The SAS Similarity Theorem asserts that two triangles are similar if two sides in one triangle are proportionate to two sides in another triangle and the included angle in both is congruent.
what is side-angle-side similarity theorem?The side-angle-side (SAS) theorem is one such example. Triangles are congruent if their two sides and included angles are equivalent to those of another triangle's two sides and included angle. SAS similarity analysis: When the ratio of two sides' lengths in one triangle equals the ratio of sides' lengths in another triangle, and the included angles are also equal, the two triangles are said to be comparable.
Area of triangle =
[tex]1/2 X b X h\\b= 10\\h=5\\A = 1/2 X 10X 5\\A = 25 unit sq.[/tex]
and also by heron's formula
Area = [tex]\sqrt{s(s - a)(s - b)(s - c) }[/tex]
and, here s = half the perimeter,
[tex](a + b + c)/2.[/tex]
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For the first 3% of Pam's salary, her employer matches 100% of her 401(k) contributions, and from 3% to 12%, Pam's employer matches 50% of her 401(k) contributions. Pam's salary is $30,000, and last year, she contributed $4000 to her 401(k) plan. What was her employer's contribution to the 401(k)?  A. $4000  B. $3600  C. $2250  D. $1800
Her employer's contribution to the 401(k) was $2,500.
CalculusGiven that for the first 3% of Pam's salary, her employer matches 100% of her 401(k) contributions, and from 3% to 12%, Pam's employer matches 50% of her 401(k) contributions, and Pam's salary is $30,000 , and last year, she contributed $4000 to her 401(k) plan, to determine what was her employer's contribution to the 401(k) the following calculation must be made:
4000 / 12 x 3 = X1000 = X(4000 / 12 x 9) / 2 = X3000 / 2 = X1500 = X1000 + 1500 = 2500Therefore, her employer's contribution to the 401(k) was $2,500.
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Answer: C. $2250
Step-by-step explanation: took the quiz.
7(x-2)=21 help me with this answer plz show work
Answer:
x=5
Step-by-step explanation:
7 times x
7 times 2
7x-14= 21
14+14= 21+ 14
7x=35
x=5
7 times five equals 35
Please help! This is past due and i need it in in like 30 minutes. Ill be posting more questions soon so stay here.
Answer:
384 square inches
Step-by-step explanation:
The side is 10×5=50
There are 4 sides of equal surface area so we are at 200
The floor is 8×10=80 so we are at 280
The front is 8×5=40 and the back is the same so add another 40 so we are at 360
Add the little triangles which are 4×3=12 and you add the back as well so we get 384 square inches
Find the slope of the line segment shown
A . -1/2
B.-1
C.1/2
D.1
Answer:
1 is the correct answer
Step-by-step explanation:
y2-y1/x2-x1=slope
-2-3/-3-2
-5/=-5
1
On Monday, a local hamburger shop sold a combined total of 592 hamburgers and cheeseburgers. The number of cheeseburgers sold was three times the number of hamburgers sold. How many hamburgers were sold on Monday?
Answer:
148
Step-by-step explanation:
148 x 3 = 444
444 + 148 = 592
(っ◔◡◔)っ ♥ Hope It Helps ♥
148 hamburgers were sold on Monday.
Let x be the number of hamburgers sold.
Since the number of cheeseburgers sold was three times the number of hamburgers sold, the number of cheeseburgers sold can be represented as 3x.
The total number of hamburgers and cheeseburgers sold was 592. So, we can set up the equation:
x + 3x = 592
Combine like terms:
4x = 592
Now, solve for x by dividing both sides by 4:
x = 592 / 4
x = 148
Therefore, 148 hamburgers were sold on Monday.
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O D.y = -2x + 2
Q. If m=3 and b=6, what is the correct slope intercept equation?
answer choices
y=3-6
y=3X-6
y=3x+6
y=6x+3
US OP 10:31
Using the probabilities given, find the probability that a student earns a grade of A. (enter number in decimal form rounded to the nearest hundredth)
Answer:
0.14
Step-by-step explanation:
Here, we want to find the probability that a student earns the grade of A
Mathematically, we have this as the frequency of A divided by the sum of all frequencies
From the question, the sum of all frequencies will be (5 + 10 + 15+ 3 +2) = 35
Now we place the frequency of A over this
This gives;
5/35 = 1/7 = 0.14
Greg invests $500 in a savings account that earns 4% simple interest annually. If he does not make any additional deposits or withdrawals, how much money will be in the savings account after 5 years?
Answer:
600
Step-by-step explanation:
Multiply and simplify the following products. V stands for radical.
Example: (V5)2= (V5) (V5) = v(5 x 5) = 5
1. (19)
2. (V2) (13)
3. 2(12) x 3(3)
Answer:
(1) 9
(2) [tex]\sqrt{6}[/tex]
(3) 6([tex]\sqrt{6}[/tex])
Step-by-step explanation:
From the question,
(1) ([tex]\sqrt{9}[/tex])²
Applyin the law of multiplication of surds
([tex]\sqrt{9}[/tex])² = (
(2) ([tex]\sqrt{2}[/tex])× ([tex]\sqrt{3}[/tex]) =
Also applying the the law of multiplication of surd
([tex]\sqrt{2\\}[/tex])×([tex]\sqrt{3}[/tex]) = ([tex]\sqrt{6}[/tex]) ( This is an irational answer)
∴ ([tex]\sqrt{2}[/tex])×([tex]\sqrt{3}[/tex]) = [tex]\sqrt{6}[/tex]
(3) 2([tex]\sqrt{2}[/tex])×3([tex]\sqrt{3}[/tex])
Also applying the law of multiplication of surds i.e Multiply surds to surds and whole number to whole number
= 2×3×([tex]\sqrt{2}[/tex])×([tex]\sqrt{3}[/tex])
6×([tex]\sqrt{6}[/tex]) = 6(
Select the equivalent expression. −4(2a−3)+5a
1. 3(a+4)
2. −3(a−4)
3. −3(a+4)
4. 3(a−4)
Just need help with this !
Please anyone answer as soon as you can
Don’t send the link that hacks you :/
Answer:
check all boxes except for the last 1
Anne surveyed the 12 slowest runners in PE, class about their favorite sports,
Is this sample of the students in the PE, class likely to be biased?
Acar traveled 50 miles in 40 minutes. Assume that the car will continue at this constant
rate of speed. Which equation would accurately give the total number of miles, M, for
any given number of hours, h?
Answer:
M = 75h
Step-by-step explanation: The way you get this answer is my dividing 50/40 = 1.25. then do 1.25x60 (1 hr because you have to continue to miles per hour) which gives 75H.
3/2 inches of snow fell in 3/4 of an hour. Which TWO statements are correct?
A) The unit rate is 2 inches of snow per hour.
B) The unit rate is 3 inches of snow per hour.
C) The unit rate is 9/8 inches of snow each hour.
D) At the same rate, 4 inches of snow will fall in 6 hours.
E) At the same rate, 12 inches of snow will fall in 6 hours.
Answer:
A) The unit rate is 2 inches of snow per hour.
&
E) At the same rate 12 inches of snow will fall in 6 hours.
Step-by-step explanation:
Answer:
a and e
Step-by-step explanation:
did it on usatestprep
Can any of you guys help
Answer:
5
Step-by-step explanation:
Pythagoras theorem is a² = b² + c² (where a is the hypotenuse or the longest side)
To find the shorter side, you rearrange it so it becomes c² = a² - b² (whether it is c or b doesn't matter)
So √13² - 12² = 5
Which of the following 95% confidence intervals would lead us to reject Hp =0.30 in favor of
Hp *0.30 at the 5% significance level?
(a) (0.30, 0.38)
(b) (0.19, 0.27)
(c) (0.27, 0.31)
(d) (0.24, 0.30)
(e) None of these
According to the hypothesis tested, the confidence interval that would lead us to reject [tex]H_0: p = 0.3[/tex] in favor of [tex]H_0: p < 0.3[/tex] is given by:
(b) (0.19, 0.27)
What are the hypothesis tested?At the null hypothesis, we test if the proportion is of 0.3, that is:
[tex]H_0: p = 0.3[/tex]
At the alternative hypothesis, we test if the proportion is less than 0.3, that is:
[tex]H_1: p < 0.3[/tex]
We want to reject [tex]H_0: p = 0.3[/tex] in favor of [tex]H_1: p < 0.3[/tex], hence we need an interval that is entirely below 0.3, which is given by option b.
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Find the area of the compound shape: *
Tú tienes la mitad de lo que tenías y tendrás el triple de lo que tienes. Si tuvieras lo que tienes, tenías y tendrás, tendrías lo que yo tengo que es 180 dólares más de lo que tú tendrás ¿Cuánto tenías? Ayuda por favor
Answer:
Nosotros teníamos 120 dólares.
Step-by-step explanation:
Sean [tex]x[/tex], [tex]y[/tex], [tex]z[/tex] lo teníamos, lo que tenemos y lo que tendremos, respectivamente. A continuación, traducimos puntos claves del enunciado en expresiones matemáticas:
(i) Tu tienes la mitad de lo que tenías:
[tex]y = \frac{1}{2}\cdot x[/tex] (1)
(ii) Tendrás el triple lo que tienes:
[tex]z = 3\cdot y[/tex] (2)
(iii) Si tuvieras lo que tienes, tenías y tendrás, tendrías lo que yo tengo que es 180 dólares más de lo que tu tendrás:
[tex]x+y+z = z + 180[/tex]
[tex]x + y = 180[/tex] (3)
En consecuencia, tenemos el siguiente sistema de ecuaciones lineales:
[tex]\frac{1}{2}\cdot x -y = 0[/tex] (1)
[tex]3\cdot y - z = 0[/tex] (2)
[tex]x + y = 180[/tex] (3)
La solución del sistema de ecuaciones es: [tex]x = 120[/tex], [tex]y = 60[/tex], [tex]z = 180[/tex].
Nosotros teníamos 120 dólares.
find a distance between the two points
i dont seem to understamd
Step-by-step explanation:
To find the distance you need the distance formula. The distance formula is [tex]\sqrt{(x_{2}-x_{1} )^{2} + (y_{2}-y_{1})^2 }[/tex]. Order the pairs with a 1 or a 2. Look at he point that you labeled 2. Substitute any of the points with a 2 subscript into the equation. The x value is the first number in the ordered pair and the y value is the second number in the ordered pair. Repeat this with the ordered pair you labeled as 1. Substitute the numbers in. You should get something like this: [tex]\sqrt{(-7-5)^{2} + (-7-9)^{2} }[/tex]. If you are doing this without a calculator, it is easier than you think. Remember PEMDAS? Well apply that with this. Find out the solution to the parenthesis first. The first parenthesis should come out with[tex](-12)^{2}[/tex]. Finish the expression off by evaluating the expontent. That comes out to 144. Try this with the next parenthesis... The answer should be 256. Your square root should look like this: [tex]\sqrt{144+256}[/tex]. Add the numbers under the parenthesis together and you should get [tex]\sqrt{400}[/tex]. I'm sure you have a calculator in you hand ready to solve this. NOW YOU FIND THE ANSWER!!!
twice a certain number x is less than 8. Find the range of values of the number
Answer:
F=2x +2
Step-by-step explanation:
The range of values for the certain number "x" is all real numbers less than 4.
Let's represent the certain number as "x."
The problem states that twice the certain number (2x) is less than 8. Mathematically, we can write this as:
2x < 8
Now, to find the range of values for "x," we need to solve for "x."
Divide both sides by 2:
x < 8/2
x < 4
So, the range of values for the certain number "x" is all real numbers less than 4. In interval notation, the range is (-∞, 4). This means "x" can take any value less than 4, including negative values and fractions that are less than 4.
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There are 4 red cars and 8 black cards in a bag. How is it likely that you will randomly draw a blue card
Answer:
C) Impossible
Step-by-step explanation:
Since there are no blue cards, the probability that you'd draw one is 0/12, which means that there is no chance you'll draw one.
G(b) = 5b- 9 h(b) = (b - 1)^2 Evaluate. (hog)(-6) =
Given:
The two functions are:
[tex]g(b)=5b-9[/tex]
[tex]h(b)=(b-1)^2[/tex]
To find:
The value of [tex](h\circ g)(-6)[/tex].
Solution:
We have,
[tex]g(b)=5b-9[/tex]
[tex]h(b)=(b-1)^2[/tex]
We know that,
[tex](h\circ g)(b)=h(g(b))[/tex]
[tex](h\circ g)(b)=h(5b-9)[/tex]
[tex](h\circ g)(b)=[(5b-9)-1]^2[/tex]
[tex](h\circ g)(b)=[5b-10]^2[/tex]
Putting [tex]b=-6[/tex], we get
[tex](h\circ g)(-6)=[5(-6)-10]^2[/tex]
[tex](h\circ g)(-6)=[-39-10]^2[/tex]
[tex](h\circ g)(-6)=[-49]^2[/tex]
[tex](h\circ g)(-6)=2401[/tex]
Therefore, the value of [tex](h\circ g)(-6)[/tex] is 2401.
help mee please i need this one right now
Answer:
where is the question
Step-by-step explanation:
chai
HELPP MEE PLSSSS RNNNN NO LINKS OR I WILL REPORT YOU!!
In the slope-intercept equation for a line, the coefficient of the
-term gives the slope
Answer:
x
Step-by-step explanation:
The formula of a line in its slope-intercept form is
y= mx + b
the slope is indicated by “m” that multiply the x
if bc is the diameter of the circle below, what is the area of the circle
Answer:
option a.
radius of the circle=3 units.
area of the circle= pi×r²
area of circle=pi×3²
area of circle=pi×9units²
Answer:
It's A. 9π square units.
Step-by-step explanation:
You know that bc is equaled to 6 since when you count it inside the circle, you get 6. Then you find the radius by dividing 6 by 2. So the radius is 3. You find the area by using this formula. A = π*[tex]r^{2}[/tex]. r = 3, so 3 square is 9. You don't know what is pi so you just write 9π. Therefore, the answer is A. 9π square units.
f(x) = cos(x - 90°)
Which is the value of f(0°)?
A 1
B 0
C-1
1
2
find the value of x in the triangle shown below
Answer:
√27
Step-by-step explanation:
use the pythagorean theorem
3²+x²=6²
9+x²=36
x²=27
√x²=√27
x=√27
what is the square root of 30
Answer:
hi
Step-by-step explanation:
i think so...
[tex] \sqrt{30} = 5.47[/tex]
have a nice day
Write an equivalent ratio for 1:2
Answer:
2:4
Step-by-step explanation:
Answer:
3:6
4:8
5:10
6:12
7:14
8:16
etc...
Which of these expressions or phrases can be used to represent the model choose all the correct answers
Pls no BOT part ;(
Step-by-step explanation:
anyway.. for your answer i only know that number of fifths in 1 is correct I dont know about the rest.