Answer:
Step-by-step explanation:
This is a parabola. If we plot the vertex and the focus, we see that the focus is below the vertex. What this tells us is that the parabola opens "upside down" since the parabola wraps itself around the focus. If it opens upside down, then the format for the equation is
[tex]4p(y-k)=-(x-h)^2[/tex]
where p is the distance between the vertex and the focus (4), h is the first coordinate of the vertex (0), and k is the second coordinate of the vertex (0). Filling in the formula then:
[tex]4(4)(y-0)=-(x-0)^2[/tex] which simplifies down to
[tex]16y=-x^2[/tex] and then finally,
[tex]y=-\frac{1}{16}x^2[/tex]
Add or subtract. Write your answer in scientific notation. 6.4 x 10^3+ 1.4 x 10^4+ 7.5 x 10^3
Answer:
2.79 * 10^4
Step-by-step explanation:
6.4 x 10^3+ 1.4 x 10^4+ 7.5 x 10^3
The exponents need to be the same
6.4 x 10^3+ 14 x 10^3+ 7.5 x 10^3
Add the numbers
6.4 + 14+ 7.5 =27.9
Multiply by the exponent
27.9 * 10 ^3
But this is not in scientific notation
Move the decimal one place to the left and add one to the exponent
2.79 * 10^4
PLEASE HELP!!!
Which expression shows a way to find the area of the following rectangle?
Answer:
B
Step-by-step explanation:
This rectangle appears to have 7 boxes on the bottom, and 3 box for the side.
Since area is base×height
It would be 7×3
We can calculate EEE, the amount of euros that has the same value as DDD U.S. Dollars, using the equation E=\dfrac{17}{20}DE= 20 17 DE, equals, start fraction, 17, divided by, 20, end fraction, D. How many euros have the same value as 111 U.S. Dollar? euros How many U.S. Dollars have the same value as 111 euro? dollars
Answer: 1 U.S.dollar = 0.85 euro.
1 euro = 1.18 dollars.
Step-by-step explanation:
The given equation: [tex]E=\dfrac{17}{20}D[/tex]
, where 'E' is the amount of euros that has the same value as 'D' U.S. Dollars.
At D= 1,
[tex]E=\dfrac{17}{20}=0.85\text{ euro}[/tex]
i.e. 1 U.S.dollar = 0.85 euro.
At E= 1 , we have
[tex]1=\dfrac{17}{20}D\\\\\Rightarrow\ D= 20/17\approx1.18\text{ dollars}[/tex]
Hence, 1 euro = 1.18 dollars.
What the answer now
Answer:
Area of the triangle = 98.1 km²
Step-by-step explanation:
In the given triangle WXV,
m∠W + m∠X + m∠V = 180°
m∠W + 119° + 34° = 180°
m∠W = 180° - 153°
m∠W = 27°
By applying Sine rule in the given triangle,
[tex]\frac{\text{SInW}}{\text{XV}}=\frac{\text{SinX}}{\text{WV}}[/tex]
[tex]\frac{\text{SIn27}}{\text{XV}}=\frac{\text{Sin119}}{26}[/tex]
[tex]XV=\frac{26\times (\text{Sin27})}{\text{Sin119}}[/tex]
XV = 13.496 km
Area of the ΔWXV = [tex]\frac{1}{2}(\text{WV})(\text{XV})(\text{SinV})[/tex]
= [tex]\frac{1}{2}(26)(13.496)(0.55919)[/tex]
= 98.109
≈ 98.1 km²
What is the quotient ? -4 /5 divide 2 A . - 1 3/5 B . -2 /5 c. 1/2 D . 1 3/ 5
Answer:
[tex] \boxed{ - \frac{2}{5} }[/tex]Option B is the correct option.
Step-by-step explanation:
[tex] \mathrm{ - \frac{4}{5} \div 2}[/tex]
[tex] \mathrm{dividing \: a \: negative \: and \: a \: positive \: equals \: a \: negative \:. \: ( - ) \div ( + ) = ( - )}[/tex]
[tex] \mathrm{ - \frac{4}{5} \div 2}[/tex]
[tex] \mathrm{dividing \: is \: equivalent \: to \: multiplying \: with \: the \: reciprocal}[/tex]
[tex] \mathrm{ - \frac{4}{5} \times \frac{1}{2} }[/tex]
[tex] \mathrm{reduce \: the \: numbers \: with \: G.C.F \: 2}[/tex]
[tex] \mathrm{ - \frac{2}{5} }[/tex]
Hope I helped!
Best regards!
The quotient of -4 /5 divide 2 would be equal to -2/5 in simplified form.
What are the Quotients?Quotients are the number that is obtained by dividing one number by another number. We can use the fact that division can be taken as multiplication but with the denominator's multiplicative inverse.
We have been given that -4 /5 divide 2
Thus, we have to divide the terms as;
-4 /5 ÷ 2
Therefore, -4 /5 x 1/ 2
-2/5
Hence, the quotient of -4 /5 divide 2 would be equal to -2/5 in simplified form.
Learn more about the quotient;
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The sums of which two pairs from the table will give you the same result? For example, A + B = C + D.
Answer:
D + E = F + H
Step-by-step explanation:
We have to identify the two pairs from the give table which have the same result.
These pairs show the relation as A + B = C + D
We take a pair of expressions given in options (D) and (E)
By adding them,
D + E = (-4 + 9i) + (6 - 6i)
= 2 + 3i
Similarly we add the expressions given in options (F) and (H),
F + H = (-9 + 15i) + (11 - 12i)
= 2 + 3i
Therefore, D + E = F + H will be the answer.
What is the slope of the line that cuts through the points (1, 2) and (5, 4)?
Answer:
[tex]slope=\frac{1}{2}[/tex]
Step-by-step explanation:
Use the following equation:
[tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{rise}{run}[/tex]
Rise over run is the change in the y-axis over the change of the x-axis, otherwise known as the slope.
Insert the values:
[tex](1_{x1},2_{y1})\\(5_{x2},4_{y2})[/tex]
[tex]\frac{4-2}{5-1}=\frac{2}{4} =\frac{1}{2}[/tex]
The slope is [tex]\frac{1}{2}[/tex].
:Done
Answer:
1/2
Step-by-step explanation:
The formula for slope is: y1-y2/x1-x2
The points given are: (x-coordinate, y-coordinate)
In the formula:
y1 is the y-coordinate of the first point
y2 is the y-coordinate of the second point
x1 is the x-coordinate of the first point
x2 is the x-coordinate of the second point
This said, we can plug our points in.
2-4/1-5
Subtract.
-2/-4
Simplify.
-1/-2
The negatives will cancel each other out.
1/2
The slope of the line that cuts through the points (1,2) and (5,4) is 1/2.
Five different cookies and four different drinks are served at the Junior Honor Society reception. In how many ways can Sara select three different cookies and two different drinks?
A. 60
B.10
C.6
D.20
E.30
F.120
[tex]_5C_3\cdot _4C_2=\dfrac{5!}{3!2!}\cdot\dfrac{4!}{2!2!}=\dfrac{4\cdot5}{2}\cdot\dfrac{3\cdot4}{2}=2\cdot5\cdot3\cdot2=60[/tex]
Answer:
[tex]\large \boxed{\mathrm{A. \ 60}}[/tex]
Step-by-step explanation:
[tex]\displaystyle nC_r=\frac{n!}{r!(n-r)!}[/tex]
[tex]5C_3 \times 4C_2[/tex]
[tex]\displaystyle \frac{5!}{3!(5-3)!} \times \frac{4!}{2!(4-2)!}=10 \times 6 = 60[/tex]
solution for x+4 is equal to 10
Answer:
x = 6
Step-by-step explanation:
x + 4 = 10
x = 10 - 4
x = 6
hope it helps
Simplify this expression:
4(1 - 3x) + 7 x - 8
4(1-3x) + 7x -8
Use distributive property:
4 -12x + 7x -8
Now combine like terms:
-5x -4
Answer:
[tex]-5x-4[/tex]
Step-by-step explanation:
With the expression [tex]4(1-3x) + 7x - 8[/tex], we can simplify it down by applying the distributive property, then combining like terms.
[tex]4(1-3x)+7x-8\\\\4-12x+7x-8\\\\4-5x-8\\\\-5x-4[/tex]
Hope this helped!
martin ordered a pizza with a 16-inch diameter. Ricky ordered a pizza with a 20-inch diameter. What is the approximate difference in area of the two pizzas?
Answer:
14
Step-by-step explanation:
Consider line A which is defined by the equation:
y=5/6x-5/2
and the point P(-3,6) and then answer the following questions:
a. How would you find the line (B) that passes through point P and is perpendicular to line A? What is the equation of that line?
b. How would you find the length of the segment of line B from point P to line A?
c. How would you find the midpoint between point P and the intersection of line A and line B ?
Answer:
y = -6/5x +12/5distance from P to A: (66√61)/61 ≈ 8.4504midpoint: (-18/61, 168/61) ≈ (-0.2951, 2.7541)Step-by-step explanation:
a. The slope of the perpendicular line is the negative reciprocal of the slope of the given line, so is ...
m = -1/(5/6) = -6/5
Then the point-slope form of the desired line through (-3, 6) can be written as ...
y = m(x -h) +k . . . . . line with slope m through (h, k)
y = (-6/5)(x +3) +6
y = -6/5x +12/5 . . . equation of line B
__
b. The distance from point P to the intersection point (X) can be found from the formula for the distance from a point to a line.
When the line's equation is written in general form, ax+by+c=0, the distance from point (x, y) to the line is ...
d = |ax +by +c|/√(a² +b²)
The equation of line A can be written in general form as ...
y = 5/6x -5/2
6y = 5x -15
5x -6y -15 = 0
Then the distance from P to the line is ...
d = |5(-3) -6(6) -15|/√(5² +(-6)²) = 66/√61
The length of segment PX is (66√61)/61.
__
c. To find the midpoint, we need to know the point of intersection, X. We find that by solving the simultaneous equations ...
y = 5/6x -5/2
y = -6/5x +12/5
Equating y-values gives ...
5/6x -5/2 = -6/5x +12/5
Adding 6/5x +5/2 gives ...
x(5/6+6/5) = 12/5 +5/2
x(61/30) = 49/10
x = (49/10)(30/61) = 147/61
y = 5/6(147/61) -5/2 = -30/61
Then the point of intersection of the lines is X = (147/61, -30/61).
So, the midpoint of PX is ...
M = (P +X)/2
M = ((-3, 6) +(147/61, -30/61))/2
M = (-18/61, 168/61)
IT IS FOR NOW IM GIVING BRAINLIEST HRRY UP AND 10 POINTS Simplify the expression. What classification describes the resulting polynomial? (8x2 + 3x) − (12x2 − 1) A. linear binomial B. quadratic binomial C. quadratic trinomial D. linear monomial
Answer:
The equation would be a quadratic trinomial
Step-by-step explanation:
Step 1: Expand the equation to remove the brackets
0 = 8x² + 3x - 12x² + 1
Step 2: Collect like terms
0 = -4x² + 3x + 1
Step 3: Count number of terms
0 = -4x² + 3x + 1
1 2 3
Therefore there are 3 terms and this is a quadratic equation making the answer B, a quadratic trinomial
Let f and g be inverse functions. Find f(g(8)).
Answer:
8
Step-by-step explanation:
If f and g are inverse functions , they undo each other
f(g(8))= 8 when f and g are inverses
Answer:
8
Step-by-step explanation:
I have no further information so this is the only answer.
A man lends 12,500 at 12% for the first
year, at 15% for the second year and at 18%
for the third year. If the rates of interest are
compounded yearly; find the difference
between the C.I. of the first year and the
compound interest for the third year.
Answer: $1398
Step-by-step explanation:
Given , Principal (P) = $12,500
Rate of interest for 1st year [tex](R_1)[/tex]= 12% =0.12
Rate of interest for 2nd year [tex](R_2)[/tex]= 15% =0.15
Rate of interest for 3rd year [tex](R_3)[/tex]= 18% =0.18
Interest for first year = [tex]I=P\times R_1\times T[/tex]
= [tex]12500\times 0.12\times 1[/tex]
= $1500
Now, For second year new principal [tex]P_2 = \$12,500+\$1,500 =\$14,000[/tex]
Interest for second year = [tex]I=P_2\times R_2\times T[/tex]
= [tex]14000\times 0.15\times 1[/tex]
= $2100
Now, For third year new principal [tex]P_3 = \$14000+\$2,100 =\$16,100[/tex]
Interest for third year = [tex]I=P_3\times R_3\times T[/tex]
= [tex]16100\times 0.18\times 1[/tex]
= $2898
Difference between the compound interest of the first year and the compound interest for the third year. = $2898 - $1500 = $1398
Hence, the difference between the compound interest of the first year and the compound interest for the third year is $1398 .
what is the value of 14 - a² given a = -3? A. 23 B. 11 C. 8 D. 5
Answer:
The answer is D. 5
Step-by-step explanation:
14-(-3)^2=
14-9=5
The value of f(a) = 14 - [tex]a^{2}[/tex] at x = -3 is 5.
We have the following function of [tex]a[/tex] -
f(a) = 14 - [tex]a^{2}[/tex]
We have to determine the value of this function at a = -3.
What is the value of f(x) = 2x - 3 at x = 3?\The value of f(x) = 2x - 3 at x = 3 can be calculated as follows -
f(3) = 2 x 3 - 3 = 6 - 3 = 3
According to the question -
f(a) = 14 - [tex]a^{2}[/tex]
Now, the value of the function f(a) can be calculated as follows -
f(- 3) = 14 - [tex](-3)^{2}[/tex]
f(- 3) = 14 - 9
f(- 3) = 5
Hence, the value of f(a) = 14 - [tex]a^{2}[/tex] at x = -3 is 5.
To solve more questions on evaluating expressions, visit the link below -
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Round 5.9496 to the nearest thousandth
Answer:
5.95
Step-by-step explanation:
that is because 96 is rounded too 100
so its 5.9500 = 5.95
Answer:
5.950
Step-by-step explanation:
5.9496
ones . tenths hundredths thousandths ten thousandths
5 . 9 4 9 6
We are rounding to the thousandths place
so we look at the ten thousandths place
6 > 5 so we round up the the thousandths place
9 will go up so that forces the hundreds place up
4 becomes 5 in the hundreds place
5.950
A piece of art is in the shape of an equilateral triangle with sides of 6 in. Find the area of the piece of art. Round your answer to the nearest tenth.
Answer:
15.6
Step-by-step explanation:
We can take this equilateral triangle and split it in half to form a 30-60-90 triangle. This will have base of 3, and height of 3[tex]\sqrt{3}[/tex]. The area of this is
1/2 ( 3 )( 3[tex]\sqrt{3}[/tex] ), but the 1/2 cancels since we have 2 halves of the triangle, and so the area is 9.
[tex]\sqrt{3}[/tex] is approx. 1.732, so multiplying this by 9, our answer is 15.6
Answer:
15.6 inches squared.
Step-by-step explanation:
According to the diagram below, the formula for the area of an equilateral triangle is the square root of 3 times the side length squared divided by 4.
The side length is 6. So, the area of the triangle is...
[tex]\frac{\sqrt{3} * 6^2}{4}[/tex]
= [tex]\frac{6^2 * \sqrt{3}}{4}[/tex]
= [tex]\frac{36\sqrt{3}}{4}[/tex]
= [tex]9\sqrt{3}[/tex]
= 9 * 1.732050808
= 15.58845727, which is about 15.6 inches squared.
Hope this helps!
If the zeros of f(x) are x=-1 and x=2, then the zeros of f(x/2) are
A. -1, 2
B. -1/2, 5/2
C. -3/2, 3/2
D. -1/2, 1
E. -2/4
Answer:
E. -2, 4
Step-by-step explanation:
If the zeroes of a function are given as [tex]\alpha, \beta[/tex], then the function can be written as:
[tex](x-\alpha)(x-\beta) = 0[/tex]
Here, we are given that zeros of [tex]f(x)[/tex] are x=-1 and x=2.
As per above, we can write the function [tex]f(x)[/tex] as:
[tex](x- (-1))(x-2) = 0\\\Rightarrow (x+1)(x-2)=0[/tex]
So, [tex]f(x) =(x+1) (x-2)[/tex]
To find:
Zeroes of [tex]f(\frac{x}2)[/tex].
Solution:
We have found that [tex]f(x) =(x+1) (x-2)[/tex]
Replacing [tex]x[/tex] with [tex]\frac{x}2[/tex]:
[tex]f(\frac{x}2) =(\frac{x}2+1) (\frac{x}2-2)[/tex]
Now, Let us put it equal to 0 to find the zeroes.
[tex]f(\frac{x}2) =(\frac{x}2+1) (\frac{x}2-2) = 0\\\Rightarrow (\frac{x}2+1) = 0 \ OR\ (\frac{x}2-2) =0\\\Rightarrow \frac{x}{2} = -1\ OR\ \frac{x}{2}=2\\\Rightarrow \bold{x =-2, 4}[/tex]
So, the zeroes are -2, 4.
How to do this question plz answer me step by step plzz plz
Answer:
£13496.80
Step-by-step explanation:
We can ignore the £ sign for now, that is just units.
If we decrease a number by 4.5%, we will have to find [tex]100-4.5=95.5[/tex]% of 14132.77.
We can easily do this by setting up a proportion.
[tex]\frac{x}{14132.77} = \frac{95.5}{100}[/tex]
Multiply 14132.77 by 95.5:
[tex]14132.77\cdot95.5=1349679.535[/tex]
Divide by 100:
[tex]1349679.535\div100=13496.79535[/tex]
Rounding this to two decimal places, it simplifies to 13496.80.
Hope this helped!
EASY QUESTION What is the difference between history and world history? Please explain it easily :D
Answer:
Assuming you mean "American History V World History"
American History tends to focus on the history of the United States, beginning largely with the colonial era and tracking forwards towards the present. It's largely a national history. World History, on the other hand, is far more encompassing, both geographically as well as temporally.
Assuming you mean "Global History V World History"
World history encompasses a history that is not necessarily completely interconnected through globalization, while global history examines this specific history of inter-connectivity. World History examines the individual histories of different locations around the world, whereas Global History examines how those locations are connected.
Answer:
World history encompasses a history that is not necessarily completely interconnected through globalization, while global history examines this specific history of interconnectivity. ... Furthermore, the fluid nature of what world and global histories mean ensures a number of disagreements with these definitions.
Plz help Solve: y-17= -37
Answer:
-20
Step-by-step explanation:
First thing you do is set up your equation:
y-17= -37
+17 +17 Next you add 17 to both sides
------------- Follow your integer rules
y= -20
We can check this by putting it back into the solution
-20-17= -37 Integer Rules
You use KCC aka Keep Change Change
= -20+ -17= -37
A box has a base of 12 inches by 12 inches and a height of 30 inches. What is the length of the interior diagonal of the box? Round to the nearest hundredth.
This is a problem using the Pythagorean theorem.
The square of the length required is 122 + 122 + 302 = 1188
The length is the square root of this number; I will leave it to you to extract the square root.
Answer:
34.47
Step-by-step explanation:
Escreva expressões algébricas mais simples e equivalentes às expressões abaixo.
Answer:
Step-by-step explanation:
(4a+8)/2 = 4a/2 + 8/2 = 2a + 4(5x + 6x + 22)/11 = (11x+22)/11 = 11x/11 + 22/11 = x + 2{6(x+2)-12}/3 = {6x+12 - 12}/3 = 6x/3 = 2x(Allie, Ben, and Cliff plant ceilings in the neighborhood park. Ali plans 40% of the total number of ceiling, then place 45% of the total number of seed wings, and Cliff plans the rest of the siblings. If Cliff +84 siblings how many seedling do the three boys play together
Answer:
The number of seedlings the three boys planted together is 560 seedlings
Step-by-step explanation:
The possible information in the question are;
Percentage of the seedlings planted by Ali = 40%
Percentage of the seedling planted by Ben = 45%
The percentage of the seedling planted by Cliff = The rest of the seedling
The number of seedling planted by Cliff = 84 siblings
Therefore, the percentage of the seedling planted by Cliff = 100% - 45% - 40% = 15%
Given that Cliff planted 15% of the seedlings, we have;
15% of seedlings Cliff planted = 84
Let X = the total number of seedlings
15/100 × X = 0.15×X = 84
X = 84/0.15 = 560
The total number of seedlings = The number of seedlings the three boys planted together = 560 seedlings.
On a cold February morning, the temperature of the radiator fluid in Stanley’s car is . When the engine is running, the temperature of the fluid goes up per minute. Approximately how long will it take before the radiator fluid temperature reaches ?
Answer:
18.18 min
Step-by-step explanation:
The complete question is
On a cold February morning, the radiator fluid in Stanley’s car is -18F. When the engine is running, the temperature goes up 5.4 F per minute. Approximately how long will it take before the radiator fluid temperature reaches 80 F?
The initial temperature of the engine [tex]T_{1}[/tex] = -18 F
rate of increase in temperature r = 5.4 F/min
Final temperature [tex]T_{2}[/tex] = 80 F
Difference in temperature ΔT = [tex]T_{1} -T_{2}[/tex] = 80 - (-18) = 98 F
time taken to reach this 80 F will be = ΔT/r
where ΔT is the difference in temperature
r is the rate of change of temperature
time taken = 98/5.4 = 18.18 min
1. Which of the following is a true statement?
?
a. To square a number, multiply the number
by 2.
b. The inverse of squaring a number is to
divide the number by 2.
c. To square a number, multiply the number
by itself.
d. A perfect square is a number who's
square root is an even number.
Answer:
C
Step-by-step explanation:
Definitely not a! To square a number you multiply it by itself. for example, if you were squaring 3, you would do 3x3.
Not b either! You will have to take the SQUARE ROOT of the number!
C is the right answer, as I said for a.
D is wrong! The perfect square 49 has a sqrt (square root) of 7. That is NOT even, so d cannot be true.
C is the only true statement. Also, if this is right, can I get branliest answer? Thx :)
PLEASE HELP ME FAST...
Answer:
Sequence a) Pattern: (-2) -9, -11, -13, -15, -17
Sequence b) Pattern: (-5) -15, -20, -25, -30, -35
Sequence c) Pattern: (-6) -13, -19, -25, -31, -37
Hope this helps!
Hi there! Hopefully this helps!
-------------------------------------------------------------------------------------------------------------
A (Subtracting by 2): -9, -11, -13, -15, -17.
B(Subtracting by 5): -15, -20, 25, -30, -35
C(Subtracting by 6): -13, -19, -25, -31, -37
What is the standard form of function f ?
Answer:
f(x) = 4x² + 48x + 149
Step-by-step explanation:
f(x) = 4(x + 6)² + 5
The above expression can be written as: f(x) = ax² + bx + c, by doing the following:
1. Expand (x + 6)²
(x + 6)² = (x + 6)(x + 6)
(x + 6)(x + 6)
x(x + 6) + 6(x +6)
x² + 6x + 6x + 36
x² + 12x + 36
(x + 6)² = x² + 12x + 36
2. Substitute x² + 12x + 36 for (x + 6)² in
f(x) = 4(x + 6)² + 5
This is illustrated below:
f(x) = 4(x + 6)² + 5
(x + 6)² = x² + 12x + 36
f(x) = 4(x² + 12x + 36) + 5
Clear bracket
f(x) = 4x² + 48x + 144 + 5
f(x) = 4x² + 48x + 149
Therefore, the standard of the function:
f(x) = 4(x + 6)² + 5
is
f(x) = 4x² + 48x + 149
Drag a vertex of the triangle to change its shape.
Double-click or double-tap a vertex or side to prevent it from
changing.
Problem: Construct a triangle with interior angle
measures of 60° and 75°.
What is the measure of the third angle?
O 30°
2C = 41°
O 45°
48°
9.2
10
50°
ZA = 49°
6.0 ZB = 90°
Answer:
The correct option is;
45°
Step-by-step explanation:
By angle sum theorem, we have that the sum of angles in a triangle = 180°
Therefore, we have;
When the interior angles of the triangle are constructed to be 60° and 75°, we have by the angle sum theorem;
The third angle + 60° + 75° = 180°
Which gives;
The third angle = 180°- 60° - 75° = 180°- 135° = 45°
The measurement of the third angle by the angle sum theorem will be 45°
The correct option is ∠third angle = 45°.
