Answers
Answer:
Equation: [tex]\sf 3x + x + 14 = 90[/tex]
m∠1 = 57°
m∠2 = 33°
Explanation:
A right angle triangle has 90° angle measure.
Here:
m∠1 + m∠2 = 90°
(a)
Substitute given values:
(3x) + (x + 14) = 90
simplify
4x = 90 - 14
evaluate
4x = 76
divide both sides by 4
x = 19
(b)
m∠1 = 3x = 3(19) = 57°
m∠2 = x + 14 = 19 + 14 = 33°
Answer:
[tex]\textsf{(a)} \quad (3x)^{\circ}+(x+14)^{\circ}=90^{\circ}[/tex]
[tex]\textsf{(b)} \quad m \angle 1=\boxed{57}\:^{\circ}[/tex]
[tex]m \angle 2=\boxed{33}\:^{\circ}[/tex]
Step-by-step explanation:
From inspection of the given diagram:
[tex]m \angle 1=(3x)^{\circ}[/tex][tex]m \angle 2=(x+14)^{\circ}[/tex]Part (a)A right angle is 90° and is represented by the ∟ symbol.
To find x, equal the sum of the angles to 90° and solve for x:
[tex]\implies m \angle 1+m\angle2=90^{\circ}[/tex]
[tex]\implies (3x)^{\circ}+(x+14)^{\circ}=90^{\circ}[/tex]
[tex]\implies 3x+x+14=90[/tex]
[tex]\implies 4x+14=90[/tex]
[tex]\implies 4x+14-14=90-14[/tex]
[tex]\implies 4x=76[/tex]
[tex]\implies 4x \div 4=76 \div 4[/tex]
[tex]\implies x=19[/tex]
Part (b)To find the degree measure of each angle, substitute the found value of x into the expression for each angle.
[tex]\implies m \angle 1=(3 \cdot 19)^{\circ}=57^{\circ}[/tex]
[tex]\implies m \angle 2=(19+14)^{\circ}=33^{\circ}[/tex]
Related Questions
What is 20 as a mixed number?
Answers
Answer:
c: 3 ⅓
Step-by-step explanation:
C has been simplified. If we converted the fraction ⅓ to 2/6 the answer would equal 20.
This is because we can do (whole number × denominator) 3 × 6 = 18 and then 18 + 2 (numerator) = 20
Answer:
Step-by-step explanation:
Sarah took the advertising department from her company on a round trip to meet with a potential client. Including Sarah a total of 6 people took the trip. She was able to purchase
coach tickets for $270 and first class tickets for $1250. She used her total budget for airfare for the trip, which was $3580. How many first class tickets did she buy? How many coach
tickets did she buy?
number of first class tickets bought =
number of coach tickets bought =
x= number of coach tickets bought
Y= number of first class tickets bought
Answers
The total number of tickets bought is 6 and the number of coach tickets bought is 4 while the number of first class tickets bought is 2
How to solve algebra word problems?We are told that a total of 6 people took the trip. If x is the coach tickets and y is the first class tickets and she bought tickets for 6 of them, then we can say that;
x + y = 6 ------(1)
Now, coach tickets cost $270 and first class tickets costs $1250. She used her total budget for airfare for the trip, which was $3580. Thus;
270x + 1250y = 3580 ----(2)
Solving both equations simultaneously gives;
x = 4 and y = 2
Thus, we conclude that the number of coach tickets bought is 4 while the number of first class tickets bought is 2.
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3.5+2=2x-10help me HELP ME JIGGABOOS
Answers
5.5 = 2x -10
+10 +10
—————————
15.5 = 2x
—— ——
2 2
7.75 = x
7.75 is the answer
HELP 20 pointssss mathhhhh
Answers
A town has accumulated 4 inches of snow and the snow depth is increasing by 3 inches every hour . a nearby town has accumulated 1 inch and the depth is increasing by 5 inches every hour. how many hours will the snowfall of the towns be equal if the snow continues at the given rates?
answer as an equation and solve, please help!!
Answers
The equation which represents the given situation as described about snow depths in the task content is; 4 + 3x = 1 + 5x and the solution is; x = 1 and a half hours.
At what time will the snow fall of the towns in discuss have the same snow depth according to the given rates?It follows from the task content that the time at which the snowfall in the towns in discuss will be equal be determined.
According to.the word phrases given;
A town has accumulated 4 inches of snow and the snow depth is increasing by 3 inches every hour. Hence, we have;
4 + 3x.
Also, a nearby town has accumulated 1 inch and the depth is increasing by 5 inches every hour. Hence ,we have;
1 + 5x
Consequently, when the snowfalls are equal, we have;
4 + 3x = 1 + 5x
3 = 2x
x = 3/2.
x = 1 and a half hours.
Ultimately, the equation which represents the given situation as described about snow depths in the task content is; 4 + 3x = 1 + 5x and the solution is; x = 1 and a half hours.
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joe bought a condo for $200,000. he put down 20%, which was $40,000. how much does he owe on the condo?
Answers
By taking the difference between the total cost of the condo and the amount that he already paid, we conclude that Joe owes a total of $160,000 for the condo.
How much does he owe on the condo?To find how much he owes on the condo, we need to find the difference between the total cost of the condo, which is $200,000, and the amount that he already paid, which is $40,000.
(Remember that difference means a subtraction)
It gives.
$200,000 - $40,000 = $160,000
In this way, we conclude that Joe owes a total of $160,000 for the condo.
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which expression is equivalent to startfraction startroot 2 endroot over rootindex 3 startroot 2 endroot endfraction?one-fourthrootindex 6 startroot 2 endrootstartroot 2 endrootstartfraction startroot 2 endroot over 2 endfraction
Answers
One-fourth root index 6 start root 2 - this expression is equivalent to start fraction start root 2 end root over root index 3 start root 2 end root end fraction.
What is equivalent?A comparable is how much a substance that responds with an erratic measure of one more substance in a given synthetic response. Comparable weight can be characterized as the mass of one likeness a given substance that will consolidate with or uproot a decent amount of the other substance. Identical loads not entirely set in stone by try, however (to the extent that they are as yet utilized) are currently gotten from molar masses. Identical load in science is the most widely recognized term utilized and one of the fundamental ideas of science in the actual science part. The significance of 'identical' by and large alludes to two numbers, articulations, or amounts with a similar worth. There are numerous ways of communicating a comparable amount - it tends to be indicated either by a bar or an identical image.
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the rainfall this year was 18.6 cm this is 3.2 cm less than half of the rainfall last year what was the rainfall
Answers
Answer: 43.6 cm
Step-by-step explanation:
18.6+3.2= 21.8
21.8*2= 43.6
Обчислив площу поверхні Куба ребро якого дорівнює 4,2 м
Answers
Answer: I calculated the surface area of a cube whose edge is 4.2 m
Step-by-step explanation: hope this helps
What is the volume of a rectangular prism with a base area of 32 cm and a height 7cm
Answers
Answer:
224 cm³
Step-by-step explanation:
Volume = Area of base x height
V = 32 x 7
V = 224 cm³
In this question, all the required information is given so we'll simply have to solve.
[tex]\large\boxed{\bold{V= \ base \ area× \ height}}[/tex]
Now, substitute the values according to the formula.
[tex]V= \ 32 × 7[/tex]
[tex]\large\boxed{\bold{ V= \ 224 \ {cm}^{3}}}[/tex]
The answer is a whole number so we won't have to round off.
Hence, the volume of the given rectangular prism is 224 cubic centimeters.
an equation in slope-intercept form for the line described. slope -13/5, passes through(5,-7)
Answers
Answer:
shebolixashebshe is she she is she she he she and he are in love go to xvideos.com to see them rápīng each other
Step-by-step explanation:
426;/7/(/&/)m
I don’t really understand I think it’s distance formula but I got it wrong pls help
Answers
Perimeter of rectangular garden = 34 ft
Area of rectangular garden = 60 ft²
What is the Perimeter and Area of a Rectangle?Perimeter = 2(length + width)
Area = (length)(width)
The rectangular garden has the following vertices:
Q(-5, 3)R(7, 3)S(7, -2)T(-5, -2)Length of the rectangular garden = QR = |-5 - 7| = |-12| = 12 units
Width of the rectangular garden = RS = |3 -(-2)| = |3 + 2| = 5 units
Perimeter = 2(length + width) = 2(12 + 5) = 34 units = 34 ft
Area = (length)(width) = (12)(5) = 60 units = 60 ft²
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show work needed please.
Answers
First do 7/100 to convert the percent to a decimal, you will get 0.07, now to get 7% of $5136 multiply .07 and 5136 to get 359.52. So she had to pay $359.52 in GST
Helpppppp 20 pointssss mathhh
Answers
Root 40 to the nearest 10
Answers
Root 40 to the nearest 10 is 6.3
The root of a number in math is a number that when multiplied by itself produces the original number. For example, the square root of 49 is 7 because 7×7=49.
Rounding off to the nearest 10 means that we wish to round off the last two digits of a number, that is up to the tens place of a number.
We have been given that 40 is the number whose root we have to round off so here are step-by-step instructions for how to get the square root of 40 to the nearest tenth:
Step 1: Calculate. We calculate the square root of 40 to be: √40 = 6.32455532033676.
Step 2: Reduce. 6.32.
Step 3: Round. Round 6.32 so you only have one digit after the decimal point to get the answer: 6.3.
So therefore the nearest 10 of root 40 is 6.3
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Kiara has​ $520 in her bank account. each week she deposits​ $80 and withdraws​ $35. gael has​ $310 in his account. each week he deposits​ $95 and withdraws​ $20. write and solve an equation to determine the week w when gael and kiara have the same amount of money in their accounts.
Answers
Answer:
fuimaa
Step-by-step explanation:
Samir can rent a moving truck from Company A for $135 plus $0.50 per mile or from Company B for $125 plus $0.70 per mile. Which statement is true?
Answers
Renting from Company B will be cheaper if Samir drives the truck 100 miles. Then the correct option is D.
What is a linear equation?
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
Let y be the total amount and x be the number of miles.
Samir can rent a moving truck from Company A for $35 plus $0.50 per mile. Then the equation will be
y = 0.5x + 35 ....1
Company B for $25 plus $0.70 per mile. then the equation will be
y = 0.7x + 25 ....2
For the same rent, the number of miles will be
0.7x + 25 = 0.5x + 35
0.2x = 10
x = 50 miles
Renting from Company B will be cheaper if Samir drives the truck 100 miles. Then the correct option is D.
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Samir can rent a moving truck from Company A for $35 plus $0.50 per mile or from
Which statement is true?
Company B for $25 plus $0.70 per mile .
A. Renting from Company A will always be cheaper.
B. Renting from Company B will always be cheaper.
C. Renting from both companies will cost the same if Samir drives the truck 50 miles.
D. Renting from Company B will be cheaper if Samir drives the truck 100 miles.
1/2 log25/4base10-2log4/5base10+log320/125base10
Answers
Answer: 1
Step-by-step explanation:
[tex]\displaystyle\\\frac{1}{2}lg\frac{25}{4} -2lg\frac{4}{5} +lg\frac{320}{125}=\\\\lg\sqrt{\frac{5^2}{2^2} } -lg(\frac{4}{5})^2+lg\frac{5*64}{5*25}=\\\\lg\sqrt{(\frac{5}{2})^2 } -lg\frac{4^2}{5^2} +lg\frac{64}{25}=\\\\[/tex]
[tex]lg\frac{5}{2} -lg\frac{16}{25}+lg\frac{64}{25} =\\\\ lg\frac{5}{2}+lg\frac{64}{25} -lg\frac{16}{25} =\\\\lg\frac{5*64}{2*25} -lg\frac{16}{25}=\\\\ lg\frac{5*2*32}{2*5*5}-lg\frac{16}{25}= \\\\lg\frac{32}{5}-lg\frac{16}{25}=\\\\lg\frac{32*25}{5*16}=\\\\lg\frac{16*2*5*5}{5*16} =\\\\lg(2*5)=\\\\lg10 =\\\\1[/tex]
Find the point of intersection between the plane that contains the axis intercepts p(4, 0, 0)
Answers
The equation is 7x+11y+14z=33.
What is an equation?A mathematical statement made up of two gestures joined by an equal sign is known as an equation. 3x - 5 = 16 is an example of an equation. We get the value for the variable x as x = 7 after solving this equation.So,
The family of planes equation passing through the intersection of the planes x+2y+3z4=0 and 2x+yz+5=0 is:
(x + 2y + 3z − 4) + k(2x + y − z + 5)=0(2k+1)x+(k+2)y+(3−k)z=4−5k ......(1)[tex]\frac{\mathrm{x}}{\left(\frac{4-5 \mathrm{k}}{2 \mathrm{k}+1}\right)}+\frac{\mathrm{y}}{\left(\frac{4-5 \mathrm{k}}{\mathrm{k}+2}\right)}+\frac{\mathrm{z}}{\left(\frac{4-5 \mathrm{k}}{3-\mathrm{k}}\right)}=1[/tex]It is assumed that the required plane's x-intercept is twice its z-intercept.
[tex]\left(\frac{4-5 \mathrm{k}}{2 \mathrm{k}+1}\right)=2\left(\frac{4-5 \mathrm{k}}{3-\mathrm{k}}\right)[/tex](4−5k) (3−k) = (4k+2) (4−5k)(4 − 5k) (3 − k − 4k −2) = 0(4 − 5k) (1 − 5k) = 04 − 5k = 0 or 1−5k = 0k = 4/5 or k = 1/5Substitute k = 4/5 in equation (1) as follows:
[tex]\left(2 \times \frac{4}{5}+1\right) x+\left(\frac{4}{5}+2\right) y+\left(3-\frac{4}{5}\right) z=4-5 \times \frac{4}{5}[/tex]7x + 11y + 14z = 15As a result, the required plane's equation is 7x+11y+14z=15.
Also,
7x+11y+14z=15 is the equation of the plane passing through the point (2,3,1) and parallel to the plane.
7(x−2) + 11(y−3) + 14(z+1) = 07x + 11y + 14z = 33Therefore, the equation is 7x+11y+14z=33.
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the complete question is given below;
Find the equation of the plane which contains the line of intersection of the planes x+2y+3z−4=0 and 2x+y−z+5=0 and whose x−intercept is twice its z−intercept. Hence, write the equation of the plane passing through the point (2,3,−1) and parallel to the plane obtained above.
what 3+3 divided by 3 *6
Answers
Answer:
9
Step-by-step explanation:
8.2 - 4.3 i really need help-
Answers
Answer:
3.9
Step-by-step explanation:
8.2-4.3=3.9
3.9+4.3=8.2
a company's charge for electricity is ¢6.434 per kilowatt-hour. in addition, each monthly bill contains a customer charge of $7.81. if last year's bills ranged from a low of $51.74 to a high of $192.28, over what range did usage vary (in kilowatt-hours)? course hero
Answers
The range in which the usage vary is from 682.77 kilowatt-hours to 2867.11 kilowatt-hours.
Given the charge of electricity charge is 6.434 cents per kilowatt-hour.
Fixed customer charge = $7.81
Bill range = $51.74 to $192.28
Since every value is in $ , we will first convert cents to dollar
per kilowatt-hour charge will be $6.434/100 ( as $1 = 100 cents )
per kilowatt-hour charge = $ 0.06434 …(1)
Lets us first find the lower range of usage
Last year's lowest bill was $51.74 (including the customer charge)
So last year lowest bill = $51.74-$7.81 = $43.93 …(2)
We know that (per KWh charge)x(no. of KWh used)=Total bill. …(3)
Substituting the values from (1) & (2) we get
(0.06434)x(no. of KWh used)=$43.93
no. of KWh used=[tex]\frac{43.93}{0.06434} = 682.77 KWh[/tex]
Similarly we will solve for maximum KWh used
Lets us find the maximum range of usage
Last year's highest bill was $192.28 (including the customer charge)
So last year highest bill = $192.28-$7.81 = $184.47 …(4)
Substituting the value of (1) & (4) in (3) we get
(0.06434)x(no. of KWh used)=$184.47
no. of KWh used=[tex]\frac{184.47}{0.06434} =2867.11 KWh[/tex]
Therefore , the The range in which the usage vary is from 682.77 kilowatt-hours to 2867.11 kilowatt-hours.
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neve has 12 full box of jars of slime and 7 lose jars of slime if neve has a total of 187 jars of slime which equation can be used to find the number of jars in each box
Answers
Solving a linear equation, we can see that each box has 15 jars.
Which equation can be used to find the number of jars in each box?
We know that Neve has 12 full boxes of jars of slime, and 7 jars of slime, then if each box has N jars, the total number of jars that Neve has is given by the linear equation:
12*N + 7
Now we know that Neve has 187 jars in total, then we can write:
12*N + 7 = 187
We want to find the value of N, which is the number of jars in each box, so we need to solve the linear equation:
12*N + 7 = 187
12*N = 187 - 7
12*N = 180
N = 180/12 = 15
We conclude that there are 15 jars in each full box.
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B The table represents the location of QRST before and after a reflection. Use the table to
answer 3-5.
3. Give a verbal description of the transformation.
PRE-IMAGE
Q(-9,-8)
R(-9, -2)
S(-4,-2)
T(-4,-8)
IMAGE
Q'(9,-8)
R(9,-2)
S(4, -2)
?
4. Which best represents the transformation algebraically?
a. (x, y) b. (-x, y) c. (-x, -y)
d. (x + 18, y)
5. Find the location of T
Answers
3. The x-coordinate of the image is equal to the negative of that of the pre-image. The y-coordinate remains the same.
4. The transformation is best represented algebraically by (-x, y).
5. The location of the image of T is (4, -8).
3. The transformation makes the x-coordinate of the image equal to the negative of that of the pre-image. The y-coordinate remains the same.4. The transformation is best represented algebraically by (-x, y).5. The coordinates of the preimage of T are (-4, -8). On applying the transformation, the image of T becomes (-(-4), 8), i.e., (4, -8).To learn more about pre-image, visit :
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Is -2.5 greater than or less than 2.1?
Answers
Answer: less
Step-by-step explanation:
Answer: The answer is less than
because negative are always less than positives
Step-by-step explanation:
I hope this helps
PLS HELP
NOW IF POSSIBLE
Answers
Answer:
i think it is 4
Step-by-step explanation:
(Please Help) The vertex of a parabola is (−2,8) and its y-intercept is (0,4). The parabola is the boundary of a quadratic inequality. The boundary is drawn with a solid line, and the exterior of the parabola is shaded.
What is the inequality represented?
(i got it graphed like what i have already but I don't know if its right even thought i gotten it)
Answers
Using the equation of the parabola, the inequality represented is:
y ≥ -(x + 2)² + 8.
What is the equation of a parabola given it’s vertex?The equation of a quadratic function, of vertex (h,k), is given by:
y = a(x - h)² + k
In which a is the leading coefficient.
For this problem, the vertex is at (-2,8), hence:
h = -2, k = 8.
y = a(x + 2)² + 8.
The y-intercept is of (0,4), when when x = 0, y = 4, which we use to find a as follows:
4 = 4a + 8
4a = -4
a = -1.
Hence the parabola is:
y = -(x + 2)² + 8.
The exterior of the parabola is shaded, that is, the part that is above the concave down parabola, hence the inequality is:
y ≥ -(x + 2)² + 8.
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researchers are concerned that the weight of the average american school child is increasing implying, among other things, that children's clothing should be manufactured and marketed in larger sizes. if x is the weight of school children sampled in a nationwide study without rounding, what is x an example of?
Answers
X in an example of stochastic variable.
What is meant by stochastic variables?
Typically, a random (or stochastic) variable is defined as a variable that can assume more than one value due to chance.
The correct answers are: (a) stochastic variable: By stochastic variable we mean a variable (here X: the weight of students) whose values are subject to variation due to chance.
Here since X is the weight of the children sampled, hence X will vary along with change in the sampling units which gets selected by chance.
Hence X for a sample A and X value for a different sample B will be different. So the values of X vary due to chance ( chance takes part in the selecton of the sample). So X is a stochastic variable.
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The complete question is -
Researchers are concerned that the weight of the average American school child is increasing implying, among other things, that children's clothing should be manufactured and marketed in larger sizes. If X is the weight of school children sampled in a nationwide study, then X is an example of a stochastic variable. a parameter. a categorical variable. a continuous variable.
Please just give the answer no calculations .
Answers
according to the rational root theorem, which function has the same set of potential rational roots as the function g(x)
Answers
Option (A)'s f(x) = 3x⁵ -2x⁴ - 9x³ + x² -12 has the same set of potential rational roots as the given function g(x).
What are roots of an equation?Roots of an equation refer to the values that when put into the variable of the equation, satisfy the equation and give the required value as 0.
Given:
g(x) = 3x⁵ - 2x⁴ + 9x³ - x² + 12 = 0
To find: Function having same set of potential rational roots as g(x).
Finding:
Finding the rational roots of g(x):Let 'm' denote the rational roots of 12.=> Then, m = ±1, ±2, ±3, ±4, ±6
2. Let 'n' denote the rational roots of 3.
=> Then n = ±1, ±3
Hence, the rational roots [tex]\frac{m}{n}[/tex] will be given by: ±1, ±2, ±3, ±4, ±6, ±[tex]\frac{1}{3}[/tex], ±[tex]\frac{2}{3}[/tex], ±[tex]\frac{4}{3}[/tex].
Now, in the Option A's equation: f(x) = 3x⁵ -2x⁴ - 9x³ + x² -12,The rational roots will be taken of 12 and 3 in the same position as in g(x).
Hence, the rational roots of f(x) will also be given by: ±1, ±2, ±3, ±4, ±6, ±[tex]\frac{1}{3}[/tex], ±[tex]\frac{2}{3}[/tex], ±[tex]\frac{4}{3}[/tex].
Thus, Option (A)'s f(x) = 3x⁵ -2x⁴ - 9x³ + x² -12 has the same set of potential rational roots as the given function g(x).
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(COMPLETE QUESTION:
According to the Rational Root Theorem, which function has the same set of potential rational roots as the function g(x) = 3x5 – 2x4 + 9x3 – x2 + 12?
A).f(x) = 3x5 – 2x4 – 9x3 + x2 – 12
B).f(x) = 3x6 – 2x5 + 9x4 – x3 + 12x
C).f(x) = 12x5 – 2x4 + 9x3 – x2 + 3
D).f(x) = 12x5 – 8x4 + 36x3 – 4x2 + 48)