Answer:
k = 5
Step-by-step explanation:
First, add 3 to both sides;
[tex]7k = 35[/tex]
Divide by 7:
[tex]\frac{7}{7}k = \frac{35}{7}\\k = 5[/tex]
Now, let's check our answer:
[tex]7(5) - 3 = 32\\35 - 3 = 32\\32 = 32[/tex]
I hope this helps!!
If you have any questions feel free to ask!
- Kay :)
Isabella baked 10 cookies with 2 scoops of flour. How many scoops of flour does Isabella need in order to bake 45 cookies? Assume the relationship is directly proportional
Answer:
9 scoops
Step-by-step explanation:
If 10 cookies took 2 scoops of flour, then 4 scoops would make 20 cookies, 6 scoops would make 30, 8 scoops would make 40. If you need 5 cookies, then split 2 scoops in half, which would be one scoop. 8 scoops(which is 40 cookies)+ 1 scoop(5 cookies) = 9 scoops (45 cookies)
The angle of elevation from me to the top of a hill is 51 degrees. The angle of elevation from me to the top of a tree is 57 degrees. The tree stands 20 ft off the hill. How high is the top of the tree from the base of the hill?
Answer:
Approximately [tex]101\; \rm ft[/tex] (assuming that the height of the base of the hill is the same as that of the observer.)
Step-by-step explanation:
Refer to the diagram attached.
Let [tex]\rm O[/tex] denote the observer.Let [tex]\rm A[/tex] denote the top of the tree.Let [tex]\rm R[/tex] denote the base of the tree.Let [tex]\rm B[/tex] denote the point where line [tex]\rm AR[/tex] (a vertical line) and the horizontal line going through [tex]\rm O[/tex] meets. [tex]\angle \rm B\hat{A}R = 90^\circ[/tex].Angles:
Angle of elevation of the base of the tree as it appears to the observer: [tex]\angle \rm B\hat{O}R = 51^\circ[/tex].Angle of elevation of the top of the tree as it appears to the observer: [tex]\angle \rm B\hat{O}A = 57^\circ[/tex].
Let the length of segment [tex]\rm BR[/tex] (vertical distance between the base of the tree and the base of the hill) be [tex]x\; \rm ft[/tex].
The question is asking for the length of segment [tex]\rm AB[/tex]. Notice that the length of this segment is [tex]\mathrm{AB} = (x + 20)\; \rm ft[/tex].
The length of segment [tex]\rm OB[/tex] could be represented in two ways:
In right triangle [tex]\rm \triangle OBR[/tex] as the side adjacent to [tex]\angle \rm B\hat{O}R = 51^\circ[/tex].In right triangle [tex]\rm \triangle OBA[/tex] as the side adjacent to [tex]\angle \rm B\hat{O}A = 57^\circ[/tex].For example, in right triangle [tex]\rm \triangle OBR[/tex], the length of the side opposite to [tex]\angle \rm B\hat{O}R = 51^\circ[/tex] is segment [tex]\rm BR[/tex]. The length of that segment is [tex]x\; \rm ft[/tex].
[tex]\begin{aligned}\tan{\left(\angle\mathrm{B\hat{O}R}\right)} = \frac{\,\rm {BR}\,}{\,\rm {OB}\,} \; \genfrac{}{}{0em}{}{\leftarrow \text{opposite}}{\leftarrow \text{adjacent}}\end{aligned}[/tex].
Rearrange to find an expression for the length of [tex]\rm OB[/tex] (in [tex]\rm ft[/tex]) in terms of [tex]x[/tex]:
[tex]\begin{aligned}\mathrm{OB} &= \frac{\mathrm{BR}}{\tan{\left(\angle\mathrm{B\hat{O}R}\right)}} \\ &= \frac{x}{\tan\left(51^\circ\right)}\approx 0.810\, x\end{aligned}[/tex].
Similarly, in right triangle [tex]\rm \triangle OBA[/tex]:
[tex]\begin{aligned}\mathrm{OB} &= \frac{\mathrm{AB}}{\tan{\left(\angle\mathrm{B\hat{O}A}\right)}} \\ &= \frac{x + 20}{\tan\left(57^\circ\right)}\approx 0.649\, (x + 20)\end{aligned}[/tex].
Equate the right-hand side of these two equations:
[tex]0.810\, x \approx 0.649\, (x + 20)[/tex].
Solve for [tex]x[/tex]:
[tex]x \approx 81\; \rm ft[/tex].
Hence, the height of the top of this tree relative to the base of the hill would be [tex](x + 20)\; {\rm ft}\approx 101\; \rm ft[/tex].
4 ones + blank = 1 ten
Answer:
6 ONES
Step-by-step explanation:
Answer:
6 ones
Step-by-step explanation:
A jar contains 24 blue marbles 16 red marbles and 14 white marbles find the simplified ratio of total marbles to red marbles
Answer:
27:2
Step-by-step explanation:
List the first six prime numbers
Answer:
2,3,5,7,11,13
Step-by-step explanation:
the prime divisors of 10 are 2 and 5.
while the first six prime numbers are 2,3,5,7,11,13
14 compact cars at 56% of cars sold that day
Answer:
4
Step-by-step explanation:
The Precision Writing Instruments Company makes two pen designs - the Cordova design and the Savannah design. These data apply, regardless of which of two pen designs is being implemented. Materials cost per pen is $6. Labor cost per pen is $5. Production overhead is
$1,000,000. Advertising and promotion is $1,000,000. Marketing research has estimated the following demand functions for the next year of sales for the two pen designs where Q represents demand in thousands and P represents price. For the Cordova design, Q = 150 - 2.5P. For the Savannah design, Q = 175 - 2.1P. A penetration strategy is proposed for the Savannah design and a price of $25 is selected. What will be the profit or loss for the first year?
9514 1404 393
Answer:
loss of $285,000
Step-by-step explanation:
The demand for the Savannah design is estimated to be ...
Q = 175 -2.1P = 175 -2.1(25) = 122.5 . . . . thousand pens
Then the contribution margin from sales will be ...
122,500($25 -$6 -$5) = $1,715,000
Against a total of $2,000,000 in production and advertising costs, the net will be a loss of ...
$2,000,000 -1,715,000 = $285,000
The first-year loss will be $285,000.
Complete this division sentence.
763 + 23 =
r
Answer:
is it a division or addition
Step-by-step explanation:
for me the answer is 786
Describe a real-world example on how coordinate geometry is/can be used in the real-world. Then, create a sample question based on your example for the rest of your classmates to solve.
Answer:
Step-by-step explanation:
I think jhonnu
For a sample size of 55 and a population parameter of 0.2, what is the standard error of the sampling distribution? Round your answer to three
decimal places.
A. 0.028
B. 0.054
C. 0.035
D. 0.043
The standard error of the sampling distribution is given as follows:
B. 0.054.
How to obtain the standard error of the sampling distribution?By the Central Limit Theorem, for a proportion p in a sample of size n, the standard error of the sampling distribution of sample proportions is given as follows:
[tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
The parameter values for this problem are given as follows:
p = 0.2, n = 55.
Hence the standard error is given as follows:
[tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
[tex]s = \sqrt{\frac{0.2(0.8)}{55}}[/tex]
s = 0.054.
Meaning that the correct option is given by option B.
More can be learned about the Central Limit Theorem at https://brainly.com/question/25800303
#SPJ1
Joseph loves the Tennessee Titans, so his mother decides to buy
him a Titans cake for his birthday. If the cake cost $ 35.00
before taxes and $ 37.10 after taxes, please and answer
the following questions:
$ 35
1. How much will Joseph's mom pay in taxes?
2. By setting up a percent proportion, determine the percent tax rate.
(The "of" is the price of the cake before taxes and the "is" is the amount of taxes.)
is
of
100
Answer:
Step-by-step explanation:
question one: his mom will pay $2.1 in taxes
thats all i can answer
pls help nmn po bukas na pasahan
Step-by-step explanation:
yan na po yung answer .....................................
What is the length of x?
Answer:
The length of 'x' is 4
Step-by-step explanation:
We can use the pythagorean theorem to solve this.
The pythagorean theorem is:
[tex]a ^{2} + b^{2} = {c}^{2} [/tex]
[tex]a ^{2} + b^{2} = c^{2} \\ {3}^{2} + {b}^{2} = 5^{2} \\ 9 + {b}^{2} = 25 \\ \frac{ - 9 \: \: \: \: \: \: \: \: = - 9}{b ^{2} = \sqrt{16} } \\ b = 4[/tex]
Therefore x = 4
(5x+3) - (2x-6) i need help ? ToT
Answer:
3x + 9
General Formulas and Concepts:
Pre-Algebra
Distributive PropertyAlgebra I
Combining Like TermsStep-by-step explanation:
Step 1: Define
(5x + 3) - (2x - 6)
Step 2: Simplify
Distribute negative: 5x + 3 - 2x + 6Combine like terms (x): 3x + 3 + 6Combine like terms (Z): 3x + 9use distributive property to simplify -1(4+x)=6
Answer:
[tex]\huge\boxed{\boxed{x=-10}}[/tex]
Step-by-step explanation:
Hello.
The Distributive Property states that
a(b+c)=ab+ac
Simplify:
-1(4+x)=6
-4-x=6
Add 4 to both sides:
-4+4-x=6+4
-x=10
Divide both sides by -1 in order to get rid of the minus sign:
x=-10
And we're done!
I hope it helps & have an outstanding day!
~ST2710 :)
???? Help me and I’ll mark as brainliest
Answer:
15
Step-by-step explanation:
Answer:
I believe the answer is 6.
Step-by-step explanation:
What is the Slope for these graph ?
Answer:
The slope of the first graph is [tex]\frac{2}{3}[/tex] and the slope of the second graph is [tex]\frac{4}{2} = 2[/tex]
Step-by-step explanation:
First Graph
1. use rise over run to find the slope
2. the line goes up 2 numbers before it touches again
3. the line goes ever 3 numbers before it touches again
Second Graph
1. use rise over run to find the slope
2. the line goes up 4 numbers before touching again
3. the line goes over 2 numbers before touching again
a(7x + 3) = b + 14x?
Answer:
Step-by-step explanation:
So first add 7 +3 adn get 10, then add 14, and then you will get 24
24 is your answer.
NUMBER 6 ONLY. Please help. Only if you are SURE
Answer:
I think it should be zero
Amplitude: 6 Period: 44
Phase shift:
Step-by-step explanation:
provide more details, please
Find a · b.
a = 5i + 4j − k, b = −4i + 9k
Answer
a · b= the square root of b(5i + 4j - k) divided by b
A particle starts to move from rest in a straight line with an acceleration which increases with constant time rate from 1 ft./sec^{2} to 4 ft./sec^{2} in one second. prove that the particle will move a distance of 1 ft. in this second.
The particle's acceleration a increases at a constant rate, so that its average rate of change is equal to its instantaneous rate of change, which is equal to
(4 ft/s² - 1 ft/s²) / (1 s) = 3 ft/s³
The particles starts with acceleration a (0) = 1 ft/s², so we can determine its acceleration at time t by the fundamental theorem of calculus:
a(t) = a (0) + ∫₀ᵗ (3 ft/s³) du
a(t) = 1 ft/s² + (3 ft/s³) t
It also starts from rest, so with initial velocity v (0) = 0. Integrating again gives us the velocity function,
v(t) = v (0) + ∫₀ᵗ a(u) du
v(t) = ∫₀ᵗ (1 ft/s² + (3 ft/s³) u) du
v(t) = (1 ft/s²) t + 1/2 (3 ft/s³) t ²
Taking the particle's initial position to be x (0) = 0, compute the integral again to determine the distance it travels in 1 s:
x(t) = x (0) + ∫₀ᵗ v(u) du
x(t) = ∫₀ᵗ ((1 ft/s²) u + 1/2 (3 ft/s³) u ²) du
x(t) = 1/2 (1 ft/s²) t ² + 1/6 (3 ft/s³) t ³
→ x (1 s) = 1/2 (1 ft/s²) (1 s)² + 1/6 (3 ft/s³) (1 s)³ = 1 ft
Consider the function represented by the equation x – y = 3. What is the equation written in function notation, with x as the independent variable? f(x) = y + 3 f(x) = –y – 3 f(x) = –x + 3 f(x) = x – 3 ANSWER WITHIN 1O MINUTES AND WILL GIVE BRAINLIEST
Answer:
d
Step-by-step explanation:
Answer:
the answer is D i think.
PLEASE HELP IF UR GOOD AT MATH!!!
which fraction has an equivalent decimal value that repeats
Answer:
The answer is 2/3
Step-by-step explanation:
2/3 = 0.6666666666... with it repeating forever
Answer:
2/3
Step-by-step explanation:
The answer you selected is correct.
The decimal form of 2/3 is 0.66666666 (it repeats forever), unlike the other three:
3/4 = 0.75
4/5= 0.80
7/8= 0.875
What is the slope of the following equation? y =- 1/2×+1
Answer:
-1/2
Step-by-step explanation:
Answer: -1/2
Reason: In the equation of y = mx + b. The m is the slope, and the b is the y intercept, so that is how I figured out the Slope of the equation. I hope this helps, and Happy Holidays! :)
a nursery owner buys 7 panes of glass to fix some damage to her greenhouse. The 7 panes cost $16.45. Unfortunately, she breaks 2 more panes while repairing the damage. What is the cost of another 2 panes of glass?
Answer:
It would be $ for 2 other planes of glass because if you take 7 divided by 7 to get 1 pane of glass you have to divide 16.45 by 7 to get how much it costs for 1 pane of glass. So for 1 pane of glass, it is $2.35 then lastly you can either add 2.35 and 2.35 to get $4.70 or take 2.35 times 2 to get your total. So it will cost $4.70 to get 2 panes of glass.
Step-by-step explanation:
HELP HELP HELP .............
Answer:
Sorry i don't know what's the actual answer, but you can use Desmos app for graphing, hope that helps
Answer:
there you go if you want mark brainlest if not its okay with me
Step-by-step explanation:
In a dance competition, a participant has to score a total of at least 30 points in the first four rounds combined to move on to the fifth and final round. Steward scored 5 points in the first round. He then went on to score additional points in the second, third, and fourth rounds. In each of those rounds, his score was identical. Which inequality best shows the number of points, p, that Steward scored in each of the second, third, and fourth rounds if he earned a place in the finals?
5 + 3p ≥ 30
5 + 3p ≤ 30
5p + 3 ≥ 30
5p + 3 ≤ 30
Answer:
A) 5+3p ≥ 30
Step-by-step explanation:
The 5+3p has to be greater than 30 to move on to the next round. The student scored 5 points in the first round and since the other 3 rounds he scored the same amount of points, your equation would be 5+3p ≥ 30 :)
If you were to solve this, you would subtract 5 from both sides to find that 3p≥ 25. Divide 25 by 3 to find out that Steward needed to score at least 9 points in each of rounds 2,3, and 4, so a possible solution could be that he earned 5 points in round 1, 9 in round 2, 9 in round 3, and 9 in round 4 for a total of 32, which is enough to qualify for the final round :)
What is the value of sin {3sin^-1 (2/5)} ?
Answer:
[tex]\displaystyle \frac{118}{125}[/tex]
Step-by-step explanation:
Trigonometry
Calculate
[tex]\sin (3\sin^{-1}(2/5))[/tex]
We use the formula for the sine of triple angle:
[tex]\sin 3x=3\sin x-4\sin^3 x[/tex]
And recall:
[tex]\sin \sin^{-1}x=x[/tex]
For this problem, we set:
[tex]x=\sin^{-1}(2/5)[/tex]
Thus:
[tex]\sin 3x=3\sin (\sin^{-1}(2/5))-4\sin^3 (\sin^{-1}(2/5))[/tex]
[tex]\displaystyle \sin 3x=3*\frac{2}{5}-4\left(\frac{2}{5}\right)^3[/tex]
[tex]\displaystyle \sin 3x=\frac{6}{5}-4*\frac{8}{125}[/tex]
[tex]\displaystyle \sin 3x=\frac{6}{5}-\frac{32}{125}[/tex]
[tex]\displaystyle \sin 3x=\frac{6*25}{125}-\frac{32}{125}[/tex]
[tex]\displaystyle \sin 3x=\frac{150-32}{125}[/tex]
[tex]\mathbf{\displaystyle \sin 3x=\frac{118}{125}}[/tex]