[tex]\bf \textit{Pythagorean Identities} \\\\ sin^2(\theta)+cos^2(\theta)=1 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ sin^2(x)+sin^2(x)cot^2(x)\implies sin^2(x)+\underline{sin^2(x)}\cdot \cfrac{cos^2(x)}{\underline{sin^2(x)}} \\\\\\ sin^2(x)+cos^2(x)\implies 1[/tex]
a weight lifter uses both 2 kg blocks as well as 5 kg blocks to set up his bar. he has a total of 30 blocks if the total weight of the bar is observed to be 120 kg then calculate the number of 5 kg blocks and 2 kg blocks
Answer:
The number of the 2 kg blocks is 10
The number of the 5 kg blocks is 20
Step-by-step explanation:
Let the number of the 2 kg blocks be x and the number of the 5 kg blocks be y.
The total number of blocks in terms of x and y is;
x + y
We are informed that he has a total of 30 blocks, implying that;
x + y = 30
The total weight of the bar in terms of x and y will be;
2x + 5y
We are also informed that the total weight of the bar is observed to be 120, implying that;
2x + 5y = 120
We therefore have two equations in two unknowns.;
x + y = 30
2x + 5y = 120
We can solve these equations simultaneously via elimination method;
multiply the first equation by 2;
2x + 2y = 60
2x + 5y = 120
Subtracting the first equation from the second one yields;
5y - 2y = 120 - 60
3y = 60
y = 20
But x + y = 30, implying that;
x = 30 - 20
x = 10
HELP. See attached for question and choices.
Answer: Second Option
{m| [tex]m\leq-0.48[/tex]}
Step-by-step explanation:
We have the following equation
[tex]10(10m+6)\leq12[/tex]
To solve this equation apply the distributive property
[tex]10(10m+6)\leq12[/tex]
[tex]10*10m+6*10\leq12[/tex]
[tex]100m+60\leq12[/tex]
Subtract 60 on both sides of the inequality
[tex]100m+60-60\leq12-60[/tex]
[tex]100m\leq12-60[/tex]
[tex]100m\leq-48[/tex]
Divide between 100 both sides of the inequality
[tex]m\leq-\frac{48}{100}[/tex]
[tex]m\leq-0.48[/tex]
The solution is
{m| [tex]m\leq-0.48[/tex]}
______ of symmetry- ALine that divides an object into two congruent halves.
Answer:
"A line"
Step-by-step explanation:
A line of symmetry is a line that divides an object into two congruent halves.
_____
However, not every line that does so is a line of symmetry. The vertical line in the attached diagram divides both figures into congruent halves. It is only a line of symmetry for the green figure.
Answer:
Axis of symmetry
Step-by-step explanation:
That's the "axis of symmetry." It's most often associated with parabolas.
Given: AB ≅ BC BD − median of ΔABC, m∠ABD = 40° Find: m∠ABC, m∠BDC
Answer:
m∠ABC= 80°, m∠BDC= 90°
Step-by-step explanation:
If m∠ABD = 40°, then add 40°+40° to get m∠ABC because AB ≅ BC, meaning their angles would be congruent.
For m∠BDC, just look at the picture and deduce that it's a 90 degree angle.
Answer:
m∠ABC=80° and m∠BDC=90°
Step-by-step explanation:
Given the ΔABC in which AB ≅ BC, m∠ABD = 40° and BD is median of ΔABC.
we have to find the measure of angle ∠ABC and ∠BDC.
As the median of isosceles triangle split the angle at the vertex into two equal parts i.e ∠ABC is twice the angle ∠ABD
⇒ [tex]\angle ABC=2\angle ABD[/tex]
[tex]\angle ABC=2\times 40=80^{\circ}[/tex]
Also the median of isosceles triangle is perpendicular to the opposite side i.e to the base. Here, BD is perpendicular to AC
⇒ ∠BDC=90°
Therefore, the measure of angle ABC and BDC is 80° and 90° respectively.
PLEASE HELP!!!!! TIMED!!! Will give brainliest!! 70 POINTS!!!!!
Matteo wants to write a statement that can be represented by the inequality P<9 Which describes the correct method to write a statement to match this inequality?
Use the inequality symbol to determine the relationship between the variable and the constant. Decide what the variable will represent. Decide what the constant will represent. Write a statement using the same relationship. An example is “Alva spent more than $9.”
Decide what the variable will represent. Decide what the constant will represent. Write a statement using the same relationship. An example is “Alva spent less than $9.” Use the inequality symbol to determine the relationship between the variable and the constant.
Decide what the variable will represent. Decide what the constant will represent. Use the inequality symbol to determine the relationship between the variable and the constant. Write a statement using the same relationship. An example is “Alva spent less than $9.”
Decide what the variable will represent. Decide what the constant will represent. Use the inequality symbol to determine the relationship between the variable and the constant. Write a statement using the same relationship. An example is “Alva spent more than $9.”
Answer:C
Step-by-step explanation:
The constant and the variable relationship is p<9.That means it is "Alva spent less than 9%"
Answer:
it is c
Step-by-step explanation:
A computer company produced this graph to show how many computers it expects to sell based on
how much the company spends on Internet advertising. The company expects to sell 40 million
computers, spending $5 million on Internet advertising. Which set of units and scales are appropriate
for the two axes?
Answer: Hence, Fourth option is correct.
Step-by-step explanation:
Since we have given that
Number of computers expected to sell = 40 millions
Cost price of internet advertising = $5 million
According to the graph, we can see that
40 millions is the y-coordinate and $5 million is the x-coordinate.
so, Horizontal axis - y- axis is the "Number of computers".
Vertical axis - x- axis is the "Advertising cost ":
Hence, Fourth option is correct.
Horizontal axis will have number of computers in millions and vertical axis will have advertising dollars in millions.
Given information:
The graph of computer production and advertising amount spent is given in the question.
Total number of computer sell = 40 millions
Cost of internet advertising = $5 million
Now , by looking the graph one can conclude that, Y coordinate of the graph is 40 million and the X coordinate of the graph is $5 million.
Hence, from the above conclusion one can write as:
Horizontal axis (X-axis) is the number of computers and the Vertical axis is (Y-axis) the advertising cost of computers.
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What are the solution(s) to the quadratic equation 50 – x2 = 0?
x = ±2
x = ±6
x = ±5
no real solution
Answer:
x = ±[tex]5\sqrt{2}[/tex]
Step-by-step explanation:
We have been given the quadratic equation;
[tex]50-x^{2}=0[/tex]
The first step is to subtract 50 from both sides of the equation;
[tex]50-x^{2}-50=0-50[/tex]
[tex]-x^{2}=-50[/tex]
Multiplying both sides by -1 yields;
[tex]x^{2}=50[/tex]
The final step is to obtain square roots on both sides;
[tex]\sqrt{x^{2} }=\sqrt{50}\\x=+/-\sqrt{50}[/tex]
Therefore, x = ±[tex]5\sqrt{2}[/tex]
Write an equation for the line below.
Answer:
x = 3
Step-by-step explanation:
A vertical line has the form x = constant. The graph shows the constant you want is 3.
*help please* What is the amplitude of the function graphed?
So amplitude is the length from the highest (or lowest) point from the mid-line of the function
In this case the mid-line is y = 1
The highest point, which has a y of 3 is 2 units away from the mid-line. This means that the amplitude is 2!
Hope this helped!
The amplitude of the function graphed will be 2.
What is amplitude ?The amplitude of a function is the amount by which the graph of the function travels above and below its midline, i.e. it is the height from the mean value of the function to its maximum or minimum.
We have,
A graph,
The highest value = 3,
Lowest value = -1
So,
From the definition mentioned above,
Amplitude [tex]=\frac{3+|-1|}{2}[/tex]
We get,
Amplitude = 2
Hence, we can say that the amplitude of the function graphed will be 2.
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