Answer:
[tex]28.07^{\circ}[/tex]
Step-by-step explanation:
We can use basic trig. for a right triangle to solve this problem. In any right triangle, the tangent of an angle is equal to its opposite side divided by the hypotenuse (longest side) of the triangle.
The right triangle we're looking at involves the two dotted lines and an edge of the prism.
The bottom dotted line is a diagonal of the rectangular base of the prism. We can use the Pythagorean Theorem to find its length.
The Pythagorean Theorem states that for any right triangle, [tex]a^2+b^2=c^2[/tex], where [tex]a[/tex] and [tex]b[/tex] are the two legs of the triangle and [tex]c[/tex] is the hypotenuse.
In this case, the two legs are 9 and 12 and we are solving for [tex]c[/tex]:
[tex]9^2+12^2=c^2,\\81+144=c^2,\\225=c^2,\\c=15[/tex]
This is theta's adjacent side. Its opposite side is an edge of the prism labelled as 8 inches. Therefore, we have the following equation:
[tex]\tan \theta = \frac{8}{15}[/tex]
Take the inverse tangent of both sides:
[tex]\arctan(\tan \theta)=\arctan(\frac{8}{15})[/tex]
Simplify using [tex]\arctan(\tan\theta)=\theta, \theta \in (-90^{\circ}, 90^{\circ})[/tex]:
[tex]\theta=\arctan(\frac{8}{15}),\\\theta=28.07248694\approx \boxed{28.07^{\circ}}[/tex]
A macaroni and cheese recipe calls for 's of a 2 % pound block of cheese. How many pounds
are needed?
Mr. Williams ask to buy 1/2 of a pan of brownies that is 2/3 full. What fraction of the original pan does he buy?
4/6
Mr. williams wants to buy 4/6
Answer:
there is some missing information here
if the pas is a dozen brownies
1/2 of a pan is 6 2/3 of 6 would be "4"
how much mac-n-cheese are being made?
that information would be needed to solve this
Step-by-step explanation:
Rational between √16 and √17
Answer:
41/10
Explanation:
sqrt16 = 4
sqrt17 = 4.12
4.1 = 41/10 and 4<4.1<4.12
please help me with this
Answer:
4y2 - 12y
Step-by-step explanation:
2+4y-16y+32(Combine like-terms)
2−12y+32(Combine like-terms)
Answer:
The answer is [tex]4y^{2} -12y[/tex]
Step-by-step explanation:
To simplify the polynomial, start by combining like terms. Add [tex]y^{2}[/tex] and [tex]3y^{2}[/tex] to get [tex]4y^{2}[/tex]. Then, subtract [tex]16y[/tex] from [tex]4y[/tex] to get [tex]-12y[/tex]. Finally, the simplified answer is [tex]4y^{2} -12y[/tex].
Which of the following contains a variable?
A. He scored a 95 on the test.
B. The bug crawled 15 inches per second.
C. The area is 56 square centimeters.
D. Ana is 3 years older than Mark.
Answer:
D. Ana is 3 years older than Mark.
Step-by-step explanation:
We do not know how old Mark is. That is the variable
Which angles are adjacent to each other?
• Angle KGD and Angle AEB
• Angle BEC and Angle AEB
• Angle AEB and Angle ECU
• Angle JCI and Angle KGD
Answer:
Step-by-step explanation:
adjacent angles have a common vertex and a common ray
∠BEC and ∠AEB (common vertex E common ray EB)
Jalil and Victoria are each asked to solve the equation ax – c = bx + d for x. Jalil says it is not possible to isolate x because each x has a different unknown coefficient. Victoria believes there is a solution, and shows Jalil her work:
ax – c = bx + d
ax – bx = d + c
x (a – b) = d + c
x = x equals StartFraction d plus c Over a minus b EndFraction.
How can Victoria justify Step 3 of her work?
Answer:
A: Rewrite the expression on the left using the distributive property.
According to the synthetic division below, which of the following statements are true? Check all that apply
The true statements are A , B , E
What is division?It is the inverse of the multiplication operation. It is defined as the act of forming equal groups. While dividing numbers, we break down a larger number into smaller numbers such that the multiplication of those smaller numbers will be equal to the larger number taken.
Here, In the synthetic calculation we use the coefficient of the dividend
with the factors of the function
∴ 2 , -2 , -12 are the coefficient of the dividend 2x² - 2x - 12
∵ The divisor is 3
∴ x = 3 is a root of F(x) = 2x² - 2x - 12
∵ x = 3 is the root of F(x) = 2x² - 2x - 12
- Subtract the two sides by 3
∴ x - 3 = 0
∴ (x - 3) is a factor of the dividend F(x) = 2x² - 2x - 12
- The quotient is the last line of the synthetic division
∴ The coefficients of quotient are 2 , 4
- The quotient is 1 degree less than the dividend
∵ The degree of the dividend is 2
∴ The degree of the quotient is 1
∴ The quotient is 2x + 4
* Lets check the answers to chose the write statements
A. The number 3 is a root of F(x) = 2x² - 2x - 12 ⇒ true
B. (x - 3) is a factor of 2x² - 2x - 12 ⇒ true
E. (2x² - 2x - 12) ÷ (x - 3) = 2x + 4 ⇒ true
Thus, the true statements are A , B , E.
Learn more about Division from:
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Holly invited her friends to her pool party. She decided to add trail mix to the snack menu. In the trail mix, the ratio of cups of peanuts to cups of raisins is 6:4. How many cups of raisins would be needed for a mix that included 9 cups of peanuts
Answer:my dog is cute
Step-by-step explanation:because
please help,
all i have is 16 x 33 = 528cm2 ?!!!
Answer:
732 m^2
Step-by-step explanation:
Find the area of the full rectangle
33*24 =792
Find the area of the triangle
24-16 = 8
33 -18 =15
The area of the triangle is
A = 1/2 bh = 1/2 ( 15)(8) = 60
Subtract the triangle from the rectangle
792 - 70=732 m^2
Answer:
732 [tex]m^2[/tex]
Step-by-step explanation:
First we can find the area of the shape if the triangle wasn't there. That would be:
24×33=792.
Then, we can find the area of the triangle to subtract that from the total.
The formula for the area of a triangle is [tex]A=\frac{1}{2} bh[/tex].
So [tex]A=\frac{1}{2} (8)(15)[/tex]
I found the base of the triangle by subtracting 16 from 24.
I found the height of the triangle by subtracting 18 from 33.
Now, solve the equation.
[tex]A=\frac{1}{2}( 120)[/tex]
A=60
Then finally, Subtract 60 from 792.
You get 732.
I hope this helps!
i don't know just curious do you guys still got school?
yes i do got school
and what about you
the distance between the points (tan a, 1) , (0,2)
Answer:
Answer
Step-by-step explanation:
please like and mark me brainlist
A man sold a ratet for Rs 252 at 5% pofi't percent is the profit?
Answer:
Step-by-step explanation:
Selling price (SP) = Rs. 252
Profit% = 5%
[tex]CP=\frac{100}{100+profit}*SP\\\\\ = \frac{100}{105}*252\\\\[/tex]
CP = Rs. 240
Profit = 252 - 240 = Rs. 12
Which situation would be represented by zero?
A) a $3 loss and à $4 profit
B) a $3 loss
C) a $4 loss and a $4 profit
D) a $4 profit
Pls help me I’m timed, I’ll give brainliest
Answer:
C) a $4 profit and $4 loss is the correct answer.
!!ASAP!!
1.
25
40
75
2.
40
75
140
Answer:
C= 40
D= 75
Alternate interior angle
○●○●○●○●○
Hope it helps...
Have a great day!!!
The expression y2 – 10y + 24 has a factor of y – 4. What is another factor of y2 – 10y + 24?
y – 20
y – 14
y – 8
y – 6
Answer:
Step-by-step explanation:
If we divide 24 by 6, we get 4, which is the other factor of 24 when given the one factor of 6. Same goes here. In order to find out what the other factor of [tex]y^2-10y+24=0[/tex] is when given one factor of y - 4, we simply divide the second degree polynomial by y - 4 to get the quotient. The quotient, then, is the other factor. Synthetic division is the easiest way to do this.
If y - 4 is the factor, then by the Zero Product Property, y - 4 = 0 and y = 4. Setting up synthetic division:
4| 1 -10 24
____________
The rule is to start by bringing down the first term, multiplying it by the number outside, then putting that product up under the next term in line:
4| 1 -10 24
4
1
Then add the column, multiply the sum by the number outside, and put that product up under the next term in line:
4| 1 -10 24
4 -24
1 -6
And add the last column and that is the remainder. We get a 0 remainder. That means that y - 4 goes evenly into the polynomial and the other factor we are looking for is found in the numbers under the addition line. These numbers are the leading coefficients of the depressed polynomial, the polynomial that serves as the other factor: 1y - 6.
Therefore, the 2 factors that multiply together to give us [tex]y^2-10y+24=0[/tex] are (y - 4)(y - 6) and we can check ourselves by multiplying this out by FOILing to see if the result is the polynomial we started with. It is, so we're all done!
Answer:
its ( y-6 )
Step-by-step explanation:
well if you use the FOIL method you will get that answer. also i took the test and got a 100 so there u go.
Solve the equation for x: (4x+38) + (2x-18)=180
Answer:
80/3
Step-by-step explanation:
try mathw4y it helps alot.
Answer:
x = 80/3
Step-by-step explanation:
(4x+38) + (2x-18)=180
Combine like terms
6x +20 = 180
Subtract 20 from each side
6x+20 -20 = 180-20
6x = 160
Divide by 6
6x/6 = 160/6
x = 80/3
help please i’ve been in here for hours looking for answers
Answer:the 2nd row, x=0, f(x)=2
Step-by-step explanation:
When x=0, the line touches the y-axis because the f(x) has a value. therefore when x=0, y=2
you'll understand better if you sketch it out
Can someone help me by please
=============================================================
Explanation:
10% in decimal form is 0.10
25% in decimal form is 0.25
The jump from 0.10 to 0.25 is "times 2.5" since (0.25)/(0.10) = 2.5
This means that we have 2.5 times as many apples compared to oranges.
If we have 2 oranges, as mentioned in every answer choice, then we must have 2*2.5 = 5 apples.
Based on this, the answer is either A or B.
----------------
65% turns into 0.65
The jump from 0.10 to 0.65 is 6.5 since (0.65)/(0.10) = 6.5
So we have 6.5 times as many pears as oranges.
If we had 2 oranges, then we have 2*6.5 = 13 pears
----------------
To summarize, we have:
2 oranges, 5 apples, 13 pears.
The answer is therefore choice A
1. Which of the following expressions are equivalent to? Select all that apply. A. 31 . 36 B. 31 . 35 C. 3-2 . 3-4 D. 32 . 3-8 E. 3 • 3-6 F.3-1 . 3-5
Answer: A and C
Step-by-step explanation:
UR SO COOL IF UOU ANSWERRR PLEASE ANSWERRRR
Answer:
1/6 is less than 1/2
Step-by-step explanation:
1/6 is close to 0
8/9 is close to 1
1/6 is less than 1/2
A shopkeeper buys TVs for Nu 15000 and marks them up 15% to sell them. What is the mark up amount? *
[tex] \\ \sf \longmapsto \: 15000 \times 15\% \\ \\ \sf \longmapsto \: 15000 \times \frac{15}{100} \\ \\ \sf \longmapsto \: 150 \times 15 \\ \\ \sf \longmapsto \: 2250[/tex]
Markup amount is 2250Nu
What is this equation rewritten in logarithmic form?
9X = 3
A. log 3 = x
B. log, 3 = 9
C. log3 9 = x
D. log3 x = 9
Answer:
A. log9 3=x
Step-by-step explanation:
The logarithmic form with base 9 is log₉ 3 = x.
The correct option is A.
The equation 9ˣ = 3 can be rewritten in logarithmic form by identifying the base and the result of the exponential operation. In this case, the base is 9, the result is 3, and the exponent is x.
The logarithmic form with base 9 is log₉ 3 = x.
Option A, log₉ 3 = x, is the correct representation of the equation in logarithmic form.
The logarithmic form states that the logarithm of a number (3 in this case) to a specific base (9 in this case) is equal to the exponent (x in this case).
In the equation, 9ˣ = 3, the logarithmic form log₉ 3 = x indicates that the logarithm of 3 with base 9 is equal to x. This means that 3 is the result of raising 9 to the power of x.
Therefore, option A, log₉ 3 = x, is the correct answer representing the equation 9ˣ = 3 in logarithmic form.
To learn more about the logarithms;
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I needddd help it’s urgenttttt!!!!
PLEASE HELP!! would this be symmetric or reflexive property?
Answer: It's "reflexive" because the equation is equal on both sides
Step-by-step explanation: The reason it isn't symmetric property, is because the variables are mismatched (it's not the same on both sides.)
Hope this helped!!
99, 159, 219, ___. To find the next number after 219, we should a. Add 69 to 219 b. Subtract 60 from 219 c. Add 60 to 219 d. Add 40 to 219
Answer:
C
Step-by-step explanation:
99+60=159.
159+60=219
219+60=279
square of (1\4A+1\4B)^2
Answer:4a = 2⋅(2a)⋅1 4 a = 2 ⋅ ( 2 a) ⋅ 1
Step-by-step explanation:
Factor 4a^2-4a+1. 4a2 − 4a + 1 4 a 2 - 4 a + 1. Rewrite 4a2 4 a 2 as (2a)2 ( 2 a) 2. (2a)2 − 4a+1 ( 2 a) 2 - 4 a + 1. Rewrite 1 1 as 12 1 2. (2a)2 − 4a+12 ( 2 a) 2 - 4 a + 1 2. Check that the middle term is two times the product of the numbers being squared in the first term and third term. 4a = 2⋅(2a)⋅1 4 a = 2 ⋅ ( 2 a) ⋅ 1.
Abram completes one lap of a go-cart track every 40 seconds. Joshua completes one lap of the same track every 30 seconds. Suppose Abram and Joshua cross the starting line at the same time.
a. How many seconds will pass before they cross the starting line at the same time again?
b. How many laps will Abram have completed in that time?
c. How many laps will Joshua have completed in that time?
Answer:
Below in bold.
Step-by-step explanation:
a. This is the Lowest common multiple of 30 and 40 which is
120 seconds.
b. In 120 seconds Abram had completed 120/40
= 3 laps.
c. Joshua completed 120/30 = 4 laps.
Answer:
Step-by-step explanation:
A, Lowest common mutiple of 30 and un is 120 seconds
(40x3 = 120, 30x4 = 120)
6.120/40 = 3 laPs Abram did 3 laps.
L. 120/30 = u laPs Jeshya did u laps
Choose the graph that correctly corresponds to the equation y = −4
Answer:
e
Step-by-step explanation:
the graph should look something like this
6) Given that the point (3, −10) lies on the graph of a function , what point must be on the graph of ℎ
where ℎ() = ( − 4) + 2?
Answer:
(7,-8)
Step-by-step explanation:
Given
(x,y) = (3,-10)
Required
The equivalent point on h(x) = k(x - 4) + 2
(x,y) = (3,-10) means
k(3) = -10
Substitute 7 for x in h(x)
h(7) = k(7-4) + 2
h(7) = k(3) + 2
Substitute -10 for k(3)
h(7) = -10 + 2
h(7) = -8
So, the equivalent point on h(x) is
(7,-8)
Sam buys a carpet for his apartment. The diagonal length of the carpet is 12 feet and the width is 10 feet. Find the length of the carpet.
Answer: 6.633 Feet
Step-by-step explanation:
