The distance between the points (-8, -3) and (-2, -5) is √40 units
How to find distance between two points?Using distance formula,
d = √(x₂ - x₁)² + (y₂ - y₁)²
Therefore, using (-8, -3) and (-2, -5).
x₁ = -8
x₂ = -2
y₁ = -3
y₂ = -5
d = √(-2 + 8)² + (-5 + 3)²
d = √(6)² + (-2)²
d = √36 + 4
d = √40
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Zara is preparing a juice blend.In her recipe, the amount of water is twice the amount of strawberry juice, and amount of lemon juice is 1/5 the amount of strawberry juice. What is the ratio of the lemon water?
The ratio of the lemon water is 10:1
How to determine the ratioFrom the information, we have that;
The ratio of water to strawberry juice is 2 : 1
That of strawberry juice to lemon juice is 5: 1
The, we have that of water to lemon juice to be 10: 1 when compared
Hence, the ratio of the lemon water is 10: 1
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You must write your answer in fully simplified form.
2t= -12
Answer:
t=-6
Step-by-step explanation:
What is the solution to this system of equations x-2 y=15 2x+4y=-18
Answer:
(3, - 6 )
Step-by-step explanation:
x - 2y = 15 ( add 2y to both sides )
x = 2y + 15 → (1)
2x + 4y = - 18 → (2)
substitute x = 2y + 15 into (2)
2(2y + 15) + 4y = - 18 ← distribute parenthesis and simplify left side
4y + 30 + 4y = - 18
8y + 30 = - 18 ( subtract 30 from both sides )
8y = - 48 ( divide both sides by 8 )
y = - 6
substitute y = - 6 into (1)
x = 2(- 6) + 15 = - 12 + 15 = 3
solution is (3, - 6 )
Answer:
x is 3 y is -6 I really hope this helps
Joe's company sold insurance policies over the phone. Last month, 2 employees sold three hurricane policies, 6 employees sold two hurricane policies, and 9 employees sold a single hurricane policy. If a single employee is picked at random, what is the probability that the employee sold two hurricane policies or sold one hurricane policy
The probability that the employee sold two hurricane policies or sold one hurricane policy is 15/17.
According to the statement
Number of employees who sold three hurricane policies is 2
Number of employees who sold two hurricane policies is 6
Number of employees who sold 1 hurricane policies is 9
SO,
The total number of employees is 2+6+9=17.
The number that sold two hurricane policies or sold one hurricane policy is 6+9=15,
so the Probability = Total number of policies sold / total number of employees
Probability = 15/17
So, The probability that the employee sold two hurricane policies or sold one hurricane policy is 15/17.
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A comet is estimated to be about 960,000,000 km from Earth. Write this distance in scientific notation. [?] × 10 km Enter 13
Answer:
[tex](9*10^{9})( 6*10^{8})[/tex] or 9.6×10^8
Step-by-step explanation:
The answer is written above.
Hope this helps!
Answer:
9.6 * 10^8 km.
Step-by-step explanation:
960,000,000
= 9.6 * 10^8 km.
The value of the exponent = number of digits after the 9, which = 8.
Shota invests $2000 in a certificate of deposit that earns 2, percent interest each year write a function that gives the total value v(t) in dollars, of the investment t years from now
V(t)=2000(1.02)^t function that gives the total value in dollars of the investment t years from now given that Shota invests $2000 in a certificate of deposit that earns 2 percent interest each year. This can be obtained by using the formula of compound interest formula.
What is the required function?Equation of compound interest compounded yearly,
A = P(1 + R/100)^t
where,
A = amount
P = principal amount
R = rate
t = number of years
Given that P = $2000, R = 2%, number of years = t,
V(t) = 2000(1+2/100)^t
V(t) = 2000(1+0.02)^t
V(t) = 2000(1.02)^t
Hence V(t)=2000(1.02)^t function that gives the total value in dollars of the investment t years from now given that Shota invests $2000 in a certificate of deposit that earns 2 percent interest each year.
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x/4 ÷ 2/3 = 1/5
solve for x
The value of x from the equation x/4 ÷ 2/3 = 1/5 is 8/15
Fractionx/4 ÷ 2/3 = 1/5
x/4 × 3/2 = 1/5
(x × 3) / (4 × 2) = 1/5
3x / 8 = 1/5
cross product3x × 5 = 8 × 1
15x = 8
x = 8/15
Therefore, value of x from the equation x/4 ÷ 2/3 = 1/5 is 8/15
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A civil engineer is designing a public parking lot for the new town hall. The number of cars in each row should be six less than the number of rows in the lot. The mayor has requested that the new lot should hold twice as many cars as the current parking lot, which has space for 56 cars.
Determine which equation the civil engineer can use to find the number of rows, x, he should include in the new parking lot.
A.
6x2 − 56 = 112
B.
x2 − 6 = 112
C.
x2 − 6x = 112
D.
2x2 − 12x = 112
The equation which the civil engineer can use to find the number of rows is 2x² - 12x = 112. Option D
How to determine the equation
Let the number of rows be x
Number of cars in each row = x - 6 = 56
Number of rows for parking lot = 2x
Then,
Number of cars for new parking lot = 2x ( x - 6 = 56)
Expand the expression,
2 ( x - 6 = 56)
2x² - 12x = 112
Thus, the equation which the civil engineer can use to find the number of rows is 2x² - 12x = 112. Option D
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Travis traveled 135 miles in 5 hours. what is his unit rate of speed in miles per hour?
s= d/t
s= 135/5
s= 27 mph
pls mark as brainliest thanks!
how do I solve for x? (the picture has the problem)
Answer:
x = 21.013155617496
Step-by-step explanation:
we have a right triangle then ,
[tex]\cos \left( 36\right) =\frac{17}{x}[/tex]
Then
[tex]x=\frac{17}{\cos \left( 36\right) } = 21.013155617496[/tex]
Then
x ≈ 21
Step-by-step explanation:
imagine this right-angled triangle is the sine and cosine scenario in a circle. just turn it in your mind or on the paper until it looks like this.
the point with the 36° angle is the center of this circle.
x is the radius of the circle, that is under 36° connecting the center of the circle with the arc of the circle.
17 is the cosine of the angle multiplied by the radius (as the standard cosine function is normed for the standard circle with radius 1).
and the other leg is the sine of the angle multiplied by the radius (this is FYI, we don't need that for the solution here).
so,
17 = cos(36) × x
x = 17/cos(36) = 21.01315562...
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Warm Up
What is the exact distance between the points (4,-2) and (-6,4)?
Select the correct answer.
O 4√10
O2√34
O2√26
O 10√6
Submit
The distance between two points (4,-2) and (-6,4) exists [tex]2\sqrt{34}.[/tex]
How to estimate the distance between two points?Distance between two points exists the length of the line segment that joins the two given points. Distance between two points in coordinate geometry can be estimated by finding the length of the line segment merging the provided coordinates.
Let the points be (4,-2) and (-6,4).
The distance between two points [tex](x_{1} ,y_{1})[/tex] and [tex](x_{2} , y_{2} )[/tex] exists provided by the distance between the two points
[tex]= $\sqrt\\(x_{2} -x_{1} )^{2} +(y_{2} -y_{1})^{2}[/tex]
substituting the points in the equation, we get
[tex]$=\sqrt\\(-6-(4)^{2} +(4-(-2)^{2}[/tex]
simplifying the equation, we get
[tex]$=\sqrt{136}[/tex]
[tex]$=2\sqrt{34}[/tex]
The distance between two points (4,-2) and (-6,4) exists [tex]2\sqrt{34}.[/tex]
Therefore, the correct answer is option c. [tex]$2\sqrt{34}.[/tex]
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Are the triangles similar? If so, state the similarity and the postulate or theorem that justifies your answer.
Answer: The triangles are not similar.
Step-by-step explanation:
Two figures are similar simply if they have the same shape, but not necessarily the same size. In a more mathematical sense, similar figures have the same angle measures and proportionate side lengths.
For reference, side lengths are proportionate when the ratios between corresponding/matching sides are the same.
Since we do not have any angles, we will try using the SSS Similarity Theorem, which states that if all three sides of both triangles are in proportion, then the triangles are similar. We will first list all the side lengths and match corresponding ones.
[tex]\triangle ABC \rightarrow 18,20,32\\ \triangle UVT \rightarrow 14,15,24[/tex]
Since we matched corresponding sides, we can now check whether they have the same ratio).
[tex]\frac{18}{14}=\frac{20}{15}=\frac{32}{24}[/tex]
[tex]\frac{9}{7}=\frac{4}{3}=\frac{4}{3}[/tex]
Not all of the side lengths have the same ratio, so these triangles aren't similar. you must multiply 14 by 9/7 to get to 18, but you need to multiply the other two sides by 4/3 to get to their
[tex]y = 6x + 3 \\ y = 6x - 4[/tex]
state whether each pair of lines are parallel or perpendicular
pls help
Answer:
The lines are parallel, this is because they both have the same slope/gradient of 6.
Answer:
parallel lines
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = 6x + 3 ← is in slope- intercept form
with slope m = 6
y = 6x - 4 ← is in slope- intercept form
with slope m = 6
• Parallel lines have equal slopes
then the 2 given lines are parallel
This figure represents a design found in a glass panel. ABCD is a rectangle with
midpoints X, Y, Z, and W. Emily states that the quadrilateral formed by the segments
that join the midpoints of the sides is a rhombus. Do you agree with her? Explain why
or why not.
Answer: Yes
Step-by-step explanation:
Since ABCD is a rectangle, [tex]\angle AXY[/tex], [tex]\angle YBZ[/tex], [tex]\angle WCZ[/tex], and [tex]\angle WDX[/tex] are all right angles, and are thus all congruent because all right angles are congruent. Furthermore, because ABCD is a rectangle, we know that [tex]\overline{AB} \cong \overline{CD}[/tex] and [tex]\overline{AD} \cong \overline{BC}[/tex]. Because we are given that X, Y, Z, and W are midpoints, using the fact that halves of congruent segments are congruent, we can conclude that [tex]\overline{AY} \cong \overline{YB} \cong \overline{CW} \cong \overline{WD}[/tex] and that [tex]\overline{AX} \cong \overline{XD} \cong \overline{BZ} \cong \overline{ZC}[/tex]. As a result, we can conclude that [tex]\triangle AYX \cong \triangle DXW \cong \triangle CWZ \cong \triangle BYZ[/tex] by SAS, and thus by CPCTC, [tex]\overline{AY} \cong \overline{XW} \cong \overline{ZW} \cong \overline{YZ}[/tex]. Therefore, since the quadrilateral formed by the midpoints has four congruent sides, it must be a rhombus.
PLEASE I NEED HELP ON THIS QUESTION
Answer:
Option c is the correct answer
Step-by-step explanation:
distance of satrun - distance of jupiter
A bag contains 50 tokens: 20 pink ,13 blue and 17 purble.if a person selects one token, replaces it,and then selects a second token,what is the probability of selecting 2 of the same colour
Answer:
Step-by-step explanation:
this is independent
20/50= 2/5= 40% of getting pink, probability of getting 2= 20%
13/50=0.26= 26% of getting blue, probability of getting 2= 13%
17/50=0.34=34% of getting purple, probability of getting 2 = 17%
70%
Which statement below correctly depicts the expected value of a fair game?
E(X) = 0
E(X) = 1
E(X) > 0
E(X) >1
Answer:
e(x)=0 will be your answer
Step-by-step explanation:
First of all it is important to know about the fair game. A game is said to be fair if it has equal chances of winning for both the parties.
In Statistical terms, this can be said as expected value =0
If E(X) = 1 where X is from the player, then organizer of the game would have more chances of losing.
Similarly if E(X)>0where X is from the player, then organizer of the game would have more chances of losing.
Also if E(X)>1, where X is from the player, then organizer of the game would have more chances of losing.
Hence a fair game is one where
Answer: A. E(X) = 0
Step-by-step explanation:
a cube with volume 343 cubic inches is inscribed in a sphere so that each vertex of the cub touches the sphere. what is the lenght of the radius in inches of the sphere
The length of the radius of the sphere is 9.26 inches.
What is a sphere?A sphere is a geometrical object that resembles a two-dimensional circle in three dimensions. In three-dimensional space, a sphere is a collection of points that are all located at the same r-distance from a single point. The radius of the sphere is denoted by the letter r, and the specified point represents its center.
Volume of cube=343 cubic inches
Side of cube=[tex]\sqrt[3]{343}[/tex] = 7 inches
The radius of the sphere is equal to half the diagonal length of the cube since the cube is inscribed inside the sphere, whose diameter is the cube's diagonal length. Utilizing the distance formula, we can determine the cube's diagonal length.
[tex]d=\sqrt{7^{2}+7^{2}+7^{2} } \\=\sqrt{7*7^{2} } \\=7\sqrt{7}[/tex]
To determine the radius of the sphere, divide the value by two.
Radius of sphere=[tex]\frac{7\sqrt{7} }{2}[/tex] = 9.26 inches
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8 x -1/4 x -7 cara ngerjain nya bagaimana?
20 points!
i need help with these rational numbers
The rational numbers are explained below.
What are rational numbers?The complete question can't he found. Therefore, an overview will be given. Rational numbers are the numbers that can be represented by the quotient p/q of two integers.
In this case, p and q are integers and p isn't equal to 0.
The examples include 1/5, 1/3, -2, 5, etc.
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What is the area of this trapezoid?
Answer:
315
Step-by-step explanation:
Find the midpoints of A(-3,-9) and B (-8,-2) graphically
The midpoints of A(-3,-9) and B (-8,-2) is the coordinate points (-5.5, -3.5)
Midpoint of coordinatesCoordinate points are written in the form (x, y). The midpoint of two points (x1, y1) and (x2, y2) is expressed as:
M(x, y) ={(x1+x2)/2, (y1+y2)/2}
Given the following coordinates A(-3,-9) and B (-8,-2)
M(x, y) = {(-3+(-8))/2, (-9-(-2))/2}
M(x, y) = {(-3-8)/2, (-9+2)/2}
M(x, y) = (-11/2, -7/2)
M(x, y) = (-5.5, -3.5)
Hence the midpoints of A(-3,-9) and B (-8,-2) is the coordinate points (-5.5, -3.5)
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5
Sample Space and Venn Diagrams: Mastery Test
Type the correct answer in each box. If necessary, use / for the fraction bar.
A bag contains 5 blue marbles, 2 black marbles, and 3 red marbles. A marble is randomly drawn from the bag.
The probability of not drawing a black marble is
. The probability of drawing a red marble is
m. All rights reserved.
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The probability of not drawing a black marble is 4/5
The probability of drawing a red marble is 3/10
What are the probabilities?Probability determines the odds of the occurrence of a random event. The probability the event occurs is 1 and the probability that the event does not occur is 0.
Probability of not drawing a black marble = total marbles that are not black / total number of marbles
(5 + 3) / (5 + 3 + 2) = 8/10 = 4/5
The probability of drawing a red marble = total number of red marbles / total number of marbles
= 3/10
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Answer:
See image
Step-by-step explanation:
Plato
Express sin S as a fraction in simplest terms. R S
Answer:
[tex]\sf Sin \ S = \dfrac{2}{9}[/tex]
Step-by-step explanation:
Trigonometry ratios:[tex]\sf \boxed{\bf Sin \ S = \dfrac{opposite \ side \ of \ \angle S}{hypotenuse}}[/tex]
[tex]\sf = \dfrac{RQ}{SQ}\\\\= \dfrac{2}{9}[/tex]
Which graph represents y= cos(2x - π) +5?
The graph that represents y= cos(2x - π) +5 is illustrated below.
What is a graph?It should be noted that a graph simply means a series of connections among variables given.
In this case the graph that represents y= cos(2x - π) +5 is illustrated below.
The graph is attached.
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Find the volume of the prism. Round to the nearest tenth if necessary.
Answer:
14.7 (Because you asked for no units)
Step-by-step explanation:
The volume of this triangular prism is 1/2 BHL
0.5 * 3.5 * 2 * 4.2 = 14.7 ft^3
Write down two irrational numbers with a sum of 4
Answer:
π & 4-π
Step-by-step explanation:
Taking, a = π & b = 4-π ,a + b = π + 4 - π = 4A rectangle measures 3.5 ft by 7 ft. It is enlarged by a scale factor of two. What is the area of the enlarged rectangle? T a m a
Answer:
98
Step-by-step explanation:
Solution 1, (quick)
When enlarging by a scale factor, the shape's area is multiplied by the scale factor squared.
3.5*7*2^2=98
This works because for a rectangle width x and length y, width 2x and length is 2y, area is 4xy compared to area xy originally.
Solution 2, (technical)
Scale factor of 2 means multiplying by 2
3.5^2=7
7*2=14
7*14=98
If sinx + sin^2x = 1 then, show that cos^12x + 3cos^10x + 3cos^8x + cos^6x = 1
This can be proved by using identities of trigonometry.
Prove that cos¹²x + 3cos¹⁰x + 3cos⁸x + cos⁶x = 1:Given that,
sin x + sin²x = 1 ⇒ sin x = 1 - sin²x
⇒ sin x = cos²x (∵sin²x + cos²x = 1)
We have to prove that,
cos¹²x + 3cos¹⁰x + 3cos⁸x + cos⁶x = 1
LHS = cos¹²x + 3cos¹⁰x + 3cos⁸x + cos⁶x
= sin⁶x + 3sin⁵x + 3sin⁴ + sin³x
= (sin²x)³ + 3(sin²x)²sin x + 3(sin²x) (sin x)² + (sin x)³
= (sin²x + sin x)³ (∵(a+b)³ = a³ + 3a²b + 3 ab² + b³)
= 1³ = 1 = RHS
LHS = RHS
Hence the equation is proved since both sides of the equation are equal.
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Rachel is getting a sundae where the cost is proportional to the weight of the sundae she makes. last time rachel went she bought a 12-ounce sundae for $4.20. this time she buys a 17-ounce sundae. let c be the cost of the sundae. set up and solve a proportion for c.
Using proportions, the cost of the 17-ounce sundae is of $5.95.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.
Considering the 12-ounce sundae bought for $4.2, the cost per ounce is given by the following proportion:
$4.2/12 = $0.35.
Hence the cost of a 17-ounce sundae is:
$0.35 x 17 = $5.95.
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