Answers
Answer:
A) x = 113°
Explanation:
Given three sides: 6.4 cm, 5.8 cm, 10.2 cm
Use the cosine rule:
c² = a² + b² - 2ab cos(C)
Insert/put variables:
[tex]\rightarrow \sf 10.2^2 = 5.8^2 + 6.4^2 - 2(5.8)(6.4) cos(x)[/tex]
[tex]\rightarrow \sf -74.24 cos(x) = 10.2^2 - 5.8^2 - 6.4^2[/tex]
[tex]\sf \rightarrow -74.24 cos(x) = 29.44[/tex]
[tex]\rightarrow \sf cos(x) = \dfrac{29.44}{-74.24}[/tex]
[tex]\rightarrow \sf x = cos^{-1}(-\dfrac{23}{58})[/tex] = 113.36° ≈ 113° (rounded to nearest degree)
Related Questions
please help meeeee will mark them brain
from biggest to smallest
Answers
0.83 (5/6), 0.77 (7/9), 0.75 (3/4), 0.66 (2/3), 0.583 (7/12), 0.5 (1/2).
I paid $8000 to burrow $50000 for 2 years. What was the rate of simple interest charged?
[make brainliest if got correct and 20pts]
Answers
[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$8000\\ P=\textit{original amount deposited}\dotfill & \$5000\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\dotfill &2 \end{cases} \\\\\\ 8000=5000[1+(\frac{r}{100})(2)]\implies \cfrac{8000}{5000}=1+\cfrac{r}{50}\implies \cfrac{8}{5}=1+\cfrac{r}{50} \\\\\\ \cfrac{8}{5}-1=\cfrac{r}{50}\implies \cfrac{3}{5}=\cfrac{r}{50}\implies \cfrac{3(50)}{5}=r\implies 30=r[/tex]
What is the solution to the following system of equations? (2 points) y = x2 + 10x + 11 y = x2 + x − 7
Answers
Answer:
y=x^(2)+10x+11,y=x^(2)+x-7
Step-by-step explanation:
I think so bro
Step-by-step explanation:
I assume you mean
y = x² + 10x + 11
y = x² + x - 7
well, I subtract equation 2 from equation 1 :
0 = 9x + 18
9x = -18
x = -2
y = x² + x - 7 = (-2)² - 2 - 7 = 4 - 2 - 7 = -5
the solution (the intersection point of both graphs) is the point (-2, -5).
Mitra created a mosaic design using square 2x2 cm white tiles and 2x3 cm rectangular centimeter black tiles. She used twice as many white tiles as black tiles. The finished pattern was 1092 square centimeters in area. How many rectangular tiles did she use?
Answers
Mitra used 156 white tiles of 2x2 cm and 76 black tiles of 2x3 cm to form a pattern with an area of 1092 cm²
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let x represent the number of white tiles and y represent the number of black tiles.
Area of white tiles = 2 cm * 2 cm = 4 cm²
Area of black tiles = 2 cm * 3 cm = 6 cm²
She used twice as many white tiles as black tiles. Hence:
x = 2y (1)
Also, the finished pattern was 1092 square centimeters in area. Hence:
4x + 6y = 1092 (2)
From both equations:
x = 156, y = 78
Mitra used 156 white tiles of 2x2 cm and 76 black tiles of 2x3 cm to form a pattern with an area of 1092 cm²
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Determine the length of side QS.
A) 1.9
B) 3.4
C) 2.4
D) 5.7
Answers
square root 3.4 = 1.84
Answer = A-1.9
Answer: C) 2.4
Given one opposite angle, two known sides and one missing side.
Hence use cosine rule:
[tex]\sf c = \sqrt{a^2 + b^2- 2ab \ cos\theta}[/tex]
insert values
[tex]\sf c = \sqrt{1.2^2 + 1.4^2- 2(1.2)(1.4) \ cos(134)}[/tex]
simplify
[tex]\sf c = 2.3945 \quad \approx \quad 2.4[/tex]
Which equation can be used to solve for c?
Triangle A B C is shown. Angle A C B is 90 degrees and angle A B C is 35 degrees. The length of C B is 5 inches, the length of A C is b, and the length of B A is c.
Answers
The equation which is used to find the value of c will be c = 5/Cos 35
What is trigonometry?The branch of mathematics sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry.
We are given the following
m<ACB = 90degrees
m<ABC = 35degrees
The side opposite to m<ABC is AC
BA = hypotenuse
CB = adjacent = 5inches
Required
The equation to solve BA which is c
Using the Pythagoras theorem;
Cos Ф = Adjacent/Hypotenuse
Cos m<ABC = CB/BA
Cos m<ABC = 5/c
c = 5/cosm<ABC
c = 5/Cos 35
Hence the equation that can be used to solve for c is c = 5/Cos 35
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Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
is parallel to . and are perpendicular to and .
The ratio of the lengths of and is
:
.
Answers
The ratio of the lengths of and is 1: 1
PQ parallel to RS
PR and PS; perpendicular to PQ and RS.
What are the perpendicular lines?
Perpendicular lines are lines that intersect at a 90 degrees angle. Parallel lines are lines that are always the same distance apart.
FOR parallel lines, the perpendicular line joining then is always the same; here the 4 angles formed are all 90°
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Your answer should be an expanded polynomial in standard form.
(7a³-2a-2) + (-5a + 3) =
Answers
Answer:
7a^3-7a+1
Step-by-step explanation:
(7a³-2a-2) + (-5a + 3) =
Combine like terms
7a^3-2a-5a-2+3
7a^3-7a+1
If x = -3, then x 2 - 7x + 10 equals
37
40
22
Answers
40
Step-by-step explanation:
[tex]{ \red{ \tt{given \: }}} \: :- \: { \green{ \tt{x = - 3}}}[/tex]
Then, Substitute the value of "x" in this below equation..
[tex]{ \orange{ \tt{ {x}^{2} - 7x + 10}}}[/tex]
[tex]{ \orange{ \tt{ {( - 3)}^{2} - 7( - 3) + 10}}}[/tex]
[tex]{ \orange{ \tt{9}}} \: + \: { \orange{ \tt{21}}} \: + \: { \orange{ \tt{10}}}[/tex]
[tex] = { \orange{ \tt{40}}}[/tex]
A die is tossed. Find the odds against rolling a number greater than 4.
Answers
Reason:
There are 4 outcomes we don't want (rolling 1,2,3 or 4) and 2 outcomes we do want (rolling 5 or 6)
This gives the odds against ratio of 4:2 or 2:1
This can be written out as "2 to 1" or "two to one".
Having 2 to 1 odds means that we're twice as likely to get something we don't want vs something we do want.
Side note: the odds in favor will have us flip the ratio.
Sum of 1 OK. Now, think of two numbers with a sum of 1.
Answers
Answer:
0+1
Step-by-step explanat
Any two consecutive number in which the greater number is positive and smaller number is negative will give the sum of 1.
What is sum?The result we get after adding some quantity is called the sum of the data.
Given we need to find two numbers whose sum is 1,
So, we can consider in this case two consecutive numbers of opposite sign the greater number should have a positive sign and the smaller number should have negative sign,
For example =
-4+5 = 1
-3+4 = 1
-2+3 = 1
-9+10 = 1
So, any two consecutive number in which the greater number is positive and smaller number is negative will give the sum of 1.
Hence, there can be many numbers which can give sum of 1.
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Suppose there is this little town with a finite number of people: (1) No two inhabitants have exactly the same number of hairs. (2) No inhabitant has exactly 743 hairs or no hairs at all. (3) There are more inhabitants than there are hairs on the head of any inhabitant. So, what is the highest possible number of inhabitants in that little town?
Answers
The highest possible number of inhabitants in that little town are 743.
What are inhabitant?A person or animal that lives in a place is called as the inhabitant.
Suppose there is this little town with a finite number of people: (1) No two inhabitants have exactly the same number of hairs. (2) No inhabitant has exactly 743 hairs or no hairs at all. (3) There are more inhabitants than there are hairs on the head of any inhabitant.
Let say there are 519 people in the town. and make them stand in a line with increasing number of hairs on their heads. This way, there will be a person on the last, who has no hair.
There are more number of people than the hairs. From bald to 742 hairs, 743 is the limit.
Thus, the highest possible number of inhabitants in that little town are 743.
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What is the name of the expression under the radical symbol in a radical function?
Answers
An expression is defined as a set of numbers, variables, and mathematical operations. The name of the expression under the radical symbol in a radical function is called a radicand.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The radical is the symbol that is used to represent the root in the expression n√x. The name of the expression under the radical symbol in a radical function is called a radicand.
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1) FILL IN THE SPACES:
a. 2.5 liters (L) = ______ml
b. 1320g = ________kg
c. 1.2g = _________mg
d. 1025mcg =_______mg
and. 2TBS=_______tsp
F. 1 TBS =_______ml
g. 2 fl oz =_______ml
h. 75kg =________pounds (lb)
PROBLEMS
1) Add the following: 30 mg, 2.5 kg and 7.0 g. Express the answer in g.
2) Express the amount of 1.243 g as:
mg ________
kg ________
mcg _______
3) How many grams of the active ingredient "aspirin" would be needed to make 500 aspirin tablets if each tablet must contain 325 mg?
Answers
4. The diameter of a circle is 10 in. What is the approximate circumference? Show your work to receive
full credit. **You must include the units of measurement to receive full credit.**
Show work :))
Answers
Answer:
31.4 in
Step-by-step explanation:
The circumference of of a circle given the diameter is πd :
C = π×d = 10π = 31.4159....
C ≈ 31.4
The units will still be in as this is a length not an area .
Hope this helped and brainliest please
Find the volume (to the nearest cubic foot) of a cone with base radius 4 ft. and height 8 ft.
Answers
Answer:
135 ft^3
Step-by-step explanation:
The volume of a cone is [tex]\frac{1}{3} \pi r^{2}h[/tex]. The radius is 4 and the height is 8, so these values can be plugged in:
[tex]V = \frac{1}{3} \pi \times 4^{2} \times 8[/tex]
[tex]V = \frac{128\pi }{3}[/tex]
This is about 134.041286553 which rounds to 135 ft^3.
How to find the average collection period
Answers
Answer:
dividing a company's yearly accounts receivable balance by its yearly total net sales
Graph the system of inequalities:
-x + 2y - 4 <0
3x + 4y + 420
Answers
Step-by-step explanation:
draw the graph then use the graph to answer the following questions
The function f(x) = 2x2 + 3x + 5, when evaluated, gives a value of 19. What is the function’s input value?
Answers
Answer:
-7/2 or 2 are inputs that give 19 as output.
Step-by-step explanation:
The problem gives us a quadratic function [tex]\displaystyle \large{f(x)=2x^2+3x+5}[/tex]. When its output is 19, we want to know the input value(s).
Since an output which is f(x) = 19. Therefore:
[tex]\displaystyle \large{19=2x^2+3x+5}[/tex]
Rearrange the expression in quadratic equation.
[tex]\displaystyle \large{0=2x^2+3x+5-19}\\\\\displaystyle \large{0=2x^2+3x-14}\\\\\displaystyle \large{2x^2+3x-14=0}[/tex]
Factor the expression.
[tex]\displaystyle \large{(2x+7)(x-2)=0}[/tex]
Solve like linear equation which we get:
[tex]\displaystyle \large{x=-\dfrac{7}{2}, 2}[/tex]
If you input these x-values in the function, you will get 19 as the output which satisfies the condition.
Hence, inputs are -7/2, 2
Answer:
[tex]x=2, \quad x=-\dfrac{7}{2}[/tex]
Step-by-step explanation:
Set the function to 19:
[tex]\implies 2x^2+3x+5=19[/tex]
Subtract 19 from both sides:
[tex]\implies 2x^2+3x-14=0[/tex]
To factor a quadratic in the form [tex]ax^2+bx+c[/tex]
Find two numbers that multiply to [tex]ac[/tex] and sum to [tex]b[/tex]: 7 and -4
Rewrite [tex]b[/tex] as the sum of these two numbers:
[tex]\implies 2x^2-4x+7x-14=0[/tex]
Factorize the first two terms and the last two terms separately:
[tex]\implies 2x(x-2)+7(x-2)=0[/tex]
Factor out the common term (x - 2):
[tex]\implies (2x+7)(x-2)=0[/tex]
Therefore the function's input values that when evaluated give a value of 19 are:
[tex](2x+7)=0 \implies x=-\dfrac{7}{2}[/tex]
[tex](x-2)=0 \implies x=2[/tex]
In the diagram, points D and E are marked by drawing arcs of equal size centered at B such that the arcs intersect and . Then, intersecting arcs of equal size are drawn centered at points D and E. Point P is located at the intersection of these arcs.
Based on this construction, m∠ABP is
°, and m∠ABC is
Answers
Based on this construction, the value of m∠ABC is 64°.
How to find the angle?From the point, E and D, two arcs are made which are intersecting each other at point P.
It means, that line BP is the bisector of angle ABC. ABC will be:
= 2 * 32=64
Therefore, based on this construction, the value of m∠ABC is 64°.
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Find the surface area of the prism. 8 4 14
Answers
Answer:
4 8 1 4 0,683 the (783)-213=509
which equation has the correct sign on the product
Answers
The equation which has the correct sign on the product is 27(-5) = -135
Sign of product- × - = +
- × + = -
+ × - = -
+ × + = +
Given equations:
27(-5) = -135
(-4)(-4) = -16
(-61) (3) = 183
22 × 4 = -88
Correct equation:
27(-5) = -135
(-4)(-4) = 16
(-61) (3) = -183
22 × 4 = 88
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Factor out the GCF from the given polynomial. 38x-8
Answers
Answer:
2(19x - 1)
Step-by-step explanation:
The GCF of 38 and 8 is 2 :
Now we take a common factor of 2 :
2(19x - 1)
Hope this helped and have a good day
Answer:
2(19x-4)
The gcf of 38 and 8 is 2 so factor it out.
find the area of the shaded regions. give your answer as a completely simplified exact value in terms of π
20 POINTS!!!
WILL MARK BRAINLIEST!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
V=r^2π => 36π·3/4 = 27π
im really not sure with my answer, please tell which is the correct choice.
Answers
Answer:
the orange one
Step-by-step explanation:
(10 + 10) : (5-3) =
20 : 2 =
10
can you please help me with this two questions
Answers
Answer:
2) d. 60°
3) a. AB
Step-by-step explanation:
Question 2
ΔABC and ΔCDA are congruent because:
they are both right trianglesthey share one side (AC)their hypotenuse are parallel (marked by the arrows)This means the corresponding side lengths and angles are equal.
Therefore,
∠CDA = ∠ABC
⇒ x = 60°
Question 3
The hypotenuse is the longest side of a right triangle - the side opposite the right angle (the right angle is shown as a small square).
Therefore, the hypotenuse of ΔABC is the line AB.
Alejandro and Emila ordered a pizza. Alejandro at 1/3 of the pizza and Emila ate 2/5 of the pizza. How much did they eat together? Was there any pizza left? How much?
Answers
Answer: [tex]\frac{4}{15}[/tex] of the pizza was left
Step-by-step explanation:
lets first get the denominators the same..
[tex]\frac{1}{3} = \frac{5}{15}[/tex]
[tex]\frac{2}{5} = \frac{6}{15}[/tex]
To find the total pizza eaten we add these two fractions
[tex]\frac{5}{15} +\frac{6}{15} =\frac{11}{15}[/tex]
we can think of [tex]\frac{15}{15}[/tex] as 1 pizza because it simplifies to 1
[tex]\frac{15}{15} -\frac{11}{15} =\frac{4}{15}[/tex]
Therefore, [tex]\frac{4}{15}[/tex] of the pizza was left
Answer:Amount left=4/15
Step-by-step explanation:
The solution is in the image
Help please…………………..
Answers
2. vertical
3. x = 0
4. all real numbers
5. Continuous
6. 0 to infinity
That’s all I have without seeing the drop down menu options
Help please! Drag the tiles to the boxes to form correct pairs. Not all tiles will be used. Determine each segment length in right triangle ABC.
(file is posted below)
Answers
The measure of BD and BC are 7 and 7√2 respectively
Triangular altitude theoremA triangle is a shape with 3 sides and angles.
According to the theorem
CD/BD = BD/DA
From the given figure
CD = DA = 14/2
CD = DA = 7
Substitute
7/BD = BD/7
BD² = 7²
BD² = 49
BD = 7
Determine the measure of BC
sin 45 = BD/BC
sin45 = 7/BC
BC = 7/sin45
BC = 7√2
Hence the measure of BD and BC are 7 and 7√2 respectively
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What is the area of the parallelogram?
Answers
Answer:
Area = 120 in²Step-by-step explanation:
follow the formula in the picture
Area = b * h
Area = 15 * 8
Area = 120 in²