Answer:
The answer is B. 9
Use cosine rule. In this case, I am using SOH and the right triangle:
sin 60°= a ÷ 6 root 3
(6 root 3)(sin 60°)= a
a=9
Step-by-step explanation:
Longhorn High School opens its door in 2005 with 800 students. The school grows 5% every year. How long will it take for the school to reach 3000 students?
Answer:
157.741
Step-by-step explanation:
3000=800 ( 1 + 0.05)^t
-800
2200=1.05^t
log(1.05)2200=t
log2200/log1.05
t=157.7...
This tank can hold a volume of 49 062.5 cm3 of water when it is full. The top face of the tank is missing so the tank is open.
a) What volume of water (in cm3) is needed to fill this tank to a height of 15 cm from the top?
Answer:
Multiply length by width to get area.
Step-by-step explanation:
Find the surface area of the cylinder to the nearest whole number.
15 in
19 in.
Not drawn to scale
Select one:
a. 1791 in. 2
b. 11281 in. 2
c. 3204 in. 2
d. 5815 in. 2
Answer:
the answer you are looking for is C
PQ=RQ
470
R
17
b = [?]
Answer:
17
Step-by-step explanation:
you can use SAS to prove two triangles are congruent
Then by CPCTC PS = RS so b is also 17
The bearing of P from Q is 046º.
The bearing of R from Q is 124º.
QR = QP.
Work out the bearing of R from P.
Answer:
175°
Step-by-step explanation:
Bearing angles are usually measured clockwise from North. Reverse bearing angles differ from forward bearing angles by 180°. These relations and the usual angle sum relation for a triangle can be used to solve this problem.
Angle PQR will be the difference in the bearings from Q to P and Q to R:
∠PQR = 124° -46° = 78°
Triangle PQR is isosceles, so the base angle at P will be ...
∠QPR = (180° -78°)/2 = 51°
__
The bearing from P to R will be 51° less than the bearing from P to Q. The bearing from P to Q is 180° more than the bearing from Q to P.
PR bearing = PQ bearing - ∠QPR
= PQ bearing - 51°
= (46° +180°) -51° = 175°
The bearing of R from P is 175°.
HELP ASAP PLEASE! 100 POINTS!
We will use graphical method to solve it.
The inequalities are
y<2/3xy≥-x+2Graph both
We can see that the solution region is rightwards
The solution is (1.2,0.8)
Option D as the intersection point is ahead 1 unlike option A
Answer:
Given system of inequalities:
[tex]\large\begin{cases}y < \frac{2}{3}x\\y\geq-x+2\end{cases}[/tex]
When graphing inequalities:
< or > = dashed line≤ or ≥ = solid line< or ≤ = shade below the line> or ≥ = shade above the line[tex]y < \dfrac{2}{3}x[/tex]
The slope of the first inequality is 2/3, therefore at x = 1, y = 2/3.
So the correct line for the first inequality is the dotted line with the shallower slope.
As the relation is < for this inequality, the shading should be below the dotted line.
[tex]y\geq-x+2[/tex]
From inspection of the given graphs, the line of the second inequality (solid line) is the same in all graphs.
As the relation is ≥ for this inequality, the shading should be above the solid line.
Therefore, the only graph that satisfies these conclusions is graph D (attached).
how to change 35/21 into its mixed fraction
Answer:
[tex]1\frac{2}{3}[/tex]
Step-by-step explanation:
INFORMATION/REMINDS ALREADY KNOWN:
Numerator. This is the number above the fraction line. For 35/21, the numerator is 35.Denominator. This is the number below the fraction line. For 35/21, the denominator is 21.Improper fraction. This is a fraction where the numerator is greater than the denominator.Mixed number. This is a way of expressing an improper fraction by simplifying it to whole units and a smaller overall fraction. It's an integer (whole number) and a proper fraction.Step 1: Find the whole numberWe need to find the whole number first, which we accomplish by dividing the numerator by the denominator. We ignore any digits to the right of the decimal point since we are only interested in whole numbers.
[tex]35/21= 1.6666666666667 = 1[/tex]
Now that we have our whole number for the mixed fraction, we need to find our new numerator for the fraction part of the mixed number.
Step 2: Get the new numeratorWe'll use the whole number we calculated in step one (1) and multiply it by the original denominator to figure this out (21). The numerator is then subtracted from the result of that multiplication:
[tex]35 - (21 * 1) = 14[/tex]
Step 3: Our mixed fractionWe've now simplified 35/21 to a mixed number. To see it, we just need to put the whole number together with our new numerator and original denominator:
[tex]1\frac{14}{21}[/tex]
Step 4: Simplifying our fractionOur fraction (14/21) can be simplified even more in this example. To do so, we must determine the GCF (greatest common factor) of those two numbers. If you want to do it yourself, you can use our handy GCF calculator. We've done it earlier, and the GCF of 14 and 21 equals 7.
We can now divide both the new numerator and the denominator by 7 to simplify this fraction down to its lowest terms.
[tex]\frac{14}{7} = 2\\\frac{21}{7} = 3[/tex]
When we put that together, we can see that our complete answer is:\
[tex]1\frac{2}{3}[/tex]
a 150 pound person uses 6.2 calories per minute when walking at speed of 4 mph . How long must a person walk at this speed to used at least 200 calories ?
Answer:
4960
Step-by-step explanation:
6.2 cal = 4mph
1 cal = 6.2 * 4 = 24.8mph
200 cal = 24.8 * 200 = 4960mph
Do mark BRAINLIEST
PLS HELP ASAP THANKS ILL GIVE BRAINLKEST PLS THANKS PLS
Answer:
(4,10)
Step-by-step explanation:
If its reflected over the x axis it goes from -4,-10 to 4,10
1. Trey just planted a small tree. He wanted to help it grow straight so he anchored the tree to the ground in three places using equal lengths of wire. The wires are tied to the tree 8 feet above the base of the tree. If Trey anchored each wire to the ground 6 feet from the base of the tree, what length of wire, in feet, is required for each anchor?
Answer:The correct answer is:
90 feet.
Explanation:
Each wire forms a right triangle with the tree and the ground. The height from the ground to the point on the tree the wire is attached to, 3 feet, is one leg. The length from the tree to where the wire is staked in the ground, 4 feet, is the other leg.
We use the Pythagorean theorem to find the hypotenuse: 3²+4²=c²; 9+16=c²; 25=c²; √25=√(c²); 5=c
This means each wire will be 5 feet long. There are 3 wires per tree, which gives us 5*3 = 15 feet. There are 6 tree, so this is 15*6 = 90 feet of wire.
Step-by-step explanation:
Jason has 5 packs of pencils with the same number of pencils in each one. If Jason has 50 pencils total, which equations could be used to find the number of pencils in each pack?
Answer:
5x=50
Step-by-step explanation:
Divide 50 by 5x so you get x = 10 (or just do basic multiplication)
Put these numbers in order of size, smallest to largest: 6, -2, 4, -3, 1 3
Answer:
-3,-2,4,6,13
Step-by-step explanation:
put them in order of increment
3. Three Bean Salad Puzzle #2
A bean salad has 6 beans in all. It is made up of:
1/6 lima beans
1/3 red beans
1/2 black-eyed peas
How many of each type of bean is in the salad?
Answer: 1 lima bean, 2 red beans, 3 black-eyed peas
Step-by-step explanation:
If 1/6 of the beans are lima beans, then there are 6 * 1/6 lima beans in the salad. 6 * 1/6 = 6/6 = 1.
If 1/3 of the beans are red beans, then there are 6 * 1/3 red beans in the salad. 6 * 1/3 = 6/3 = 2.
If 1/2 of the beans are black-eyed peas, then there are 6 * 1/2 black-eyed peas in the salad. 6 * 1/2 = 6/2 = 3.
Answer:
Lima Beans: 6 x [tex]\frac{1}{6}[/tex] = 1
Red Beans: [tex]\frac{1}{3}[/tex] x 6 = 2
Black Eyed-Peas: [tex]\frac{1}{2}[/tex] x 6 = 3
Hope this helps!
What is the value of f(2)
A) -1
B) -0.75
C) 3
D) 12
When we are finding f(x) given a value of x, we must identify the value of y that results from the value of x.
Solving the QuestionWe are asked to find f(2).
On the graph, first find the location of x=2.
Then, identify where the function is at x=2.
Finally, identify the corresponding y-value: 12.
AnswerThe value of f(2) is 12.
Futhe Mathematics
[tex](Cos {}^{4}t -Sin {}^{4}t ) \div Cos {}^{2}t[/tex]
Answer:
cos2t/cos²t
Step-by-step explanation:
Here the given trigonometric expression to us is ,
[tex]\longrightarrow \dfrac{cos^4t - sin^4t }{cos^2t } [/tex]
We can write the numerator as ,
[tex]\longrightarrow \dfrac{ (cos^2t)^2-(sin^2t)^2}{cos^2t } [/tex]
Recall the identity ,
[tex]\longrightarrow (a-b)(a+b)=a^2-b^2[/tex]
Using this we have ,
[tex]\longrightarrow \dfrac{(cos^2t + sin^2t)(cos^2t-sin^2t)}{cos^2t}[/tex]
Again , as we know that ,
[tex]\longrightarrow sin^2\phi + cos^2\phi = 1 [/tex]
Therefore we can rewrite it as ,
[tex]\longrightarrow \dfrac{1(cos^2t - sin^2t)}{cos^2t}[/tex]
Again using the first identity mentioned above ,
[tex]\longrightarrow \underline{\underline{\dfrac{(cost + sint )(cost - sint)}{cos^2t}}}[/tex]
Or else we can also write it using ,
[tex]\longrightarrow cos2\phi = cos^2\phi - sin^2\phi [/tex]
Therefore ,
[tex]\longrightarrow \underline{\underline{\dfrac{cos2t}{cos^2t}}}[/tex]
And we are done !
[tex]\rule{200}{4}[/tex]
Additional info :-
Derivation of cos²x - sin²x = cos2x :-
We can rewrite cos 2x as ,
[tex]\longrightarrow cos(x + x ) [/tex]
As we know that ,
[tex]\longrightarrow cos(y + z )= cosy.cosz - siny.sinz [/tex]
So that ,
[tex]\longrightarrow cos(x+x) = cos(x).cos(x) - sin(x)sin(x) [/tex]
On simplifying,
[tex]\longrightarrow cos(x+x) = cos^2x - sin^2x [/tex]
Hence,
[tex]\longrightarrow\underline{\underline{cos (2x) = cos^2x - sin^2x }} [/tex]
[tex]\rule{200}{4}[/tex]
Paul surveyed students in a high school about their favorite sport of the 1, 200 students in the school, 67 tenth-grade students were surveyed. More than half of the 67 students said their favorite sport is basketball. Based on the survey, Paul concluded that the favorite sport of most high school students is basketball.
Why is Paul's conclusion incorrect?
1 Paul surveyed too many students.
2 Paul's survey sample only included tenth graders.
3 Paul did not survey any middle school students.
4 Paul did not include enough sports in the survey.
Answer:
2 Paul's Survey sample only included tenth graders
Step-by-step explanation:
The reson why this is your answer is simple
Because this is true, he ONLY surveyed tenth-graders. He should have found for all of the students, including the other 1,100 students that didn't get surveyed.
Thanks!
answer for points !!!!!!!
Answer:
2 and 4
Step-by-step explanation:
I need help answering this. Please and thanks
Knowing the angles are equal, the value for y is 40.
Angle BisectorThe angle bisector is the line segment that divides the angle into two equal angles.
Thus, if OF is the angle bisector for EOG, the angles EOF and FOG are equal.
For finding y, you can write:
EOG=FOG
y+30=3y-50
y-3y=-50-30
-2y=-80
y=80/2
y=40
Read more about the angle bisector here:
https://brainly.com/question/24677341
You want to compare the numbers of hours spent on recreation each week by teachers and non-teachers in your state. You take 100 random samples of 15 teachers and 100 random samples of 15 non-teachers throughout the state and record the median value of each sample. The double box-and-whisker plot shows the distributions of sample medians. Are the samples likely to be representative of all teachers and non-teachers in your state?
Yes, the samples are likely to be representative of all teachers and non-teachers in the state.
Statistical measure of central tendencyThe median, in similarity with the mean is a statistical measure of central tendency.
Since, the double box-and-whisker plot shows the distribution of sample medians, it follows that the samples are likely to be representative of all teachers and non-teachers.
Read more on central tendency measure;
https://brainly.com/question/17726154
Greg has 4 shirts: a white one, a black one, a red one, and a blue one. He also has two pairs of pants, one blue and one tan. What is the probability, if Greg gets dressed in the dark, that he winds up wearing the white shirt and tan pants? Show your work.
Answer:
he has 1/2 of a chance to get tan pants and 1/4 of a chance to get a white shirt.
Step-by-step explanation:
hope that helps, mr cleann
Answer: 1/8
Step-by-step explanation:
(W) white (B) black (R) red (BL) blue (BP) blue pants (TP) tan pants
|-------------(B)
|-------------(W)
(TP)------------- |-------------(R)
| |-------------(BL)
| |--------------(B)
| |--------------(W)
(BP)-------------|--------------(R)
|--------------(BL)
From the tree diagram, a white shirt with tan pants is one out of eight possible outcomes, so the probability of getting tan pants and a white shirt is 1/8.
Write a conditional statement from the following statement: a) A horse has 4 legs. b) If it has 4 legs, then it is a horse. c) Every horse has 4 legs. d) If it is a horse, then it has 4 legs. e) It has 4 legs and it is a horse.
Answer:
D
Step-by-step explanation:
it is conditional statement because it starts with if and after the comma it starts with then
Answer: D
Step-by-step explanation: the correct answer.
HELP ME PLEASE thank you so much to who helps me :)
Answer:
π(12.1)²
Step-by-step explanation:
12.1 is the radius
Formula for base = πr²
= π(12.1)²
2.9 months to 4.9 months
9xsquared -49 factorise
Answer:
(3x-7)(3x+7)
Step-by-step explanation:
3^2 * x^2 -7^2 (expand that out)
(3x)^2 - 7^2
(3x-7)*(3x+7)
Answer:
(3x+7)(3x-7)
Step-by-step explanation:
Applying the Difference of Two Squares(D.O.T.S) formula:
[tex]x^{2} -y^{2} =(x+y)(x-y)[/tex]
9x²= (3x)²
49=7²
Put 3x as x and 7 as y into the D.O.T.S formula:
(3x+7)(3x-7)
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A circle labeled Internal Medicine Doctors. It is connected to 4 other circles. Circle 1 is labeled Veterinarians. Circle 2 is labeled Epidemiologists. Circle 3 is labeled Virologists. Circle 4 is labeled Food Investigators. This web diagram presents different types of internal medicine doctors. Why is a web diagram a good choice for illustrating this information? A web diagram allows pictures to help with understanding. A web diagram shows what connects these different types of doctors. A web diagram compares and contrasts the doctors best. A web diagram looks best on the page.
Answer:
B
Step-by-step explanation:
I got it right on the assignment
Hope this helps :)
Answer:
B. A web diagram shows what connects these different types of doctors.
Step-by-step explanation:
pls help me plsssssss!!!!!!
x/3 + 7 ≥ 14←←←←←←←←←←←
Answer:
x bigger than or equals to 21
Step-by-step explanation:
[tex] \frac{x}{3} + 7 \geqslant 14[/tex]
[tex] \frac{x}{3} \geqslant 7[/tex]
[tex]x \geqslant 21[/tex]
HELP PLEASE YOU'LL GET BRAINLIEST!!!!!
Step-by-step explanation:
oh, come on !
we have a point on the curve : (3, -2)
we simply put the values in and calculate the missing factor of x² :
-2 = f × 3² = f × 9
f = -2/9
y = -2/9 x² = -0.222222222... x²
Help me pleasee !!!!
Answer:
here (edit I made a mistake)
Step-by-step explanation:
9) [tex]y=\frac{3}{5} x +5[/tex]
10) y = x - 3
11) [tex]y=-\frac{3}{5} x - 3[/tex]
12) [tex]y=\frac{5}{4} x + 2[/tex]
these are the slop int forms, my bad...
sorry
Answer:
9) -3/5x + y = 5
10) -x + y = -3
11) 3/5x + y = -3
12) -5/4x + y = 2
Step-by-step explanation:
Which expression is a difference of squares with a factor of 5x − 8? 25x2 − 16 25x2 16 25x2 − 64 25x2 64.
The product of the factors (5x − 8) and (5x + 8) is 25x² − 64. Then the correct option is C.
What is polynomial?Polynomial is an algebraic expression that consists of variables and coefficients. Variable are called unknown. We can apply arithmetic operations such as addition, subtraction, etc. But not divisible by variable.
One factor of the polynomial is given which is 5x − 8.
Then the polynomial will be
Let the other factor be 5x + 8
Then their product will be
(5x − 8)(5x + 8)
(5x)² − 8²
25x² − 64
More about the polynomial link is given below.
https://brainly.com/question/17822016
The circle C has equation x2 + y2 +4x - 2y - 11 = 0.
Find
i) The coordinates of the centre of C. [2]
ii) The radius of C. [2]
ii) The coordinates where the circle cuts the y axis, giving your answers in exact surds.
Answer:
where is circle pls send picture of circle
Step-by-step explanation:
please mark me as brainlist please