Answer:
see below
Step-by-step explanation:
We know that distance = rate * time
100 meters = 8 m/s * time
100 = 8t
Divide each side by 8
100/8 = 8t/8
12.5 = t
If we know the rate and the time, we can find the distance
d = rt
Two buses leave towns 1060 kilometers apart at the same time and travel toward each other. One bus travels 14 kilometers an hour faster than the other. If they meet in 5 hours, what is the rate of each bus?
Answer:
99, 113
Step-by-step explanation:
X-the first bus
X+14-the second bus
5x+5(x+14)=1060
10x+70=1060
10x=990
X=99-the first bus
99+14=113-the second bus
use the figure to find x.
Answer:
[tex]20\sqrt{6}[/tex]
Step-by-step explanation:
In all 30-60-90 triangles, the side lengths are in the ratio [tex]x:x\sqrt{3}:2x[/tex], where [tex]2x[/tex] is the hypotenuse and [tex]x[/tex] is the side opposite to the 30 degree angle. Therefore, the hypotenuse of the 30-60-90 triangle (left) is [tex]2\cdot 10\sqrt{3}=20\sqrt{3}[/tex]. This hypotenuse also represents one leg of the 45-45-90 triangle.
In all 45-45-90 triangles, the side lengths are in ratio [tex]x:x:x\sqrt{2}[/tex] where [tex]x\sqrt{2}[/tex] is the hypotenuse of the triangle. Therefore, since [tex]x[/tex] is the hypotenuse of the triangle marked and [tex]20\sqrt{3}[/tex] is one of the legs, the value of [tex]x[/tex] must be:
[tex]20\sqrt{3}\cdot \sqrt{2}=\boxed{20\sqrt{6}}[/tex]
Answer:
[tex]x = 20\sqrt6[/tex]
Step-by-step explanation:
The triangle with the side that has a measure of ([tex]10 \sqrt{3}[/tex]) is a (30 - 60 - 90) triangle. This means that its angles are (30), (60), and (90) degrees. One property of a (30 - 60 -90) triangle is the ratio of its sides. This ratio, in simple terms, can be defined as the following:
angle : opposite side
[tex]30 : z\\60 : z\sqrt{3}\\90 : 2z[/tex]
Use this property here to find the measure of the side opposite the (90) degree angle, that is shared between the two triangles.
This side is opposite the (30) degree angle, therefore, multiply this side by (2) will yield the measure of the side opposite the (90) degree angle. Therefore the side opposite the (90) degree angle has the following measure:
[tex]20\sqrt{3}[/tex]
The triangle with a side of (x) is a (45 - 45 - 90) triangle. This means that its angles have a measure of (45 - 45 - 90). The ratios of the sides of a (45 - 45 - 90) triangle are as follows:
angle : opposite side
[tex]45:y\\45:y\\90:y\sqrt{2}[/tex]
Apply this ratio here; multiply the side shared between the (30 - 60 - 90) triangle and (45 - 45- 90) triangle by ([tex]\sqrt{2}[/tex]) in order to get the side with a measure of (x). When this is done, one gets the following result:
[tex]x = 20\sqrt{3}*\sqrt{2}\\x = 20\sqrt{6}[/tex]
The entire graph of the function g is shown in the figure below.
Write the domain and range of g as intervals or unions of intervals.
Step-by-step explanation:
here's the answer to your question
Find the value of x in each case:
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Answer:
x = 36
Step-by-step explanation:
The interior angle at E is (180-2x). The interior angle at F is (180-4x). The sum of the interior angles of the triangle is 180, so we have ...
(180 -2x) +x +(180 -4x) = 180
180 = 5x . . . . . . add 5x-180 to both sides
36 = x . . . . . . . divide by 5
__
Additional comment
This value of x makes the exterior angles at E and F be 72° and 144°, respectively. The internal angles at E, F, G are then 108°, 36°, 36°, making the triangle isosceles with EF = EG.
44 and 45 are alternate interior
angles. Find the measure of 44.
t
115/65°
43/44
44 = [?]
t
45/46
47/48
274
Fnter
Answer:
115
Step-by-step explanation:
The opposite angles (115degree angle and angle 4) are equal.
Angle 3=65
Angle 4=115
Angle 5=115
Angle 6=65
Angle 7=65
Angle 8=115
Brainliest please~
what is the area of a triangle of base 10m and height of 8m
Answer:
40m
Step-by-step explanation:
to find the area of a triangle you must do bh/2
So you do 10 times 8 which is 80.
Then you do 80 divided by 2 which is 40.
I hope this helps!
4. As part of your retirement planning, you purchase an annuity that pays 4 % annual
interest compounded quarterly
a. If you make quarterly payments of $900 how much will you have saved in 5
years?
b. Instead, if you make quarterly payments of $450, how much will you have saved
in 10 years?
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Answer:
a. $19817.10
b. $21998.87
Step-by-step explanation:
The formula for the future value of an annuity with payments "A" and interest at rate r compounded quarterly for t years is ...
FV = A((1 +r/4)^(4t) -1)/(r/4)
The attachment shows this evaluated for ...
a. A = 900, r = 0.04, t = 5. FV = $19817.10
b. A = 450, r - 0.04, t = 10. FV = 21,998.87
What is the yintercept of the function, represented by the table of values below?
A. 9
B. 3
C. 6
D. 12
Answer:
A. 9
Step-by-step explanation:
First find the slope (m) using two given pairs of values form the table, say (1, 6) and (2, 3):
Slope (m) = change in y/change in x
Slope (m) = (3 - 6)/(2 - 1) = -3/1
Slope (m) = -3
Next, substitute (1, 6) = (x, y) and m = -3 into y = mx + b and solve for y-intercept (b).
Thus:
6 = -3(1) + b
6 = -3 + b
Add 3 to both sides
6 + 3 = -3 + b + 3
9 = b
b = 9
y-intercept = 9
14) The height, h metres, of a ball projected directly upwards from the ground can be modelled by h = 56t - 71, where t is the time in seconds after it leaves the ground. a) Find the height of the ball 3.5 seconds after it leaves the ground. b) At what time will the ball strike the ground again? c) When will the ball be 49 m above the ground? Briefly explain why there are two possible answers.
X^2 + bx + 49 is a perfect squad trinomial what is one possible value of b?
a perfect square trinomial, (x + y)² = x² + 2xy + y²
so, if we have the x of the bx, what is left is the b
the expression would have to be (x + 7)², since we have the 49 and the x²
so, what's left: x² + 14x + 49,
b = 14
hope it helps :)
The distance, y, in miles, traveled by a car in a certain amount of time, x, in hours, is shown in the graph below:
A graph titled Motion of Car is shown with Time in hours labeled on x-axis and Distance from Starting Point in miles labeled on y-axis. The scale on the x-axis shows the numbers 1, 2, 3, 4, 5, 6, and the scale on the y-axis shows the numbers 0, 14, 28, 42, 56, 70, 84. There are three straight lines in the graph. The first line joins ordered pair 0, 0 with 3, 42. The second straight line joins 3,42 and 4,42 and the third straight line joins ordered pair 4,42 with the ordered pair 5,56.
Which of the following best describes the motion of the car shown?
It travels for 2 hours, then stops for 1 hour, and finally travels again for 5 hours.
It travels for 3 hours, then stops for 1 hour, and finally travels again for 1 hour.
It travels for 3 hours, then stops for 4 hours, and finally travels again for 5 hours.
It travels for 2 hours, then stops for 2 hours, and finally travels again for 1 hour.
Answer:
The last choice
Step-by-step explanation:
:)
In investing $6,200 of a couple's money, a financial planner put some of it into a savings account paying 4% annual simple interest. The rest was invested in a riskier mini-mall development plan paying 9% annual simple interest. The combined interest earned for the first year was $428. How much money was invested at each rate?
Answer:
$ 2,600 was invested at 4% and $ 3,600 was invested at 9%.
Step-by-step explanation:
Given that in investing $ 6,200 of a couple's money, a financial planner put some of it into a savings account paying 4% annual simple interest, and the rest was invested in a riskier mini-mall development plan paying 9% annual simple interest, and the combined interest earned for the first year was $ 428, to determine how much money was invested at each rate, the following calculation must be performed:
3000 x 0.04 + 3200 x 0.09 = 408
2500 x 0.04 + 3700 x 0.09 = 433
2600 x 0.04 + 3600 x 0.09 = 428
Therefore, $ 2,600 was invested at 4% and $ 3,600 was invested at 9%.
10(2x-3)=10
find the value of x
[tex]\boxed{\large{\bold{\blue{ANSWER~:) }}}}[/tex]
10(2x-3)=1020x-30=1020x=10+3020x=40x=40/20X=2It is given that,
→ 10(2x-3) = 10
Then find required value of x,
→ 10(2x-3) = 10
→ 20x-30 = 10
→ 20x = 10+30
→ 20x = 40
→ x = 40/20
→ [x = 2]
Hence, the value of x is 2.
Which equation is equivalent to 15-7x=14
[tex]\huge\text{Hey there!}[/tex]
[tex]\large\text{15 - 7x = 14}[/tex]
[tex]\large\text{-7x + 15 = 14}[/tex]
[tex]\underline{\large\text{SUBTRACT 15 to BOTH SIDES}}[/tex]
[tex]\large\text{-7x + 15 - 15 = 14 - 15}[/tex]
[tex]\underline{\underline{\large\text{CANCEL out: 15 - 15 because that gives you 0}}}[/tex]
[tex]\underline{\underline{\large\text{KEEP: 14 - 15 because that helps solve for the x-value}}}[/tex]
[tex]\large\text{14 - 15 = \bf -1}[/tex]
[tex]\underline{\underline{\underline{\large\text{NEW EQUATION: -7x = -1}}}}[/tex]
[tex]\underline{\large\text{DIVIDE -7 to BOTH SIDES}}[/tex]
[tex]\mathsf{\dfrac{-7\mathsf{x}}{-7}=\dfrac{-1}{-7}}[/tex]
[tex]\underline{\underline{\large\text{CANCEL out: } \dfrac{-7}{-7} \large\text{ because that gives you 1}}}[/tex]
[tex]\underline{\underline{\large\text{KEEP: }\dfrac{-1}{-7}\large\text{ because helps you get the x-value}}}[/tex]
[tex]\mathsf{x = \dfrac{-1}{-7}}[/tex]
[tex]\mathsf{x = \dfrac{-1\div-1}{-7\div-1}}[/tex]
[tex]\mathsf{x =\bf \dfrac{1}{7}}[/tex]
[tex]\boxed{\boxed{\large\text{Therefore, your answer is: \bf x = }\bf \dfrac{1}{7}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
A store sells 5 different shirts, 6 different pants, 3 different shoes, and 9 different socks. You are making an outfit with one of each article of clothing. How many outfits can you make?
Answer:
you can make 3 outfits
Step-by-step explanation:
because,if you just have 3 shoes aotomaticly you just wear 3 shirt and 3 pants.
for the socks, one people wear 2 socks so there you have 3 outfits
Answer:
[tex]810[/tex]
Step-by-step explanation:
For each shirt, there are 6 different pairs of pants to pair with it. For each of these pairs of pants, there are 3 different shoes to pair and so on.
Therefore, there are [tex]5\cdot 6\cdot 3\cdot 9=\boxed{810}[/tex] combinations you can make.
A kite is a quadrilateral with two pairs of adjacent, congruent sides. The vertex angles are those angles in between the pairs of congruent sides. Prove the diagonal connecting these vertex angles is perpendicular to the diagonal connecting the non-vertex angles. Be sure to create and name the appropriate geometric figures. This figure does not need to be submitted.
Which of the following numbers is rational? Assume that the decimal patterns continue.
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Answer:
(c) √49
(d) 2.544544...(3-digit repeat)
Step-by-step explanation:
Square roots of perfect squares are rational, as are repeating decimals.
If 12x + 16y = 11, what is the value of 6x + 8y?
Answer:
11/2
Step-by-step explanation:
Given 12x+16y=11
Halving both sides gives 6x+8y=11/2.
Solve 3x to the second power +17x-6=0
The solution of the equation 3x² + 17x - 6 = 0 are, x = 1/3 and x = - 6.
What is Quadratic equation?An algebraic equation with the second degree of the variable is called an Quadratic equation.
We have to given that;
The quadratic equation is,
⇒ 3x² + 17x - 6 = 0
Now, We can solve the equation as;
⇒ 3x² + 17x - 6 = 0
⇒ 3x² + (18 - 1)x - 6 = 0
⇒ 3x² + 18x - x - 6 = 0
⇒ 3x (x + 6) - 1 (x + 6) = 0
⇒ (3x - 1) (x + 6) = 0
This gives two solutions,
⇒ 3x - 1 = 0
⇒ x = 1/3
And, x + 6 = 0
⇒ x = - 6
Learn more about the quadratic equation visit:
brainly.com/question/1214333
#SPJ2
The profit (in thousands of dollars) of a company is given by P(x) = -8x2 + 32x + 14.
Find the maximum profit of the company.
O a. 40 thousand dollars
O b. 45 thousand dollars
O c. 46 thousand dollars
Answer:
C
Step-by-step explanation:
The profit (in thousands of dollars) of a company is given by the function:
[tex]\displaystyle P(x) = -8x^2+32x+14[/tex]
And we want to find the maximum profit of the company.
Since the function is a quadratic with a negative leading coefficient, the maximum profit will occur at its vertex. Recall that the vertex of a quadratic is given by:
[tex]\displaystyle \text{Vertex} = \left(-\frac{b}{2a}, f\left(-\frac{b}{2a}\right)\right)[/tex]
Find the x-coordinate of the vertex. In this case, a = -8, b = 32, and c = 14. Hence:
[tex]\displaystyle x=-\frac{(32)}{2(-8)}=\frac{32}{16}=2[/tex]
To find the maximum profit, substitute this value back into the function. Hence:
[tex]\displaystyle P(2) = -8(2)^2+32(2) + 14 = 46[/tex]
Therefore, the maximum profit of the company is 46 thousand dollars.
Our answer is C.
ASAP!!!!!! SHOW WORK!!!! Thank you
Answer:
y = -6Step-by-step explanation:
If the three points are collinear, the slopes of RS and ST are same:
m(RS) = (4 - 8)/(1 + 1) = -4/2 = -2m(ST) = (y - 4)/(6 - 1) = (y - 4)/5Since the sloes are equal we have the following equation:
(y - 4)/5 = -2y - 4 = -10y = -10 + 4y = -6Slopes must be equal
slope of RS
m=4-8/1+1m=-4/2m=-2Now
Slope of ST=-2
y-4/6-1=-2y-4/5=-2y-4=-10y=-10+4y=-6Describe how to transform the graph of f(x) = x2 to obtain the graph of the related function g(x).
Then draw the graph of g(x).
1. g(x) = f(x + 1)
2. g(x) = f(x) - 2
Please help i also need to graph
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Answer:
left 1 unitdown 2 unitsStep-by-step explanation:
The transformation g(x) = f(x -h) +k is a translation of f(x) to the right by h units and up k units.
1. h = -1, so the graph of g(x) is the graph of f(x) shifted left 1 unit. (blue)
__
2. k = -2, so the graph of g(x) is the graph of f(x) shifted down 2 units. (green)
A jar of gumballs contains 4 reds, 2 greens, and 6 blues. What is the probability of getting two blues in a row without replacement?
Select one:
a. 3/4
b. 1/2
c. 5/22
d. 5/11
Answer:
C
Step-by-step explanation:
Hypergeometric distribution
[tex]\frac{{6\choose2}}{{12\choose2}}=\frac{15}{66}= \frac{5}{22}[/tex]
what is the length of AB? round to one decimal place
Answer:
A=0
Step-by-step explanation:
DAC=BAD
A=0
What ordered pairs are the solutions of the system of equations shown in the graph below?
Answer:
The solutions of this system of equation is (-5,3) and (-1,-5).
Answer: (-3,-1) and (-5,3)
Step-by-step explanation:
Find the fourth proportion to : 2,3,16
Answer is 24
Step by step:
2,3,16
Let the fourth proportion be x
2/3 = 16/x
or, 2x = 3×16
or, x = 3×16/2
or, x = 3×8
or, X = 24
a family has two children. what is the probability that both are girls, given that at least one is a boy
Answer: The probability would be zero
Step-by-step explanation:
There are two children and one is a boy, so the probability of both being girls is a zero
Convert 333 to base three.
Answer:
110100
Step-by-step explanation:
Michelin Tires would like to estimate the average tire life of its Latitude Tour tire in terms of howmany miles it lasts. Assume the standard deviation for the tire life of this particular brand is 6000miles. Determine the sample size needed to construct a 95% confidence interval with a margin oferror within 2000 miles.ShowWork:
Answer:
6 samples
Step-by-step explanation:
Given :
Sample size, = n
Standard deviation, = 6000
Margin of Error = 2000
Confidence interval, α = 95%
Zcritical at 95% = 1.96
n = (Zcritical * σ) / margin of error
n = (1.96 * 6000) /2000
n = 11760 / 2000
n = 5.88
n = 6 samples
x to the power of 3 - 7x + 6 factorise please whole step by step
Answer:
[tex](x + 3)(x - 2)(x - 1)[/tex]
Step-by-step explanation:
[tex] {x}^{3} - 7x + 6[/tex]
Factor using Rational Root Theorem.
This means our possible roots are
positve or negative (1,2,3,6). If we try positve 1, it is indeed a root.
This means that
[tex](x - 1)[/tex]
is a root.
We can divide the top equation by the root (x-1). Our new equation is
[tex]( {x}^{2} + x - 6)[/tex]
Now we can factor this completely
[tex](x + 3)(x - 2)[/tex]
So this equation in factored form is
[tex](x + 3)(x - 2)(x - 1)[/tex]
