value of X in the equation?
Answer:
x= -33
Step-by-step explanation:
expand the equation : 2/3x +4 =-18
Then simplify to 2/3x=-22
multiply both sides by 3/2x to get x=-33
Answer:
x = -33
Step-by-step explanation:
2/3(x+6) = -18
x + 6 = (3/2)(-18)
x + 6 = -27
x = -33
Evaluate the integral.
Answer:
D
Step-by-step explanation:
[tex]\int\limits^4_1 {\frac{7^{lnx}}{x} } \, dx \\put~ln~x=y\\diff.\\\frac{1}{x} dx=dy\\when~x=1,y=ln1=0\\when x=4,y=ln~4\\\int\limits^{ln4}_0 {7^y} \, dy\\=\frac{7^y}{ln7} |0 ~\rightarrow~ ln 4\\= \frac{7^{ln4}}{7}[/tex]
The entry for a science exhibition is $5 for students and four dollars more than the students for adults. On a particular day, 600 people visited the exhibition and $3500 was collected. How many students and adults visited on that day?
Answer:
475 students, 125 adults
Step-by-step explanation:
x + y= 600......equation 1
5x +9y= 3500.......equation 2
From equation 1
x +y = 600
x= 600-y
Substitute 600-y for x in equation 2
5(600-y) +9y= 3500
3000-5y+9y= 3500
3000+4y= 3500
4y= 3500-3000
4y= 500
y= 500/4
y= 125
Substitute 125 for y in equation 1
x + y= 600
x + 125= 600
x = 600-125
x= 475
Hence there are 475 students and 125 adults
wo runners are saving money to attend a marathon. The first runner has $112 in savings, received a $45 gift from a friend, and will save $25 each month. The second runner has $50 in savings and will save $60 each month.
Which equation can be used to find m, the number of months it will take for both accounts to have the same amount of money?
112 – 25m + 45 = 50 – 60m
112 + 25 + 45m = 50m + 60
112 + 25 – 45m = –50m + 60
112 + 25m + 45 = 50 + 60m
Answer:
I believe the last answer is correct
Step-by-step explanation:
Both runners are gaining money
Neeedddd answweerrrr plaeeessee
9514 1404 393
Answer:
B. log_b(a) - log_b(d)
Step-by-step explanation:
The applicable rule of logarithms is ...
log(a/b) = log(a) -log(b)
All the logs need to have the same base.
__
Here, the base is 'b', but the rule still applies:
[tex]\log_b{\dfrac{a}{d}}=\log_b{(a)}-\log_b{(d)}[/tex]
Marcel and Floyd are playing games at an arcade. Marcel has $8.25 and is only playing $0.25 games. Floyd has $9.75 and is only playing $0.75 games. Jorge wants to find the number of games after which Marcel and Floyd will have the same amount of money remaining. Jorge’s work is shown below.
Answer:
3 games
Step-by-step explanation:
A certain area can support 124 deer. Initially, there were 2 deer in the area, and the number has been growing at an average rate of 10% per month. Approximately how long will it take for the deer to have a population of 76, assuming logistic growth
Answer:
≈ 38.16 monthsStep-by-step explanation:
Initial number of deer = 2Growth rate is 1.1 times as 100% + 10% = 110% = 1.1Target number is 76.The equation of the growth is:
d(n) = 2*1.1^nSince the target number is 76 we get:
2*1.1^n = 761.1^n = 38log 1.1^n = log 38n = log 38/log 1.1n ≈ 38.16Answer: 46 months
Step-by-step explanation:
Solve the solution of this inequality 4/9x-10>x/3-12